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, 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 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, 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.

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.

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.

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 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, 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 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.

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.

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.

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 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.

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.

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.

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.

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.

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.

Students studying dentistry and nursing experience anxiety daily, which affects both their general well-being and academic achievement. Anxiety is exacerbated by several circumstances, such as stressors in one's personal life, clinical environment exposure, and academic expectations. To effectively regulate anxiety and support students' achievement, treatments that take these elements into account must be designed. In this study, 271 students from the National and Kapodistrian University of Athens, Greece's departments of dentistry and nursing were polled. Being the following resources, participants filled out an electronic questionnaire that was uploaded to Google Forms and assessed their levels of stress, anxiety, depression, resilience, hope, and spiritual well-being: a) the Depression, Anxiety, Stress Scale (DASS-21), b) the Functional Assessment of Chronic Illness Therapy-Spiritual Well-Being Scale (FACIT-12), c) the Adult Hope Scale (AHS), d) the Resilience Assessment Questionnaire (RAQ8), and e) the Brief Resilience Scale (BRS). Additionally, demographic data was gathered, such as gender, educational attainment, family income, and country of origin. Statistical analyses were performed to investigate the relationships between the variables, including hierarchical multiple linear regression and t-tests. The sample consisted of 271 students from the Department of Nursing (n=126, 46.5%) and Dentistry (n=145, 53.5%), with 68.60% of them being female, 80.10% being undergraduate students, and 48.30% being from Athens, the country's capital. Comparatively speaking, 74.50 percent of nursing students were female, while 62.80% of dental students were. Compared to dental students (2.10%), nurses (40.50%) participated in postgraduate studies at a higher rate. Compared to dental students (44.80%), nursing students reported a household income of just 13.90%, which is much less than €35,000. Anxiety was reported by 51.30% of participants overall, with dental students reporting higher anxiety than nursing students. Higher family wealth was associated with reduced stress levels, while female undergraduate students reported higher levels of anxiety than their male counterparts. Hope was a strong predictor of resilience, but stress and worry had a negative correlation. Promoting students' well-being and academic success requires effective stress-reduction and resilience-building techniques aimed to not only improve student performance but also support future healthcare professionals' personal sustainability and holistic growth.

(Background) Canine mammary tumors (CMT) have emerged as an important model for understanding pathophysiological aspects of human disease. Liquid biopsy (LB), which relies on blood-borne biomarkers and offers minimal invasiveness, holds promise for reflecting the disease status of patients. Small extracellular vesicles (SEVs) and their protein cargo have recently gained attention as potential tools for disease screening and monitoring. (Objectives) This study aimed to isolate SEVs from canine patients and analyze their proteomic profile to assess their diagnostic and prognostic potential. (Methods) Plasma samples were collected from female dogs grouped into CMT (malignant and benign), healthy controls, relapse, and remission groups. SEVs were isolated and characterized using ultracentrifugation (UC), nanoparticle tracking analysis (NTA) and transmission electron microscopy (TEM). Proteomic analysis of circulating SEVs was conducted using Liquid Chromatography–Mass Spectrometry (LC–MS). (Results) While no significant differences were observed in the concentration and size of exosomes among the studied groups, proteomic profiling revealed important variations. Mass spectrometry identified exclusive proteins that could serve as potential biomarkers for mammary cancer. These included Inter-alpha-trypsin inhibitor heavy chain (ITIH2 and ITI4), phosphopyruvate hydratase or alpha enolase (ENO1), eukaryotic translation elongation factor 2 (eEF2), actin (ACTB), transthyretin (TTR), beta-2-glycoprotein 1 (APOH) and gelsolin (GSN) found in female dogs with malignant tumors. Additionally, Vitamin D-binding protein (VDBP), also known as group-specific component (GC), was identified as a protein present during remission. (Conclusion) The results underscore the potential of proteins found in SEVs as valuable biomarkers in CMT. Despite the lack of differences in vesicle concentration and size between the groups, the analysis of protein content revealed promising markers with potential applications in CMT diagnosis and monitoring. These findings suggest a novel approach in the development of more precise and effective diagnostic tools for this challenging clinical condition.

Despite their Nobel prize-winning empirical confirmation, the interpretation of the Bell inequality remains controversial. By carefully analyzing Bell's work on nonlocality, we show how the correct appreciation of Bell's rationale calls for reformulating a widespread argument on quantum nonlocality, yielding a more consistent formulation of the problem. We delve into a formal proof of quantum mechanics' violation of local causality strikingly overlooked in favor of less appropriate arguments. For completeness, we also mention a few alternatives that may rationally justify considering quantum mechanics as a local theory.

Medical image segmentation is a critical step in various healthcare applications, aiding in diagnosis, treatment planning, and disease monitoring. In this study, we investigate the efficacy of a segmentation approach based on the 2D wavelet transform. Leveraging a dataset comprising 10 diverse medical images, we evaluate the performance of our segmentation method using three key metrics: accuracy, precision, and recall. Our findings demonstrate that the proposed approach enhances segmentation accuracy, offering promising results compared to existing methods. By harnessing the multi-resolution feature extraction capabilities of the 2D wavelet transform, our method achieves improved delineation of medical image structures, paving the way for more accurate and efficient healthcare interventions.

This study investigates the microbial composition of a commercially available Swiss fermented milk and colostrum product with a history of use in chronic condition management since 2014. The analysis, performed using the Axiom Microbiome Array, identified a high number of targets corresponding to microbial species classified as probiotics belonging to the Bifidobacteriaceae family. The array provided 28 unique targets, each corresponding to a specific microbe. Next, the amino acid sequences of beta-galactosidase and sialidase from Bifidobacteria and humans were studied because these enzymes are responsible for the production of GcMAF (Gc protein-derived Macrophage Activating Factor) from the Gc protein that is abundant in colostrum. The Bifidobacterial enzymes showed striking functional similarities with their human counterparts. In addition, the study explores the potential health benefits of this product with a focus on GcMAF and chondroitin sulfate, a glycosaminoglycan highly represented in milk and colostrum. The high concentration of specific Bifidobacteria strains contributes to these benefits through two mechanisms: enhanced GcMAF production and activation of chondroitin sulfate, which in turn exhibits GcMAF-like activity. These findings suggest that the Bifidobacteria-rich Swiss product could offer health benefits through these combined mechanisms.

Infrared thermography is a contactless imaging technique, useful to measure surface temperature at distance which has been widely applied in animal production. The possible applications within the pig husbandry include sow heat detection, reduction of the incidence of neonatal mortality, recognition of febrile state caused by pathogens, study of metabolic efficiency, evaluation of stress caused by heat, by constraints, or by aggressive interaction and meat quality prediction. Even if this technique could be easily influenced by environmental factors, the continuous improvement in the procedures and the decrease in the cost of the equipment will allow in the next future new and more applications in swine farming.

