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The global stress distribution and state parameter analysis of the building's main structure is an urgent problem to be solved in the online state assessment technology of building structure health. In this paper, a stress curve clustering algorithm of fiber Bragg grating stress sensor based on density clustering algorithm is proposed. To solve the problem of large dimension and sparse sample space of sensor stress curve, the distance between samples is measured based on improved cosine similarity. Aiming at the problem of low efficiency and poor effect of traditional clustering algorithm, density clustering algorithm based on mutual nearest neighbor is used to cluster. Finally, the classification of the daily stress load characteristics of the sensor is realized, which provides a basis for constructing the mathematical analysis model of building health. The experimental results show that the stress curve clustering method proposed in this paper is better than the latest clustering algorithms such as HDBSCAN, CBKM, K-mean++,FINCH and NPIR, and is suitable for the feature classification of stress curves of fiber Bragg grating sensors. [ABSTRACT FROM AUTHOR]

Doubly salient permanent magnet machine (DSPMM), which is a branch of stator-Permanent Magnet (PM) machine, is becoming more and more attractive due to higher power density and fault-tolerant capability, better mechanical robustness, simpler rotor configuration, lower PM consumption and higher PM material utilization efficiency. Thus, it has great application potential in the fields of transportation electrification and renewable energy generation. However, due to the special doubly salient structure, PM flux-linkage and inductance have the same variation period, which would complicate the relationship between the current and torque, and bring difficulties in the modeling and control (even after Park's transformation). In order to solve these problems, this paper will develop, analyze and compare the different current waveforms which could theoretically reduce the torque ripple and the transformations which could decouple the model in the rotating stationary frame for a simplified DSPMM model neglecting the higher harmonics. Based on the mathematical analysis, this paper would provide a clear relationship between the current waveforms and the torque with the DSPMM parameters, and the possible transformation which could simplify the model and be used in the control system. [ABSTRACT FROM AUTHOR]

The underground pipeline network in the city is so intertwined that the concealed excavation of a metro station inevitably leads to a series of underground pipelines, causing settlement deformation and further risk of leakage. The existing theoretical methods for analysing settlement deformation are mostly for circular chambers, whereas metro stations have a nearly square cross-sectional form and different construction methods are very different, which have a greater impact on the deformation of the overlying pipelines. In this paper, based on the random medium theory and Peck's formula, the improved random medium model for predicting ground deformation is modified, the correction coefficients λ and η for the influence of different construction methods are proposed, the prediction model of underground pipeline deformation under different construction methods is obtained, and the numerical models of four work methods commonly used in urban tunnel construction: pillar hole method, side hole method, middle hole method and Pile-Beam-Arch (PBA) method are constructed through simulation, and the mathematical analysis software was used to fit the results to the model and obtain the range of correction coefficients λ and η for each of the four methods, and the accuracy and applicability of the theoretical model was verified by combining with actual engineering cases. The influence on the overlying pipes is in descending order: side hole method, pillar hole method, middle hole method and PBA method. The theoretical model provided in this paper for predicting the deformation of pipes in any overlying strata of the tunnel is well suited to the actual project and has a high degree of correlation with the measured results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global exponential synchronization issues for variable-order fractional complex dynamic networks (FCDNs). Firstly, a new derivative operator, which is called as the generalized Caputo variable-order fractional derivative, is developed, and some properties and lemmas are rigorous proved. Secondly, a new dynamic event-triggered control mechanism is designed to realize the synchronization objective, where the generalized Caputo variable-order fractional derivative is applied to characterize the evolution state of internal dynamic variable. And the exclusion for Zeno behavior is verified by contradiction analysis method. Thirdly, a class of functions, which is an extension of the Lipschitz function, is introduced to model the nonlinear dynamics for the considered system. With the aid of fractional Lyapunov functional method, some auxiliary functions and advanced mathematical analysis techniques, the global exponential synchronization conditions are established in terms of linear matrix inequalities (LMIs). Finally, the correctness of the theoretical results and the feasibility of the designed controller in this paper are confirmed by applying a numerical simulation example. [ABSTRACT FROM AUTHOR]

Dictionary learning is an effective feature learning method, leading to many remarkable results in data representation and classification tasks. However, dictionary learning is performed on the original data representation. In some cases, the capability of representation and discriminability of the learned dictionaries may need to be performed better, i.e., with only sparse but not low rank. In this paper, we propose a novel efficient data representation learning method by combining dictionary learning and self-representation, which utilizes both properties of sparsity in dictionary learning and low-rank in low-rank representation (LRR) simultaneously. Thus both the sparse and low-rank properties of the data representation can be naturally captured by our method. To obtain the solution of our proposed method effectively, we also innovatively introduce a more generalized data representation model in this paper. To our best knowledge, its closed-form solution is first derived analytically through our rigorous mathematical analysis. Experimental results show that our method not only can be used for data pre-processing but also can realize better dictionary learning. The samples in the same class can have similar representations by our method, and the discriminability of the learned dictionary can also be enhanced. [ABSTRACT FROM AUTHOR]

