Vector-valued Functions Research Articles

Superconductivity and strain-enhanced phase stability of Janus tungsten chalcogenide hydride monolayers

Janus transition metal-dichalcogenide materials have attracted a great deal of attention due to their remarkable physical properties arising from the two-dimensional geometry and the breakdown of the out-of-plane symmetry. Using first-principles density functional theory, we investigated the phase stability, strain-enhanced phase stability, and superconductivity of Janus WSeH and WSH. In addition, we investigated the contribution of the phonon linewidths from the phonon energy spectrum responsible for the superconductivity and the electron-phonon coupling as a function of phonon wave vectors and modes. Previous work has examined hexagonal 2H and tetragonal 1T structures, but we found that neither is a ground-state structure. The metastable 2H phase of WSeH is dynamically stable with Tc≈11.60K, similar to WSH. Compressive biaxial strain—the two-dimensional equivalent of pressure—can stabilize the 1T structures of WSeH and WSH with Tc≈9.23K and 10.52 K, respectively. Published by the American Physical Society 2024

A Note on APN Permutations and Their Derivatives

Prior to the discovery of an APN permutation in six dimension it was conjectured that such functions do not exist in even dimension, as none had been found at that time. However, finding APN permutations in even dimension ≥8 remains a significant challenge. Understanding and determining more properties of these functions is a crucial approach to discovering them. In this note, we study the properties of vectorial Boolean functions based on the weights of the first-order and second-order derivatives of their components. We show that a function is an APN permutation if and only if the sum of the squares of the weights of the first-order derivatives of its components is exactly 22n−1(2n−1+1)(2n−1). Additionally, we determined that the sum of the weights of the second-order derivatives of the components of any vectorial Boolean function is at most 22n−1(2n−1)(2n−2). This bound is achieved if and only if a function is APN.

Dominated and absolutely summing operators on the space Crc(X,E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,C_{rc}(X,E)$$\\end{document} of vector-valued continuous functions

Let X be a completely regular Hausdorff space and E and F be Banach spaces. Let Crc(X,E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{rc}(X,E)$$\\end{document} denote the Banach space of all continuous functions f:X→E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:X\\rightarrow E$$\\end{document} such that f(X) is a relatively compact set in E, and βσ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _\\sigma $$\\end{document} be the strict topology on Crc(X,E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{rc}(X,E)$$\\end{document}. We characterize dominated and absolutely summing operators T:Crc(X,E)→F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T:C_{rc}(X,E)\\rightarrow F$$\\end{document} in terms of their representing operator-valued Baire measures. It is shown that every absolutely summing (βσ,‖·‖F)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\beta _\\sigma ,\\Vert \\cdot \\Vert _F)$$\\end{document}-continuous operator T:Crc(X,E)→F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T:C_{rc}(X,E)\\rightarrow F$$\\end{document} is dominated. Moreover, we obtain that every dominated operator T:Crc(X,E)→F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T:C_{rc}(X,E)\\rightarrow F$$\\end{document} is absolutely summing if and only if every bounded linear operator U:E→F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U:E\\rightarrow F$$\\end{document} is absolutely summing.

Mimetic Weyl geometric gravity

We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space–time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained by starting from a conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and an effective matter term, respectively. After linearizing the action in the Weyl scalar by introducing an auxiliary scalar field, we include the mimetic field, constructed from the same auxiliary scalar field used to linearize the action, via a Lagrange multiplier. The conformal invariance of the action is maintained by imposing the trace condition on the effective matter energy–momentum tensor, built up from the ordinary matter Lagrangian, and some specific functions of the Weyl vector, and the scalar field, respectively, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the Mimetic Weyl geometric gravity by considering the dynamics of an isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker FLRW Universe. The generalized Friedmann equations of the model are derived, and their solutions are obtained numerically for a dust filled Universe. Moreover, we perform a detailed comparison of the predictions of the considered model with a set of observational data for the Hubble function, and with the results of the ΛCDM standard paradigm. Our results indicate that the present model give a good description of the observational data, and they reproduce almost exactly the predictions of the ΛCDM scenario. Hence, Mimetic Weyl geometric gravity can be considered a viable alternative to the standard approaches to cosmology, and to the gravitational phenomena.

