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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]

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]

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]

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]

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]

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]

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]

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]

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]

A new solution to the continuous-time bilinear quadratic regulator optimal control problem (CBQR) was recently developed using Krotov's Method. This paper provides two theoretical results related to the properties of that solution. The first discusses the equivalent representation of the cost-to-go performance index. The second one breaks down this equivalence into smaller identities referencing the components of the performance index. The paper shows how these results can be used to verify the numerical accuracy of the computed solution. Additionally, the meaning of the improving function and the equivalent representation, which are the main elements in the discussed CBQR's solution, are explained according to the derived notions. A numerical example of structural control application exemplifies the significance of these results and how they can be applied to a specific CBQR problem. [ABSTRACT FROM AUTHOR]

Fault detection and localization are vital for ensuring the stability of data center networks (DCNs). Specifically, adaptive fault diagnosis is deemed a fundamental technology in achieving the fault tolerance of systems. The highly scalable data center network (HSDC) is a promising structure of server-centric DCNs, as it exhibits the capacity for incremental scalability, coupled with the assurance of low cost and energy consumption, low diameter, and high bisection width. In this paper, we first determine that both the connectivity and diagnosability of the m-dimensional complete HSDC, denoted by H S D C m (m) , are m. Further, we propose an efficient adaptive fault diagnosis algorithm to diagnose an H S D C m (m) within three test rounds, and at most N + 4 m (m − 2) tests with m ≥ 3 (resp. at most nine tests with m = 2 ), where N = m · 2 m is the total number of nodes in H S D C m (m) . Our experimental outcomes demonstrate that this diagnosis scheme of HSDC can achieve complete diagnosis and significantly reduce the number of required tests. [ABSTRACT FROM AUTHOR]

In the paper, we iteratively solve a scalar nonlinear equation f (x) = 0 , where f ∈ C (I , R) , x ∈ I ⊂ R , and I includes at least one real root r. Three novel two-step iterative schemes equipped with memory updating methods are developed; they are variants of the fixed-point Newton method. A triple data interpolation is carried out by the two-degree Newton polynomial, which is used to update the values of f ′ (r) and f ″ (r) . The relaxation factor in the supplementary variable is accelerated by imposing an extra condition on the interpolant. The new memory method (NMM) can raise the efficiency index (E.I.) significantly. We apply the NMM to five existing fourth-order iterative methods, and the computed order of convergence (COC) and E.I. are evaluated by numerical tests. When the relaxation factor acceleration technique is combined with the modified D z ˇ uni c ´ 's memory method, the value of E.I. is much larger than that predicted by the paper [Kung, H.T.; Traub, J.F. J. Assoc. Comput. Machinery 1974, 21]. for the iterative method without memory. [ABSTRACT FROM AUTHOR]

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs' resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. [ABSTRACT FROM AUTHOR]

In this paper, a theoretical model of the propagation of a shear horizontal wave in a piezoelectric semiconductor semi-infinite medium is established using the optimized spectral method. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are derived with the consideration of biased electric fields. Then, considering the propagation of a shear horizontal wave in the piezoelectric semiconductor semi-infinite medium, two equivalent mathematical models are established. In the first mathematical model, the Schottky junction is theoretically treated as an electrically imperfect interface, and an interface characteristic length is utilized to describe the interface effect of the Schottky junction. To legitimately confirm the interface characteristic length, a second mathematical model is established, in which the Schottky junction is theoretically treated as an electrical gradient layer. Finally, the dispersion and attenuation curves of shear horizontal waves are numerically calculated using these two mathematical models to discuss the influence of the Schottky junction on the dispersion and attenuation characteristics of shear horizontal waves. Utilizing the equivalence of these two mathematical models and the above numerical results, the numerical value of the interface characteristic length is reliably legitimately confirmed; this value is independent of the thickness of the upper metal layer, the doping concentration of the lower n-type piezoelectric semiconductor substrate, and biasing electric fields. Only the biasing electric field parallel to the Schottky junction can provide an evident influence on the attenuation characteristics of shear horizontal waves and enhance the interface effect of the Schottky junction. Since the second mathematical model is also a validation of our previous mathematical model established through the state transfer equation method, some numerical results calculated using these two mathematical models are compared with those obtained using the previous method to verify the correctness and superiority of the research work presented in this paper. Since these two mathematical models can better calculate the dispersion and attenuation curves of high-frequency waves in micro- and nano-scale piezoelectric semiconductor materials, the establishment of mathematical models and the revelation of physical mechanisms are fundamental to the analysis and optimization of micro-scale resonators, energy harvesters, and amplifications. [ABSTRACT FROM AUTHOR]

