In this research, Assume a neutrosophic SuperHyperGraph. Then a ``Failed SuperHyperStable $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common; a ``neutrosophic Failed SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's a neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an SuperHyperStable and Neutrosophic SuperHyperStable. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer's Recognitions'' are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex'' but the relations amid them all officially called ``SuperHyperEdge''. The frameworks ``SuperHyperGraph'' and ``neutrosophic SuperHyperGraph'' are chosen and elected to research about ``Cancer's Recognitions''. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer's Recognitions''. Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Then a``SuperHyperStable'' $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's no SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperStable'' is a \underline{maximal} SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperStable'' is a \underline{maximal} neutrosophic SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. It's useful to define a ``neutrosophic'' version of an SuperHyperStable. Since there's more ways to get type-results to make an SuperHyperStable more understandable. For the sake of having neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of an ``SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume an SuperHyperStable. It's redefined a neutrosophic SuperHyperStable if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph'' with the key points, ``The Values of The Vertices \& The Number of Position in Alphabet'', ``The Values of The SuperVertices\&The maximum Values of Its Vertices'', ``The Values of The Edges\&The maximum Values of Its Vertices'', ``The Values of The HyperEdges\&The maximum Values of Its Vertices'', ``The Values of The SuperHyperEdges\&The maximum Values of Its Endpoints''. To get structural examples and instances, I'm going to introduce the next SuperHyperClass of SuperHyperGraph based on an SuperHyperStable. It's the main. It'll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there's a need to have all SuperHyperConnectivities until the SuperHyperStable, then it's officially called an ``SuperHyperStable'' but otherwise, it isn't an SuperHyperStable. There are some instances about the clarifications for the main definition titled an ``SuperHyperStable''. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on an SuperHyperStable. For the sake of having a neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of a ``neutrosophic SuperHyperStable'' and a ``neutrosophic SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It's redefined ``neutrosophic SuperHyperGraph'' if the intended Table holds. And an SuperHyperStable are redefined to an ``neutrosophic SuperHyperStable'' if the intended Table holds. It's useful to define ``neutrosophic'' version of SuperHyperClasses. Since there's more ways to get neutrosophic type-results to make a neutrosophic SuperHyperStable more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are ``neutrosophic SuperHyperPath'', ``neutrosophic SuperHyperCycle'', ``neutrosophic SuperHyperStar'', ``neutrosophic SuperHyperBipartite'', ``neutrosophic SuperHyperMultiPartite'', and ``neutrosophic SuperHyperWheel'' if the intended Table holds. A SuperHyperGraph has a ``neutrosophic SuperHyperStable'' where it's the strongest [the maximum neutrosophic value from all the SuperHyperStable amid the maximum value amid all SuperHyperVertices from an SuperHyperStable.] SuperHyperStable. A graph is a SuperHyperUniform if it's a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It's SuperHyperPath if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it's SuperHyperCycle if it's only one SuperVertex as intersection amid two given SuperHyperEdges; it's SuperHyperStar it's only one SuperVertex as intersection amid all SuperHyperEdges; it's SuperHyperBipartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it's SuperHyperMultiPartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it's a SuperHyperWheel if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph'' and ``Neutrosophic SuperHyperGraph''. In this SuperHyperModel, The ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperVertices'' and the common and intended properties between ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperEdges''. Sometimes, it's useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``neutrosophic''. In the future research, the foundation will be based on the ``Cancer's Recognitions'' and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it's called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be neutrosophic SuperHyperGraph] to have convenient perception on what's happened and what's done. There are some specific models, which are well-known and they've got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperStable or the strongest SuperHyperStable in those neutrosophic SuperHyperModels. For the longest SuperHyperStable, called SuperHyperStable, and the strongest SuperHyperCycle, called neutrosophic SuperHyperStable, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it's not enough since it's essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn't any formation of any SuperHyperCycle but literarily, it's the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn't form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously; failed independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Failed-Independent Number,” and “Setting of Failed Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, two neighbors, form maximal set but with slightly differences, in cycle-neutrosophic graphs, two neighbors forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of all vertices leads us to neutrosophic failed-independent number and failed independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices containing only center and one other vertex, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices including two vertices from different parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of t vertices from different parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic failed-independent number but the neutrosophic cardinality of a set has eligibility to call failed independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connections amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

In this research, new setting is introduced for new SuperHyperNotions, namely, an 1-failed SuperHyperForcing and Neutrosophic 1-failed SuperHyperForcing. Assume a SuperHyperGraph. Then an ``1-failed SuperHyperForcing'' $\mathcal{Z}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex; a ``neutrosophic 1-failed SuperHyperForcing'' $\mathcal{Z}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. Then an ``$\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

in this research, new setting is introduced for new SuperHyperNotion, namely, Neutrosophic SuperHyperStable. In this research article, there are some research segments for ``Neutrosophic SuperHyperStable'' about some researches on neutrosophic SuperHyperStable. With researches on the basic properties, the research article starts to make neutrosophic SuperHyperStable theory more understandable. Assume a neutrosophic SuperHyperGraph. Then a ``neutrosophic SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

In this research, new setting is introduced for new SuperHyperNotion, namely, 11 Neutrosophic 1-failed SuperHyperForcing. Two different types of SuperHyperDefinitions 12 are debut for them but the research goes further and the SuperHyperNotion, 13 SuperHyperUniform, and SuperHyperClass based on that are well-defined and 14 well-reviewed. The literature review is implemented in the whole of this research. For 15 shining the elegancy and the significancy of this research, the comparison between this 16 SuperHyperNotion with other SuperHyperNotions and fundamental 17 SuperHyperNumbers are featured. The definitions are followed by the examples and the 18 instances thus the clarifications are driven with different tools. The applications are 19 figured out to make sense about the theoretical aspect of this ongoing research. The 20 “Cancer’s Neutrosophic Recognition” are the under research to figure out the challenges 21 make sense about ongoing and upcoming research. The special case is up. The cells are 22 viewed in the deemed ways. There are different types of them. Some of them are 23 individuals and some of them are well-modeled by the group of cells. These types are all 24 officially called “SuperHyperVertex” but the relations amid them all officially called 25 “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic 26 SuperHyperGraph” are chosen and elected to research about “Cancer’s Neutrosophic 27 Recognition”. Thus these complex and dense SuperHyperModels open up some avenues 28 to research on theoretical segments and “Cancer’s Neutrosophic Recognition”. Some 29 avenues are posed to pursue this research. It’s also officially collected in the form of 30 some questions and some problems. Assume a SuperHyperGraph. Then a “1-failed 31 SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 32 is the maximum cardinality of a SuperHyperSet S of black SuperHyperVertices 33 (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) isn’t 34 turned black after finitely many applications of “the color-change rule”: a white 35 SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white 36 SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred 37 by “1-” about the usage of any black SuperHyperVertex only once to act on white 38 SuperHyperVertex to be black SuperHyperVertex; a “neutrosophic 1-failed 39 SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 40 is the maximum neutrosophic cardinality of a SuperHyperSet S of black 41 SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such 42 that V (G) isn’t turned black after finitely many applications of “the color-change rule”: 43 a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only 44 1/128 white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is 45 referred by “1-” about the usage of any black SuperHyperVertex only once to act on 46 white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. 47 Then an “δ−1-failed SuperHyperForcing” is a maximal 1-failed SuperHyperForcing of 48 SuperHyperVertices with maximum cardinality such that either of the following 49 expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : 50 |S ∩N(s)| > |S ∩(V \N(s))|+δ, |S ∩N(s)| < |S ∩(V \N(s))|+δ. The first Expression, 51 holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an 52 “δ−SuperHyperDefensive”; a“neutrosophic δ−1-failed SuperHyperForcing” is a maximal 53 neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with maximum 54 neutrosophic cardinality such that either of the following expressions hold for the 55 neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > 56 |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. 57 The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the 58 second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to 59 define “neutrosophic” version of 1-failed SuperHyperForcing. Since there’s more ways to 60 get type-results to make 1-failed SuperHyperForcing more understandable. For the sake 61 of having neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the 62 notion of “1-failed SuperHyperForcing”. The SuperHyperVertices and the 63 SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this 64 procedure, there’s the usage of the position of labels to assign to the values. Assume a 65 1-failed SuperHyperForcing. It’s redefined neutrosophic 1-failed SuperHyperForcing if 66 the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, 67 HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” 68 with the key points, “The Values of The Vertices & The Number of Position in 69 Alphabet”, “The Values of The SuperVertices&The maximum Values of Its Vertices”, 70 “The Values of The Edges&The maximum Values of Its Vertices”, “The Values of The 71 HyperEdges&The maximum Values of Its Vertices”, “The Values of The 72 SuperHyperEdges&The maximum Values of Its Endpoints”. To get structural examples 73 and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph 74 based on 1-failed SuperHyperForcing. It’s the main. It’ll be disciplinary to have the 75 foundation of previous definition in the kind of SuperHyperClass. If there’s a need to 76 have all SuperHyperConnectivities until the 1-failed SuperHyperForcing, then it’s 77 officially called “1-failed SuperHyperForcing” but otherwise, it isn’t 1-failed 78 SuperHyperForcing. There are some instances about the clarifications for the main 79 definition titled “1-failed SuperHyperForcing”. These two examples get more scrutiny 80 and discernment since there are characterized in the disciplinary ways of the 81 SuperHyperClass based on 1-failed SuperHyperForcing. For the sake of having 82 neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the notion of 83 “neutrosophic 1-failed SuperHyperForcing” and “neutrosophic 1-failed 84 SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned 85 by the labels from the letters of the alphabets. In this procedure, there’s the usage of 86 the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. 87 It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And 88 1-failed SuperHyperForcing are redefined “neutrosophic 1-failed SuperHyperForcing” if 89 the intended Table holds. It’s useful to define “neutrosophic” version of 90 SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make 91 neutrosophic 1-failed SuperHyperForcing more understandable. Assume a neutrosophic 92 SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended 93 Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, 94 SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are 95 “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic 96 SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic 97 2/128 SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table 98 holds. A SuperHyperGraph has “neutrosophic 1-failed SuperHyperForcing” where it’s 99 the strongest [the maximum neutrosophic value from all 1-failed SuperHyperForcing 100 amid the maximum value amid all SuperHyperVertices from a 1-failed 101 SuperHyperForcing.] 1-failed SuperHyperForcing. A graph is SuperHyperUniform if it’s 102 SuperHyperGraph and the number of elements of SuperHyperEdges are the same. 103 Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as 104 follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given 105 SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one 106 SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s 107 only one SuperVertex as intersection amid all SuperHyperEdges; it’s 108 SuperHyperBipartite it’s only one SuperVertex as intersection amid two given 109 SuperHyperEdges and these SuperVertices, forming two separate sets, has no 110 SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as 111 intersection amid two given SuperHyperEdges and these SuperVertices, forming multi 112 separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one 113 SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has 114 one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes 115 the specific designs and the specific architectures. The SuperHyperModel is officially 116 called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this 117 SuperHyperModel, The “specific” cells and “specific group” of cells are 118 SuperHyperModeled as “SuperHyperVertices” and the common and intended properties 119 between “specific” cells and “specific group” of cells are SuperHyperModeled as 120 “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, 121 indeterminacy, and neutrality to have more precise SuperHyperModel which in this case 122 the SuperHyperModel is called “neutrosophic”. In the future research, the foundation 123 will be based on the “Cancer’s Neutrosophic Recognition” and the results and the 124 definitions will be introduced in redeemed ways. The neutrosophic recognition of the 125 cancer in the long-term function. The specific region has been assigned by the model 126 [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is 127 identified by this research. Sometimes the move of the cancer hasn’t be easily identified 128 since there are some determinacy, indeterminacy and neutrality about the moves and 129 the effects of the cancer on that region; this event leads us to choose another model [it’s 130 said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s 131 happened and what’s done. There are some specific models, which are well-known and 132 they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves 133 and the traces of the cancer on the complex tracks and between complicated groups of 134 cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, 135 SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). 136 The aim is to find either the longest 1-failed SuperHyperForcing or the strongest 137 1-failed SuperHyperForcing in those neutrosophic SuperHyperModels. For the longest 138 1-failed SuperHyperForcing, called 1-failed SuperHyperForcing, and the strongest 139 SuperHyperCycle, called neutrosophic 1-failed SuperHyperForcing, some general results 140 are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have 141 only two SuperHyperEdges but it’s not enough since it’s essential to have at least three 142 SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of 143 any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, 144 literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph 145 theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Neutrosophic Failed SuperHyperClique theory, SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Extreme SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then an “δ−SuperHyperForcing” is a minimal SuperHyperForcing of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : |S∩N(s)|>|S∩(V \N(s))|+δ, |S∩N(s)|<|S∩(V \N(s))|+δ.Thefirst Expression, holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an “δ−SuperHyperDefensive”; a“neutrosophic δ−SuperHyperForcing” is a minimal neutrosophic SuperHyperForcing of SuperHyperVertices with minimum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperForcing. Since there’s more ways to get type-results to make SuperHyperForcing more understandable. For the sake of having neutrosophic SuperHyperForcing, there’s a need to “redefine” the notion of “SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperAlliances and Neutrosophic SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperAlliances, then it’s officially called “SuperHyperAlliances” but otherwise, it isn’t SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperAlliances. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperAlliances” and “neutrosophic SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperAlliances are redefined “neutrosophic SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperAlliances.] SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperAlliances or the strongest SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperAlliances, called SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperDefensive SuperHyperAlliances and Neutrosophic SuperHyperDefensive SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperDefensive SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperDefensive SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperDefensive SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperDefensive SuperHyperAlliances, then it’s officially called “SuperHyperDefensive SuperHyperAlliances” but otherwise, it isn’t SuperHyperDefensive SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperDefensive SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperDefensive SuperHyperAlliances. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperDefensive SuperHyperAlliances” and “neutrosophic SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperDefensive SuperHyperAlliances are redefined “neutrosophic SuperHyperDefensive SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperDefensive SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperDefensive SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperDefensive SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperDefensive SuperHyperAlliances.] SuperHyperDefensive SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperDefensive SuperHyperAlliances or the strongest SuperHyperDefensive SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperDefensive SuperHyperAlliances, called SuperHyperDefensive SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperDefensive SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty neutrosophic SuperHyperEdges but $E_2$ is a loop neutrosophic SuperHyperEdge and $E_4$ is an neutrosophic SuperHyperEdge. Thus in the terms of neutrosophic SuperHyperNeighbor, there's only one neutrosophic SuperHyperEdge, namely, $E_4.$ The neutrosophic SuperHyperVertex, $V_3$ is neutrosophic isolated means that there's no neutrosophic SuperHyperEdge has it as an neutrosophic endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ is excluded in every given neutrosophic SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an neutrosophic SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an neutrosophic SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an neutrosophic R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an neutrosophic R-SuperHyperGirth SuperHyperPolynomial.}} $ The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is an neutrosophic type-SuperHyperSet with the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperGirth isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth is an neutrosophic SuperHyperSet includes only less than four neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth isn't up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth and it's an neutrosophic SuperHyperGirth . Since it 's the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are only less than four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, thus the obvious neutrosophic SuperHyperGirth, is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth, is: ,is the neutrosophic SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with neutrosophic SuperHyperGirth theory, SuperHyperGraphs, and neutrosophic SuperHyperGraphs theory are proposed.

I introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic, and of neutrosophic propositional logic. In order for the paper to be self-contained, I also recall the etymology and definition of neutrosophy and of neutrosophic logic. Several examples are presented as well.

In this research, assume a SuperHyperGraph. Then a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with neutrosophic SuperHyperMatching theory, SuperHyperGraphs theory, and neutrosophic SuperHyperGraphs theory are proposed.

New setting is introduced to study quasi-degree and quasi-co-degree arising from co-neighborhood. quasi-degree and quasi-co-degree is about a vertex which are applied into the setting of neutrosophic graphs. . The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs and star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-multipartite-neutrosophic graphs are investigated in the terms of a vertex which is called either quasi-degree or quasi-co-degree. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form quasi-degree and quasi-co-degree. Quasi-degree is a value of a vertex which is maximum amid all values of vertices which are neighbors to a fixed vertex. Quasi-co-degree is a value of an edge which is maximum amid all values of edges which are neighbors to a fixed vertex but corresponded vertex is representative for this notion. Using different values which are related to a vertex inspire us to focus on edge and vertices which are corresponded to a fixed vertex. The notion of neighborhood is used to collect either vertices are titled neighbors or edges are incident to fixed vertex. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definitions are provided. Using fixed vertex has key role to have these notions in the form of vertex or edge. The value of an edge has eligibility to call quasi-co-degree but the value of a vertex has eligibility to call quasi-degree. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connection together, open the way to define neighborhood and co-neighborhood. The maximum values in neighborhood and co-neighborhood introduces quasi-degree and quasi-co-degree, respectively. New name is chosen from degree. Since amid all vertices with different degrees, one vertex is chosen. In other words, one vertex is fixed and its degree turns out quasi-degree where two degrees could be assigned to a vertex. Degree of edges and degree of vertices. The number of edges which are incident to the vertex and the number of vertices which are neighbors to the vertex. Degree and co-degree are the notions which are transformed to use in quasi-style. Two neutrosophic values introduce two neutrosophic vertices separately in each settings. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to purse this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another denitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

Objectives to assess COVID-19 mortality rates per country population. To determine what if any independent country-specific variables from 9 different databases were correlated. Design population based retrospective cohort study. Setting analysis of global COVID-19 treatment and containment strategies using data from 9 worldwide websites. Participants 108 countries worldwide. Interventions none. Main Outcome Measures were COVID-19 death rates per country population analyzed by univariate and multivariate analysis. The main outcome parameters were to determine if there are any correlations between the percentage of countrywide COVID-19 deaths/population by the countries’ percent vaccinated. Secondary outcome measures include the effect of other independent variables on COVID-19 death rates per country population including: health expenditures per capita, annual income per capita, COVID-19 tests per 1000 people, stringency index (a measure of each countries containment strategies), hydroxychloroquine score (a measure of each countries use), ivermectin score (a measure of each countries use), hypertension, obesity, diabetes, and specific countries and geographic locations. Results COVID-19 vaccination rates ranged from 0-99% in 108 countries. Univariate analysis demonstrates the following independent variables to correlate with COVID-19 deaths/population (correlation coefficient, p value): countrywide COVID-19 vaccination rates (+0.2936, p=0.002); healthcare costs per capita (+0.3212, p=0.0007), income per capita (+0.3051, p=0.0013), COVID-19 tests per 1000 population (+0.6981 p=0.0307); stringency index (+0.3098, p=0.0011); hydroxychloroquine index (-0.1337, p=0.0678); and ivermectin index (-0.1383, p=0.1535). Conclusions Increasing rates of COVID-19 vaccination are associated with increase COVID-19 death rates per country population (p=0.002). Other variables associated include healthcare costs per capita (+0.3212, p=0.0007), income per capita (+0.3051, p=0.0013), COVID-19 tests per 1000 population (+0.6981 p=0.0307); and stringency index (+0.3098, p=0.0011).

In this research article, the notions of SuperHyperDominating and SuperHyperResolving are defined in the setting of neutrosophic SuperHyperGraphs. Some ideas are introduced on both notions of SuperHyperDominating and SuperHyperResolving, simultaneously and as the same with each other. Some neutrosophic SuperHyperClasses are defined based on the notion, SuperHyperResolving. The terms of duality, totality, perfectness, connectedness, and stable, are added to basic framework and initial notions, SuperHyperDominating and SuperHyperResolving but the concentration is on the “perfectness” to figure out what’s going on when for all targeted SuperHyperVertices, there’s only one SuperHyperVertex in the intended set. There are some instances and some clarifications to make sense about what’s happened and what’s done in the starting definitions. The key point is about the minimum sets. There are some questions and some problems to be taken as some avenues to pursue this study and this research. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

Various authors have highlighted the importance of marriage as a social marker that alter the so-cial categorization of individuals and their relationships from youth to adulthood according to the cultural construction of the life course in Arab countries. This article aims to analyze the in-teraction between the socio-political framework (structure) and the capacity for individual action (agency) in the context of biographical experiences to achieve emancipation in Morocco. This per-spective responds to the demand of different authors to include the subjective approaches of young people in the process of analysis. This analysis will be guided by some questions: Which is the capacity of young Arabs to decide the orientation of their life trajectories? What factors (cultural, family, socioeconomic, educational, etc.) create and shape the expectations of young people re-garding their transition to adult life? Is there a specific model of emancipation in the Arab Medi-terranean countries?

