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We introduce a new class of neutrosophic crisp set, and then it presented some operations via this sets like, NCT\intersection, NCT -union and algebraic NCT -difference to arrive at the algebraic ring construction. Also, we introduce the NCT - points, which showed that a NCT -set is NCT -union of its NCT -points, and so did we introduced the concept of the function on this sets, called NCT - function and some of their important properties. Finally, we introduced the concept of the topology and some of the concepts entrusted to it, as an introduction to those spaces that can be studied in detail in the future. [ABSTRACT FROM AUTHOR]

With the development of the IoT, Wireless Rechargeable Sensor Networks (WRSNs) derive more and more application scenarios with diverse performance requirements. In scenarios where the energy consumption rate of sensor nodes changes dynamically, most existing charging scheduling methods are not applicable. The incorrect estimation of node energy requirement may lead to the death of critical nodes, resulting in missing events. To address this issue, we consider both the spatial imbalance and temporal dynamics of the energy consumption of the nodes, and minimize the Event Missing Rate (EMR) as the goal. Firstly, an Energy Consumption Balanced Tree (ECBT) construction method is proposed to prolong the lifetime of each node. Then, we transform the goal into Maximizing the value of the Evaluation function of each node's Energy Consumption Rate prediction (MEECR). Afterwards, the setting of the evaluation function is explored and the MEECR is further transformed into a variant of the knapsack problem, namely "the alternating backpack problem", and solved by dynamic programming. After predicting the energy consumption rate of the nodes, a charging scheduling scheme that meets the Dual Constraints of Nodes' energy requirements and MC's capability (DCNM) is developed. Simulations demonstrate the advantages of the proposed method. Compared to the baselines, the EMR was reduced by an average of 35.2% and 26.9%. [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]

Set-based association analysis is a valuable tool in studying the etiology of complex diseases in genome-wide association studies, as it allows for the joint testing of variants in a region or group. Two common types of single nucleotide polymorphism (SNP)–disease functional models are recognized when evaluating the joint function of a set of SNP: the cumulative weak signal model, in which multiple functional variants with small effects contribute to disease risk, and the dominating strong signal model, in which a few functional variants with large effects contribute to disease risk. However, existing methods have two main limitations that reduce their power. Firstly, they typically only consider one disease–SNP association model, which can result in significant power loss if the model is misspecified. Secondly, they do not account for the high-dimensional nature of SNPs, leading to low power or high false positives. In this study, we propose a solution to these challenges by using a high-dimensional inference procedure that involves simultaneously fitting many SNPs in a regression model. We also propose an omnibus testing procedure that employs a robust and powerful P-value combination method to enhance the power of SNP-set association. Our results from extensive simulation studies and a real data analysis demonstrate that our set-based high-dimensional inference strategy is both flexible and computationally efficient and can substantially improve the power of SNP-set association analysis. Application to a real dataset further demonstrates the utility of the testing strategy. [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]

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]

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]

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]

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]

Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in ensuring computational efficiency and convergence of the optimization algorithm to a globally optimal solution. While many design variables in physical systems take discrete values, optimization algorithms often benefit from a continuous design space. This work demonstrates the use of level set functions as a continuous basis for designing material distributions for metasurface arrays and introduces an improved parameterization which is termed the periodic level set function. We explore the use of alternate norms in the definition of the level set function and define a new pseudo-inverse technique for upsampling basis coefficients with these norms. The level set method is compared to the fragmented parameterization and shows improved electromagnetic responses for two dissimilar cost functions: a narrowband objective and a broadband objective. Finally, we manufacture an optimized level set metasurface and measure its scattering parameters to demonstrate real-world performance. [ABSTRACT FROM AUTHOR]

A mathematical formalism for calculating the intrinsic profile of a diffraction maximum through a convolution process using a set of linear functions by intervals is presented. This convolution process is implemented in the formalism for the direct solution of a diffraction pattern of a layered crystalline structure affected by planar defects. It allows the correlation length (AC) to be calculated, which describes the degree of disorder in this type of crystalline structure. The obtained result is validated through the Warren-Averbach method for microstructural analysis. [ABSTRACT FROM AUTHOR]