Inspired by the airway for phonation, fluid flow in an idealized model within a sudden expansion and contraction channel with a geometrically symmetric structure is investigated, and the nonlinear behaviors of the flow therein are explored via numerical simulations. Numerical simulation results show that, as the Reynolds number (Re = U0H/ν) increases, the numerical solution undergoes a pitchfork bifurcation, an inverse pitchfork bifurcation and a Hopf bifurcation. There are symmetric solutions, asymmetric solutions and oscillatory solutions for flows. When the sudden expansion ratio (Er) = 6.00, aspect ratio (Ar) = 1.78 and Re ≤ Rec1 (≈185), the numerical solution is unique, symmetric and stable. When Rec1 < Re ≤ Rec2 (≈213), two stable asymmetric solutions and one symmetric unstable solution are reached. When Rec2 < Re ≤ Rec3 (≈355), the number of numerical solution returns one, which is stable and symmetric. When Re > Rec3, the numerical solution is oscillatory. With increasing Re, the numerical solution develops from periodic and multiple periodic solutions to chaos. The critical Reynolds numbers (Rec1, Rec2 and Rec3) and the maximum return velocity, at which reflux occurs in the channel, change significantly under conditions with different geometry. In this paper, the variation rules of Rec1, Rec2 and Rec3 are investigated, as well as the maximum return velocity with the sudden expansion ratio Er and the aspect ratio Ar. [ABSTRACT FROM AUTHOR]

Network public opinion plays a crucial role in the behavior and decision making of various stakeholders, including farmers, middlemen, and consumers. It also affects the price fluctuations of small-scale agricultural products. Understanding the transmission path and spillover effect of network public opinion on the price fluctuations of these products is essential for ensuring their sustainable development and price stability. This paper selects the monthly data of network public opinion and related market prices of small-scale agricultural products from January 2014 to December 2021, constructs a network public opinion value through the sentiment classification results of deep learning models, and uses the trivariate VAR-BEKK-GARCH(1,1) model and spillover index model to study the spillover effect and spillover index of network public opinion on the market prices of small-scale agricultural products (national average price and origin price). The results show that: (1) There is a bidirectional volatility spillover effect between public opinion sentiment and the market prices of small-scale agricultural products. Additionally, this two-way volatility spillover effect is also evident between the average market prices and the origin prices of these commodities. (2) The influence of network public opinion on the market prices of small-scale agricultural products is substantial, with the spillover index being more pronounced for origin prices than for national average prices and reaching its zenith earlier. Consequently, based on these results, recommendations are provided to adapt planting and inventory strategies, enhance vigilance towards price risk transmission amongst small-scale agricultural product markets, and improve the comprehensive information platform encompassing the entire industry chain. [ABSTRACT FROM AUTHOR]

This paper investigates diverse classes of multidimensional Weyl and Doss ρ -almost periodic functions in a general measure setting. This study establishes the fundamental structural properties of these generalized ρ -almost periodic functions, extending previous classes such as m-almost periodic and (equi-)Weyl-p-almost periodic functions. Notably, a new class of (equi-)Weyl-p-almost periodic functions is introduced, where the exponent p > 0 is general. This paper delves into the abstract Volterra integro-differential inclusions, showcasing the practical implications of the derived results. This work builds upon the extensions made in the realm of Levitan N-almost periodic functions, contributing to the broader understanding of mathematical functions in diverse measure spaces. [ABSTRACT FROM AUTHOR]

