Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the truncation error and add correction terms. Numerical studies on test functions show that the proposed method reduces errors significantly near boundaries compared to quasi-interpolation without corrections, for both equally spaced and Chebyshev points. The convergence and accuracy with the boundary corrections are generally better with Chebyshev points compared to equally spaced points. The proposed method provides an efficient way to perform quasi-interpolation on compact intervals while controlling the boundary errors.

Let BT4l denotes a subclass of bounded turning functions connected with a four-leaf-type domain. The goal of the study is to probe into coefficients of |b6|, |b7|, |b8|, the bounds of the logarithmic coefficients and the third-order determinants of H3,1, H3,2, H3,3 for functions in this class.

The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition, and its complementary, here referred to as the bias, allow to analyze various conditions of similarity between an arbitrary scale and a regular scale. Interesting particular cases are scales having limited bias because their tones are distributed along interval fractions of a regular partition. The most typical case in music concerns partitions associated with well-formed scales generated by a single tone h. These scales are maximal even sets that combine two elementary intervals. Then, the normalized entropy depends on the number of tones as well as the relative size of both elementary intervals. When well-formed scales are refined, several nested families stand out with increasing regularity. It is proven that a scale of minimal bias, i.e. with less bias than those with fewer tones, is always a best rational approximation of log2h.

In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.

In this paper, two double Jordan-type inequalities are introduced based on the papers [1]-[5]. These inequalities generalize the inequalities obtained in [1]-[5]. As a result, some new upper and lower bounds of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions elaborated in [6]. Based on this approach, some optimal approximations of the sinc function are derived by determining corresponding minimax approximants, also described in the paper [6].

Euler-Poisson equations of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles subject to holonomic constraints. The final equations are written for the center-of mass-coordinate, rotation matrix and angular velocity. General solution to the equations of motion is obtained for the case of a charged ball. For the case of a symmetrical charged body (solenoid), the task of obtaining the general solution is reduced to the problem of a one-dimensional cubic pseudo-oscillator. Besides, we present a one-parametric family of solutions to the problem in elementary functions.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

Abstract Cholesterol has ruled the history of atherosclerotic cardiovascular diseases (CVD) for decades, and the transport of cholesterol by lipoproteins has become a cornerstone of our view of etiology of the disease. Discovery of the lipoprotein-specific transport of lipid oxidation products (LOP) has opened a new and exciting area in research of CVD by revealing strong connections between atherogenic LOP, lipoprotein transport functions and CVD. This review goes through the evidence in support of the lipoprotein-specific LOP transport and speculates of possible consequences of the proposed role of lipoprotein LOP transport as a risk factor. Association of lipoprotein LOP with known risk factors of CVD are largely parallel with those of cholesterol, and due to the common transport and cellular intake mechanisms the elucidation of independent effects of either cholesterol or LOP is difficult. Yet, unlike cholesterol, LOP can directly initiate and boost atherogenic processes. It therefore appears inevitable that increasing knowledge of the lipoprotein-specific LOP transport will affect the present view of the role of cholesterol in aetiology and as a risk factor of CVD.

It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

SARS-CoV-2 Omicron variant spike RBD epitopes in complex with spike (S) -protein D614G mutations now predominate globally and increase infectivity by assembling more functional S proteins into the virion. On average, homeopathic medicine contains less than one molecule per dose on average. Single variable SphericalHarmonicY, LaguerreL, WhittakerM, SphericalBesselJ, LegendreP, LegendreQ, LaguerreL, ChebyshevT, and Hypergeometric1F1 Functions pFqarise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. A quantum interpretation of the homeopathic method is presented here through a novel algebraic topology approach to supersymmetry and symmetry breaking in quantum fields and quantum gravity theory with the aim of developing a wide range of physical-based drug design applications in a Small Molecule Quantized Water Memory Network suggesting that the Hidden Black Hole Paradox of Information Loss might be solved under suitable conditions.

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb-Douglas functions embed the endogenous space factor as new capital to form the space travel firm's production function, which is also transformed into the consumer's utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT presents the equivalence between the spatial geometric tensor and the energy-momentum tensor, which explains the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers' incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and analogy method was applied to infer the space travel pricing by the model of profit maximization, single-minded, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the math models and algorithm. Results show that space travel pricing remains the principle of market equilibrium but needs to be extended to the spacetime tensor of GRT.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

Abstract: Brassinosteroids (BR) are essential plant hormones that play a crucial role in regulating plant growth and development, as well as their resistance to abiotic and biotic stresses, including pathogen infections. In the context of plant im-munity, BR influence various processes such as the expression of genes related to pathogen defense, the production of antimicrobial compounds, and the re-inforcement of the plant cell structure. The aim of work is understand the role of BR in plant defense against abiotic and biotic stresses. BR are involved in the regulation of metabolic processes, water economy, and photosynthesis, contributing to increased plant resistance to abiotic stresses. The study discusses various mechanisms of BR action on plant immunity, including the regulation of gene expression related to defense, activation of the plant defense system, in-teraction with other plant hormones, regulation of water and salt balance, and influence on photosynthetic processes. In the context of plant immunity, BR influence various processes, including the expression of genes related to pathogen defense, the production of antimicrobial compounds, and the reinforcement of the plant cell structure. Additionally, BR are involved in the regulation of metabolic processes, water economy, and photosynthesis, con-tributing to increased plant resistance to abiotic and biotic stresses. The paper emphasizes the importance of further research on the role and mechanisms of action of BR in plant immunity, which may contribute to the development of more effective strategies for the use of BR in agriculture, horticulture, and plant protection.

One of the most important unresolved mysteries in mathematics is the Riemann Hypothesis, which suggests a fundamental connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers. Here, we explore the fascinating union of trigonometric functions, prime numbers, and the Riemann zeta function through an examination of the zeros in the statement ln(sec(π·n log(n))). We demonstrate a strong mathematical connection between these components, providing information on the mysterious properties of prime numbers and their complex relationships to basic mathematical operations. Our thorough investigation adds to the current discussion of the Riemann Hypothesis by offering possible solutions and deepening our comprehension of the intricate relationship between number theory and analytic functions.

Videogames have been the focus of research since their widespread popularity, with particular emphasis on their effects on cognitive and affective abilities, especially in children and adolescents. Despite numerous correlational studies, robust evidence on the causal relationship between videogames and cognition remains scarce, hindered by the absence of a comprehensive assessment tool for gaming skills across various genres. This study aimed to develop and validate the Gaming Skill Questionnaire (GSQ) and to assess the impact of gaming skills in six different genres (Sport, First-Person Shooters, Role-Playing Games, Action-Adventure, Strategy, and Puzzle Games) on adolescents’ cognitive and affective abilities. The GSQ exhibited strong reliability and validity, highlighting its potential as a valuable tool. Gaming skills positively affected executive function, memory, overall cognition, cognitive flexibility, and emotion recognition, except for empathy. Various game genres had different effects on cognitive and affective abilities, with verbal fluency influenced mainly by sports, executive functions by action, strategy, and puzzle, and emotion recognition positively impacted by action and puzzle but negatively by sports and strategy games. Both age and gaming skills influenced cognitive flexibility, with gaming having a greater effect. These intriguing genre-specific effects on cognitive and affective functioning postulate further research with GSQ's contribution.

This article is devoted to the problem of genetically coding of inherited cyclic structures in biological bodies, whose life activity is based on a great inherited set of mutually coordinated cyclic processes. The author puts forward and arguments the idea that the genetic coding system is capable of encoding inherited cyclic processes because it itself is a system of cyclic codes connected with Boolean algebra of logic. In other words, the physiological processes in question are cyclical because they are genetically encoded by cyclic codes. In support of this idea, the author presents a set of his results on the connection of the genetic coding system with cyclic Gray codes, which are one of many known types of cyclic codes. This opens up the possibility of using for modeling inherited cyclic biostructures those algebraic and logical theories and constructions that are associated with Gray codes and have long been used in engineering technologies: Karnaugh maps, Hilbert curve, Hadamard matrices, Walsh functions, dyadic analysis, etc. Additionally, the connections of these constructions with statistical rules of genomic DNAs and binary-genomic numbers are considered.

We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we obtained, analytically, the corresponding solutions for the conditional moment generating functions and conditional characteristic functions. Such solutions recover verbatim those of the uncorrelated case. We believe that the The aforementioned model encompasses a range of processes similar to that produced by a bivariate square-root process in which entries are correlated in the standard way, i.e., via a constant correlation coefficient. Note that, for the latter, closed-form solutions for the conditional characteristic functions are not available. We focus on the financial scenario of obtaining closed-form expressions for the exact price of a zero-coupon bond and Asian option prices via a Fourier cosine series method.

This review article aims to delve into several aspects of sweetpotatoes and their leaves, including their nutritional composition, health benefits, culinary uses, and potential future implications as a superfood. It suggests an in-depth exploration of sweet potatoes' history, status, and prospects, highlighting their significance and potential economic value. Sweetpotatoes, often referred to as a powerhouse of nutrients, have gained popularity recently due to their remarkable nutritional composition and versatile culinary uses. This starchy root vegetable comes from the Convolvulaceae family and is consumed worldwide, playing a significant role in diverse cultures and cuisines. Besides their vibrant colors ranging from orange to purple, sweetpotatoes offer many health benefits, making them an essential addition to a well-balanced diet. Its extraordinary nutritional profile and numerous health benefits make it a superfood. Incorporating it into the diet can improve digestion, strengthen immunity, and reduce the risk of chronic diseases. With their versatility in the kitchen, there is no deficiency of charming and healthy recipes to explore. So, make room for sweet potatoes on your plate and unlock their vast potential to enhance your overall health and well-being. Overall, the future of sweetpotatoes looks bright as research and innovation aim to improve their nutritional value, adapt them to changing climate conditions, develop new varieties and products, and promote sustainable production practices. These developments can contribute to food security, economic growth, and healthier diets. Future research should focus on nutritional composition, health benefits, sustainable farming practices, cultivar development, and industrial applications to ensure sustainable and efficient production. By prioritizing research in these areas, we can enhance the utilization of sweet potatoes in various fields and secure their future for the next century.

