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.

In this paper, we make research on fractal characteristics of the superposition of fractal surfaces in the view of fractal dimension. We give the upper bound of the lower and upper Box dimension of the graph of the sum of two bivariate continuous functions and calculate the exact values of them under some particular conditions. Further, it has been proved that the superposition of two continuous surfaces cannot keep the fractal dimensions invariable unless both of them are two-dimensional. A concrete example of numerical experiment has been provided to verify our theoretical results. This study can be applied to the fractal analysis of metal fracture surfaces or computer image surfaces.

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.

In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic phenomena that can only be understood in terms of the outer, extrinsic reality.

In two dimensional disordered lattices, presence of interaction makes particles less localized than the non-interacting ones within the range of disorder strength W ≤ 4 and interaction strength V ≤ 4. If the interaction strength is higher, then particles localize more. Although, a localization-delocalization transition is not found, a transition with changes in the dominant correlations is observed. The nature of correlations between the particles as nearest neighbors become dominant beyond certain disorder strengths.

Introduction: When analyzing the current situation in Spain, derived from our current lifestyles far from following a Mediterranean lifestyle, there is an alarming prevalence of diabesity, which increases the global risk of suffering from cardiovascular disease (CVD) and decreases the quality of life related to health (QLRH). In order to guarantee, beyond glycemic control of patients with type 2 diabetes (DM2), adequate control of cardiovascular risk factors (CVRF) in DM2, it will be necessary to carry out a community intervention focused on the application of education programs focused on promoting the acquisition of healthy eating habits through the Mediterranean diet (DMED). This dietary pattern, together with physical exercise, has been shown to contribute to improving the QLRH of patients. Objective: To analyze the quality of life related to health, present in patients with poorly controlled type 2 diabetes, to determine the possible relationship between this and the degree of adherence to the Mediterranean diet and to examine whether there are differences between the sexes. Material and methods: Observational descriptive study in 93 patients diagnosed with DM2 with poor glycemic control (1Ac ≥ 7%), carried out in various health centers in Albacete and Cuenca, in which the baseline relationship between adherence to DMed and the HRQoL. They were administered a data collection sheet that included a survey of the degree of adherence to the DMed (MEDAS-14) and QLRH (SF-12v2) in the Primary Care (PC) medical and nursing consultations. The variables were analyzed: age groups, sex, years of evolution of DM2, body mass index (BMI), as well as basal glycemia (GB) and glycosylated hemoglobin (HbA1c). The “MEDAS-14” (adherence to DMED) was the main variable and the “SF-12v2” (QLRH) was the secondary variable. Material and methods: Observational descriptive study in 93 patients diagnosed with DM2 with poor glycemic control (1Ac ≥ 7%), carried out in various health centers in Albacete and Cuenca, in which the baseline relationship between adherence to DMed and the HRQoL. They were administered a data collection sheet that included a survey of the degree of adherence to the DMed (MEDAS-14) and QLRH (SF-12v2) in the Primary Care (PC) medical and nursing consultations. The variables were analyzed: age groups, sex, years of evolution of DM2, body mass index (BMI), as well as basal glycemia (GB) and glycosylated hemoglobin (HbA1c). The “MEDAS-14” (adherence to DMED) was the main variable and the “SF-12v2” (QLRH) was the secondary variable. Results: Patients with poorly controlled DM2 and with low adherence to the MedDM show a non-significantly greater affectation in the physical sphere: fair general state of health, physical function I (limitation to make moderate efforts such as moving a table, vacuuming or walk more than an hour), physical function II (limitation to climb several flights of stairs), physical role (problems at work or daily activities doing less than loved ones), physical role II (they had to stop performing some tasks at work or activities of daily living) and regular body pain. Presenting less affectation in the mental field: emotional role I, emotional role II, mental health I, vitality and mental health II. Without affectation in the social function since they consider that rarely the emotional or physical problems have hindered their social activities. Conclusions: Diabetic patients with poor glycemic control have low adherence to the MedMD (<9 points) and have poor QLRH. Low adherence to the DMed and obesity are related to a greater affectation in the physical dimension and less affectation in the mental dimension without affectation in the "social function".

The accuracy of sales prediction models based on the big data of online word-of-mouth (eWOM) is still not satisfied. We argue that eWOM contains heat and sentiments of different product dimensions, which can improve the accuracy of these models. In this paper, we propose a dynamic topic analysis (DTA) framework in order to extract heat and sentiments of product dimensions from the big data of eWOM. Finally, we propose an autoregressive-heat-sentiment (ARHS) model, which integrates heat and sentiments of dimensions into the baseline predictive model. The empirical study in movie industry confirms that heat and sentiments of dimensions can improve the accuracy of sales prediction model. ARHS model is better for movie box-office revenue prediction than other models.

In this outlet, I’ve devised the concept of relation amid two points where these points are coming up to make situation which in that the set of objects are greed to represent the story of how to be in whatever situations when these two points have the styles of being everywhere in the highlights of the concept which are coming from the merits of these points where are eligible to make capable situation to overcome every situation when they’re participant in the hugely diverse situations which mean too styles of graphs with have the name or the general results for the general situation as possible as are.

In the last years, we have witnessed a remarkable progress of algorithms solving Boolean satisfiability (SAT). The success of these algorithms has been especially relevant in a large number of industrial or real-world applications, for which these SAT solvers are nowadays an essential core part of their solving processes. Interestingly enough, these applications include a very diverse and heterogeneous range of domains, such as hardware verification, planning, and cryptography, among others. Unfortunately, the reasons of the good performance of these solvers on this variety of industrial benchmarks are not completely understood yet. Since SAT solvers’ efficiency is fundamental in various domains, obtaining a better understanding of these algorithms and the reasons of their good performance is crucial. In order to shed light on this question, SAT solvers are often viewed as complex systems with many interconnected components (e.g., conflict analysis and learning mechanism, database management, search restarts) interacting in many unpredictable ways. There is the common belief that the resulting emergent behavior of these complex systems takes advantage of a certain underlying structure of the SAT formula, which is shared by the majority of these industrial problems regardless the domain they come from. Recently, there have been some attempts of characterizing this structure under the lens of complex networks, with the purpose of better understanding the success of the solvers, and potentially improving them. In this paper, we analyze the structure of industrial SAT instances under the lens of self-similarity, and study how the execution of SAT solvers affect that structure. Many real-world graphs exhibit self-similar structure (with small fractal dimension), which means that after rescaling (replacing groups of nodes by a single node), the same kind of structure can be observed. In our analysis, in which we represent SAT instances as graphs, we observe that many industrial SAT formulas exhibit the same kind of structure. Moreover, we analyze how this structure evolves by effects of learning new clauses during the search. In particular, we observe that learned clauses usually contain variables that are close in the graph representation of the formula. This is, the learning mechanism tends to work locally. On the contrary, this learning mechanism on random SAT formulas –which do not exhibit any structure at all– is unable to generate these local clauses. This difference contributes to explain the success of modern SAT solvers on industrial problems.