The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a bivariate analog of critical points, and may correspond to features of interest. In the specific case of time-varying fields and when one of the scalar fields is time, the Jacobi set corresponds to temporal tracks of critical points, and serves as a feature-tracking graph. The Jacobi set of a bivariate field or a time-varying scalar field is complex, resulting in cluttered visualizations that are difficult to analyze. This paper addresses the problem of Jacobi set simplification. Specifically, we use the time-varying scalar field scenario to introduce a method that computes a reduced Jacobi set. The method is based on a stability measure called robustness that was originally developed for vector fields and helps capture the structural stability of critical points. We also present a mathematical analysis for the method, and describe an implementation for 2D time-varying scalar fields. Applications to both synthetic and real-world datasets demonstrate the effectiveness of the method for tracking features. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187, 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models' hyperparameters, the proposed algorithm particularly solves the open problem of Linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of Linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity and, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude. [ABSTRACT FROM AUTHOR]

In this paper, a new application of the Taylor series method (TSM) and its properties is used to solve partial differential equation problems with a singular limit value problem. We are particularly interested in applying this method to a certain class of physical problems such as Lane Emden–Fowler partial differential equations. The results obtained show that this analytical technique is very simple and effective compared to other methods. [ABSTRACT FROM AUTHOR]

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]

In this paper I explore how intellectual humility manifests in mathematical practices. To do this I employ accounts of this virtue as developed by virtue epistemologists in three case studies of mathematical activity. As a contribution to a Topical Collection on virtue theory of mathematical practices this paper explores in how far existing virtue-theoretic frameworks can be applied to a philosophical analysis of mathematical practices. I argue that the individual accounts of intellectual humility are successful at tracking some manifestations of this virtue in mathematical practices and fail to track others. There are two upshots to this. First, the accounts of the intellectual virtues provided by virtue epistemologists are insightful for the development of a virtue theory of mathematical practices but require adjustments in some cases. Second, the case studies reveal dimensions of intellectual humility virtue epistemologists have thus far overlooked in their theoretical reflections. [ABSTRACT FROM AUTHOR]

This paper aims at mathematical analyzing of a parabolic chemotaxis model with nonlinear cross-diffusion transposed from the euclidean case into weighted networks. Taking into account certain applications in neurobiology, data transmission and wound healing process, a modified Keller–Segel model with volume-filling effect is studied. The novelty with respect to other related papers lies in the numerical investigation of chemotaxis process in weighted networks and of asymptotic self-similar behavior of solutions by time dependent scaling. The global existence and the large-time dynamics of solutions are detailed. Finally, the theoretical characteristics of the discrete solutions are explored numerically. [ABSTRACT FROM AUTHOR]

This paper is concerned with time-asymptotic nonlinear stability of rarefaction waves to the Cauchy problem for one-dimensional compressible non-isentropic magnetohydrodynamics (MHD) equations (including its isentropic case), which describe the motion of a conducting fluid in a magnetic field. Through some elaborate and rigorous mathematical analysis, we can construct the rarefaction waves v r , u r , θ r , b r (x / t) where magnetic component b r x / t is a nontrivial profile, namely a non-constant function. Then the solution of the compressible MHD equations is proved to tend towards the rarefaction waves time-asymptotically under small initial perturbations and weak wave strength, and also under a technical assumption that the parameter β = v + b + is bounded by a specific constant. The proof of the main result is based on elementary L 2 energy methods. [ABSTRACT FROM AUTHOR]

The presented paper is a compendium or a kind of précis of relationships between the four classical theorems of mathematical analysis. More precisely, the first aim of this paper is to present the equivalence of the four classical theorems: the Hahn–Banach theorem, the Mazur–Orlicz theorem, the Markov–Kakutani fixed-point theorem and the von Neumann theorem on amenability of Abelian groups. The second purpose is to prove these equivalences in Zermelo–Fraenkel set theory with the axiom of choice replaced by the Boolean prime ideal theorem, from which we can also prove the Hahn–Banach theorem. [ABSTRACT FROM AUTHOR]

Object detection is one of the core tasks of computer vision, and bounding box (bbox) regression is one of the basic tasks of object detection. In recent years of related research, bbox regression is often used in the Intersection over Union (IoU) loss and its improved version. In this paper, for the first time, we introduce the Dice coefficient into the regression loss calculation and propose a new measure which is superior to and can replace the IoU. We define three properties of the new measure and prove the theory by mathematical reasoning and analysis of the existing work. This paper also proposes the N-IoU regression loss family. And the superiority of the N-IoU regression loss family is proved by designing simulation experiments and comparative experiments. The main results of this paper are: (1) The proposed new measure is better than IoU which can be used to evaluate bounding box regression, and the three properties of the new measure can be used as a broad criterion for the design of regression loss functions; and (2) we propose N-IoU loss. The parameter n of N-IOU can be debugged, which can be widely adapted to different application scenarios with higher flexibility, and the regression performance is better. [ABSTRACT FROM AUTHOR]

The emergence of cross-border e-commerce has brought new opportunities to traditional enterprises. This paper discusses the partner selection of cross-border e-commerce companies in the B2B mode. It constructs a theoretical model of partner selection of cross-border e-commerce enterprises based on literature review. Through the mathematical analysis of an asymmetric evolutionary game model, it is considered that the model has an evolutionarily stable strategy. Based on it, a multi-agent model is constructed. The results of the simulation reveal the mediation role of trust between corporate reputation and enterprise cooperation. Simultaneously, it verified the moderation effect of information sharing between the trust and cooperation of cross-border e-commerce companies. It also provides explanations for the inconsistency in the relationship between trust and cooperative behavior. From both mathematical and data perspectives, this paper attempts to test the theoretical model proposed, which enriches the methodology to test the theory. [ABSTRACT FROM AUTHOR]

