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Considering the storage increasing demand of 'multi-variety, small-batch' characteristic goods, we developed a new type of compact warehouse a three-dimensional double-ended compact storage system. Compared with the traditional three-dimensional automated storage and retrieval system (AS/RS) and existing three-dimensional compact AS/RS model, the storage system we designed exhibits excellent characteristics such as high density, high throughput efficiency, and more flexible configuration. There are three key points in our work listed as follows. Firstly, we establish the continuous travel time model under specific operating conditions in this new three-dimensional compact warehouse. Secondly, the three-dimensional size of the storage rack is optimised. The optimal three-dimensional proportion of the storage rack is obtained based on the model's optimal solution. Finally, numerical examples are given to analyse the influence of the I/O port layouts and related parameters on the system throughput efficiency. According to the optimisation results of the system model, a more reasonable rack dimension can be designed, which can provide an effective reference for the construction of a three-dimensional double-ended compact warehouse. [ABSTRACT FROM AUTHOR]

This work considers a short‐term, continuous time setting characterized by a coupled power supply system controlled exclusively by a single provider and comprising a cascade of hydropower systems (dams), fossil fuel power stations, and a storage capacity modeled by a single large battery. Cascaded hydropower generators introduce time‐delay effects in the state dynamics, which are modeled with differential equations, making it impossible to use classical dynamic programming. We address this issue by introducing a novel Lagrangian relaxation technique over continuous‐time constraints, constructing a nearly optimal policy efficiently. This approach yields a convex, nonsmooth optimization dual problem to recover the optimal Lagrangian multipliers, which is numerically solved using a limited memory bundle method. At each step of the dual optimization, we need to solve an optimization subproblem. Given the current values of the Lagrangian multipliers, the time delays are no longer active, and we can solve a corresponding nonlinear Hamilton–Jacobi–Bellman (HJB) Partial Differential Equation (PDE) for the optimization subproblem. The HJB PDE solver provides both the current value of the dual function and its subgradient, and is trivially parallelizable over the state space for each time step. To handle the infinite‐dimensional nature of the Lagrange multipliers, we design an adaptive refinement strategy to control the duality gap. Furthermore, we use a penalization technique for the constructed admissible primal solution to smooth the controls while achieving a sufficiently small duality gap. Numerical results based on the Uruguayan power system demonstrate the efficiency of the proposed mathematical models and numerical approach. [ABSTRACT FROM AUTHOR]

We consider a continuous-time two-dimensional risk model, in which the claims from the two lines of insurance businesses satisfy an extensive asymptotic independence structure and the stochastic return is driven by a geometric Lévy process. Under a mild technical condition regarding the Laplace exponent of the Lévy process, we obtain explicit asymptotic expansions for both finite-time and infinite-time ruin probabilities when the claim sizes have regularly varying distributions. [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]

Despite the progress in medical data collection the actual burden of SARS‐CoV‐2 remains unknown due to under‐ascertainment of cases. This was apparent in the acute phase of the pandemic and the use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under‐reporting. Since daily deaths occur from past infections weighted by their probability of death, one may infer the total number of infections accounting for their age distribution, using the data on reported deaths. We adopt this framework and assume that the dynamics generating the total number of infections can be described by a continuous time transmission model expressed through a system of nonlinear ordinary differential equations where the transmission rate is modeled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We develop this flexible Bayesian tool in Stan and study 3 pairs of European countries, estimating the time‐varying reproduction number (Rt$$ {R}_t $$) as well as the true cumulative number of infected individuals. As we estimate the true number of infections we offer a more accurate estimate of Rt$$ {R}_t $$. We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities. [ABSTRACT FROM AUTHOR]