This paper presents new classes of strong fuzzy negations, fuzzy implications and Copulas. It begins by presenting two theorems with function classes involving the construction of strong fuzzy negations. These classes are based on a well-known equilibrium point theorem. After that, a construction of fuzzy implication is presented, which is not based on any negation. Finally, moving on to the area concerning copulas, we present proof about the third property of copulas. To conclude, we will present two original constructions of copulas. All the above constructions are motivated by a specific formula. For some specific conditions of the variables x, y and other conditions for the function f(x), the formula presented produces strict and strong fuzzy negations, fuzzy implications and copulas. [ABSTRACT FROM AUTHOR]

Automated protein function prediction is a crucial and widely studied problem in bioinformatics. Computationally, protein function is a multilabel classification problem where only positive samples are defined and there is a large number of unlabeled annotations. Most existing methods rely on the assumption that the unlabeled set of protein function annotations are negatives, inducing the false negative issue, where potential positive samples are trained as negatives. We introduce a novel approach named PU-GO, wherein we address function prediction as a positive-unlabeled ranking problem. We apply empirical risk minimization, i.e. we minimize the classification risk of a classifier where class priors are obtained from the Gene Ontology hierarchical structure. We show that our approach is more robust than other state-of-the-art methods on similarity-based and time-based benchmark datasets. Availability and implementation Data and code are available at https://github.com/bio-ontology-research-group/PU-GO. [ABSTRACT FROM AUTHOR]

The transient receptor potential melastatin (TRPM) tetrameric cation channels are involved in a wide range of biological functions, from temperature sensing and taste transduction to regulation of cardiac function, inflammatory pain, and insulin secretion. The structurally conserved TRPM cytoplasmic domains make up >70 % of the total protein. To investigate the mechanism by which the TRPM cytoplasmic domains contribute to gating, we employed electrophysiology and cryo-EM to study TRPM5--a channel that primarily relies on activation via intracellular Ca2+. Here, we show that activation of mammalian TRPM5 channels is strongly altered by Ca2+-dependent desensitization. Structures of rat TRPM5 identify a series of conformational transitions triggered by Ca2+ binding, whereby formation and dissolution of cytoplasmic interprotomer interfaces appear to control activation and desensitization of the channel. This study shows the importance of the cytoplasmic assembly in TRPM5 channel function and sets the stage for future investigations of other members of the TRPM family. [ABSTRACT FROM AUTHOR]

A study of s...-open sets in generalized topological spaces started in 2011 by Min [4]. In this paper, we introduce the concepts of s ...-open sets, s...-closed sets, s...-continuous functions and s...-irresolute functions on generalized topological spaces. We also study some basic properties of such sets and functions. 2020 Mathematics Subject Classifications: 54A05 [ABSTRACT FROM AUTHOR]

A subset A of a bitopological space (X, τ1, τ2) is called an (i, j)-ψgs-closed set if (i, j)-ψcl(A) ⊆ U whenever A ⊆ U, U is (i, j)-semi-open in (X, τ1, τ2). In this work, the properties of this set are considered to investigate the concepts of ψgs-functions in bitopological spaces. Specifically, this study establishes some properties and provides characterizations of ψgs-open and ψgs-closed functions, ψgs-continuous functions, and ψgs-irresolute functions in bitopological spaces. [ABSTRACT FROM AUTHOR]

This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. [ABSTRACT FROM AUTHOR]

A common practice in computational investigations of rate-independent plasticity is to approximate the rate-independent behavior by a visco-plastic regularization. As the fidelity of the approximation increases, the numerical solution of the non-linear problem becomes challenging and it can eventually lead to divergence; thus, there is a numerical limit to the regularization parameter. This limit may be exacerbated by complex material models and critical values of material parameters. Due to these constraints, the regularization may be rendered insufficient and the artificially introduced rate-dependency may lead to a behavior that can be mistakenly attributed to the material model and that we thus identify as spurious in a rate-independent context. To study these spurious effects and their onset, here the problem of an infinite strip under shear loading is numerically solved using a visco-plastic regularized gradient crystal plasticity formulation. The required accuracy of the rate-dependent approximation is found to vary with respect to the type of loading. Furthermore, a set of sigmoid functions used for the regularization is investigated and a subset is shown to deliver improved approximation of the rate-independent case. [ABSTRACT FROM AUTHOR]

