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This document provides a summary of a special issue of the journal Mathematics, which features research papers in the field of algebraic, analytic, and computational number theory. The papers cover a wide range of topics, including generalized Lucas pseudoprimality, Fibonacci numbers, piecewise linear difference equations, properties of Euler's function, regularities in ordered semihypergroups, zero-density results for automorphic functions, properties of Fibonacci finite operator quaternions, and more. The authors of the special issue believe that the techniques used in these papers have the potential to yield new results in these areas of mathematics. [Extracted from the article]

This document is a special issue of the journal Mathematics dedicated to recent advances in discrete optimization and scheduling. The issue includes 10 papers covering a range of topics such as batch loading and scheduling, optimization algorithms, scheduling surgeries, routing problems, and mathematical models for simplification. The papers present various approaches and algorithms for solving these problems, and they have been reviewed by experts in the field. The authors express their gratitude to the contributors, reviewers, and editorial staff, and hope that the readers will find stimulating ideas for further research in this area. [Extracted from the article]

This document is an editorial for a special issue of the journal Mathematics titled "Differential Equations of Mathematical Physics and Related Problems of Mechanics." The special issue covers a range of topics related to differential equations in mathematical physics and mechanics, including wave equations, spectral theory, scattering, and inverse problems. The editorial provides a summary of the published papers in the special issue, highlighting their contributions to the field. The document emphasizes the importance of the special issue in covering both applied and fundamental aspects of mathematics, physics, and their applications in various fields. The author expresses gratitude to the authors, reviewers, assistants, associate editors, and editors for their contributions to the special issue. The report does not provide specific details about the content of the papers or the nature of the special issue. [Extracted from the article]

The study introduces a novel approach to identify potential citation manipulation within academic papers. This method utilizes perturbations of a deep embedding model, integrating Graph-Masked Autoencoders to merge textual information with evidence of graph connectivity. Consequently, it yields a more intricate model of citation distribution. By training a deep network with partial data and reconstructing masked connections, the approach capitalizes on the inherent characteristics of central connections amidst network perturbations. It demonstrates its ability to pinpoint trustworthy citations within the analyzed dataset through comprehensive quantitative evaluations. Additionally, it raises concerns regarding the reliability of specific references, which may be subject to manipulation. [ABSTRACT FROM AUTHOR]

This paper presents our research on a traffic signal control system (TSCS) at V2X intersections. The overall objective of the study is to create an implementable TSCS. The specific objective of this paper is to investigate a distributed system towards implementation. The objective function of minimizing queue delay is formulated as the integral of queue lengths. The discrete queueing estimation is mixed with macro and micro traffic flow models. The novel proposed architecture alleviates the communication network bandwidth constraint by processing BSMs and computing queue lengths at the local intersection. In addition, a two-stage distributed system is designed to optimize offsets, splits, and cycle length simultaneously and in real time. The paper advances TSCS theories by contributing a novel analytic formulation of delay functions and their first degree of derivatives for a two-stage optimization model. The open-source traffic simulation engine Enhanced Transportation Flow Open-Source Microscopic Model (ETFOMM version 1.2) was selected as a simulation environment to develop, debug, and evaluate the models and the system. The control delay of the major direction, minor direction, and the total network were collected to assess the system performance. Compared with the optimized TSCS timing plan by the Virginia Department of Transportation, the system generated a 21% control delay reduction in the major direction and a 7% control delay reduction in the minor direction at just a 10% penetration rate of connected vehicles. Finally, the proposed distributed and centralized systems present similar performances in the case study. [ABSTRACT FROM AUTHOR]

With the development of the Internet, the types and quantities of malware have grown rapidly, and how to identify unknown malware is becoming a new challenge. The traditional malware detection method based on fixed features is becoming more and more difficult. In order to improve detection accuracy and efficiency for mobile terminals, this paper proposed a malware detection method for mobile terminals based on application programming interface (API) call sequence, which was characterized by the API call sequence and used a series of feature preprocessing techniques to remove redundant processing of the API call sequence. Finally, the recurrent neural network method (RNN) was used to build the model and perform detection and verification. Furthermore, this paper constructed a malware detection model based on a two-way recurrent neural network and used the two-way long short-term memory network model (LSTM) to train the data set containing 5986 malware samples and 5065 benign software samples to obtain the final detection model and its parameters. Finally, the feature vector of the APK file to be detected was passed into the model and obtained the detection results. The experimental results indicated that the detection accuracy of this method can reach 93.68%. [ABSTRACT FROM AUTHOR]

Although the stability regions of wind turbines in the islanding mode have been widely researched, small-signal modeling of grid-forming wind turbines (GFWTs) in the islanding mode has yet to be explored. In addition, the state-space matrix of the wind turbine system has yet to be fully represented. Therefore, this paper proposes a small-signal modeling of GFWT and a method for identifying the stabilization region of a system with variable parameters. First, small-signal modeling of a GFWT based on virtual synchronous generator control is developed. Second, the bialternate sum matrix approach is used to determine the system stabilization region. The system matrix with multiple variable parameters is first decomposed into the sum of several matrices in this paper. Furthermore, the rotor-side generator control is simplified. It can reduce the dimensionality of the system matrix model. Finally, the simulation shows that the proposed method for determining the stabilization region of the variable system is accurate. [ABSTRACT FROM AUTHOR]