The popularity of football among fans to analyze the game has been immense with the advent of internet. The concept of making a dream team in football has become a new fashion for the football lovers. The paper focuses in helping achieving this prediction of a football dream team. The aim of this research is to assess the dynamics of a complex topological structure when prompted with random entities whose attributes are known to us. Using graph theory and vectorial distances, the dream team is evaluated on the basis of individual abilities and interplayer synergy. Instead of focusing on discrete events in a match, this framework proposes an idea in which a dream team is quantified on the basis of their positional attributes. Each player is rated in accordance to the position he is playing, which eventually helps in finding the overall team rating. The second part of this research uses graph theory to evaluate structural and topological properties of interpersonal interactions of teammates. Teammates are treated as nodes of a graph, where each edge exemplifies the strength of their interpersonal interaction. The strength of the bond depends on on-field interactions via ball passing, ball receiving and communication which depend on experience of playing together, Nationality and Club. The methodology adopted in this paper can be a formidable basis for similarly situated larger setups involving much larger intricacies. Using this framework, we can see the behavior of a hypothetical topological structure whose node attributes are known to us, thus projecting its performance as a team and individual entities. [ABSTRACT FROM AUTHOR]

A unique photonic technique has been suggested and explained for different types of waveform generation, the proposed technique employs double LiNbO3 Mach–Zehnder single drive cascading modulators for pulse shaping and responsive modulators for polarization. By ordering the incident light polarized states it can produce accordingly dual distinct Spectra on two components of orthogonal polarization. The desired waveform would be obtained by detecting the photocurrents from the photodetector. This paper describes the complete mathematical analysis of polarization dependent cascade Mach–Zehnder modulators to generate a variety of microwave forms. Comprehensive mathematical analyses including simulations have been presented, and therefore we have successfully developed as well as generated delta waveform, half-wave rectifier waveform, full-wave rectifier waveform, and square wave types waveform. At the end of the paper experimental analysis has been done for the proof of concept purpose while the experimental results of a variety of microwave waveforms are compared with theoretical ones. There are good agreements between theoretical results with experimental ones. [ABSTRACT FROM AUTHOR]

This study examines Einstein's field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated. [ABSTRACT FROM AUTHOR]

Deblurring is a challenging problem in image restoration. It's important to use both local details and global information of the image for deblurring. Therefore, this paper proposes a deblurring model that integrates Convolution and Transformer in a parallel manner. Unlike existing methods that use single operators or serial combinations, the convolution operation and self-attention mechanism in this model are learned in parallel and extract features separately, and then the features are fused in the frequency domain. The convolution operation is beneficial in extracting local information while the self-attention mechanism focuses more on global information. The parallel structure enables the model to capture both local and global information simultaneously. Additionally, the frequency domain fusion module is proposed based on the analysis of the mathematical model of image blur, and the results indicate that the proposed model is reasonable. Experiments on multiple deblurring datasets verify that the proposed parallel structure of Convolution-Transformer and frequency domain fusion method are effective. [ABSTRACT FROM AUTHOR]

It is widely accepted that biased data leads to biased and thus potentially unfair models. Therefore, several measures for bias in data and model predictions have been proposed, as well as bias mitigation techniques whose aim is to learn models that are fair by design. Despite the myriad of mitigation techniques developed in the past decade, however, it is still poorly understood under what circumstances which methods work. Recently, Wick et al. showed, with experiments on synthetic data, that there exist situations in which bias mitigation techniques lead to more accurate models when measured on unbiased data. Nevertheless, in the absence of a thorough mathematical analysis, it remains unclear which techniques are effective under what circumstances. We propose to address this problem by establishing relationships between the type of bias and the effectiveness of a mitigation technique, where we categorize the mitigation techniques by the bias measure they optimize. In this paper we illustrate this principle for label and selection bias on the one hand, and demographic parity and "We're All Equal" on the other hand. Our theoretical analysis allows to explain the results of Wick et al. and we also show that there are situations where minimizing fairness measures does not result in the fairest possible distribution. [ABSTRACT FROM AUTHOR]

Federated learning is a mechanism for model training in distributed systems, aiming to protect data privacy while achieving collective intelligence. In traditional synchronous federated learning, all participants must update the model synchronously, which may result in a decrease in the overall model update frequency due to lagging participants. In order to solve this problem, asynchronous federated learning introduces an asynchronous aggregation mechanism, allowing participants to update models at their own time and rate, and then aggregate each updated edge model on the cloud, thus speeding up the training process. However, under the asynchronous aggregation mechanism, federated learning faces new challenges such as convergence difficulties and unfair model accuracy. This paper first proposes a fairness-based asynchronous federated learning mechanism, which reduces the adverse effects of device and data heterogeneity on the convergence process by using outdatedness and interference-aware weight aggregation, and promotes model personalization and fairness through an early exit mechanism. Mathematical analysis derives the upper bound of convergence speed and the necessary conditions for hyperparameters. Experimental results demonstrate the advantages of the proposed method compared to baseline algorithms, indicating the effectiveness of the proposed method in promoting convergence speed and fairness in federated learning. [ABSTRACT FROM AUTHOR]