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

This article presents a new method of segmenting images with gray levels. The method is based on determining several thresholds for separation of gray levels. The determination of these thresholds is done using the certainty of the neutrosophic information. The concept of this method can be stated simply: to choose the local maximums for the neutrosophic certainty.

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

New setting is introduced to study resolving number and chromatic number alongside dominating number. Different types of procedures including set, optimal set, and optimal number alongside study on the family of neutrosophic hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtains these numbers and the representatives of the colors, dominating sets and resolving sets. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing resolving sets and dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about numbers and sets in the way that some numbers get understandable perspective. Family of neutrosophic hypergraphs are studied to investigate about the notions, dimension and coloring alongside domination in neutrosophic hypergraphs. In this way, sets of representatives of colors, resolving sets and dominating sets have key role. Optimal sets and optimal numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, three notions are applied into neutrosophic hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtain chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing representatives of the colors are applied in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about number, degree and co-degree in the way that some number, degree and co-degree get understandable perspective. Neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are studied to investigate about the notions, coloring, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. In this way, sets of representatives of colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, notions chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges are applied into neutrosophic hypergraphs, especially, neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets appear in the current literature. In the present paper we propose the score, accuracy functions for neutrosophic cubic sets and prove their basic properties. We firstly develop TODIM method to solve multi attribute group decision making in neutrosophic cubic set environment, which we call NC-TODIM. Also, we solve a MAGDM problem using the proposed NC-TODIM method to show the applicability and effectiveness of the developed method. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of attenuation factor of losses for multi-attribute group decision making problem.

Purpose: There is limited research on the reasons behind startup failure, and none of the available studies use a competency approach. In this study we applied Spencer’s competency model to identify the competencies in startups which, according to their CEOs, contributed to failure. Methodology: Three coders analyzed the stories of 50 startup failures published online using modified Critical Incident Technique. Findings: Two salient competencies were identified playing a fundamental role in startup failures if missing: Information seeking and Customer service orientation. A network pattern of 9 more prevalent competency deficits was created: Technical/professional/managerial expertise, Analytical thinking, Flexibility, Self-control, Concern for order, quality and accuracy, Interpersonal understanding, Self-confidence, Team leadership and Teamwork and cooperation. Besides startup-specific behavior descriptions were added to Spencer’s competencies. Research implications: Competency approach and Critical Incident Technique method proved to be feasible to identify competency deficits in failed startups. Practical implications: The identified competency deficits offer relevant focus areas for the assessment and development of startup teams. Originality: The study provided research evidence to describe the competency deficits of startup teams that are connected to their failure.

Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.

The research is on the SuperHyperGirth and the neutrosophic SuperHyperGirth. A SuperHyperGraph has SuperHyperGirth where it’s the longest SuperHyperCycle. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperGirth. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. This SuperHyperClass is officially called “SuperHyperFlower”. If there’s a need to have all SuperHyperCycles until the SuperHyperGirth, then it’s officially called “SuperHyperOrder” but otherwise, it isn’t SuperHyperOrder. There are two instances about the clarifications for the main definition titled “SuperHyperGirth”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperGirth and they’re called “SuperHyperFlower.” A SuperHyperGraph has “neutrosophic SuperHyperGirth” where it’s the strongest [the maximum value from all SuperHyperCycles amid the minimum value amid all SuperHyperEdges from a SuperHyperCycle.] SuperHyperCycle. In “Cancer’s Recognitions”, the aim is to find either the longest SuperHyperCycle or the strongest SuperHyperCycle in those neutrosophic SuperHyperModels. For the longest SuperHyperCycle, called SuperHyperGirth, and the strongest SuperHyperCycle, called neutrosophic SuperHyperGirth, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study the alliances. Alliances are about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define these notions. Also, neighborhood is defined based on the edges, strong edges and some edges which are coming from connectedness. These three types of edges get a framework as neighborhood and after that, too close vertices have key role to define offensive alliance, defensive alliance, t-offensive alliance, and t-defensive alliance based on three types of edges, common edges, strong edges and some edges which are coming from connectedness. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, bipartite, t-partite, star and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study but it seems that analogous results are determined. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on different edges illustrate open way to get results. A set is alliance when two sets partitioning vertex set have uniform structure. All members of set have different amount of neighbors in the set and out of set. It leads us to the notion of offensive and defensive. New ideas, offensive alliance, defensive alliance, t-offensive alliance, t-defensive alliance, strong offensive alliance, strong defensive alliance, strong t-offensive alliance, strong t-defensive alliance, connected offensive alliance, connected defensive alliance, connected t-offensive alliance, and connected t-defensive alliance are introduced. Two numbers concerning cardinality and neutrosophic cardinality of alliances are introduced. A set is alliance when its complement make a relation in the terms of neighborhood. Different edges make different neighborhoods. Three types of edges are applied to define three styles of neighborhoods. General edges, strong edges and connected edges are used where connected edges are the edges arising from connectedness amid two endpoints of the edges. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for this notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

Myostatin inhibition therapy has held much promise for the treatment of muscle wasting disorders. This is particularly true for the fatal myopathy, Duchenne Muscular Dystrophy (DMD). Following on from promising pre-clinical data in dystrophin-deficient mice and dogs, several clinical trials were initiated in DMD patients using different modality myostatin inhibition therapies. All failed to show modification of disease course as dictated by the primary and secondary outcomes measures selected: the myostatin inhibition story thus far, is a failed clinical story. These trials have recently been extensively reviewed and reasons why pre-clinical data collected in animal models has failed to translate into clinical benefit to patients has been purported. However, the biological mechanisms underlying translational failure need to be examined to ensure future myostatin inhibitor development endeavors do not meet with the same fate. Here, we explore the biology which could explain the failed translation of myostatin inhibitors in the treatment of DMD.

Despite all scientific efforts and many protracted and expensive clinical trials, no new drug has been approved by FDA for treatment of Alzheimer disease (AD) since 2003. Indeed, more than 200 investigational programs have failed or have been abandoned in the last decade. The most probable explanations for failures of disease-modifying treatments (DMTs) for AD may include late initiation of treatments during the course of AD development, inappropriate drug dosages, erroneous selection of treatment targets, and mainly an inadequate understanding of the complex pathophysiology of AD, which may necessitate combination treatments rather than monotherapy. Clinical trials’ methodological issues have also been criticized. Current drug-development research for AD is aimed to overcome these drawbacks. Preclinical and prodromal AD populations, as well as traditionally investigated populations representing all the clinical stages of AD, are included in recent trials. Systematic use of biomarkers in staging preclinical and prodromal AD and of a single primary outcome in trials of prodromal AD are regularly integrated. The application of amyloid, tau, and neurodegeneration biomarkers, including new biomarkers—such as Tau positron emission tomography, neurofilament light chain (blood and CSF biomarker of axonal degeneration) and neurogranin (CSF biomarker of synaptic functioning)—to clinical trials allows more precise staging of AD. Additionally, use of the Bayesian statistics, modifiable clinical trial designs, and clinical trial simulators enrich the trial methodology. Besides, combination therapy regimens are currently assessed in clinical trials. The abovementioned diagnostic and statistical advances, which have been recently integrated in clinical trials, are consequential to the recent failures of studies of disease-modifying treatments. Their experiential rather than theoretical origins may better equip potentially successful drug-development strategies.

Extracorporeal membrane oxygenation (ECMO) can be a life-saving intervention in cases of potentially reversible refractory respiratory failure. One such indication can be bleomycin-induced lung injury. However, in some cases, the injury can be so severe that it becomes irreversible and creates complex medical decisions regarding life support and the continuation of care when no additional therapeutic options are feasible, particularly in cases of patients who were young and fully functional prior to an acute illness. In cases of full pulmonary replacement with mechanical support and the degree of functionality that can be attained utilizing modalities such as ECMO can obscure the true severity of illness and make end-of-life decisions significantly harder for families and caregivers.

Background: The coronavirus disease-19 (COVID-19) has spread globally with more than 80,000 people infected, and nearly 3000 patients died. Currently, we are in an urgent need for effective treatment strategy to control the clinical deterioration of COVID-19 patients. Methods: The clinical data of 10 COVID-19 patients receiving short-term moderate-dose corticosteroid (160mg/d) plus immunoglobulin (20g/d) were studied in the North Yard of The First Hospital of Changsha, Hunan from January 17^th to February 27^th, 2020. Epidemiological, clinical, laboratory, radiological findings were analyzed. Results: After treatment with combination of low-dose corticosteroid (40-80mg/d) and immunoglobulin (10g/d), patients’ lymphocyte count (0.88±0.34 vs 0.59±0.18, P<0.05), oxygenation index including SPO₂ (94.90±2.51 vs 90.50±5.91, P<0.05) and PaO₂/FiO₂ (321.36±136.91 vs 129.30±64.97, P<0.05) were significantly lower than pre-treatment, and CT showed that the pulmonary lesion deteriorated in all patients. While after treatment of short-term moderate-dose corticosteroid plus immunoglobulin, patients’ APACHE Ⅱ score (9.10±6.15 vs 5.50±9.01, P<0.05), body temperature (37.59±1.16 vs 36.46±0.25, P<0.05), lymphocyte count (0.59±0.18 vs 1.36±0.51, P<0.05), Lactate dehydrogenase (419.24±251.31 vs 257.40±177.88, P<0.05), and C-reactive protein (49.94±26.21 vs 14.58±15.25, P<0.05) significantly improved compared with post-treatment with low-dose therapy. In addition, oxygenation index including SPO₂ (90.50±5.91 vs 97.50±1.18, P<0.05), PaO₂ (60.47±14.53 vs 99.07±34.31, P<0.05), and PaO₂/FiO₂ (129.30±64.97 vs 340.86±146.72, P<0.05) significant improved. Furthermore, CT showed that pulmonary lesions obviously improved in 7 patients. After systematic therapy, 4 out of 10 COVID-19 patients recovered and discharged. Conclusions: Short-term moderate-dose corticosteroid plus immunoglobulin is effective for reversing the continued deterioration of COVID-19 patients who failed to respond to the low-dose therapy. Funding: This work was supported by the Innovative Major Emergency Project Funding against the New Coronavirus Pneumonia in Hunan Province (Dr. Ji-Yang Liu, number 2020SK3014; Dr. Yuan-Lin Xie, number 2020SK3013).