Thedistribution of products stands out as one of the pivotal activities for logistics companies in recent years, particularly in the aftermath of the COVID-19 pandemic and other geopolitical events. Intense competition compels companies to efficiently execute their logistical processes, with cross-docking emerging as a frequently applied solution. However, the location of cross-dock terminals in urban areas remains a problem insufficiently addressed in the literature, with a dearth of studies and models tackling this issue. This paper introduces a novel and innovative model for locating cross-dock terminals based on the CI-DEA–IDOCRIW–MABAC (Composite Indicators–Data Envelopment Analysis-Integrated Determination of Objective Criteria Weights–Multi-Attributive Border Approximation Area Comparison) methods. In the process of defining input indicators, the following three sources were utilized: relevant literature, practical insights from logistics experts, and the knowledge and experience of the authors. Eight inputs and three outputs were considered (the number of users in the observed channel; the area served by the channel; the average distance a vehicle travels in one delivery; the required number of vehicles; labor availability; competition; construction, and expansion possibilities; proximity to the main infrastructure and traffic facilities; the average number of deliveries; average delivered quantity; and service level). The model underwent testing in a case study analyzing nine distribution channels (areas within the observed urban zone). The results indicated that alternative A4 (in the southwest area) ranked the highest since it was the best-ranked in accordance with the most important criteria, suggesting that the terminal is best located in the southwest zone. The accuracy of the results was confirmed by company management. By developing a completely new model and addressing the identified gap in the literature, this paper provides unequivocal scientific contributions. [ABSTRACT FROM AUTHOR]

This paper focuses on optimizing the Zuker RNA folding algorithm, a bioinformatics task with non-serial polyadic dynamic programming and non-uniform loop dependencies. The intricate dependence pattern is represented using affine formulas, enabling the automatic application of tiling strategies via the polyhedral method. Three source-to-source compilers—PLUTO, TRACO, and DAPT—are employed, utilizing techniques such as affine transformations, the transitive closure of dependence relation graphs, and space–time tiling to generate cache-efficient codes, respectively. A dedicated transpose code technique for non-serial polyadic dynamic programming codes is also examined. The study evaluates the performance of these optimized codes for speed-up and scalability on multi-core machines and explores energy efficiency using RAPL. The paper provides insights into related approaches and outlines future research directions within the context of bioinformatics algorithm optimization. [ABSTRACT FROM AUTHOR]

The open-source software platform hosts a large number of software defects, and the task of relying on administrators to manually assign developers is often time consuming. Thus, it is crucial to determine how to assign software defects to appropriate developers. This paper presents DARIP, a method for assigning developers to address software defects. First, the correlation between software defects and issues is considered, predicting related issues for each defect and comprehensively calculating the textual characteristics of the defect using the BERT model. Second, a heterogeneous collaborative network is constructed based on the three development behaviors of developers: reporting, commenting, and fixing. The meta-paths are defined based on the four collaborative relationships between developers: report–comment, report–fix, comment–comment, and comment–fix. The graph-embedding algorithm metapath2vec extracts developer characteristics from the heterogeneous collaborative network. Then, a classifier based on a deep learning model calculates the probability assigned to each developer category. Finally, the assignment list is obtained according to the probability ranking. Experiments on a dataset of 20,280 defects from 9 popular projects show that the DARIP method improves the average of the Recall@5, the Recall@10, and the MRR by 31.13%, 21.40%, and 25.45%, respectively, compared to the state-of-the-art method. [ABSTRACT FROM AUTHOR]

Keyword pools are used as search queries to collect web texts, largely determining the size and coverage of the samples and provide a data base for subsequent text mining. However, how to generate a refined keyword pool with high similarity and some expandability is a challenge. Currently, keyword pools for search queries aimed at collecting web texts either lack an objective generation method and evaluation system, or have a low utilization rate of sample semantic information. Therefore, this paper proposed a keyword generation framework that integrates sample and semantic information to construct a complete and objective keyword pool generation and evaluation system. The framework includes a data phase and a modeling phase, and its core is in the modeling phase, where both feature ranking and model performance are considered. A regression model about a topic vector and word vectors is constructed for the first time based on word embedding, and keyword pools are generated from the perspective of model performance. In addition, two keyword generation methods, Recursive Feature Introduction (RFI) and Recursive Feature Introduction and Elimination (RFIE), are also proposed in this paper. Different feature ranking algorithms, keyword generation methods and regression models are compared in the experiments. The results show that: (1) When using RFI to generate keywords, the regression model using ranked features has better prediction performance than the baseline model, and the number of generated keywords is refiner, and the prediction performance of the regression model using tree-based ranked features is significantly better than that of the one using SHAP-based ranked features. (2) The prediction performance of the regression model using RFI with tree-based ranked features is significantly better than that using Recursive Feature Elimination (RFE) with tree-based one. (3) All four regression models using RFI/RFE with SHAP- based/tree-based ranked features have significantly higher average similarity scores and cumulative advantages than the baseline model (the model using RFI with unranked features). (4) Light Gradient Boosting Machine (LGBM) using RFI with SHAP-based ranked features has significantly better prediction performance, higher average similarity scores, and cumulative advantages. In conclusion, our framework can generate a keyword pool that is more similar to the topic, and more refined and expandable, which provides certain research ideas for expanding the research sample size while ensuring the coverage of topics in web text collecting. [ABSTRACT FROM AUTHOR]

In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and Sullivant. In the second part of the paper, we give a brief tutorial on the Hadamard.m2 package of Macaulay2. [ABSTRACT FROM AUTHOR]