In my paper, a divisibility rule named the Queen function is de- scribed, which has been generalized for every integer and encompasses all pre- viously established divisibility rules. Subsequently, the paper discusses other areas where this function is instrumental. These include simplifying ratios, generating prime numbers, and more. Towards the end of the paper, a set of hypotheses is also presented. Among these, the most significant is the novel approach involving the application of the Queen function for prime number generation.

The aging of the global population has increased the prevalence of neurodegenerative conditions. Bacopa monnieri (BM), an herb with active compounds, such as bacosides A and B, betulinic acid, loliolide, asiatic acid, and quercetin, demonstrates the potential for brain health. Limited research has been conducted on the therapeutic applications of BM in neurodegenerative conditions. This systematic review aims to project BM's beneficial role in brain disorders. BM has anti-apoptotic and antioxidant actions and can repair damaged neurons, stimulate kinase activity, restore synaptic function, improve nerve transmission, and increase neuroprotection. The included twenty-two clinical trials demonstrated that BM can reduce Nuclear Factor-κB phosphorylation, improve emotional function, cognitive functions, anhedonia, hyperactivity, sleep routine, depression, attention deficit, learning problems, memory retention, impulsivity, and psychiatric problems. Moreover, BM can reduce the levels of pro-inflammatory biomarkers and oxidative stress. Here, we highlight that BM provides notable therapeutic benefits and can serve as a complementary approach for the care of patients with neurodegenerative conditions associated with brain disorders. This review adds to the growing interest in natural products and their potential therapeutic applications by improving our understanding of the mechanisms underlying cognitive function and neurodegeneration and informing the development of new therapeutic strategies for neurodegenerative diseases.

Direct assessments of executive function (EF) are increasingly used in research and clinical settings, with a central assumption that they assess “universal” underlying skills. Their use is spreading globally, raising questions about the cultural appropriateness of assessments devised in Western, industrialized countries. We reviewed multidisciplinary evidence and theory to identify sets of cultural preferences that may be at odds with the implicit assumptions of EF assessments. These preferences relate to motivation and compliance; cultural expectations for interpersonal engagement; contextualized vs. academic thinking; cultural notions of speed and time; the willingness to be silly, be incorrect, or do the opposite; and subject-matter familiarity. In each case, we discuss how the cultural preference may be incompatible with the assumptions of assessments, and how future research and practice can address the issue. Many of the cultural preferences discussed differ between interdependent and independent cultures and between schooled and unschooled populations. Adapting testing protocols to these cultural preferences in different contexts will be important for expanding our scientific understanding of EF from the narrow slice of the human population that has participated in the research to date.

The architecture, organization and functioning of biocatalytic reaction networks, which are coded in the cell specific genome and which work together in the small space of biological cells, are a fascinating feature of life evolved over more than 3 billion years. The knowledge about the diversity of biocatalytic functions and metabolic pathways sustaining life on our planet is highly important, especially as the currently occurring loss of biodiversity is considered a planetary boundary which is at high risk, and knowledge about the life of current biological organisms should be gained before they become extinct. In addition to the well-known enzymatic reactions involved in biochemical pathways, the enzyme universe offers numerous opportunities for discovering novel functions and pathways. Maintaining thousands of molecules and reactions functioning properly within biological cells, which may be exposed to various kinds of external hazards, environmental stress, enzymatic side reactions or non-enzymatic chemical reactions, is key for keeping cellular life healthy. This review aims at outlining advances in assigning enzyme functions to protein sequences and the discovery of novel biocatalytic functions and pathways.

Ribosomal proteins (r-proteins) are abundant, highly conserved, and multifaceted cellular proteins in all domains of life. Most r-proteins have RNA-binding properties and are able to form protein-protein contacts. Bacterial r-proteins govern the co-transcriptional rRNA folding during ribosome assembly and participate in formation of the ribosome functional sites such as the mRNA binding site, tRNA binding sites, the peptidyl- transferase center, and the protein exit tunnel. In addition to their primary role in a cell as integral components of the protein synthesis machinery, many of r-proteins can function beyond the ribosome (the phenomenon known as moonlighting), acting either as individual regulatory proteins or in complexes with various cellular components. Extraribosomal activities of r-proteins have been intensively studied over decades (reviewed in [1]). The past decade brought significant advancement in our knowledge of r-protein functions due to expanding studies on ribosomes and gene expression mechanisms not only in model bacteria like Escherichia coli or Bacillus subtilis, but also in previously little-explored bacterial species from various phyla. This review is aimed to update the information on multiple functions of r-proteins in bacteria.

Brain models present a viewpoint on the fundamental structural components of the brain and their mutual organization, generally relative to a particular concept of the brain axis. A model may be based on adult brain structure or on developmental morphogenetic aspects. Brain models usually have functional implications, depending on which functional properties derive from the postulated organization. This essay examines the present scenario about brain models, emphasizing the contrast between columnar or other longitudinal models and transverse subdivisional neuromeric models. In each case, the main functional implications and apparent problems are explored and commented. Particular attention is given to the modern molecularly based ‘prosomeric model’, which postulates a set of 20 transverse prosomeres as the developmental units that serve to construct all the cerebral parts and the particular typology of many different neuronal populations within the forebrain and the hindbrain, plus a number of additional spinal cord units. These metameric developmental units (serially repeated, but with unique molecular profiles) confer to this model remarkable functional properties based mainly on its multiplicity and modularity. Many important brain functions can be decomposed into subfunctions attended to by combined sets of neuronal elements derived from different neuromeres. Each neuromere may participate in multiple functions. Most aspects related to creation of precise order in neural connections (axonal navigation and synaptogenesis) and function is due to the influence of neuromeric anteroposterior and dorsoventral positional information. Research on neuromeric functionality aspects is increasing significantly in recent times.

Although crop conversion from annual to perennial crops has been considered as one path towards climate-smart and resource-efficient agriculture, the effects of this conversion on soil multifunctionality and biomass yields remain unclear. Here, we investigated the effects of one annual and three perennial crops (a grass (Lolium perenne), a legume (Medicago sativa), and their mixture) on soil multifunctionality and biomass yield on the Yellow River floodplain. Soil multifunctionality was assessed by the capacity of water regulation and the multifunctionality of carbon (C), nitrogen (N), and phosphorus (P) cycles. Results showed that perennial crops enhanced soil multifunctionality by 207% for L. perenne, 311% for M. sativa, and 438% for L. perenne + M. sativa, compared with annual winter wheat (Triticum aestivum). The effect of perennial crops on soil multifunctionality increased with infiltration rate, dissolved organic C, microbial biomass C, and extracellular enzymatic activities for both C and N acquisition. However, we observed that perennial crops had lower biomass yield than annual crop. Therefore, the transition of agricultural landscapes to perennials needs to take into account the balance between environmental protection and food security, as well as environmental heterogeneity, to promote sustainable agricultural development.

Provenance trials provide a valuable opportunity to evaluate the impact of extreme events on growth and wood properties. In this study, we have evaluated 81 Norway spruce provenances, tested in three provenance trials established in the Romanian Carpathians in 1972. The response to drought of the Norway spruce provenances – resistance, recovery, resilience, and relative resilience, has been examined, as well as the relationship between climate and growth, and the correlations between wood traits, the coordinates of origin and drought resilience indices. In each provenance trial, there were significant differences between provenances and years regarding wood widths and latewood percentage (LWP). Regarding the drought extreme events, the years when it occurred in all three provenance trials were 2000 and 2003. Significant differences between provenances for at least one drought resilience index have been found in all provenance trials, for the year 2000. By using subperiods of 25 years, changes in the relationship between climate and growth have been observed. Several provenances with high radial growth and good resistance and/or recovery have been identified. Provenances that performed better in common garden experiments could be used in assisted migration even beyond the current natural range.

This article presents a hybrid approach to assessing students’ foreign language proficiency in a cyber-physical educational environment. It focuses on the advantages of integrated assessment of student knowledge by considering the impact of automatic assessment, learners’ independent work, and their achievements to date. An assessment approach is described using the mathematical theory of fuzzy functions, which are employed to ensure fair evaluation of students. The largest possible number of students, whose re-evaluation of test results will not affect the overall performance of the student group, is automatically determined. The study also models the assessment process in the cyber-physical educational environment through the formal semantics of calculus of context-aware ambients (CCA).

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

Real and complex analytic functions are largely studied in the field of complex analysis and are seen as very useful tools in solving problems in mathematics, physics and engineering. Real and complex numbers are a subset of semi-structured complex numbers (a new number set created to algebraically solve division by zero). Nevertheless, the properties of analytic functions made up of semi-structured complex variables (called semi-structured complex analytic functions) is yet to be explored. This limits the range of possible problems that can be resolved using analytic functions). In this regard, the aim of this paper was to expound upon the properties of semi-structured complex analytic functions and show their application in solving engineering problems. The results of this paper included (1) developing a full set of Cauchy–Riemann Equations for the semi-structured complex -space; (2) define sufficient and necessary conditions for a semi-structured complex function to be analytic; (3) determine the relationship between semi-structured complex analytic functions, Laplace’s Equations and Poisson’s Equations; and (5) provide an example of the use of these functions.