Due to the increasing use of computer equipment, institutions and companies face challenges, such as sensitive data leaks and the spread of hate speech, which have severe consequences for organizations and their employees. Addressing these challenges is essential to avoid financial losses, reputational damage, and impacts on the psychological health of those involved. This paper presents a solution based on microservices for monitoring computers used by employees in organizations, including capturing information from the equipment using spyware techniques and a web application for managing alerts. The solution seeks to detect data leaks, suspicious behaviour, and hate speech. The results of the evaluation indicate that the proposed solution has an efficient data capture time and can identify unwanted behaviour in a short period. The solution also includes applying prediction models to detect hate speech, achieving an average accuracy of approximately 87%. The performance, scalability, and security evaluation demonstrate that the solution is suitable for dealing with data leakage and hate speech challenges in the corporate environment.

The COVID-19 virus was first detected in Wuhan, China and its genesis was traced to infected bats, passed through an intermediate host to humans. COVID-19 or “Coronavirus” reached approximately 4 million confirmed cases in the United States by July 2020. The spread of this virus has affected both social and economic affairs on a global scale with more than 15 million confirmed cases worldwide in July 2020. The pandemic has proven a global public health and socio-economic crisis. In addition, the shelter-in-place orders provide an unprecedented opportunity for examining the resulting reduction in greenhouse gases and aerosols on the atmosphere. The Sentinel-5P satellite has shown distinct changes in atmospheric compounds over the COVID-19 epicenter in Wuhan. After Texas, U.S.A. established similar shelter-in-place orders to prevent the spread of the virus, the state’s industrial activity experienced an economic slowdown. This paper quantifies the changes in the atmosphere during the time of the COVID-19 slowdown over major cities in Texas and compares it to similar changes in Wuhan, China using satellite imagery.

In this paper, we introduce a new causal formula to distinguish Gliosarcoma (GSM) from Glioblastoma (GBM). Our formula combines Probabilistic Easy Variational Causal Effect (PEACE) with XGBoost, or eXtreme Gradient Boosting algorithm. Unlike prior research, which often relied on statistical models to reduce dataset dimensions before causal analysis, our approach uses the complete dataset with PEACE and XGBoost algorithm. PEACE provides a comprehensive measurement of direct causal effects, applicable to both continuous and discrete variables. It offers a spectrum of both positive and negative causal effects of the events causal effect values based on the degree ?, reflecting the rarity and frequency of the events. By using PEACE with XGBoost, we achieve a detailed and nuanced understanding of the causal relationships within the dataset features, facilitating accurate differentiation between GSM and GBM.

Integrated crop-livestock production (ILP) is an interesting alternative for more sustainable soil use. However, more studies are needed to analyze soil pore properties under ILP at the micrometer scale. Thus, this study proposes a detailed analysis of soil pore architecture at the micrometer scale in three dimensions. For this purpose, samples of an Oxisol under ILP subjected to minimum tillage (MT) and no-tillage (NT) with ryegrass as cover crop (C) and silage (S) were investigated. The soil micromorphological properties of the soil were analyzed using X-ray microtomography. The MT(C) system showed the highest values of porosity (c. 20.4%), connectivity (c. 32.8×103), volume (c. 26%), and number of pores (c. 32%) in a rod-like shape. On the other hand, the MT(S), NT(C), and NT(S) systems showed higher tortuosities (c. 2.2, c. 2.0, and c. 2.1) and lower pore connectivities (c. 8.3×103, c. 6.9×103, and c. 6.2×103), especially in S use. Ellipsoidal and rod-shaped pores predominated over spheroidal and disc-shaped pores in all treatments. The results of this study show that the use of ryegrass as a cover crop improves soil physical properties, especially in MT. For S use, the type of soil management (MT or NT) did not show any differences.

Purpose: Proximal Femur Fractures (PFFs) in elder patients lead to decreased productivity. Skilled nursing facilities (SNFs) and inpatient rehabilitation facilities (IRFs) are non-home destinations for post-discharge disposition. This study aims to evaluate the loss of independence (LOI) following PFFs and examine the economic impact it entails. Method: Literature from various databases was collected and analyzed retrospectively. The inclusion criteria included patients age >18 years and articles published after 1990. All studies were screened and a PRISMA chart was used to demonstrate the search process. 24 studies were finally used for review. Results: LOI following PFFs significantly increases with age. Fractures in geriatrics avail a significant amount of post-care resources and had longer lengths of stay. Furthermore, six pre-operative risk factors were identified for non-home disposition including age >75, female, non-Caucasian race, Medicare status, prior depression, Charlson Comorbidity Index. Patients discharged directly to home have lower total cost compared to those discharged to rehabilitation units. Loss of independence increases with advancing age. Discussion: PFFs can lead to serious loss of independence among elderly patients with direct impact on economic, social, psychological aspects and the healthcare system.

Antimicrobial peptides (AMPs) are promising tools for combating microbial resistance. However, their therapeutic potential is hindered by two intrinsic drawbacks – low target affinity and poor in vivo stability. Macrocyclization, a process that improves the pharmacological properties and bioactivity of peptides, can address these limitations. As a result, macrocyclic peptides represent attractive drug candidates. Moreover, many drugs are macrocycles that originated from natural product scaffolds, suggesting that nature offers solutions to the challenges faced by AMPs. In this review, we explore natural cyclic peptides from the DBAASP database. DBAASP is a comprehensive repository of data on antimicrobial/cytotoxic activities and structures of peptides. We analyze the data on small (≤25 AA) ribosomal and non-ribosomal cyclic peptides from DBAASP according to their amino acid composition, bonds used for cyclization, targets they act on, and mechanisms of action. This analysis will enhance our understanding of the small cyclic peptides that nature has provided to defend living organisms.

The detection accuracy of bridge superficial defect using the deep neural network approach decreases significantly under light variation and weak texture condition. To address these issues, an enhanced intelligent detection method based on the YOLOv8 deep neural network is proposed in this study. Firstly, multi-branch coordinate attention (MBCA) is proposed to improve the accuracy of coordinate positioning by introducing a global perception module in coordinate attention mechanism. Furthermore, a deformable convolution based on MBCA is developed to improve the adaptability for complex feature shapes. Lastly, the deformable convolutional network-attention-YOLO (DAC-YOLO) detection algorithm is formed by replacing the deep C2F structure in the YOLOv8 architecture with deformable convolution. A supervised dataset consisting of 4794 bridge surface damage images is employed to verify the proposed method, and results show that it achieves improvements of 2.0% and 3.4% in mAP and R. Meanwhile, the model complexity decreases by 1.2G, increasing the detection speed by 3.5/f·s-1.

Staphylococcus aureus bacteremia continues to be associated with significant morbidity and mortality, despite improvements in diagnostics and management. Persistent infections pose a major challenge to clinicians and have been consistently shown to increase the risk of mortality and other infectious complications. S. aureus, while typically not considered an intracellular pathogen, has been proven to utilize an intracellular niche, through several phenotypes including small colony variants, as a means for survival that has been linked to chronic, persistent, and recurrent infections. This intracellular persistence allows for protection from the host immune system and leads to reduced antibiotic efficacy through a variety of mechanisms. These include antimicrobial resistance, tolerance, and/or persistence in S. aureus that contribute to persistent bacteremia. This review will discuss the challenges associated with treating these complicated infections and the various methods that S. aureus uses to persist within the intracellular space.