Recent research has revealed that subtle imperceptible perturbations can deceive well-trained neural network models, leading to inaccurate outcomes. These instances, known as adversarial examples, pose significant threats to the secure application of machine learning techniques in safety-critical systems. In this paper, we delve into the study of one-pixel attacks in deep neural networks, recently reported as a kind of adversarial examples. To identify such one-pixel attacks, most existing methodologies rely on the differential evolution method, which utilizes random selection from the current population to escape local optima. However, the differential evolution technique might waste search time and overlook good solutions if the number of iterations is insufficient. Hence, in this paper, we propose a gradient ascent with momentum approach to efficiently discover good solutions for the one-pixel attack problem. As our method takes a more direct route to the goal compared to existing methods relying on blind random walks, it can effectively identify one-pixel attacks. Our experiments conducted on popular CNNs demonstrate that, in comparison with existing methodologies, our technique can detect one-pixel attacks significantly faster. [ABSTRACT FROM AUTHOR]

This paper discusses finding solutions to the modified Fractional Black–Scholes equation. As is well known, the options theory is beneficial in the stock market. Using call-and-pull options, investors can theoretically decide when to sell, hold, or buy shares for maximum profits. However, the process of forming the Black–Scholes model uses a normal distribution, where, in reality, the call option formula obtained is less realistic in the stock market. Therefore, it is necessary to modify the model to make the option values obtained more realistic. In this paper, the method used to determine the solution to the modified Fractional Black–Scholes equation is a combination of the finite difference method and the fractional differential transformation method. The results show that the combined method of finite difference and fractional differential transformation is a very good approximation for the solution of the Fractional Black–Scholes equation. [ABSTRACT FROM AUTHOR]

The keyword extraction of patents is crucial for technicians to master the trends of technology. Traditional keyword extraction approaches only handle short text like title or claims, but ignore the comprehensive meaning of the description. This paper proposes a novel patent keyword extraction method based on corpus classification (PKECC), which simulates the patent understanding methods of human patent examiners. First of all, a corpus classification model based on multi-level attention mechanism adopts the Bert model and hierarchical attention mechanism to classify the sentences of patent description into four parts including technical field, technical problem, technical solution, and technical effect. Then, the proposed keyword extraction method based on the fusion of BiLSTM and CRF is incorporated to extract keywords from the four parts. The proposed PKECC simulates understanding style of patent examiner by extracting keywords from the description. Meanwhile, PKECC may reduce the complexity of extracting keywords from a long text and improve the accuracy of keyword extraction. The proposed PKECC is compared with 5 traditional or state-of-the-art models and achieves better accuracy, F1 score and recall rate; its recall rate is above 62%, its accuracy reaches over 84%, and the F1 score arrives at 69%. In addition, the experimental results shows the proposed PKECC has a better universality in keyword extraction. [ABSTRACT FROM AUTHOR]

With developments in global economic integration and the increase in future economic uncertainty, it is imperative to have the ability to predict future capital in relation to financial capital inflow and outflow predictions to ensure capital optimization is within a controllable range within the current macroeconomic environment and situation. This paper proposes an automated capital prediction strategy for the capital supply chain using time series analysis artificial intelligence methods. Firstly, to analyze the fluctuation and tail risk of the financial characteristics, the paper explores the financial characteristics for measuring the dynamic VaR from the perspectives of volatility, tail, and peak with the Bayesian peaks over threshold (POT) model. Following this, in order to make the modeling more refined, the forecast targets are split before modeling with seasonal Autoregressive Integrated Moving Average (ARIMA) models and Prophet models. Finally, the time series modeling of the wavelet Long Short-Term Memory (LSTM) model is carried out using a two-part analysis method to determine the linear separated wavelet and non-linear embedded wavelet parts to predict strong volatility in financial capital. Taking the user capital flow of the Yu'e Bao platform, the results prove the feasibility and prediction accuracy of the innovative model proposed. [ABSTRACT FROM AUTHOR]

This paper conducts a brief survey of spatial unit roots within the context of spatial econometrics. We summarize important concepts and assumptions in this area and study the parameter space of the spatial autoregressive coefficient, which leads to the idea of spatial unit roots. Like the case in time series, the spatial unit roots lead to spurious regression because the system cannot achieve equilibrium. This phenomenon undermines the power of the usual Ordinary Least Squares (OLS) method, so various estimation methods such as Quasi-maximum Likelihood Estimate (QMLE), Two Stage Least Squares (2SLS), and Generalized Spatial Two Stage Least Squares (GS2SLS) are explored. This paper considers the assumptions needed to guarantee the identification and asymptotic properties of these methods. Because of the potential damage of spatial unit roots, we study some test procedures to detect them. Lastly, we offer insights into how to relax the compactness assumption to avoid spatial unit roots, as well as the relationship between spatial unit roots and other models, such as the Spatial Dynamic Panel Data (SDPD) model and Lévy–Brownian motion. [ABSTRACT FROM AUTHOR]

Large-scale wind farms incorporating doubly-fed induction generators (DFIGs) are considered a promising direction for modern energy supply systems due to their role in reducing dependence on fossil energy sources. However, the dynamic interactions between DFIGs and AC grids sometimes lead to sub-synchronous oscillation (SSO) that threatens the safe and stable operation of wind power systems. Therefore, it is essential to develop a mathematical model and design an algorithm to quantitatively design the control parameters. Such algorithms are helpful in preventing or mitigating system stability problems coming from wind power connected to the grid and reducing damage to power equipment. The traditional state-space model is mainly established to determine the stable operating point and analyze the influence of parameters on the system operating mode. However, this method does not provide the selection area for the system parameters. To address this shortcoming, this paper introduces a modular state-space model for DFIGs containing series compensation lines and proposes an algorithm for calculating the parameter selection area based on the Guardian map method. First, a detailed modular state-space model based on the virtual synchronous generator (VSG) control is established. The modular model helps to reflect the relationship between state variables and focuses on describing the operating state of DFIGs in wind farms. Second, this paper focuses on the influence of VSG control parameters and compensation capacitance on SSO. It aims to clarify the role of the series compensation level and control parameters on SSO based on VSG control. Then, an algorithm for the parameter selection area based on the Guardian map is proposed and the area of the VSG-controlled DFIG is obtained. Finally, the accuracy and validity of the algorithm are verified by time domain simulation in MATLAB/Simulink and HIL experiment. [ABSTRACT FROM AUTHOR]