This study addresses the central question that how can a precise measurement of the gluon Parton Distribution Function (PDF) be attained, thereby enhancing our understanding of the intricate quark-gluon composition within nucleons? Through a dual approach involving Quantum Chromodynamics (QCD) and high-energy particle collisions, the research combines computational tools and experimental techniques, focusing on protons and neutrons. Scattering experiments and advanced detectors are utilized to probe nucleon structure. Theoretical frameworks like QCD equations and the Momentum Sum Rule investigate Parton Distribution Functions at specific momentum fractions and energy scales. The primary goal is to achieve an accurate measurement of the gluon PDF, crucial for unraveling strong force complexities and internal nucleon dynamics. The study's theoretical plots and equations illustrate hypothetical behaviors of gluon distribution, quark distribution, and splitting functions, contributing to a deeper understanding of fundamental particles.

In this study we introduce the new classes $\mathcal{M}_{\alpha}(\sin)$ and $\mathcal{M}_{\alpha}(\cos)$ of $\alpha$-convex functions associated with sine and cosine functions. Also, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of Zalcman functional for the class $\mathcal{M}_{\alpha}(\cos)$ for the case $n=3$, showing that the Zalcman conjecture holds for this value. Moreover, the problem of the Fekete-Szeg\H{o} functional estimate for these classes is studied.

The objectives of this article are to examine whether the application of digitalization in enterprise budgeting affects the fulfilment of budgeting functions and their qualitative characteristics, and to investigate whether the realization of budgeting functions brings benefits. The research was conducted from the perspective of contingency theory, both internal and external conditions. The study used an online survey targeting company budgeting staff. Structural Equation Modelling was utilized to validate the structural model (PLS-SEM technique). The conclusions confirm that the application of digitalization, which particularly pertains to ERP, Business Intelligence systems and accounting systems with budgeting solutions, positively impacts the fulfilment of budgeting functions and most of their qualitative characteristics, while Blockchain makes a minor contribution. Our research suggests that contingency variables, particularly internal ones such as company size, the quality of the organizational structure, and support for competitive strategy, continue to affect budgeting implementation even with the participation of digitalization in budgeting. Budgeting functions and their qualitative aspects are notably correlated with the advantages derived from budgeting, including financial performance, sustainable development and budget task execution.

In this paper, we demonstrate that fixed-weight layers, generated from random distribution or logistic functions, can effectively extract significant features from input data, resulting in high accuracy on a variety of tasks, including Fisher’s iris, Wisconsin Breast Cancer, and MNIST datasets. We have observed that logistic functions yield high accuracy with less dispersion in results. We have also assessed the precision of our approach under conditions of minimizing spikes number generated in the network, it is a practically useful for reducing energy consumption in spiking neural networks. Our findings reveal that the proposed method demonstrates a highest accuracy on Fisher’s iris and MNIST datasets with logistic regression. Furthermore, they surpass the accuracy of the conventional (non-spiking) approach using logistic regression in the case of Wisconsin Breast Cancer. We have also investigated the impact of non-stochastic spike generation on accuracy.

Background: This study investigates cognitive function changes in severe carotid stenosis patients undergoing carotid endarterectomy (CEA) and carotid stenting (CAS), across two decades. Methods: We compared cognitive function within 30 days post-procedure in 267 patients (first 100 each for CEA and CAS in two periods: 2008–2012 and 2018–2022) at a single institution. Assessments used Adenbrooke's Cognitive Examination–Revised (ACE-R), Mini-Mental State Examination (MMSE), Speech Fluency Test (SFT), and Clock Drawing Test (CDT), conducted before and 30 ± 2 days after surgery. Results: Patients (mean age 67.2 years, 70%+ carotid stenosis) exhibited different cognitive changes over the periods. In 2008–2012, significant declines in MMSE (CEA, p = 0.049) and CDT (CAS, p = 0.015) were noted among asymptomatic patients. Conversely, in 2018–2022, improvements were observed in ACE-R and MMSE for both symptomatic and asymptomatic patients undergoing CEA and CAS. Conclusion: Over a decade, advancements in interventional techniques and patient management have reduced cognitive decline risks in asymptomatic carotid stenosis patients, also improving cognitive functions in both symptomatic and asymptomatic individuals.

Partially automated driving functions (SAE Level 2) can control a vehicle's longitudinal and lateral movements. However, taking over the driving task involves automation risks that the driver must manage. In severe accidents, the driver's ability to avoid a collision must be assessed, considering their expected reaction behavior. The primary goal of this study is to generate essential data on driver reaction behavior in case of malfunctions in partially automated driving functions for use in legal affairs. A simulator study with two scenarios involving 32 subjects was conducted for this purpose. The first scenario investigated driver reactions to system limitations during cornering. The second scenario examined driver responses to phantom braking caused by the AEBS. As a result, the first scenario shows that none of the subjects could control the situation safely. Due to partial automation, we could also identify a new part of the reaction time, the hands-on time, which leads to increased steering reaction times of 1.18 to 1.74 seconds. In the second scenario, we found that 25 of the 32 subjects could not override the phantom braking by pressing the accelerator pedal, although 16 subjects were informed about the system analog to the actual vehicle manuals. Overall, the study suggests that the current legal perspective on vehicle control and the expected driver reaction behavior for accident avoidance should be reconsidered.

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi univalent function defined in open unit disk connected with a linear q-convolution operator, which are associated with the quasi-subordination. We find coefficients estimate |h_2 |,|h_3 | for functions in these subclasses. Several known and new consequences of these results are also pointed out.

Blood biomarkers represent a promising future for studying cognitive impairment, particularly in Alzheimer's Disease (AD), as they offer a non-invasive alternative to cerebrospinal fluid tests and have potential as population screening tools. However, the relationships between these biomarkers and specific cognitive functions, as well as their utility in predicting longitudinal cognitive decline, are not yet fully understood. This descriptive review surveys the literature from 2018 to 2023, focusing on the associations between Amyloid-β, Total Tau, Phosphorylated Tau (p-tau), Neurofilament Light (Nfl), and Glial Fibrillary Acidic Protein (GFAP) with cognition. The reviewed studies are heterogeneous, varying in design and population (mixed, cognitively impaired, or unimpaired), and show results that are sometimes conflicting. Generally, cognition positively correlates with Aβ levels, especially when evaluated through the Aβ42/Aβ40 ratio. In contrast, Tau, Nfl, and GFAP levels typically show a negative correlation with cognitive performance. While p-tau measures tend to show stronger associations with cognitive functions than other biomarkers, no single blood marker has emerged as predominantly associated with a specific cognitive domain. These findings add to our understanding of the complex relationship between blood biomarkers and cognitive performance and underscore their potential utility in clinical evaluations of cognition.

Background. ADHD is a neurodevelopmental disorder that is accompanied by executive deficits. Objectives. To obtain evidence of the usefulness of the BRIEF-P and to analyse the possible ceiling and floor effect of its scores in the assessment of executive function in preschoolers with signs compatible with a possible diagnosis of ADHD. Methods. Seven articles were selected from 2538 potentially eligible articles from different databases. We included studies assessing samples of individuals with symptoms compatible with ADHD, with age range 2-6 years, published in English or Spanish, during the period 2012-2022. References published in: Science Direct, NCBI (PubMed), ProQuest Education Journals in the last decade. Risk of bias was assessed using the QUADAS-2 questionnaire. The main variables were: age and executive functioning. Conclusions. Executive deficits in early-life individuals with ADHD-compatible symptoms are more extensive than deficits in working memory. BRIEF-P is an instrument that facilitates obtaining a sensitive and discriminative executive profile. It should be used in combination with other neuropsychological performance tests, finding a floor effect in tests associated with warm executive functions and a ceiling effect in cold executive functions. This requires using a variety of tests to assess executive performance in preschoolers with symptoms compatible with ADHD and designing intervention proposals in line with them...

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>0 on I. Additionally, we prove that the fractal dimension of ksD−σf(x) of one-dimensional continuous functions f(x) is still one.

Pure silver as well as silver compounds have been used as antiseptics for centuries. Nowadays, the most frequently applied form of silver is a nanoparticle form. Several studies demonstrate the ability of silver nanoparticles and silver salts to accumulate in the brain of laboratory ani-mals as well as the ability of silver nanoparticles to influence behavioral and cognitive functions of laboratory mammals. For the first time, the influence of a silver salt, in particular, silver citrate on the change dynamics of behavioral and cognitive functions of laboratory mice at the daily oral exposure during 30, 60, 120 and 180 days is investigated in the present research. We observed the anxiety increase after 30 days of the exposure as well as the ability of mice to adapt to the prolonged oral exposure of silver citrate manifested in the anxiety decrease, increase of locomotor activity and the tendency of long-term contextual memory improvement. Increase of locomotor activity and memory improvement might be associated with the sensitivity increase and regarded as compensatory mechanism to anxiety increase. The observed phenomenon is classified as a hormetic effect. A comparison with the analogous study implemented polyvi-nylpyrrolidone coated silver nanoparticles is carried out. It was concluded that the nanoform is more neurotoxic.