Hydrotherapy, including the use of therapeutic showers and bathtubs, has been studied for its potential benefits in labor pain management. Previous research has indicated that hydrotherapy can alleviate pain, but comparative studies between therapeutic showers and bathtubs are scarce. Objective: This study aims to compare the effects of therapeutic showers and bathtubs on pain perception, labor duration, use of epi-dural analgesia, and maternal and neonatal outcomes during labor. Methods: A total of 124 pregnant women were included in this study. Participants were divided into two groups: those who used a thera-peutic shower and those who used a bathtub during labor. Pain levels were measured using a visual analog scale (VAS). Labor duration, use of epidural analgesia, types of delivery, maternal outcomes (postpartum hemorrhage, perineal status, maternal hypotension, fever, and breastfeeding), and neonatal outcomes (APGAR scores, fetal heart rate, complications, and neonatal unit admissions) were recorded and analyzed. Results: Both the therapeutic shower and the bathtub effectively reduced pain perception, with the bathtub showing a greater reduction in VAS scores. The therapeutic shower group experienced a signifi-cantly shorter labor duration compared to the bathtub group. The majority of participants in both groups did not require epidural analgesia, with no significant differences between the groups. There were no sig-nificant differences in the types of delivery. Maternal outcomes indicated a lower incidence of perineal tears and episiotomies in the therapeutic shower group. Neonatal outcomes, including APGAR scores and fetal heart rate, were similar between the groups, with no significant differences in complications or neo-natal unit admissions. Conclusions: Both therapeutic showers and bathtubs are effective for pain relief during labor, with the bathtub showing a higher reduction in pain intensity. The therapeutic shower is as-sociated with a shorter labor duration and a lower incidence of perineal tears and episiotomies. Both meth-ods are safe for neonatal well-being, making hydrotherapy a viable non-pharmacological option for pain management in labor. However, the therapeutic shower may offer additional benefits in terms of labor du-ration and maternal outcomes.

This study investigates the application of frequency augmentation techniques to improve condition-based maintenance (CBM+) systems for airborne weapon systems, focusing on the predictive accuracy of velocity and acceleration parameters. Utilizing MIL-STD-1553B MUX data from 138 sorties of fixed-wing aircraft, we explored six augmentation methods, including traditional interpolations (linear, quadratic, cubic spline) and advanced machine learning models (K-Nearest Neighbor, LSTM, and Bi-LSTM). Our findings indicate that while traditional methods like linear interpolation are more effective for velocity parameters, advanced ML techniques, particularly Bi-LSTM, provide better results for acceleration parameters, which exhibit more complex and rapid variability. The study underscores the necessity of tailoring augmentation approaches to specific parameter characteristics and highlights the potential of ML models in capturing intricate patterns within time-series data. These insights are critical for advancing CBM+ systems in military avionics, enhancing reliability and operational efficiency through improved data processing strategies. Future work should explore more performant augmentation techniques, such as by integrating multi-dimensional datasets, and explore ways to develop automated tools for a more powerful predictive maintenance framework.

Energy storage systems play a crucial role in the overall performance of hybrid electric vehicles. Therefore, the state of the art in energy storage systems for hybrid electric vehicles has been discussed in this paper along with appropriate background information for facilitating future research in this domain. Specifically, we have compared the key parameters such as cost, power density, energy density, cycle life, and response time for various energy storage systems. For the energy storage systems employing ultra capacitors, we have presented the characteristics such as cell voltage, cycle life, power density and energy density. Furthermore, we have discussed and evaluated the interconnection topologies for the existing energy storage systems. We have also discussed the hybrid battery-flywheel energy storage system as well as the mathematical modeling of the battery-ultracapacitor energy storage system. Toward the end, we have discussed energy efficient powertrain for hybrid electric vehicles.

One of the most prevalent and deadly types of cancer is breast cancer. The value and effectiveness of the current pharmacological therapy are, however, constrained. Using computational methods and publicly available data, the current study set out to identify the genes and molecular pathways linked to breast cancer. It also looked into potential treatments for the disease that would target these molecular processes. In this study, we mined genes that were strongly associated with breast cancer using text mining and GeneCodis. Using STRING and Cytoscape, protein-protein interaction (PPI) study was carried out. Candidate medications were then derived based on the drug-gene interaction study of the final genes. 2,658 genes linked to breast cancer were found by our investigation using text mining searches. Out of which 166 genes have been taken which are relevant to breast cancer. Ten genes representing ten pathways—which a total of ten proteins could target—were found by gene enrichment analysis. We have taken Holy Basil as our lead as it contains various bioactive compounds such as flavonoids, terpenoids, and phenolics, which have shown antioxidant, anti-inflammatory, and anticancer properties. For this analysis we choose the molecular docking technique to check the effects of different chemical constituents of Holy Tulsi on breast cancer targeted protein and compare their results. We’ve performed the molecular docking in between chemical constituents of Holy Basil and the targeted proteins and determined the binding affinity with the help of PyRx and BIOVIA Discovery studio software. Anti-mitotic activity of Pisum sativum using tulsi extract to check the cytotoxicity effect was done. To determine the toxicity level of the extract on rat liver was performed in the end. In conclusion, investigating candidate medications that target the genes/pathways relevant to breast cancer in order to uncover possible treatments may be accomplished through drug discovery employing in silico text mining and pathway analysis technologies along with the wet lab experimentation with plants and preclinicals.

Barley is rich in phenolic compounds, providing health benefits and making it a valuable addition to a balanced diet. However, most studies focus on these compounds at barley's final maturity, neglecting their synthesis during grain development and its impact on barley quality for food applications. This study investigates phenolic profiles during grain development in four hull-less barley genotypes with different grain colors, specifically bred for food applications. The objectives were to determine the phenolic profile and identify the optimal maturity stage for maximum phenolic content and antioxidant capacity. Using UPLC-MS/MS and in-vitro antioxidant capacity assays, results show that total phenolic compounds decrease as grain matures due to increased synthesis of reserve components. Flavan-3-ols, phenolic acids, and flavone glycosides peaked at immature stages, while anthocyanins peaked at physiological maturity. The harvest stage had the lowest phenolic content, with a gradient from black to yellow, purple, and blue genotypes. Antioxidant capacity fluctuated during maturation, correlating positively with phenolic compounds, especially bound phenolic acids and anthocyanins. These findings suggest that early harvesting of immature grain can help retain bioactive compounds, promoting the use of immature barley grains in foods. To support this market, incentives should offset costs associated with decreased grain weight.