The 3D integrated circuit (3D-IC) is garnering significant attention from academia and industry as a key technology leading the post-Moore era, offering new levels of efficiency, power, performance, and form-factor advantages to the semiconductor industry. However, thermal management in 3D-ICs presents a critical challenge that must be overcome to ensure prosperity for this technology. Unlike traditional thermal management solutions that perceive heat generation in 3D-ICs negatively and aim to eliminate it, this paper proposes, for the first time, a thermal management method that positively utilizes heat to achieve low-power operation in 3D-ICs. This approach is based on a novel discovery that circuits can reduce power consumption at higher temperatures by leveraging the temperature effect inversion (TEI) phenomenon in ultralow-voltage (ULV) operating circuits, a characteristic of low-power techniques (TEI-LP techniques). Along with a detailed explanation of this discovery, this paper introduces new thermal management technologies for practical application in 3D-ICs. Furthermore, to achieve optimal energy efficiency with the proposed technology, we develop a temperature controller essential for this purpose. The developed controller is a deep learning-based PID autotuner. This paper proves the theoretical validity of the AI control algorithm designed for this purpose and demonstrates the functional correctness and power-saving effectiveness of the developed controller through intensively conducted simulations. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel method to construct Goethals–Seidel (GS) sequences with special structures. In the existing methods, utilizing Turyn sequences is an effective and convenient approach; however, this method cannot cover all GS sequences. Motivated by this, we are devoted to designing some sequences that can potentially construct all GS sequences. Firstly, it is proven that a quad of ± 1 polynomials can be considered a linear combination of eight polynomials with coefficients uniquely belonging to { 0 , ± 1 } . Based on this fact, we change the construction of a quad of Goethals–Seidel sequences to find eight sequences consisting of 0 and ± 1 . One more motivation is to obtain these sequences more efficiently. To this end, we make use of the k-block, of which some properties of (anti) symmetry are discussed. After this, we can then look for the sequences with the help of computers since the symmetry properties facilitate reducing the search range. Moreover, we find that one of the eight blocks, which we utilize to construct GS sequences directly, can also be combined with Williamson sequences to generate GS sequences with more order. Several examples are provided to verify the theoretical results. The main contribution of this work is in building a bridge linking the GS sequences and eight polynomials, and the paper also provides a novel insight through which to consider the existence of GS sequences. [ABSTRACT FROM AUTHOR]

The effective allocation of limited resources and the establishment of targeted goals play a pivotal role in enhancing the overall efficiency of large enterprises and organizations. To achieve optimal organizational efficiency, managers seek dynamic strategies that adapt to the constraints of limited and uncertain historical data. This paper introduces an evaluation of organizational efficiency through a stochastic framework, employing a bilevel data envelopment analysis (DEA) approach. This decision-making process is centralized within a decision-making unit (DMU) overseeing subordinate decision-making units (subDMUs). Discrete scenarios, each associated with a realization probability, define the uncertain parameters in the bilevel DEA-based model. This stochastic approach allows for recourse actions upon scenario realization leading to an enhanced overall organizational strategy. Decision-makers acting within uncertain and dynamic environments can benefit from this research since it allows the investigation of efficiency assessment under alternative scenarios in the presence of volatility and risk. The potential impact of applying this methodology varies depending on the specific domain. Although, the context of this paper focuses on banking, in general, enhancing resource allocation and target setting under stochasticity, contributes to advancing sustainability across all its three dimensions (economic, environmental, social). As mentioned earlier, the practical application of our approach is demonstrated via a case study in the banking sector. [ABSTRACT FROM AUTHOR]

This paper tests using two-regime Markov-switching models with asymmetric, time-varying exponential generalized autoregressive conditional heteroskedasticity (MS-EGARCH) variances in random-length lumber futures trading. By assuming a two-regime context (a low s = 1 and high s = 2 volatility), a trading algorithm was simulated with the following trading rule: invest in lumber futures if the probability of being in the high-volatility regime s = 2 is lower or equal to 50%, or invest in the 3-month U.S. Treasury bills (TBills) otherwise. The rationale tested in this paper was that using a two-regime Markov-switching (MS) algorithm leads to an overperformance against a buy-and-hold strategy in lumber futures. To extend the current literature in MS trading algorithms, two location parameter scenarios were simulated. The first uses an unconditional mean or expected value (no factors), and the second incorporates market and behavioral factors. With weekly simulations form 2 January 1994 to 28 July 2023, the results suggest that using MS-EGARCH models in a no-factors scenario is appropriate for active lumber futures trading with an accumulated return of 158.33%. Also, the results suggest that it is not useful to add market and behavioral factors in the MS-GARCH estimation because it leads to a lower performance. [ABSTRACT FROM AUTHOR]