Wireless Body Area Networks (WBANs) are critical in medical emergency services within the Internet of Things (IoT). Ensuring efficient channel utilization while avoiding collisions and optimizing route allocation is a significant research focus in this field. However, the existing CSMA/CA methods need help updating the contention window and achieving fair node distribution. This paper proposes a novel Prime number-based Backoff Counter Adjustment (PBCA) strategy to address this issue. The PBCA algorithm dynamically adjusts the contention window based on the success counter and the prime backoff stages (BS). A mathematical analysis of the proposed PBCA algorithm uses Discrete-Time Markov Chains to study its impact on saturated throughput and collision probability. The proposed algorithm simulation experiments demonstrate the superiority of the PBCA algorithm over existing approaches. The proposed strategy significantly enhances throughput, reduces packet loss and delay, and ensures the reliability of the WBAN network. Compared to existing algorithms, the PBCA algorithm optimizes 48.1% in throughput, 39.47% in packet loss, 45.11% in delay, and 78.62% in reliability. These results outstand the performance of the existing algorithms. This advancement holds promise for enhancing performance and reliability in medical emergency services within IoT applications. The future extension of this work involves integrating reinforcement learning techniques to assess network status accurately, enabling adaptive and intelligent channel allocation in wireless body area networks. [ABSTRACT FROM AUTHOR]

In particular, the four papers address the following issues: In his paper "How to justify the symmetrization postulate in quantum mechanics", Tomasz Bigaj examines the question of how quantum mechanics justifies the Symmetrisation Postulate - mainly with respect to many particle systems. Still, these distinguishable particles cannot be those that are labelled by the tensor product indices "1" and "2", since both particle 1 and particle 2 - if there is any such particle - would be in the same mixed state. For example, in such a state (1) there apparently is a particle located at I R i with spin-up and another particle located at I L i with spin-down; two (not merely weakly) distinguishable particles apparently emerge within such states. [Extracted from the article]

Along with the significant growth of applications and facilities provided by the Internet of Things (IoT) in recent years, security challenges and related issues to privacy become considerable interest of researchers. On the other hand, the de facto IoT routing protocol for low-power and lossy networks called RPL is vulnerable to various types of routing attacks. Many researchers have investigated RPL security solutions focusing on effective detection of prevalent and destructive routing attacks such as blackhole attack, selective forwarding attack, rank attack and so on. Recent studies are proposing trust-based mechanisms with the aim of replacing traditional cryptography-based operations with lightweight security models in order to cover the inherent challenges of IoT devices, including energy and computational limitations. Therefore, in this paper, focusing on the problem of RPL vulnerability against well-known routing attacks, we have proposed a trust-based attack detection model, which investigates traffic behavior in different attack scenarios and detects malicious nodes relying on behavior deviation exactly at the same time as the start of any attack activity. Expected behavior is predicted by our learning model trained from the historical routing behavior pattern, using recurrent neural networks as a powerful deep learning method, which leads to attack detection with high-level accuracy and precision. Both mathematical analysis and simulation results on multiple RPL attack scenarios show clearly that the proposed trust-based defense mechanism is an effective approach capable of timely and precisely detection of routing behavior pattern deviation of malicious nodes exactly at the start time of the attack occurrence, which leads to attack detection and attacker identification based on trust scores extracted from the detected fluctuations between expected and real routing behavior patterns. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel protection scheme for N-qubit Greenberger–Horne–Zeilinger (GHZ) states against amplitude damping noise, using unilateral operations. The key innovation lies in the implementation of local operations on a single qubit, irrespective of the total number of qubits, thereby significantly reducing the operational complexity and resource requirements compared to existing methods. The scheme involves a unilateral rotation to transform the GHZ state into a less vulnerable configuration before exposing it to noise, followed by a weak measurement and another unilateral rotation to recover the initial state. We provide a comprehensive mathematical analysis of the proposed unilateral protection scheme, deriving expressions for both fidelity and success probability. The practical feasibility of our scheme is demonstrated through simulations using the Qiskit SDK, in which we provide the corresponding quantum circuit for performing the partial weak measurement used in our scheme. Comparative analysis with pioneer protection schemes reveals a substantial enhancement in success probability and fidelity for both GHZ and generalized GHZ states, emphasizing the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

Sulfidation-vacuum distillation is a sustainable approach for extracting elemental tellurium from industrial copper telluride slag, but the volatilization law of tellurium in the Te–Cu2S system is unclear, which hinders the development of tellurium recovery methods. In this paper, vacuum differential gravimetric mathematical statistical analysis was conducted to determine the evaporation rate of tellurium in the Te–Cu2S system under the conditions of 773 K to 923 K and 10–10,000 Pa. The experimental results showed that the relationship model between the evaporation rate and the pressure was ω = A2 + (A1 − A2)/(1 + (P/P0)m) at a constant distillation temperature. The evaporation rate satisfied the linear Eq. lg ω = A + B/T at the 95 pct confidence level under a constant system pressure. The experiments verified that the accuracy of the model was about 95 pct. The qualitative and quantitative relationship between the evaporation rate, time, and evaporation of tellurium in the Te–Cu2S system was discussed through experimental research and data analysis. The evaporation dynamics were summarized and used to predict the vacuum separation process in the Te–Cu2S system. This research is oriented by practical problems and aims to quantitatively determine the conceptual relationship among time, so as to provide practical reference for the production process and save time and cost. [ABSTRACT FROM AUTHOR]