Autonomous control systems can enhance the economic viability of complex systems such as nuclear microreactors. Advanced forms of these control systems benefit from techniques for high-resolution field data reconstruction from sensor data. Basis projection methods present a useful set of methodologies for nonparametric reconstruction of these field data. In this work, high fidelity multiphysics simulations are used to generate microreactor temperature distributions that are then used to evaluate the viability of a basis projection method which employs a generalized set of basis functions, or dictionaries. Additionally, metrics for evaluating the accuracy of the temperature distribution are presented that are motivated both from the fields of traditional signal processing and statistics. The performance of a method based on matching pursuits is compared to a method that uses the sequential ordering of basis functions. The matching pursuits-based method gives improved performance for highly sparse representations of temperature distributions. Additionally, accuracy is analyzed for multiple temperature distributions which represent different potential reactor operation configurations. Overall, the results from this work should be considered as an upper bound on the performance of basis projection methods which employ generalized basis functions for real time reactor control. • Autonomous systems enhance nuclear microreactor economic viability. • Basis projection methods aid in nonparametric field data reconstruction. • Matching pursuits-based method outperforms sequential basis function method. • Theoretical foundation provided for evaluating alternative bases. • Generalized bases evaluated for nuclear reactor field reconstruction. [ABSTRACT FROM AUTHOR]

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order ( aN 3 LO ). We construct an approximation to the N 3 LO splitting functions that includes all available partial information from both fixed-order computations and from small and large x resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known N 3 LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to O α s 3 accuracy. We determine a set of aN 3 LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N 3 LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the aN 3 LO PDFs from the MSHT group. We examine the phenomenological impact of aN 3 LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN 3 LO PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the aN 3 LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell–Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order. [ABSTRACT FROM AUTHOR]

This paper proposed a two-dimensional steady-state field prediction approach that combines B-spline functions and a fully connected neural network. In this approach, field data, which are determined by corresponding control vectors, are fitted by a selected B-spline function set, yielding the corresponding best-fitting weight vectors, and then a fully connected neural network is trained using those weight vectors and control vectors. The trained neural network first predicts a weight vector using a given control vector, and then the corresponding field can be restored via the selected B-spline set. This method was applied to learn and predict two-dimensional steady advection–diffusion physical fields with absorption and source terms, and its accuracy and performance were tested and verified by a series of numerical experiments with different B-spline sets, boundary conditions, field gradients, and field states. The proposed method was finally compared with a generative adversarial network (GAN) and a physics-informed neural network (PINN). The results indicated that the B-spline neural network could predict the tested physical fields well; the overall error can be reduced by expanding the selected B-spline set. Compared with GAN and PINN, the proposed method also presented the advantages of a high prediction accuracy, less demand for training data, and high training efficiency. [ABSTRACT FROM AUTHOR]

Let be a graph of order . For , the set is defined as the external neighborhood of such that all vertices in have at least one neighbor in . The differential of is defined to be , and the 2-packing differential of a graph is defined as A function with the sets , where is a unique response Roman dominating function if implies that and implies that . The unique response Roman domination number of , denoted by , is the minimum weight among all unique response Roman dominating functions on . Let be the complement of a graph . The complementary prism of is the graph formed from the disjoint union of and by adding the edges of a perfect matching between the respective vertices of and . The present paper deals with the computation of the 2-packing differential and the unique response Roman domination of the complementary prisms by the use of a proven Gallai-type theorem. Particular attention is given to the complementary prims of special types of graphs. Furthermore, the graphs such that and are small are characterized. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced crayfish optimization algorithm (ECOA). The ECOA includes four improvement strategies. Firstly, the Halton sequence was used to improve the population initialization of the crayfish optimization algorithm. Furthermore, the quasi opposition-based learning strategy is introduced to generate the opposite solution of the population, increasing the algorithm's searching ability. Thirdly, the elite factor guides the predation stage to avoid blindness in this stage. Finally, the fish aggregation device effect is introduced to increase the ability of the algorithm to jump out of the local optimal. This paper performed tests on the widely used IEEE CEC2019 test function set to verify the validity of the proposed ECOA method. The experimental results show that the proposed ECOA has a faster convergence speed, greater performance stability, and a stronger ability to jump out of local optimal compared with other popular algorithms. Finally, the ECOA was applied to two real-world engineering optimization problems, verifying its ability to solve practical optimization problems and its superiority compared to other algorithms. [ABSTRACT FROM AUTHOR]