Adolescence is a formative life phase for the development of personality characteristics. Although past findings suggest Big Five traits alongside self-esteem as indicators for successful development, little is known about their longitudinal interplay. We addressed this research gap by integrating data from three longitudinal studies (NT1 = 1,088; Mage = 16.02 years, 72% female). We apply continuous time modeling to investigate longitudinal associations between Big Five traits and self-esteem in a period of up to 1 year. Results illustrate four main findings: First, rank-order stabilities were overall high for all personality characteristics. Second, longitudinal associations between Big Five traits and self-esteem were reciprocal for extraversion, neuroticism, and openness but one-sided for agreeableness and conscientiousness on self-esteem. Effects peaked within the first month and mostly faded after 2 months. Third, the majority of cross-effects were similar in size; however, the effect from neuroticism on later values of self-esteem was stronger than vice versa. Fourth, most effects were robust against influences of gender, age, and study characteristics. Analyses with acquaintance-reports supported the results but suggested stronger effects that lasted longer than effects of self-reports. We conclude that the development of personality characteristics acts as possible sources of development for each other. All in all, the interplay between Big Five and self-esteem development appears reciprocal for some traits but was most often driven by Big Five traits. We integrate our findings into three contrasting theoretical perspectives and discuss the importance of time for a better understanding of personality development. [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]

This article presents two innovative mathematical models for the dynamics of Chikungunya virus contamination by using Caputo fractional derivative. By applying the recently developed numerical technique to find the approximate solutions for the Chikungunya virus system which allowing us for the valuable insights. Through a rigorous analysis of the obtained numerical and graphical solutions, the impact of fractional orders on the infection dynamics is thoroughly examined. Additionally, Banach's fix point theorm is used to investigates the existence, uniqueness, and stability properties of the solutions, providing a deeper understanding of the key parameters that affect the spread and persistence of the infection. [ABSTRACT FROM AUTHOR]

Cognitive Radio Networks (CRNs) block new arriving services and remove existing services to increase the spectrum efficiency. Particularly, Secondary Users (SUs) experience a decline in service deprivation in the arrival of Primary Users (PUs). To overcome this, a Spectrum and energy Efficiency in Cognitive Radio Networks using Dynamic Channel Reservation and Komodo Mlipir Optimization (SE-KMOA-CRN) is proposed. The proposed method splits reserved and non-reserved bands from the accessible spectrum. Numerous channels from the non-reserved band are dynamically assigned to the reserved band to support services that experience disruptions when functioning on non-reserved band. From the non-reserved band, a count of channels dynamically assigned to the reserved band to support services that experience disruptions when functioning on the non-reserved band. It enables priority-based channel assignment and termination while providing dynamic access to the obtainable spectrum. Here, Allocation of channels to Reserved Band CRN using Dynamic Channel Reservation Algorithm (DCRA). Komodo Mlipir Optimization Algorithm (KMOA) is employed for Service selection and Channel restoration. The proposed SE-KMOA-CRN method is modelled utilizing Continuous Time Markov Chain (CTMC) with mathematical equations for some quality of service (QoS) factors is obtained. The SE-KMOA-CRN approach attains higher Throughput, lower End-to-End Delay, higher Energy Efficiency, greater spectral efficiency and higher Packet Delivery Ratio compared with existing methods, like Multiple objective optimization for spectrum along energy efficacy trade-off in IRS-assisted CRNs using NOMA (SE-MOO-CRN), Energy efficacy in CRN utilizing cooperative spectrum sensing under hybrid spectrum handoff (SE-TOA-CRN) and Energy-effectual cross-layer spectrum sharing on CR green IoT (SE-CRG-CRN) respectively. [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]

Keel bone fractures (KBF) are prevalent in commercial laying hens and are considered one of the greatest welfare concerns in the egg-production industry. While clear associations exist between KBF and animal mobility, suggesting that KBF impair mobility, the effect of mobility on KBF remains unclear. We combined data from three studies that assessed keel bone fracture severity through radiographs and monitored hens' transitions between different zones of a multi-tier aviary system (the three tiers, a littered floor, and a winter garden) the week prior to radiograph. For each hen, we extracted two daily movement behaviours: the vertical distance travelled and the mean number of zones crossed within one transition; and two daily space-use behaviours: the time spent in the top tier and the unevenness of time spent across zones. We used hierarchical Bayesian continuous time dynamic modelling to estimate how a change in a behaviour predicted a later change in keel bone fracture severity, and vice versa. Increased fracture severity did not predict later changes in space-use behaviours, but it did predict changes in movement behaviours. Specifically, increased fracture severity led to decreased vertical travelled distance and a tendency to cross more zones within one transition, suggesting impaired mobility in hens with increased fracture severity. In contrast, we found no evidence that movement or space-use behaviours predict later change in fracture severity, challenging previous literature suggesting that vertical locomotion through jumping and flying may exacerbate keel bone fractures in complex three-dimensional systems due to increased risk of collisions. However, similar efforts accounting for the location of fractures on the keel could unveil the potential influence of movement and space-use behaviours in the formation and change (healing or worsening) of KBF and increase our ability to mitigate their effects. [ABSTRACT FROM AUTHOR]

Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of forest fires opening the way to more realistic models. We propose a stochastic spreading model continuous in space and time that has the potentiality to use such data in their full power. The state of the forest fire is described by the subprobability densities of the green trees and of the trees on fire that can be estimated thanks to data coming from satellites and earth detectors. The fire dynamics is encoded into a kernel function that can take into account wind conditions, land slope, spotting phenomena, and so on, bringing to a system of integrodifferential equations whose solutions provide the evolution in time of the subprobability densities. That makes the model complementary to models based on cellular automata that furnish single instantiations of the stochastic phenomenon. Moreover, stochastic models based on cellular automata can be derived from the present model by space and time discretization. Existence and uniqueness of the solutions is proved by using Banach's fixed‐point theorem. The asymptotic behavior of the model is analyzed as well. By specifying a particular structure for the kernel, we obtain numerical simulations of the fire spreading under different conditions. For example, in the case of a forest fire evolving toward a river, the simulations show that the probability density of the trees on fire is different from zero beyond the river due to the spotting phenomenon. The kernel could be slightly modified to include firefighters interventions and weather changes. [ABSTRACT FROM AUTHOR]

Accelerated longitudinal designs (ALDs) provide an opportunity to capture long developmental periods in a shorter time framework using a relatively small number of assessments. Prior literature has investigated whether univariate developmental processes can be characterized with data obtained from ALDs. However, many important questions in psychology and related sciences imply working with several variables that are intercorrelated as they unfold over time, such as cognitive and cortical development. Therefore, bivariate developmental models are required. This study aimed to assess the effectiveness of continuous-time bivariate Latent Change Score (CT-BLCS) models for recovering the trajectories of two interdependent developmental processes using data from diverse ALDs. Through a Monte Carlo simulation study, the efficacy of different sampling designs and sample sizes was examined. The study fills a gap in the literature by examining the performance of ALDs in bivariate systems, providing specific recommendations for future application of ALDs for studying interrelated developmental variables. [ABSTRACT FROM AUTHOR]

Existing methods for fitting continuous time Markov models (CTMM) in the presence of covariates suffer from scalability issues due to high computational cost of matrix exponentials calculated for each observation. In this article, we propose an optimization technique for CTMM which uses a stochastic gradient descent algorithm combined with differentiation of the matrix exponential using a Padé approximation. This approach makes fitting large scale data feasible. We present two methods for computing standard errors, one novel approach using the Padé expansion and the other using power series expansion of the matrix exponential. Through simulations, we find improved performance relative to existing CTMM methods, and we demonstrate the method on the large-scale multiple sclerosis NO.MS data set. [ABSTRACT FROM AUTHOR]

Fish production integrates changes in biomass from growth, reproduction, and mortality, and is a useful indicator for fisheries management. However, calculation of fish production has been limited by the intensive requirements for data on abundance, biomass, age structure, and vital rates, and so it is uncommon to find estimates of fish production for wetlands. We developed an approach to directly estimate production that is suitable for data-limited systems: a continuous time model of production describing individual growth over short time intervals with continuous time models of abundance and biomass over longer timescales. We applied this model for 18 Great Lakes coastal wetlands (GLCWs) on Lake Ontario, including Big Island Wetland (BIW). In BIW, most species were dominated in abundance and biomass by younger cohorts and, as a result, these young, fast-growing individuals contributed disproportionately to fish production. In total, BIW produced 336.1 kg·ha·year of fish and the other 17 neighbouring ranged between 447.7 and 1119.9 kg·ha·year. These are some of the first estimates of fish production for GLCWs, highlighting their value for managing Great Lakes fisheries. [ABSTRACT FROM AUTHOR]