Navigation aids play a crucial role in guiding ship navigation and marking safe water areas. Therefore, ensuring the accurate and efficient recognition of a navigation aid's state is critical for maritime safety. To address the issue of sparse features in navigation aid data, this paper proposes an approach that involves three distinct processes: the extension of rank entropy space, the fusion of multi-domain features, and the extraction of hidden features (EFE). Based on these processes, this paper introduces a new LSTM model termed EFE-LSTM. Specifically, in the feature extension module, we introduce a rank entropy operator for space extension. This method effectively captures uncertainty in data distribution and the interrelationships among features. The feature fusion module introduces new features in the time domain, frequency domain, and time–frequency domain, capturing the dynamic features of signals across multiple dimensions. Finally, in the feature extraction module, we employ the BiLSTM model to capture the hidden abstract features of navigational signals, enabling the model to more effectively differentiate between various navigation aids states. Extensive experimental results on four real-world navigation aid datasets indicate that the proposed model outperforms other benchmark algorithms, achieving the highest accuracy among all state recognition models at 92.32%. [ABSTRACT FROM AUTHOR]

COPA, introduced by Andreeva et al., is the first online authenticated encryption (AE) mode with nonce-misuse resistance, and it is covered in COLM, which is one of the final CAESAR portfolios. However, COPA has been proven to be insecure in the releasing unverified plaintext (RUP) setting. This paper mainly focuses on the integrity under RUP (INT-RUP) defect of COPA. Firstly, this paper revisits the INT-RUP security model for adaptive adversaries, investigates the possible factors of INT-RUP insecurity for "Encryption-Mix-Encryption"-type checksum-based AE schemes, and finds that these AE schemes with INT-RUP security vulnerabilities utilize a common poor checksum technique. Then, this paper introduces an improved checksum technique named polynomial intermediate checksum (PIC) for INT-RUP security and emphasizes that PIC is a sufficient condition for guaranteeing INT-RUP security for "Encryption-Mix-Encryption"-type checksum-based AE schemes. PIC is generated by a polynomial sum with full terms of intermediate internal states, which guarantees no information leakage. Moreover, PIC ensures the same level between the plaintext and the ciphertext, which guarantees that the adversary cannot obtain any useful information from the unverified decryption queries. Again, based on PIC, this paper proposes a modified scheme COPA-PIC to fix the INT-RUP defect of COPA. COPA-PIC is proven to be INT-RUP up to the birthday-bound security if the underlying primitive is secure. Finally, this paper discusses the properties of COPA-PIC and makes a comparison for AE modes with distinct checksum techniques. The proposed work is of good practical significance. In an interactive system where two parties communicate, the receiver can effectively determine whether the information received from the sender is valid or not, and thus perform the subsequent operation more effectively. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known. [ABSTRACT FROM AUTHOR]

This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems. [ABSTRACT FROM AUTHOR]

One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation J f (z) = f (z ¯) ¯ . It is well known that the complex symmetry is equivalent to 2-complex symmetry for the weighted composition operators studied in the paper. However, the interesting fact that 3-complex symmetry is not equivalent to 2-complex symmetry for such operators is found in the paper. Finally, the complex normal of such operators on the weighted Bergman space of the right half-plane with the conjugation J is characterized. [ABSTRACT FROM AUTHOR]

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

For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory to design formation topology and dynamically adjust the distances between UAVs in real time. Secondly, we introduced APF to avoid obstacles in complicated environments. This algorithm innovatively integrates the Leader–Follower formation method. The design of this attractive field is replaced by the leader's attraction to the followers, overcoming the problem of unreachable targets in APF. Meanwhile, the introduced Leader–Follower mode reduces information exchange within the swarm, realizing a more efficient "few controlling many" paradigm. Afterwards, we incorporated rotational force to assist the swarm in breaking free from local minima. Ultimately, the stability of the integrated formation strategy was demonstrated using Lyapunov functions. The feasibility and effectiveness of the proposed strategy were validated across multiple platforms. [ABSTRACT FROM AUTHOR]