A timelike (TL) constant axis ruled surface in E 1 3 (Minkowski 3-space), as determined by its ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this article, we employ the symmetry through point geometry of Lorentzian dual curves and the line geometry of TL ruled surfaces. This produces the capability to expound a set of curvature functions that specify the local configurations of TL ruled surfaces. Then, we gain some new constant axis ruled surfaces in Lorentzian line space and their geometrical illustrations. Further, we also earn several organizations among a TL constant axis ruled surface and its striction curve. [ABSTRACT FROM AUTHOR]

Intensity inhomogeneity (IIH) and noise are ubiquitous in images acquired by a variety of imaging modalities, which pose an ongoing challenge for segmentation methods used in many applications. This paper proposes a level set evolution equation based on fractional derivative to address the IIH and noise issues in image segmentation, which integrates the information from the input and guidance images. The proposed model is a linear diffusion equation of level set function with nonlinear edge-stopping and guidance sources, in which the edge-stopping source is derived from the input image and a local statistical model (Bayesian formulation) in the level set framework, whereas the guidance source is derived from the guidance image and the fitting term of the popular Chan-Vese model. The guidance source ensures swift contour movement toward the boundary of the objects and enhances the robustness to noise and contour initialization, while the edge-stopping source is used to stop the evolving contour on the boundary of the objects later in the evolution. To tackle the challenge of obtaining accurate guidance images for many applications, an adaptive variable-order of fractional derivative robust to IIH and noise is introduced to generate the desired guidance image from the input image. The proposed diffusion equation with sources is solved numerically by the series splitting method and finite difference scheme. Experimental results on synthetic and real images show that the proposed model has higher performance in terms of accuracy and efficiency of segmentation, compared to several state-of-the-art level set models. • Propose guided active contours via level set evolution for noisy images with intensity inhomogeneity (IIH). • Design an adaptive order of fractional derivative that is basically not affected by IIH and noise. • Present a fractional derivative based method for generating guidance image from the input image. • Our model is experimentally very effective and efficient in segmenting images with IIH and noise. [ABSTRACT FROM AUTHOR]

Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q -calculus. The class is proved to be not empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on | α 2 | and | α 3 | coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. [ABSTRACT FROM AUTHOR]

The detailed, high-resolution images captured by drones pose challenges to target detection algorithms with complex scenes and small-sized targets. Moreover, targets in unmanned aerial vehicle images are usually affected by factors such as viewing perspective, occlusion, and light, which increase the difficulty of target detection. In response to the above issues, we propose an improved SDMSEAFYOLOv8 for target detection based on YOLOv8, combined with a Bidirectional Feature Pyramid Network, to improve the sensing ability of the model for multiscale targets. A Space-to-depth layer replaces the traditional strided convolution layer to enhance the extraction of fine-grained information and small-sized target features. A Multi-Separated and Enhancement Attention module enhances the feature learning ability of the occluded target region, thus reducing missed and false detections. Four detection heads are employed for tiny target detection, each responsible for different size ranges, so as to improve the accuracy and robustness of small target detection. The conventional non-maximum suppression algorithm is improved, so as to reduce the problem of missed detections under a densely occluded scene by setting the attenuation function to adjust the confidence of the treated box based on the overlap between it and the highest-scoring box. Experiments demonstrate that the accuracy of SDMSEAF-YOLOv8 exceeds that of state-of-the-art models on the VisDrone2019-DET-val dataset, with a mAP of 42.9% at 640-pixel resolution, 14.8% over the baseline YOLOv8-x algorithm model, and 6.0% over the known state-of-the-art Fine-Grained Target Focusing Network model and with twice as fast detection. [ABSTRACT FROM AUTHOR]

Support Vector Machines (SVMs) can learn from high-dimensional and small amounts of training data, thanks to effective optimization methods and a diverse set of kernel functions (KFs). The adaptability of SVM to numerous real-world problems has increased interest in the SVM method, and studies conducted with this method carry significant weight in various fields. The fixed parameter "AtanK" for KFs must be specified before the SVM model training process. Therefore, determining the appropriate kernel parameter values can be timE−consuming and may lead to slow convergence of the SVM model. On the other hand, the method provides faster and more robust convergence due to the adaptive parameter in the SVM model. In this study, a new Adaptive Arctan (AA) KF, tailored to the characteristics of different datasets, is proposed as an enhancement to the AtanK KF for the SVM algorithm. The proposed AA KF is compared with experimental results on 30 public KEEL and UCI datasets, alongside AtanK, adaptive Gaussian, Radial Basis Function, linear, and polynomial KFs. The results demonstrate that the proposed AA KF outperforms the other KFs, and it exhibits superior learning ability. [ABSTRACT FROM AUTHOR]