Introducing knowledge graphs into recommender systems effectively solves sparsity and cold start problems. However, existing KG recommendation methods such as MKR mostly rely on static knowledge graphs, ignoring that nodes and edges in the graph dynamically change over time, leading to problems such as insufficient timeliness, inability to describe context dependencies, data redundancy, and noise. We propose a multi-task learning method for recommendation enhancement based on dynamic knowledge graphs, MTRDKG, which models the dynamic knowledge graph as a series of continuous time events. Specifically, after node events (node-level or interactions between nodes) occur, the memory state of the nodes is updated through a temporal graph network (TGN), and node temporal embeddings are generated to capture the nodes' attributes, contextual relationships, and dynamic change information. We use the node embeddings generated by TGN in conjunction with the recommended items as a shared part, aiming to integrate dynamic knowledge graph information into the recommendation task, thereby improving the recommendation effect. Extensive experiments were conducted with four real-world datasets and state-of-the-art baseline methods. The results show that MTRDKG outperforms existing methods in terms of recommendation accuracy and knowledge graph embedding quality, especially in dealing with datasets of different sparsity levels. [ABSTRACT FROM AUTHOR]

We consider the system of reaction–diffusion–advection equations describing the evolution of the spatial distributions of two populations of predators and two prey populations. This model allows us to consider directed migration, the Holling functional response of the second kind, and the hyperbolic prey growth function. We obtain conditions on the parameters under which cosymmetries exist. As a result, multistability is realized, i.e., the one- and two-parameter families of stationary solutions appear. For a homogeneous environment, we analytically derive explicit formulas for equilibria. With a heterogeneous habitat, we computed distributions of species using the method of lines and the scheme of staggered grids. We present the results of violation of cosymmetry and transformation of the family in the case of invasion of a predator. [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]

Risk aversion rate plays a significant role in mean-variance portfolio selection. Most existing literature assumes it to be constant or wealth dependent, which is unrealistic. In this study, I contend that it is both wealth and volatility dependent because it varies across economic status: either steady or fluctuated. In addition, I decompose the risk aversion rate into a wealth prudence rate and a volatility prudence rate and investigate their mutual effect on portfolio selection under a continuous-time mean-variance framework. Using Game theoretic approach and asymptotic expansion, I derive the optimal trading rule analytically. [ABSTRACT FROM AUTHOR]

Let |$S$| and |$\tilde S$| be two independent and identically distributed random variables, which we interpret as the signal, and let |$P_{1}$| and |$P_{2}$| be two communication channels. We can choose between two measurement scenarios: either we observe |$S$| through |$P_{1}$| and |$P_{2}$|⁠ , and also |$\tilde S$| through |$P_{1}$| and |$P_{2}$|⁠ ; or we observe |$S$| twice through |$P_{1}$|⁠ , and |$\tilde{S}$| twice through |$P_{2}$|⁠. In which of these two scenarios do we obtain the most information on the signal |$(S, \tilde S)$| ? While the first scenario always yields more information when |$P_{1}$| and |$P_{2}$| are additive Gaussian channels, we give examples showing that this property does not extend to arbitrary channels. As a consequence of this result, we show that the continuous-time mutual information arising in the setting of community detection on sparse stochastic block models is not concave, even in the limit of large system size. This stands in contrast to the case of models with diverging average degree, and brings additional challenges to the analysis of the asymptotic behavior of this quantity. [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]

Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence, the underlying rational transfer functions are allowed to have poles in general domains in the complex plane. In particular, this covers the case of specific conservative partial differential equations such as the linear Schrödinger and the undamped linear wave equation with spectra on the imaginary axis. By an appropriate modification of the classical continuous time Hardy space H 2 , a new H 2 -like optimal model reduction problem is introduced and first-order optimality conditions are derived. As in the classical H 2 case, these conditions exhibit a rational Hermite interpolation structure for which an iterative model reduction algorithm is proposed. Numerical examples demonstrate the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