Environmental pollution by plasticizers and the relationship to vector dengue mosquito Aedes aegypti: Bisphenol A (BPA) affect the development and viral immune pathway response

Bisphenol A (BPA) is a widely used industrial chemical found in various products, leading to human exposure through dietary and non-dietary sources. It acts as an endocrine disruptor, affecting reproductive processes in vertebrates by binding to estrogen receptors. While its effects on vertebrates have been extensively studied, much less is known about its impact on invertebrates. This study investigates the effects of BPA on the development and immune response of Aedes aegypti mosquitoes, which are important vectors for arboviral diseases, such as dengue, an emergent viral disease worldwide. Artificial aquatic niches (AAN) were sampled, and BPA concentrations were quantified. Ae. aegypti larvae were exposed to varying BPA concentrations, and their development, fecundity, fertility, and immune response were assessed. Results show delayed development and decreased emergence of mosquitoes exposed to BPA. Females exposed to BPA exhibited reduced oviposition while hatching rates remained unaffected. Furthermore, BPA exposure altered the expression of immune response genes in adult mosquitoes, with differential effects observed between sexes. This suggests that BPA exposure during early developmental stages can modulate the antiviral immune response in adult mosquitoes, possibly through the 20-hydroxyecdysone (20E) signaling pathway. Overall, this study highlights the potential impact of BPA on the development and immune function of mosquito vectors, with implications for vector competence and disease transmission.

Determination of Velocities of Thread Axis Points When Interacting with a Direct Large Curvature Taking into Account the Deformation in the Contact Zone

The theoretical study of the process of the movement of the thread, which is deformed in the contact zone with the guide, from the point of view of determining the speed, is of great importance for solving a number of specific applied problems. When determining the speed, it was assumed that the start of the Lagrangian and Euler coordinates coincided. Taking into account that the crumpling of the thread in the contact zone occurs at forces much lower than the forces required to stretch the thread, the thread was considered as non-extensible. To determine the law of the distribution of the speed of the points of the thread, an independent vector, which is always connected to the main triangle, was introduced into consideration. The relationship between the vector of total curvature and the vector of absolute angular velocity is obtained. The obtained values of the speed at an arbitrary point of the axis of the thread as a function of the deformation vector, which determines the degree of twisting of the thread in the contact zone. The obtained results can be used to study various technological processes in the sewing, knitting, and textile industries, where the movement of the thread takes place along the guide surface of great curvature.

A weakly coupled system of p-Laplace type in a heat conduction problem

Abstract Given is a bounded domain Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} , and a vector-valued function defined on ∂ ⁡ Ω {\partial\Omega} (depicting temperature distributions from different sources), our objective is to study the mathematical model of a physical problem of enclosing ∂ ⁡ Ω {\partial\Omega} with a specific volume of insulating material to reduce heat loss in a stationary scenario. Mathematically, this task involves identifying a vector-valued function 𝐮 = ( u 1 , … , u m ) {\mathbf{u}=(u^{1},\dots,u^{m})} ( m ≥ 1 {m\geq 1} ) that represents the temperature within Ω and gives rise to a free boundary, somehow reminiscent of, but not equivalent to, the Bernoulli free boundary problem.

Dynamic Response Analysis of Asphalt Pavement under Pavement-Unevenness Excitation

This paper investigates and analyzes the dynamic response of asphalt pavement under pavement-unevenness excitation based on an orthogonal vector function system and efficient DVP (dual variable and position) method. Firstly, starting from the pavement unevenness of the vehicle excitation source, the pavement-unevenness excitation is established by using the filtered white-noise method, and the random load of the vehicle model is obtained by simulation. Then, based on the basic governing equation of the road-surface problem under the random load, the analytical solution of the road-surface mechanical response is obtained by using the orthogonal vector function system and DVP method. The effects of pavement-unevenness grade, vehicle speed, vehicle load, interlayer contact condition, and transverse isotropy on the mechanical response of the road surface are analyzed via the analytical results. The results show that DVP can effectively solve the dynamic response of pavements under the excitation of pavement unevenness; in addition, it can also be applied to certain situations, such as transverse isotropy of materials and interface conditions. The results show that the pavement unevenness does not affect the average stress and strain of each layer but has a significant effect on the peak value and dispersion degree. An increase in vehicle speed causes a peak in strain and a larger coefficient of variation. Poor bonding between interfaces can lead to increased stress and strain at the bottom of the surface layer.