Mahāyāna sūtras are obviously texts in the conventional sense of the word, but how they work as texts, the purposes they serve, and the manner in which they are constructed have so far attracted comparatively little sustained theoretical attention of the sort that goes beyond specific examples. This paper addresses itself to two well-known formal features of this voluminous genre which have yet to receive the critical reflection they deserve. The first is a pervasive self-referentiality, taking various forms, some of them fairly straightforward, even banal, others highly challenging and paradoxical in their effect. The second feature is the use of formulas and lists, not singly, but in combination, in a way which expands a theme along two or more axes or vectors concurrently. These two features, while by no means exhaustive of all the things that make Mahāyāna sūtras the distinctive type of scripture they are, provide evidence of a passion for complexity which seems to be part of their DNA. Intensely generative of ever greater amounts of text, these features blur and even erase the boundaries between the creators of texts, the writers and speakers, and their consumers, the readers and hearers. In this paper they are explored with special reference to a small number of sūtras, some of which are demonstrably early productions of the Mahāyāna movement. [ABSTRACT FROM AUTHOR]

Autonomous network management is crucial for Fifth Generation (5G) and Beyond 5G (B5G) networks, where a constantly changing environment is expected and network configuration must adapt accordingly. Modeling tools are required to predict the impact on performance (packet and delay loss) when new traffic demands arrives and when changes in routing paths are applied in the network. Mathematical analysis and network simulators are techniques for modeling networks but both have limitations, as the former provides low accuracy and the latter requires high execution times. To overcome these limitations, machine learning (ML) algorithms, and more specifically, graph neural networks (GNNs), are proposed for network modeling due to their ability to capture complex relationships from graph-like data while predicting network properties with high accuracy and low computational requirements. However, one of the main issues when using GNNs is their lack of generalization capability to larger networks, i.e., when trained in small networks (in number of nodes, paths length, links capacity), the accuracy of predictions on larger networks is poor. This paper addresses the GNN generalization problem by the use of fundamental networking concepts. Our solution is built from a baseline GNN model called RouteNet (developed by Barcelona Neural Networking Center-Universitat Politècnica de Catalunya (BNN-UPC)) that predicts the average delay in network paths, and through a number of simple additions significantly improves the prediction accuracy in larger networks. The improvement ratio compared to the baseline model is 101, from a 187.28% to a 1.828%, measured by the Mean Average Percentage Error (MAPE). In addition, we propose a closed-loop control context where the resulting GNN model could be potentially used in different use cases. [ABSTRACT FROM AUTHOR]

The adaptive interference cancellation technique has been widely utilized in radar, GPS, data link, etc., systems to address challenges from external interference, such as co-site and hostile interference. Since the anti-jamming performance of the adaptive interference cancellation technique is sensitive to group delay mismatch between channels, the group delay mismatch becomes one of the main factors that limit the system's anti-jamming capability. However, the traditional adaptive interference cancellation system's mathematical model cannot quantitatively characterize the group delay mismatch effect on the wideband interference cancellation performance. In this paper, the mathematical model of the wideband adaptive spatial interference cancellation (ASIC) system is established, which considers the group delay mismatch, to quantitatively analyze the impact of group delay mismatch on the hostile interference cancellation. The mathematical model utilizes the weighted multi-tone signals to fit the wideband interference, and then, delay differences are attached to each tone signal to simulate the group delay mismatch. Then, the analytic expressions of weight and interference cancellation ratio are derived, which consider the interference bandwidth and group delay mismatch, to quantitatively analyze the group delay mismatch effect on the anti-jamming performance of the wideband ASIC system. Simulation results indicate that the theoretical analysis based on the mathematical model of wideband ASIC system are accurate, which can achieve the quantitative analysis of the group delay mismatch effect on the WIC performance. [ABSTRACT FROM AUTHOR]

Current-day data centers and high-volume cloud services employ a broad set of heterogeneous servers. In such settings, client requests typically arrive at multiple entry points, and dispatching them to servers is an urgent distributed systems problem. This paper presents an efficient solution to the load balancing problem in such systems that improves on and overcomes problems of previous solutions. The load balancing problem is formulated as a stochastic optimization problem, and an efficient algorithmic solution is obtained based on a subtle mathematical analysis of the problem. Finally, extensive evaluation of the solution on simulated data shows that it outperforms previous solutions. Moreover, the resulting dispatching policy can be computed very efficiently, making the solution practically viable. [ABSTRACT FROM AUTHOR]

