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The isolated current‐fed push‐pull dc‐dc converter has some practical advantages such as improved cross regulation characteristics, reduced output noise, and good overall efficiency. Although detailed insight on this converter is available in the literature, the use of digital peak current mode with slope compensation control methodology has not been explicitly presented. This paper discusses digital peak current mode control of a current‐fed push‐pull converter with a novel double digital pulse‐by‐pulse current limiting scheme. Push‐pull topology is implemented on the primary side of an isolation transformer in a dc‐dc bidirectional converter. Achieving this control solution of isolated push‐pull converter is attractive especially in controlling battery power flow in smart micro‐grids. By using a digitally controlled push‐pull converter, the ability to change controller parameters and the use of droop control methods for storage are easier. Furthermore, current mode control provides capability of equal current sharing between parallel converters and eliminates the transformer saturation problem that is common in push‐pull topology. Using continuous time model of the converter, a Type II compensator is designed and implemented in discrete time domain. Digital slope compensation is applied to eliminate the high frequency oscillations caused by current feedback loop. The control method and slope compensation are implemented on STM32F303 mixed‐signal microcontroller. On‐chip analog comparator disabled the PWM output if the sensed current exceeds the reference current until next PWM cycle. The digital controller performance is confirmed by 13 W hardware implementation including fast transient response and stable operation. [ABSTRACT FROM AUTHOR]

Medium-voltage DC (MVDC) technology has gained increasing attention in recent years. Power electronics devices dominate these grids. Accurate simulation of such a grid, with detailed models of switching semiconductors, can quickly became very time-consuming, according to the number of connected devices to be simulated. A simulation approach based on interactions on a continuous time model can be very interesting, especially for developing a system-level control model of such a modern MVDC distribution grid. The aim of this paper is to present all the steps required for obtaining a continuous time modelling of a +/−10 kV MVDC grid case study, including a solid-state transformer (SST)- and modular multilevel converter (MMC)-based active front end (AFE). An additional aim of this paper is to supply educational content about the use of the continuous time simulation approach, thanks to a detailed description of the various devices modelled into the presented MVDC grid. The results of a certain number of simulation scenarios are eventually presented. [ABSTRACT FROM AUTHOR]

With the aggregation of renewable energy in the power system, the uncertainty caused by the renewable energy affects the planning and operation of power systems. Meanwhile, the existing planning models fail to consider renewable energy uncertainty methods, specifically concerning renewable energy confidence and future possible scenarios; thus, a confidence-based scenario cluster method is presented. A novel generator, network, load, and energy storage (GNLS) co-planning model is proposed in the paper. First, a confidence-based scenario cluster is built, which can reflect uncertainties by clustering and analyzing wind, solar, and load. Second, the proposed model focuses on load and energy storage co-planning, and in addition, relevant flexible indices are used to assess the model. Finally, the GNLS co-planning model is built as a bi-level stochastic model on continuous time scales. The model is solved using the Benders decomposition algorithm. The method in this paper is validated using an IEEE RTS 24-bus and a real test system in China to demonstrate the reduction in renewable energy curtailment and optimization of economic factors in power system planning. [ABSTRACT FROM AUTHOR]

The special issue of the journal Simulation titled "Distributed and Real-Time Simulation of Next-Generation Complex Systems" explores innovative methodologies for modeling and optimizing complex systems in various domains such as transportation, industry, biology, and social interactions. Traditional simulation methods struggle to capture the adaptive and nonlinear nature of these systems, leading to the need for more effective tools. The special issue showcases five research papers that delve into distributed and real-time simulation techniques, including simulating agent-based models, estimating network performance for IoT multimedia applications, modeling disease spread using geographical models, improving navigation accuracy in urban environments, and assessing communication protocols for road traffic simulation. The special issue aims to highlight the potential and diversity of these simulation methods while encouraging further research and innovation in the field. [Extracted from the article]

In this paper, a mathematical model is formulated, suitable to explain the evolution of income distribution over a population in the presence of production. The model is conceived from the perspective of complexity. Indeed, the income distribution emerges as the result of a myriad of economic exchanges taking place between individuals. In fact, the aim of the paper is to provide a framework and mathematical tools for the construction and the investigation of models having an exploratory character. The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. Numerical solutions of these systems are constructed under different assumptions on the law of production and in the presence of different fiscal systems, which provides an example of the versatility of the method. [ABSTRACT FROM AUTHOR]

Continuous Time Echo State Networks (CTESNs) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). A key determinant of the generalization accuracy of a CTESN surrogate is the method of projecting the reservoir state to the output. This paper shows that of the two common projection methods (linear and nonlinear), the surrogates developed via the nonlinear projection consistently outperform those developed via the linear method. CTESN surrogates are developed for several challenging benchmark cases governed by stiff ODEs, and for each case, the performance of the linear and nonlinear projections is compared. The results of this paper demonstrate the applicability of CTESNs to a variety of problems while serving as a reference for important algorithmic and hyper-parameter choices for CTESNs. [ABSTRACT FROM AUTHOR]

