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The present paper describes, in a theoretical fashion, a variational approach to formulate fourth-order dynamical systems on differentiable manifolds on the basis of the Hamilton–d'Alembert principle of analytic mechanics. The discussed approach relies on the introduction of a Lagrangian function that depends on the kinetic energy and the covariant acceleration energy, as well as a potential energy function that accounts for conservative forces. In addition, the present paper introduces the notion of Rayleigh differential form to account for non-conservative forces. The corresponding fourth-order equation of motion is derived, and an interpretation of the obtained terms is provided from a system and control theoretic viewpoint. A specific form of the Rayleigh differential form is introduced, which yields non-conservative forcing terms assimilable to linear friction and jerk-type friction. The general theoretical discussion is complemented by a brief excursus about the numerical simulation of the introduced differential model. [ABSTRACT FROM AUTHOR]

In recent years, the escalating risk of natural disasters caused by Near-Earth Objects (NEOs) has garnered heightened scrutiny, particularly in the aftermath of the 2013 Chelyabinsk event. This has prompted increased interest from governmental and supranational entities, leading to the formulation of various measures and strategies aimed at mitigating the potential threat posed by NEOs. This paper delves into the analysis of the 2011 AG5 asteroid within the context of small celestial bodies (e.g., asteroids, comets, or meteoroids) exhibiting resonant orbits with Earth's heliocentric revolution. Initial observations in 2011 raised alarms regarding the asteroid's orbital parameters, indicating a significant risk of Earth impact during its resonant encounter in 2040. Subsequent observations, however, mitigated these concerns. Here, we manipulate the orbital elements of the 2011 AG5 asteroid to simulate its behavior as a virtual impactor (a virtual asteroid whose orbit could impact Earth). This modification facilitates the assessment of impact mitigation resulting from a deflection maneuver utilizing a kinetic impactor. The deflection maneuver, characterized as an impulsive change in the asteroid's momentum, is executed during a resonant encounter occurring approximately two decades before the potential impact date. The paper systematically evaluates the dependence of the deflection maneuver's efficacy on critical parameters, including the position along the orbit, epoch, and momentum enhancement factor. [ABSTRACT FROM AUTHOR]

With the frequent occurrence of financial risks, financial innovation supervision has become an important research issue, and excellent regulatory strategies are of great significance to maintain the stability and sustainable development of financial markets. Thus, this paper intends to analyze the financial regulation strategies through evolutionary game theory. In this paper, the delayed replication dynamic equation and the non-delayed replication dynamic equation are established, respectively, under different reward and punishment mechanisms, and their stability conditions and evolutionary stability strategies are investigated. The analysis finds that under the static mechanism, the internal equilibrium is unstable, and the delay does not affect the stability of the system, while in the dynamic mechanism, when the delay is less than a critical value, the two sides of the game have an evolutionary stable strategy, otherwise it is unstable, and Hopf bifurcation occurs at threshold. Finally, some numerical simulation examples are provided, and the numerical results show the correctness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Deep learning technology has made significant progress in agricultural image recognition tasks, but the parameter adjustment of deep models usually requires a lot of manual intervention, which is time-consuming and inefficient. To solve this challenge, this paper proposes an adaptive parameter tuning strategy that combines sine–cosine algorithm with Tent chaotic mapping to enhance sea horse optimization, which improves the search ability and convergence stability of standard sea horse optimization algorithm (SHO). Through adaptive optimization, this paper determines the best parameter configuration in ResNet-50 neural network and optimizes the model performance. The improved ESHO algorithm shows superior optimization effects than other algorithms in various performance indicators. The improved model achieves 96.7% accuracy in the corn disease image recognition task, and 96.4% accuracy in the jade fungus image recognition task. These results show that ESHO can not only effectively improve the accuracy of agricultural image recognition, but also reduce the need for manual parameter adjustment. [ABSTRACT FROM AUTHOR]

This paper investigates the relationship between generalized orthogonality and Gâteaux derivative of the norm in a normed linear space. It is shown that the Gâteaux derivative of x in the y direction is zero when the norm is Gâteaux differentiable in the y direction at x and x and y satisfy certain generalized orthogonality conditions. A case where x and y are approximately orthogonal is also analyzed and the value range of the Gâteaux derivative in this case is given. Moreover, two concepts are introduced: the angle between vectors in normed linear space and the ⊥ Δ coordinate system in a smooth Minkowski plane. Relevant examples are given at the end of the paper. [ABSTRACT FROM AUTHOR]

On the basis of K. Kuratowski's definitions of a topological structure with a closure or interior operator, the concept of a modal topological structure (MTS) with one of these operators was introduced by the author. This new structure was illustrated with examples with intuitionistic fuzzy topological operators from both examples, and for this reason, these structures were named intuitionistic fuzzy MTSs (IFMTSs). In a series of papers, the author introduced some modifications and extensions to the IFMTSs, e.g., intuitionistic fuzzy temporal topological structures, intuitionistic fuzzy level topological structures and others, and intuitionistic fuzzy multi modal topological structures and others. In the present paper, four new examples of intuitionistic fuzzy multi modal topological structures are given. On their base, the concepts of a modal multi-topological structure and of a multi-modal multi-topological structure are introduced and illustrated with examples from the area of the intuitionistic fuzzy sets—intuitionistic fuzzy modal multi-topological structure with a closure or an interior operator; and intuitionistic fuzzy multi-modal multi-topological structure with one of these operators. Two intuitionistic fuzzy topological operators are defined. Their basic properties are studied and they are used in the new structures. [ABSTRACT FROM AUTHOR]