The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be generalized to this setting. First, we study the generalizations of dynamical properties, such as invariance and limit sets and show that compact weakly invariant sets can be characterized in terms of the corresponding shift-invariant sets in the function space. This result enables us to consider weakly invariant sets in terms of shift-invariant sets. Next, we compare the axiomatic theory of ODE with other formalisms of generalized dynamical systems, namely generalized semiflow and multivalued semigroup. Finally, we introduce the notion of invariant measures and show that we can generalize classical results, such as Poincaré recurrence theorem. [ABSTRACT FROM AUTHOR]

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q -calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on | α 2 | and | α 3 | coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. [ABSTRACT FROM AUTHOR]

In this paper we consider decision functions in which voters have three options and one of them is abstention or indifference and the output is a binary decision between two alternatives so that a tie is not possible. These resolute decision functions appear frequently in grading, in some sport competitions, in voting situations in which the status quo is put to the vote, etc. It is a more restricted case of the voting context considered in the seminal article by Kenneth May on decision functions, published in Econometrica in 1952, because the output set does not admit a tie. Among these resolute decision functions we focus on the study of majority functions, in which the number of favorable votes to an alternative must be strictly greater than the number of votes against it. This work provides an axiomatic characterization for the set of majority functions and for the relative majority function with status quo bias. Both characterizations are based on weaker versions of neutrality. Other complementary characterizations are also provided. [ABSTRACT FROM AUTHOR]

The study on how equilibria behave when perturbations occur in the data of a game is a fundamental theme, since actions and payoffs of the players may be affected by uncertainty or trembles. In this paper, we investigate the asymptotic behavior and the variational stability of the subgame perfect Nash equilibrium (SPNE) in one-leader one-follower Stackelberg games under perturbations both of the action sets and of the payoff functions. To pursue this aim, we consider a general sequence of perturbed Stackelberg games and a set of assumptions that fit the usual types of perturbations. We study if the limit of SPNEs of the perturbed games is an SPNE of the original game and if the limit of SPNE-outcomes of perturbed games is an SPNE-outcome of the original game. We fully positively answer when the follower's best reply correspondence is single-valued. When the follower's best reply correspondence is not single-valued, the answer is positive only for the SPNE-outcomes; whereas the answer for SPNEs may be negative, even if the perturbation does not affect the sets and affects only one payoff function. However, we show that under suitable non-restrictive assumptions it is possible to obtain an SPNE starting from the limit of SPNEs of perturbed games, possibly modifying the limit at just one point. [ABSTRACT FROM AUTHOR]

This paper deals with α -core of set payoffs games with finitely many players and finite coalition α -core of set payoffs games with infinitely many players. We present an existence theorem of α -core of set payoffs games with finitely many players. By virtue of finite intersection property, we also establish an existence theorem of finite coalition α -core of set payoffs games with infinitely many players. Besides, we obtain some stability results of solution mapping of α -core of set payoffs games, where set payoff functions and action sets of agents involve perturbed parameters. Moreover, as applications, we obtain the corresponding results for α -core of vector payoffs games. [ABSTRACT FROM AUTHOR]

The definitions provided by the authors of the current study are offered together with a discussion of the recent advances that they have contributed. We begin with an introduction to fn-Fr#bϱN, which includes the concepts of closed and open sets. We explore characteristics in fn-βd#bϱN and fn-℮bϱN(ϱN), and provide an idea of obtained results by adding the notion of FNbϱNOS and analyzing a few of their properties in fnts. We've researched the contrasts between the derived, exterior, and frontier notions that are provided. We also looked at the ideas of 〈TbϱN〉 C-functions and Γs-segregated functions and examined and determined the traits. [ABSTRACT FROM AUTHOR]

