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We investigate the numerical accuracy of the extended Koopmans's theorem (EKT) in reproducing the full configuration interaction (FCI) and complete active-space configuration interaction (CAS-CI) ionization energies (IEs) of atomic and molecular systems calculated as the difference between the energies of N and (N − 1) electron states. In particular, we study the convergence of the EKT IEs to their exact values as the basis set and the active space sizes vary. We find that the first FCI EKT IEs approach their exact counterparts as the basis set size increases. However, increasing the basis set or the active space sizes does not always lead to more accurate CAS-CI EKT IEs. Our investigation supports the observation of Davidson et al. [J. Chem. Phys. 155, 051102 (2021)] that the FCI EKT IEs can be systematically improved with arbitrary numerical accuracy by supplementing the basis set with diffuse functions of appropriate symmetry, which allow the detached electron to travel far away from the reference system. By changing the exponent and the center of the diffuse functions, our results delineate a complex pattern for the CAS-CI EKT IE of LiH, which can be important for the spectroscopic studies of small molecules. [ABSTRACT FROM AUTHOR]

Basis sets consisting of functions that form linearly independent products (LIPs) have remarkable applications in quantum chemistry but are scarce because of mathematical limitations. We show how to linearly transform a given set of basis functions to maximize the linear independence of their products by maximizing the determinant of the appropriate Gram matrix. The proposed method enhances the utility of the LIP basis set technology and clarifies why canonical molecular orbitals form LIPs more readily than atomic orbitals. The same approach can also be used to orthogonalize basis functions themselves, which means that various orthogonalization techniques may be viewed as special cases of a certain nonlinear optimization problem. [ABSTRACT FROM AUTHOR]

Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided. [ABSTRACT FROM AUTHOR]

Vector inversion generators or spiral generators are compact, high voltage pulse generators consisting of a pair of conducting foils wound in a spiral and a switch. We developed an improved analytical model predicting the time evolution of the output voltage of such spiral generators. Our model (i) takes into account that the current in the switch results from the current on active and passive waveguides and (ii) takes into account the losses of the conductor in equations describing the propagation of voltage and current pulses in both waveguides. The model is compared to experimental results involving different input switches and at different temperatures to investigate the influence of resistive losses on the output voltage. The model is further developed to obtain the time evolution of the current in the switch. Our model is then used to predict the amplitude of the first two peaks of the oscillatory response of spiral generators as a function of a set of dimensionless parameters. [ABSTRACT FROM AUTHOR]

We present a method to compute the photoionization spectra of atoms and molecules in linear-response, time-dependent density functional theory. The electronic orbital variations corresponding to ionized electrons are expanded on a basis set of delocalized functions, obtained as the solution of the inhomogeneous Helmholtz equation, with gaussian basis set functions as the right-hand side. The resulting scheme is able to reproduce the photoionization spectra without any need for artificial regularization or localization. We demonstrate that this Green's function-based approach is able to produce accurate spectra for semilocal exchange-correlation functionals, even using relatively small standard gaussian basis sets. [ABSTRACT FROM AUTHOR]

We investigate, in this paper, the Gaussian (G) function with odd powers of r, rxaybzc exp(−αr2), called the r-Gaussian or simply the rG function. The reason we investigate this function here is that it is generated as the elements of the complement functions (cf's) when we apply the free complement (FC) theory for solving the Schrödinger equation to the initial functions composed of the Gaussian functions. This means that without the rG functions, the Gaussian set of functions cannot produce the exact solutions of the Schrödinger equation, showing the absolute importance of the rG functions in quantum chemistry. Actually, the rG functions drastically improve the wave function near the cusp region. This was shown by the applications of the present theory to the hydrogen and helium atoms. When we use the FC-sij theory, in which the inter-electron function rij is replaced with its square s i j = r i j 2 that is integrable, we need only one- and two-electron integrals for the G and rG functions. The one-center one- and two-electron integrals of the rG functions are always available in a closed form. To calculate the integrals of the multi-centered rG functions, we proposed the rG-NG expansion method, in which an rG function is expanded by a linear combination of the G functions. The optimal exponents and coefficients of this expansion were given for N = 2, 3, 4, 5, 6, and 9. To show the accuracy and the usefulness of the rG-NG method, we applied the FC-sij theory to the hydrogen molecule. [ABSTRACT FROM AUTHOR]