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number R0 of the model and studied the influence of orders a and b on R0. Second, we found that frSIS has a disease-free equilibrium point E0 and an endemic equilibrium point E∗. Moreover, we proved frSIS global stability of the model using R0. If R0<1, the model of E0 is globally asymptotically stable. If R0>1, the model of E∗ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease. [ABSTRACT FROM AUTHOR]

In this paper we further develop a notion of causal predictability defined in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] as a concept of dependence which is based on Granger's definition of causality. More precisely, in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] causal predictability is defined between filtrations, but now we introduce causal predictability between stochastic processes and filtrations. Also, we provide some properties of this new concept. Then we apply the given causality concept to the uniqueness of weak solutions of the stochastic differential equations and in financial mathematics. Granger [Investigating causal relations by econometric models and cross spectral methods, Econometrica. 37 (1969), pp. 424–438] has considered causality concept between time series. In this paper we consider continuous time processes, since continuous time models represent the first step in various applications, such as in finance, econometric practice, neuroscience, epidemiology, climatology, demographic, etc. [ABSTRACT FROM AUTHOR]

This paper considers the problem of admissibility and admissibilization of 2D singular continuous systems described by the Roesser model. A necessary and sufficient admissibility condition is first proposed for 2D singular continuous systems in terms of a strict Linear Matrix Inequality (LMI). Then, a necessary and sufficient condition is established for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). Moreover, the stability condition is completed to give a sufficient condition to ensure a specified H∞ disturbance attenuation level for the state feedback closed loop. To illustrate the effectiveness of the proposed methodology, a numerical example is given to illustrate an admissibilization of a state feedback closed-loop system. [ABSTRACT FROM AUTHOR]

Background: Malaria is a potentially life-threatening disease caused by Plasmodium protozoa transmitted by infected Anopheles mosquitoes. Controlled human malaria infection (CHMI) trials are used to assess the efficacy of interventions for malaria elimination. The operating characteristics of statistical methods for assessing the ability of interventions to protect individuals from malaria is uncertain in small CHMI studies. This paper presents simulation studies comparing the performance of a variety of statistical methods for assessing efficacy of intervention in CHMI trials. Methods: Two types of CHMI designs were investigated: the commonly used single high-dose design (SHD) and the repeated low-dose design (RLD), motivated by simian immunodeficiency virus (SIV) challenge studies. In the context of SHD, the primary efficacy endpoint is typically time to infection. Using a continuous time survival model, five statistical tests for assessing the extent to which an intervention confers partial or full protection under single dose CHMI designs were evaluated. For RLD, the primary efficacy endpoint is typically the binary infection status after a specific number of challenges. A discrete time survival model was used to study the characteristics of RLD versus SHD challenge studies. Results: In a SHD study with the continuous time survival model, log-rank test and t-test are the most powerful and provide more interpretable results than Wilcoxon rank-sum tests and Lachenbruch tests, while the likelihood ratio test is uniformly most powerful but requires knowledge of the underlying probability model. In the discrete time survival model setting, SHDs are more powerful for assessing the efficacy of an intervention to prevent infection than RLDs. However, additional information can be inferred from RLD challenge designs, particularly using a likelihood ratio test. Conclusions: Different statistical methods can be used to analyze controlled human malaria infection (CHMI) experiments, and the choice of method depends on the specific characteristics of the experiment, such as the sample size allocation between the control and intervention groups, and the nature of the intervention. The simulation results provide guidance for the trade off in statistical power when choosing between different statistical methods and study designs. [ABSTRACT FROM AUTHOR]

This paper mainly addressed the study of the transmission dynamics of infectious diseases and analysed the effect of two different types of viruses simultaneously that cause immunodeficiency in the host. The two infectious diseases that often spread in the populace are HIV and measles. The interaction between measles and HIV can cause severe illness and even fatal patient cases. The effects of the measles virus on the host with HIV infection are studied using a mathematical model and their dynamics. Analysing the dynamics of infectious diseases in communities requires the use of mathematical models. Decisions about public health policy are influenced by mathematical modeling, which sheds light on the efficacy of various control measures, immunization plans, and interventions. We build a mathematical model for disease spread through vertical and horizontal human population transmission, including six coupled nonlinear differential equations with logistic growth. The fundamental reproduction number is examined, which serves as a cutoff point for determining the degree to which a disease will persist or die. We look at the various disease equilibrium points and investigate the regional stability of the disease-free and endemic equilibrium points in the feasible region of the epidemic model. Concurrently, the global stability of the equilibrium points is investigated using the Lyapunov functional approach. Finally, the Runge-Kutta method is utilised for numerical simulation, and graphic illustrations are used to evaluate the impact of different factors on the spread of the illness. Critical factors that effect the dynamics of disease transmission and greatly affect the rate and range of the disease's spread in the population have been determined through a thorough analysis. These factors are crucial in determining the expansion of the disease. [ABSTRACT FROM AUTHOR]

In this paper, a case study is presented to study the effects of increasing nutrients and macrophytes on survival of fish population in Varthur lake, Bangalore, India. Several fish kill episodes have occurred in Varthur lake over past years. Aim of the present study is to investigate the effects mathematically as huge amount of nutrients from industries, domestic sewage is constantly release into the lake which is leading to abundant growth of macrophytes leaving less room for fish survival. The above-mentioned parameters are considered to formulate a mathematical model. Equilibrium points are studied and analysed in detail for stability via Routh-Hurwitz criteria. Numerical simulation is carried out to illustrate the analytical findings of the case study. [ABSTRACT FROM AUTHOR]