The mechanical properties of the materials stored inside agricultural silos influence the loads generated inside them. The different silo calculation methodologies allow predicting these loads under static and dynamic conditions if the mechanical properties of the stored materials are known. It has been known for many years that these properties are highly dependent on the moisture content of the material. However, to date there are not many studies focused on its determination. The goal of this research is the determination of the angle of internal friction, apparent cohesion, dilatancy angle and apparent specific weight of maize subjected to different moisture contents. Direct shear and oedometer assay devices were used for this purpose. In addition, the maize samples used were moistened using a climatic chamber. Moisture contents applied to maize sample ranged from 9.3% to 17.4%. The results obtained for the angle of internal friction and apparent cohesion, as well as those obtained for the apparent specific weight, were similar to those reported in the literature. However, the values obtained for the dilatancy angle of maize as a function of moisture content could not be compared because nothing has been published so far. The values obtained for this parameter overlap with those published for this material under ambient conditions. In addition, no direct relationship between the values obtained for this parameter and the moisture content of the sample could be found. Finally, the apparent specific weight increased with increasing moisture content of the samples, which differed from that published in the literature. The values provided here can be used for the optimization of storage and handling structures for granular agricultural materials using numerical methods.

The prevalence of multidrug-resistant Gram-negative infections, particularly carbapenem-resistant strains, has become a significant global health concern. Ceftazidime-avibactam (CZA) has emerged as a promising treatment option. However, data on its efficacy and safety in children are scarce, necessitating further investigation. We conducted a retrospective study at a tertiary hospital in Spain from February 2019 to January 2022. Pediatric patients (<16 years) treated with CZA for confirmed or suspected multidrug-resistant Gram-negative infections were included. Clinical and microbiological characteristics, treatment approaches, and outcomes were examined. Eighteen children received CZA treatment. All had complex chronic conditions, with the most frequent underlying main diseases being liver transplantation (n=8) and biliary atresia (n=4). The predominant type of infection for which they received CZA was intra-abdominal infections caused or suspected to be caused by OXA-48-producing Klebsiella pneumoniae. CZA was generally well tolerated. Within the first month of starting CZA therapy, 2 patients died, with one case directly linked to the infection’s fatal outcome. Some patients needed repeated courses of therapy due to recurrent infections, yet no resistance development was noted. In summary, the use of CZA showed effectiveness and safety, while the lack of resistance development highlights CZA’s potential as a primary treatment option against OXA-48-producing infections.

This article examines varying viewpoints on the single-submission policy in scientific publishing, which has recently come under attack. The rule permits the sequential, rather than simultaneous, submission of a manuscript to more than one journal and dictates that an author(s) must wait for a response from one journal before resubmitting the same work to another for consideration. A corollary is that legitimising multiple-submissions would create more problems than it could solve.

This study investigates the impact of integrating ChatGPT on the academic writing performance and engagement of English as a Foreign Language (EFL) undergraduate students in Delhi, India, during the first semester of the academic year 2024/2025. It addresses the challenges within the Indian education system by exploring the effectiveness of AI-driven writing tools in enhancing writing skills and motivation among EFL learners. Employing a mixed-methods approach, the research evaluates ChatGPT's influence on 32 EFL Indian undergraduate students through draft revisions, questionnaires, and interviews. The findings highlight ChatGPT's positive impact on writing quality, engagement levels, and immediate feedback appreciation, emphasizing its potential in improving writing instruction and student outcomes in EFL contexts. Recommendations are provided for practitioners to integrate ChatGPT in writing exercises and for researchers to conduct longitudinal studies and explore ethical considerations in AI use for educational purposes, ultimately contributing to enhanced EFL education and technology-mediated learning.

In the context of evolving perceptions of sexuality, particularly within the realm of health and disability, this study investigates the impact of multiple sclerosis (MS) on female sexual function and quality of life. A quantitative study involving 130 female MS patients aged 35 to 50 was conducted, employing measures such as The Female Sexual Function Index (FSFI), The Multiple Sclerosis Intimacy and Sexuality Questionnaire-19 (MSISQ-19), and The Fatigue Severity Scale (FSS). Results indicate a significant association between greater sexual dysfunction and poorer quality of sex life, alongside the correlation of increased fatigue with diminished sexual satisfaction. Factors such as education level, time of diagnosis, and treatment regimen also influenced outcomes. Findings underscore the importance of supportive interventions, including counseling, to enhance the quality of sex life for women with disabilities, particularly those with MS.

A new approach based on input-output (IO) analysis has emerged to estimate the carbon footprints of companies and their products from cradle to gate. While they rely on the same principles as the GHG Protocol, they use a distributed iterative framework to improve the footprint estimations and reduce their uncertainty. While optimal estimations would result if all the world’s companies would enter such a system, this paper shows how such a distributed system could apply to the real world where many enterprises would stay out of the system. We show how it would increase the quality of the estimations with respect the GHG Protocol by integrating scope 1 and scope 2 data of the value chains in the footprint estimations and reducing the part of remaining scope 3 data. To help analyzing uncertainty, we show how to use the scope 1/2/3 decomposition to estimate the biases and the standard deviations of the computed production intensities. We illustrate the model on macroeconomic data for 44 sectors and two regions (Europe and Rest of World), using the Inter-Country Input-Output database (ICIO). Such a system would necessarily rely on Information and Communication Technology since the companies would be permanently interconnected in a large-scale meshed network, using an application protocol for data exchange.

During the development of new medicines mutually exclusive specificity appears to be required but hitherto is most often included at the late clinical trial stage. Here, I describe the use of Hedgehog signalling in Drosophila as a model to represent a mutually exclusive relationship within the context and report the identification of CG43658, a putative Rho guanine nucleotide exchange factor and orthologue of the Charcot-Marie-Tooth disease associated gene ARHGEF10. Furthermore, a Computer that is able to consider the whole and describe the sum of everything in it absolutely in unambiguous terms is a useful tool. Here I describe such a computer with a suggestion for an application to examine any component in the context where a medicine is sought. Taken, together I would like to propose this method as a fundamental necessity and improvement upon current existing methods related not only to Hedgehog signalling but plausibly to life science research and the search for medicines in general.

The quality of waste activated sludge produced in urban wastewater treatment systems varies according to the efficiency of the operation of treatment units along the content of microflora and organic carbon. However, these represent a biogas-energy alternative through anaerobic co-digestion, contributing to reducing the environmental impacts caused by their inadequate disposal. Biogas production by the Two-stage production method in batch digesters was evaluated by two qualities of waste activated sludge (SLB50 y SLB90) and with a mixture of two co-substrates: cattle manure (CEV50 y CEV90) and residual edible oil with mixing, pH and temperature control. Bacteria in good quality sludge (SLB90) showed a faster adaptation of 2 days than those in low quality (SLB50) with 25 days lag phase. The highest CH4 production was for SLB90 (303.99cm3 d-1) compared to SLB50 (4.33 cm3 d-1); while cow manure sludge mixture (CEV90) contributed to increasing production of CH4 (42 422.8 cm3 d-1) compared to CEV50 (12 881.45 cm3 CH4 d-1), while in residual edible oil mixture they were 767.32 cm3 d-1 and 211.42 cm3 d-1 for CAV90 y CAV50, respectively. The addition of sludge co-substrates improves the nutrient balance, C/N rate and micro flora diversity; consequently methane production improves too; this methodology could be integrated into concepts of Circular economy.