It is well known that in C [ X ] , the product of two polynomials is equal to the product of their greatest common divisor and their least common multiple. In a recent paper, we proved a similar relation between the ranks of matrix polynomials. More precisely, the sum of the ranks of two matrix polynomials is equal to the sum of the rank of the greatest common divisor of the polynomials applied to the respective matrix and the rank of the least common multiple of the polynomials applied to the respective matrix. In this paper, we present three new proofs for this result. In addition to these, we present two more applications. [ABSTRACT FROM AUTHOR]

In this paper, a filterless 32-tupling millimeter wave generation scheme based on eight MZMs is proposed. The system has an upper and lower parallel two-branch structure. The upper branch consists of two subsystems Sub-A and Sub-B in cascade, each subsystem contains four MZMs, and the MZMs are all operating at maximum transfer point (MATP). Sub-A mainly generates ±8th order optical sideband signal as the incident light signal of Sub-B. After modulation of Sub−B, the output signal is mainly ±16th order optical sideband signal containing the central optical carrier component. The optical attenuator (OATT) and optical phase shifter (OPS) of the lower branch are used to regulate the phase and amplitude of the optical carrier. The upper and lower branches are coupled, and the central optical carrier component is superimposed and cancelled so only the ±16th order optical sideband signal is retained. Finally, the 32-tupling frequency millimeter is generated by the photodiode (PD) receiver after photoelectric detection which receives and generates a 32-tupling frequency millimeter wave signal. The simulation results show that the 160 GHz millimeter wave signal can be obtained by driving the MZM with a 5 GHz RF signal, and the optical sideband suppression ratio (OSSR) and the RF sideband suppression ratio (RFSSR) are 52.6 dB and 44.75 dB, respectively. Theoretical analysis and simulation experiments are carried out for the proposed scheme which proves the feasibility of the scheme. [ABSTRACT FROM AUTHOR]

One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times by a few minutes will have a significant impact on the number of trips made by an aircraft, as well as enabling improvements in key measures such as the median and 75th and 95th percentiles. Looking at such measures other than the mean is critical as it is well known that the mean can under- or overestimate the performance of any model. While there is considerable literature on the study of strategies to decrease boarding times, the same cannot be said about the study of the boarding time given a particular strategy for boarding. Thus, the focus of this paper is to study analytically (using suitable stochastic models) and numerically the impact of reducing the average time on the key measures to help the system to plan accordingly. This is achieved using a well-known probability distribution, namely the phase type distribution, to model various events involved in the boarding process. Illustrative numerical results show a reduction in the percentile values when the average boarding times are decreased. Understanding the percentiles of the boarding times, as opposed to relying only on the average boarding times, will help management to adopt a better boarding strategy that in turn will lead to an increase in the number of trips that an aircraft can make. [ABSTRACT FROM AUTHOR]

This paper discusses a reduction in the optimal time due to the presence of input redundancy in time-optimal control problems. By introducing a non-idle channel to represent an active input channel, we establish the necessary and sufficient conditions that ensure a strict reduction in the optimal time for affine nonlinear systems. In cases of identical input redundancy, its impact varies according to the type of input constraint, and certain types may not lead to a reduction in the optimal time. Ultimately, in linear time-invariant (LTI) systems, the extent of the optimal time reduction depends on the system's controllability. [ABSTRACT FROM AUTHOR]

Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear constraints are assumed to hold in the parameter space. The Liu estimator is used to address the multicollinearity, while robust methods are used to handle the outlier problem. In the literature on the Liu methodology, obtaining the best value for the biased parameter plays an important role in model prediction and is still an unsolved problem. In this regard, some robust estimators of the biased parameter are proposed based on the least trimmed squares (LTS) technique and its extensions using a semidefinite programming approach. Based on a set of observations with a sample size of n, and the integer trimming parameter h ≤ n, the LTS estimator computes the hyperplane that minimizes the sum of the lowest h squared residuals. Even though the LTS estimator is statistically more effective than the widely used least median squares (LMS) estimate, it is less complicated computationally than LMS. It is shown that the proposed robust extended Liu estimators perform better than classical estimators. As part of our proposal, using Monte Carlo simulation schemes and a real data example, the performance of robust Liu estimators is compared with that of classical ones in restricted partially linear models. [ABSTRACT FROM AUTHOR]

Aiming at the problem of high failure rate and inconvenient maintenance of wind turbine gearboxes, this paper establishes a stochastic differential equation model that can be used to fit the change of gearbox oil temperature and adopts an iterative computational method and Markov-based modified optimization to fit the prediction sequence in order to realize the accurate prediction of gearbox oil temperature. The model divides the oil temperature change of the gearbox into two parts, internal aging and external random perturbation, adopts the approximation theorem to establish the internal aging model, and uses Brownian motion to simulate the external random perturbation. The model parameters were calculated by the Newton–Raphson iterative method based on the gearbox oil temperature monitoring data. Iterative calculations and Markov-based corrections were performed on the model prediction data. The gearbox oil temperature variations were simulated in MATLAB, and the fitting and testing errors were calculated before and after the iterations. By comparing the fitting and testing errors with the ordinary differential equations and the stochastic differential equations before iteration, the iterated model can better reflect the gear oil temperature trend and predict the oil temperature at a specific time. The accuracy of the iterated model in terms of fitting and prediction is important for the development of preventive maintenance. [ABSTRACT FROM AUTHOR]