The paper is organized to study some mathematical properties and dynamics of a simple Cournot duopoly game based on a computed quadratic cost. The time evolution of this game is described by a two-dimensional noninvertible discrete time map using the bounded rationality mechanism. For this map, some dynamic characteristics such as multistability and synchronization are investigated. Its equilibrium points are obtained for the asymmetric case, and their conditions of stability are obtained. Our results investigate that the Nash equilibrium point may be unstable due to flip bifurcation and under certain parameter values, and Neimark–Sacker bifurcation is born after the period-4 cycle. Through some restrictions, the coordinate axes of the map construct an invariant manifold, and therefore, their dynamics can be analyzed by using a one-dimensional map. In the symmetric case, both firms behave identically, and this implies that the diagonal set forms an invariant manifold, and hence the synchronization phenomena take place. Furthermore, the global bifurcation of the map is confirmed through contact between critical curves and the boundaries of infeasible domains. [ABSTRACT FROM AUTHOR]

With the goal of solving the problem of feature extractors lacking strong supervision training and insufficient time information concerning single‐sequence model learning, a hierarchical sequence memory network with a multi‐level iterative optimisation strategy is proposed for continuous sign language recognition. This method uses the spatial‐temporal fusion convolution network (STFC‐Net) to extract the spatial‐temporal information of RGB and Optical flow video frames to obtain the multi‐modal visual features of a sign language video. Then, in order to enhance the temporal relationships of visual feature maps, the hierarchical memory sequence network is used to capture local utterance features and global context dependencies across time dimensions to obtain sequence features. Finally, the decoder decodes the final sentence sequence. In order to enhance the feature extractor, the authors adopted a multi‐level iterative optimisation strategy to fine‐tune STFC‐Net and the utterance feature extractor. The experimental results on the RWTH‐Phoenix‐Weather multi‐signer 2014 dataset and the Chinese sign language dataset show the effectiveness and superiority of this method. [ABSTRACT FROM AUTHOR]

A time continuous statistical model of chirp signal observed against the background of stationary Gaussian noise is considered in the paper. Asymptotic normality of the LSE for parameters of such a sinusoidal regression model is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we extend the classical theory of normal forms for continuous and difference dynamical systems to dynamic equations on discrete time scales. As consequences of the well known results from the theory of analytic differential equations, we obtain some versions of the Poincaré and Siegel theorems for dynamic equations on discrete time scales. Using these results and known results on the stability of dynamic equations on time scales, we obtain some stability results for the nonlinear dynamic equations. We also prove some results on generic properties of bifurcation curves and the saddle-node bifurcation for one-parameter families of dynamic equations on arbitrary time scales. [ABSTRACT FROM AUTHOR]

To examine developmental processes, intervention effects, or both, longitudinal studies often aim to include measurement intervals that are equally spaced for all participants. In reality, however, this goal is hardly ever met. Although different approaches have been proposed to deal with this issue, few studies have investigated the potential benefits of individual variation in time intervals. In the present paper, we examine how continuous time dynamic models can be used to study nonexperimental intervention effects in longitudinal studies where measurement intervals vary between and within participants. We empirically illustrate this method by using panel data (N = 2,877) to study the effect of the transition from primary to secondary school on students' motivation. Results of a simulation study also show that the precision and recovery of the estimate of the effect improves with individual variation in time intervals. [ABSTRACT FROM AUTHOR]

The pandemic of Gompertz virus disease remains a pressing issue in agricultural production. Moreover, the dynamics of various infectious diseases is usually investigated by the method of mathematical modelling. A new mathematical model for dynamics on Gompertz virus disease impulsive system is proposed and analyzed in this paper. We prove the dynamic characteristics about the permanence and globally exponential stability of Gompertz virus disease model. Moreover, we also give the sufficient condition that one positive solution which satisfies E (t) ≥ q 2 if R 1 ∗ > 1 exists. Eventually, numerical simulations are utilized to validate the validity of the theoretically analyzed conclusion in this paper. [ABSTRACT FROM AUTHOR]

State‐structured populations are ubiquitous in biology, from the age‐structure of animal societies to the life cycles of parasitic species. Understanding how this structure contributes to eco‐evolutionary dynamics is critical not only for fundamental understanding but also for conservation and treatment purposes. Although some methods have been developed in the literature for modelling eco‐evolutionary dynamics in structured population, such methods are wholly lacking in the G function evolutionary game theoretic framework.In this paper, we integrate standard matrix population modelling into the G function framework to create a theoretical framework to probe eco‐evolutionary dynamics in structured populations. This framework encompasses age‐ and stage‐structured matrix models with basic density‐ and frequency‐dependent transition rates and probabilities.For both discrete and continuous time models, we define and characterize asymptotic properties of the system such as eco‐evolutionary equilibria (including ESSs) and the convergence stability of these equilibria. For multistate structured populations, we introduce an ergodic flow preserving folding method for analysing such models.The methods developed in this paper for state‐structured populations and their extensions to multistate‐structured populations provide a simple way to create, analyse and simulate eco‐evolutionary dynamics in structured populations. Furthermore, their generality allows these techniques to be applied to a variety of problems in ecology and evolution. [ABSTRACT FROM AUTHOR]