Introduction: This empirical study investigates the impact of two distinct mathematical problem-solving methods – the Algebraic Formula Method and the Newton Sum Method – on enhancing ChatGPT's competence in effectively solving quadratic root functions. The integration of Artificial Intelligence (AI) into mathematical problem-solving has paved the way for innovative approaches. In this study, we delve into the Algebraic Formula Method and the Newton Sum Method, essential techniques for solving quadratic root functions. We aim to showcase the profound influence of these methods on ChatGPT's capacity to excel in solving quadratic equations. Evidence Through concrete evidence, we demonstrate ChatGPT's adept utilization of the Newton Sum Method for quadratic root function calculations. While ChatGPT can compute quadratic root functions of the form α^15 + β^15 using this method, its proficiency in using algebraic formula methods typically extends only up to α^4 + β^4. This marked discrepancy underscores the pivotal role that different methods play in amplifying the AI system's mathematical capabilities Result The results of this study provide concrete evidence of ChatGPT's superior utilization of the Newton Sum Method for calculating quadratic root functions. The model adeptly computes expressions of the form α^15 + β^15 using this method, while its proficiency using algebraic formula methods is generally limited to α^4 + β^4. This striking discrepancy underscores the transformative impact that different methods can have on elevating the AI system's mathematical prowess. Conclusion :Pushing Boundaries: Pioneering Novel Maths Approaches for Overcoming Limitations in AIThis study serves as an illuminating testament to the significance of pioneering innovative methodologies, rules, theorems, or formulas to surmount the current limitations in AI systems like ChatGPT. These innovative pursuits hold the key to unlocking the untapped potential that lies within, propelling AI systems to greater heights of proficiency. In essence, they offer a strategic pathway towards expanding the capabilities of AI and pushing the boundaries of what can be achieved. Discussion The outcomes derived from this study underscore the significant influence wielded by the method selection in augmenting the mathematical competencies of ChatGPT. Particularly noteworthy is the application of the Newton Sum Method, which surfaces as a compelling exemplar. This method serves as a pivotal conduit through which the model surpasses its prior constraints, allowing it to venture into the realm of calculations entailing higher exponents. Implications and Future Research: These findings not only contribute to AI's mathematical competencies but also emphasize the need for pioneering new methods, rules, theorems, or formulas to further enhance AI systems like ChatGPT. Future research could explore the development of novel mathematical techniques tailored to AI systems, thus expanding their capabilities across diverse problem-solving domains.

Here in it is described a new genetic microvascular obstructive disease causing progressive hypo-perfusion of human brain, heart and kidney. Since the age of 30 years a male patient developed recurrent angina with normal coronary epicardial vessels but remarkable slow flow at angiography causing cardiac micro-aneurysms that at endomyocardial biopsy were associated to obstructive microvascular dysplasia. His history was followed in the seven decade by micro-hematuria characterized at kidney biopsy by renal microvascular dysplasia and frequent cerebral ischemic attacks with preserved structure of main brain arteries. Analysis of 5,600 genetic disease-causing genes revealed mutation of ABCC6, MMP2 and XYLT1 genes.

This paper deals with the analysis of the cognitive functions of the cerebral cortex or cortex in the evolutionary context. The triune brain model is presented given its notorious popularity in fields that are not strictly neuroscientific, and its limitations and inaccuracies are also shown. Although it is an outdated theory, this one represented the passage to a new era, because it really was the model of the movement towards understanding the brain in evolutionary terms. Next, the paper illustrates the different areas of the cortex and their functions, as well as the evolution of the brain and the cortex in vertebrates. To date, the expansion of the cortex with the amniotes was placed 300 million years ago, although recent studies place it in the lampreys more than 500 million years ago. Evolutionary changes in mammalian brain and cortex size are discussed, showing the evolution from three to six cell layers and trends in different groups of mammals. Finally, the most recent contributions in the field of research are illustrated, such as the role of neurogenesis and the evolution of the connectivity of the cortex.

This study is grounded on evidence-based decision-making in the implementation of devolved functions in Kenya. Promulgation of the constitution of Kenya 2010 set stage for devolution of functions, power, resources, and representation closer to the people. The researcher applies principles of technology acceptance modelling to investigate the extrinsic factors, Perceived-Ease-Of-Use, Perceived-Usefulness, attitudes, behavioural-intention and actual use of Research findings, Innovations and Technologies. Furthermore, the researcher applies contingent valuation technique to investigate cost-benefit analysis of using research findings, innovations and technologies. Multi-stage cluster sample of 156 managers from ten counties, randomly distributed in the six devolved functions that were randomly selected, including: agriculture, county health service, early childhood education and village polytechnic, natural resources and environment, county administration and governance, and county public works and services, took part in this study. Building on basic statistical analysis, structural equation modelling was employed to explain the adoption process. Results proved that all TAM model constructs were decisive in the adoption process. Furthermore, managers were willing to pay extra to optimize decision making and for accrued benefits on service delivery. Findings from this study are critical for stimulating the uptake of research findings, innovations, and technologies in making informed decisions for improved service delivery.

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.

The main aim of this study is to predict whether the type of breast cancer is “benign” or “malignant” by classical generalized linear model (GLM) approach and an extended family of GLM called generalized linear mixed model (GLMM) approach for binomially distributed response variable with binary link functions. In this study, an advanced statistical modeling approach based on the GLMM to the traditional statistical modeling approach based on the GLM for binomially distributed response variable with various binary link functions is proposed to investigate the relationships between the “malignant or benign diagnosis of the BC in patients” and “nine attributes” of 699 BC diagnosed patients. This study also focuses on the statistical significance of the accurate classification of the BC diagnosed patients in cancer studies in medicine in “benign” or “malignant” type based on the WBC dataset. In this study, the superiority of the GLMM approach over the GLM approach for the binary response variable especially belonging to the WBC dataset is emphasized in the field of cancer diagnosis in medicine. Also the importance and the power of the IC and performance metrics as the goodness-of-fit test statistics are strongly emphasized for accurate statistical inferences from the “best” fitted model. In this study, from the main findings, the best fitted model among the GLM and GLMM approaches for the binary response variable is determined as the GLMM under “logit” link function with “id” random effect with the most statistically significant odds of the occurance of the BC being “malignant” as 7.9104, 5.6888, 5.6643, 4.9842, 4.1212, 2.0679, 1.8755, and 1.3970 times more than being “benign” for every one-unit increase in the quantities of “clump thickness”, “bland chromatin”, “mitoses”, “bare nuclei”, “cell shape”, “marginal adhesion”, “epithelial cell size”, and “cell size”, respectively.

Machine Learning techniques can be used to identify whether deficits in cognitive functions contribute to antisocial and aggressive behavior. This paper initially presents the results of tests conducted on delinquent and non-delinquent youths to assess their cognitive functions. The dataset extracted from these assessments, consisting of 37 predictor variables and one target. was used to train three algorithms that aim to predict whether the data corresponds to that of a young offender or a non-offending youth. Prior to this, statistical tests were conducted on the data to identify characteristics that exhibited significant differences in order to select the most relevant features and optimize the prediction results. Additionally, other feature selection methods, such as Boruta, RFE, and Filter, were applied, and their effects on the accuracy of each of the three machine learning models used (SVM, RF, and KNN) were compared. 80% of the data were utilized for training, while the remaining 20% were used for validation. The best result was achieved by the K-NN model trained with 19 features selected by the Boruta method, followed by the SVM model trained with 24 features selected by the filter method.

A drinking strategy aiming to replace a given percentage of the sweat losses incurred during exercise should result in reproducible fluid intake volume and, hence, fluid balance from one exercise session to the other performed under similar scenarios. Whether this may also be the case with ad libitum drinking during exercise is unclear. We characterized the repeatability of ad libitum fluid intake during repeated 1 h exercise sessions and examine its effect over time on fluid balance and selected physiological functions and perceptual sensations. Twelve (3 women) healthy individuals participated in this study. At weekly intervals, they completed 4, 2 x 30 min walking/jogging exercise bouts (55% VO2max, 40°C, 20-30% relative humidity) interspersed by a 3 min recovery period. During exercise, participants replaced water (20°C) ad libitum. There were no significant differences among the 4 exercise sessions for absolute fluid intake volume (~ 1000 mL · h-1), percent body mass loss (~ 0.4%), sweat rate (~ 1300 mL · h-1) and percent of sweat loss replaced by fluid intake (~ 80%). Heart rate, rectal temperature and perceived thirst and heat stress did not differ significantly between the first and fourth exercise session. Perceived exertion was significantly lower during the fourth vs. the first exercise session, but the difference was trivial, < 1 arbitrary unit. In conclusion, ad libitum fluid intake during 4 successive identical 1 h walking/jogging sessions conducted in the heat will result in similar fluid intake volumes and perturbations in fluid balance, heart rate, rectal temperature and perceived thirst, heat stress and exertion.

. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

Data Extraction is a technique is called as clustering which is used to retrieve data either from the files or data bases or both. This paper focuses on the performance evaluation parameters of the clustering algorithms based on different parameters or conditions or constraints and parameters which are used to perform the clustering process to get the clusters on the data sets. Therefore best clusters are retrieved when best parameters or conditions or constraints or preferences which are applied on the data sources for the clustering process. These parameters or conditions or constraints are opted by the user called as user preferences.