The appearance quality of fair-faced concrete plays a crucial role in evaluating the engineering quality, as the abundance of small-area bubbles generated during construction diminishes the surface quality of concrete. However, existing methods are plagued by sluggish detection speed and inadequate accuracy. Therefore, this paper proposes an improved method based on YOLOv5 to rapidly and accurately detect small bubble defects on the surface of fair-faced concrete. Firstly, to address the issue of YOLOv5 in generating prior boxes for imbalanced samples, we divide the image preprocessing part into small-, medium-, and large-area intervals corresponding to the number of heads. Additionally, we propose an area-based k-means clustering approach specifically tailored for the anchor boxes within each of these intervals. Moreover, we adjust the number of prior boxes generated by k-means clustering according to the training loss function to adapt to bubbles of different sizes. Then, we introduce the ECA (Efficient Channel Attention) mechanism into the neck part of the model to effectively capture inter-channel interactions and enhance feature representation. Subsequently, we incorporate feature concatenation in the neck part to facilitate the fusion of low-level and high-level features, thereby improving the accuracy and generalization ability of the network. Finally, we construct our own dataset containing 980 images of two classes: cement and bubbles. Comparative experiments are conducted on our dataset using YOLOv5s, YOLOv6s, YOLOxs, and our method. Experimental results demonstrate that the proposed method achieves the highest detection accuracy in terms of mAP0.5, mAP0.75, and mAP0.5:0.95. Compared to YOLOv5s, our method achieves a 7.1% improvement in mAP0.5, a 3.7% improvement in mAP0.75, and a 4.5% improvement in mAP0.5:0.95. [ABSTRACT FROM AUTHOR]

Some problems exist in classical optimization algorithms to solve multi-modal optimization problems and other complex systems. A Dynamic Niches-based Improved Hybrid Breeding Optimization (DNIHBO) algorithm is proposed to address the multi-modal optimization problem in the paper. By dynamically adjusting the niche scale, it effectively addresses the issue of niche parameter sensitivity. The structure of the algorithm includes three distinct groups: maintainer, restorer, and sterile lines for updating operations. However, the maintainer individuals often stagnate, leading to the risk of the local optima. To overcome this, neighborhood search and elite mutation strategies are incorporated, enhancing the balance between exploration and exploitation. To further improve individual utilization within niches, a niche restart strategy is introduced, ensuring sustained population diversity. The efficacy of DNIHBO is validated through simulations on 16 multi-modal test functions, followed by comparative analyses with various multi-modal optimization algorithms. The results convincingly demonstrate that DNIHBO not only effectively locates multiple global optima but also consistently outperforms other algorithms on test functions. These findings underscore the superiority of DNIHBO as a high-performing solution for multi-modal optimization. [ABSTRACT FROM AUTHOR]

This paper is concerned with the novel exact solitons for the truncated M-fractional (1+1)-dimensional nonlinear generalized Bretherton model with arbitrary constants. This model is used to explain the resonant nonlinear interaction between the waves in different phenomena, including fluid dynamics, plasma physics, ocean waves, and many others. A series of exact solitons, including bright, dark, periodic, singular, singular–bright, singular–dark, and other solitons are obtained by applying the extended sinh-Gordon equation expansion (EShGEE) and the modified (G ′ / G 2) -expansion techniques. A novel definition of fractional derivative provides solutions that are distinct from previous solutions. Mathematica software was used to obtain and verify the solutions. The solutions are shown through 2D, 3D, and density plots. A stability process was conducted to verify that the solutions are exact and accurate. Modulation instability was used to determine the steady-state results for the corresponding equation. [ABSTRACT FROM AUTHOR]

This paper studies an artificial neural network (ANN) for multi-asset European options. Firstly, a simple three-layer ANN-3 is established with undetermined weights and bias. Secondly, the time–space discrete PDE of the multi-asset option is given and the corresponding discrete data are fed into the ANN-3. Then, using least squares error as the objective function, the weights and bias of ANN-3 are trained well. Numerical examples are carried out to confirm the stability, accuracy and efficiency. Experiments show the ANN's relative error is about  0.8 % . This method can be extended into multi-layer ANN- q (q > 3)  and extended into American options. [ABSTRACT FROM AUTHOR]

Computer systems and applications generate large amounts of logs to measure and record information, which is vital to protect the systems from malicious attacks and useful for repairing faults, especially with the rapid development of distributed computing. Among various logs, the anomaly log is beneficial for operations and maintenance (O&M) personnel to locate faults and improve efficiency. In this paper, we utilize a large language model, ChatGPT, for the log parser task. We choose the BERT model, a self-supervised framework for log anomaly detection. BERT, an embedded transformer encoder, with a self-attention mechanism can better handle context-dependent tasks such as anomaly log detection. Meanwhile, it is based on the masked language model task and next sentence prediction task in the pretraining period to capture the normal log sequence pattern. The experimental results on two log datasets show that the BERT model combined with an LLM performed better than other classical models such as Deelog and Loganomaly. [ABSTRACT FROM AUTHOR]