The problem is considered to find the time-optimal control that transfers a fourth-order system that consists of a double integrator and a harmonic oscillator, coupled by one control channel, between two arbitrary states. That fourth-order system is equivalent to the Hill-Clohessy-Wiltshire model of the relative dynamics of an orbiting spacecraft in proximity of a second spacecraft on a circular reference orbit, subjected to a thrust parallel to the orbital velocity vector and having time-continuous amplitude. A new method is here introduced to determine the time-optimal control problem stated above. This method combines two previously discovered optimal control synthesis methods: the method by Romano and Curti (2020), that enables to find (analytically, in some case) the optimal control transferring a general Linear Time Invariant Normal system between two arbitrary states; and, the method by Belousova and Zarkh (1996), that enables to find the optimal control transferring a fourth-order system consisting of a double integrator and a harmonic oscillator, coupled by one control channel, from an arbitrary initial state to the origin of the state space, if the optimal control is a priori known, that transfers the same system from a reference state to the origin. The here proposed combined method utilizes two phases. During the first phase, a number of reference minimum-time controls are obtained that transfer the system from specific reference states to the state space origin; this is achieved by exploiting Pontryagin's principle together with back-propagation from the origin of the state space. During the second phase, a search is run along a particular curve in the state space (named extremal search path) that depends on the boundary states of the problem at hand. In particular, a minimum-time control problem is iteratively solved to find the optimal control history that steers the system from a state on that curve to the origin, by exploiting Belousova and Zarkh method, until a particular state is found which satisfies an equivalency condition that, as demonstrated by Romano and Curti, guarantees that the optimal control history pertaining to the problem of transferring the system from that state to the origin is the same optimal control history that transfers the system between the arbitrarily set initial and final states. The new results, substantiated by numerical experiments, have both a theoretical and a practical value, as they could be applied for the optimal guidance of spacecraft performing autonomous proximity maneuvers. [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]

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria based on a drug-concentration rescaling approach. We show how the resistance to drugs in space, and the consequent adaptation of growth rate, is governed by a Price equation with diffusion, integrating features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Although in many evolution models, per capita growth rate is a natural surrogate for fitness, in spatially-extended, potentially heterogeneous habitats, fitness is an emergent property that potentially reflects additional complexities, from boundary conditions to the specific spatial variation of growth rates. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical metric for characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem, λ1. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits to the relative advantage of each mutant across the environment. Our approach allows one to predict the precise outcomes of selection among mutants over space, ultimately from comparing their λ1 values, which encode a critical interplay between growth functions, movement traits, habitat size and boundary conditions. Such mathematical understanding opens new avenues for multi-drug therapeutic optimization. Author summary: In this study we develop a framework to model multi-drug resistance evolution in space by combining drug-rescaling arguments with a reaction-diffusion type model. In response to multi-drug environmental gradients, each independent mutant can grow and diffuse following an individual spatially-varying growth function and diffusion rate. Applying concepts from perturbation theory and reaction-diffusion models, we propose an analytical metric to quantify average mutant fitness in the spatial system and to predict the outcome of selection. Our findings highlight that in spatially-extended habitats fitness is an emergent property that potentially integrates many complexities, from boundary conditions to environmental variation, as well as individual growth and diffusion traits. [ABSTRACT FROM AUTHOR]

This study proposes and analyzes a deterministic mathematical model to describe the dynamics of corruption transmission. We began by proving that the solution to the model is bounded and positive. The next-generation matrix approach is used to compute the basic reproduction number (TZQ) in relation to corruption-free equilibrium. The Jacobian and Lyapunov functions are used to show that corruption-free equilibrium is asymptotically stable in both locally and globally when TZQ < 1, and otherwise, an endemic corruption equilibrium develops. Furthermore, the sensitivity of the model's parameters was investigated. The findings demonstrate that religious precepts govern public education. The two sectors most susceptible to corruption controlare education and corrections. The study recommends investing more in the provision of public education to citizens by creating awareness among all and including it in the education curriculum and religious leaders to teach their followers seriously about the impact of corruption as well as the use of jail as punishment. The numerical simulation results agreed with the analytical results. [ABSTRACT FROM AUTHOR]

Background: Computational models in systems biology are becoming more important with the advancement of experimental techniques to query the mechanistic details responsible for leading to phenotypes of interest. In particular, Boolean models are well fit to describe the complexity of signaling networks while being simple enough to scale to a very large number of components. With the advance of Boolean model inference techniques, the field is transforming from an artisanal way of building models of moderate size to a more automatized one, leading to very large models. In this context, adapting the simulation software for such increases in complexity is crucial. Results: We present two new developments in the continuous time Boolean simulators: MaBoSS.MPI, a parallel implementation of MaBoSS which can exploit the computational power of very large CPU clusters, and MaBoSS.GPU, which can use GPU accelerators to perform these simulations. Conclusion: These implementations enable simulation and exploration of the behavior of very large models, thus becoming a valuable analysis tool for the systems biology community. [ABSTRACT FROM AUTHOR]