Long Short-Term Memory (LSTM) is an effective method for stock price prediction. However, due to the nonlinear and highly random nature of stock price fluctuations over time, LSTM exhibits poor stability and is prone to overfitting, resulting in low prediction accuracy. To address this issue, this paper proposes a novel variant of LSTM that couples the forget gate and input gate in the LSTM structure, and adds a "simple" forget gate to the long-term cell state. In order to enhance the generalization ability and robustness of the variant LSTM, the paper introduces an attention mechanism and combines it with the variant LSTM, presenting the Attention Mechanism Variant LSTM (AMV-LSTM) model along with the corresponding backpropagation algorithm. The parameters in AMV-LSTM are updated using the Adam gradient descent method. Experimental results demonstrate that the variant LSTM alleviates the instability and overfitting issues of LSTM, effectively improving prediction accuracy. AMV-LSTM further enhances accuracy compared to the variant LSTM, and compared to AM-LSTM, it exhibits superior generalization ability, accuracy, and convergence capability. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consensus control problem of Euler–Lagrange systems which can be used to describe the motion of various mechanical systems such as manipulators and quadcopters. We focus on consensus control strategies, which are important for achieving coordinated behavior in multi-agent systems. The paper considers the key challenges posed by random communication delays and packet losses that are increasingly common in networked control systems. In addition, it is assumed that each system receives information from neighboring agents intermittently. Addressing these challenges is critical to ensure the reliability and efficiency of such systems in real-world applications. Communication delay is time-varying and can be very large, but should be smaller than some bounded constant. To decrease the frequency of control input updates, we implement an event-triggered scheme that regulates the controller's updates for each agent. Specifically, it does not update control inputs at traditional fixed intervals, but responds to predefined conditions and introduces a dynamic consensus item to handle information irregularities caused by communication delays and intermittent information exchange. The consensus can be achieved if the communication graph of agents contains a spanning tree with the desired velocity as the root node. That is, all Euler–Lagrange systems need to obtain the desired velocity, directly or indirectly (via neighbors), to reach consensus. We establish that the Zeno behavior can be avoided, ensuring a positive minimum duration between successive event-triggered instances. Finally, we provide simulation results to show the performance of our proposed algorithm. [ABSTRACT FROM AUTHOR]

This correction notice provides updates and corrections to a research paper on deep machine learning model-based cyber-attacks detection in smart power systems. The paper proposes a deep learning-based attack detection model that addresses system disturbances caused by natural events and cyber-attacks. It discusses the use of principal component analysis (PCA) for feature selection and the potential of deep learning-based and decision tree classifiers for detecting cyber-attacks in intelligent energy grids. The notice also includes updates to references, clarifications on the experimental data set, and feature selection based on PCA. The study evaluates the effectiveness of the proposed model using various assessment indexes and compares it to conventional methods, concluding that the proposed model is effective in detecting cyber-attacks and demonstrates good performance in detecting destructive attacks. [Extracted from the article]

In this paper, we investigate the Besov space and the Besov capacity and obtain several important capacitary inequalities in a strictly local Dirichlet space, which satisfies the doubling condition and the weak Bakry–Émery condition. It is worth noting that the capacitary inequalities in this paper are proved if the Dirichlet space supports the weak (1 , 2) -Poincaré inequality, which is weaker than the weak (1 , 1) -Poincaré inequality investigated in the previous references. Moreover, we first consider the strong subadditivity and its equality condition for the Besov capacity in metric space. [ABSTRACT FROM AUTHOR]

The rational field Q is highly desired in many applications. Algorithms using the rational number field Q algebraic number fields use only integer arithmetics and are easy to implement. Therefore, studying and designing systems and expansions with coefficients in Q or algebraic number fields is particularly interesting. This paper discusses constructing quasi-tight framelets with symmetry over an algebraic field. Compared to tight framelets, quasi-tight framelets have very similar structures but much more flexibility in construction. Several recent papers have explored the structure of quasi-tight framelets. The construction of symmetric quasi-tight framelets directly applies the generalized spectral factorization of 2 × 2 matrices of Laurent polynomials with specific symmetry structures. We adequately formulate the latter problem and establish the necessary and sufficient conditions for such a factorization over a general subfield F of C , including algebraic number fields as particular cases. Our proofs of the main results are constructive and thus serve as a guideline for construction. We provide several examples to demonstrate our main results. [ABSTRACT FROM AUTHOR]

This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, existence of periodic and bounded variation right continuous (BVRC) solutions. Second-order evolution inclusions and fractional (Caputo and Riemann–Liouville) differential inclusions are also considered. A result of the Skorohod problem driven by a time- and space-dependent operator under rough signal and a Volterra integral perturbation in the BRC setting is given. The paper finishes with some results for fractional differential inclusions under rough signals and Young integrals. Many of the given results are novel. [ABSTRACT FROM AUTHOR]

We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. In this MSS, Fibonacci systematically describes finding the integer part of the square root of an integer in numerous examples with three to seven decimal digits. The results of these examples are summarized in a table in the paper. Liber Abaci also describes in detail finding an approximation to the fractional part of the square root. However, in other examples in Liber Abaci and De Practica Geometrie, only the approximate values of the fractional part of the square roots are stated. This paper further explores these approximate values using techniques like reverse engineering. Contrary to many claims that Fibonacci also used other methods or approximations, we show that all examples can be explained using one digit-by-digit method to compute the integer part of the square root and one approximation scheme for the fractional part. Further, it is shown that the approximation scheme is tied to the method to compute the integer part of the square root. [ABSTRACT FROM AUTHOR]

This work surveys the use of directed weighted graphs in conducting comparative static analyses. The paper discusses the implementation of a computer-aided process for building spreadsheet-based graph models for inter- and intra-regional financial flows. The graph-theoretic techniques are programmed to enable the interactive visualization and analysis of financial data using Wolfram technologies (i.e., Mathematica software v. 11.3 or later, Wolfram player v. 12 or later). The paper describes the workflow for several interactive visualizations applicable to financial networks. The author provides four programs, written in the Wolfram language, that customize input–output financial models by combining the Manipulate command with built-in Mathematica functions and functions of the IGraph package (IGraph/M). The study is a tutorial article for the generation of a suite of visual schemes that provide patterns, practices, and roadmaps of the financial markets across the globe. [ABSTRACT FROM AUTHOR]