This paper proposes a scheme that adds XOR bit operations into the encoding and decoding process of the conventional non-orthogonal multiple access (NOMA) system to alleviate performance degradation caused by the power distribution of the original signal. Because the conventional NOMA combines and sends multiple data within limited resources, it has a higher data rate than orthogonal multiple access (OMA), at the expense of error performance. However, by using the proposed scheme, both error performance and sum rate can be improved. In the proposed scheme, the transmitter sends the original data and the redundancy data in which the exclusive OR (XOR) values of the data are compressed using the superposition coding (SC) technique. After this process, the data rate of users decreases due to redundancy data, but since the original data are sent without power allocation, the data rate of users with poor channel conditions increases compared to the conventional NOMA. As a result, the error performance and sum rate of the proposed scheme are better than those of the conventional NOMA. Additionally, we derive an exact closed-form bit error rate (BER) expression for the proposed downlink NOMA design over Rayleigh fading channels. [ABSTRACT FROM AUTHOR]

Influence maximization in online social networks is used to select a set of influential seed nodes to maximize the influence spread under a given diffusion model. However, most existing proposals have huge computational costs and only consider the dyadic influence relationship between two nodes, ignoring the higher-order influence relationships among multiple nodes. It limits the applicability and accuracy of existing influence diffusion models in real complex online social networks. To this end, in this paper, we present a novel information diffusion model by introducing hypergraph theory to determine the most influential nodes by jointly considering adjacent influence and higher-order influence relationships to improve diffusion efficiency. We mathematically formulate the influence maximization problem under higher-order influence relationships in online social networks. We further propose a hypergraph sampling greedy algorithm (HSGA) to effectively select the most influential seed nodes. In the HSGA, a random walk-based influence diffusion method and a Monte Carlo-based influence approximation method are devised to achieve fast approximation and calculation of node influences. We conduct simulation experiments on six real datasets for performance evaluations. Simulation results demonstrate the effectiveness and efficiency of the HSGA, and the HSGA has a lower computational cost and higher seed selection accuracy than comparison mechanisms. [ABSTRACT FROM AUTHOR]

We revisit the problem of the computation of the limiting characteristics of (in)homogeneous continuous-time Markov chains with the finite state space. In general, it can be performed only numerically. The common rule of thumb is to interrupt calculations after quite some time, hoping that the values at some distant time interval will represent the sought-after solution. Convergence or ergodicity bounds, when available, can be used to answer such questions more accurately; i.e., they can indicate how to choose the position and the length of that distant time interval. The logarithmic norm method is a general technique that may allow one to obtain such bounds. Although it can handle continuous-time Markov chains with both finite and countable state spaces, its downside is the need to guess the proper similarity transformations, which may not exist. In this paper, we introduce a new technique, which broadens the scope of the logarithmic norm method. This is achieved by firstly splitting the generator of a Markov chain and then merging the convergence bounds of each block into a single bound. The proof of concept is illustrated by simple examples of the queueing theory. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for some existence results for nonlinear impulsive differential equations involving causal operators. Our method is based on the monotone iterative technique, a new differential inequality, and the Schauder fixed point theorem. Moreover, we consider three impulsive differential equations as applications to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we offer Ostrowski-type inequalities that extend the findings that have been proven for functions of one variable with values in Banach spaces, conducted in a remarkable study by Dragomir, to functions of two variables containing values in the product Banach spaces. Our findings are also an extension of several previous findings that have been established for functions of two variable functions. Prior studies on Ostrowski-type inequalities incriminated functions that have values in Banach spaces or Hilbert spaces. This study is unique and significant in the field of mathematical inequalities, and specifically in the study of Ostrowski-type inequalities, because they have been established for functions having values in a product of two Banach spaces. [ABSTRACT FROM AUTHOR]

In network data analysis, one of the important problems is determining if two collections of networks are drawn from the same distribution. This problem can be modeled in the framework of two-sample hypothesis testing. Several graph-based two-sample tests have been studied. However, the methods mainly focus on binary graphs, and many real-world networks are weighted. In this paper, we apply empirical likelihood to test the difference in two populations of weighted networks. We derive the limiting distribution of the test statistic under the null hypothesis. We use simulation experiments to evaluate the power of the proposed method. The results show that the proposed test has satisfactory performance. Then, we apply the proposed method to a biological dataset. [ABSTRACT FROM AUTHOR]

In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified Generalized-α time integration scheme combined with a nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the buckling and post-buckling problems of cylindrical shell structures. Additionally, geometric imperfections are constructed based on NURBS surface fitting, which can be naturally incorporated into the isogeometric analysis framework due to its seamless CAD/CAE integration feature. For stochastic analysis, the method of separation is adopted to model the stochastic geometric imperfections of cylindrical shells based on a set of measurements. We tested the accuracy and convergence properties of the proposed method with a cylindrical shell example, where measured geometric imperfections were incorporated. The ABAQUS reference solutions are also presented to demonstrate the superiority of the inherited smooth and high-order continuous properties of the isogeometric approach. For stochastic dynamic buckling analysis, we evaluated the buckling load variability and reliability functions of the cylindrical shell with 500 samples generated based on seven nominally identical shells reported in the geometric imperfection data bank. It is noted that the buckling load variability in the cylindrical shell obtained with static nonlinear analysis is also presented to show the differences between dynamic and static buckling analysis. [ABSTRACT FROM AUTHOR]