The combination of machine learning and topology optimization has preliminarily mitigated the enormous computational costs incurred during optimization processes. Its powerful design capabilities are warmly welcomed by many scholars, but this strategy still faces many problems, such as unclear structural boundaries and high dependence on big data. Here, we propose a new machine learning topology optimization paradigm that learns the mapping relationship between the initial and optimized Level set functions in the infinite-dimensional function space under the Fourier neural operator to truly parameterize the structural model and its mechanical information, thereby achieving purely data-driven topology optimization. A base model trained under the proposed approach could obtain a topological structure with clear and smooth structural boundaries within 0.4 seconds, making it faster than traditional methods by tens of times. In addition, a lightweight retraining strategy under the base model was proposed. Four additional numerical examples were used to demonstrate that this strategy requires only 100 or 200 new samples and 3-6 seconds of retraining time to attain prediction capabilities under different boundary conditions, different meshes (resolution), various initial level set functions, and multiple loads. In addition, we discussed all the experiments and found that most of the mechanical properties of the results were close to the ground truths, while some results were even better than those of the traditional method. Although we only used the maximum structural stiffness as an example, this method can be extended to different objective functions. • FNO-based topology optimization framework: faster and more powerful. • Purely data-driven TO of parameterized structures and their mechanical models. • A lightweight retraining strategy for attaining various predictive capabilities. • Instantly predicting topological structure with clear and smooth boundaries. • The predicted structure has high accuracy in terms of mechanical properties and volume. [ABSTRACT FROM AUTHOR]

Statistical analysis of samples of the orbits of celestial bodies is complicated by the fact that the Keplerian orbit is a multidimensional object, the coordinate representation of which non-linearly depends on the choice of orbital elements. In this work, using the construction of the Fréchet mean, concepts of mean orbit and dispersion of the orbit family are introduced, consistent with the distance function on the orbit set. The introduced statistical characteristics serve as analogues of sample mean and variance of a one-dimensional random variable. Exact formulas for calculating the elements of mean orbits and dispersion quantities with respect to two metrics on the orbit space are derived. For a large sample of meteoroid orbits from the Geminid stream, numerical simulations of orbit evolution over 20 000 yr in the past were conducted. By analysing the dependency of statistical characteristics on time, estimates for the age of the stream and the gas outflow velocity are obtained under the assumption of the birth of the Geminids due to the rapid destruction of the cometary nucleus. The estimate of the age of the stream lies in the interval from 1200 to 2400 yr, and the speed of gas outflow at perihelion should have been more than 1.2 km s−1. [ABSTRACT FROM AUTHOR]

Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified properties. This article is devoted to issues related to the construction of such combinatorial generation algorithms for a wide class of directed lattice paths. The main method used is based on the representation of a given combinatorial set in the form of an AND/OR tree structure. To apply this method, it is necessary to have an expression for the cardinality function of a combinatorial set that satisfies certain requirements. As the main result, we have found recurrence relations for enumerating simple directed lattice paths that satisfy the requirements of the applied method and have constructed the corresponding AND/OR tree structure. Applying the constructed AND/OR tree structure, we have developed new algorithms for ranking and unranking simple directed lattice paths. Additionally, the obtained results were generalized to the case of directed lattice paths. [ABSTRACT FROM AUTHOR]

Summary: Plants possess a large variety of nonacquisitive belowground organs, such as rhizomes, tubers, bulbs, and coarse roots. These organs determine a whole set of functions that are decisive in coping with climate, productivity, disturbance, and biotic interactions, and have been hypothesized to affect plant distribution along environmental gradients.We assembled data on belowground organ morphology for 1712 species from Central Europe and tested these hypotheses by quantifying relationships between belowground morphologies and species optima along ecological gradients related to productivity and disturbance. Furthermore, we linked these data with species co‐occurrence in 30 115 vegetation plots from the Czech Republic to determine relationships between belowground organ diversity and these gradients.The strongest gradients determining belowground organ distribution were disturbance severity and frequency, light, and moisture. Nonclonal perennials and annuals occupy much smaller parts of the total environmental space than major types of clonal plants. Forest habitats had the highest diversity of co‐occurring belowground morphologies; in other habitats, the diversity of belowground morphologies was generally lower than the random expectation.Our work shows that nonacquisitive belowground organs may be partly responsible for plant environmental niches. This adds a new dimension to the plant trait spectrum, currently based on acquisitive traits (leaves and fine roots) only. [ABSTRACT FROM AUTHOR]