The design of continuum structures often presents challenges related to stress concentration, which can cause significant structural damage. To address this issue, the current study presents a new stress minimization method that utilizes the Windowed Evolutionary Structural Optimization (WESO) framework. The method aims to improve algorithm stability by optimizing design variables with an intermediate density. The use of a P‐norm stress aggregation method improves the assessment of global stress levels and enhances computational efficiency. Furthermore, a stable element sensitivity formulation, derived from the adjoint sensitivity analysis of the global stress measure, effectively handles the nonlinear stress behavior. Mesh filtering techniques are utilized to convert sensitivity from elements to nodes, and the structural topological solution is represented using the level set function (LSF) based on element‐node sensitivity. This method addresses the singularity issue commonly found in density‐based optimization methods and facilitates the achievement of smooth topological solutions. Through 2D and 3D benchmark designs, the proposed method's feasibility, stability, and superiority are thoroughly demonstrated. A parametric study is conducted to identify the optimal parameter range for the algorithm, leading to the development of a rational method for parameter selection. The optimized topology, with its smooth boundaries, can guide the design of structures without the need for redesign or post‐processing, helping to drive innovation and development in engineering. [ABSTRACT FROM AUTHOR]

The biological system has attracted many researchers with a lot of smart advances in the control system field. The control approaches have been effectively utilized in biological application to regulate the biological parameter functions based on the set point and threshold value. However, the controller's high disturbance has resulted in low gain and tuning performance. So, the current work has expected to plan a new African Buffalo based Recurrent Fractional-Order Sliding Mode (ABR-FOSM) for the biological system to tune the specific parameters like protein, pancreas, and Genetic Regulatory Network (GRN). Here, the incorporation of the buffalo algorithm has provided better tuning results. Moreover, the robustness of the designed controller has been validated by gaining the finest tuning performance and reduced Error and settling time. [ABSTRACT FROM AUTHOR]

AbstractLow-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relationships between the cardinalities of the set of injections, the set of surjections, and the set of all functions on a set which is of cardinality m$\mathfrak {m}$, denoted by I(m)$I(\mathfrak {m})$, J(m)$J(\mathfrak {m})$ and mm$\mathfrak {m}^\mathfrak {m}$, respectively. Among our results, we show that “seq1−1(m)≠I(m)≠seq(m)$\operatorname{seq}^{1-1}(\mathfrak {m})\ne I(\mathfrak {m})\ne \operatorname{seq}(\mathfrak {m})$”, “seq1−1(m)≠J(m)≠seq(m)$\operatorname{seq}^{1-1}(\mathfrak {m})\ne J(\mathfrak {m})\ne \operatorname{seq}(\mathfrak {m})$” and “seq1−1(m)

Some properties and applications of generalized convex sets and generalized convex functions in multidimensional real, complex, and hypercomplex spaces are described. [ABSTRACT FROM AUTHOR]

Emergy is a concept that is important for understanding problems in accounting for the health and integrity of ecological and social systems. Success in the evolutionary competition among systems depends on maximizing the emergy captured by a system that is then fed back to bring in more exergy. For this reason, "emergy" in the form of maximum empower (i.e., maximum emergy flow measured in solar emjoules or sej/unit time) provides a unified, thermodynamically controlled decision criterion by which the behavior of all systems is constrained. The fact that maximum empower and not maximum profit is nature's decision criterion makes it critical that more people become familiar with emergy evaluations and how to use the results of these analyses in decision-making. A new approach to emergy evaluation is proposed that focuses on developing more accurate assessments of the spatial and temporal emergy accounting required for the creation of products and services. These emergy evaluations include the accumulated past action of exergy in creating key system components such as vegetation biomass and the accumulated knowledge of workers in the economy, which will result in emergy assessments that better reflect the capacity of the products and services to do work in their systems. An analysis of the Geobiosphere is presented as a "white box" model of the secondary and tertiary flows of wind and water in the global system. The key factors identified are the separation of wind into two components: a factor controlling vertical diffusion with transformity of =715 sej J-1 and a second transformity governing surface friction of =1,215 sej J-1. Also, water systems are fully defined with transformities of 302,900 sej J-1 to 1,440,000 sej J-1 for geostrophic flows. Past emergy analyses show that managers should develop policies that will maximize the empower flowing through their systems. The problem of maximizing the empower captured occurs within the context of a set of forcing functions impinging on a system from the next larger system, and since these forcing functions are always changing, maximum power should not be thought of as a fixed endpoint but rather as a constant state of seeking this goal. [ABSTRACT FROM AUTHOR]