This research clarifies the horizontal and vertical alignment of the capacitive coupler to be used in electric vehicles for wireless power transfer. Using various compensation techniques, capacitive power transfer circuits were modeled and analyzed. For safety purposes, this concept is used to identify mutual capacitance and field emission around the charging system. The methodology of circuit formation for an effective coupler design was described. The output power of the compensation circuits implemented in the coupler design was obtained from mathematical analysis. The finite element analysis (FEA) method was used in the ANSYS Maxwell software package to find mutual capacitances and field emission area by the transmitter. The suitable compensation network was identified from various ways to calculate the output power. The coupler design with the alignment of the parallel plates in both vertical and horizontal orientations was proposed. The response of the mutual capacitance upon varying the length of the plates, air gap distance and misalignment positions were predicted. This paper contains suitable dimensions of capacitive plates and their respective capacitance value for different airgaps and misalignments of the plates placed on source and vehicle sides of the circuit. In addition to the modified-coupler design with the horizontally aligned plates, the coupler model with vertically aligned capacitive plates is proposed. This model is more suitable for wireless power transfer as it does not cause misalignment issues because of its symmetrical structure. [ABSTRACT FROM AUTHOR]

We study linear time-dependent Maxwell equations on a cuboid consisting of two homogeneous subcuboids. At the interface, we allow for nonzero surface charge density and surface current. This model is a first step towards a detailed mathematical analysis of the interaction of single-layer materials with electromagnetic fields. The main results of this paper provide several wellposedness and regularity statements for the solutions of the Maxwell system. To prove the statements, we employ extension arguments using interpolation theory, as well as semigroup theory and regularity theory for elliptic transmission problems. [ABSTRACT FROM AUTHOR]

This paper develops a coupled chemo-mechanical model for stress-assisted diffusion in the framework of micropolar elasticity. The two-way interaction of mechanical and chemical driving forces as well as internal microstructure of the polar media is taken into account. The fundamental governing equations of chemo-mechanics with kinetics driven by diffusion and stress are developed, and mathematical expressions for stress and concentration fields are derived. Using Airy stress functions, a simplified formulation for two-dimensional chemo-elasticity problems under chemical equilibrium is presented. Using a perturbation approach to solve the presented system of equations, closed-form expressions for different field parameters can be obtained. As an illustrative case study, expressions for the stress and solute concentration in an infinite plate with circular hole embedded in a chemical medium have been written. The derived equation and proposed solution approach can be applied to various plane micropolar chemo-elasticity problems for studying the interaction between mechanical and chemical driving forces as well as material length-scale parameters. [ABSTRACT FROM AUTHOR]

Fog computing is a computing structure which is distributed in nature. Low latency, reasonably low communication overhead and ability to support real time applications are the reasons for which fog computing approach said to provide better performance than cloud computing. Although, it is an extension of the cloud computing. Fog computing also inherits some critical security and privacy issues of cloud computing. Secure key management and user authentication are among the key issues faced by fog computing. Various schemes with probable solutions of these issues have been proposed by many authors in this context. Among them, a notable scheme has been presented by Wajid et al. known as SAKA-FC, where authors used three-factor authentication with privacy preservation for remote user based on ECC, hash functions, fuzzy extractor and symmetric bivariate polynomial function. This paper analyses the SAKA-FC protocol and found that it is not resilient against fog server insider attack, message intercept attack and replay attack. Consequently, an improved, lightweight and secure authentication scheme in context of fog-centric IoT communication is proposed in this paper to eradicate all the above mentioned security shortfalls of Wajid et al scheme. The proposed scheme is verified using mathematical security analysis and simulated using AVISPA which proves that the proposed scheme prevents all pertinent security threats. The performance analysis of our scheme proves its effectiveness over other related existing schemes in this context. [ABSTRACT FROM AUTHOR]

The main goal of mathematical modeling and analysis of queueing systems is to understand the dynamic behavior of the underlying processes, enabling informed and intelligent management decisions. While the queueing systems with random factors have received extensive scrutiny, this paper introduces an uncertain queueing model that considers the belief degree of customer behavior. In this model, customers arrive in groups and the interarrival times and service times are treated as uncertain variables. To evaluate the performance of this proposed uncertain queueing model, the busy index and busy period are also discussed, and the analytical formulas and uncertainty distribution are derived respectively. Additionally, two numerical examples are also given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In cognitive radio networks (CRNs), rendezvous is the vital step prior to the communication between two unlicensed secondary users (SUs), where the SUs hop on the same channel at the same time to establish a link. With the dramatic fall in the cost and size of wireless transceivers, it becomes more reasonable to apply multiple radios to achieve significant improvement in the rendezvous performance. However, most of the existing multiradio rendezvous algorithms are proposed for homogeneous CRNs where all the SUs are equipped with an equal number of radios and do not possess backward compatibility to SU with a single radio. In reality, the CRNs are heterogeneous in nature as SUs may have different numbers of radios. In this paper, a composite CH algorithm is proposed for an asynchronous and heterogeneous network to achieve blind rendezvous with full rendezvous diversity. An SU with m number radios are categorized into three groups those follow different channel hopping (CH) algorithms. The upper bound of the rendezvous latency is being evaluated with a brief theoretical and mathematical analysis. Extensive simulations have conducted for different performance metrics, and the results are compared with the state-of-art algorithms. Overall, the proposed algorithm shows better performance in heterogeneous CRNs. [ABSTRACT FROM AUTHOR]