Numerical weather prediction is an initial-value problem, for determination of the initial conditions, there are many methods and one of the most classical methods is variational methods in three dimensions, or 3D-Var. In this approach, with a defined cost function proportional to the square of the distance between the analysis and both the background and the observations, one can obtain the analysis. In the cost function, the background and the observations are reshaped to vectors; within this step, the order of the background error covariance matrix and the observational error covariance matrix becomes huge, which is not convenient to one to obtain the analysis. In this paper, according to the matrix analysis approach, we put forward some possible improvements to the dimension-reduction algorithm of 3D-Var, so that provide some references for data assimilation.

In this work we study the following problem, from a computational point of view: If three points are selected in the unit square at random, what is the probability that the triangle obtained is obtuse, acute or right? We provide two convergent strategies: the frst derived from the ideas introduced in [2] and the second built on the combinatorics theory. The combined use of these two methods allows us to address the random triangle theory from a new perspective and, we hope, to work out a general method of dealing with some classes of computational problems.

In this paper we use the additive thermodynamic formalism to obtain new bounds of the Hausdorff and box-counting dimension of certain non conformal hyperbolic repellers defined by piecewise smooth expanding maps on a $d$-dimensional smooth manifold $M$.

Kronecker products of matrices have some striking operation properties, one of which is called the mixed-product property $(A \!\otimes\! B)(C \!\otimes\! D) = AC \!\otimes\! BD$. In view of this property, the two-term Kronecker product $A_1 \otimes A_2$ can be rewritten as $A_1 \otimes A_2 = (A_1 \otimes I_{m_2})(I_{m_1} \otimes A_2)$ of dilation forms of $A_1$ and $A_2$, and three-term Kronecker product $A_1 \otimes A_2 \otimes A_3$ can be rewritten as the products $A_1 \otimes A_2 \otimes A_3 = (A_1\otimes I_{m_2} \otimes I_{m_3})(I_{m_1} \otimes A_2 \otimes I_{m_3})(I_{m_1} \otimes I_{m_2} \otimes A_3)$ of the dilation forms of $A_1$, $A_2$, and $A_3$, respectively, where the matrices on the right-hand sides of the two factorizations are commutative. In this note, we approach the commutative Kronecker products on the right-hand sides of the two factorization equalities, and present a variety of new and useful analytical formulas for calculating the ranks, dimensions, orthogonal projectors, and ranges of matrices composed of these Kronecker products.

Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to quantum computations performed in higher dimensions. We illustrate the operational procedure to build a quantum computer able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information. This novel, relatively straightforward architecture not only permits to increase the amount of available qbits in a fixed volume, but also converges towards a solution to the problem of optical computers, that are not allowed to tackle quantum entanglement through their canonical superposition of electromagnetic waves.

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), s_ex, and the pair-correlation contribution, s₂. Thus, the RMPE represents the net contribution to s_ex due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1 < d < 3 has been proposed [Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction ϕ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δs_min at a packing fraction ϕ_min, and then rapidly increases, becoming positive beyond a certain packing fraction ϕ₀. Interestingly, while both ϕ_min and ϕ₀ monotonically decrease as dimensionality increases, the value of Δs_min exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d ≃ 2.38. A plot of the scaled RMPE Δs/|Δs_min| shows a quasiuniversal behavior in the region −0.14 ≲ ϕ − ϕ₀ ≲ 0.02.

In a recent paper, we have shown how gravity and information can be related. The relation is based on the thermodynamic extension of the gravitational system under consideration using the holographic principle. Using this idea, we were able to derive the Gullstrand-Painlevé (GP) metric. In this short paper, we re-derive the GP metric using information. However, we now extend the spacetime to 5D with the fifth dimension being time, that is, the (3+1)D spacetime is now promoted to (3+1+1)D spacetime. We also comment on the possible Braneworld interpretation of this model.

The issue of monitoring and early warning of rock instability has received increasing critical attention in the study of rock engineering. To investigate the damage evolution process of granite under triaxial compression tests, acoustic emission (AE) tests were performed simultaneously. This study firstly introduced two novel parameters, i.e., the coefficient of variation (CoV) of the information entropy and correlation dimension of the amplitude data from the AE tests, to identify the precursor of the failure of granite. Then the relationship between the changes in these parameters and the stress-time curve was compared and analyzed. The results of this study show that: (1) There is a strong correlation between the CoV of the information entropy and the failure process of granite. The granite failed when the CoV curve raised to a plateau. (2) The fluctuation of the correlation dimension indicates the different stages of the loading process, i.e., the initial compaction stage, the linear elastic stage, the yield stage, and the failure stage. Each stage contains a descending and a rising process in the correlation dimension curve, which indicates that this parameter could be used to identify the precursor of the failure as well. (3) The combined analysis of the two can improve the accuracy of rock instability prediction. This study provides new insights into the prediction of rock instability, which has theoretical implications for the stability of subsurface engineering rock masses.

So called Higuchi’s method of fractal dimension estimation is widely used and the term Higuchi’s fractal dimension even occurs in many publications. This paper deals with this method from mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. Definition of Higuchi’s dimension was comparated with mathematical definition of the distance and dimension. It is showed, that the definition of the Higuchi’s dimension does not satisfy axioms of distance and dimension. So called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.

In this article, some kinds of triple belongs to metric dimensions are defined. Some classes of graphs in the matter of these kinds, are studied and the relation amid these kinds are considered. The kind of having equivalency amid these notions and some classes of graphs, is obtained. The kind of locating some vertices by some vertices when the number of locating vertices is increased, has the key role to analyze the classes of graphs, general graphs, and graph's parameters.

Suppose set

The holographic principle states that the information about the volume of space is stored on its boundary. Assuming this holds, we can explain the aspects of gravity. The spacetime needs to be extended to 5D to explain gravity in this context. This naturally explains the four classical tests of gravity namely the gravitational redshift, the perihelion precession, the bending of light, and the gravitational time delay. We also show a novel way in which the universe expands in an accelerated manner at late times without the need for any form of dark energy.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

Chilean geography is highly variable, not only from a climatic and hydrological point of view, but also a morphological one, showing unpredictable natural patterns with marked contrasts throughout the country, for which sometimes it is considered as a "crazy" geography. In this paper we have investigated this apparent disorganized character by exploring the fractal properties of fluvial networks extracted from basins distributed across the continental territory. Analytical and semi-empirical methods were applied, finding striking patterns of organization in the distributions of Horton parameters and the fractal dimension of the drainage networks. Fractal dimension reveals to be quite dependent on the drainage area of each unit, showing clear groupings by tectonic and climatological factors. Such dimension reveals to be an important geomorphic parameter, if not the only one able to capture the real morphology of a fluvial network. From our results and despite the diversity of landforms, hydrological, climatic and tectonic conditions, Chilean’s geography is perhaps not as crazy and disorganized as believed.