We study the set of curvature functions which a given compact manifold with boundary can possess. First, we prove that the sign demanded by the Gauss–Bonnet Theorem is a necessary and sufficient condition for a given function to be the geodesic curvature or the Gaussian curvature of some conformally equivalent metric. Our approach allows us to solve problems that are impossible to solve in the pointwise conformal case. Moreover, we obtain a deep and more delicate information on pointwise conformal deformations. We prove new existence and nonexistence results for metrics with prescribed curvature in the conformal setting, which depend on the Euler characteristic. [ABSTRACT FROM AUTHOR]

The real world consists of mass phenomena, such as iridescence on thin film and metal oxide layers, that is only explicable by wave optics. Existing research can reproduce such effects with simple point lights or low‐frequency environmental lighting. However, it remains a difficult task to efficiently rendering these effects when near‐field, high‐frequency area lights are involved. This paper presents a high‐fidelity, real‐time rendering algorithm for the iridescence effect under polygonal lights. We introduce a novel set of spherical functions, Monomial‐Gaussians, to accurately fit iridescent materials' reflectance. With a precomputed lookup table, the Monomial‐Gaussians are easily integrated over spherical polygons in linear time. Importance sampling of Monomial‐Gaussians is also supported to efficiently reduce Monte‐Carlo error. Our approach produces accurate renderings of the iridescence effect while still preserving high frame rates. [ABSTRACT FROM AUTHOR]

Many real-world applications arising from social networks, personalized recommendations, and others, require extracting a relatively small but broadly representative portion of massive data sets. Such problems can often be formulated as maximizing a monotone set function with cardinality constraints. In this paper, we consider a streaming model where elements arrive quickly over time, and create an effective, and low-memory algorithm. First, we provide the first single-pass linear-time algorithm, which is a a deterministic algorithm, achieves an approximation ratio of [ γ 4 a (1 + γ + γ 2 + γ 3) − ] for any ≥ 0 with a query complexity of ⌈ n / a ⌉ + a and a memory complexity of O (a k log (k) log (1 /)) , where a is a positive integer and γ is the submodularity ratio. However, the algorithm may produce less-than-ideal results. Our next result is to describe a multi-streaming algorithm, which is the first deterministic algorithm to attain an approximation ratio of 1 − e − γ − with linear query complexity. [ABSTRACT FROM AUTHOR]

Context: Analytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses. Method: All calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt3Cu)n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores. [ABSTRACT FROM AUTHOR]

Research and development of power factor corrector (PFC) for AC/DC converters of single-phase AC power supply network are discussed within this article. Two-channel bridgeless PFC is proposed in this paper. The proposed converter allows us to lower current DC component generation in the power network and to reduce static and dynamic losses of semiconductor devices. The suggested solution characteristic features are the absence of a diode bridge while using two identical converters operating in different power network voltage half periods. Due to cumulative chokes in each converter, the function setting the consumption current sinusoidal form is realized with the ability of wide-range output voltage regulation. A number of Simulink-models have been developed in order to study operating modes and to test control algorithms of the proposed bridgeless PFC. The input current harmonic content, efficiency coefficient, passive elements' electrical parameters, and output voltage pulsation coefficient of the proposed bridgeless PFC were researched by Simulink-models. The results obtained show the efficiency of the proposed solutions regarding PFC. The THD value does not exceed 1.3% in steady state mode and is not over 4% during the voltage stabilization process; the minimal value of the output voltage pulsation coefficient is 3.1%. The suggested solutions can be applied in accumulator batteries' charging sets and DC motors' reduced-current start. [ABSTRACT FROM AUTHOR]