In this paper, we investigate mathematical models of meteorological forecasting based on the work of neural networks, which allow us to calculate presumptive meteorological parameters of the desired location on the basis of previous meteorological data. A new method of grouping neural networks to obtain a more accurate output result is proposed. An algorithm is presented, based on which the most accurate meteorological forecast was obtained based on the results of the study. This algorithm can be used in a wide range of situations, such as obtaining data for the operation of equipment in a given location and studying meteorological parameters of the location. To build this model, we used data obtained from personal weather stations of the Weather Underground company and the US National Digital Forecast Database (NDFD). Also, a Google remote learning machine was used to compare the results with existing products on the market. The algorithm for building the forecast model covered several locations across the US in order to compare its performance in different weather zones. Different methods of training the machine to produce the most effective weather forecast result were also considered. [ABSTRACT FROM AUTHOR]

This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples. [ABSTRACT FROM AUTHOR]

Due to the facts that epidemic-related parameters vary significantly in different stages of infectious diseases and are relatively stable within the same stage, infectious disease models should be switch-type models. However, research on switch-type infectious disease models is scarce due to the complexity and intricate design of switching rules. This scarcity has motivated the writing of this paper. By assuming that switching instants and impulse times occur at different moments, this paper proposes switch rules suitable for impulse control and derives synchronization criteria for reaction–diffusion switch-type infectious disease systems under impulse control. The effectiveness of this method is validated through numerical simulations. It is important to mention that, based on the information available to us, this paper is currently the sole study focusing on switch-type reaction–diffusion models for infectious diseases. [ABSTRACT FROM AUTHOR]

The application of blockchain has become a trend in the development of supply chain finance. Aiming to bridge the gap in the existing literature, this paper investigates a supply chain finance system based on blockchain technology which contains a manufacturer, a retailer and a financial institution and incorporates blockchain costs into the model. Firstly, this paper establishes a supply chain finance model based on blockchain technology and it presents a comparison with the process employed under the traditional model. Secondly, this paper establishes the revenue mathematical model of supply chain finance based on blockchain technology. Thirdly, the optimal decisions of each participant under centralized and decentralized decision-making are proved and obtained, respectively, and the influencing factors of the optimal decisions are analyzed. Finally, the conclusions are verified via simulations. This study finds that, when blockchain is used, the benefits of each participant in the chain are increased. In addition, centralized decision-making, which is more optimal in the traditional model, is also enhanced under blockchain. This paper demonstrates the superiority of blockchain-enabled supply chain finance in terms of model and revenue. This provides some suggestions for companies in the supply chain with regard to solving the problem of financing difficulties. [ABSTRACT FROM AUTHOR]

The object of the investigation is a model of the incomplete financial market. It includes a bank deposit with a known interest rate and basic risky securities. The instant interest rate and volatility are governed by a hidden market regime, represented by some finite-state Markov jump process. The paper presents a solution to two problems. The first one consists of the characterization of the derivatives based on the existing market securities, which are valid to complete the considered market. It is determined that for the market completion, it is sufficient to add the number of derivatives equal to the number of possible market regimes. A generalization of the classic Black–Scholes equation, describing the evolution of the fair derivative price, is obtained along with the structure of a self-financing portfolio, replicating an arbitrary contingent claim in the market. The second problem consists of the online estimation of the market regime, given the observations of both the underlying and derivative prices. The available observations are either a combination of the time-discretized risky security prices or some high-frequency multivariate point processes associated with these prices. The paper presents the numerical algorithms of the market regime tracking for both observation types. The comparative numerical experiments illustrate the high quality of the proposed estimates. [ABSTRACT FROM AUTHOR]