Whether resurfacing or not resurfacing the patella during total knee arthroplasty (TKA) still is a challenge to orthopedic surgeons. A significant reason for this controversy is the far from perfect outcomes of both techniques, resulting from inadequate knowledge of normal patellar dimensions in a diseased one. The primary purpose of the current study is to find the pre-diseased patellar dimensions and the ethnic differences in patellar dimensions. We measured the patella's dimensions on 927 normal young adult knee MRIs from seven different ethnicities. Besides comparing the dimensions between sexes, ages, and sides, we analyzed the differences among ethnic groups. The average thickness was 25.12±2.33 mm; the average width was 44.57±4.32 mm, the average articular surface length was 32.69±3.75 mm, with significant gender, age, and ethnic differences. There were also significant differences in dimensions among ethnic groups, except for between the Indians and Far Eastern Asians and between the Arabs and North Africans. We could also find a robust mathematical relationship between the patella's width, length, and thickness. The ethnic differences in patellar dimensions found in this study can help optimize surgical technique and implant designs for patellar resurfacing. The mathematical equation will help the surgeons find the normal, pre-diseased patella thickness to prevent over-or under-stuffing during the patellar resurfacing.

Dark energy and dark matter are described as different manifestations of vacuum energy within the framework of Extra Dimensional Symmetry (EDS) that doubles large spatial dimensions with microscopic partners. In this framework, the bare vacuum energy component exists in a gravitationally inert state where actual gravitational constant G_o= 0G, while real particles oscillate between this inert state and the active state where G_o = 2G. Neutrinos induce small component of the gravitational constant in the inert state, causing the gravitation of virtual particles as dark matter. A small component of vacuum energy from the inert state also spills into the gravitationally active state as dark energy due to an energy density constraint and a speed limit asymmetry. This form of dark energy and dark matter, are parameterized by a gravitational potential suppressed asymmetry parameter. The dynamics of dark matter is further parameterized by the flavour, phase and kinetic energy parameters of its neutrino substrate. This results in the existence of a dominant light form of dark matter and a detectable heavy form of dark matter. EDS predicts a curvature suppressed Gravitational Wave Reheating (GWR) mechanism, enhanced by negative pressure. It converts gravitational wave energy to photon energy.

The fractal dimension of geomagnetic variations at the Baigazan magnetic station at Russian Altay for 2011-2013 was calculated using the Higuchi method. The daily variation of Higuchi Fractal Dimension (HFD) for the D,H,Z-components of the geomagnetic field has been investigated, its contribution to the variability of HFD is from 30 to 40 percent of the total variance. A correlation analysis of the fractal dimension of the variations of the D,H,Z-components with Auroral Electrojet (AE) index and solar wind characteristics was carried out. A negative correlations with logarithms of AE-index, interplanetary magnetic field (IMF) strength and solar wind velocity were found. About 25 percent of the fractal dimension variance is controlled by the variability of these characteristics. Pair and partial correlation coefficients for these parameters were calculated for every month of 2011-2013.

Low-dimensional carbon-based (LDC) materials have attracted extensive research attentions in electrocatalysis because of their unique advantages such as structural diversity, low cost, and chemical tolerance. They have been widely used in a broad range of electrochemical reactions to relief environmental pollution and energy crisis. Typical examples include hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR), carbon dioxide reduction reaction (CO₂RR), and nitrogen reduction reaction (NRR). Traditional “trial and error” strategies seriously slowed down the rational design of electrocatalysts for these important applications. Recent studies show that the combination of density functional theory (DFT) calculations and experimental research is capable of accurately predicting the structures of electrocatalysts, thus could reveal the catalytic mechanisms. Herein, current well-recognized collaboration methods of theory and practice are reviewed. The history of modern DFT, commonly used calculation methods, and basic functionals are briefly summarized. Special attention is paid to descriptors that are widely accepted as a bridge links the structure and activity, and the breakthroughs for high-volume accurate prediction of electrocatalysts. Importantly, correlating multiple descriptors are used to systematically describe the complicated interfacial electrocatalytic processes of LDC catalysts. In addition, machine learning and high-throughput simulations are crucial in assisting the discovery of new multiple descriptors and reaction mechanisms. This review will guide the further development of LDC electrocatalysts for extended applications from the aspect of DFT computations.

Suitable soil structure and nutrient security are important for plant growth and development, characteristics of soil fractal dimension and distribution of physical and chemical properties and their interactions play an important role in studying the stability of soil structure and water and fertilizer cycles. As a sustainable management model, intercropping has positive benefits for erosion control, spatial optimization of resources, as well as improving system productivity. The effects of four intercropping methods on soil fractal dimension and physicochemical properties were investigated by intercropping Salvia miltiorrhiza with forage and S. miltiorrhiza with forest under typical karst rock desertification habitats in Guizhou. The results showed that soil nutrient content of intercropping was significantly higher than that of monoculture, the organic carbon content of soil grown under forest is higher than other treatments, and there was a non-significant change in soil water content of intercropping compared with monoculture. The soil fine-grained matter of intercropping was significantly higher than that of monoculture, while the soil fractal dimension showed a tendency to become larger with the increase of fine-grained matter. The intercropping planting, due to its component types and spatial and temporal configurations, leads to differences in soil water and fertilizer interactions, which can be combined with other ecological restoration measures to optimize the composite model and jointly promote the restoration and development of ecologically fragile areas.

We establish a Gröbner-Shirshov bases theory for trialgebras and show that every ideal of a free trialgebra has a unique reduced Gröbner-Shirshov basis. As applications, we give a method for the construction of normal forms of elements of an arbitrary trisemigroup, in particular, A.V. Zhuchok’s (2019) normal forms of the free commutative trisemigroups are rediscovered and some normal forms of the free abelian trisemigroups are first constructed. Moreover, the Gelfand-Kirillov dimension of finitely generated free commutative trialgebra and free abelian trialgebra are calculated respectively.

In 2020, the pandemic caused by the Coronaviruses (CoV) that are a large family of viruses that cause illness ranging from the common cold to more severe diseases such as Middle East Respiratory Syndrome (MERS-CoV) and Severe Acute Respiratory Syndrome (SARS-CoV2). The Coronavirus disease (COVID-19) is a new strain that was discovered in 2019 and has not been previously identified in humans. It is the high time to investigate the quantitative and/or qualitative genomic informations of the virus SARS-CoV2 in order to strengthen the healthcare facility to fight against this viral disease. In this article, a through quantitative understanding of the purine and pyrimidine spatial distribution/organization of all 89 complete sequences of SARS-CoV (available as on date in the NCBI virus database, is made using different parameters such as fractal dimension, Hurst exponent, Shannon entropy and GC content of the nucleotide sequences of the genome of SARS-CoV2. Also a cluster among all the the SARS-CoV sequences of nucleotide have been made based on their phylogeny made through their closeness (Hamming distance) based on respective purine-pyrimidine distribution.