Variational multiscale methods and their precursors, stabilized methods, which are sometimes supplemented with discontinuity-capturing (DC) methods, have been playing their core-method role in flow computations increasingly with isogeometric discretization. The stabilization and DC parameters embedded in most of these methods play a significant role. The parameters almost always involve some local-length-scale expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. The direction-dependent expressions introduced earlier target B-splines meshes for complex geometries. The key stages of deriving these expressions are mapping the direction vector from the physical element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. Here, we extend the local-length-scale calculation method to meshes built from T-splines. T-splines meshes are a superset of B-splines meshes. They provide smooth basis functions in complex geometry and effective refinement without subdividing where we do not need higher resolution. In this article, we focus on the product form T-splines basis functions. They are represented individually in product form, from multiplication of n pd 1D basis functions, where n pd is the number of parametric dimensions. Each 1D basis function comes from the set of functions associated with one of the parametric directions and the set of functions is defined considering the T-splines nature of the mesh. The product-form basis functions satisfy the partition of unity without using rational functions. For these T-splines, based on the method introduced for B-splines, the local length scales are calculated with Bézier-extraction row operators, which are element-level constants. Using T-splines involves element splitting also for increased integration accuracy. Our local-length-scale expressions are invariant with respect to element splitting performed for integration accuracy but account for the element splitting that is for enhancing the function space. [ABSTRACT FROM AUTHOR]

A Fan-Theobald-von Neumann system [7] is a triple (V , W , λ) , where V and W are real inner product spaces and λ : V → W is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decomposition systems (Eaton triples). The present article is a continuation of [9] where the concepts of commutativity, automorphisms, majorization, and reduction were introduced and elaborated. Here, we describe some transfer principles and present Fenchel conjugate and subdifferential formulas. [ABSTRACT FROM AUTHOR]

In this paper, we first present necessary and sufficient conditions for the existence of global error bounds for a convex function without additional conditions on the function or the solution set. In particular, we obtain characterizations of such global error bounds in Euclidean spaces, which are often simple to check. Second, we prove that under a suitable assumption the subdifferential of the supremum function of an arbitrary family of convex continuous functions coincides with the convex hull of the subdifferentials of functions corresponding to the active indices at given points. As applications, we study the existence of global error bounds for infinite systems of linear and convex inequalities. Several examples are provided as well to explain the advantages of our results with existing ones in the literature. [ABSTRACT FROM AUTHOR]

Traditional deterministic optimization algorithms are difficult to effectively solve many real-world nonlinear, complex, and high-dimensional optimization problems. The metaheuristic optimization algorithm has evolved in recent years into a kind of very popular algorithm due to its gradient-free and random nature. In this paper, a new metaheuristic algorithm, namely the literature research optimization algorithm (LRO), is proposed. In this algorithm, the literature research process is represented as a mathematical model, and new mechanisms are designed to help realize the global exploration and local exploitation. To evaluate the performance of LRO, three sets of test functions including the standard benchmark set, CEC2017, and CEC2019 are applied first, and then, six engineering problems are employed to further verify it. The Friedman test and Wilcoxon rank sum test are also used to statistically compare the proposed LRO algorithm with ten common existing metaheuristics. The results show that the LRO algorithm outperforms the comparison algorithms on most benchmark functions and that it also performs well in practical engineering applications. The LRO algorithm can provide superior solutions to most optimization problems compared to other metaheuristic algorithms and become a promising candidate for many real-life optimization problems. [ABSTRACT FROM AUTHOR]

We investigate finite sets of rational functions { f 1 , f 2 , ... , f r } defined over some number field K satisfying that any t 0 ∈ K is a K p -value of one of the functions f i for almost all primes p of K. We give strong necessary conditions on the shape of functions appearing in a minimal set with this property, as well as numerous concrete examples showing that these necessary conditions are in a way also close to sufficient. We connect the problem to well-studied concepts such as intersective polynomials and arithmetically exceptional functions. [ABSTRACT FROM AUTHOR]

New continuous-time models and statistical methods have been developed to estimate some sets related to animal movement, such as the home-range and the core-area among others, when the information of the trajectory is provided by a GPS. Because data transfer costs and GPS battery life are practical constraints, the experimental designer must make critical sampling decisions to maximise information. We introduce the on–off sampling scheme, where the GPS is alternately on and off. This scheme is already used in practice but with insufficient statistical theoretical support. We prove the consistency of home-range estimators with an underlying reflected diffusion model under this sampling method. The same rate of convergence is achieved as in the case where the GPS is always on for the whole experiment. This is illustrated by a simulation study and real data. We also provide estimators of the stationary distribution, its level sets and the drift function. [ABSTRACT FROM AUTHOR]