The Midwestern region of the United States has been experiencing periodic forage shortages due to frequent droughts, a growing livestock population, and reliance on traditional farming practices. This study evaluated the dry matter yield (DMY), forage nutritive value, water use efficiency (WUE), and economic viability of forage soybean [Glycine max (L.) Merr.] in a no-till winter wheat-based rainfed cropping system in the Midwest, USA. The research aimed to identify alternative summer forage crops that are drought-resilient, require lower inputs, mitigate seasonal gaps, and provide higher DMY and forage nutritive value compared to traditional forages. A four-year field experiment in a randomized complete block design with four replications assessed these parameters at various growth stages and planting dates. Results showed that forage soybean had a high DMY (~13 Mg ha-1), especially when optimally planted and harvested at the R3 stage. Forage nutritive value, including crude protein (CP), in vitro dry matter digestibility (IVDMD), and relative feed value (RFV), was highest at early vegetative stages (V2-V3), meeting livestock nutritional requirements. Forage soybean also demonstrated good WUE (21 kg ha-1 mm-1), making it suitable for water-limited regions. Economic analysis indicated substantial net profits ($322 per hectare), confirming its economic viability. The study concludes that forage soybean is a promising summer forage option for Midwest growers, offering high-quality forage, efficient water use, and economic benefits. Further research, particularly animal feeding trials, is recommended to validate its potential for widespread adoption in cropping systems.

In this research, we present the Combined Theoretical Signal (CTS) model, which integrates influences from dark matter, quantum fluctuations, and higher-dimensional effects. Our goal is to provide a potential framework for unifying gravity and quantum physics. We validate the CTS model against observational gravitational wave data and perform residual analysis to assess its accuracy. The results suggest that CTS aligns well with the observational data and provides a robust theoretical model that may contribute significantly to the quest for a universal theory. This model has the potential to enhance our understanding of the fundamental forces and the structure of the universe, supporting a hierarchical tree structure rather than parallel universes.

Kisspeptin, a key neuropeptide derived from the KISS1 gene, is renowned for its critical role in regulating the hypothalamic-pituitary-gonadal axis and reproductive hormone secretion. Beyond its primary function in reproductive biology, emerging research has illuminated its influence in various cancers, mediating significant effects through its interaction with the G-protein coupled receptor, Kisspeptin receptor. This interaction has been implicated in modulating cellular pro-cesses such as proliferation and metastasis, making it a potential target for therapeutic interven-tion. Our study initially screened ten kisspeptin-10 analogs through cytotoxic effects of kisspep-tin-10 (KP10) and its analogs in several cancer types, including cervical, prostate, breast, and gastric cancers, with a particular focus on cervical cancer where the most profound effects were observed. Further exploration using kinase array assays revealed that these analogs specifically alter key kinases involved in cancer progression. Migration assays demonstrated a substantial decrease in cell motility, and Bioluminiscence Resonance Energy Transfer assays confirmed these analogs strong interactions with the kisspeptin receptor. Overall, our results indicate that these KP10 analogs not only hinder cervical cancer cell proliferation but also curtail migration through targeted modulation of kinase signaling, suggesting their potential as therapeutic ayfgents in managing cervical cancer progression. This comprehensive approach underscores the therapeutic promise of exploiting kisspeptin signaling in cancer treatment strategies.

This paper is a study of a generalization of the quantum Riemannian Hamiltonian evolution, previously analyzed by us in our work [6], in the geometrization of quantum mechanical evolution in a Finsler geometry. We find results with dynamical equations governing the evolution of the trajectories defined by the expectation values of position. The analysis appears to provide an underlying geometry described by a geodesic equation, with connection form with a second term which is an essentially quantum effect. These dynamical equations provide a new geometric approach to the quantum evolution where we suggest a definition for "local instability" in the quantum theory.

This study investigates the correlation between the California Bearing Ratio (CBR) and the Dynamic Cone Penetrometer (DCP) for subgrade soil analysis. The paper aims to provide practical equations for predicting CBR values from DCP test results, enhancing the efficiency of soil assessments in engineering practice. By analyzing test data and proposing correlations for different soil groups, the study introduces recalibrated correlations that demonstrate high accuracy in predicting CBR values. The newly proposed equations offer reliable predictions with R2 values of 0.89, 0.92, and 0.94 for clean sand, silty sand or sandy silt, and cohesive soil, respectively. These correlations serve as valuable tools for engineers, enabling rapid and accurate CBR estimations for improved decision-making in various engineering projects.

This work aimed to develop an anionic cellulose nanofiber (CNF) bio-adsorbent from palm date tree waste and to investigate its removal efficiency against cationic methylene blue dye from contaminated water. Palm date pulp was first prepared from palm date leaves through acid hydrolysis using H2SO4, followed by hydrolysis in a basic medium using KOH, in which the process completely removed the components of hemicellulose, lignin, and silica. To obtain anionic CNF, the resulting pulp was further treated with H2SO4, followed by centrifugation. Biogel formation of the CNF suspension was promoted by sonication, where its removal efficiency of methylene blue dye was studied as a function of dye concentration, temperature, contact time, and pH value. Two equilibrium models, the Langmuir and Freundlich models were employed, and the Langmuir model was found to be consistent with the experimental data. The highest removal efficiency was obtained at 60oC and was 5mg/gm. Furthermore, several kinetic models were used to gain insight into the adsorption mechanism. The pseudo-second-order model provided an accurate description of the adsorption process, while the Elovich equation suggested a chemical reaction between methylene blue dye and CNF. The study’s findings were in agreement with the pseudo-second-order model, indicating general chemical reactions. The study indicates that CNF adsorbents derived from renewable natural waste sources such as palm date leaves can be effective in removing cationic contaminants such as methylene blue dye.

Based on the electron-deficient property of picric acid (PA), two neutral Ir(III) complexes 1 and 2 modified with the electron-rich carbazolyl groups were synthesized and characterized. Both 1 and 2 exhibit aggregation-induced phosphorescence emission (AIPE) properties in THF/H2O. Among them, 2 is extremely sensitive for detecting PA with a limit of detection of 0.15 μM in THF/H2O. Furthermore, the selectivity for PA is significantly higher compared to other analytes, enabling efficient detection of PA in four common water samples. The density functional theory calculations and the spectroscopic results confirm that the sensing mechanism is photo-induced electron transfer.