This paper conducts a rigorous game-theoretic analysis on multi-task deep learning, providing mathematical insights into the dynamics and interactions of tasks within these models. Multi-task deep learning has attracted significant attention in recent years due to its ability to leverage shared representations across multiple correlated tasks, leading to improved generalization and reduced training time. However, understanding and examining the interactions between tasks within a multi-task deep learning system poses a considerable challenge. In this paper, we present a game-theoretic investigation of multi-task deep learning, focusing on the existence and convergence of Nash equilibria. Game theory provides a suitable framework for modeling the interactions among various tasks in a multi-task deep learning system, as it captures the strategic behavior of learning agents sharing a common set of parameters. Our primary contributions include: casting the multi-task deep learning problem as a game where each task acts as a player aiming to minimize its task-specific loss function; introducing the notion of a Nash equilibrium for the multi-task deep learning game; demonstrating the existence of at least one Nash equilibrium under specific convexity and Lipschitz continuity assumptions for the loss functions; examining the convergence characteristics of the Nash equilibrium; and providing a comprehensive analysis of the implications and limitations of our theoretical findings. We also discuss potential extensions and directions for future research in the multi-task deep learning landscape. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) have attracted enormous attention in recent years due to their potentials in mitigating energy crisis and air pollutions. However, the long battery charging time and lack of sufficient charging infrastructure highly restrict the popularization of EVs. In this context, it is promising to establish battery charging and swapping systems (BCSSs) based on the concept of battery swapping services. To optimally achieve the combined operation of BCSSs, this paper proposes a hybrid swapped battery charging and logistics dispatch model in continuous time domain. Identifying the special structure of the mathematical models of the two problems, this paper innovatively formulated the swapped battery charging strategy as the rectangle packing problem and the battery logistics model as the vehicle routing problem. The two models are closely linked by the delivery time of transporting the well-charged batteries from battery charging stations to battery swapping stations. A hybrid optimal operation model of BCSSs is further formulated as a mixed-integer linear programming model by incorporating the interaction between the battery charging and battery logistics. Finally, case studies are conducted on several BCSSs and numerical results validate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Complex domestic airspace requires collision risk models and monitoring tools suitable for arbitrary aircraft trajectories. This paper presents a new mathematically based collision risk approach that extends the International Civil Aviation Organisation (ICAO) models to full aircraft encounters based on real trajectory data. A new continuous time intervention model is presented, along with a position uncertainty propagation model that better reflects aircraft behaviour and allows generalisation to all trajectories to eliminate degenerate cases. The proposed risk model is computationally efficient compared to the models it is based on and can be applied to large-scale trajectory data. The utility of the model is demonstrated through a series of case studies using real aircraft trajectories. [ABSTRACT FROM AUTHOR]

Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF- α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology. [ABSTRACT FROM AUTHOR]

In physics, in particular, acoustics, time is traditionally considered as a continuous coordinate. Some exception is signal processing, where sampling is necessary for calculations on computers. But all acoustic problems are formulated and solved using time-continuous models described by differential equations and their solutions in the form of continuous time functions. Meanwhile, these problems can be formulated and solved in an equivalent way using discrete-time models described by finite-difference equations and their solutions in the form of time series. As the experience of some other fields of science, for example, control theory, shows, the discrete approach has a number of advantages over the continuous approach, the use of which greatly facilitates the solution of many problems. This paper aims to partially fill the gap in acoustics that exists here and is aimed at creating the theoretical foundations of a discrete-time approach to solving acoustic problems. The paper is limited to the consideration of one oscillatory system widely used in acoustics—a linear structure with N degrees of freedom consisting of lumped inertial, elastic and dissipative elements, to which, in particular, the finite element method leads. For several continuous models of this system, equivalent discrete-time models are constructed in the paper, finite-difference equations are derived and their solutions are obtained. The criterion of equivalence of continuous and discrete models in the paper is the mathematically exact equality of the corresponding solutions at all discrete points in time. Based on this criterion, analytical relations have been established between the parameters of continuous and discrete models and their equations, which make it possible to build its discrete-time model based on a continuous model of the system and, conversely, to build its continuous model based on a known discrete model. Special attention is paid in the paper to the forced vibrations of the system under the action of kinematic excitation, which is important in many acoustic problems, whereas in the literature only force excitation is considered. The paper also discusses one of the most useful properties of discrete modeling—the simplicity of constructing discrete models based on experimentally measured signals. A corresponding example is given. Note that the term "ARMA-model" is an abbreviation for "autoregressive and moving average model", generally accepted in control theory, systems theory and other fields of science. [ABSTRACT FROM AUTHOR]