The primary purpose of this paper is to generalize the classical Riemann zeta function to the setting of Krull monoids with torsion class groups. We provide a first study of the same generalization by extending Euler's classical product formula to the more general scenario of Krull monoids with torsion class groups. In doing so, the Decay Theorem is fundamental as it allows us to use strong atoms instead of primes to obtain a weaker version of the Fundamental Theorem of Arithmetic in the more general setting of Krull monoids with torsion class groups. Several related examples are exhibited throughout the paper, in particular, algebraic number fields for which the generalized Riemann zeta function specializes to the Dedekind zeta function. [ABSTRACT FROM AUTHOR]

We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situations. [ABSTRACT FROM AUTHOR]

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum scalarization of the MOIP. At unsupported solutions, the convex hull relaxation is not tight and a Lagrangian relaxation may provide a tighter bound. Using the Lagrangian relaxation, we define a Lagrangian dual of an MOIP that satisfies weak duality and is strong at supported solutions under certain conditions on the primal feasible region. We include a numerical experiment to illustrate that bound sets obtained via Lagrangian duality may yield tighter bounds than those from a convex hull relaxation. Subsequently, we generalize the integer programming value function to MOIPs and use its properties to motivate a set-valued superadditive dual that is strong at supported solutions. We also define a simpler vector-valued superadditive dual that exhibits weak duality but is strongly dual if and only if the primal has a unique nondominated point. [ABSTRACT FROM AUTHOR]

We conjecture a formula for the rational q, t-Catalan polynomial C r / s that is symmetric in q and t by definition. The conjecture posits that C r / s can be written in terms of symmetric monomial strings indexed by maximal Dyck paths. We show that for any finite d ∗ , giving a combinatorial proof of our conjecture on the infinite set of functions { C r / s d : r ≡ 1 mod s , d ≤ d ∗ } is equivalent to a finite counting problem. [ABSTRACT FROM AUTHOR]

In this article, we consider a modified version of minimal L2 integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As applications, we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces. [ABSTRACT FROM AUTHOR]

Background: This cross-sectional study aimed to explore the variation trend of renal function for healthy pregnant women at different gestational ages and aimed to establish RIs for renal function set tests according to the trimester of pregnancy. Methods: A total of 120 healthy pregnant women and 40 healthy non-pregnant women were enrolled in this study and divided into early trimester (1 - 13 weeks of gestation, n = 40), second trimester (14 - 27 weeks of gestation, n = 40), third trimester (≥ 28 weeks of gestation, n = 40), and a non-pregnant women group (n = 40). Analytes of UA, BUN, Cr, β2-MG, Cys-C, RBP, NAG, CO2, HCY, C1q, and NGAL were measured by using the analytical systems of the Second Xiangya Hospital. The RIs were defined by using non-parametric 95% intervals. Results: The RIs for UA, Cr, β2-MG, NAG, CO2, Hcy, and C1q were established for the first and second trimester group and the third trimester group. There were huge differences after pregnancy. The RIs for BUN were different for the 1 - 13 weeks group and the after 14 weeks group. There were significant differences for NGAL in pregnant and non-pregnant women, but not for Cys-C and RBP. Conclusions: The RIs for renal function tests in pregnant women were established, thus providing clinical reference intervals for the clinicians. [ABSTRACT FROM AUTHOR]

Employing the scaled memoryless BFGS (Broyden–Fletcher–Goldfarb–Shanno) updating formula, a multiplier of the identity matrix is proposed as an estimation of the inverse Hessian of the objective function. Incorporated into the proximal operator, the suggested spectral gradient vector has been employed to solve the nonsmooth sparse recovery problem. Taking sparsity property into consideration, a nonmonotone backtracking line search technique is put forward which is adjusted for the nonsmooth sparse recovery cost function. Convergence of the algorithm is analyzed based on the given line search. Ultimately, computational advantages of the algorithm are depicted on a class of randomly generated test problems as well as a set of the CUTEr functions. [ABSTRACT FROM AUTHOR]