We propose a pricing formula for a defaultable zero-coupon bond with imperfect information under a regime switching model using a structural form of credit risk modelling. This paper provides explicit representations of risky debt under regime switching with a constant interest rate and risky debt under regime switching with a regime switching interest rate. While the value of the firm's equity is observed continuously, we assume that the total value of the firm is only observed at discrete times, such as the dates of the release of the firm's annual reports, or quarterly reports. This uncertainty about the true value of the firm results in credit spreads that do not approach zero as the debt approaches maturity, which is a problem with many structural models. The firm's value is typically decomposed into its equity and debt; however, we consider the asset–to–equity ratio, an accounting ratio used to examine a firm's financial well-being. The parameters in our model are regime switching, where the regime can be thought of as the state of the economy. A Markov chain with a constant transition rate matrix produces the regime switching. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to identify an optimal coefficient for evaluating a player's batting average, strike rate, and bowling average, aimed at achieving an optimal team score through dynamic modeling using a path integral method. Additionally, it introduces a new model for run dynamics, represented as a stochastic differential equation, which factors in the average weather conditions at the cricket ground, the specific weather conditions on the match day (including abrupt changes that may halt the game), total attendance, and home field advantage. An analysis of real data is been performed to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the application of the Verhulst logistic equation to model in retrospect the total COVID-19 cases in Senegal during the period from April 2022 to April 2023. Our predictions for April 2023 are compared with the real COVID-19 data for April 2023 to assess the accuracy of the model. The data analysis is conducted using Python programming language, which allows for efficient data processing and prediction generation. [ABSTRACT FROM AUTHOR]

The economic growth of developed or emerging countries through globalization has prompted them to increase their supply chain performance. A large number of concepts, tools, and methodologies have been proposed in support of this performance improvement. They are mainly based on the use of classical optimization or enterprise modeling methods. However, environmental and social issues, not to mention digital transformation, are often ignored or not sufficiently integrated. Indeed, the world geopolitical situation, the increase in oil prices, and the commitment to protect our earth require the integration of sustainability aspects and Industry 4.0 concepts like digital twin and artificial intelligence in transforming the supply chain. This paper focuses on defining a conceptual framework to support sustainable supply chain management and digital transformation. It aims to exploit the sustainability and digital maturity of companies to transform their supply chains and enhance their performance to meet the challenges of Industry 5.0. Several practices related to sustainability, as well as two use cases on optimization and digital twin, are presented to illustrate this framework. Finally, based on the previous practices and use cases, an adapted framework for the supply chain manager to support the transition from Industry 4.0 to Industry 5.0 has been developed, as well as a performance dashboard. [ABSTRACT FROM AUTHOR]

This paper studies a continuous-review stochastic replenishment model for a multi-component system with regular and emergency orders. The system consists of N parallel and independent components, each of which has a finite life span. In addition, there is a warehouse with a limited stock of new components. Each broken component is replaced by a new component from the stock. When no component is available, an emergency supply is ordered. The stock is managed according to an ((s , S) , (0 , Q e)) policy, which is a combination of an (s , S) policy for the regular order and a (0 , Q e) policy for the emergency order. The regular order is delivered after an exponentially distributed lead time, whereas the emergency order is delivered immediately. We study three sub-policies for emergency orders, which differ from each other in size and in relation to the regular order. Applying the results from queueing theory and phase-type properties, we derive the optimal thresholds for each sub-policy and then compare the economic benefit of each one. [ABSTRACT FROM AUTHOR]

This paper explores the numerical intergator of ODE based on combination of Appelroth's quadratization of dynamical systems with polynomial right-hand sides and Kahan's discretization method. Utilizing Appelroth's technique, we reduce any system of ordinary differential equations with a polynomial right-hand side to a quadratic form, enabling the application of Kahan's method. In this way, we get a difference scheme defining the one-to-one correspondence between the initial and final positions of the system (Cremona map). It provides important information about the Kahan method for differential equations with a quadratic right-hand side, because we obtain dynamical systems with a quadratic right-hand side that have movable branch points. We analyze algebraic properties of solutions obtained through this approach, showing that (1) the Kahan scheme describes the branch points as poles, significantly deviating from the behavior of the exact solution of the problem near these points, and (2) it disrupts algebraic invariant variety, in particular integral relations describing the relationship between old and Appelroth's variables. This study advances numerical methods, emphasizing the possibility of designing difference schemes whose algebraic properties differ significantly from those of the initial dynamical system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a novel T-S fuzzy parameter varying system with Markov jump, in which parameters depend not only on a Markov chain but also on linear parameter varying elements that take values in convex polytopic sets. Stable conditions and the gain-scheduling controller design method for this system are obtained. Applying Lyapunov function depending on the operation mode and full block S-procedure lemma, we obtain stochastic stabilization conditions. We find that this novel system has two distinct advantages. On the one hand, it inherits the advantages of traditional T-S fuzzy systems in handling nonlinear objects under the frame of T-S fuzzy systems; on the other, it obtains the advantages of dealing with time-varying characteristics from the point of linear parameter varying (LPV) systems. Finally, the theory results are illustrated via numerical simulation. [ABSTRACT FROM AUTHOR]

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ -Fibonacci statistical convergence, strong Δ -Fibonacci summability, and Δ -Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers. [ABSTRACT FROM AUTHOR]

Nonautonomous nonlinear (NN) systems have broad application prospects and significant research value in nonlinear science. In this paper, a new synchronization type—namely, generalized bi-variable function projective synchronization (GBVFPS)—is proposed. The scaling function matrix of GBVFPS is not one-variable but bi-variable. This indicates that the GBVFPS can be transformed into various synchronization types such as projective synchronization (PS), modified PS, function PS, modified function PS, and generalized function PS. In order to achieve the GBVFPS in two different NN systems with various perturbations, by designing a novel Zhang neuro-PID controller, an effective and anti-perturbation GBVFPS control method is proposed. Rigorous theoretical analyses are presented to prove the convergence performance and anti-perturbation ability of the GBVFPS control method, especially its ability to suppress six different perturbations. Besides, the effectiveness, superiority, and anti-perturbation ability of the proposed GBVFPS control method are further substantiated through two representative numerical simulations, including the synchronization of two NN chaotic systems and the synchronization of two four-dimensional vehicular inverted pendulum systems. [ABSTRACT FROM AUTHOR]