Traditional claim estimation in general insurance works with accident year cohorts and development patterns. For the impending International Financial Reporting Standard (IFRS) 17 Insurance Contracts and often for reinsurance purposes, claim estimates must be split by contract year. This paper proposes to add contract year as a cohort classifier and to adjust the development patterns accordingly. To this end, we use the continuous time models of Hesselager and Norberg. Having contract year as an additional cohort classifier, display of claim estimates by contract year and/or accident year becomes a simple matter of summation across the appropriate dimensions. The continuous time model also enables us to derive mutually consistent development patterns for discrete time intervals of different length, such as years and quarters. In addition to delivering consistent development patterns in discrete time, continuous time modelling offers the advantage of requiring only a fixed number of model parameters. Although most of the derivations in this paper are explained in terms of claim numbers, the mechanics can also be applied to claim payments. [ABSTRACT FROM AUTHOR]

In this paper it is shown, that if a possibly inhomogeneous Markov chain with continuous time and finite state space is weakly ergodic and all the entries of its intensity matrix are locally integrable, then, using available results from the perturbation theory, its time-dependent probability characteristics can be approximately obtained from another Markov chain, having piecewise constant intensities and the same state space. The approximation error (the taxicab distance between the state probability distributions) is provided. It is shown how the Cauchy operator and the state probability distribution for an arbitrary initial condition can be calculated. The findings are illustrated with the numerical examples. [ABSTRACT FROM AUTHOR]

The main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic formulae for its motions. In particular, we determine existence and uniqueness of solutions. We find all possible grazing impacts of the ball. Besides, we demonstrate that for almost every initial condition, the ball goes to infinity exponentially fast, with the time intervals between neighboring collisions tending to zero. The approach developed in this paper is an original combination of methods of Billiards and Vibro-Impact Dynamics. It could be a base for studying more complicated systems of similar types. [ABSTRACT FROM AUTHOR]

Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus. [ABSTRACT FROM AUTHOR]

Summary: A partial model‐free, data‐driven adaptive optimal output feedback (OPFB) control scheme with low computational cost continuous‐time is proposed in this paper. The design objective is to obtain the optimal control law by using measurable input and output data, without some knowledge of system model information. Firstly, the system states are decoupled into measurable and unmeasurable parts, and a new state‐space equation is built to estimate the unmeasurable states by using a reduced‐order observer. Based on this, a parametrization method is utilized to reconstruct the system states. Subsequently, by using the reconstructed states, the adaptive dynamic programming (ADP) Bellman equations based on policy‐iteration (PI) and value‐iteration (VI) are presented to solve the control problems with initially stable and unstable conditions, respectively. Then, the convergence of the system is proved. Compared with the early proposed OPFB algorithms, only the unknown internal state needs to be reconstructed. Therefore, the computation cost and design complexity are reduced for the proposed scheme. The effectiveness of the proposed scheme is verified through two numerical simulations. In addition, a practical inverted pendulum experiment is carried out to demonstrate the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

Let L be a nonnegative integer and ΓL the power set of the set {0, 1,…,L}. Then there is an adjacency relation in ΓL such that ΓL together with the relation forms a regular graph. In this paper, we propose a model of continuous-time magnetic quantum walk (MQW) on the graph ΓL, and investigate its properties from a viewpoint of probability and quantum information. We first introduce a magnetic Laplacian ΔL(휃) on the graph ΓL and examine its spectrum. And then, with ΔL(휃) as the Hamiltonian, we construct our model of continuous-time MQW on the graph ΓL. We find that the model has probability distributions that are completely independent of the magnetic potential at all times. And we show that it has perfect state transfer at time t = π 2 when the magnetic potential satisfies some mild conditions. Some other interesting results are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, based on a linearized mathematical model of the dynamics of a quadrotor, an optimal controller is constructed to control the spatial motion of a quadrotor when it is raising to a given altitude with simultaneous heading maneuver in a horizontal plane. Moreover, the maneuver trajectory must satisfy certain boundary conditions. The feature of this paper is the application of LQR synthesis to optimize the control of the translational motions of a quadrotor along all three axes of the inertial coordinate system, as well as to control its rotational motion relative to the vertical axis. The effectiveness of the developed control laws has been proven by modeling the above-described spatial motion of a quadrotor using the MATLAB package. [ABSTRACT FROM AUTHOR]

Coffee berry disease (CBD) is a fungal disease caused by Colletotrichum kahawae. CBD is a major constraint to coffee production to Kenya and Africa at large. In this research paper, we formulate a mathematical model of the dynamics of the coffee berry disease. The model consists of coffee plant population in a plantation and Colletotrichum kahawae pathogen population. We derived the basic reproduction number R k 0 , and analyzed the dynamical behaviors of both disease-free equilibrium and endemic equilibrium by the theory of ordinary differential equations. Using the MATLAB ode45 solver, we carried out numerical simulation, and the findings are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

The Fermi–Pasta–Ulam–Tsingou (FPUT) problem addresses fundamental questions in statistical physics, and attempts to understand the origin of recurrences in the system have led to many great advances in nonlinear dynamics and mathematical physics. In this work, we revisit the problem and study quasiperiodic recurrences in the weakly nonlinear α -FPUT system in more detail. We aim to reconstruct the quasiperiodic behavior observed in the original paper from the canonical transformation used to remove the three-wave interactions, which is necessary before applying the wave turbulence formalism. We expect the construction to match the observed quasiperiodicity if we are in the weakly nonlinear regime. Surprisingly, in our work, we find that this is not always the case and in particular, the recurrences observed in the original paper cannot be constructed by our method. We attribute this disagreement to the presence of small denominators in the canonical transformation used to remove the three-wave interactions before arriving at the starting point of wave turbulence. We also show that these small denominators are present even in the weakly nonlinear regime, and they become more significant as the system size is increased. We also discuss our results in the context of the problem of equilibration in the α -FPUT system and point out some mathematical challenges when the wave turbulence formalism is applied to explain thermalization in the α -FPUT problem. We argue that certain aspects of the α -FPUT system such as thermalization in the thermodynamic limit and the cause of quasiperiodicity are not clear, and that they require further mathematical and numerical studies. [ABSTRACT FROM AUTHOR]