For the distance function from any closed subset of any complete Finsler manifold, we prove that the singular set is equal to a countable union of delta‐convex hypersurfaces up to an exceptional set of codimension two. In addition, in dimension two, the whole singular set is equal to a countable union of delta‐convex Jordan arcs up to isolated points. These results are new even in the standard Euclidean space and shown to be optimal in view of regularity. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a generalization of (η1,η2)-convex functions using the local fractional calculus developed by Yang [Advanced Local Fractional Calculus and its Applications (World Science Publisher, New York, 2012)], namely generalized (η1,η2)-convex functions. Among other results, we obtain some Fejér-type inequalities for this class of functions. As applications, we present some inequalities with generalized probability density functions and generalized special means. [ABSTRACT FROM AUTHOR]

Weakly supervised semantic segmentation (WSSS) aims to segment objects without a heavy burden of dense annotations. Pseudo-masks serve as supervisory information for training segmentation models, which is crucial to the performance of segmentation models. However, the generated pseudo-masks contain significant noisy labels, which leads to poor performance of the segmentation models trained on these pseudo-masks. Few studies address this issue, as these noisy labels remain inevitable even after the pseudo-masks are improved. In this paper, we propose an uncertainty-weight transform module to mitigate the impact of noisy labels on model performance. It is noteworthy that our approach is not aimed at eliminating noisy labels but rather enhancing the robustness of the model to noisy labels. The proposed method adopts a frequency-based approach to estimate pixel uncertainty. Moreover, the uncertainty of pixels is transformed into loss weights through a set of well-designed functions. After dynamically assigning weights, the model allocates attention to each pixel in a significantly differentiated manner. Meanwhile, the impact of noisy labels on model performance is weakened. Experiments validate the effectiveness of the proposed method, achieving state-of-the-art results of 69.3% on PASCAL VOC 2012 and 39.3% on MS COCO 2014, respectively. [ABSTRACT FROM AUTHOR]

The article focuses on the importance of expanding and coordinating global regulatory capacity to better prepare for future pandemics. Topics include the need for equitable access to essential medical products; the challenges posed by the concentration of regulatory capacity in high-income countries; and the benefits of decentralizing regulatory review to accelerate access to diagnostics, therapeutics and vaccines.

We have introduced the R package jmBIG to facilitate the analysis of large healthcare datasets and the development of predictive models. This package provides a comprehensive set of tools and functions specifically designed for the joint modelling of longitudinal and survival data in the context of big data analytics. The jmBIG package offers efficient and scalable implementations of joint modelling algorithms, allowing for integrating large-scale healthcare datasets. By utilizing the capabilities of jmBIG, researchers and analysts can effectively handle the challenges associated with big healthcare data, such as high dimensionality and complex relationships between multiple outcomes. With the support of jmBIG, analysts can seamlessly fit Bayesian joint models, generate predictions, and evaluate the performance of the models. The package incorporates cutting-edge methodologies and harnesses the computational capabilities of parallel computing to accelerate the analysis of large-scale healthcare datasets significantly. In summary, jmBIG empowers researchers to gain deeper insights into disease progression and treatment response, fostering evidence-based decision-making and paving the way for personalized healthcare interventions that can positively impact patient outcomes on a larger scale. [ABSTRACT FROM AUTHOR]

This paper proposes a novel optimization method inspired by radar technology: wave search algorithm (WSA). The WSA algorithm not only draws on radar technology for its unique algorithmic design for the first time but also uses a new initialization method and boundary restriction rules, adopts various improved greedy mechanisms, and makes use of the gradient information of the problem to be optimized. As a result, the WSA algorithm is characterized by accuracy, efficiency, and adaptability. The superiority of the WSA algorithm is experimentally demonstrated by testing it with a rich set of test functions (23 benchmark test functions and 30 CEC-2017 test functions) and comparing it with state-of-the-art and highly cited algorithms. Finally, the WSA algorithm is applied to six common engineering problems and mobile robot path planning problems. The experimental results demonstrate that the optimization ability of the WSA algorithm is better than other state-of-the-art optimization algorithms, and it can efficiently solve practical engineering problems. The MATLAB code for WSA is available at https://github.com/haobinzhang123/A-heuristic-algorithm.git. [ABSTRACT FROM AUTHOR]