Classifying fabric wrinkle via regularized random vector function link optimized by African vultures optimization algorithm

The wrinkling of fabrics not only affects their aesthetic appeal and comfort but also leads to increased wear and a reduced lifespan. Consequently, wrinkle resistance has become a critical metric in evaluating fabric performance. Traditional wrinkle grading methods rely heavily on expert assessments, which are susceptible to visual fatigue, resulting in subjective and inconsistent classification outcomes. To address this issue, this article proposes an automatic wrinkle grading model based on an improved African Vultures Optimization (AVO) algorithm, which optimizes a regularized random vector functional link (RRVFL) network. The model enhances convergence speed and classification accuracy by incorporating the Harris Hawks Optimization (HHO) algorithm to provide a superior initial population for the AVO algorithm. Additionally, the AVO algorithm’s local search capability is strengthened during the optimization process, improving the model’s stability and resistance to overfitting. Experimental results demonstrate that the proposed HHO-AVO-RRVFL model achieves an average classification accuracy of 97.86% across multiple datasets, significantly outperforming other comparative algorithms while also excelling in classification stability and convergence speed.

Tests for equality of several mean vector functions for multivariate functional data with applications

In various scientific and technological fields, it is common to encounter multivariate functional data, where continuous vector functions for statistical units are observed over a specific interval. This paper aims to investigate the equality of mean vector functions in multi-sample multivariate functional data. To accomplish this, two novel global testing statistics are introduced by integrating or maximising the pointwise Lawley-Hotelling trace test statistic. The paper also provides asymptotic expressions for these proposed testing statistics under the null hypothesis and establishes their consistency with respect to the square root of the sample size. The performance of the two new testing procedures is demonstrated through simulation studies and the analysis of a real-world data example, highlighting their advantages over existing methods.

Interval observers for hybrid continuous-time stationary systems

The problem of interval observer design for hybrid continuous-time stationary systems under external disturbances and measurement noise is studied. It is assumed that continuous-time dynamic of such systems is described by linear or nonlinear differential state equations with linear function of output. System parameters depend on system states and are switched based on the control system with finite set of states. The relations allowing designing hybrid interval observer of minimal dimension estimating the set of admissible values of the prescribed linear vector function of the system states are derived. To solve the problem, algebra of partitions and linear algebra are used. Theoretical results are illustrated by example.

Contrast gain control is a reparameterization of a population response curve.

Neurons in primary visual cortex (area V1) adapt in varying degrees to the average contrast of the environment, suggesting that the representation of visual stimuli may interact with the state of cortical gain control in complex ways. To investigate this possibility, we measured and analyzed the responses of neural populations in mouse V1 to visual stimuli as a function of contrast in different environments, each characterized by a unique distribution of contrast values. Our findings reveal that, for a fixed stimulus, the population response can be described by a vector function r(gec), where the gain ge is a decreasing function of the mean contrast of the environment. Thus, gain control can be viewed as a reparameterization of a population response curve, which is invariant across environments. Different stimuli are mapped to distinct curves, all originating from a common origin, corresponding to a zero-contrast response. Altogether, our findings provide a straightforward, geometric interpretation of contrast gain control at the population level and show that changes in gain are well-matched among members of a population.

Modified Tn7 transposon vectors for controlled chromosomal gene expression.