Matrix-variate Gaussian type or Wishart type distributions in the real domain are widely used in the literature. When the exponential trace has an arbitrary power and when a factor involving a determinant enters into the model or a matrix-variate gamma type or Wishart type model with exponential trace having an arbitrary power, is extremely difficult to handle. Evaluation of the normalizing constant in such a model is the most important part because when studying the properties of such a model, the method used in the evaluation of the normalizing constant will be the relevant steps in all the computations involved. One such model with a factor involving a trace and the exponential trace having an arbitrary power, in the real domain, is known in the literature as Kotz' model. No explicit evaluation of the normalizing constant in the model involving trace with an exponent and determinant with an exponent entering into the model and at the same time the exponential trace having an arbitrary exponent seems to be available in the literature. The normalizing constant widely used in the literature and interpreted as the normalizing constant in the general model and refers to as a Kotz' model does not seem to be correct. Corresponding model in the complex domain, with the correct normalizing constant, does not seem to be available in the literature. One of the main contributions in this paper is the matrix-variate distributions in the complex domain belonging to Gaussian type, gamma type, type-1 and type-2 beta type when the exponential trace has an arbitrary power. All these models are believed to be new. A second main contribution is the explicit evaluation of the the normalizing constants, in the real and complex domains especially in the complex domain, in a matrix-variate model involving a determinant and a trace as multiplicative factors and at the same time the exponential trace having an arbitrary power. Another main contribution is the introduction of matrix-variate models with exponential trace having an arbitrary exponent, in the categories of type-1 beta, type-2 beta and gamma distributions or in the family of Mathai's pathway models [1], both in the real and complex domains. Another new contribution is the logistic-based extensions of models in the real and complex domains with exponential trace having an arbitrary exponent and connecting to extended zeta functions introduced by this author recently. Some properties of such models are indicated but not derived in detail in order to limit the size of the paper. The techniques and steps used at various stages in this paper will be highly useful for people working in multivariate statistical analysis as well as people applying such models in engineering problems, communication theory, quantum physics and related areas, apart from statistical applications.

Cosmic strings can arise from spontaneous phase transitions during the inflationary period and are describable as disclination topological defects in spacetime. Analytical integration of the geodesic equations for a particle around a cosmic string reveals distinct orbit patterns dependent on the disclination intensity $\beta_{0}$. After its interaction with the cosmic string, the particle's behavior becomes random. To categorize these patterns, we describe the geodesic motion as iterated maps of a discrete parameter. Through the stabilization values of these functions, we correlate the scattering angle and the number of loops for the particle with $\beta_{0}$. Therefore, we interpret the gravitational field mathematically as an instructor of a particle's next position, given its previous one. We find that the radial function in the small displacement limit is similar to the logistic map. This leads us to conjecture the potential of the discrete parameter being a multiple of Planck's time, suggesting a method for the geometric discretization of spacetime around a cosmic string.

Physical activity (PA) is a modifiable factor that may have an influence on the course of Parkinson’s disease (PD). This study aimed to apply a simple behavioral intervention to encourage PD sufferers to increase their everyday physical activity and assess which parameters of motor functions will be improved. The research covered 50 PD patients (28 men and 22 women) aged 40-81 years (65.38 ± 9.23), with a duration of the disease 2-4 years, in stages 1-3 on the Hoehn and Yahr scale. The patients were randomly divided into two groups: the experimental group with behavioral therapy, and the control group without intervention. During 12 weeks the patients from the experimental group had five phone conversations. Each conversation lasted 15 minutes and was an interview about the subjects’ physical activity in the last month. The results were assessed by the Timed Up and Go test (TUG), Unified Parkinson's Disease Rating Scale (UPDRS) – part III, FIR (Functional Index “Repty” – own modification of Functional Independence Measure (FIM)), Functional Ambulation Category (FAC) and International Physical Activity Questionnaire (IPAQ). The results showed that spontaneous physical activity increased in the experimental group and motor functions improved. Physical activity improvement depended on age, body mass index, and gender.

This work introduces an approach to investigate the existence of zeros for holomorphic complex functions, defined on open and simply connected subdomains of C, in a systematic and direct way. This is achieved by means of the theory of dynamical systems (Poincar\'e index) and the perception that a zero of a specific complex function is an equilibtium for the associated dynamical system. The logical basis of proof is to find the mathematical expression for the Poincaré index of the vector field associated to the function under study, assuming the existence of a zero, and investigating the consequences. Depending on the value of the index, an inconsistency may occur, establishing a contradiction.

Increasing evidence supports the direct healing effects of forests, partly attributed to the exposure to plant-emitted monoterpenes available in the forest atmosphere. The potential benefits on respiratory functions from inhaling monoterpenes have gained attention, especially due to the global rise in respiratory diseases. This study involved 42 asthmatic adolescents attending a summer rehabilitation camp at an Altitude Pediatric Asthma Center within a densely forested area in the Eastern Italian Alps. Volatile organic compound measurements indicated a pristine atmosphere, enabling modeling of continuous hourly monoterpenes concentration. Monoterpene concentration exposure and total inhaled dose were assessed over a 14-day stay, during which spirometry, lung oscillometry, and fractional exhaled nitric oxide were measured. Statistically significant correlations were observed between modifications in lung function parameters among asthmatic adolescents and monoterpenes exposure. These findings suggest a potential localized airway effect specific to monoterpenes. This pilot cohort study might pave the way for further investigations into the therapeutic effects of forest monoterpenes on lung function tests, asthma, and the broader healing potential of forest environments.

Among the various generalizations of persistent topology, the one based on rank functions and leading to indexing-aware functions appears to be particularly suited to catch graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies "simple" and "single-vertex" features in directed and undirected graphs, by which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the "sink" feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.

In this paper, we constructed and analyzed a modified SIR-type model for the epidemic problem which considering waning-immunity class in the population, with the nonlinear incidence and recovery rates. Depending on the basic reproduction ratio, we investigated conditions for both non-endemic and co-existing cases. The RouthHurwitz criteria is used to verify the local stability of equilibria, whereas for the global stability, the suitable Lyapunov function is selected to analyze the behavioral stability for each equilibria. Moreover, we studied the optimal control problem for this case. Numerically, we give some simulations to support our analitycal findings.

The degradation of Proton-exchange membrane fuel cell (PEMFC) gasket materials is crucial in electric vehicles as it can cause hazardous hydrogen fuel leaks, which are usually due to high temperatures, pressures, and hydrogen fuel exposure. Degradation of gasket materials in PEMFC presents a critical concern for electric vehicle safety due to potential hydrogen fuel leaks. This study utilizes finite element analysis (FEA) to assess the suitability of gasket materials for PEMFC applications, focusing on aging and tensile conditions. The dual degradation framework, incorporating contact pressure and von Mises stress, is employed to evaluate Liquid Silicon Rubber (LSR) and Ethylene Propylene Diene Monomer (EPDM) materials. Under aging techniques, the Yeoh model exhibits the least Mean Absolute Percentage Error (MAPE) and computational cost of 0.27 seconds, while the Ogden model records the highest computational cost of 0.89 seconds. In evaluating MAE, Root Mean Square Error (RMSE), and R-squared metrics, LSR and EPDM materials demonstrate respective averages of 0.25%, 0.275%, 0.945%, and 0.815%, 0.685%, 0.77%. Tensile testing (Uniaxial) reveals RMSE and MAE values of 0.30%, 0.40%, and 0.50%, 0.40%, respectively. FEA proves instrumental in identifying suitable gasket materials for PEMFC applications. LSR emerges as the superior choice, demonstrating enhanced FEA modelling performance under aging and tensile conditions. These findings contribute valuable insights to the design and development of improved gasket materials, bolstering the safety and reliability of electric vehicles.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

In this paper, we classify the function space of all real-valued functions on R denoted as F(R,R) into 28 distinct blocks. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between four well-known real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

We say that a system {zmF(z)}m=0∞ is a Beurling system if F is an outer function. Beurling’s approximation theorem asserts that if F is an outer function from H2(D) then the system {zmF(z)}m=0∞ is complete in the space H2(D). We prove that a Beurling system with F∈Hp(D),1≤p<∞ is an M−bases in Hp(D) with an explicit dual system. Any function f∈Hp(D),1≤p<∞ can be expanded as a series by the system {zmF(z)}m=0∞. For different methods of summation we characterize outer functions F for which the expansion converges to f. Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesis.

The discovery of microRNAs and their role in disease today represents a substantial breakthrough that has inspired and propagating research on microRNAs as targets for diagnosis and therapy. Cardiovascular disease is an area where the limitations of early diagnosis and conventional pharmacotherapy are evident and deserve attention. Thus microRNA-based drugs have substantial potential for development. Research and its application can progress considerably as witnessed in preclinical and clinical trials. The use of miRNAs remains experimental at the time of writing but has a promising role in the diagnosis and prognosis of a variety of acute coronary syndrome presentations. Its use, alone or in combination with currently available biomarkers, could be adopted soon, especially if diagnostic ambiguity exists. In this review, we explore the current state of knowledge about microRNAs as potential targets for diagnosis and therapy in the cardiovascular system. We report recent improvements in the acknowledgment and characterization of microRNAs focusing on clinical translation. The new dares and outlooks toward clinical application are discussed.

In the past decades, one of the most widely reported phenomena on Caribbean reefs is the general fall in coral cover and rise in macroalgae. Reefs with low coral cover and high macroalgal abun-dances are often presumed to provide poorer ecosystem functions and services. In this study, we assessed the condition of coral reefs on the Caribbean Coast of Costa Rica and determined how eight key ecosystem metrics varied in response to differential coral and fleshy macroalgae covers. Most reefs surveyed had high fleshy macroalgae and low live coral covers, with an average (± SD) of 31 ± 28% and 14 ± 13% per site. We found that the rugosity, urchin density, fish richness, total fish biomass, large fish density, and the potential fishery value of the reef were higher in sites with low fleshy macroalgae covers (>10%). The value of many of the ecosystem metrics estimated for coral reefs of the region appears to be lower than what’s been reported for other areas in the Caribbean, which may be related to the high macroalgae covers found on the reefs. Our results concur with the prevailing paradigm that an increase in macroalgae abundance could reduce the ecosystem services provided by coral reefs.