Consider a robot that is navigating in a space modeled by a graph, and that wants to know its current location. It can send a signal to determine how far it is from each landmark among a set of fixed landmarks. We study the problem of computing the minimum required number of landmarks, and where they should be placed so that the robot can always determine its location. Since the problem is an NP-complete problem, the robot's responses to the actions are slow. To accelerate this response, we can use the parallel version of this problem. In this work, we introduce a new parallel implementation for determining the metric dimension of a given graph. We run the proposed algorithm on a symmetric multi-processing (SMP) cluster using C programming language and the Message Passing Interface (MPI) library. Finally, we run our implementation on four categories of graphs (the tracks in which the robot moves): a cycle graph Cn, a path graph Pn, a triangular snake graph and a ladder graph Ln. Preliminary computational results indicate that the metric dimension problem is an NP-complete problem and prove the ability of the proposed algorithm to achieve a speedup of 6 for 8 processors.

A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: briefly describe the main methods or treatments applied; (3) Results: summarize the article’s main findings; (4) Conclusions: indicate the main conclusions or interpretations. The abstract should be an objective representation of the article and it must not contain results that are not presented and substantiated in the main text and should not exaggerate the main conclusions. This study presents a comprehensive literature review on the convergence of affective computing, interactive installation art, multi-dimensional sensory stimulation, and artificial intelligence (AI) in measuring emotional responses. It addresses the problem of understanding emotional response and measurement in the context of interactive installation art under artificial intelligence (AI). The study aims to fill the existing research gaps by examining three key aspects: sensory stimulation, multi-dimensional interactions, and engagement, which have been identified as significant contributors to profound emotional responses in interactive installation art. The study proposed approach involves conducting a process analysis of emotional responses to interactive installation art, aiming to develop a conceptual framework that explores the variables influencing emotional responses. The study will formulate hypotheses that make specific predictions about the relationships between sensory stimulation, multi-dimensional interactions, engagement, and emotional responses. By employing the ASSURE model combined with experimental design, the research methodology ensures a systematic and comprehensive study implementation. The implications of this project lie in advancing the understanding of emotional experiences in interactive installation art under AI, providing insights into the underlying mechanisms that drive these experiences. The contributions of this research include bridging the identified research gaps, refining theoretical frameworks, and guiding the design of more impactful and emotionally resonant interactive artworks. Ultimately, this research aims to contribute to the broader field of human-computer interaction and enhance the development of immersive and emotionally engaging interactive installations.

(1) Background: Breast cancer is the second leading cause of cancer death among women. The accurate prediction of survival intervals will help physicians make informed decisions on treatment strategies or the use of palliative care for patients; (2) Methods: The gene expression is predictive and correlates to patient prognosis. To establish a reliable prediction tool, we collected the RNA-seq data of breast cancer patients, a total of 1187 RNA-seq data (median age 58 years), in FPKM format from the TCGA database. Among them, 144 RNA-seq data with date of death information was selected to establish the SaBrcada-AD dataset. We first normalized the SaBrcada-AD dataset to transcripts per million (TPM) to build survival prediction model SaBrcada. After normalization and dimension raising, the differential gene expression data were used for testing eight different deep learning architectures. Among them, GoogLeNet performed the best. Considering the effect of age on prognosis, we examined all ages between the lower and upper quartiles of patient age for a stratified random sampling test; (3) Results: Stratifying by age based on a cut-off of 61 years of age improved the accuracy of SaBrcada compared to previous findings, resulting in an accuracy of 0.798. We also built a free website tool to provide 5 kinds of predicted survival period information for clinician reference; (4) Conclusions: We established a breast cancer survival analysis prediction model, SaBrcada, and a website tool with the same name. Through this highly reliable survival analysis model and website tool, information on survival intervals will be provided for clinicians as part of precision medicine.

With the rise of Internet of Things (IoT) devices and Cyber-Physical Systems, the demand for more functional and high-quality software has increased tremendously. To meet this need, we must reengineer and reuse existing software, as well as develop new software formal verification methods. One such method is based on physical quantities defined by the System International, which have physical dimensions. The homogeneity of physical dimensions in software code enables us to check the software code in the space of base units, making it the first basis of the new software verification method. However, this method cannot check expressions with angles, angle speed, and other similar features. To address this, a transformation for physical value orientation introduced by Siano allows us to check software code for orientational, stabilization, and other related branches. This makes the orientational homogeneity the second basis of the new software verification method. To assess the effectiveness of the proposed method, we developed special software defect models based on the statistical characteristics of software code. We used a special statistical analysis tool to define the statistical characteristics of modern software and analyzed over 2 GB of C++ GITHUB code for drones. Based on the actual distribution of software characteristics, the proposed method can detect over 60% of latent software defects. Implementing this method can significantly reduce testing time, improve reliability, and enhance overall software quality.

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

This article is a study on the (k,s)-Riemann-Liouville fractional integral, a generalization of the Riemann-Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore, we make the estimation of the Box dimension of the graph of continuous functions after the extended integral. It presents that the upper Box dimension of the (k,s)-Riemann-Liouville fractional integral for any continuous functions is no more than the upper Box dimension of the functions on the unit interval I=[0,1], which indicates that the upper Box dimension of the integrand f(x) will not be increased by the σ-order (k,s)-Riemann-Liouville fractional integral ksD−σf(x) where σ&gt;0 on I. Additionally, we prove that the fractal dimension of ksD−σf(x) of one-dimensional continuous functions f(x) is still one.

A method of direction-of-arrival (DoA) estimation for FMCW radars is presented. In addition to MUSIC and ESPRIT, which are well-known high-resolution DoA estimation algorithms, deep learning has recently emerged as a very promising alternative. It is proposed in this paper to use a 3D convolutional neural network (CNN) for DoA estimation. The 3D-CNN extracts from the radar data cube spectrum features of the region of interest (RoI) centered on the potential positions of the targets, thereby capturing the spectrum phase shift information, which corresponds to DoA, along the antenna axis. Finally, the results of simulations and field experiments are provided to demonstrate the superior performance, as well as the limitations, of the proposed 3D-CNN.