In this paper, we study a method of polynomial interpolation that lies in-between Lagrange and Hermite methods. The novelty is that we use very general nodal systems on the unit circle as well as on the bounded interval only characterized by a separation property. The way in which we interpolate consists in considering all the nodes for the prescribed values and only half for the derivatives. Firstly, we develop the theory on the unit circle, obtaining the main properties of the nodal polynomials and studying the convergence of the interpolation polynomials corresponding to continuous functions with some kind of modulus of continuity and with general conditions on the prescribed values for half of the derivatives. We complete this first part of the paper with the study of the convergence for smooth functions obtaining the rate of convergence, which is slightly slower than that when equidistributed nodal points are considered. The second part of the paper is devoted to solving a similar problem on the bounded interval by using nodal systems having good properties of separation, generalizing the Chebyshev–Lobatto system, and well related to the nodal systems on the unit circle studied before. We obtain an expression of the interpolation polynomials as well as results about their convergence in the case of continuous functions with a convenient modulus of continuity and, particularly, for differentiable functions. Finally, we present some numerical experiments related to the application of the method with the nodal systems dealt with. [ABSTRACT FROM AUTHOR]

This paper discusses the challenges of the hyperparameter tuning in deep learning models and proposes a green approach to the neural architecture search process that minimizes its environmental impact. The traditional approach of neural architecture search involves sweeping the entire space of possible architectures, which is computationally expensive and time-consuming. Recently, to address this issue, performance predictors have been proposed to estimate the performance of different architectures, thereby reducing the search space and speeding up the exploration process. The proposed approach aims to develop a performance predictor by training only a small percentage of the possible hyperparameter configurations. The suggested predictor can be queried to find the best configurations without training them on the dataset. Numerical examples of image denoising and classification enable us to evaluate the performance of the proposed approach in terms of performance and time complexity. [ABSTRACT FROM AUTHOR]

In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth's crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data inversion, we face three problems: topography with large amplitude, the sphericity of the planet, and a long computation time because of the large amount of data. In our previous works, we have already considered those problems separately but without explaining the details of the computation of the closed-form solution for a polyhedron. In this paper, we present for the first time a performance-effective numerical method for the inversion of gravity data based on topography. The method is based on closed-form expression for the gravity field of a spherical density model of the Earth's crust with the upper topography layer, and provides great accuracy and speed of calculation. There are no restrictions on the model's geometry or gravity data grid. As a case study, a spherical density model of the Earth's crust of the Urals is created. [ABSTRACT FROM AUTHOR]

In recent years, various forms of progressive hybrid censoring schemes (PHCS) have gained significant traction in survival and reliability analysis studies due to their versatility. However, these PHCS variants are often characterized by complexity stemming from the multitude of parameters involved in their specification. Consequently, the primary objective of this paper is to propose a unified approach termed combined type II progressive hybrid censoring scheme ( ComT 2 PHCS) capable of encompassing several existing PHCS variations. Our analysis focuses specifically on the exponential distribution (ExDist). Bayesian inference techniques are employed to estimate the parameters of the ExDist under the ComT 2 PHCS. Additionally, we conduct fundamental distributional analyses and likelihood inference procedures. We derive the conditional moment-generating function (CondMGF) of maximum likelihood estimator (MLE) for parameters of the ExDist under ComT 2 PHCS. Further, we use CondMGF for the distribution of MLE for parameters of ExDist under ComT 2 PHCS. Finally, we provide an illustrative example to elucidate the inference methods derived in this paper. [ABSTRACT FROM AUTHOR]

The COVID-19 epidemic has required countries to implement different containment strategies to limit its spread, like strict or weakened national lockdown rules and the application of age-stratified vaccine prioritization strategies. These interventions have in turn modified the age-dependent patterns of social contacts. In our recent paper, starting from the available age-structured real data at the national level, we identified, for the Italian case, specific virulence parameters for a two-age-structured COVID-19 epidemic compartmental model (under 60, and 60 years and over) in six different diseases transmission scenarios under concurrently adopted feedback interventions. An interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19 disease has been accordingly provided. In this paper, which can be viewed as a sequel to the previous one, we mainly apply the same general methodology therein (involving the same dynamic model) to new data covering the three subsequent additional scenarios: (i) a mitigated coordinated intermittent regional action in conjunction with the II vaccination phase; (ii) a super-attenuated coordinated intermittent regional action in conjunction with the II vaccination phase; and (iii) a last step towards normality in conjunction with the start of the III vaccination phase. As a new contribution, we show how meaningful updated information can be drawn out, once the identification of virulence parameters, characterizing the two age groups within the latest three different phases, is successfully carried out. Nevertheless, differently from our previous paper, the global optimization procedure is carried out here with the number of susceptible individuals in each scenario being left free to change, to account for reinfection and immunity due to vaccination. Not only do the slightly different estimates we obtain for the previous scenarios not impact any of the previous considerations (and thus illustrate the robustness of the procedure), but also, and mainly, the new results provide a meaningful picture of the evolution of social behaviors, along with the goodness of strategic interventions. [ABSTRACT FROM AUTHOR]

Modeling and verification of the correct behavior of embedded real-time systems with strict timing constraints is a well-known and important problem. Failing to fulfill a deadline in system operation can have severe consequences in the practical case. This paper proposes an approach to formal modeling and schedulability analysis. A novel extension of Petri Nets named Constraint Time Petri Nets (C-TPN) is developed, which enables the modeling of a collection of interdependent real-time tasks whose execution is constrained by the use of priority and shared resources like processors and memory data. A C-TPN model is reduced to a network of Timed Automata in the context of the popular Uppaal toolbox. Both functional and, most importantly, temporal properties can be assessed by exhaustive model checking and/or statistical model checking based on simulations. This paper first describes and motivates the proposed C-TPN modeling language and its formal semantics. Then, a Uppaal translation is shown. Finally, three models of embedded real-time systems are considered, and their properties are thoroughly verified. [ABSTRACT FROM AUTHOR]