Modern cryptographic protocols such as zero-knowledge proofs and secure multi-party computation have increased the demand for a novel category of symmetric primitives. These primitives are not optimized for traditional platforms such as servers, microcontrollers, and desktop computers but rather for their ability to be implemented in arithmetic circuits. To enable efficient arithmetic operations, they define operations over larger finite fields and use low-degree invertible functions to construct their non-linear layers. Grendel is an arithmetization-oriented permutation that leverages the Legendre Symbol to enhance the growth of algebraic degrees in its non-linear layer. In this paper, we present a preimage attack on the sponge hash function instantiated with the full rounds of the Grendel permutation using algebraic methods. We introduce a technique that allows us to eliminate two full rounds of substitution permutation networks (SPN) in the sponge hash function with minimal or no additional cost. This method can be combined with univariate root-finding techniques and Gröbner basis attacks to break the number of rounds claimed by the designers. By utilizing this strategy, our attack achieves an improvement of two additional rounds compared to the previous state-of-the-art attack. While not breaking its security margin, it allows us to further understand the design and analysis of such cryptographic primitives.

Missing observation is a common problem in scientific and industrial experiments, particularly in a small-scale experiment. They often present significant challenges when experiment repetition is infeasible. In this research, we propose a multi-objective genetic algorithm as a practical alternative for generating optimal mixture designs that remain robust in the face of missing observation. Our algorithm prioritizes designs that exhibit superior D-efficiency while maintaining a high minimum D-efficiency due to missing observation. The focus on D-efficiency stems from its ability to minimize the impact of missing observations on parameter estimates, ensure reliability across the experimental space, and maximize the utility of available data. We study problems with three mixture components where the experimental region is an irregularly shaped polyhedral within the simplex. Our designs have proven to be D-optimal designs, demonstrating exceptional performance in terms of D-efficiency and robustness against missing observations. We provide a well-distributed set of optimal designs derived from the Pareto front, enabling experimenters to select the most suitable design based on their priorities using the desirability function.

In history, theta function identities have been studied extensively and deeply. In this paper, applying the residue theorem of an elliptic function, we obtain a parameterized theta function identity. Then, by selecting the appropriate parameter, we derive some famous Jacobi identities, as well as other relatively simple theta function identities.

Empirical Orthogonal Functions (EOF) analysis between the anomalies of Lake Titicaca water levels (WLs) and the Pacific Interdecadal Oscillation (IPO) reveals a correlation coefficient of 0.71 between the WLs and the principal component (PC1). These findings demonstrate the high accuracy of the IPO in representing the positive and negative phases of the water levels. By utilizing wavelet functions, we identified multi-decadal variability with periods ranging between 20 and 30 years. The statistical techniques employed indicate a relationship between IPO and ENSO; however, they operate on different timescales of climate variability. The IPO exhibits longer-term variability, typically spanning 20-30 years, while ENSO events occur on average every 2-7 years. Nevertheless, the IPO has the ability to modulate the strength and frequency of El Niño and La Niña events, and vice versa. During the positive phase of the IPO, there is a tendency for more frequent and intense El Niño events, accompanied by fewer La Niña events. This can be attributed to warmer sea surface temperatures in the central and eastern Pacific, which create favorable conditions for El Niño development. Conversely, during the negative phase of the IPO, there is a tendency for more frequent and intense La Niña events, with fewer occurrences of El Niño events, due to cooler sea surface temperatures in the central and eastern Pacific.

In this study, we introduce a new class of bi-univalent functions using q-Janowski Function. We derive the Fekete-Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes are3 presented by customizing the parameters employed in our initial discoveries.

The present work concerns with presenting an explicit formula for new shifted wavelet (NSW) functions. Wavelet functions have many applications and advantages in both applied and theoretical fields. They are formulated with different orthogonal polynomials to construct new techniques for treating some problems in sciences, and engineering. A new important differentiation property of NSW in terms of NSW themselves is obtained and proved in this paper. Then it is utilized together with the state parameterization technique to find solution of optimal control problem (OCP) approximately. The suggested method converts the OCP into a quadratic programming problem, which can be easily determined on computer. As a result, the approximate solution closes with the exact solution even with a small number of NSW utilized in estimation. The error bound estimation for the proposed method is also discussed. Some test numerical examples are solved to demonstrate the applicability of the suggested method. For comparison, the exact known solutions against the obtained approximate results are listed in Tables.

Data security is a fundamental aspect to be considered in Internet of Things (IoT) information gathering systems, as IoT is a network of interconnected devices that collect and share real-time data, becoming increasingly prevalent in our lives. However, data security in IoT systems presents unique challenges due to the large number of devices and access points involved. This study aims to conduct a literature review on IoT security to analyze the performance of security mechanisms on current development platforms, specifically on a Raspberry Pi 3. Some functions from the OpenSSL library were used, including popular hash functions and cipher algorithms. Additionally, a bash code was developed to obtain the time spent in seconds and the memory consumption in kilobytes. In addition to time and memory calculations, statistical values such as variance and standard deviation were also obtained and compared with results obtained on a personal computer. The tests conducted in this study demonstrated that it is possible to implement these algorithms on platforms with more limited resources, with AES and RSA algorithms being the most suitable for IoT scenarios.

This paper proposes an imperfectly vaccinated SVEIR model for latent age. We calculate the equilibrium points and basic reproduction number of the model. The asymptotic smoothness, uniform persistence and the existence of the attractor of the semi-flow generated by the solutions of the system are addressed. Moreover, using LaSalle’s invariance set principle and constructing Volterra-type Lyapunov functions, we can prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number R0 is less than one, the disease will gradually disappear. On the other hand, if the number is greater than one, the disease will become endemic and persist. Finally, measures that can effectively control the ongoing transmission of the disease have been obtained.

In this paper, we extend the Merton model of investment in discrete time to the cases when there is a finite number of investors and the market is with frictions represented by convex penalty functions defined for each investor. In the main result of this paper, we proved the existence of optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model.

In the present paper we introduce three new classes of bi-univalent functions connected with Gregory coefficients. For functions in each of these three bi-univalent function classes we have derived the estimates of the Taylor--Maclaurin coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ and Fekete-Szeg\H{o} functional problems for functions belonging to these new subclasses. We defined three subclasses of the class of the bi-univalent functions $\Sigma$, namely $\mathfrak{HG}_{\Sigma}$, $\mathfrak{GM}_{\Sigma}(\mu)$ and $\mathfrak{G}_{\Sigma}(\lambda)$ by using the subordinations with the function whose coefficients are Gregory's numbers. First, we proved that these classes are not empty, i.e. contains other functions than the identity one. Using the well-known Carath\'eodory Lemma for the functions with real positive parts in the open unit disk, together with an estimation due to P. Zaprawa (see https://doi.org/10.1155/2014/357480) and another one of Libera and Zlotkiewicz, we gave upper bounds for the above mentioned initial coefficients and for the Fekete-Szeg\H{o} functionals. The main results are followed by some particular cases, and the novelty of the definitions and the proofs could involve further studies for such type of similarly defined subclasses.

Tumor-associated macrophages (TAMs) play critical roles in the tumor microenvironment (TME), where they are recruited by signals released by cancer cells. Although they have great potential as therapeutic targets for cancer treatment, the dual roles of TAMs in promoting or inhibiting tumor growth, invasion, and metastasis make their function in cancer progression complex. In this review, we provide an overview of the current understanding of TAMs, including their phenotypic diversity, regulatory signaling pathways, and interactions with other cells in the TME. We also discuss the challenges related to the standard isolation protocols of TAMs, inconsistent research results, and translation of TAM knowledge into clinical applications. Additionally, we review the status of clinical trials involving TAMs and potential strategies to overcome the limitations. The future direction of TAM research should focus on developing more targeted therapies that specifically regulate TAM function and non-invasive methods for monitoring TAM activity in cancer patients. A comprehensive understanding of the complex role of TAMs in cancer may lead to the development of more effective treatments and improved outcomes for cancer patients.

The present paper contains data on the density (ρ), sound velocity (u), specific heat capacity (c_p ) of the mixture of N,N-dimethylformamide + 1-butanol (DMF + BuOH) determined in the entire concentration range of solution and in the temperature range: (293.15–318.15) K. The analysis of thermodynamic functions such as isobaric molar expansion, isentropic and isothermal molar compression, isobaric and isochoric molar heat capacity, as well as their excess functions (〖 E〗_(p,m)^E,〖 K〗_(S,m)^E,〖 K〗_(T,m)^E,〖 C〗_"p,m" ^E,〖 C〗_"V,m" ^E) and also V_m^E was undertaken. The analysis of changes in the physicochemical quantities was based on consideration of the system in an aspect of intermolecular interactions with resulting changes in the mixture structure. The results available in the literature are confusing during the analysis and became the reason for our decision to thoroughly examine the system. What is more, for a system whose components are widely used, there is no information in the literature regarding the heat capacity of the tested mixture, which was also achieved and presented in this publication. The conclusions drawn from so many data allow us to approximate and understand the changes that occur in the structure of the system due to repeatability and consistency of the obtained results

Deep learning has been applied in many areas that have had a significant impact on applications that improves real-life challenges. The success of deep learning in a wide range of areas is due in part to the use of activation functions, which are particularly effective at solving non-linear problems. Activation functions are a key focus for researchers in artificial intelligence who aim to improve the performance of neural networks. This article provides a comprehensive explanation and comparison of different activation functions, with a focus on the arc tangent and its variations specifically. The paper presents experimental results that show that variations of the arc tangent using irrational numbers such as pi, the golden ratio, and Euler’s number, as well as a self-arctan function, produce promising results. Since we experimented with promising activation functions on two different problems, and datasets, we reached a result that different irrationals work well for different problems. In other words, arctan ϕ gives the best results mostly for multiclass classification and arctan e gives the best results for time series prediction problems. The paper focuses on a multiclass classification problem applied to the Reuters Newswire dataset and a time-series prediction problem on Türkiye energy trade value to show the impacts of activation functions.