The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and minimum operators, we define new similarity measures and prove their basic properties. Using the proposed similarity measures, we propose a novel multi attribute decision making strategy in interval bipolar neutrosophic set environment. Lastly, we solve an illustrative example of multi attribute decision making and present comparison analysis to show the feasibility, applicability and effectiveness of the proposed strategy.

In this research, the extreme SuperHyperNotion, namely, extreme SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty extreme SuperHyperEdges but $E_2$ is a loop extreme SuperHyperEdge and $E_4$ is an extreme SuperHyperEdge. Thus in the terms of extreme SuperHyperNeighbor, there's only one extreme SuperHyperEdge, namely, $E_4.$ The extreme SuperHyperVertex, $V_3$ is extreme isolated means that there's no extreme SuperHyperEdge has it as an extreme endpoint. Thus the extreme SuperHyperVertex, $V_3,$ is excluded in every given extreme SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an extreme SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an extreme SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an extreme R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an extreme R-SuperHyperGirth SuperHyperPolynomial.}} $ The following extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices] is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices], is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is an extreme type-SuperHyperSet with the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive sequence of the extreme SuperHyperVertices and the extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are not only four extreme SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious extreme SuperHyperGirth isn't up. The obvious simple extreme type-SuperHyperSet called the extreme SuperHyperGirth is an extreme SuperHyperSet includes only less than four extreme SuperHyperVertices. But the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth isn't up. To sum them up, the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth. Since the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is the extreme SuperHyperSet $S$ of extreme SuperHyperVertices[SuperHyperEdges] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle given by that extreme type-SuperHyperSet called the extreme SuperHyperGirth and it's an extreme SuperHyperGirth . Since it 's the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are only less than four extreme SuperHyperVertices inside the intended extreme SuperHyperSet, thus the obvious extreme SuperHyperGirth, is up. The obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth, is: ,is the extreme SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected extreme SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple extreme type-SuperHyperSet called the extreme SuperHyperGirth amid those obvious[non-obvious] simple extreme type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with extreme SuperHyperGirth theory, SuperHyperGraphs, and extreme SuperHyperGraphs theory are proposed.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Bipartite and Neutrosophic SuperHyper-Path are introduced. More instances and more clarifications alongside sufficient references.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperStable'' $\mathcal{I}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

In this research, new setting is introduced for new notions, namely, SuperHyperDegree and Co-SuperHyperDegree. Two different types of definitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The cancer’s treatments are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “cancer’s treatments”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “cancer’s treatments”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. If there’s a SuperHyperEdge between two SuperHyperVertices, then these two SuperHyperVertices are called SuperHyperNeighbors. The number of SuperHyperNeighbors for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperNeighbors for some SuperHyperVertices is called Co-SuperHyperDegree for them and used SuperHyperVertices are called Co-SuperHyperNeighbors. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The number of SuperHyperEdges for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperEdges for some SuperHyperVertices is called Co-SuperHyperDegree for them. The number of SuperHyperVertices for a given SuperHyperEdge is called SuperHyperDegree. The number of common SuperHyperVertices for some SuperHyperEdges is called Co-SuperHyperDegree for them. The model proposes the specific designs. The model is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this model, The “specific” cells and “specific group” of cells are modeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are modeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise model which in this case the model is called “neutrosophic”. In the future research, the foundation will be based on the caner’s treatment and the results and the definitions will be introduced in redeemed ways. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, assume a SuperHyperGraph. Then an extreme SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; an extreme R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. Assume a SuperHyperGraph. Then $\delta-$SuperHyperMatching is a maximal of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a neutrosophic $\delta-$SuperHyperMatching is a maximal neutrosophic of SuperHyperVertices with maximum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta;$ and $ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperDefensive It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with Extreme SuperHyperMatching theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Wheel and Neutrosophic SuperHyper-Star are introduced. More instances and more clarifications alongside sufficient references are featured with a specific type of independency of SuperHyperVertices.

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

Along with the economic growth, the companies must contribute to social progress and promote environmental sustainability in equal harmony. Sustainable human resource management (SHRM) strategies make it possible to attain the economic, social and environmental goals of a firm. In this regard, a survey method is discussed using the literature review and online questionnaire to identify the main factors/indicators during the SHRM evaluation of manufacturing firms in India. Uncertainty is commonly occurred in the assessment of SHRM factors. As a generalized version of fuzzy sets, single-valued neutrosophic set (SVNS) has been demonstrated as a valuable tool to illustrate the indeterminate, inconsistent and uncertain data of realistic decision-making problems. Considering the idea of SVNSs, this study develops a hybrid multi-criteria group decision-making (MCGDM) approach for assessing the SHRM of manufacturing firms under uncertainty settings. For this purpose, an SVN-alternative ranking order method accounting for two-step normalization (AROMAN) is proposed based on VIFI-score function-based decision experts’ (DEs’) weighting tool and integrated criteria weight-determining model to solve the MCGDM problems with fully unknown DEs and criteria weights. In this regard, we develop new SVN-distance measure to compute the degree of difference between SVNSs. Some examples are presented to demonstrate the efficacy of developed measure over the existing ones. In addition, new criteria weight-determination model is presented with the integration of objective weights through IVIF-distance measure-based model and subjective weights through ranking comparison (RANCOM) tool on SVNSs. The proposed ranking method is applied to an empirical study of SHRM assessment for manufacturing firms in India, which shows its applicability and feasibility. In this study, the evaluation criteria are characterized into social, environmental and economic aspects with DE’s opinions. Comparative and sensitivity analyses are made to show the strength and steadiness of presented approach. This study provides an innovative MCGDM analysis framework, which makes a significant contribution to the SHRM assessment problem under indeterminate, inconsistent and uncertain setting.

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

In this research, new setting is introduced for assuming a SuperHyperGraph. Then a ``SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperClique'' is a \underline{maximal} SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperClique'' is a \underline{maximal} neutrosophic SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme SuperHyperClique theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

While paresthesia-based spinal cord stimulation (SCS) has been proven effective to treat chronic neuropathic pain, initial benefits may lead to the development of “Failed SCS Syndrome’ (FSCSS) defined as decrease over time related to Loss of Efficacy (LoE) with or without Loss of Coverage (LoC). Development of technologies associating new paresthesia-free stimulation waveforms and implanted pulse generator adapters provide opportunities to manage patients with LoE. The main goal of our study was to investigate salvage procedures, through neu-rostimulation adapters, in patients already implanted with SCS and experienced LoE. We retro-spectively analyzed a cohort of patients who were offered new SCS programs/waveforms through an implanted adapter between 2018 and 2021. Patients were evaluated before, and at 1, 3, 6 and 12-month follow-up. Outcomes included pain intensity rating with Visual Analog Scale (VAS), pain/coverage mappings and stimulation preferences. Last follow-up evaluations (N=27) showed significant improvement in VAS (p = 0.0001), ODI (p = 0.021) and Quality of Life (p=0.023). In the 11/27 patients with LoC, SCS efficacy on pain intensity (36.89%) was accompa-nied by paresthesia coverage recovery (55.57%) and pain surface decrease (47.01%). At 12-month follow-up, 81.3% preferred to keep tonic stimulation in their waveform portfolio. SCS conver-sion using adapters appears promising as a salvage solution, with an emphasis on paresthesia recapturing enabled by spatial retargeting. In light of these results, adapters could be integrated to SCS rescue algorithms or should be considered in SCS rescue.

Studies in animal models have suggested that the ketogenic diet may be effective in the treatment of cancer. However, human cohort studies on the ketogenic diet have, thus far, failed to show benefits in cancer survival or in any other hard clinical endpoints of the disease. This paper presents a case report of a patient with glioblastoma multiforme. The patient had initially been treated with standard oncotherapy including surgery, radiotherapy and chemotherapy. Despite standard treatment, the patient experienced a recurrence of the glioblastoma seven months later. Subsequently, the patient refused radiotherapy and chemotherapy and opted to use the paleolithic ketogenic diet (PKD) as a stand-alone therapy. Following the adoption of the PKD, progression of the disease has been completely halted. At the time of writing, the patient has remained in remission for 48 months, is without side-effects and experiences an excellent quality of life without the use of any drugs.

Dipole antennas, fundamental components in wireless communication systems, have garnered significant attention due to their versatility and efficiency across various applications. This literature review explores the performance analysis of dipole antennas, focusing on recent advancements and methodologies from 2019 to 2024. Employing a systematic approach, the review synthesizes findings from multiple databases, emphasizing peer-reviewed studies that delve into dipole antenna designs and applications. Through meticulous data extraction, key parameters influencing dipole antenna performance, such as material properties and operating frequency, are identified and analyzed. Results highlight the widespread utilization of dipole antennas in wireless communication systems, including indoor positioning, mobile communication, and antenna calibration, among others. Discussions underscore the evolution of dipole antennas in base station environments and their role in filtering applications. The review concludes by emphasizing the continued relevance and evolution of dipole antennas, showcasing their adaptability and potential across diverse wireless communication contexts.

Glucose is a simple sugar molecule. The sugar molecule is chemically symbolised as C6H12O6. This means that the glucose molecule contains 6 carbon atoms (C), 12 hydrogen atoms (H) and 6 oxygen atoms (O). In human blood, the molecule glucose circulates as blood sugar. Normally after eating or drinking, our body breaks down the sugars in food and uses them to obtain energy for our cells. To do this, our pancreas produces insulin. Insulin "pulls" sugar from the blood and puts it into the cells for use. If someone has diabetes, their pancreas can't produce enough insulin. As a result, the level of glucose in the blood rises. This can lead one to many potential complications, including blindness, disease, nerve damage, amputation, stroke, heart attack and damage to blood vessels etc. In this study, a non-invasive method for monitoring blood glucose has been developed and is therefore easily usable. The device developed can measure the glucose level continuously and eliminates the disadvantages of the invasive system. Near-IR sensors (optical sensors) were used to estimate the concentration of glucose in the blood; these sensors have a wavelength of 940 nm. The sensor is placed on the tip of the finger and the output of the optical sensor is then connected to the microcontroller at the analogue input. Another sensor used, but only to provide more medical information was the heartbeat sensor. After processing and regression analysis, the glucose level is predicted, and data is sent via the Bluetooth network to a developed APP. The results of the implemented device were compared with available invasive methods. The study consists of a hardware platform inserted into an armband and then a small black parallelepiped-shaped box in which the optical sensors are inserted. The hardware consists of a microcontroller, a Near-IR optical sensor, a heartbeat sensor and a Bluetooth module.