Objective: This systematic review investigates the diagnostic, prognostic, and therapeutic implications of immunohistochemical markers in dentigerous cysts (DC) and odontogenic keratocysts (OKC) associated with impacted third molars. Materials and Methods: A comprehensive search strategy was employed across major databases including MEDLINE/PubMed, EMBASE, and Web of Science, from the inception of the databases to March 2024. Keywords and Medical Subject Heading (MeSH) terms such as "dentigerous cysts," "odontogenic kerato-cysts," "immunohistochemistry," "Ki-67," and "p53" were used. The PRISMA 2020 guidelines were followed to ensure methodological rigor. Inclusion criteria encompassed studies on humans and animals providing de-finitive diagnoses or specific signs and symptoms related to DC and OKC, with results on protein expression derived from immunohistochemistry, immune antibody, proteomics, or protein expression methods. Results: Of the 159 studies initially identified, 138 met the inclusion criteria. Our analysis highlighted sig-nificantly higher expressions of Ki-67 (22.1% ± 4.7 vs. 10.5% ± 3.2, p < 0.001), p53 (15.3% ± 3.6 vs. 5.2% ± 1.9, p < 0.001), and Bcl-2 (18.4% ± 3.2 vs. 8.7% ± 2.4, p < 0.001) in OKCs compared to DCs, indicating a higher proliferative index, increased cellular stress, and enhanced anti-apoptotic mechanisms in OKCs. Ad-ditionally, PCNA levels were higher in OKCs (25.6% ± 4.5 vs. 12.3% ± 3.1, p < 0.001). Genetic mutations, particularly in the PTCH1 gene, were frequently observed in OKCs, underscoring their aggressive behavior and potential malignancy. Conclusion: The findings emphasize the significant role of immunohistochemical markers in distinguishing between DCs and OKCs, with elevated levels of Ki-67, p53, Bcl-2, and PCNA in OKCs suggesting a higher potential for growth and recurrence. Genetic insights, including PTCH1 mutations, further support the need for personalized treatment approaches. These markers enhance diagnostic accuracy and inform targeted thera-peutic strategies, potentially transforming patient management in oral and maxillofacial surgery.

Solifenacin (SFC) is a potent muscarinic antagonist that effectively reduces bladder muscle contraction, thereby alleviating symptoms such as frequency of micturition and urgency. Oxidation of SFC leads to the formation of impurities like Impurity K. Effective analysis and control of this impurity is crucial for ensuring compliance with regulatory standards and safeguarding patient health. To address these challenges, we propose a novel one-step synthesis of Impurity K from SFC. Impurity K was synthesized using cerium ammonium (IV) nitrate (CAN) in water/acetonitrile as the solvent. Additionally, we describe a new HPLC-MS method for the detection of Impurity K in solifenacin succinate tablets.

Background: The aim of the current study is to evaluate the effects of inflammation markers, on infection and mortality in patients over 65 years of age monitored in the intensive care unit. In the study, the significance of pan-immune inflammation (PIV), neutrophil-lymphocyte ratio (NLR), platelet-lymphocyte ratio (PLR), monocyte-lymphocyte ratio (MLR), systemic immune-inflammatory index (SII), systemic immune response index (SIRI), multi-inflammatory index (MII) 1-2-3, and CRP/albumin ratios, new biomarkers, were attempted to be determined as prognostic and mortality markers in patients over 65 years of age monitored in the ICU. Methods: This multicenter, retrospective cohort study was conducted in two tertiary-level ICUs with patients aged 65 and over who were admitted. Patients with cirrhosis, bone marrow transplantation, hematologic malignancy, undergoing chemotherapy, and neutropenia at admission to the ICU were excluded from the study. Results: A total of 333 patients were included in the study. The 28-day mortality was found to be 31.8%. When each inflammatory marker associated with 28-day mortality was examined the CRP/albumin ratio performed better than both NLR and SIRI, and the results were statistically significant (AUC: 0.665, 95% CI: 0.604-0.726 and p <0.001). NLR had a moderate discriminative ability in distinguishing mortality risk (AUC: 0.593, 95% CI: 0.526-0.660 and p = 0.006). Although SIRI was lower than NLR, it had a statistically significant result (AUC: 0.580, 95% CI: 0.514-0.646 and p = 0.019). CRP/albumin ratio was the most effective inflammatory marker in predicting mortality risk in geriatric patients admitted to the ICU.

Multi-stakeholder participation processes in watershed management face challenges due to limited monitoring and baseline data, resulting in a lack of awareness among stakeholders about the current state of the watershed. This knowledge gap often leads to conflicts of interest, where the broader impacts of individual decisions are overlooked. To overcome these limitations, this paper explores the design and implementation of a Serious Game (SG) aimed at co-producing a watershed management plan at the basin scale within the specific context of the Campoalegre River basin in Colombia. By providing an interactive platform, the SG facilitates collaboration between local actors, who may be unfamiliar with existing watershed plans, and decision-makers. The goal is to create a participatory space where stakeholders can comprehend the watershed management plan structure and prioritize actions based on various climatic, social, and economic conditions. Following the application of the SGs, stakeholders demonstrated an improved understanding of the basin, fostering increased participation, open debate, and the proposal of actions. These outcomes serve as valuable inputs for the implementation of water management planning policies, showcasing the potential of SGs in bridging knowledge gaps, and fostering effective multi-stakeholder engagement.

The COVID-19 pandemic underscores the significance of vaccine hesitancy in shaping vaccination outcomes. Understanding the factors underpinning COVID-19 vaccination hesitancy is crucial for tailoring effective vaccination strategies. This cross-sectional study, conducted in three communities across the United States and Lebanon, employed surveys to assess respondents' knowledge, attitudes, and perceptions regarding COVID-19 infection and vaccination. Among the 7,196 participants, comprising 6,775 from the US and 422 from Lebanon, vaccine hesitancy rates were comparable at 12.2% and 12.8%, respectively. Notably, a substantial proportion of respondents harbored misconceptions, such as attributing the potential to alter DNA (86.4%) or track individuals (92.8%) to COVID-19 vaccines, and believing in the virus's artificial origins (81%). Primary determinants of hesitancy included perceptions that the vaccine poses greater risk than the infection itself (aOR = 8.7 and 9.4, respectively) and negative recommendations from healthcare providers (aOR = 6.5 and 5.4, respectively). Conversely, positive endorsements from healthcare providers were associated with reduced hesitancy (aOR = 0.02 and 0.4, respectively). Targeting healthcare providers to dispel misinformation and elucidate COVID-19 vaccine risks holds promise for enhancing vaccination uptake.

Although the field of geomatics has seen multiple technological advances in the recent years which enabled new applications and simplified the consolidated ones, some tasks remain challenging, inefficient, and time- and cost-consuming. This is the case of accurate tridimensional surveys of narrow spaces. Static laser scanning is an accurate and reliable approach but impractical for extensive tunnel environments; portable laser scanning is on the other hand time-effective and efficient but not very reliable without ground control constraints. This paper describes the development process of a novel image-based multi-camera system meant to solve this specific problem: delivering accurate, reliable, and efficient results. The development is illustrated from the system conceptualization and initial investigations to the design choices and requirements for accuracy. The resulted working prototype has been put to the test to verify effectiveness of the proposed approach.

While there are well-known synthetic methods in the literature to find the image of a point under circular inversion in l2−normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach spaces. In this study, we have succeeded in giving a synthetic construction for the circular inversion in l1−normed spaces, which is one of the most fundamental examples of Minkowski geometry. Moreover, this synthetic construction has been given using the Euclidean circle, independently of the l1−norm.