Autism Spectrum Disorder (ASD) is a complex neurodevelopmental disorder characterised by poor social interaction and communication, as well as restricted and stereotyped interests. Due of the high prevalence of gastrointestinal disorders in individuals with ASD, researchers have investigated the gut microbiota as a potential contributor to its aetiology. The relationship between the microbiome, gut, and brain (microbiome-gut-brain axis) has been acknowledged as a key factor in modulating brain function and social behaviour, but its connection to the aetiology of ASD is not well understood. Recently, there has been increasing attention on the relationship between the immune system, gastrointestinal disorders, and neurological issues in ASD, particularly in relation to the loss of specific species or a decrease in microbial diversity. It focuses on how gut microbiota dysbiosis can affect gut permeability, immune function, and microbiota metabolites in ASD. Although a very complete study suggests that dysbiosis is a consequence of the disease and that it has practically no effect on autistic manifestations. This is a review of the relationship between the immune system, microbial diversity, and the microbiome-gut-brain axis in the development of autistic symptoms severity and, a proposal of a novel role of gut microbiome in ASD, where dysbiosis is a consequence of ASD-related behaviour and where dysbiosis in turn accentuates the autistic manifestations of the patients via microbiome-gut-brain axis in a feedback circuit.

This study mostly analyzes the pragmatic viewpoints of speech acts and language functions through Halliday’s (1975) language functions and Searle’s (1976) speech acts were adapted to analyze the functional aspects of the conversations and it was also intended to explore the teachers’ perception toward teaching and learning English as a Foreign Language (EFL) learners’ textbooks and the teacher’s components of communicative knowledge regarding the functions of language in daily activity. The participants of this paper consisted of thirteen Sunrise 10, 11, 12 grades of Kurdish teachers at high school English in Iraqi Kurdistan. Through semi-structured interview, it was found that the conversations in the mentioned textbooks are insufficient from the pragmatic point of view. Some recommendation for the textbook designers, teachers, material developer were raised to make up the shortcomings of the textbooks. The findings reveal that the conversation texts in Sunrise textbooks are not meeting the systematic standard of pragmatic competence the English language learners and the book designer must be recommended to be aware of those shortcomings of the textbook series if they are required to develop their speaking skills in both student and activity series. The implications of this paper can be helpful in comparing the results of this study with other similar studies to check if there is a universal pattern in performing the speech acts and language functions and the interest to Kimberley Education for Life learners in increasing their knowledge of pragmatics in general and the role of language functions and speech acts investigated in this study.

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

A deterministic compartment model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The model is quantitatively analyzed to investigate it's local asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using Routh-Hurwitz criteria, that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than the unity. When the reproduction number is greater than the unity, we prove the existence of a locally asymptotically stable endemic equilibrium. Furthermore, bifurcation analysis was done by investigating the possibility of the co-existence of the equilibria of the model at R0<0 but near R0=0 by Center Manifold Theory.

Recent studies show that repetitive transcranial magnetic stimulation (rTMS) improves cognitive and motor functions in patients with Parkinson’s Disease (PD). Gamma rhythm low-field magnetic stimulation (LFMS) is a new non-invasive rTMS technique that generates diffused and low-intensity magnetic stimulation to deep cortical and subcortical areas. To investigate potential therapeutic effects of LFMS in PD, we subjected an experimental mouse model to LFMS (as early treatment). We examined the LFMS effect on motor functions as well as neuronal and glial activities in 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) induced male C57BL/6J mice. Mice received MPTP injection (30 mg/kg, i.p., once daily for 5 days) followed by LFMS treatment, 20 minutes each day for 7 days. LFMS treatment improved motor functions compared to the sham-treated MPTP mice. Further, LFMS significantly improved tyrosine hydroxylase (TH) and decreased glial fibrillary acidic protein (GFAP) levels, in substantia nigra pars compacta (SNpc) and non- significantly in striatal (ST) regions. LFMS treatment improved neuronal nuclei (NeuN) level in SNpc. Our findings suggest that early LFMS treatment improved the neuron survival and in turn, motor functions in MPTP intoxicated mice brain. Further investigation is required to clearly define the molecular mechanisms by which LFMS improves motor and cognitive function in PD patients.

Blood flow-restricted training (BFR) is constantly growing in popularity. Despite growing evidence of the significant influence of BFR training on different body functions, its impact on the vascular system, especially the arteries, is controversial. Therefore, the objective of our study was to analyze how BFR exercise, compared to other types of exercise without restriction of blood flow or other active intervention, influences arterial functions and angiogenesis in adults. Studies comparing the effect of BFR versus non-BFR training on arterial parameters are divided into three categories. Endothelial function, angiogenesis, and other vasculature functions. The search was based on three databases (Cochrane Library, PubMed®, Embase). In this systematic review, 38 studies were included. Meta-analysis revealed a more significant improvement in flow-mediated dilatation (FMD) (p=0.002) and the production of the primary angiogenesis biomarker Vascular Endothelial Growth Factor (VEGF) (p=0.009) after training in BFR compared to nonBFR (p=0.002). Analysis of pulse wave velocity, ankle-brachial index, systolic blood pressure, or heart rate did not show a significant difference in changes between BFR and non-BFR training. Other parameters examined were not sufficiently provided to be included in the meta-analysis. The results obtained, present trends suggesting the significant impact of BFR training on endothelial functions and angiogenesis. Unfortunately, there is still a lack of multicenter randomized clinical trials, including many participants, that are necessary to confirm the advantage of BFR over non-BFR activity.

The article considers an internal boundary value problem of the distribution of an electrostatic field in a lens formed by two identical semi-infinite circular cylinders coaxially located inside an infinite external cylinder. The problem is reduced to solving a system of singular Wiener-Hopf integral equations, which is further solved by the Wiener-Hopf method using factorized Bessel functions. Solutions to the problem for each region inside the infinite outer cylinder are presented as exponentially converging series in terms of eigenfunctions and eigenvalues.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.

Deep learning has been applied in many areas that have had a significant impact on applications that improves real-life challenges. The success of deep learning in a wide range of areas is due in part to the use of activation functions, which are particularly effective at solving non-linear problems. Activation functions are a key focus for researchers in artificial intelligence who aim to improve the performance of neural networks. This article provides a comprehensive explanation and comparison of different activation functions, with a focus on the arc tangent and its variations specifically. The paper presents experimental results that show that variations of the arc tangent using irrational numbers such as pi, the golden ratio, and Euler’s number, as well as a self-arctan function, produce promising results. Since we experimented with promising activation functions on two different problems, and datasets, we reached a result that different irrationals work well for different problems. In other words, arctan ϕ gives the best results mostly for multiclass classification and arctan e gives the best results for time series prediction problems. The paper focuses on a multi-class classification problem applied to the Reuters Newswire dataset and a time-series prediction problem on Türkiye energy trade value to show the impacts of activation functions.

The proliferation of devices for the Internet of Things (IoT) and their implication in many activities of our lives have led to a considerable increase in concern about the security of these devices, posing a double challenge for designers and developers of products. On the one hand, the design of new security primitives, suitable for resource-limited devices, that can facilitate the inclusion of mechanisms and protocols to ensure the integrity and privacy of the data exchanged over the Internet. On the other hand, the development of techniques and tools to evaluate the quality of the proposed solutions as a step prior to their deployment, as well as to monitor their behavior once in operation against possible changes in operating conditions arising naturally or as a consequence of a stress situation forced by an attacker. To address these challenges, this paper first describes the design of a security primitive that plays an important role as a component of a hardware-based root of trust, as it can act as a source of entropy for true random number generation (TRNG) or as a physical unclonable function (PUF) to facilitate the generation of identifiers linked to the device on which it is implemented. The work also illustrates different software components that allow carrying out a self-assessment strategy to characterize and validate the performance of this primitive in its dual functionality, as well as to monitor possible changes in security levels that may occur during operation as a result of device aging and variations in power supply or operating temperature. The designed PUF/TRNG is provided as a configurable IP module, which takes advantage of the internal architecture of the Xilinx Series-7 and Zynq-7000 programmable devices and incorporates an AXI4-based standard interface to facilitate its interaction with soft- and hard-core processing systems. Several test systems that contain different instances of the IP have been implemented and subjected to an exhaustive set of on-line tests to obtain the metrics that determine its quality in terms of uniqueness, reliability, and entropy characteristics. The results obtained prove that the proposed module is a suitable candidate for various security applications. As an example, an implementation that uses less than 5% of the resources of a low-cost programmable device is capable of obfuscating and recovering 512-bit cryptographic keys with virtually zero error rate.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

The health equipment are used to keep track of significant health indicators, automate health interventions, and analyze health indicators. People have begun using mobile applications to track health characteristics and medical demands because all devices are linked to high-speed internet and phones. Such a combination of smart devices, the internet, and mobile applications expands the usage of remote health monitoring through the Internet of Medical Things (IoMT). The accessibility and unpredictable aspects of IoMT create massive security and confidentiality threats in IoMT systems. In this proposed paper - Octopus, Physically Unclonable Functions (PUFs) have been used to provide privacy to the healthcare device by masking the data, and machine learning (ML) technique is used to retrieve the health data back and for reducing security breaches on networks. This technique has exhibited 99.45% accuracy, which proves that this technique could be used to secure health data with masking.