In this study, we extended the applicability of a derivative-free algorithm to encompass the solution of operators that may be either differentiable or non-differentiable. Conditions weaker than the ones in earlier studies are employed for the convergence analysis. The earlier results considered assumptions up to the existence of the ninth order derivative of the main operator, even though there are no derivatives in the algorithm, and the Taylor series on the finite Euclidian space restricts the applicability of the algorithm. Moreover, the previous results could not be used for non-differentiable equations, although the algorithm could converge. The new local result used only conditions on the divided difference in the algorithm to show the convergence. Moreover, the more challenging semi-local convergence that had not previously been studied was considered using majorizing sequences. The paper included results on the upper bounds of the error estimates and domains where there was only one solution for the equation. The methodology of this paper is applicable to other algorithms using inverses and in the setting of a Banach space. Numerical examples further validate our approach. [ABSTRACT FROM AUTHOR]

The problem of a stabilisation system synthesis for the motion of a control object along a given spatial trajectory is considered. The complexity of the problem is that the preset trajectory is defined in the state subspace and not in time. This paper describes a stabilisation system synthesis for motion along a trajectory specified in time and along a trajectory specified in the form of a manifold in a state space. In order to construct a stabilisation system, it is necessary to determine a distance between an object and the given trajectory at each moment in time. For trajectories that are not given in time, the determination of this distance can be ambiguous. An object may be exactly on a trajectory but at a different time. This paper proposes some approaches to solve the problem. One of the approaches is to transform a given trajectory in a state subspace into a trajectory given in time. A description of a universal method to perform this transformation is presented. In order to solve the synthesis problem automatically, without having to analyse the mathematical model of the control object, it is suggested that machine learning control by symbolic regression is used. In computational experiments, examples of stabilisation system syntheses for quadcopter motion along a given spatial trajectory are presented. [ABSTRACT FROM AUTHOR]

Product disassembly is an effective means of waste recycling and reutilization that has received much attention recently. In terms of disassembly efficiency, the number of disassembly skills possessed by workers plays a crucial role in improving disassembly efficiency. Therefore, in order to effectively and reasonably disassemble discarded products, this paper proposes a partial parallel disassembly line balancing problem (PP-DLBP) that takes into account the number of worker skills. In this paper, the disassembly tasks and the disassembly relationships between components are described using AND–OR graphs. In this paper, a multi-objective optimization model is established aiming to maximize the net profit of disassembly and minimize the number of skills for the workers. Based on the bat algorithm (BA), we propose an improved discrete bat algorithm (IDBA), which involves designing adaptive composite optimization operators to replace the original continuous formula expressions and applying them to solve the PP-DLBP. To demonstrate the advantages of IDBA, we compares it with NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA/D. Experimental results show that IDBA outperforms the other five algorithms in real disassembly cases and exhibits high efficiency. [ABSTRACT FROM AUTHOR]

Distributed scheduling has become a common manufacturing mode, and the distributed job scheduling problem (DJSP) has attracted more manufacturers and researchers in the field of operation research. For the distributed scheduling problem, it emphasizes the flexibility of factory assignment and determines the sequence of operation related to each machine in related factories. In this paper, a mixed-integer linear programming model for the DJSP is formulated to be optimized by an SMA. Also in this paper, a self-adaptive memetic algorithm (SMA) is proposed to obtain a near-optimal solution in a limited time for the DJSP. To strengthen the effectiveness of the SMA, an independent encoding is designed with jobs assigned to factories and the sequence of operation. In the proposed algorithm, various local search strategies related to the critical path in the critical factory are designed to enhance the quality of the solution. Moreover, the self-adaptive scheme for solution improvement is formulated to reduce the search time and avoid prematurity effectively. To demonstrate the performance of the proposed algorithm, numerical experiments are carried out on 120 different instances extended from the well-known job shop scheduling benchmarks. The proposed SMA has updated 30 instance records in 120 instances and it has obtained the 91 best records in 120 instances. According to the comparison, an SMA is a more effective algorithm that could update several records of benchmarks. [ABSTRACT FROM AUTHOR]

One of the modern, recently developed mathematical approaches for modeling various complex chaotic processes (the bacteria migration is apparently one of them), is the application of fractional differential equations. Introduction of fractional derivatives is also a very effective approach for investigation of the reactive processes (growth of bacteria in our case). Our recent advances in application of fractional differential equations for modeling the anomalous transport of reactive and non-reactive contaminants (see our recent publications in the References) allow us to expect that the anomalous transport of growing bacteria can also be effectively described by the models with fractional derivatives. Based on these modern approaches, utilizing fractional differential equations, in this paper we developed a reliable mathematical model that could be properly calibrated and, consequently, provide an adequate description of the growing bacteria transport. This model accounts for the memory effects in the bacteria transport due to the random character of bacteria trapping and release by the porous matrix. Two types of bacteria in the saturated porous medium are considered: mobile and immobile bacteria. Bacteria in the mobile phase are migrating in the fluid and have the velocity of the bulk flow, whereas bacteria in the immobile phase are the bacteria that are captured by the porous matrix. These bacteria have zero velocity and can cause clogging of some pores (therefore, porosity is possibly not constant). Examining different conventional models and comparing computations based on these models, we show that this extremely complex character of bacteria transport cannot be described by the traditional approach based on classical partial differential equations. In this paper we suggest fractional differential equations as a simple but very effective tool that can be used for constructing the proper model capable of simulating all the above-mentioned effects associated with migration of alive bacteria. Using this approach, a reliable model of the growing bacteria transport in the porous medium is developed and validated by comparison with experimental laboratory results. We proved that this novel model can be properly linearized and calibrated, so that an excellent agreement with available experimental results can be achieved. This simple model can be used in many applications, for example, as a part of more general mathematical models for predicting the outcomes of the bioremediation of contaminated soils. [ABSTRACT FROM AUTHOR]