This study examines the effects of the δ phase and annealing twins on the hardness, Charpy impact toughness, and tensile properties of Inconel 718 fabricated using L-PBF. Two heat treatment methods, involving solid solution and precipitation hardening, were utilized. The δ phase was formed through solid solution heat treatment at 980C for 1 hour while annealing twins were generated at 1100C for 3 hours. After precipitation hardening, specimens with a higher concentration of  precipitates exhibited increased ultimate tensile strength (13%), yield strength (27%), and hardness (12%) compared to those with annealing twins. This can be attributed to the smaller grain size, subgrains, and δ precipitates, which contribute to the differences in mechanical strength. On the contrary, specimens with annealing twins showed significantly higher impact toughness (4 times) and ductility (twice) than those with δ precipitates. This is caused by the formation of  precipitates, which serve as sites for void formation and crack propagation, leading to a decrease in plasticity due to lattice mismatches with the matrix. Microstructural, compositional, phase, crystallographic, and fractographic analyzes were performed using OM, SEM, TEM and XRD techniques to identify the factors responsible for the variations in the measurements. The results demonstrate that the heat treatment method involving annealing twins significantly improves the ductility of Inconel 718 while maintaining the required mechanical strength.

Despite substantial evidence supporting the efficacy of prebiotics for promoting host health and stress resilience, few experiments present evidence documenting the dynamic changes in microbial ecology and fecal microbial-modified metabolites across time. Furthermore, the literature reports a lack of reproducible effects of prebiotics on specific bacteria and bacterial-modified metabolites. The current experiments examined whether consumption of diets enriched in prebiotics (galactooligosaccharides, GOS and polydextrose, PDX) compared to control diet, would consistently impact the gut microbiome and microbial-modified bile acids across time and between two research sites. Male Sprague Dawley rats were fed control or prebiotic diets for several weeks, and their gut microbiome and metabolome were examined using 16S rRNA gene sequencing and untargeted LC-MS/MS analysis. Dietary prebiotics altered beta diversity, relative abundances of bacterial genera, and microbially modified bile acids across time. PICRUSt2 analyses identified four inferred functional metabolic pathways modified by prebiotic diet. Correlational network analyses between inferred metabolic pathways and microbial-modified bile acids revealed deoxycholic acid as a potential network hub. All these reported effects were consistent between the two research sites supporting the conclusion that dietary prebiotics robustly changed the gut microbial ecosystem. Consistent with our previous work demonstrating that GOS/PDX reduces the negative impacts of stressor exposure, we propose that ingesting a diet enriched in prebiotics facilitates the development of a health-promoting gut microbial ecosystem.

The objective was to investigate associations of serum vitamin D concentration with depressive symptoms and assess the impact vitamin D concentration has on the occurrence of depressive symptoms in 20–44-year-old pregnant mothers, postpartum mothers, women (non-pregnant/postpartum women), and men, including a separate subgroup analysis of postpartum breastfeeding and non-breastfeeding mothers. The study populations were selected from 2007-2018 NHANES public data. Subjective interview data and objective laboratory data, including depressive symptoms, serum vitamin D concentration, nutrient intake, and demographic information were utilized. Two diet patterns were created using principal component analysis and a Bayesian multinomial model was fit to predict depression outcomes for each subpopulation. The estimates for the log vitamin D slope parameter were negative for all cohorts; as vitamin D increased, the probability of having no depression increased, while the probability of depression decreased. The pregnant cohort had the steepest vitamin D slope, followed by postpartum, then other women and men. Higher vitamin D concentration had more impact on decreasing depression risk in pregnant and postpartum mothers compared to other women and men. Among postpartum mothers, higher vitamin D concentration had a greater influence on decreasing breastfeeding mothers' depression risk than non-breastfeeding mothers.

A beverage made from a combination of Agave sap (AS) and prickly pear juice (PPJ) was ana-lyzed for its nutrients, bioactive and potentially health-promoting compounds. The beverage was evaluated for its ability to act as an antioxidant, regulate glycemic properties, and undergo gut bacterial fermentation in vitro. The major mono- and oligosaccharides present in the beverage were galacturonic acid (217.74±13.46 mg/100 mL), rhamnose (227.00±1.58 mg/100 mL), and fructose (158.16±8.86 mg/mL). The main phenolic compounds identified were protocatechuic acid (440.31±3.06 mg/100 mL) and catechin (359.72±7.56 mg/100 mL). It was observed that the beverage had a low glycemic index (

The digital model of airborne frequency selective surface radomes (AFSSRs) is the basis of design, simulation analysis, manufacturing, and other related research of AFSSRs. This paper proposes a rapid modeling method of AFSSRs based on dynamic customizable primitives. Firstly, a layered digital model construction scheme of AFSSR is presented based on the typical radome wall structure. Then, according to the characteristics of various surface configurations and complex wireframe information of AFSSRs, the dynamic primitives are raised to express the boundary and contour information of all kinds of radomes. Focusing on the undevelopable characteristics of the aero-dynamic shape surface of the AFSSR, the arrangement solution and mapping method for frequency selective elements on undevelopable surfaces are proposed. Furthermore, the imple-mentation logic of this method on the creation of each layer model and the assembly of the whole machine model is introduced. Finally, according to this method, a rapid modeling system (RMS) is established, and the modeling effect and efficiency of the RMS are demonstrated and compared, which verifies the feasibility and effectiveness of this method.

This paper focuses on environmental policies for mitigating the impacts of climate change on the Taj Mahal, an iconic structure built on the banks of the Yamuna River from 1632 to 1653 with a blend of Persian and Indian architectural styles. The Taj Mahal is threatened by damage caused by climate change, including air pollution resulting in acid rain and floods that lead to erosion and discoloration of the main marble material of the Taj Mahal. This study employs a Systematic Literature Review (SLR) of peer-reviewed journal articles with a primary focus on environmental policy, the impacts of climate change, and the preventive measures undertaken by the Indian government. Based on the analysis of 270 papers, it is concluded that out of the total, 30 papers specifically address objectives relevant to this research. The study period spans from 2014 to 2024. The research findings reveal that air pollution has a significantly adverse impact on the Taj Mahal. Furthermore, nine policies are generally identified from the journal literature review aimed at preserving and protecting the Taj Mahal from the negative effects caused by air pollution.

Steel damper columns (SDCs) are energy-dissipating members that are suitable for reinforced concrete (RC) moment-resisting frames (MRFs) and those often used for multistory housing. In a previous study, an energy-based prediction procedure for the peak and cumulative response of an RC frame building with SDCs was proposed. In this procedure, the accuracy of the equivalent velocity of the maximum momentary input energy (V_ΔE1^*)–peak equivalent displacement (D₁^*_max) relationship is essential for improved prediction. In this article, the seismic capacity curve (V_ΔE1^*–D₁^*_max relationship) of RC MRFs with and without SDCs is evaluated using incremental critical pseudo-multi impulse analysis (ICPMIA). In the ICPMIA, which is based on a study by Takewaki and coauthors, the structure is subjected to various intensities of critical pseudo-multi impulsive lateral force. An ICPMIA of four 8- and 16-story RC MRFs with and without SDCs is performed to obtain their structural behaviors under various intensities of pulsive input. Then, the seismic capacity curve obtained from the ICMPIA results are compared with the predicted results based on the simplified equations. The main findings of this article are as follows. (i) The seismic capacity curve of RC MRFs without SDCs strongly depends on the number of impulsive lateral forces (N_p). As N_p increases, the seismic capacity decreases. The predicted seismic capacity curve severely underestimates that obtained from the ICMPIA in the case of large N_p. This trend is notable when the level of pinching behavior in the RC members is severe. (ii) In the case of an RC MRF with SDCs, however, the influence of N_p on its seismic capacity curve is small. The predicted seismic capacity curve agrees very well with that obtained from the ICMPIA. The influence of the level of pinching behavior in RC members on the seismic capacity curve is small.

Stress during a pandemic increased the risk of alcohol consumption, which may require pharmacological management. The characteristics of emergency calls for alcohol-related issues for patients pharmacologically treated, admitted to, or not admitted to the emergency department (ED) were analyzed. An observational single-center retrospective study was conducted from January 1, 2018 to December 31, 2021, and divided into 2-year periods (2018–2019 and 2020–2021). This study focused on calls to one of the EDs of seven hospitals in the Bari (Italy) metropolitan area for patients requiring emergency services (ES) who were either admitted or not admitted, due to their refusal. A 30% reduction in emergency calls for alcohol-related issues and a 41.17% reduction in calls for patients who refused to be admitted to the ED were observed during the pandemic. During the pandemic, a reduced rate of pharmacological treatment for calls coded green (non-critical), and an increase in calls coded yellow (fairly critical) and red (very critical) were recorded. Metadoxine was administered in almost all alcohol-related emergencies, primarily in conjunction with drugs acting on the gastrointestinal tract, irrespective of age, the period considered, and whether patients were admitted or not admitted to the ED. ES is the first and only out-of-hospital service encountered by numerous patients with alcohol-use disorders who refuse to be admitted to the ED. These patients should be directed by ES personnel to a multidisciplinary program to receive treatment for drinking, improve their quality of life, and reduce sanitation costs.

This study is dedicated to understanding and simulating the mechanical properties of concrete, with a specific focus on the mesoscopic scale. Investigating concrete at this level involves examining its composition as a heterogeneous amalgamation comprising mortar, aggregates, and the interfacial transition zone (ITZ). Such an approach provides a detailed examination of the material's behavior and attributes. Numerical models are utilized, leveraging the finite element method (FEM), to examine the behavior of concrete. The study employs MATLAB programming to develop three-dimensional models, subsequently subjected to FEM analysis. Various mesoscopic Representative Volume Elements (RVEs) are formulated, encompassing varied shapes and dimensions. The MATLAB framework generates input files for numerical FEM simulations, replicating compression strength tests. As complexity increases with the inclusion of the ITZ, prismatic RVEs are developed. The proposed mesoscopic model establishes a foundational framework for a numerical simulation methodology tailored to laboratory compression tests. It provides detailed insights into concrete behavior, elucidating deformation, and fracture mechanisms. Although not a complete substitute for experimental methods, these models offer a cost-effective and expeditious alternative, pinpointing vulnerable areas and exploring the implications of additional materials on concrete behavior. Experimental data and virtual tests pave the way for mitigating carbon footprint and improving concrete sustainability.