Poor social skills in autism spectrum disorder (ASD) are associated with reduced independence in daily life. Current interventions for improving the social skills of individuals with ASD fail to represent the complexity of real-life social settings and situations. Virtual reality (VR) may facilitate social skills training in social environments and situations proximal to real life, however, more research is needed for elucidating aspects such as the acceptability, usability, and user experience of VR systems in ASD. Twenty-five participants with ASD attended a neuropsychological evaluation and three sessions of VR social skills training, incorporating 5 social scenarios with three difficulty levels for each. Participants reported high acceptability, system usability, and user experience. Significant correlations were observed between performance in social scenarios, self-reports, and executive functions. Working memory and planning ability were significant predictors of functionality level in ASD and the VR system’s perceived usability respectively. Yet, performance in social scenarios was the best predictor of usability, acceptability, and functionality level in ASD. Planning ability substantially predicted performance in social scenarios, postulating an implication in social skills. Immersive VR social skills training appears effective in individuals with ASD, yet an error-less approach, which is adaptive to the individual’s needs, should be preferred.

Non-linear activation functions are one of the main parts of deep neural network architectures. The choice of the activation function can affect model speed, performance and convergence. Most popular activation functions don't have any trainable parameters and don't alter during the training. We propose different activation functions with and without trainable parameters. Said activation functions have a number of advantages and disadvantages. We'll be testing the performance of said activation functions and comparing the results with widely known activation function ReLU. We assume that the activation functions with trainable parameters can outperform functions without ones, because the trainable parameters allow the model to "select'' the type of each of the activation functions itself, however, this strongly depends on the architecture of the deep neural network and the activation function itself.

Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron-electron interactions and one-loop quantum electrodynamics effects. Here we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO2 molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac-Coulomb and Dirac-Coulomb-Gaunt Hamiltonians.

There is great interest in automatically detecting road weather and understanding its impacts on the overall safety of the transport network. This can, for example, support road condition-based maintenance or even serve as detection systems that assist safe driving during adverse climate conditions. In computer vision, previous work has demonstrated the effectiveness of deep learning in predicting weather conditions from outdoor images. However, training deep learning models to accurately predict weather conditions using real-world road-facing images is difficult due to: (1) the simultaneous occurrence of multiple weather conditions; (2) imbalanced occurrence of weather conditions throughout the year; and (3) road idiosyncrasies, such as road layouts, illumination, road objects etc. In this paper, we explore the use of focal loss function to force the learning process to focus on weather instances that are hard to learn with the objective to help address data imbalance. In addition, we explore the attention mechanism for pixel based dynamic weight adjustment to handle road idiosyncrasies using state-of-the-art vision transformer models. Experiments with a novel multi-label road weather dataset show that focal loss significantly increases the accuracy of computer vision approaches for imbalanced weather conditions. Furthermore, vision transformers outperforms current state-of-the-art convolutional neural networks in predicting weather conditions with a validation accuracy of 92% and F1-score of 81.22%, which is impressive considering the imbalanced nature of the dataset.

Silver in different forms is used for medical purposes from ancient times. It is not yet well known, which form of silver is more biocompatible and less toxic. Here we considered silver nanoparticles and silver citrate. Also, the relationships of neurotoxicity of silver compaunds with ageing factor is not yet described. To assess the role of nanoform in neurotoxicity of silver and role of ageing a long-term experiment was conducted. We had four control groups of intact mice and four experimental groups which were exposed to silver nanoparticles and silver citrate for two months. Four groups of mice were introduced into the experiment since the age of five months to assess ageing factors. It was shown that the nanoform does play a certain role in neurotoxicity of silver. Silver citrate seems to be a more preferable silver compound. Ageing can be regarded as a positive factor that neutralizes toxic action of silver compounds. It may be due to the development of physiological/cognitive functions with the age as well as adaptation to unnatural content in the individual cages that is definitely stressful for mice.

Based on some geometrical properties of the Rabinovich system the closed-form solutions of the equations has been established. Moreover the Rabinovich system is reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions are built using the Optimal Auxiliary Functions Method (OAFM). A good agreement between the analytical and corresponding numerical results has been performed. The accuracy of the obtained results emphasizes that this procedure could be successfully applied for more dynamical systems with these geometrical properties.

Since its introduction, back in the late 1970s, the non-affine or slip parameter, ξ, has been routinely employed by numerous constitutive models as a constant parameter. However, the evidence seems to imply that it should be a function of polymer deformation. In the present work, we phenomenologically modify a constitutive model for the rheology of unentangled polymer melts [P. S. Stephanou et al. J. Rheol. 53, 309 (2009)] to account for a non-constant slip parameter. The revised model predictions are compared against newly accumulated rheological data for a C48 polyethylene melt obtained via direct non-equilibrium molecular dynamics simulations in shear. We find that the conformation tensor data are very well predicted; however, the predictions of the material functions are noted to deviate from the NEMD data, especially at large shear rates.

Generation of unique identifiers extracted from the physical characteristics of the underlying hardware ensures the protection of electronic devices against counterfeiting and provides security to the data they store and process. This work describes the design of an efficient Physical Unclonable Function (PUF) based on the differences in the frequency of Ring Oscillators (ROs) with identical layout due to variations in technological processes involved in the manufacture of the integrated circuit. The logic resources available in the Xilinx Series-7 programmable devices are exploited in the design to make it more compact and achieve an optimal bit-per-area rate. On the other hand, the design parameters can also be adjusted to provide a high bit-per-time rate for a particular target device. The PUF has been encapsulated as a configurable Intellectual Property (IP) module, providing it with an AXI4-Lite interface to ease its incorporation into embedded systems in combination with soft- or hard-core implementations of general-purpose processors. The capability of the proposed RO-PUF to generate implementation-dependent identifiers has been extensively tested, using a series of metrics to evaluate its reliability and robustness for different configuration options. Finally, in order to demonstrate its utility to improve system security, the identifiers provided by RO-PUFs implemented on different devices have been used in a Helper Data Algorithm (HDA) to obfuscate and retrieve a secret key.

The paper investigates new robust code constructions based on bent functions and spline–wavelet transformation. Implementation of bent functions in codes construction increases the probability of error detection in the data channel and cryptographic devices. Meanwhile, use of spline–wavelets theory for constructing the codes gives the possibility to increase system security from the actions of an attacker. Presented constructions combines spline–wavelets functions and bent functions. Developed robust codes, compared to existing ones, have a higher parameter of maximum error masking probability. Illustrated codes are ensuring the security of transmitted information. Some of the granted constructions were implemented on FPGA.

The Internet of Things (IoT) is experiencing widespread adoption across industry sectors ranging from supply chain management to smart cities, buildings, and health monitoring. However, most software architectures for IoT deployment rely on centralized cloud computing infrastructures to provide storage and computing power, as cloud providers have high economic incentives to organize their infrastructure into clusters. Despite these incentives, there has been a recent shift from centralized to decentralized architecture that harnesses the potential of edge devices, reduces network latency, and lowers infrastructure cost to support IoT applications. This shift has resulted in new edge computing architectures, but many still rely on centralized solutions for managing applications. A truly decentralized approach would offer interesting properties required for IoT use cases. To address these concerns, we introduce a decentralized architecture tailored for large scale deployments of peer-to-peer IoT sensor networks and capable of run-time application migration. The solution combines a blockchain consensus algorithm and verifiable random functions to ensure scalability, fault tolerance, transparency, and no single point of failure. We build on our previously presented theoretical simulations with many protocol improvements and an implementation tested in a use case related to monitoring a Slovenian cultural heritage building located in Bled, Slovenia.

It is one of the central goals of cognitive neuroscience to understand how structure and function relate in the brain. We review how cognitive function characterization has been approached in the past. In addition, we examine the ongoing efforts, as well as the implications for the future. Clinical studies on patients with lesions have provided key insights into the relationship between brain areas and behavior over the past century. We describe cognitive function according to localization considering these early efforts for characterization. We chose a perceptual-cognitive function, namely body perception, to describe our current efforts. Using body perception as an example, we summarize contemporary techniques. Finally, we outline the trajectory of current progress into the future and discuss the implications for clinical and basic neuroscience.

Successful fertilization treatments targeted to improve stand productivity while reducing operational complexities and cost depend on a clear understanding of soil nutrient availability under varying environmental conditions. Soil nutrient data collected from 154 forest sites throughout the Inland Northwest, USA were analyzed to examine soil nutrient characteristics on different geologic soil parent materials and to rank soil fertility. Results show that soil parent material explains significant differences in soil nutrient availability. Soils developed from volcanic rocks have the highest CEC and are relatively high in P, K, S, Mg, Cu, Ca, and B, but generally poor in N. Forest soils developed from plutonic rocks exhibit the lowest CEC and are low in N, S, K, Mg, Cu, and Ca, but higher in P. Some soils located on mixed glacial till are low only in K, Cu, Mg, and Ca, but many glacial soils are relatively rich in other nutrients, albeit the second lowest CEC. Soils developed from metasedimentary and sedimentary rocks are among those with lowest soil nutrient availability for P and B. Sulfur was found to have the highest concentrations in metasedimentary influenced soils and the least in sedimentary derived soils. Our results should be useful in designing site-specific fertilizer and nutrient management prescriptions for forest stands growing on soils developed from these major geologies within the Inland Northwest region of the United States.