The fungus Fusarium oxysporum (f.sp. albedinis) causes Bayoud disease. It is one of the epiphytotic diseases that affects a wide range of palm species and has no known cure at present. However, preventive measures can be taken to reduce the effects of the disease. Bayoud disease has caused enormous economic losses due to decreased crop yield and quality. Therefore, it is essential to develop a mathematical model for the dynamics of the disease to propose some affordable methods for disease management. In this study, we propose a novel mathematical model that describes the transmission dynamics of the disease in date palm trees. The model incorporates various factors such as the contact rate of the fungi with date palm trees, the utilization of fungicides, and the introduction of a quarantine compartment to prevent disease dissemination. We first prove a few key properties of the proposed model to ensure that the model is well-posed and suitable for numerical investigations. We establish that the model has a unique positive solution that is bounded and stable over time. We use sensitivity analysis to identify the parameters that have the greatest effect on the reproduction number R 0 and illustrate this effect graphically. We then formulate an optimal control problem to identify the most suitable and cost-effective disease control approaches. As a first approach, we solely focus on the application of fungicide to susceptible trees and determine the best spray rates for a greater decrease in exposed and infected trees. Secondly, we emphasize quarantining exposed and infected trees at optimal quarantine rates. Finally, we explore the combined effect of fungicide spraying and isolating infected trees on disease control. The findings of the last approach turn out to be the most rewarding and cost-effective for minimizing infections in date palm trees. [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]

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]

Summary: Across the perinatal transition, existing research focuses mainly on significant changes in sleep duration and quality, neglecting sleep timing. This study investigated change trajectories of sleep timing and chronotype from late pregnancy to 2 years postpartum and examined longitudinal associations of chronotype with symptoms of insomnia, daytime sleep‐related impairment, and mood. Data were from a two‐arm randomised controlled trial testing parent‐focused wellbeing interventions. Participants were a community sample of nullipara without severe sleep/mental health conditions. Participants self‐reported bedtime, rise‐time, chronotype, insomnia symptoms, sleep‐related impairment, depression, and anxiety at seven time points: gestation Weeks 30 and 35, and postpartum Months 1.5, 3, 6, 12 and 24. Trajectories were estimated using mixed‐effects models with continuous time, quadratic splines, and a knot at childbirth, controlling for age and group allocation. A total of 163 participants (mean [SD] age 33.35 [3.42] years) took part. Bedtime and rise‐times delayed during late pregnancy (~8 and ~20 min, respectively) but became progressively earlier (~20 and ~60 min, respectively) over the 2 postpartum years. Chronotype became more eveningness in late pregnancy, and more morningness after childbirth, however changes were small. Controlling for sleep duration and efficiency, greater morningness was associated with significantly less symptoms of insomnia and sleep‐related impairment over time (all p < 0.001); longitudinal associations between chronotype and symptoms of depression and anxiety were non‐significant (all p > 0.65). Sleep–wake timing and chronotype became progressively earlier from pregnancy to 2 years postpartum. Morningness chronotype may be sleep‐protective during the transition from pregnancy to parenthood. Mechanisms underlying these associations require further research. [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]

In this research article, we present a novel Non-Linear Fractional Order Tuberculosis mathematical model (NLFOTB) and introduce an efficient technique to obtain its solution. Fractional Order Models (FOMs) have garnered significant attention in contemporary research due to their widespread applicability. We address the challenge of solving the coupled Initial Value Problems (IVPs) associated with NLFOTB models by utilizing the groundbreaking LRPS method, which combines the RPS approach with the Laplace transform operator. This innovative approach generates approximate solutions in rapidly converging series forms, offering enhanced efficiency and reduced computational effort compared to conventional methods. Through the implementation of the LRPS method, we successfully derive an approximate solution for the NLFOTB model, contributing significantly to the field. Furthermore, our proposed approach demonstrates its efficacy in accurately capturing the dynamics of Tuberculosis (TB) through extensive computations and graphical representations, contributing to a deeper understanding of TB dynamics within a mathematical framework. Additionally, the LRPS method shows promise in tackling real world problems involving differential equations of various orders. Future investigations can extend the application of the LRPS method to explore other Fractional Order Models, further validating its effectiveness in a wide range of epidemic scenarios. Consequently, our study not only provides valuable insights into Tuberculosis dynamics but also introduces a powerful computational tool applicable to various practical problems in diverse disciplines, making a substantial contribution to the field of mathematical modeling and computation. [ABSTRACT FROM AUTHOR]