Complementation remains a foundation for demonstrating molecular Koch's postulates. While this is frequently achieved using plasmids, limitations such as increased gene copy number and the need for antibiotic supplementation to avoid plasmid loss can restrict their use. Chromosomal integration systems using the Tn7 transposon provide an alternative to plasmids for complementation and facilitate the stable insertion of genes at the chromosomal attTn7 site without the need for selection pressure. Here, we enhanced the utility of mini-Tn7 insertion vectors by the addition of inducible (Pcym) and constitutive (PcL and PrpsM) promoters, allowing differential transcriptional control of genes integrated into the chromosome. We validated the utility of these promoters by cloning the gfp gene, encoding green fluorescent protein, downstream of each promoter and integrating a mini-Tn7 construct harboring these elements into the attTn7 site on the chromosome of the Escherichia coli K-12 strain MG1655. The PcL and PrpsM promoters provided equivalent levels of GFP expression and offered flexibility based on the target host strain. Activation of the tightly regulated Pcym promoter with its inducer cumate resulted in tunable expression of GFP in a dose-dependent manner. We further demonstrated the tight control of the Pcym promoter using the toxic impCAB genes, and the expression of which is detrimental to E. coli viability. Together, these modified mini-Tn7 vectors allowing differential control of genes integrated into the chromosome at a conserved site offer an efficient system for complementation where plasmid use is restricted.IMPORTANCEChromosomal integration using mini-Tn7 vectors provides an efficient means to insert genes into the chromosome of many gram-negative bacteria. Insertion occurs at a conserved site and allows for the stable integration of genes in single copy. While this system has multiple benefits for enabling complementation, a cornerstone for fulfilling molecular Koch's postulates, greater flexibility for controlled gene expression would enhance its utility. Here, we have added to the function of mini-Tn7 vectors by the addition of inducible and constitutive promoters and demonstrated their capacity to drive the controlled expression of target genes integrated into the chromosome. In addition to complementation, these modified vectors offer broad application for other approaches including chromosomal tagging, in vivo expression, metabolic engineering, and synthetic biology.

On the Univariate Vector-Valued Rational Interpolation and Recovery Problems

In this paper, we consider a novel vector-valued rational interpolation algorithm and its application. Compared to the classic vector-valued rational interpolation algorithm, the proposed algorithm relaxes the constraint that the denominators of components of the interpolation function must be identical. Furthermore, this algorithm can be applied to construct the vector-valued interpolation function component-wise, with the help of the common divisors among the denominators of components. Through experimental comparisons with the classic vector-valued rational interpolation algorithm, it is found that the proposed algorithm exhibits low construction cost, low degree of the interpolation function, and high approximation accuracy.

Construction of Vector-Valued Weak Separation Functions with Applications to Conjugate Duality in Vector Optimization

Construction of Vector-Valued Weak Separation Functions with Applications to Conjugate Duality in Vector Optimization

A mean shift algorithm incorporating reachable distance for spatial clustering

Spatial clustering is a widely used technique in spatial analysis that groups similar objects together based on their proximity in space. However, traditional clustering algorithms often fail to ensure the accessibility of cluster centers, which limits their validity in practical applications such as facility location problems. To address this issue, this article introduces a novel Mean Shift algorithm that incorporates reachable distance and an iterative mechanism to accurately locate cluster centers. The proposed algorithm initially labels clustering elements with road network coordinates to facilitate the calculation of reachable distance and the cluster center iterative mechanism. Subsequently, the mean shift vector function is modified to employ reachable distance as the measure of geographic reachable similarity. Unlike existing algorithms, our approach allows for cluster centers to be positioned independently of the clustering elements, guaranteeing geographical accessibility. Through simulation experiments, we demonstrate that our proposed algorithm not only outperforms existing methods in terms of solution quality, but also effectively addresses the limitations of disregarding geographical obstacles and unreachable cluster centers.

On the Dai–Liao conjugate gradient method for vector optimization

Several conjugate gradient (CG) parameters have led to promising methods for optimization problems. However, some parameters, such as the Dai-Liao (DL+) and modified Polak-Ribière-Polyak (EPRP) methods, have not yet been explored in the vector optimization setting. This paper addresses this gap by proposing the DL+ and EPRP+ methods to vector optimization. We start by developing a self-adjusting DL+ algorithm to find critical points of vector-valued functions within a closed, convex, pointed cone with a nonempty interior. The algorithm is designed to satisfy the sufficient descent condition (SDC) with a Wolfe line search; if this condition is not satisfied, the algorithm adjusts by redefining the DL+ to meet the SDC. We establish the global convergence of this algorithm under the assumption of SDC without requiring regular restarts or convexity assumption on the objective functions. Similarly, we developed the EPRP+ algorithm using the same approach as the DL+ algorithm. Furthermore, under exact line search, the DL+ and EPRP+ methods reduce to Hestenes-Stiefel (HS) and Polak-Ribière-Polyak (PRP) methods, respectively. We present numerical experiments on some selected test problems sourced from the multiobjective optimization literature that demonstrate the effectiveness and practical implementation of the proposed algorithms, highlighting their promising potential.