In this paper we introduce Cayley digraphs associated to finitely generated polygroups, where the vertices correspond to finite products of the generators of polygroups and the edges to multiplication by vertices and generators. We investigate some properties of the Cayley digraphs, emphasizing connectivity and existence of cycles for each vertex of the Cayley digraphs. Particularly, we identify Cayley digraphs on polygroups derived from conjugate classes of dihedral groups. Moreover, we examine some fundamental illustrative examples of Cayley digraphs through the class of gmg-polygroups. [ABSTRACT FROM AUTHOR]

Various metaheuristic algorithms inspired by nature have been designed to deal with a variety of practical optimization problems. As an excellent metaheuristic algorithm, the improved particle swarm optimization algorithm based on grouping (IPSO) has strong global search capabilities. However, it lacks a strong local search ability and the ability to solve constrained discrete optimization problems. This paper focuses on improving these two aspects of the IPSO algorithm. Based on IPSO, we propose an improved particle swarm optimization algorithm based on variable neighborhood search (VN-IPSO) and design a 0-1 integer programming solution with constraints. In the experiment, the performance of the VN-IPSO algorithm is fully tested and analyzed using 23 classic benchmark functions (continuous optimization), 6 knapsack problems (discrete optimization), and 10 CEC2017 composite functions (complex functions). The results show that the VN-IPSO algorithm wins 18 first places in the classic benchmark function test set, including 6 first places in the solutions for seven unimodal test functions, indicating a good local search ability. In solving the six knapsack problems, it wins four first places, demonstrating the effectiveness of the 0-1 integer programming constraint solution and the excellent solution ability of VN-IPSO in discrete optimization problems. In the test of 10 composite functions, VN-IPSO wins first place four times and ranks the first in the comprehensive ranking, demonstrating its excellent solving ability for complex functions. [ABSTRACT FROM AUTHOR]

Safety signal detection is an integral component of Pharmacovigilance (PhV), which is defined by the World Health Organization as "science and activities relating to the detection, assessment, understanding, and prevention of adverse effects or any other possible drug related problems". The purpose of safety signal detection is to identify new or known adverse events (AEs) resulting from the use of pharmacotherapeutic products. While post-marketing spontaneous reports from different sources are commonly utilized as a data source for detecting these signals, there are underlying challenges arising from data complexity. This paper investigates the implementation of the Apriori algorithm, a popular method in association rule mining, to identify frequently co-occurring drugs and AEs within safety data. We discuss previous applications of the Apriori algorithm for safety signal detection and conduct a detailed study of an improved method specifically tailored for this purpose. This enhanced approach refines the classical Apriori method to effectively reveal potential associations between drugs/vaccines and AEs from post-marketing safety monitoring datasets, especially when AEs are rare. Detailed comparative simulation studies across varied settings coupled with the application of the method to vaccine safety data from the Vaccine Adverse Event Reporting System (VAERS) demonstrate the efficacy of the improved approach. In conclusion, the improved Apriori algorithm is shown to be a useful screening tool for detecting rarely occurring potential safety signals from the use of drugs/vaccines using post-marketing safety data. [ABSTRACT FROM AUTHOR]

The ABS (atom-bond sum-connectivity) index of a graph G is denoted by A B S (G) and is defined as ∑ x y ∈ E (G) (d x + d y) − 1 (d x + d y − 2) , where d x represents the degree of the vertex x in G. In this paper, we derive the best possible upper bounds on the ABS index for fixed-order trees possessing a given maximum degree, which provides a solution to the open problem proposed quite recently by Hussain, Liu and Hua. [ABSTRACT FROM AUTHOR]

With the rapid expansion of global trade, the complexity and diversification of supply chains have become increasingly significant. In particular, the supply chain for hazardous materials, involving chemicals and explosives, requires stringent regulation. Managing the flow of these high-risk goods necessitates a reliable access control system to ensure safety and compliance. Traditional supply chain management systems often rely on centralized databases and record-keeping systems, which are prone to tampering and single points of failure, making them inadequate for current high-security demands. This paper combines blockchain technology with a hazardous materials supply chain model. In the blockchain network, our innovation lies in the introduction of a transaction coordinator to create transaction sets for each supply chain entity along with smart contracts to implement access control for these transaction sets. We also propose a new hazardous materials supply chain model architecture and conduct experimental verification using simulated hazardous materials supply chain data. Our experimental results show that the proposed method performs excellently in throughput and latency tests, demonstrating the potential to enhance the efficiency and security of supply chain management. [ABSTRACT FROM AUTHOR]