We study benign overfitting in the setting of nonparametric regression under mean squared risk, and on the scale of Hölder classes. We construct a local polynomial estimator of the regression function that is minimax optimal on a Hölder class with any given smoothness, and that is a continuous function interpolating the set of observations with high probability. The key element of the construction is the use of singular kernels. Moreover, we prove that adaptation to unknown smoothness is compatible with benign overfitting. Namely, we construct a continuous and interpolating local polynomial estimator attaining the minimax optimal rate in L 2 adaptively to the unknown Hölder smoothness. Our results highlight the fact that interpolation can be fundamentally decoupled from bias-variance tradeoff in the problem of nonparametric regression. [ABSTRACT FROM AUTHOR]

In this research, a novel method for enhancing the Hölder–Işcan inequality through the utilization of both integrals and sums, as well as the mean power inequality, has been introduced. This approach outperforms traditional Hölder and mean power integral inequalities by employing a finite set of functions. Through the careful selection of the function ϕ$$ \phi $$, an entirely new category of classical inequalities emerges for both Hölder and mean power inequalities. [ABSTRACT FROM AUTHOR]

Roughly speaking, the spectrum of multiplicative functions is the set of all possible mean values. In this paper, we are interested in the spectra of multiplicative functions supported over powerfull numbers. We prove that its real logarithmic spectrum takes values from − 2 / (4 + 2) = − 0.26160... to 1 while it is known that the logarithmic spectrum of real multiplicative functions over all natural numbers takes values from 0 to 1. In the course of this study, we correct and complete the proof of Granville and Soundararajan on the spectrum of all multiplicative functions. • Correct a proof of Granville and Soundararajan on the spectrum of multiplicative functions. • Extend the study of spectrum to multiplicative functions supported over powerfull / squarefull numbers. • The key idea of proof is the construction of accurate auxiliary multiplicative functions to decompose the original ones via Dirichlet convolution. [ABSTRACT FROM AUTHOR]

Membrane intrinsic proteins (MIPs), including aquaporins (AQPs) and aquaglyceroporins (GLPs), form an ancient family of transporters for water and small solutes across biological membranes. The evolutionary history and functions of MIPs have been extensively studied in vertebrates and land plants, but their widespread presence across the eukaryotic tree of life suggests both a more complex evolutionary history and a broader set of functions than previously thought. That said, the early evolution of MIPs remains obscure. The presence of one GLP and four AQP clades across both bacteria and archaea suggests that the first eukaryotes could have possessed up to five MIPs. Here, we report on a previously unknown richness in MIP diversity across all major eukaryotic lineages, including unicellular eukaryotes, which make up the bulk of eukaryotic diversity. Three MIP clades have likely deep evolutionary origins, dating back to the last eukaryotic common ancestor (LECA), and support the presence of a complex MIP repertoire in early eukaryotes. Overall, our findings highlight the growing complexity of the reconstructed LECA genome: the dynamic evolutionary history of MIPs was set in motion when eukaryotes were in their infancy followed by radiative bursts across all main eukaryotic lineages. [ABSTRACT FROM AUTHOR]

We give investigations on a kernel function approximation problem arising from learning theory and show the convergence rate from the view of classical Fourier analysis. First, we provide the general definition for a modulus of smoothness and a K -functional, and show that they are equivalent. In particular, we give explicit representation for some moduli of smoothness. Second, we establish some Jackson-type inequalities for the approximation error associated with some non-radial kernels. Also we apply these results to some concrete classical kernel function spaces and give Jackson-type inequalities for some concrete RKHS approximation problems. Finally, we apply these discussions to learning theory and describe the learning rates with the moduli of smoothness. The tools we used are Fourier analysis and the semigroup operator. The results show that the Jackson-type inequalities of approximation by some radial kernel functions on compact set with nonempty interiors cannot be expressed with the classical moduli of smoothness. [ABSTRACT FROM AUTHOR]

We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the Klein–Gordon equation having Schwartz initial data. In fact, there exist infinitely many independent such solutions. The proof is a variational argument based on the long range nature of the effective potential. We give two sets of test functions which serve to verify the hypothesis of the variational argument. One set consists of cutoff versions of the hydrogen bound states and is used to prove the existence of eigenvalues near the hydrogen spectrum. [ABSTRACT FROM AUTHOR]