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam's opinion diffusion model. For a given selection of the coefficients in our model, this proposal yields the original Galam's model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow it to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided. [ABSTRACT FROM AUTHOR]

In this paper, the unknown parameters of a SEIRS mathematical model for the dynamics of COVID-19 are estimated by the least squares approach using data of Trkiye. In the considered model, the infective group is divided into two classes consisting of diagnosed and undiagnosed individuals. Since the data for undiagnosed infective individuals in the community is unknown, three different scenarios are proposed. The numerical solutions of the model using the estimated parameter values and the actual data are demonstrated with graphs. [ABSTRACT FROM AUTHOR]

Accelerated longitudinal designs (ALD) allow studying developmental processes usually spanning multiple years in a much shorter time framework by including participants from different age cohorts, which are assumed to share the same population parameters. However, different cohorts may have been exposed to dissimilar contextual factors, resulting in different developmental trajectories. If such differences are not accounted for, the generating process will not be adequately characterized. In this paper, we propose a continuous-time latent change score model as an approach to capture cohort differences affecting the speed of maturation of psychological processes in ALDs. This approach fills an important gap in the literature because, until now, no method existed for this goal. Using a Monte-Carlo simulation study, we show that the proposed model detects cohort differences adequately, regardless of their size in the population. Our proposed model can help developmental researchers control for cohort effects in the context of ALDs. [ABSTRACT FROM AUTHOR]

This work proposes a mathematical solution for the attitude control problem of an ornithopter wing. An ornithopter is an artificial bird or insect-like aerial vehicle whose flight and lift movements are produced and maintained by flapping wings. The aerodynamical drag forces responsible for the flying movements are generated by the wing attitude and torques applied to its joints. This mechanical system represents a challenging problem because its dynamics consist of MIMO nonlinear equations with couplings in the input variables. For dealing with such a mathematical model, an Active Disturbance Rejection Control-based (ADRC) method is considered. The cited control technique has been studied for almost two decades and its main characteristics are the use of an extended state observer to estimate the nonmeasurable signals of the plant and a state-feedback control law in standard form fed by that observer. However, even today, the application of the basic methodology requires the exact knowledge of the plant's control gain which is difficult to measure in the case of systems with uncertain parameters. In addition, most of the related works apply the ADRC strategy to Single Input Single Output (SISO) plants. For MIMO systems, the control gain is represented by a square matrix of general entries but most of the reported works consider the simplified case of uncoupled inputs, in which a diagonal matrix is assumed. In this paper, an extension of the ADRC SISO strategy for MIMO systems is proposed. By adopting such a control methodology, the resulting closed-loop scheme exhibits some key advantages: (i) it is robust to parametric uncertainties; (ii) it can compensate for external disturbances and unmodeled dynamics; (iii) even for nonlinear plants, mathematical analysis using Laplace's approach can be always used; and (iv) it can deal with system's coupled input variables. A complete mathematical model for the dynamics of the ornithopter wing system is presented. The efficiency of the proposed control is analyzed mathematically, discussed, and illustrated via simulation results of its application in the attitude control of ornithopter wings. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative model for describing the hydro-mechanical drive operation of the automatic transmissions. The study is aimed at preparing a reliable model that meets the requirements of sufficient informativeness and rapidity to, basically, be used as a model for optimized control. The study relevance is stipulated by the need for simple and precise models ensuring minimal computational costs in model predictive control (MPC) procedures. The paper proposes a method for coordinating the engine's control and operating modes, with the torque converter (TC) operating mode, based on the criteria of angular acceleration derivative (jerk), which fosters including the angular acceleration in the state vector for using the optimal control. The latter provides stronger prediction quality than using only the crankshaft angular speed criterion. This moment comprises a study novelty. Additionally, the proposed approach can be helpful in tasks of powertrain automation, autonomous vehicles' integrated control, elaboration of control algorithms, co-simulations, and real-time applications. The paper material is structured by the modeling stages, including mathematics and simulations, data preparation, testing and validation, virtual experiments, analysis of results, and conclusions. The essence of the problem, goals, and objectives are first presented, followed by the overview of main approaches in modeling the automatic transmission elements. The internal combustion engine (ICE), torque converter, drivetrain, tires, and translational dynamics mathematical models are determined and discussed in detail. The proposed approach convergence on decomposing the indicators of powertrain aggregates by derivatives is demonstrated. The considered method was simulated by using the data of the Audi A4 Quattro. The gear shifting control algorithm was described in detail, and a series of virtual tests for the composed model were carried out. The comparative analysis of the results for the conventional and advanced models of the automatic transmission's hydro-mechanical drive were performed. The differences of the model outputs were discussed. The approach advantages were noted, as well as the options for extending the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, we present an innovative approach for assessing the stability of linear time-invariant (LTI) systems. The key innovations in our methodology include the calculation of Markov parameters, the extension to nonlinear continuous-time systems, and significantly improved computational efficiency. Our novel approach leverages Markov parameters derived from the characteristic polynomial of the system. Unlike traditional methods, we employ the Leverrier-Takeno algorithm to efficiently determine the coefficients of the characteristic polynomial for state-space representation. The systematic calculation of Markov parameters using a specialized Maclaurin series expansion enhances our method's precision. One of our major achievements is the rigorous verification of stability through Hankel matrices, ensuring positive definiteness using the Cholesky decomposition algorithm. In addition, we introduce a second stability criterion based on iterated polynomial long divisions, although we acknowledge its limitations in handling high-order systems due to computational inefficiency. Our pioneering contributions extend beyond LTI systems. We adapt our innovative techniques to analyze the local stability of nonlinear continuous-time systems by introducing the concept of Jacobian matrices and employing the indirect Lyapunov method. This expansion broadens the applicability of our approach to a wider range of real-world systems. Notably, our approach exhibits remarkable computational efficiency. According to CPU-time analysis, our first stability criterion outperforms the classical Routh–Hurwitz method by more than 12 times for dynamic systems with orders ranging from 2 to 180. This significant reduction in computation time positions our method as a valuable option for real-time stability analysis applications. [ABSTRACT FROM AUTHOR]