Here we study the quantitative multivariate approximation of perturbed hyperbolic tangent-activated singular integral operators to the unit operator. The engaged neural network activation function is both parametrized and deformed, and the related kernel is a density function on R N . We exhibit uniform and L p , p ≥ 1 approximations via Jackson-type inequalities involving the first L p modulus of smoothness, 1 ≤ p ≤ ∞ . The differentiability of our multivariate functions is covered extensively in our approximations. We continue by detailing the global smoothness preservation results of our operators. We conclude the paper with the simultaneous approximation and the simultaneous global smoothness preservation by our multivariate perturbed activated singular integrals. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the delayed measure differential equations with nonlocal conditions via measure of noncompactness in ordered Banach spaces. Combining (β , γ k) -resolvent family, regulated functions and fixed point theorem with respect to convex-power condensing operator and measure of noncompactness, we investigate the existence of positive mild solutions for the mentioned system under the situation that the nonlinear function satisfies measure conditions and order conditions. In addition, we provide an example to verify the rationality of our conclusion. [ABSTRACT FROM AUTHOR]

Frequency control is one of the most important tasks in electric power systems. At the same time, in modern power systems with inertia-free converter-interfaced generation, this task has become more complex. Such an issue is especially relevant for microgrids, which are characterized by a significant increase in the rate of change of frequency and its nadir or zenith. An effective way is through the use of energy storage systems (ESSs) with a grid-forming control in microgrids. For this purpose, this paper proposes a novel structure of the control algorithm based on a current-control virtual synchronous generator (CC-VSG), in which the damping is performed using a feedforward controller. In addition, a simple proportional–integral controller is added to the CC-VSG structure to control the state of charge of the ESS. The performed frequency analysis proves the independence of the different control loop operations within the developed CC-VSG. At the same time, a methodology based on the bandwidth separation of different control loops is proposed for the CC-VSG tuning, which allows for the achievement of the desired quality of frequency regulation in the microgrid, taking into account both the energy recovery and the permissible frequency variation. Finally, the time-domain simulation using PSCAD/EMTDC is performed to confirm the obtained results. [ABSTRACT FROM AUTHOR]

This paper discusses the reliability of stress and strength,R, and fuzzy stress and strength reliability, R F , based on generalized mixtures of exponential distributions. We propose several estimation methods, such as the maximize likelihood estimation, the weighted least-squares estimation, and the percentile estimation, to estimate the corresponding measures. Simulation studies have been conducted to compare the proposed estimators' performance using different settings. These comparisons are based on biases (Bias) and mean squared errors (MSEs), and we find that M S E (P E) > M S E (M L E) > M S E (W L E) and | B i a s (P E) | > | B i a s (W L E) | > | B i a s (M L E) | in most cases. Moreover, the values of R F have the same pattern as R, and the values of MSEs and biases for R F are smaller than R. As the sample size increases, the values of biases for both reliabilities decrease and approach 0. Ultimately, we apply the proposed methods to a data set to illustrate its significance. We find that the estimated values of R are greater than those of R F for all the estimation methods. Moreover, the fuzzy estimators of R F are approximately equal to the estimators R. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is developed to simulate the activation of regulatory T lymphocytes dynamics. The model considers the adaptive immune response and consists of epithelial cells, infected cells, free virus particles, helper and cytotoxic T lymphocytes, B lymphocytes, and regulatory T lymphocytes. A mathematical analysis was carried out to discuss the conditions of existence and stability of equilibrium solutions in terms of the basic reproductive number. In addition, the definitions and properties necessary to preserve the positivity and stability of the model are shown. The precision of these mathematical models can be affected by numerous sources of uncertainty, partly due to the balance between the complexity of the model and its predictive capacity to depict the biological process accurately. Nevertheless, these models can provide remarkably perspectives on the dynamics of infection and assist in identification specific immunological traits that improve our comprehension of immune mechanisms. The theoretical results are validated by numerical simulations using data reported in the literature. The construction, analysis, and simulation of the developed models demonstrate that the increased induced regulatory T lymphocytes effectively suppress the inflammatory response in contrast to similar cells at lower contents, playing a key role in maintaining self-tolerance and immune homeostasis. [ABSTRACT FROM AUTHOR]

This paper introduces a two-echelon optimization model for the integrated routing of an electric vehicle (EV) and a traditional internal combustion engine vehicle (ICEV) in an urban environment. The scientific context of this study is sustainable urban logistics. The case study focuses on the distribution of pharmaceuticals in the metropolitan area of Rome. Distributing pharmaceuticals in large cities presents significant challenges, including heavy traffic congestion, the need for strict temperature control, and the maintenance of the integrity and timely delivery of sensitive medications. Furthermore, the complexity of urban logistics and adherence to regulatory requirements introduce additional layers of difficulty. Therefore, the implementation of fast and sustainable distribution mechanisms is crucial in this context. Specifically, the model seeks to minimize both total CO2 emissions and transportation costs while optimizing the use of an EV and an ICEV, all while ensuring that service level requirements are met. Computational results demonstrate the effectiveness of the proposed method in improving the sustainability of pharmaceutical distribution. [ABSTRACT FROM AUTHOR]

Graph query languages such as Cypher are widely adopted to match and retrieve data in a graph representation, due to their ability to retrieve and transform information. Even though the most natural way to match and transform information is through rewriting rules, those are scarcely or partially adopted in graph query languages. Their inability to do so has a major impact on the subsequent way the information is structured, as it might then appear more natural to provide major constraints over the data representation to fix the way the information should be represented. On the other hand, recent works are starting to move towards the opposite direction, as the provision of a truly general semistructured model (GSM) allows to both represent all the available data formats (Network-Based, Relational, and Semistructured) as well as support a holistic query language expressing all major queries in such languages. In this paper, we show that the usage of GSM enables the definition of a general rewriting mechanism which can be expressed in current graph query languages only at the cost of adhering the query to the specificity of the underlying data representation. We formalise the proposed query language in terms declarative graph rewriting mechanisms described as a set of production rules L → R while both providing restriction to the characterisation of L, and extending it to support structural graph nesting operations, useful to aggregate similar information around an entry-point of interest. We further achieve our declarative requirements by determining the order in which the data should be rewritten and multiple rules should be applied while ensuring the application of such updates on the GSM database is persisted in subsequent rewriting calls. We discuss how GSM, by fully supporting index-based data representation, allows for a better physical model implementation leveraging the benefits of columnar database storage. Preliminary benchmarks show the scalability of this proposed implementation in comparison with state-of-the-art implementations. [ABSTRACT FROM AUTHOR]