Research shows that stress, a common problem in dense cities, can be relieved in the natural environment. As great significance has been attached to the urban environment and public health in the society, this paper aims to study the relation and interaction between the perceived sensory dimension of urban park green space, attention restoration and state empathy. Therefore, we conducted an on-site questionnaire survey in four typical parks in Chengdu in terms of age, sex, daily stress, frequency of access in parks and other basic information of the respondents. The main part consists of perceived dimension, state empathy and attention restoration. The software SPSS24.0 is applied to the test of the validity and reliability of the PSD Scale, and then the important correlation between the perceived sensory dimensions in the parks and visitors' attention restoration is analyzed through multiple linear regression. Finally, the moderation effect of state empathy is tested by PROCESS. The findings show that (1) only seven dimensions in the PSD Scale are effective; (2) Serene and Refuge in the perceived sensory dimensions have significant effect on the restorative components of attention. (3) Except the dimensions of Rich in Species and Refuge, empathy enhanced the moderation effect in the interaction between the other five dimensions the Perceived Restorative Scale(PRS), especially in the interaction between the dimension Social and PRS. However, this study needs to be further explored to provide scientific basis and design strategy guidance for the research on the restoration potential of urban park green space in high-density urban areas.

In addition to image filtering in the spatial and frequency domains, fractal characteristics induced algorithms offers considerable flexibility in the design and implementations of image processing solutions in areas such as image enhancement, image restoration, image data compression and spectrum of applications of practical interests. Facing up to a real-world problem of identifying workpiece surface defects, a generic adaptive fractal filtering algorithm is proposed, which shows advantages on the problems of target recognition, feature extraction and image denoising at multiple scales. First, we reveal the physical principles underlying between signal SNR and its representative fractal dimension indicative parameters, validating that the fractal dimension can be used to adaptively obtain the image features. Second, an adaptive fractal filtering algorithm (Abbreviated as AFFA) is proposed according to the identified correlation between the image fractal dimensions and the scales of objects, and it is verified by a benchmarking image processing case study. Third, by using the proposed fractal filtering algorithm, surface defects on a flange workpiece are identified. Compared to conventional image processing algorithms, the proposed algorithm shows superior computing simplicity and better performance Numerical analysis and engineering case studies show that the fractal dimension is eligible for deriving an adaptive filtering algorithm for diverse-scale object identification, and the proposed AFFA is feasible for general application in workpiece surface defect detection.

(RADA)4 nanoscaffolds are excellent candidates for use as peptide delivery vehicles: they are relatively easy to synthesize with custom bio-functionality, and assemble in situ to allow a focal point of release. This enables (RADA)4 to be utilized in multiple release strategies by embedding a variety of bioactive molecules in an all-in-one ‘construct’. One novel strategy focuses on the local, on-demand release of peptides triggered via proteolysis of tethered peptide sequences. However, the spatial-temporal morphology of self-assembling nanoscaffolds may greatly influence the ability for enzymes to both diffuse into as well as actively cleave substrates. Fine structure and its impact on overall affect on peptide release is poorly understood. In addition, fractal networks observed in nanoscaffolds are linked to the fractal nature of diffusion in these systems. Therefore, matrix morphology and fractal dimension of virgin (RADA)4 and mixtures of (RADA)4 and matrix metalloproteinase 2 (MMP-2) cleavable substrate modified (RADA)4 were characterized over time. Sites of high (GPQG+IASQ, CP1) and low (GPQG+PAGQ, CP2) cleavage activity were chosen. Fine structure was visualized using established according to established methods. After 2 hrs of incubation, nanofiber networks showed an established fractal nature, however nanofibers continued to bundle in all cases as incubation times increased. It was observed that despite extensive nanofiber bundling after 24 hrs of incubation time, the CP1 and CP2 nanoscaffolds were susceptible to MMP-2 cleavage. The properties of these engineered nanoscaffolds characterized herein illustrate that they are an excellent candidate as an enzymatically initiated peptide delivery platform.

This study reports fractal analysis of one-year radon in groundwater disturbances from five stations in China amid the catastrophic Wenchuan (Mw=7.9) earthquake of May 12, 2008 (day 133). Five techniques are used (DFA, fractal dimensions with Higuchi, Katz, Sevcik methods, power-law analysis) in segmented portions glided throughout each signal. Noteworthy fractal areas are outlined in the KDS, GS, MSS station data, while the portions were non-significant for PZHS and SPS. Up to day 133 critical epoch DFA-exponents have 1.5<=a<2.0 with several above 1.8. Fractal dimensions exhibit Katz’s D around 1.0-1.2, Higuchi’s D between 1.5-2.0 and Sevcik’s D between 1.0-1.5. Several power-law exponents are above 1.7 and numerous above 2.0. All fractal results of KDS-GS-MSS stations are further analysed using a novel computerised methodology which locates the exact out-of-threshold fractal areas and combines the outcomes of different methods per five, four, three, and two (maximum 13 combinations) versus nineteen Mw<=5.5 earthquakes of the area. Most different-technique coincidences are before the great Wenchuan earthquake and its post-earthquakes. This is not only with one method, but with 13 different methods. Other interpretations are also discussed.

Restoration experience is a positive response against the ever-increasing problem of stress. It is recovery of attentional capacity, clearing random thoughts and feelings of relaxation and calmness. Although there is a body of research on investigating the impact of open green space characteristics on psycho- logical restoration through attention restoration theory and supportive environment theory, there is little knowledge on how the interaction among these characteristics could promote restorative outcomes. To address this problem, using Perceived Sensory Dimension (PSD) for open green space qualities and Perceived Restorativeness (PR) as the property of restorative environment, this study assessed the extent to which the PSD and PR impact on restoration experience. Using 444 screened surveys, a Partial Least Square Structural Equation Model (PLS-SEM) was developed and the validity and reliability of it, was demonstrated. Extensive analysis of the results showed how environmental qualities can promote restoration experience using a sample of university students. These results provide information for landscape architecture and planning researchers to promote the development of open spaces as a resource of psychological restoration and stress relief.

Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about cen-tral areas with relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas with more active growth. However, effectively utilizing mul-tifractal spectrums to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator, and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time. While during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectrums alone. By integrating this index with multifractal spectrums, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure.

The doctoral defense is an important step towards obtaining the doctoral degree. As such, preparing for the event is necessary. Anecdotal evidence highlights that there is a wide variety of ways in which doctoral candidates prepare for the defense. In this work, I want to explore if there is a relation between the way in which a doctoral candidate prepares for the defense and two important aspects of the defense: the outcome of the defense, and the student perception during and after the defense. For this purpose, I first reviewed the literature on the topic of the preparation for the doctoral defense. Then, I carried out an international survey on the doctoral defense and analyzed the data of the 204 completed surveys with respect to the preparation for the defense using quantitative and qualitative methods. The methods I used included the statistical tests of the correlation between on one hand the preparation and on the other hand the defense outcome and student perception. I used inductive thematic analysis of the open-ended survey questions to gain deeper insight in the way candidates prepared for their defense. I found that candidates most often prepare by making their presentation, reading their thesis, and practicing. The most effective measure is the mock defense, followed by a preparatory course. Reading blogs, books, and chapters is a less effective preparation measure. The conclusion of this work is that doctoral candidates need to understand the format of their defense in order to be able to prepare properly, and that universities should explore either individual pathways to the defense or pilots using a mock defense and/or preparatory course to give their doctoral candidates the necessary tools to prepare for their doctoral defense.