The oviparous blow fly Calliphora vicina has shown potential as a managed pollination species to support honeybee (Apis mellifera) usage in Australian horticulture. This blow fly species lays eggs onto carrion soon after death and the resultant larvae that hatch are necrophagous and feed on the decomposing tissues of the dead animal. Newly hatched larvae of this fly were provided with plant-based meals (soya bean and canola) and compared with animal-derived meatmeal to determine if plant-based meal could be used to mass rear this blow fly species. Both soyabean and canola meal media did not support the survival of any larvae through to adult eclosion. The addition of only 10% whole egg powder to the plant-based meals enabled survival to eclosion of 39% and 13% on soyabean and canola based medias respectively compared with 76% on animal-based meatmeal with 10% whole egg powder. Larvae fed livestock meatmeal with 10% whole dried egg powder had the fastest development to the pupal stage, the highest pupation rate, the heaviest pupae and the highest subsequent adult eclosion. This study concluded that the use of plant-based meals in the mass rearing of the blow fly C. vicina was neither viable, nor economically viable.

In the era of the post-quantum Internet of Things (IoT), the implementation of anti-quantum cryptographic algorithms in numerous terminals can successfully defend against prospective quantum computing assaults. Lattice-based cryptography can withstand quantum computing attacks, making it a viable substitute for the currently prevalent classical public-key cryptographic technique. Nevertheless, the algorithm’s significant time complexity will result in a substantial computational burden on the edge computing chip in the IoT terminal. The computation of polynomial multiplication is the most demanding task in lattice-based cryptographic algorithms. Therefore, the investigation into efficient methods for calculating polynomial multiplication is highly important. Quick number theory transformations (NTT) are a widely employed technique to accelerate polynomial multiplication. This study presents a hardware implementation of an efficient number theory transformation. We utilize a multi-level pipeline architecture in the design to accomplish parallel calculations and execute it on a low-profile Artix7-XC7A100T FPGA device. The performance evaluation results demonstrate that our implementation significantly enhances performance and reduces resource usage compared to other existing proposals on the same platform. We suggested NTT core can be implemented in edge computing chips to enhance computational speed due to its small and low-latency design. The experimental results show that the proposed design, which supports both NTT and inverse NTT, achieves 417-Megahertz and consumes only 541-LUTs on Artix-7 XC7A100T.

The umami taste, one of the five primary tastes, has been shown to be a helpful tool in reducing salt intake and improving eating patterns. This study aimed to investigate how umami taste is perceived and evaluated in a sample of adult participants living in Eastern Europe, taking into account their sex, education, and travel habits. A Text Semantic-mining Analysis (TSA) was conducted using data from 300 adults (152 males and 148 females, mean age = 26.71 years). They also performed an MSG and NaCl (salt) discrimination test and were further interviewed about taste preferences, travel habits, and type of residence. The results indicated that the taste sensation elicited by the MSG solution was complex, unfamiliar and had negative valence. The descriptor most commonly used for MSG was "sour," followed by "bitter" and "salty" for the whole group, but these differed by gender. There was no difference in umami preference between males and females, but males preferred spicy flavors while females favored sweet and salty tastes. This finding underscores the potential bias and unknown significance of umami taste, suggesting the importance of establishing an accurate concept in European culture and promoting its usage in food choices for better health.

Reducing the immunogenicity of animal-derived monoclonal antibodies (mAbs) for use in humans is critical to maximize therapeutic effectiveness and preclude potential adverse events. While traditional humanization methods have primarily focused on grafting antibody Complementarity-Determining Regions (CDRs) on homologous human antibody scaffolds, framework regions can also play essential roles in antigen binding. Here, we describe the humanization of the pan-HLA-DR mAb 44H10, a murine antibody displaying significant involvement of the framework region in antigen binding. Using a structure-guided approach, we identify and restore framework residues that directly interact with the antigen or indirectly modulate antigen binding by shaping the antibody paratope and engineer a humanized antibody with affinity, biophysical profile, and molecular binding basis comparable to that of the parental 44H10 mAb. As a humanized molecule, this antibody holds promise as a scaffold for the development of MHC class II-targeting therapeutics and vaccines.

Spinal cord tumors, though rare, present formidable challenges in clinical management due to their intricate nature. Traditional treatment modalities like surgery, radiation therapy, and chemotherapy have been the mainstay for managing these tumors. However, despite significant advancements, challenges persist, including the limitations of surgical resection and the potential side effects associated with radiation therapy. In response to these limitations, a wave of innovative approaches is reshaping the treatment landscape for spinal cord tumors. Advancements in gene therapy, immunotherapy, and targeted therapy are offering groundbreaking possibilities. Gene therapy holds the potential to modify the genes responsible for tumor growth, while immunotherapy harnesses the body's own immune system to fight cancer cells. Targeted therapy aims to strike a specific vulnerability within the tumor cells, offering a more precise and potentially less toxic approach. Additionally, novel surgical adjuncts are being explored to improve visualization and minimize damage to surrounding healthy tissue during tumor removal. These developments pave the way for a future of personalized medicine for spinal cord tumors. By delving deeper into the molecular makeup of individual tumors, doctors can tailor treatment strategies to target specific mutations and vulnerabilities. This personalized approach offers the potential for more effective interventions with fewer side effects, ultimately leading to improved patient outcomes and a better quality of life. This evolving landscape of spinal cord tumor management signifies the crucial integration of established and innovative strategies to create a brighter future for patients battling this complex condition.

Purpose: This study aimed to identify the risk factors for acute pancreatitis (AP) and its impact on outcomes in Polish children treated for ALL. Methods: The study group included 2303 children who received intensive chemotherapy for ALL. The group was subdivided into patients with at least one episode of AP and those who did not develop AP following treatment for ALL. Results: The cumulative incidence of AP in the study group was 4.08%. Older age was an independent risk factor for AP development (OR 1.05; 95%CI: 1.006 – 1.098; p=0.03). The overall mortality related to AP was 2.13%. The probabilities of disease-free survival (p-DFS) and event-free survival (p-EFS) were 0.84 vs. 0.86, log-rank: p=0.65 and 0.75 vs. 0.80, log-rank: p=0.12, respectively in both subgroups. A total of 22 out of 94 patients (23.4%) with AP were re-exposed to asparaginase (ASP) during the subsequent phases of the treatment. Only one re-exposed to ASP patient (4.5%) developed a second episode of AP. There were no significant differences in p-DFS and p-EFS between patients re-exposed and not re-exposed to asparaginase (0.78 vs. 0.86, log-rank p=0.27 and 0.63 vs. 0.79, log-rank p=0.09 respectively). Conclusions: The incidence of AP in children with ALL is low and related to the patient’s age. AP development doesn’t seem to impact p-DFS and p-EFS in children with ALL. The recurrence of AP following re-exposure to asparaginase in patients with ALL and a history of AP is low (4.5%). Re-exposure to asparaginase after the first episode of AP doesn’t improve either p-DFS or p-EFS in children with ALL.