This paper focuses on joint production/inventory optimization in single and multiple horizons, respectively, within a complicated supply network (CSN) consisting of firm nodes with coupled demands and firm nodes with coupled demands. We first formulate the single-epoch joint optimal output model by allowing the production of extra quantity for stock underage, considering the fixed costs incurred by having inventory over demand and shortfalls. Then, the multi-temporal dynamic joint production model is further investigated to deal with stochastic demand fluctuations among CSN nodes by constructing a dynamic input–output model. The K-convexity defined in Rn space is proved to obtain the optimal control strategy. According to physical flow links, all demands associated to the nodes of CSN are categorized into the inter-node demand inside CSN (intermediate demand) and external demand outside CSN (final demand). We exploit the meliorated input–output matrix to describe demand relations, building dynamic input–output models where demand fluctuates randomly in single-cycle CSN and finite multi-cycle CSN. The novel monocyclic and multicyclic dynamic models have been developed to minimize system-wide operational costs. Unlike existent literature, we consider fixed costs incurred by overdemand and underdemand inventory into system operational cost functions and then demonstrate the convexity of objective functions. The cost function with two fixed penalty costs due to excess and shortage of inventory is developed in a multicycle model, and the K-convexity defined in Rn is proved to find out the optimal strategy for joint dynamic production of CSNs in the case of multi-products and multicycles. [ABSTRACT FROM AUTHOR]

The increasing complexity of deep learning models can make it difficult to interpret and fit models beyond a purely accuracy-focused evaluation. This is where interpretable and eXplainable Artificial Intelligence (XAI) come into play to facilitate an understanding of the inner workings of models. Consequently, alternatives have emerged, such as class activation mapping (CAM) techniques aimed at identifying regions of importance for an image classification model. However, the behavior of such models can be highly dependent on the type of architecture and the different variants of convolutional neural networks. Accordingly, this paper evaluates three Convolutional Neural Network (CNN) architectures (VGG16, ResNet50, ConvNext-T) against seven CAM models (GradCAM, XGradCAM, HiResCAM, LayerCAM, GradCAM++, GradCAMElementWise, and EigenCAM), indicating that the CAM maps obtained with ConvNext models show less variability among them, i.e., they are less dependent on the selected CAM approach. This study was performed on an image dataset for the classification of coffee leaf rust and evaluated using the RemOve And Debias (ROAD) metric. [ABSTRACT FROM AUTHOR]

This paper studies the output feedback H ∞ control problem of event-triggered Markov-type networked control systems. Firstly, a new Lyapunov–Krasovskii functional is constructed, which contains an event-triggered scheme, Markovian jump system, and quantified information. Secondly, the upper bound of the weak infinitesimal generation operator of the Lyapunov–Krasovskii function is estimated by combining Wirtinger's-based integral inequality and reciprocally convex inequality. Finally, based on the Lyapunov stability theory, the closed-loop stability criterion of event-triggered Markov-type networked control systems and the design method of the output feedback H ∞ controller for the disturbance attenuation level γ are given in the terms of linear matrix inequalities. The effectiveness and superiority of the proposed method are verified using three numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates a parameter-free H∞ differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H∞ control problem is reformulated as a zero-sum game between two players, leading to the establishment of the Hamilton–Jacobi–Isaacs (HJI) equation with a Nash equilibrium solution. To minimize reliance on model parameters during the solution process, an actor–critic framework employing neural networks is utilized to approximate the control policy and value function. An off-policy reinforcement learning method is implemented to iteratively solve the HJI equation. In this approach, the disturbance policy is derived directly from the value function, requiring only a limited amount of driving data to approximate the HJI equation's solution. The primary innovation of this method lies in its capacity to effectively address system nonlinearities without the need for model parameters, making it particularly advantageous for practical engineering applications. Numerical simulations confirm the method's effectiveness and applicable range. The off-policy reinforcement learning approach ensures the safety of the design process. For low-frequency road disturbances, the designed H∞ control policy enhances both ride comfort and stability. [ABSTRACT FROM AUTHOR]

Federated learning facilitates the training of global models in a distributed manner without requiring the sharing of raw data. This paper introduces two novel symmetric Alternating Direction Method of Multipliers (ADMM) algorithms for federated learning. The two algorithms utilize a convex combination of current local and global variables to generate relaxed steps to improve computational efficiency. They also integrate two dual-update steps with varying relaxation factors into the ADMM framework to boost the accuracy and the convergence rate. Another key feature is the use of weak parametric assumptions to enhance computational feasibility. Furthermore, the global update in the second algorithm occurs only at certain steps (e.g., at steps that are a multiple of a pre-defined integer) to improve communication efficiency. Theoretical analysis demonstrates linear convergence under reasonable conditions, and experimental results confirm the superior convergence and heightened efficiency of the proposed algorithms compared to existing methodologies. [ABSTRACT FROM AUTHOR]