The mealybug (Paracoccus marginatus) is one of the most important pests of papaya (Carica papaya L.). The high potential damage of this pest threatens papaya production. The objective of this paper is to explore the impact of biocontrol and temperature variations on the population dynamics of Paracoccus marginatus (P. marginatus). We first propose and study a mathematical model for the dynamics of P. marginatus within a papaya field. This model consists of a time-delayed non-autonomous system of differential equations that takes into account the egg incubation period, temperature variations, plant compensation and predators that are natural enemies of the papaya pest. We provide the basic properties of the model, compute the basic offspring number N 0 and show that there exists two threshold parameters N _ 0 and ξ 0 such that N _ 0 ≤ N 0 ≤ ξ 0 ≤ 1 and N 0 ≥ N _ 0 > 1 provide conditions for the extinction and persistence of the pest within the papaya field, respectively. After, we investigate the impact of biocontrol on the pest population. We found that the use of a control strategy based on constant releases of predators could reduce the pest population by 35.62 percent and increase the biomass by 77.50 percent, while the use of impulsive releases of predators result in a decrease of 96.31 percent of the pest population and an increases of 55.74 percent of the biomass. We also combine the use of continuous predator releases and bio-pesticides and discovered that a spray applied 90 days after germination could completely eliminate the pest population and boost the biomass by 81.58 percent. • The population dynamics of Paracoccus marginatus , papaya pest is modeled. • The model includes the egg incubation period, temperature variations and biocontrol. • The warm temperatures are favorable to the development and survival of the pest. • The use of impulsive releases of predators can reduce the pest by 96.31%. • The use of continuous releases of predators and bio-pesticides can eradicate the pest. [ABSTRACT FROM AUTHOR]

Online live streaming platforms, such as YouTube Live and Twitch, have seen a surge in popularity in recent years. These platforms allow viewers to send real-time gifts to streamers, which can bring significant profits and fame. However, there has been little research on the donation system used on live streaming platforms. This paper aims to fill this gap by building a continuous-time dynamic graph to model the interactions among viewers based on real-time chat messages and predict the real-time donations on live streaming platforms. To achieve this, we propose a novel model called the Temporal Difference Graph Neural Network (TDGNN) that incorporates imbalanced learning strategies to identify potential donors during live streaming. Our model can predict the exact time when donations will appear. We conduct extensive experiments on three live streaming video datasets and demonstrate that our proposed model is more effective and robust than other baseline methods from other fields. [ABSTRACT FROM AUTHOR]

We evaluate the performance of Whittle index policy for restless Markovian bandit. It is shown in Weber and Weiss (J Appl Probab 27(3):637–648, 1990) that if the bandit is indexable and the associated deterministic system has a global attractor fixed point, then the Whittle index policy is asymptotically optimal in the regime where the arm population grows proportionally with the number of activation arms. In this paper, we show that, under the same conditions, this convergence rate is exponential in the arm population, unless the fixed point is singular (to be defined later), which almost never happens in practice. Our result holds for the continuous-time model of Weber and Weiss (1990) and for a discrete-time model in which all bandits make synchronous transitions. Our proof is based on the nature of the deterministic equation governing the stochastic system: We show that it is a piecewise affine continuous dynamical system inside the simplex of the empirical measure of the arms. Using simulations and numerical solvers, we also investigate the singular cases, as well as how the level of singularity influences the (exponential) convergence rate. We illustrate our theorem on a Markovian fading channel model. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics of an autonomous mathematical model of COVID‐19 depending on a real bifurcation parameter is controlled by the parameter switching (PS) algorithm. With this technique, it is proved that every attractor of the considered system can be numerically approximated and, therefore, the system can be determined to evolve along, for example, a stable periodic motion or a chaotic attractor. In this way, the algorithm can be considered as a chaos control or anticontrol (chaoticization) algorithm. Contrarily to existing chaos control techniques that generate modified attractors, the obtained attractors with the PS algorithm belong to the set of the system attractors. It is analytically shown that using the PS algorithm, every system attractor can be expressed as a convex combination of some existing attractors. Interestingly, the PS algorithm can be viewed as a generalization of Parrondo's paradox. [ABSTRACT FROM AUTHOR]