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the Internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link have fractal behavior when the Hurst exponent is in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between –0.5, 0. Based on these results, it is ideal to characterize both the singularities of the traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is reaffirmed.

Selective laser melting (SLM) is one of the widely used techniques in metallic additive manufacturing, in which high-density laser powder is utilized to selectively melting layers of powders to create geometrically complex parts. Temperature distribution and molten pool geometry directly determine the balling effect, and concentrated balling phenomenon significantly deteriorates surface integrity and mechanical properties of the part. Finite element models have been developed to predict temperature distribution and molten pool geometry, but they were computationally expensive. In this paper, the three-dimensional temperature distributions are predicted by analytical models using point moving heat source and semi-ellipsoidal moving source respectively. The molten pool dimensions under various process conditions are obtained from the three-dimensional temperature predictions and experimentally validated. Ti-6Al-4V alloy is chosen for the investigation. Good agreements between the predictions and the measurements are observed. The presented models are also suitable for other metallic materials in the SLM process.

Containing hundreds of spectral bands (features), hyperspectral images (HSIs) have high ability in discrimination of land cover classes. Traditional HSIs data processing methods consider the same importance for all bands in the original feature space (OFS), while different spectral bands play different roles in identification of samples of different classes. In order to explore the relative importance of each feature, we learn a weighting matrix and obtain the relative weighted feature space (RWFS) as an enriched feature space for HSIs data analysis in this paper. To overcome the difficulty of limited labeled samples which is common case in HSIs data analysis, we extend our method to semisupervised framework. To transfer available knowledge to unlabeled samples, we employ graph based clustering where low rank representation (LRR) is used to define the similarity function for graph. After construction the RWFS, any arbitrary dimension reduction method and classification algorithm can be employed in RWFS. The experimental results on two well-known HSIs data set show that some dimension reduction algorithms have better performance in the new weighted feature space.

An overview of the link between nonequilibrium thermodynamics and complexity theory is offered. It is shown how the rate of entropy production can be quantified through the spectrum of the Lyapunov exponents. It was shown how the entropy production per unit of time meets the necessary and sufficient conditions to be a Lyapunov function and constitutes per se an extremal principle. The entropy production fractal dimension conjecture was established. It is shown how the rate of entropy production as a non-extremal criterion represents an alternative way of sensitivity analysis of differential equations. Finally, an extension to biophysical-chemical systems, on the one hand, the use of the dissipation function is shown, as a thermodynamic potential out of equilibrium, in the characterization of biological phase transitions. On the other hand, it was evidenced how the rate of entropy production represents a physical quantity to evaluate the complexity and robustness of cancer.

This comprehensive review paper provides a detailed analysis of the extraction methods employed in the dimension stone industry. Natural rock materials used in construction, have been historically extracted using primitive techniques such as thermal shock, hammer and chisel, and plug and feather. However, significant technological advancements have revolutionized the industry, leading to the widespread adoption of mechanized methods. One highly efficient technique is diamond wire cutting, which involves the utilization of diamond-engraved bits affixed to a tensioned steel wire. This method has demonstrated remarkable capabilities in minimizing waste generation and ensuring exceptional machining quality. Nonetheless, challenges such as high operating costs and wire breakage persist and require further investigation. In addition to diamond wire cutting, this review explores the utilization of circular diamond saws and frame sawing as alternative extraction methods. The geotechnical characteristics of the stone play a critical role in the selection of appropriate machinery, and researchers worldwide have conducted numerous studies to investigate the impact of each parameter on the extraction efficiency of these mechanized techniques. Moreover, controlled blasting with explosives emerges as a promising alternative for dimension stone extraction, warranting further exploration and optimization.

Fibroepithelial lesions (FL) of the breast, in particular Phyllodes tumors (PT) and fibroadenomas, pose a significant diagnostic challenge. There are no generally accepted criteria that distinguish benign, borderline, malignant PT, and FA. Combined genome-wide DNA methylation and copy number variant (CNV) profiling is an emerging strategy to classify tumors. We compiled a series of patient-derived archival biopsy specimens reflecting the FL spectrum and histological mimickers including clinical follow-up data. DNA methylation and CNVs were determined by well-established microarrays. Comparison of the patterns with a pan-cancer dataset assembled from public resources including "The Cancer Genome Atlas" (TCGA) and "Gene Expression Omnibus" (GEO) suggests that FLs form a methylation class distinct from both control breast tissue as well as common breast cancers. Complex CNVs were enriched in clinically aggressive FLs. Subsequent fluorescence in situ hybridization (FISH) analysis detected respective aberrations in the neoplastic mesenchymal component of FLs only, confirming that the epithelial component is non-neoplastic. Of note, our approach could lead to the elimination of the diagnostically problematic category of borderline PT and allow for optimized prognostic patient stratification. Furthermore, the identified recurrent genomic aberrations such as 1q gains (including MDM4), CDKN2a/b deletions and EGFR amplifications may inform therapeutic decision-making.

Eddy current based approaches have been investigated for a wide range of inspection applications. Dodd-Deeds model and the truncated region eigenfunction expansion (TREE) method are widely applied in various occasions, mostly for the cases that the sample is relatively larger than the radius of the sensor coil. The TREE method converts the integral expressions to the summation of many terms in the truncated region. In a recent work, the impedance of the co-axial air-cored sensor due to a plate of finite radius was calculated by the modified Dodd-Deeds analytical approach proposed by authors. In this paper, combining the modified analytical solution and the TREE method, a new finite region eigenfunction expansion (FREE) method is proposed. This method involves modifying its initial summation point from the first zero of the Bessel function to a value related to the radius of the plate, therefore makes it suitable for plate with finite dimensions. Experiments and simulations have been carried out and compared for the verification of the proposed method. Further, the planar size measurements of the metallic circular plate can be achieved by utilising the measured peak frequency feature.

The stability assessment of aged tunnel linings were mainly evaluated based on the visual inspection, and the Tunnel-lining Crack Index (TCI) is one of the most widely used tunnel lining health assessment indexes in Japan. However, the intersection and distribution of cracks, which can influence the stability of tunnel lining greatly, were not considered in the TCI. A new method was proposed for the health assessment of tunnel lining, which evaluate the lining states according to the fractal dimension of cracks. Based on the machine vision-based method, the crack image can be extracted efficiently. The fractal dimension of lining cracks in one span can be obtained in a few minutes. A series of comparative tests and field tests were conducted to evaluate the validity of this new method. The comparative tests confirmed that fractal dimension can characterize the density, width, and distribution of cracks. The results also certificated that the influence of crack width is larger than the crack density. The intersection of cracks, which will increase the risk of lining collapse, can also increase the fractal dimension, whereas the TCI keep constant. The fractal dimensions of tunnel lining cracks were obtained according to the digital inspection test of Hidake Tunnel in Japan for all the 65 spans. Moreover, the TCI was obtained through statistical methods. The correlation between fractal dimension and TCI of tunnel lining was studied. The significance of the new evaluation index is that it can identify some unusual spans of tunnel lining and provide a basis for further internal testing. As a complement to the conventional visual inspection method, the fractal dimension of the cracks is a promising health assessment index.

Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.

Branching patterns are ubiquitous in nature, consequently over the years many researchers have tried to characterize the complexity of their structures. Due to their hierarchical nature and resemblance to fractal trees, they are often thought to have fractal properties, however their non-homogeneity (i.e., lack of strict self-similarity) is often ignored. In this paper we review and examine the use of the box-counting and sandbox methods to estimate the fractal dimensions of branching structures. We highlight the fact that these methods rely on an assumption of self-similarity that is not present in branching structures due to their non-homogeneous nature. Looking at the local slopes of the log-log plots used by these methods reveals the problems caused by the non-homogeneity. Finally, we examine the role of the canopies (endpoints or limit points) of branching structures in the estimation of their fractal dimensions.

The present paper proposes a fractal analysis of the Covid-19 dynamics in 45 European countries. We introduce a new idea of using the box-counting dimension of the epidemiologic curves as a means of classifying the Covid-19 pandemic in the countries taken into consideration. The classification can be a useful tool in deciding upon the quality and accuracy of the data available. We also investigated the reproduction rate, which proves to have significant fractal features, thus enabling another perspective on this epidemic characteristic. Moreover, we studied the correlation between two meteorological parameters: global radiation and daily mean temperature and two Covid-19 indicators: daily new cases and reproduction rate. The fractal dimension differences between the analysed time series graphs could represent a preliminary analysis criterion, increasing research efficiency. Daily global radiation was found to be stronger linked with Covid-19 new cases than air temperature (with a greater correlation coefficient -0.386, as compared with -0.318), and consequently it is recommended as the first-choice meteorological variable for prediction models.

Here we studied Bianchi type-III string cosmological models generated by means of a cloud of strings with particles connected to them in the framework of Lyra geometry considering five-dimensional space-time. To obtain the exact solutions of field equations we consider that the shear scalar and the scalar expansion are proportional, σ∞θ which leads to D=cn and secondly we adopt the assumption considering the Reddy String Condition, ρ+λ=0. From the two different cases obtained here, first case leads to the Bianchi type-III string cosmological model in Lyra geometry in five-dimensional space-time and the second case leads to the five-dimensional vacuum universe in general relativity. The Geometrical and physical properties of the model universe are studied comparing with the present day’s observational findings. The model universe obtained here starts with the big bang and as time progresses both particle density ρp and energy density ρ decreases with expansion of our Universe.

The doctoral defense, which is an essential requirement for the doctoral degree, is considered to have three dimensions: the scholarly dimension, the emotional (affective) dimension, and the cultural dimension. In this work, I explore the link between sociodemographic factors and students’ perception of the doctoral defense. In particular, I focus on gender, ethnicity, and age at time of defense, as well as current position, and field of study. To address the influence of these aspects on the affective dimension of the doctoral defense, I first reviewed the literature on these socio-demographic aspects as well as the affective dimension of the defense. I then carried out an international survey on doctoral defenses, defense formats, and students’ perceptions and analyzed the 204 completed surveys for this study using quantitative and qualitative methods. The analysis included cross-correlations between students’ perceptions and the studied sociodemographic aspects. The main results of these analyses are that gender affects various aspects of the students’ perception of the doctoral defense and long-term perception, and that female candidates experience more issues with their committee. Ethnicity is important as well, although the participations of non-white respondents in this survey was limited. The influence of age at the defense is limited, and only for the youngest and oldest age groups I observe some differences in perception. There is no relation between current position and perception of the candidates during the defense. Finally, field of study is correlated for various aspects of student perception, committee issues, and long-term perception. The conclusion of this work is that socio-demographic aspects, and in particular gender, ethnicity, and field of study, influence how doctoral candidates experience their defense.

Perception and motor interaction with physical surroundings can be analyzed by the changes in probability laws governing two possible outcomes of neuronal activity, namely the presence or absence of spikes (binary states). Perception and motor interaction with physical environment are accounted partly by the reduction in entropy within the probability distributions of binary states of neurons in distributed neural circuits, given the knowledge about the characteristics of stimuli in physical surroundings. This reduction in the total entropy of multiple pairs of circuits in networks, by an amount equal to the increase of mutual information among them, occurs as sensory information is processed successively from lower to higher cortical areas or between different areas at the same hierarchical level but belonging to different networks. The increase in mutual information is partly accounted by temporal coupling as well as synaptic connections as proposed by Bahmer and Gupta [1]. We propose that robust increases in mutual information, measuring the association between the characteristics of sensory inputs and neural circuits connectivity patterns, are partly responsible for perception and successful motor interactions with physical surroundings. It is also argued that perception from a sensory input is the result of networking of many circuits to a common circuit that primarily processes the given sensory input.

Carotid atherosclerotic lesions are a major cause of cerebrovascular disease (CVD). Identification and quantification of carotid plaques are important for categorizing the vulnerability of plaques for rupture and assessing the impact of treatments. The irregularity of plaque surface is associated with previous plaque rupture and plays an important role in the risk of stroke. Thus, the aim of this study is to develop and validate novel vulnerability biomarkers from three-dimensional ultrasound (3DUS) images by analyzing the surface morphological characterization of carotid plaque using fractal geometry features. 3D box-counting and 3D blanket are the two types of 3D fractal dimension that were employed to describe the smoothness of plaques. This fractal dimension analysis tool was used to evaluate the effect of atorvastatin using 3DUS carotid images, which were acquired from 6 patients treated with atorvastatin with 80 mg daily and 5 patients with placebo. The Student's T Test results showed that those two fractal features were effective for detecting the statin-related changes in carotid atherosclerosis with p<0.0068 and p<0.015 respectively, suggesting that 3D fractal dimension measurements can be used effectively to analyze the surface characteristics of carotid plaques, especially for evaluating the impact of the treatment.

This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel dimension iteration sparse grid}) method, implements the sparse grid method based on a dimension iteration/reduction procedure, it does not need to store the integration points, nor does it compute the function values independently at each integration point, instead, it reuses the computation for function evaluations as much as possible by performing the function evaluations at all integration points in a cluster and iteratively along coordinate directions. It is shown numerically that the computational complexity (in terms of CPU time) of the proposed MDI-SG method is of polynomial order $O(Nd^3 )$ or better, compared to the exponential order $O(N(\log N)^{d-1})$ for the standard sparse grid method, where $N$ denotes the maximum number of integration points in each coordinate direction. As a result, the proposed MDI-SG method effectively circumvents the curse of dimensionality suffered by the standard sparse grid method for high-dimensional numerical integration.