We study the problem of the existence of a convex extension of any Boolean function to the set . A convex extension of an arbitrary Boolean function to the set is constructed. On the basis of the constructed convex extension , it is proved that any Boolean function has infinitely many convex extensions to . Moreover, it is proved constructively that, for any Boolean function , there exists a unique function being its maximal convex extensions to . [ABSTRACT FROM AUTHOR]

There are deep historical connections between symmetry, harmonic functions, and stratified sets. In this article, we prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron's method of proving the solvability of the Dirichlet problem for the soft Laplacian. [ABSTRACT FROM AUTHOR]

An enhanced dung beetle optimization algorithm (EDBO) is proposed for nonlinear optimization problems with multiple constraints in manufacturing. Firstly, the dung beetle rolling phase is improved by removing the worst value interference and coupling the current solution with the optimal solution to each other, while retaining the advantages of the original formulation. Subsequently, to address the problem that the dung beetle dancing phase focuses only on the information of the current solution, which leads to the overly stochastic and inefficient exploration of the problem space, the globally optimal solution is introduced to steer the dung beetle, and a stochastic factor is added to the optimal solution. Finally, the dung beetle foraging phase introduces the Jacobi curve to further enhance the algorithm's ability to jump out of the local optimum and avoid the phenomenon of premature convergence. The performance of EDBO in optimization is tested using the CEC2017 function set, and the significance of the algorithm is verified by the Wilcoxon rank-sum test and the Friedman test. The experimental results show that EDBO has strong optimization-seeking accuracy and optimization-seeking stability. By solving four engineering optimization problems of varying degrees, EDBO has proven to have good adaptability and robustness. [ABSTRACT FROM AUTHOR]

In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if these operators satisfy the same characteristic algebraic relations as standard differential operators of the same order on some function space. In this paper, we prove theorem that this property of the exact finite-differences is satisfies for the space of simple entire functions on the real axis (i.e., functions that can be expanded into power series on the real axis). In addition, new results that describe the exact finite-differences beyond the set of entire functions are proposed. A generalized expression of exact finite-differences for non-entire functions is suggested. As an example, the exact finite-differences of the square root function is considered. The use of exact finite-differences for numerical and computer simulations is not discussed in this paper. Exact finite-differences are considered as an algebraic analog of standard derivatives of integer order. [ABSTRACT FROM AUTHOR]

The spatial exploration of richness, endemism, and evolutionary diversity patterns has become an important part of biogeographic research and conservation planning. As the volume and complexity of biogeographical and phylogenetic data increase, the need for efficient tools to manipulate and analyze these datasets becomes essential. The 'phyloraster' package addresses this need by facilitating the analysis of evolutionary diversity and endemism for rasters. Our package offers a set of functions to support the linkage of species distribution models (SDMs) with phylogenies, providing then an understanding of the spatial distribution of biodiversity. It covers three main stages: pre‐processing, processing, and post‐processing of macroecological and phylogenetic data. During the pre‐processing step, basic functions are provided to prepare the data. The processing step combines functions to calculate indices including species richness, Faith's phylogenetic diversity, phylogenetic endemism, weighted endemism, and evolutionary distinctiveness. Additionally, this step includes functions to compute the standardized effect size for each metric using spatial and phylogenetic randomization methods, ensuring proper control for richness effects. The post‐processing stage includes functions to calculate the change of metrics between different times (e.g. present and future). In relation to processing in our functions, we show that 'phyloraster' takes up considerably less RAM than the other packages when computing the same metrics (weighted endemism). Lower RAM usage minimizes the hardware requirements to work with high‐resolution datasets from local to global scales. This broadens user accessibility of the spatialized measures of endemism and evolutionary diversity. [ABSTRACT FROM AUTHOR]