In the quest for more efficient solar thermal systems, accurately determining the thermal emittance of low-emissive materials is crucial in determining the power losses. This paper describes the calorimetric method designed to precisely measure the thermal emittance of Selective Solar Absorbers (SSAs) to be used in High Vacuum Flat Plate Collectors (HVFPCs). The method's capability is demonstrated through the successful correction of thermal emittance values for copper samples of varying sizes, including dimensions down to 49 cm². Results highlight the method's potential to significantly reduce measurement errors associated with small-size and/or low-emittance samples, providing a path forward to improve the design and efficiency of SSAs. This research marks a significant step in advancing solar thermal technology by enabling emittance measurements with a precision better than 0.003, which is essential for the development of high-performance solar thermal absorbers. The method has also been applied to correct the thermal emittance value of SSA measured in previous measurement campaigns, and it allows a better estimation of the SSA efficiency conversion curve.

This paper provides a comprehensive evaluation of the environmental impact of implementing the beverage container DRS on marine and coastal litter along the Latvian coastline. It incorporates data and insights from the assessment of deposit fractions litter in coastal areas during the post-season autumn period in three monitoring sessions from 2021 (before the introduction of the DRS in Latvia) to 2023 (post-introduction). In 2022, a 43% overall decrease in selected public coastal areas was observed, with significant reductions at 11 out of 17 sites. This positive trend continued in 2023, showcasing a further 22% decrease compared to 2022 and a substantial 56% decrease compared to 2021. The study delves into the specific impact on different material types of beverage containers, reporting significant decreases in plastic and aluminum litter fractions. While glass beverage container litter showed a smaller decrease, overall positive trends continued in 2023. However, the situation with aluminum cans remained challenging, especially in border areas with Lithuania and Estonia. The study emphasizes that beverage containers with identifiable deposit system labels constitute a minority of the total litter pressure, underscoring the need for ongoing efforts to address containers without deposit labels, particularly in specific border areas. The findings provide valuable insights into the effectiveness of the deposit system in mitigating coastal litter, contributing to sustainable waste management practices in Latvia.

The skin beetle Reesa vespulae is regularly found beyond North America where it originated. The larvae cause considerable concern in museums as it damages hides or furs in addition to being a special source of damage to collections of dried plants in herbaria or collections of insects and other zoological specimens. It arrived in Europe in the mid-20th century and was associated mostly with stored food products, but over time it has become recognised as a museum pest. Although still uncommon and may only be observed in a small fraction of museums, where the insect is found in large numbers it can cause problems. As a single female can continue to breed because the beetle is parthenogenetic, presence can persist over long periods of time. Although small populations in museums are typically found as the adult, the larval forms are more common where a site is infested by high numbers, perhaps because the larvae and adults must range more widely for food. Although Reesa vespulae can be controlled using pesticides, it is also possible to kill the larvae within infested materials through freezing or anoxia.

This review aims to comprehensively synthesize the most recent research, collected from reputable databases, focusing specifically on transmission line. It examines advancements and challenges in data transmission. Fiber optics remains dominant, with new fiber designs and signal processing techniques like SDM improving capacity. Researchers are also addressing signal distortion and crosstalk. Beyond fiber optics, the review explores findings in coaxial cables and the promise of graphene for future high-speed transmission. Novel methods for mitigating crosstalk are presented. The findings highlight a trend towards more dependable, effective, and versatile transmission methods, with implications for various industries and electronic systems.

This study aimed to investigate the efficacy of manual therapy and exercise versus synchronized telerehabilitation with self-manual therapy and exercise in treating Subacromial Pain Syndrome (SAPS). Sixty individuals diagnosed with SPS, aged 18-50 years, were randomly assigned to home exercise (HE), manual therapy (MT), and telerehabilitation (TR) groups. Treatment protocols were administered over 8 weeks and included specific exercises and therapy interventions. Out-come measures included Visual Pain Scale (VAS), shoulder range of motion (ROM) via gonio-metric measurements, Quick Disability Arm-Shoulder-Hand Problems Survey (Q-DASH), and patient satisfaction. Results revealed that both MT and TR groups exhibited reduced pain, in-creased ROM, lower Q-DASH scores, and higher patient satisfaction compared to the HE group. However, no significant differences were found between MT and TR groups in pain levels, ROM, Q-DASH scores, or patient satisfaction. The study concludes that both telerehabilitation and manual therapy effectively alleviate pain and are well-received by patients with SPS. Addition-ally, manual therapy demonstrates superiority in enhancing functional levels compared to exer-cise-based interventions. (Registration: NCT05200130)

In this study, a new nitrogen-enriched multiwall carbon nanotube is prepared and utilized to stabilize palladium species. After the characterization of this new composite, it was applied as a catalyst in the reduction of nitroarenes and hydrodesulfurization of dibenzothiophene. Using this newly established catalyst, a wide range of aromatic compounds were reduced to the corresponding amines under a very low amount of Pd (0.005 mol%) in short reaction times. Also, dibenzothiophene (a major pollutant in fuel oil) was very efficiently transformed using this catalyst. Its robustness was studied in the recycling process where, after 20 runs in the reduction of 4-nitrotoluene and 5 times in the desulfurization of dibenzothiophene, the activity of the catalyst remained intact. According to the E-factor calculations, the present Pd catalyst meets the standards of green chemistry.

Metabolic syndrome (MS), a complex pathology with features like abnormal body fat distribution, insulin resistance, and dyslipidaemia, contributes to higher cardiovascular (CV) risk. A cross-sectional study including 87 individuals, assessed CV risk in elderly patients with type 2 diabetes and MS in Algarve, Portugal. The 10-year CV risk was estimated using the ADVANCE risk score calculator. The reductions in CV risk were estimated by adjusting the data inputted on the online tool to achieve systolic blood pressure (SBP) <130 or <120 mmHg, and LDL-cholesterol <70 mg/dL. Beyond waist circumference, the mean number of clinical features of MS was 3.14±0.84, without significant sex differences. The mean CV risk was 22.5% (CI: 20.3-24.7). Sex-specific analysis showed higher risk in males (24.2%, CI: 21.3-27.0) vs. females (19.7%, CI: 16.2-23.3; p=0.028). Hypothetical risk reductions show that lowering SBP to <130 mmHg could significantly lower the risk by an average of 9.2% (CI: 7.7-10.7), whereas 34.5% of the participants would be out of the diagnostic criteria for MS. When comparing each potential intervention with current risk, all interventions significantly reduce the 10-years CV risk. The study highlights the potential of blood pressure control in reducing CV risk and the importance of multifaceted risk reduction strategies.

As the telecommunications landscape braces for the post-5G era, this paper embarks on delineating the foundational pillars and pioneering visions that define the trajectory towards 6G wireless communication systems. Recognizing the insatiable demand for higher data rates, enhanced connectivity, and broader network coverage, we unravel the evolution from the existing 5G infrastructure to the nascent 6G framework, setting the stage for transformative advancements anticipated in the 2030s. Our discourse navigates through the intricate architecture of 6G, highlighting the paradigm shifts towards super convergence, non-IP-based networking protocols, and information-centric net-works, all underpinned by a robust 360-degree cybersecurity and privacy-by-engineering design. Delving into the core of 6G, we articulate a systematic exploration of the key technologies earmarked to revolutionize wireless communication including terahertz (THz) waves, optical wireless technology, and dynamic spectrum management,while elucidating the intricate tradeoffs necessitated by the integration of such innovations. This paper not only lays out a comprehensive 6G vision accentuated by high security, affordability, and intelligence but also charts the course for addressing the pivotal challenges of spectrum efficiency, energy consumption, and the seamless integration of emerging technologies. In this study, our goal is to enrich the existing discussions and research efforts by providing comprehen-sive insights into the development of 6G technology, ultimately supporting the creation of a thoroughly connected future world that meets evolving demands.

This cross-sectional, analytical, and observational study aimed to investigate the relationship between Visceral Adiposity Index (VAI) and anthropometric, biochemical, and insulin resistance (IR) parameters in Brazilians at risk of CVD. Biochemical parameters and anthropometric measurements were evaluated. The Pearson test was used to assess the correlation between VAI and anthropometric, biochemical, and IR parameters, with a predefined significance level of 5%. The analyzed sample consisted of 88 men and 72 women, with an average age of 58.78±13.48. VAI revealed noteworthy and positive correlations with all anthropometric parameters assessed (p&lt;0.0001). Furthermore, significant positive associations were noted between VAI and total cholesterol in women (p=0.0064), glycemia in men (p=0.0105), and LDL-c (p&lt;0.01) and triglycerides in both genders (p˂0.0001). A significant negative association was observed between VAI and HDL-c in both genders (p&lt;0.0001). Notably, the correlation between VAI and total cholesterol in men, glycemia in women, and CRP in both genders was not found to be significant. However, a significant relationship between VAI and IR parameters was observed in both sexes (p&lt;0.05). The results obtained from our study suggest that VAI functions as a simple and non-intrusive instrument, demonstrating significant effectiveness in identifying metabolic changes primarily associated with adipose tissue dysfunction, particularly dyslipidemia.

Traumatic vascular injuries consist in direct or indirect damage to arteries and/or veins and accounts for 3% of all traumatic injuries. Typical consequences are hemorrhage and ischemia. Extremities vascular injuries can occur isolated or in association in major trauma with other organ injuries. They account for 1-2% of patients admitted to Emergency Department, for approximately 50% of all arterial injuries. Lower extremities are more frequently injured than the upper ones in adult population. The outcome of vascular injuries is strictly correlated to the environment and the time background. Treatment can be challenging notably in polytrauma because of the dilemma of which injury should be prioritized and treatment delay can cause disability or even death especially for limb vascular injury. Our purposes are to discuss the role of Computed Tomography Angiography (CTA) in the diagnosis of vascular trauma and its optimized protocol to achieve the definitive diagnosis, and to assess the radiological signs of vascular injuries and the possible pitfalls.

Clustering coefficient measures are key complex network analysis tools. We examine local and global clustering coefficient measures with respect to the lexicographic graph product. As a preliminary condition, we analyze the $K_3$ subgraph structure focused on vertex inclusion with respect to the product graph. From this structure, we determine both the clustering coefficient for the product graph vertices and the average clustering coefficient for the product graph.