A Demand-side management technique are deployed along with battery energy-storage systems (BESSs) to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand

(1) Aim of the study was to investigate the spatial and temporal characteristics of the airflow created by two commercially available non-contact tonometers, the CorvisST and the Ocular Re-sponse Analyser. (2) The airflow pressure was measured using a MEMS pressure sensor to inves-tigate the spatial and temporal distribution. The airflow from the CorvisST and Ocular Response Analyser were mapped to a 600µm and a 1mm resolution grid, respectively. (3) Central airflow pressure of the CorvisST (96.4 ± 1.4)mmHg was higher than the Ocular Response Analyser (91.7 ± 0.7)mmHg. The duration of the air-puffs also differed, with the CorvisST showing a shorter du-ration (21.483 ± 0.2881)ms than the ORA (23.061 ± 0.1872)ms. The rising edge of the CorvisST airflow pressure profile demonstrated a lower gradient (+8.94mmHg/ms) compared to the Oc-ular Response Analyser (+11.00mmHg/ms). Both had similar decay response edges; CorvisST -11.18mmHg/ms, Ocular Response Analyser -11.65mmHg/ms. (4) The study presents a valid method to investigate physical dimensions of the airflow pressure of non-contact tonometers. Novel findings relating to the magnitude, duration and spatial characteristics of the respective airflow pressures are reported. It is anticipated that this information will better inform clinical studies and theoretical models relating to ocular biomechanics.

In this article, the multitouch option, also called the n  touch option (or the “baseball” option when n  3 ) is analyzed and valued in closed form. This is a kind of barrier option that sets a gradual knockout / knock-in mechanism based on the number of times the underlying asset has crossed a predefined barrier in various time intervals before expiry. The higher the number of predefined time intervals during which the barrier has been touched, the lower the value of a knock-out contract at expiry, and conversely for a knock-in one. Multitouch options can be viewed as an extension of step barrier options, preserving the ability of the latter to adjust the exposure to risk over time, while eliminating the notorious danger of “sudden death” that holders of step barrier options are faced with. Unlike occupation time derivatives, the payoff at expiry does not depend on the amount of time spent outside the authorized range, but on the number of passages beyond the authorized range.

The topic of this paper is the airborne evaluation of ICESat-2 Advanced Topographic Laser Altimeter System (ATLAS) measurement capabilities and surface-height-determination over crevassed glacial terrain, with a focus on the geodetical accuracy of geophysical data collected from a helicopter. To obtain surface heights over crevassed and otherwise complex ice surface, ICESat-2 data are analyzed using the density-dimension algorithm for ice surfaces (DDA-ice), which yields surface heights at the nominal 0.7~m along-track spacing of ATLAS data. As the result of an ongoing surge, Negribreen, Svalbard, provided an ideal situation for the validation objectives in 2018 and 2019, because many different crevasse types and morphologically complex ice surfaces existed in close proximity. Airborne geophysical data, including laser altimeter data (profilometer data at 905~nm frequency), differential Global Positioning System (GPS), Inertial Measurement Unit (IMU) data, on-board-time-lapse imagery and photographs, were collected during two campaigns in summers of 2018 and 2019. Airborne experiment setup, geodetical correction and data processing steps are described here. To date, there is relatively little knowledge of the geodetical accuracy that can be obtained from kinematic data collection from a helicopter. Our study finds that (1)~Kinematic GPS data collection with correction in post-processing yields higher accuracies than Real-Time-Kinematic (RTK) data collection. (2)~Processing of only the rover data using the Natural Resources Canada Spatial Reference System Precise Point Positioning (CSRS-PPP) software is sufficiently accurate for the sub-satellite validation purpose. (3)~Distances between ICESat-2 ground tracks and airborne ground tracks were generally better than 25~m, while distance between predicted and actual ICESat-2 ground track was on the order of 9~m, which allows direct comparison of ice-surface heights and spatial statistical characteristics of crevasses from the satellite and airborne measurements. (4)~The Lasertech Universal Laser System (ULS), operated at up to 300~m above ground level, yields full return frequency (400~Hz) and 0.06-0.08~m on-ice along-track spacing of height measurements. (5)~Cross-over differences of airborne laser altimeter data are 0.1918 $\pm$ 2.385~m along straight paths over generally crevassed terrain, which implies a precision of approximately 2.4~m for ICESat-2 validation experiments. (6)~In summary, the comparatively light-weight experiment setup of a suite of small survey equipment mounted on a Eurocopter (Helicopter AS-350) and kinematic GPS data analyzed in post-processing using CSRS-PPP leads to high accuracy repeats of the ICESat-2 tracks. The technical results (1)-(6) indicate that direct comparison of ice-surface heights and crevasse depths from the ICESat-2 and airborne laser altimeter data is warranted. The final result of the validation is that ICESat-2 ATLAS data, analyzed with the DDA-ice, facilitate surface-height determination over crevassed terrain, in good agreement with airborne data, including spatial characteristics, such as surface roughness, crevasse spacing and depth, which are key informants on the deformation and dynamics of a glacier during surge.

This study purposes the use of plug-in electric vehicles for demand side management (DSM) considering uncertainties in demand as well as uncertainties due to mobility of PEV to mitigate peak demand. The solution also seeks to reduce electric cost in addition to reducing the effects of greenhouse gases. In recent years DSM using distributed storage system such as battery energy management system (BESS) and plugged-in electric vehicles (PEV) have become very prevalent with most implementations resorting to deterministic load forecast. These methods do not consider the potential growth in demand making their solutions less robust. In this study we propose a real-time density demand forecast and stochastic optimization for robust operation of PEV for a building. This method accounts for demand uncertainties in addition to uncertainties in mobile energy storage as found in PEV, making the resulting solution robust as compared to the deterministic case. A case study on a real site in South Korea is used for verification and testing. The proposed study is verified and tested against existing algorithms. The result verifies the effectiveness of the proposed approach

We assume that poetic devices have an implicit goal: producing an overall sound scheme that will induce the reader to associate intended and expressed meaning to the sound of the poem. Sounds may be organized into categories and assigned presumed meaning as suggested by traditional literary studies. In my work, I have extracted automatically the sound grids of all the sonnets by William Shakespeare and have combined them with the themes expressed by their contents. In a first experiment I have computed lexically and semantically based sentiment analysis obtaining an 80% of agreement. In a second experiment sentiment analysis has been substituted by Appraisal Theory thus obtaining a more fine-grained interpretation which in some cases contradicts the first one. The computation for the second poet - regarded by many critics the best of last century - includes both vowels and consonants. In addition, it combines automatic semantically and lexically based sentiment analysis with sound grids. The results produce visual maps that clearly separate poems into three clusters: negative harmony, positive harmony and disharmony where the latter instantiates the need by the poet to encompass the opposites in a desperate attempt to reconcile them.