This paper focuses on developing an efficient numerical approach based on Taylor-wavelets for solving three-point (nonlocal) singular boundary value problems. A special case of the considered problem, with strongly nonlinear source term, arises in thermal explosion in a cylindrical reactor. The existence of a unique solution is thoroughly discussed for the considered problem. To establish the current method, an equivalent integral equation is constructed for the original problem to overcome the singularity at the origin. The evaluation of derivatives appearing in the model is also avoided in this way. Moreover, this scheme skips the integrals while reducing them into a system of nonlinear algebraic equations. Unlike other methods, this new approach does not require any linearization, discretization, perturbation, or evaluation of nonlinear terms separately. To the best of our knowledge, this is the first application of the wavelet-based method to the considered problem. The formulation of the proposed method is further supported by its convergence and error analysis. Some numerical examples are solved to validate the efficiency and robustness of the proposed method. Further, the computational convergence rate (COR) is reported for the first few examples to assist the obtained numerical solution. Moreover, the obtained numerical results are compared with those of existing techniques in the literature. [ABSTRACT FROM AUTHOR]

Studying convection–diffusion problems of delayed type in physics helps us to understand transport phenomena and has practical applications in various fields. The mathematical analysis of this model has practical applications in various fields, such as flow dynamics, material science, and environmental modeling. In this paper, the theory of reproducing kernel spaces (RKS) is utilized to solve singularly perturbed 2D parabolic convection–diffusion problems of delayed type. To this end, a series form for the solution is first constructed in reproducing kernel Hilbert space, and then, the approximate solution is given as an N -term summation. The main contribution of the present research is that, for the first time, a novel formula is found for the homogenization of 2D initial-boundary-value problems. Furthermore, a semi-analytical RKS method is employed without employing the Gram–Schmidt orthogonalization algorithm. We derive theorems to reveal stability and convergence properties which are examined by numerical experiments. The technique is especially suited for problems having boundary-layer behavior. Numerical results are provided to demonstrate the efficiency, stability, and superiority of the proposed technique. [ABSTRACT FROM AUTHOR]

In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination of a local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the Wasserstein distance, which allows to set forth an interesting connection between PCRs and some classical problems arising in mathematical analysis, probability and statistics, e.g., Laplace methods for approximating integrals, Sanov's large deviation principles in the Wasserstein distance, rates of convergence of mean Glivenko–Cantelli theorems, and estimates of weighted Poincaré–Wirtinger constants. We first present a theorem on PCRs for a model in the regular infinite-dimensional exponential family, which exploits sufficient statistics of the model, and then extend such a theorem to a general dominated model. These results rely on the development of novel techniques to evaluate Laplace integrals and weighted Poincaré–Wirtinger constants in infinite-dimension, which are of independent interest. The proposed approach is applied to the regular parametric model, the multinomial model, the finite-dimensional and the infinite-dimensional logistic-Gaussian model and the infinite-dimensional linear regression. In general, our approach leads to optimal PCRs in finite-dimensional models, whereas for infinite-dimensional models it is shown explicitly how the prior distribution affect PCRs. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results. [ABSTRACT FROM AUTHOR]

With the advent and advancement of machine learning and deep learning techniques, machine-based recognition systems for mathematical text have captivated the attention of the research community for the last four decades. Mathematical Expression Recognition systems have been identified based on terms of their techniques, approach, dataset, and accuracies. This study majorly targets a rigorous review of both the published form of literature and the least attended literature, i.e., grey literature. Apart from the digital libraries, the papers and other instances of information have been gathered from the grey sources like google patents, archives, technical reports, app stores, etc., culminating in 262 instances. After the heedful filtration imposed on both white and grey literature, the final pool of studies has been investigated for eight formulated research questions. The answers extracted have been analyzed, providing both quantitative and qualitative insights. The analysis and surveys have systematically summed up the potentials of both white and grey shades of literature present on MER and brought exciting extractions out of 155 formal white literature and 107 grey sources. The survey extracts and brings out the highlighting observations after analysis, which sublimates the fact that 52% of grey literature is composed of mobile applications and user interfaces, whereas the published 63% of white data is presently concentrated in 39 different conferences, and the prominent conference is ICDAR (#30). A list of challenges and open issues has been extracted for directing future research dimensions. [ABSTRACT FROM AUTHOR]

Fractional calculus is an important branch of mathematical analysis and played a fundamental role in different fields including signal processing and image processing. In this paper, we proposed a sparse super-resolution (SR) technique by using the Grünwald-Letnikov (G–L) fractional differential operator, which aims to reconstruct high-resolution images by recovering pixel information from low-resolution images. We suggested a modified fractional derivative mask based on G–L for image enhancement. The proposed method suppresses block artifacts, staircase edges, and false edges near the edges. The proposed method is very flexible and preserves detailed features. The obtained experiments demonstrated that fractional operator can nonlinearly preserve the low-frequency contour information in the smooth region and also nonlinearly improve well the high-frequency edge and texture of the image. In sparse SR images, the dictionary is constructed by texture information of the images by using integer derivatives. In this work, we computed dictionary matrices by applying the fractional masks. In fact, the extracted features based on fractional derivatives are utilized in the dictionary training procedure and sparse coding. The experimental results and analysis on natural images indicated that the proposed method achieved much better results than other algorithms in terms of both quantitative measures and visual perception. [ABSTRACT FROM AUTHOR]