Perfect Monomial Prediction for Modular Addition

Modular addition is often the most complex component of typical Addition- Rotation-XOR (ARX) ciphers, and the division property is the most effective tool for detecting integral distinguishers. Thus, having a precise division property model for modular addition is crucial in the search for integral distinguishers in ARX ciphers. Current division property models for modular addition either (a) express the operation as a Boolean circuit and apply standard propagation rules for basic operations (COPY, XOR, AND), or (b) treat it as a sequence of smaller functions with carry bits, modeling each function individually. Both approaches were originally proposed for the twosubset bit-based division property (2BDP), which is theoretically imprecise and may overlook some balanced bits.Recently, more precise versions of the division property, such as parity sets, threesubset bit-based division property without unknown subsets (3BDPwoU) or monomial prediction (MP), and algebraic transition matrices have been proposed. However, little attention has been given to modular addition within these precise models.The propagation rule for the precise division property of a vectorial Boolean function f requires that u can propagate to v if and only if the monomial πu(x) appears in πv(f). Braeken and Semaev (FSE 2005) studied the algebraic structure of modular addition and showed that for x ⊞ y = z, the monomial πu(x)πv(y) appears in πw(z) if and only if u + v = w. Their theorem directly leads to a precise division property model for modular addition. Surprisingly, this model has not been applied in division property searches, to the best of our knowledge.In this paper, we apply Braeken and Semaev’s theorem to search for integral distinguishers in ARX ciphers, leading to several new results. First, we improve the state-of-the-art integral distinguishers for all variants of the Speck family, significantly enhancing search efficiency for Speck-32/48/64/96 and detecting new integral distinguishers for Speck-48/64/96/128. Second, we determine the exact degrees of output bits for 7-round Speck-32 and all/16/2 output bits for 2/3/4-round Alzette for the first time. Third, we revisit the choice of rotation parameters in Speck instances, providing a criterion that enhances resistance against integral distinguishers. Additionally, we offer a simpler proof for Braeken and Semaev’s theorem using monomial prediction, demonstrating the potential of division property methods in the study of Boolean functions.We hope that the proposed methods will be valuable in the future design of ARX ciphers.

The BSE property for some vector-valued Banach function algebras

The BSE property for some vector-valued Banach function algebras

Nonlinear conjugate gradient methods for unconstrained set optimization problems whose objective functions have finite cardinality

In this paper, we propose nonlinear conjugate gradient methods for unconstrained set optimization problems in which the objective function is given by a finite number of continuously differentiable vector-valued functions. First, we provide a general algorithm for the conjugate gradient method using Wolfe line search but without imposing an explicit restriction on the conjugate parameter. Later, we study two variants of the algorithm, namely Fletcher-Reeves and conjugate descent, using two different choices of the conjugate parameter but with the same line search rule. In the general algorithm, the direction of movement at each iterate is identified by finding out a descent direction of a vector optimization problem. This vector optimization problem is identified with the help of the concept of partition set at the current iterate. As this vector optimization problem is different at different iterations, the conventional conjugate gradient method for vector optimization cannot be straightly extended to solve the set optimization problem under consideration. The well-definedness of the methods is provided. Further, we prove the Zoutendijk-type condition, which assists in proving the global convergence of the methods even without a regular condition of the stationary points. No convexity assumption is assumed on the objective function to prove the convergence. Lastly, some numerical examples are illustrated to exhibit the performance of the proposed method. We compare the performance of the proposed conjugate gradient methods with the existing steepest descent method. It is found that the proposed method commonly outperforms the existing steepest descent method for set optimization.