In this paper, the discrete-time version of a continuous-time model with fundamentalists and momentum traders is presented. Our aim consists of studying the impact of cross-sectional momentum traders on the dynamics of the model. To this end, the continuous-time deterministic skeleton of the benchmark model is transformed using sophisticated discretization techniques. It is worth noting that the model does not always maintain the same characteristics after moving from continuous to discrete time. In spite of this, our discrete-time system preserves the dynamic properties of the continuous-time original model. Moreover, heterogeneity introduces an important non-linearity into the market dynamics, causing our deterministic financial model to generate erratic time series similar to the patterns observed in real markets. In particular, we show that the time series originated by the perturbed deterministic system capture some of the main stylized facts of the U.S. financial market. Converting the benchmark model from continuous time to discrete time allows the use of financial data available in discrete time. [ABSTRACT FROM AUTHOR]

In this paper, a simple memcapacitors-based oscillator, set up from the Colpitts' LC tank circuit is presented. The oscillator is designed by replacing the two normal capacitors of Colpitts' tank circuit with two nonlinear memcapacitors. The new resulting nonlinear circuit consists of only three dynamic elements, including two memcapacitors blocks and an inductor. The model is described as a continuous-time three-dimensional autonomous system with cubic nonlinearities. The structure of the equilibrium points and the discrete symmetries of the model equations are discussed. One of the key contributions in this area is the introduction of a simple circuit presenting peculiar behaviors such as offset bossing and coexisting of multiple attractors. An appropriate electronic circuit (analog simulator) is proposed to investigate the dynamic behavior of the proposed system and prove its feasibility. The proposed oscillator enriches the literature on simple memcapacitor-based circuits with complex dynamic behavior. [ABSTRACT FROM AUTHOR]

In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based on Bernoulli functionals and show that the model has perfect state transfer (PST), among others. Let be the space of square integrable complex-valued Bernoulli functionals, which is infinitely dimensional. First, we construct on a given subspace L ⊂ a self-adjoint operator Δ L via the canonical unitary involutions on , and by analyzing its spectral structure we find out all its eigenvalues. Then, we introduce an abstract model of CTQW with L as its state space, which is governed by the Schrödinger equation with Δ L as the Hamiltonian. We define the time-average probability distribution of the model, obtain an explicit expression of the distribution, and, especially, we find the distribution admits a symmetry property. We also justify the model by offering a graph-theoretic interpretation to the operator Δ L as well as to the model itself. Finally, we prove that the model has PST at time t = π 2 . Some other interesting results about the model are also proved. [ABSTRACT FROM AUTHOR]

At present, the absolute positioning accuracy and control accuracy of industrial serial robots need to be improved to meet the accuracy requirements of precision manufacturing and precise control. An accurate dynamic model is an important theoretical basis for solving this problem, and precise dynamic parameters are the prerequisite for precise control. The research of dynamics and parameter identification can greatly promote the application of robots in the field of precision manufacturing and automation. In this paper, we study the dynamical modeling and dynamic parameter identification of an industrial robot system with six rotational DOF (6R robot system) and propose a new method for identifying dynamic parameters. Our aim is to provide an accurate mathematical description of the dynamics of the 6R robot and to accurately identify its dynamic parameters. First, we establish an unconstrained dynamic model for the 6R robot system and rewrite it to obtain the dynamic parameter identification model. Second, we establish the constraint equations of the 6R robot system. Finally, we establish the dynamic model of the constrained 6R robot system. Through the ADAMS simulation experiment, we verify the correctness and accuracy of the dynamic model. The experiments prove that the result of parameter identification has extremely high accuracy and the dynamic model can accurately describe the 6R robot system mathematically. The dynamic modeling method proposed in this paper can be used as the theoretical basis for the study of 6R robot system dynamics and the study of dynamics-based control theory. [ABSTRACT FROM AUTHOR]

This paper derives the optimal Bayesian processing of an out-of-sequence (OOS) set of measurements in continuous-time for multiple target tracking. We consider a multi-target system modelled in continuous time that is discretised at the time steps when we receive the measurements, which are distributed according to the standard point target model. All information about this system at the sampled time steps is provided by the posterior density on the set of all trajectories. This density can be computed via the continuous-discrete trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. When we receive an OOS measurement, the optimal Bayesian processing performs a retrodiction step that adds trajectory information at the OOS measurement time stamp followed by an update step. After the OOS measurement update, the posterior remains in TPMBM form. We also provide a computationally lighter alternative based on a trajectory Poisson multi-Bernoulli filter. The effectiveness of the two approaches to handle OOS measurements is evaluated via simulations. [ABSTRACT FROM AUTHOR]