During the load distribution of hydropower units, the frequent crossing of vibration zones as well as large output fluctuations affect the stability of the power station. A multi-objective double-layer intelligent nesting model that considers the constraint of the output fluctuation of units is proposed to address these problems. The nonlinear constraint unit commitment optimization model layer is built based on outer dynamic programming, and the load distribution optimization model layer is constructed based on the improved biogeography-based optimization algorithm. Simultaneously, the unit output fluctuation constraint is established based on whether the unit combination changes in order to limit the unit output fluctuation. The results of this model indicate that compared with traditional load allocation models, the application of the method proposed in this paper can reduce the fluctuation range of unit output by 85.01%. In addition, except for the inevitable vibration zone crossings during startup and shutdown processes, the unit does not cross the vibration zone during operation, which greatly improves the unit's vibration isolation and optimization capabilities. The multi-objective double-layer intelligent nested model proposed in this paper has significant advantages in the field of load allocation for hydropower units. It effectively improves the stability and reliability of unit operation, and this method can be applied to practical load allocation processes. It is of great significance for the research on load allocation optimization of hydropower units. [ABSTRACT FROM AUTHOR]

In this paper, we study the constrained minimization problem for an energy functional which is related to a Kirchhoff-type equation. For s = 1 , there many articles have analyzed the limit behavior of minimizers when η > 0 as b → 0 + or b > 0 as η → 0 + . When the equation involves a varying non-local term ∫ R 3 | ∇ u | 2 d x s , we give a detailed limit behavior analysis of constrained minimizers for any positive sequence { η k } with η k → 0 + . The present paper obtains an interesting result on this topic and enriches the conclusions of previous works. [ABSTRACT FROM AUTHOR]

This paper presents a study of fork–join systems. The fork–join system breaks down each customer into numerous tasks and processes them on separate servers. Once all tasks are finished, the customer is considered completed. This design enables the efficient handling of customers. The customers enter the system in a MAP flow. This helps create a more realistic and flexible representation of how customers arrive. It is important for modeling various real-life scenarios. Customers are divided into K ≥ 2 tasks and assigned to different subsystems. The number of tasks matches the number of subsystems. Each subsystem has a server that processes tasks, and a buffer that temporarily stores tasks waiting to be processed. The service time of a task by the k-th server follows a PH (phase-type) distribution with an irreducible representation ( β k , S k ), 1 ≤ k ≤ K . An analytical solution was derived for the case of K = 2 when the input MAP flow and service time follow a PH distribution. We have efficient algorithms to calculate the stationary distribution and performance characteristics of the fork–join system for this case. In general cases, this paper suggests using a combination of Monte Carlo and machine learning methods to study the performance of fork–join systems. In this paper, we present the results of our numerical experiments. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive framework addressing optimal nonlinear analysis and feedback control synthesis for nonlinear stochastic dynamical systems. The focus lies on establishing connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory within a unified perspective. We demonstrate that the closed-loop nonlinear system's asymptotic stability in probability is ensured through a Lyapunov function, identified as the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation. This dual assurance guarantees both stochastic stability and optimality. Additionally, optimal feedback controllers for affine nonlinear systems are developed using an inverse optimality framework tailored to the stochastic stabilization problem. Furthermore, the paper derives stability margins for optimal and inverse optimal stochastic feedback regulators. Gain, sector, and disk margin guarantees are established for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton–Jacobi–Bellman controllers. [ABSTRACT FROM AUTHOR]

Model averaging has become a crucial statistical methodology, especially in situations where numerous models vie to elucidate a phenomenon. Over the past two decades, there has been substantial advancement in the theory of model averaging. However, a gap remains in the field regarding model averaging in the presence of missing censoring indicators. Therefore, in this paper, we present a new model-averaging method for accelerated failure time models with right censored data when censoring indicators are missing. The model-averaging weights are determined by minimizing the Mallows criterion. Under mild conditions, the calculated weights exhibit asymptotic optimality, leading to the model-averaging estimator achieving the lowest squared error asymptotically. Monte Carlo simulations demonstrate that the method proposed in this paper has lower mean squared errors compared to other model-selection and model-averaging methods. Finally, we conducted an empirical analysis using the real-world Acute Myeloid Leukemia (AML) dataset. The results of the empirical analysis demonstrate that the method proposed in this paper outperforms existing approaches in terms of predictive performance. [ABSTRACT FROM AUTHOR]

Many properties of the structure and dynamics of complex networks derive from the characteristics of the spectrum of the associated Laplacian matrix, specifically from the set of its eigenvalues. In this paper, we show that there exist graphs for which the ratio between the length of the spectrum (that is, the difference between the largest and smallest eigenvalues of the Laplacian matrix) and its spread (the difference between the second smallest eigenvalue and the smallest one) is equal to the golden ratio. We call such graphs Golden Laplacian Graphs (GLG). In this paper, we first find all such graphs with a number of nodes n ≤ 10 . We then prove several graph-theoretic and algebraic properties that characterize these graphs. These graphs prove to be extremely robust, as they have large vertex and edge connectivity along with a large isoperimetric constant. Finally, we study the synchronization properties of GLGs, showing that they are among the top synchronizable graphs of the same size. Therefore, GLGs represent very good candidates for engineering and communication networks. [ABSTRACT FROM AUTHOR]