Cancer diagnosis and classification are pivotal for effective patient management and treatment planning. In this study, we present a comprehensive approach utilizing ensemble deep learning techniques to analyze breast cancer histopathology images. Our datasets are based on two widely employed datasets from different centers for two different tasks: BACH and BreakHis. Within the BACH Dataset, we deployed an ensemble strategy incorporating VGG16 and ResNet50 architec-tures to achieve precise classification of breast cancer histopathology images. Introducing a novel image patching technique, to preprocess a high-resolution image, which facilitates focused analysis of localized regions of interest. The annotated BACH dataset encompasses 400 WSIs across four distinct classes: Normal, Benign, In Situ Carcinoma, and Invasive Carcinoma. In addition, we employed the BreakHis dataset, utilizing VGG16, ResNet34, and ResNet50 models to classify mi-croscopic images into eight distinct categories (four benign and four malignant). For both models we leveraged a five-fold cross-validation approach for rigorous training and testing. Preliminary ex-perimental results indicate a Patch classification accuracy of 95.31% (on BACH dataset) and WSI image classification accuracy of 98.43% (BreakHis). This research significantly contributes to on-going endeavors in harnessing artificial intelligence to advance breast cancer diagnosis, potentially fostering improved patient outcomes and alleviating healthcare burdens.

This scientific article outlines the Artificial Intelligence Integrated Energy Education Framework (AI-IEEF), a transformative model designed to revolutionize energy education and management practices. The framework is organized into five distinct layers: Organizational (AI-enhanced administration systems), Financial (dynamic AI financial models), Technology (advanced simulation and modeling), Methodology (AI in curriculum development and personalized learning), and Social (AI for community engagement and impact). An expert panel used the fuzzy Delphi method to achieve consensus on twenty key factors within these layers, establishing a solid foundation for analysis. Following this, the Fuzzy Analytic Hierarchy Process (AHP) was employed to calculate precise weights for each layer and their respective factors, providing a quantitative assessment of their relative importance. These weight calculations are crucial, as they guide resource allocation and strategic decision-making to ensure the framework is optimized for the evolving needs of energy management. Furthermore, the article introduces five tailored variants of the AI-IEEF, each addressing specific aspects of energy education and offering a comprehensive approach to navigating the challenges in the field. The five variants include the Smart Campus Energy Education, Global Energy Policy Analysis, Renewable Energy Research and Development, Energy Workforce Development, and Community Engagement and Outreach variants. Each provides a distinct approach to energy education, from transforming campuses into living labs for hands-on learning to fostering international collaborations that explore the global implications of energy policy. These variants emphasize practical skills, policy analysis, and community-focused solutions, ensuring that students are well-prepared to contribute effectively to the energy sector.

In this literature review, discusses the advancements in antenna design for 5G mm-wave communication, particularly in the 28 GHz frequency band. It highlights the significance of millimeter-wave technology in addressing the increasing demands on wireless networks, emphasizing the potential for achieving unprecedented data rates, ultra-low latency, and enhanced spectral efficiency. The literature review explores the current state of research on mmWave technology, antenna array technology, and potential implications for mobile broadband applications, including 5G and future 6G networks. It presents insights into novel antenna designs, such as a single layer MIMO antenna and a multiple input multiple output dielectric resonator antenna, both aimed at supporting a wide range of frequencies and applications in the mm-wave spectrum. It discusses the challenges associated with mmWave antenna arrays, offering valuable insights into the current state of research in this domain.

We solve the problem of Apollonius by applying the Lorentz transformation within the frame- work of special relativity to go to a frame of simultaneity, where the solutions are the circum- center. We transform back to get the solutions in a general frame. We show that the solutions in a general frame are the foci of the ellipse going through the centers of the given 3 circles.

Machine learning and computer vision have proven to be valuable tools for farmers to streamline their resource utilization to lead to more sustainable and efficient agricultural production. These techniques have been applied to strawberry cultivation in the past with limited success. To build on this past work, in this study two separate sets of strawberry images, along with their associated diseases, were collected and subjected to, resizing, and augmentation. Subsequently, a combined dataset consisting of 9 classes was utilized to fine-tune three distinct pre-trained models: Vision Transformer (ViT), MobileNetV2, and ResNet18. To address the imbalanced class distribution in the dataset, each class was assigned weights to ensure nearly equal impact during the training process. To enhance the outcomes, new images were generated by removing backgrounds, reducing noise, and flipping them. The performances of ViT, MobileNetV2, and ResNet18 were compared after being selected. Customization specific to the task was applied to all three algorithms, and their performances were assessed. Throughout this experiment, none of the layers were frozen, ensuring all layers remained active during training. Attention heads were incorporated into the first 5 and last 5 layers of MobileNetV2 and ResNet18, while the architecture of ViT was modified. The results indicated accuracy factors of 98.4%, 98.1%, and 97.9% for ViT, MobileNetV2, and ResNet18, respectively. Despite the data being imbalanced, the precision, which indicates the proportion of correctly identified positive instances among all predicted positive instances, approached nearly 99% with the ViT. MobileNetV2 and ResNet18 demonstrated similar results. Overall, the analysis revealed that the Vision Transformer model exhibited superior performance in strawberry ripeness and disease classification. The inclusion of attention heads in the early layers of ResNet18 and MobileNet18, along with the inherent attention mechanism in ViT, improved the accuracy of image identification. These findings offer the potential for farmers to enhance strawberry cultivation through passive camera monitoring alone, promoting the health and well-being of the population.

The Drosophila spermatogenesis has the renewal of germline stem cells, meiosis of spermatocytes, and morphological transformation of spermatids into mature sperm. We previously demonstrated that Ocnus (ocn) plays an essential role in spermatogenesis. ValRS-m (Valyl-tRNA synthetase, mito-chondrial) gene was downregulated in ocn RNAi testes. By hatchability testing, we found that ValRS-m-knockdown induced complete sterility of male flies. We also concluded that ValRS-m-knockdown inhibited the transition from spermatogonia to spermatocytes and caused accumulated spermatogonia in testes. To understand the intrinsic reason for this destruction, we further conducted transcriptome sequencing analysis in ValRS-m RNAi testes. A total of 7710 dif-ferentially expressed genes (DEGs) were identified to have at least a 2-fold change with a p-value of

Due to constraints in launch platform and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems, and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and states deviation at the control-start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

This comprehensive review delineates the extensive roles of Akkermansia muciniphila in various health domains, spanning from metabolic and inflammatory diseases to neurodegenerative disorders. A. muciniphila, known for its ability to reside in the mucous layer of the intestine, plays a pivotal role in maintaining gut integrity and interacting with host metabolic processes. Its influence extends to modulating immune responses and potentially easing symptoms across several non-communicable diseases, including obesity, diabetes, and inflammatory bowel disease. Recent studies highlight its capacity to interact with the gut-brain axis, suggesting a possible impact on neuropsychiatric conditions. Despite the promising therapeutic potential of A. muciniphila highlighted in animal and preliminary human studies, challenges remain in its practical application due to stability and cultivation issues. However, the development of pasteurized forms and synthetic mediums offers new avenues for its use in clinical settings, as recognized by regulatory bodies like the European Food Safety Authority. This narrative review serves as a crucial resource for understanding the broad implications of A. muciniphila across different health conditions and its potential integration into therapeutic strategies

This study delves into the intricate dynamics of classical mechanics, exploring the interplay between force, mass, and energy. Through fundamental principles and mathematical formulations, it elucidates key relationships governing physical systems. Beginning with an overview of classical mechanics, the study establishes the foundational principles laid down by Newton, emphasizing concepts such as inertia, acceleration, and the relationship between force and motion. Central to the investigation is Newton's second law of motion, highlighting the direct proportionality between force and acceleration, and the inverse relationship between acceleration and mass when acted upon by a force. The study extends to the concept of effective mass, elucidating how the application of force influences the inertial mass of an object and contributes to its effective mass through the acquisition of kinetic energy. Furthermore, the study examines the total energy composition of systems, emphasizing the holistic nature of energy as a combination of potential and kinetic forms. Through the work-energy theorem, a direct link between force and kinetic energy is established, revealing how mechanical work done on an object results in changes in its kinetic energy and effective mass. Mathematical formulations and conceptual analyses provide deeper insights into the intricate relationships between force, mass, and energy, shedding light on the underlying mechanisms governing classical mechanical systems. Through validation against empirical observations and experimental data, the study ensures the accuracy and reliability of derived equations, contributing to a richer understanding of classical mechanics and paving the way for further exploration in the field of physics.

Ethiopian Airlines is a leading airline in the world. Its supply chain management is one of the most critical aspects in achieving its sustainability objectives. The present study aims to assess the sustainability practices and strategies of Ethiopian Airways in its supply chain, identifying areas for improvement and recommending strategies for enhancing sustainability. The study concentrates on pertinent sustainability concerns within the aviation sector while examining antecedent research on the sustainability of Ethiopian Airlines’ supply chain management strategies. The findings of the study reveal that there are several areas in need of improvement, including the implementation of waste reduction measures, the establishment of a recycling program, and the reduction of single-use plastic usage. It is suggested that promoting responsible tourism embodying sustainable practices is imperative, particularly within the airline context.

Living systems are intricate repositories of biomolecules, where the interactions between these molecules play an important role in maintaining homeostasis. Interruptions in these interactions can lead to diseases, underscoring the significance of biomolecular interactions and their molecular basis. HUGENICS (Human Genetic Database) is a comprehensive biological database that focuses on molecular interactions between human and microbial proteins, particularly emphasizing protein-protein interactions (PPIs). This database offers insights into disease pathways by elucidating the interplay between microbial surface/secretory proteins and human disease-related proteins. This white paper highlights the significance, scope, and potential applications of HUGENICS in advancing biomedical research and improving human health.

For their speed in data processing, low heights and cheapness, patch antennas are important to 5G networks. While there have been improvements in the area of bandwidth and size reduction; however, there are still problems that need to be fixed with regards achieving high data rates as well as wideband operation and compact sizes for 5G applications. In the coming years researchers should concentrate on materials optimization and feeding methods so that they can work efficiently at shorter wavelengths for next-generation systems while still covering all necessary bands.