This paper proposes an energy-efficient hybrid medium access control protocol based on precise control of duty cycle. To save energy, the proposed protocol optimally adjusts the trans-receiver radio's turn-on and off time. By estimating slot utilization, both the cluster head and the sensing devices save energy. During the reserved slot duration, each sensor device periodically checks its buffer status and turns off its radio when the buffer becomes empty. Each sensor device sends a slot utilisation status to the cluster head device. The cluster head device also turns its radio on and off based on the slot utilisation status of sensing devices. For optimal energy consumption, a duty cycle approach is proposed. According to the mathematical and simulation results, the proposed protocol consumes less energy than existing equivalent protocols. Simulation results depict, exactly similar results of analytical and mathematical analysis prove the validity of the work. [ABSTRACT FROM AUTHOR]

This report presents a comprehensive approach to dispersion management, including various techniques, mathematical analysis, and their advantages and disadvantages in different scenarios. A deep mathematical analysis of chirped fiber Bragg grating (CFBG) is conducted for various chirping techniques and apodization profiles, highlighting the importance of this aspect in dispersion management. Additionally, a detailed study of the implementation of CFBG and dispersion compensating fiber (DCF) is performed to determine which technique is suitable for long-haul links and which is best for WDM networks, both for low and high capacity. The report also sheds light on how dispersion compensation techniques can be useful in mm wave propagation. The paper provides new insights into the field of dispersion management and the results of the study make it an interesting and valuable addition to the literature. [ABSTRACT FROM AUTHOR]

We are interested in a reduced model for corrosion of iron, in which ferric cations and electrons evolve in a fixed oxide layer subject to a self-consistent electrostatic potential. Reactions at the boundaries are modeled thanks to Butler–Volmer formulas, whereas the boundary conditions on the electrostatic potential model capacitors located at the interfaces between the materials. Our model takes inspiration in existing papers, to which we bring slight modifications in order to make it consistent with thermodynamics and its second principle. Building on a free energy estimate, we establish the global in time existence of a solution to the problem without any restriction on the physical parameters, in opposition to previous works. The proof further relies on uniform estimates on the chemical potentials that are obtained thanks to Moser iterations. Numerical illustrations are finally provided to highlight the similarities and the differences between our new model and the one previously studied in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical framework using multiple reconfigurable intelligent surfaces (RISs) for enhancing the secrecy performance of wireless systems. In particular, multiple RISs are exploited to support transmitter-legitimate user communication under the existence of an eavesdropper. Two practical scenarios are investigated, i.e., there are only transmitter-eavesdropper links (case 1) and there are both transmitter-eavesdropper and transmitter-RIS-eavesdropper links (case 2). We mathematically obtain the closed-form expressions of the average secrecy capacity (ASC) of the considered system in these two investigated cases over Nakagami-m fading channels. The impacts of the system parameters, such as the locations of the RISs, the number of REs, and the Nakagami-m channels, are deeply evaluated. Computer simulations are used to validate our mathematical analysis. Numerical results clarify the benefits of using multiple RISs for improving the secrecy performance of wireless systems. Specifically, the ASCs in cases 1 and 2 are significantly higher than that in the case without RISs. Importantly, when the locations of the RISs are fixed, we can arrange the larger RSIs near either the transmitter or legitimate user to achieve higher ASCs. In addition, when the numbers of reflecting elements (REs) in the RISs increase, the ASCs in cases 1 and 2 are greatly enhanced. [ABSTRACT FROM AUTHOR]

In the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we determine how the positive feedback loops generated by the auto- and cross-catalysis among repressive modifications affect the temporal duration of the cell identity. To this end, we conduct a stochastic analysis of a recently published chromatin modification circuit considering two limiting behaviors: fast erasure rate of repressive histone modifications or fast erasure rate of DNA methylation. In order to perform this mathematical analysis, we first show that the deterministic model of the system is a singular singularly perturbed (SSP) system and use a model reduction approach for SSP systems to obtain a reduced one-dimensional model. We thus analytically evaluate the reduced system's stationary probability distribution and the mean switching time between active and repressed chromatin states. We then add a computational study of the original reaction model to validate and extend the analytical findings. Our results show that the absence of DNA methylation reduces the bias of the system's stationary probability distribution toward the repressed chromatin state and the temporal duration of this state's memory. In the absence of repressive histone modifications, we also observe that the time needed to reactivate a repressed gene with an activating input is less stochastic, suggesting that repressive histone modifications specifically contribute to the highly variable latency of state reactivation. [ABSTRACT FROM AUTHOR]

In this paper, we tame the uncertainty about the volatility in time-averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs) based on the Lyapunov condition. That means we treat the time-averaging principle for stochastic differential equations based on the Lyapunov condition in the presence of a family of probability measures, each corresponding to a different scenario for the volatility. The main tool for the mathematical analysis is the G-stochastic calculus, which is introduced in the book by Peng (Nonlinear Expectations and Stochastic Calculus Under Uncertainty. Springer, Berlin, 2019). We show that the solution of a standard equation converges to the solution of the corresponding averaging equation in the sense of sublinear expectation with the help of some properties of G-stochastic calculus. Numerical results obtained using PYTHON illustrate the efficiency of the averaging method. [ABSTRACT FROM AUTHOR]