Formaldehyde (HCHO), an indoor volatile organic compound, is seriously harmful to human health. Therefore, green and effective decomposition of HCHO is essential. TiO₂ has been employed for the degradation of HCHO via photocatalytic generation of reactive oxygen species (ROS) (O^2-, ·OH), yet the low specific surface area of crystalline TiO₂ depressed the catalytic performance. Herein, we prepared TiO₂ aerogels with high specific surface area and high porosity by sol-gel method, and added PVA to introduce flexible molecular chains for pore size regulation. The photocatalytic performance test verifies that the pore size of TiO₂ aerogel is one of the important factors for HCHO decomposition. Notably, through the establishment of theoretical model and calculation, we validated that the efficiency of HCHO decomposition is related to the oxygen pressure in the pores of TiO₂ aerogel, and the oxygen pressure is inversely proportional to the pore size. Accordingly, the optimal pore size of TiO₂ aerogel for the photocatalytic HCHO decomposition is 2 nm~10 nm. This study provides a theoretical idea for TiO₂ aerogels in the decomposition reaction of HCHO, which is expected to inspire more breakthroughs in the study of TiO₂ aerogels for green chemistry.

From an industrial point of view, the milling of 2.5D cavities is a frequent operation, 1 consuming time and presenting optimization potential, especially through a judicious choice of 2 the tool trajectory. Among the different types of trajectories, some have a general spiral-like aspect 3 and can potentially offer a reduced machining time. They are called curvilinear trajectories and are 4 obtained by interpolation between structure curves which are the numerical solutions of a partial 5 differential equation. In this case, the machine tool will connect points and the trajectory will be made 6 up of small segments. Even if, macroscopically, these trajectories have all the qualities to allow the 7 tool to move quickly, on a small scale, the discontinuities in tangency, inherent in the discretization, 8 significantly increase machining time. This article suggests to enhancing the continuity level of the 9 toolpath by rebuilding structure curves with a set of Hermite quartic spline patches connected in 10 tangency and curvature. Thanks to this, the tool will machine at an average feedrate closer to the 11 programmed one and will, de facto, reduce traveling time. 12 This article shows that the proposed method increases, on the two tested cavities, toolpath quality 13 indicators, reduces milling time from 10% to 18% for a curvilinear method without a filter and make 14 it possible to generalize the Bieterman and Sandström method for all non convex pockets.

This paper explores the emergence of Sustainability-Linked Bonds (SLBs) as an innovative instrument to finance sustainability objectives. SLBs have emerged as a transformative financial instrument, establishing an explicit link between cost of funding and sustainability objectives. SLBs were first launched in 2019 and represent 7% of labelled bonds, still dominated by the more established green bonds. Issuance of SLBs now exceeds $250 billion. Following initial enthusiasm, they are now facing criticism. In the context of the growth of sustainable finance and concerns of greenwashing, this paper investigates ways to enhance the design of SLBs. Drawing on literature and expert interviews, the findings highlight the strong potential of SLBs to contribute to sustainability financing, especially in hard-to-abate sectors. The paper identifies the key positive attributes of SLBs and their limitations in five areas: key performance indicators’ (KPI) selection, sustainability performance targets’ (SPT) calibration, bond characteristics, reporting practices, and resource requirements. Recommendations to financial intermediaries, issuers and policy makers include defining standardized KPIs based on a materiality assessment, requesting SPTs to be supported by science and in line with an issuer’s core strategy, tailored step-up mechanisms and avoidance of call loopholes, and stricter reporting. SLBs represent an opportunity to add rigor to sustainable finance and better price externalities, where material topics have an explicit impact on cost of funding and credit ratings.

Introduction: Rotavirus-induced acute diarrhoea continues to pose a significant health threat to children under 5 years old worldwide, despite the availability of effective vaccines. This study aimed to assess the prevalence, associated risk factors, and circulating genotypes of rotavirus among children under 5 admitted to Ikom Medical Centre due to diarrhea. Methodology: Stool samples were collected from 294 children under 5 with diarrhoea at Ikom Medical Centre. Rotavirus antigen detection was performed using rapid chromatographic immunoassay. Molecular techniques such as polyacrylamide gel electrophoresis (PAGE), RT-PCR, and semi-nested multiplex RT-PCR were used to analyze rotavirus strains. Data were obtained through questionnaires, and statistical significance was assessed using the chi-square test (P < 0.05). Results: Among the 294 samples, 20.4% (60/294) tested positive for rotavirus. Significant risk factors influencing rotavirus prevalence included feeding status, toilet system, and duration of diarrhoea. The most prevalent genotype for VP7 was G4 (26.7%), and for VP4, it was genotype P[4] (23.3%). Predominant genotype combinations were G4P [4] (11.6%) and G12P[4] (6.7%), while non-typeable P[NT] was observed in 41.7% of cases. Conclusion: This study highlights the circulation of rotavirus in Ikom, Cross River State, emphasizing its neglected status despite its significant global impact on child mortality. Urgent attention is needed to address rotavirus as a serious public health concern, particularly in low-resource settings.

Visual object tracking is an important technology in camera based sensor networks, which has a wide range of practicability in auto drive system. A transformer is a deep learning model that adopts the mechanism of self-attention, and it differentially weights the significance of each part of the input data. It has been widely applied in the field of visual tracking. Unfortunately, the security of the transformer model is unclear. It makes such transformer-based applications be exposed to security threats. In this work, the security of the transformer model is investigated with the important component of autonomous driving, visual tracking. Such deep-learning-based visual tracking is vulnerable to adversarial attacks, so adversarial attacks are implemented as the security threats to conduct the investigation. First, adversarial examples are generated on top of video sequences to degrade tracking performance, and the frame-by-frame temporal motion is taken into consideration when generating perturbations over the predicted tracking results. Then, the influence of perturbations on performance is sequentially investigated and analyzed. Finally, numerous experiments on OTB100, VOT2018, and GOT-10k data sets demonstrate that the executed adversarial examples are effective on the performance drops of the transformer-based visual tracking.

Both bacteria product flagellin and macrophages are implicated in HIV infection/disease progression. However, the impact of their interaction on HIV infection and the associated mechanisms remain to be determined. We thus examined the effect of the flagellins on HIV infection of primary human macrophages. We observed that the pretreatment of macrophages with the flagellins from the different bacteria significantly inhibited HIV infection. The mechanistic investigation showed that the flagellin treatment of macrophages downregulated the major HIV entry receptors (CD4 and CCR5) and upregulated the CC chemokines (MIP-1α, MIP-1β, and RANTES), the ligands of CCR5. These effects of the flagellin could be compromised by a toll like receptor 5 (TLR5) antagonist. Given the important role of flagellin as a vaccine adjuvant in TLR5 activation-mediated immune regulation and in HIV infection of macrophages, future investigations are necessary to determine the in vivo impact of flagellin-TLR5 interaction on macrophage-mediated innate immunity against HIV infection and the effectiveness of flagellin adjuvant-based vaccines studies.