Let X be an Archimedean vector lattice and X + denote the positive cone of X. A unary operation ϖ on X + is called a truncation on X if x ∧ ϖ y = ϖ x ∧ y for all x , y ∈ X +. Let X u denote the universal completion of X with a distinguished weak element e > 0. It is shown that a unary operation ϖ on X + is a truncation on X if and only if there exists an element u ∈ X u and a component p of e such that p ∧ u = 0 and ϖ x = p x + u ∧ x for all x ∈ X +. Here, px is the product of p and x with respect to the unique lattice-ordered multiplication in X u having e as identity. As an example of illustration, if ϖ is a truncation on some L p μ -space then there exists a measurable set A and a function u ∈ L 0 μ vanishing on A such that ϖ x = 1 A x + u ∧ x for all x ∈ L p μ. [ABSTRACT FROM AUTHOR]

The Tracking Algorithm for Mesoscale Convective Systems (TAMS) is a tracking, classifying, and variable-assigning algorithm for mesoscale convective systems (MCSs). TAMS was initially developed to analyze MCSs over Africa and their relation to African easterly waves using satellite-derived datasets. This paper describes TAMS, an open-source MCS tracking and classifying Python-based package that can be used to study both observed and simulated MCSs. Each step of the algorithm is described with examples showing how to make use of visualization and post-processing tools within the package. A unique and valuable feature of this MCS tracker is its support for unstructured grids in the MCS identification stage and grid-independent tracking of MCSs, enabling application across various native modeling grids and satellite-derived products. A description of the available settings and helper functions is also provided. Finally, we share some of the current development goals for TAMS. [ABSTRACT FROM AUTHOR]

In this study, a phase-field model with imperfect interface is developed to simulate the crack behavior of concrete at the mesoscale level. Concrete is treated as a biphasic material, comprising aggregates, a cementitious matrix, and interfaces between them, which are characterized using a level set function. Both cracks and interfaces are represented in a smeared sense by scalar fields ranging from 0 to 1. On the other hand, the displacement jump at the interface is described by an auxiliary field over the entire domain. This model effectively captures the complex crack patterns in concrete, including debonding cracks and bulk cracks. Furthermore, the results show that a strong interface can significantly enhance the mechanical performance of the material. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a distance measure on single-valued neutrosophic sets by sine function which is a generalization of intuitionistic fuzzy sine distance measure. The axiom of metric on single-valued neutrosophic sets is verified and shows that the difference of distance measure from unity is a similarity measure. A new methodology for multi-attribute decision-making problems (MADM) is developed for the most common decision by the smallest measure value of the proposed single-valued neutrosophic distance measure. We further apply this distance measure to a multi-attribute decision-making problem (MADM) for student career determination in a neutrosophic environment to find the best career for suitable students. Finally, the comparison is made between the proposed distance measure and the other distance measures for the final decision chosen from the most common decisions of them. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel high‐order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving partial differential equations featuring discontinuities. To address this challenge, we solve a constrained optimization problem aiming at accurately fitting the zero iso‐contour of a level set function to the discontinuities. Additionally, we discuss various robustness measures inspired by both numerical experiments and existing literature. Finally, we showcase the capabilities of our method through a series of two‐dimensional problems, progressively increasing in complexity. [ABSTRACT FROM AUTHOR]

In the classical Geometry of Numbers, the calculation of successive minima may be quite difficult, even in R2${\bf R}^2$ using the norm coming from a distance function associated to a set. In the literature, there seem to be hardly any analogues when R${\bf R}$ is replaced by the algebraic closure of a function field in one variable and one uses a norm arising from the absolute height. Here, we calculate a one‐parameter family of examples that naturally arose in our recent paper on bounded heights. We also comment on whether the minima are attained. [ABSTRACT FROM AUTHOR]

The study presents an optimized Unmanned Surface Vehicle (USV) collision avoidance decision-making strategy in restricted waters based on the improved Proximal Policy Optimization (PPO) algorithm. This approach effectively integrates the ship domain, the action area of restricted waters, and the International Regulations for Preventing Collisions at Sea (COLREGs), while constructing an autonomous decision-making system. A novel set of reward functions are devised to incentivize USVs to strictly adhere to COLREGs during autonomous decision-making. Also, to enhance convergence performance, this study incorporates the Gated Recurrent Unit (GRU), which is demonstrated to significantly improve algorithmic efficacy compared to both the Long Short-Term Memory (LSTM) network and traditional fully connected network structures. Finally, extensive testing in various constrained environments, such as narrow channels and complex waters with multiple ships, validates the effectiveness and reliability of the proposed strategy. [ABSTRACT FROM AUTHOR]