This study addresses the importance of conducting mass movement susceptibility mapping and hazard assessment using quantitative techniques, including machine learning, in the Northern Lima Commonwealth (NLC). Previous exploration of the topographic variables revealed high correlation and multicollinearity among some of them, which led to dimensionality reduction through principal component analysis (PCA). Six susceptibility models were generated using weights of evidence, logistic regression, multilayer perceptron, support vector machine, random forest, and naive Bayes methods to produce quantitative susceptibility maps and assess the hazard associated with two scenarios: the first being an El Niño phenomenon and the second being an earthquake exceeding 8.8Mw. The main findings indicate that machine learning models exhibit excellent predictive performance for the presence and absence of mass movement events, as all models surpassed an AUC value of &gt;0.9, with the random forest model standing out. In terms of hazard levels, in the event of an El Niño phenomenon or an earthquake exceeding 8.8Mw, approximately 40% of the NLC area would be exposed to the highest hazard levels. It also highlights the importance of integrating methodologies to reduce model uncertainty, such as comprehensive analysis of variables supported by high quality data and organized workflows. The findings of this research are expected to serve as a supportive tool for land managers in formulating effective disaster prevention and risk reduction strategies.

The importance of sleep for healthy brain function is widely acknowledged. However, it remains unclear how the internal generation of dreams might facilitate cognitive processes. In this perspective we review a computational approach inspired by artificial intelligence that proposes a framework for how dreams occurring during rapid-eye-movement (REM) sleep can contribute to learning and creativity. In this framework, REM dreams are characterized by an adversarial process that, against the dream reality, tell a discriminator network to classify the internally created sensory activity as real. Such an adversarial dreaming process is shown to facilitate the emergence of real-world semantic representations in higher cortical areas. We further discuss the potential contributions of adversarial dreaming beyond learning, such as balancing fantastic and realistic dream elements, and facilitating the occurrence of creative insights. We characterize non-REM (NREM) dreams, where a single hippocampal memory is replayed at a time, as serving a complementary role of improving the robustness of cortical representations to environmental perturbations. We finally explain how subjects can become aware of the adversarial REM dreams, but less of the NREM dreams, and how the awareness phenomenon of wake, dream and lucid dreaming may appear.

Background: Nowadays vital signs in clinics are electronically monitored excepted for urine output which still requires, manual recording, which is subject to human errors. We, in-vitro, assessed in this study the ability a novel electronic device to measure by a combination of two different methods, the real time flow-output, like urine output. Methods: Flow or urine output was measured by a combination technique of gravimetry using a dynamometer and capacitive sensing to improve precision. Data were obtained in 3 different situations, low, medium, and high flow. Results: Three different situations were tested: full or empty dead space and Pasteur’s chamber. The differences between the injected and measured volume varies from 0 to 5 ml representing a maximal error of 3 % regardless of the volume injected and the flow in ml/hour. The capacitive sensors behave as expected with a parallel curve of the expected and measured flow. Conclusion: We have shown in this in-vitro study that the combination of gravimetry and capacitive sensors analysis allow accurate measurement of volume and flow-output. Clinical trials should be conducted to confirm its usefulness in urine output measurement in the real life.

Millions of children in developing countries face preventable deaths due to inadequate vaccination and malnutrition, in part due to insufficient monitoring and the absence of official identification. A reliable fingerprint recognition system can be a practical solution to address this issue. However, the scarcity of longitudinal fingerprint datasets for young children leads to unresolved questions regarding the earliest age for fingerprint biometric use, the frequency of enrollment required for reliable recognition, and the methods to accommodate agerelated changes. A few recent studies introduced high-resolution fingerprint scanners and showed promising recognition performance for young children. However, these studies were conducted on a small dataset over a shorter period with limited diversity; further evaluation of their finding is essential. This study assessed the effectiveness of a high-resolution contactless scanner in a controlled, diverse longitudinal dataset of children (0-15 years). Our results indicate that infants can be enrolled at five days old and reliably recognized after two months with a TAR= 100% @ FAR = 0.1%, and children aged 4-15 years can be recognized after one year with a TAR= 98.72% @ FAR = 0.1%.

This study explores the public library service evaluation domain through user-generated content on Google Maps, highlighting digital feedback's significant yet underexplored potential in understanding public library patronage across Taiwan's six major cities. Utilizing a mixed-methods research design, this study integrates Google Maps review content analysis with Social Network Analysis to delineate public perceptions and identify areas for service enhancement in public libraries. It innovatively leverages personal experiences extracted from over 60,000 Google Maps reviews to evaluate public library services in cities such as Taipei, New Taipei, Taoyuan, Taichung, Tainan, and Kaohsiung. The research taps into the National Library of Taiwan's National Library Statistics System to provide a robust analysis of library performance and user satisfaction, offering a novel perspective by emphasizing user-centric feedback from Google Maps as a primary data source. This approach provides quantitative data on library usage and geographic distribution and enriches our understanding of the qualitative experiences of library users. In analyzing the keywords from Google Maps reviews of public libraries, we categorize and interpret these under the three core LibQUAL+ dimensions—Affect of Service, Information Control, and Library as Place. The findings expose variances in perceived service quality among the cities, with Kaohsiung and Taichung receiving the highest accolades for service satisfaction. Simultaneously, the study identifies potential areas for improvement, particularly in cities with lower satisfaction ratings like Taipei. This personalized feedback illustrates the intimate relationship between public libraries and their communities, offering invaluable insights for policymakers and library management to enhance service delivery and user experience.

Magnetomotive ultrasound (MMUS) is a promising imaging modality for detecting magnetic nanoparticles. In MMUS, an external oscillating magnetic field induces motion of the injected magnetic nanoparticles within tissue, and phase-based tracking algorithms are used to detect the motion. However, the subwavelength scale of theses displacements (often a few micrometers) makes direct visualization on conventional ultrasound B-mode images impossible. In this work, we adapt the Eulerian motion magnification technique to create a novel ultrasound display mode for identifying the nanoparticle locations, eliminating the need for displacement tracking algorithms. Phantom and in-vivo experiments demonstrate that our technique successfully magnifies magnetomotion and the associated shear wave propagation in ultrasound B-mode imaging and pinpoints the nanoparticle vibration source, even in low-concentration scenarios. Additionally, motion magnification magnified the displacement of nanoparticles, having the potential to improve the localization accuracy of displacement tracking algorithms in MMUS.

The integration of digital technologies into construction practices has emerged as a pivotal area of interest, reflecting its substantial influence on the future trajectory of the construction industry. This study undertakes a comprehensive bibliometric analysis of literature on construction digitalization spanning from 2013 to 2023, sourced from the Elsevier Scopus database. Employing key terms such as "construction digitalization," "BIM," "construction 4.0," and "digital construction methodologies," the research methodically extracts and scrutinizes relevant articles. Advanced tools like the VOS viewer were utilized to delve into the bibliometric networks, offering insights into prevailing research trends within the built environment sector. The findings reveal a pronounced emphasis on digital modeling, automation, blockchain technologies, and emerging paradigms such as smart contracts and modular construction. This investigation enriches the academic discourse by elucidating the varied subtleties, ongoing shifts, and prospective directions in the ever-evolving landscape of construction digitalization research.

The impact of antecedent soil moisture content on soil erosion is a complicated phenomenon, which is still under argument with contradictions in research results. Hence, the objective of this study is to investigate the impact of antecedent soil moisture content to soil loss on clay soil by conducting two-year field experiments under natural rainfall on runoff plots with length of 10 meters, width of 3 meters, and uniform slope of 9%. Volumetric soil moisture sensors were used to log soil moisture changes, and soil moisture readings were used along with rainfall records to quantify the antecedent soil moisture conditions for each rainfall event. Results of this study show duration of the effective erosion event outranks the antecedent volumetric soil moisture content. Field study also suggests that accumulative rain falling within 48 hours (Pp48) prior to an effective erosion event strongly correlated with soil loss per Rainfall-Runoff Erosivity Index (Soil Loss / EI30), particularly when the duration of an effective erosion event is either between 3 ~ 7 hours or 10~ 30 hours. Hence, Pp48 can be considered as an alternative to replace antecedent soil moisture content in RUSLE 2’s cover and management factor.

With the rapid growth of the global mask market, consumers have put forward higher requirements for the functionality and ingredients of mask products. Conventional facial masks generally use ordinary non-woven fabrics as the mask base fabric, are frequently used with essence and contain preservatives. At the same time, they are susceptible to the influence of the external environment and are easily oxidized, which will cause the mask to deteriorate and skin allergic reactions. In addition, conventional facial masks exhibit poor skin fit, limited breathability, inadequate absorption of nutrient solutions, and easy to drip. The nanofiber mask prepared by electrospinning technology has a high specific surface area and high porosity, which enabling improved nutrient absorption by the skin, superior skin fit, and exceptional breathability. Nanofiber facial mask products can effectively solve consumer pain points and promote the high-end development of facial mask products. Therefore, this research combines needleless electrospinning technology to develop a novel solid-state, preservative-free, and quick-dissolving nanofiber facial mask that can be prepared on a large scale. Based on needleless electrospinning technology, this research deeply explores the process parameters and influencing mechanisms of quick-dissolving nanofiber facial masks, ultimately achieving the consistent production of nanofiber facial masks with optimal morphology. Comprehensive and evaluation of the structure and performance of nanofiber facial masks from micro and macro perspectives. The experimental results show that the mask morphology is optimal under the process conditions of using a spinning liquid of 20% collagen peptide solution, a spinning voltage of 30kV, a collection distance of 19cm, and a liquid supply speed of 130ml/h.

Medicinal activities carried out within hospitals lead to a high consumption of antibiotics and subsequently result in a high excretion rate of antibiotic residues. These antibiotics consumed in human medicine are not fully absorbed by the body and are often discharged into the environment as biological waste from infected human patients. The significant water consumption in hospitals and the pharmaceutical impact on wastewater from healthcare facilities facilitate the emergence and spread of antibiotic-resistant bacteria and antibiotic-resistant genes in the environment. Hospital effluents could be doubly involved in the dissemination of antibiotic molecules and multidrug-resistant bacteria in various ecosystems. The objective of this study is to characterize hospital effluents by assessing antibiotic concentrations and the diversity of antibiotic-resistant bacteria in these hospital wastewaters and within the environment (aquatic environments, rivers), as well as to inventory the bacteria present and those carrying antibiotic resistance in both hospital wastewater and the environment.