The emergence of infectious diseases with pandemic potential is a major public health threat worldwide. The World Health Organization reports that about 60% of emerging infectious diseases are zoonoses, originating from spillover events. Although the mechanisms behind spillover events remain unclear, mathematical modeling offers a way to understand the intricate interactions among pathogens, wildlife, humans, and their shared environment. Aiming at gaining insights into the dynamics of spillover events and the outcome of an eventual disease outbreak in a population, we propose a continuous time stochastic modeling framework. This framework links the dynamics of animal reservoirs and human hosts to simulate cross-species disease transmission. We conduct a thorough analysis of the model followed by numerical experiments that explore various spillover scenarios. The results suggest that although most epidemic outbreaks caused by novel zoonotic pathogens do not persist in the human population, the rising number of spillover events can avoid long-lasting extinction and lead to unexpected large outbreaks. Hence, global efforts to reduce the impacts of emerging diseases should not only address post-emergence outbreak control but also need to prevent pandemics before they are established. [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]

Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions for such convergence, and provide examples of novel and/or known processes that do so. These include subfamilies of the well-known stochastic actor-oriented models, as well as continuum extensions of temporal and separable temporal exponential family random graph models. We also comment on some related threads in the broader work on network dynamics, which provide additional context for the continuous time case. [ABSTRACT FROM AUTHOR]

This work examines the time complexity of quantum search algorithms on combinatorial t-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of t-designs and their incidence matrices, we identify a subset of bipartite graphs that are conducive to success compared to random-walk-based search algorithms. These graphs have adjacency matrices with eigenvalues and eigenvectors that can be determined algebraically and are also suitable for analysis in the multiple-marked vertex scenario. We show that the continuous-time quantum walk on certain symmetric t-designs achieves an optimal running time of O n , where n is the number of points and blocks, even when accounting for an arbitrary number of marked elements. Upon examining two primary configurations of marked elements distributions, we observe that the success probability is consistently o(1), but it approaches 1 asymptotically in certain scenarios. [ABSTRACT FROM AUTHOR]

A mathematical model for the dynamics of alcohol-marijuana coabuse is presented in this work. In the past years legalization of recreational marijuana in several states in the United States has added a new layer to alcohol addiction. Much research has been done for alcohol addiction or drug abuse independently, but few include the incidence of marijuana use for alcohol users. A compartmental epidemiological model is used, and results such as the existence and boundedness of solutions, the basic reproduction number using the next-generation method, the disease-free equilibrium, and an analytical expression for the endemic equilibrium are included. Numerical simulations with parameters obtained from data in the United States are performed for different compartments of the population as well as the reproduction number for the alcohol and marijuana sub-models. The model can be adapted for different regions worldwide using appropriate data. This work contributes to understanding the dynamics of the co-abuse of addictive substances. Even though alcohol and marijuana are both legal, they can be of great harm to the brain of the individual when combined, having tremendous consequences for society as a whole. Creating awareness of a public health concern with facts based on scientific research is the ultimate goal of this work. [ABSTRACT FROM AUTHOR]

In statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the network, where edges are randomly formed and dissolved over the observation horizon. In addition, covariates are observed and the goal is to model the impact of the covariates on the interactions. We distinguish two types of covariates: global, system-wide covariates (i.e., covariates taking the same value for all individuals, such as seasonality) and local, dyadic covariates modeling interactions between two individuals in the network. Existing continuous time network models are extended to allow for comparing a completely parametric model and a model that is parametric only in the local covariates but has a global nonparametric time component. This allows, for instance, to test whether global time dynamics can be explained by simple global covariates like weather, seasonality etc. The procedure is applied to a bike-sharing network by using weather and weekdays as global covariates and distances between the bike stations as local covariates. [ABSTRACT FROM AUTHOR]

Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable of encoding these geometric structures remains largely unknown. We address this open problem by introducing a universal causal geometric DL framework in which the user specifies a suitable pair of metric spaces X$\mathcal {X}$ and Y$\mathcal {Y}$ and our framework returns a DL model capable of causally approximating any "regular" map sending time series in XZ$\mathcal {X}^{\mathbb {Z}}$ to time series in YZ$\mathcal {Y}^{\mathbb {Z}}$ while respecting their forward flow of information throughout time. Suitable geometries on Y$\mathcal {Y}$ include various (adapted) Wasserstein spaces arising in optimal stopping problems, a variety of statistical manifolds describing the conditional distribution of continuous‐time finite state Markov chains, and all Fréchet spaces admitting a Schauder basis, for example, as in classical finance. Suitable spaces X$\mathcal {X}$ are compact subsets of any Euclidean space. Our results all quantitatively express the number of parameters needed for our DL model to achieve a given approximation error as a function of the target map's regularity and the geometric structure both of X$\mathcal {X}$ and of Y$\mathcal {Y}$. Even when omitting any temporal structure, our universal approximation theorems are the first guarantees that Hölder functions, defined between such X$\mathcal {X}$ and Y$\mathcal {Y}$ can be approximated by DL models. [ABSTRACT FROM AUTHOR]

The article by Naugle et al. explores the core characteristics of system dynamics modeling and the need for a clear definition. The authors argue that system dynamics modeling should focus on addressing complex problems and improving decision-making. They propose a modified definition that includes elements such as causal structure, data-informed models, and replicable predictions. The article also emphasizes the importance of collaboration with other methods and the integration of qualitative and quantitative approaches. The authors call for further research and development in both qualitative and quantitative modeling to advance the field of system dynamics. [Extracted from the article]

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]

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]

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]

The mathematical model of the dynamics of HIV/AIDS infection transmission is developed by adding the set of infected but noninfectious persons, using a conformable fractional derivative in the Liouville–Caputo sense. Some fixed point theorems are applied to this model to investigate the existence and uniqueness of the solutions. It is determined what the system's fundamental reproduction number R 0 is. The disease-free equilibrium displays the model's stability and the local stability around the equilibrium. The study also examined the effects of different biological features on the system through numerical simulations using the Adams–Moulton approach. Additionally, varied values of fractional orders are simulated numerically, demonstrating that the results generated by the conformable fractional derivative-based model are more physiologically plausible than integer-order derivatives. [ABSTRACT FROM AUTHOR]

Summary: In this article, we investigate the mean‐square consensus tracking problem of nonlinear MASs subjected to external disturbances under stochastic switching topologies. An aperiodically intermittent control strategy is proposed to guarantee consensus tracking in the mean‐square sense, which depends only on the local state information of the neighbors and the leader. The stochastic switching signal of the interaction topologies is modeled as a continuous‐time Markov process, and the aperiodically intermittent control method is driven by a discrete‐time series of stochastic samples, that are independent of each other. Moreover, several sufficient conditions are established to ensure the feasibility of the control strategy. The proofs are given by employing matrix inequality theory and Lyapunov stability theory. Finally, numerical simulations are provided to verify the feasibility of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Several variants of the autoregressive structural equation model were suggested over the past years, including, for example, the random intercept autoregressive panel model, the latent curve model with structured residuals, and the STARTS model. The present work shows how to place these models into a mixed-effects model framework and how to estimate them in mixed-effects model software, namely the R package nlme. We also show how nlme can be used to fit extensions of these models, for example, models that do not assume equally spaced time intervals between measurement occasions (i.e., continuous time models). Overall, our expositions show that autoregressive structural equations models and mixed-effects models are closely related. We think that this insight eases researchers to understand the differences between the variants of the autoregressive structural equation model and also allows them to profitably link the two different modeling perspectives. [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]

BACKGROUND: This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters. OBJECTIVE: To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform. METHODS: The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP. RESULTS: Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis. CONCLUSION: Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy. [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]