The Lerch zeta-function L(λ, α, s), s = σ + it, depends on two real parameters P λ and 0 < α ⩽ 1, and, for σ > 1, is defined by the Dirichlet series ∞ m=0 e2πiλm(m + α)-s, and by analytic continuation elsewhere. In the paper, we consider the joint approximation of collections of analytic functions by discrete shifts (L(λ1, α1, s+ikh1), . . ., L(λr, αr, s+ikhr)), k = 0, 1, . . ., with arbitrary λj, 0 < αj ⩽ 1 and hj > 0, j = 1, . . ., r. We prove that there exists a non-empty closed set of analytic functions on the critical strip 1/2 < σ < 1 which is approximated by the above shifts. It is proved that the set of shifts approximating a given collection of analytic functions has a positive lower density. The case of positive density also is discussed. A generalization for some compositions is given. [ABSTRACT FROM AUTHOR]

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research. [ABSTRACT FROM AUTHOR]

The original Harris hawks optimization (HHO) algorithm has the problems of unstable optimization effect and easy to fall into stagnation. However, most of the improved HHO algorithms can not effectively improve the ability of the algorithm to jump out of the local optimum. In this regard, an integrated improved HHO (IIHHO) algorithm is proposed. Firstly, the linear transformation escape energy used by the original HHO algorithm is relatively simple and lacks the escape law of the prey in the actual nature. Therefore, intermittent energy regulator is introduced to adjust the energy of Harris hawks, which is conducive to improving the local search ability of the algorithm while restoring the prey's rest mechanism; Secondly, to adjust the uncertainty of random vector, a more regular vector change mechanism is used instead, and the attenuation vector is obtained by modifying the composite function. Finally, the search scope of Levy flight is further clarified, which is conducive to the algorithm jumping out of the local optimum. Finally, in order to modify the calculation limitations caused by the fixed step size, Cardano formula function is introduced to adjust the step size setting and improve the accuracy of the algorithm. First, the performance of IIHHO algorithm is analyzed on the Computational Experimental Competition 2013 (CEC 2013) function test set and compared with seven improved evolutionary algorithms, and the convergence value of the iterative curve obtained is better than most of the improved algorithms, verifying the effectiveness of the proposed IIHHO algorithm. Second, the IIHHO is compared with another three state of the art (SOTA) algorithms with the Computational Experimental Competition 2022 (CEC 2022) function test set, the experiments show that the proposed IIHHO algorithm still has a strong ability to search for the optimal value. Third, IIHHO algorithm is applied in two different engineering experiments. The calculation results of minimum cost prove that IIHHO algorithm has certain advantages in dealing with the problem of search space. All these demonstrate that the proposed IIHHO is promising for numeric optimization and engineering applications. [ABSTRACT FROM AUTHOR]

A novel multi-objective robust optimization model of an integrated energy system with hydrogen storage (HIES) considering source–load uncertainty is proposed to promote the low-carbon economy operation of the integrated energy system of a park. Firstly, the lowest total system cost and carbon emissions are selected as the multi-objective optimization functions. The Pareto front solution set of the objective function is applied by compromise planning, and the optimal solution among them is obtained by the maximum–minimum fuzzy method. Furthermore, the robust optimization (RO) approach is introduced to cope with the source–load uncertainty effectively. Finally, it is demonstrated that the illustrated HIES can significantly reduce the total system cost, carbon emissions, and abandoned wind and solar power. Meanwhile, the effectiveness of the proposed model and solution method is verified by analyzing the influence of multi-objective solutions and a robust coefficient on the Chongli Demonstration Project in Hebei Province. [ABSTRACT FROM AUTHOR]

RNA is a complex macromolecule that plays central roles in the cell. While it is well known that its structure is directly related to its functions, understanding and predicting RNA structures is challenging. Assessing the real or predictive quality of a structure is also at stake with the complex 3D possible conformations of RNAs. Metrics have been developed to measure model quality while scoring functions aim at assigning quality to guide the discrimination of structures without a known and solved reference. Throughout the years, many metrics and scoring functions have been developed, and no unique assessment is used nowadays. Each developed assessment method has its specificity and might be complementary to understanding structure quality. Therefore, to evaluate RNA 3D structure predictions, it would be important to calculate different metrics and/or scoring functions. For this purpose, we developed RNAdvisor, a comprehensive automated software that integrates and enhances the accessibility of existing metrics and scoring functions. In this paper, we present our RNAdvisor tool, as well as state-of-the-art existing metrics, scoring functions and a set of benchmarks we conducted for evaluating them. Source code is freely available on the EvryRNA platform: https://evryrna.ibisc.univ-evry.fr. [ABSTRACT FROM AUTHOR]