Search Results (21)

To investigate the underlying mechanisms of talent mobility in higher-education institutions influenced by factors such as the development environment, macroeconomic policies, and evaluation mechanisms, this paper proposes a nonlinear stochastic differential equation (SDE) dynamical model that incorporates time delays and multiplicative noise. We analyze the dynamic processes of talent mobility under varying conditions regarding the number of nodes, policy implementation cycles, and noise intensity. First, we employ central manifold theory and stochastic averaging methods to reduce the system to a one-dimensional averaged $It\widehat{o}$ equation. Subsequently, with $\tau$ as a parameter, we conduct an in-depth study of the system’s stochastic bifurcation behavior using the corresponding Fok–Planck–Kolmogorov equations. Finally, we validate the theoretical conclusions through numerical simulations. The results indicate that the number of nodes, policy delay, and noise intensity all have significant effects on system stability; an increasing delay induces random P-bifurcation in the system, and when $N\le 3$ and $N>3$, the system exhibits distinctly different steady-state behaviors. We also found that excessively high noise intensity disrupts system stability, whereas moderate noise intensity has a positive effect on stability. This study not only provides theoretical insights into the dynamic evolution mechanisms of talent mobility in regional universities but also offers valuable guidance for universities in formulating talent recruitment and evaluation policies. The methodology employed in this study opens up a promising avenue for analyzing complex dynamic problems in the field of sociology. Full article

Utilizing the Kolmogorov–Arnold representation theorem, KANs have emerged as a mathematically rigorous and easily interpretable alternative to traditional neural networks. These networks decompose high-dimensional functions into sums of univariate continuous functions using adaptive activation functions. Compared to MLPs, KANs exhibit superior or comparable performance in accuracy, parameter efficiency, and interpretability. Applications highlight the advantages of KANs in solving complex partial differential equations with enhanced convergence and uncertainty quantification, modeling dynamic systems in a meaningful manner, and making reliable forecasts in the areas of power systems, environmental monitoring, and demand prediction. Based on current research on KANs, they demonstrate a promising frontier in interpretable deep learning, with increasing influence across numerous interdisciplinary scientific and engineering fields. Full article

It is very important to create mathematical models for real world problems and to propose new solution methods. Today, symmetry groups and algebras are very popular in mathematical physics as well as in many fields from engineering to economics to solve mathematical models. This paper introduces a novel methodological framework based on the SO(3) Lie method to estimate time-dependent correlation matrices (correlation flows) among three variables that have chaotic, entropy, and fractal characteristics, from 11 April 2011 to 31 December 2024 for daily data; from 10 April 2011 to 29 December 2024 for weekly data; and from April 2011 to December 2024 for monthly data. So, it develops the stochastic SO(2) Lie method into the SO(3) Lie method that aims to obtain the correlation flow for three variables with chaotic, entropy, and fractal structure. The results were obtained at three stages. Firstly, we applied entropy (Shannon, Rényi, Tsallis, Higuchi) measures, Kolmogorov–Sinai complexity, Hurst exponents, rescaled range tests, and Lyapunov exponent methods. The results of the Lyapunov exponents (Wolf, Rosenstein’s Method, Kantz’s Method) and entropy methods, and KSC found evidence of chaos, entropy, and complexity. Secondly, the stochastic differential equations which depend on S² (SO(3) Lie group) and Lie algebra to obtain the correlation flows are explained. The resulting equation was numerically solved. The correlation flows were obtained by using the defined covariance flow transformation. Finally, we ran the robustness check. Accordingly, our robustness check results showed the SO(3) Lie method produced more effective results than the standard and Spearman correlation and covariance matrix. And, this method found lower RMSE and MAPE values, greater stability, and better forecast accuracy. For daily data, the Lie method found RMSE = 0.63, MAE = 0.43, and MAPE = 5.04, RMSE = 0.78, MAE = 0.56, and MAPE = 70.28 for weekly data, and RMSE = 0.081, MAE = 0.06, and MAPE = 7.39 for monthly data. These findings indicate that the SO(3) framework provides greater robustness, lower errors, and improved forecasting performance, as well as higher sensitivity to nonlinear transitions compared to standard correlation measures. By embedding time-dependent correlation matrix into a Lie group framework inspired by physics, this paper highlights the deep structural parallels between financial markets and complex physical systems. Full article

We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant domain, and we analyze the linearization around the asymptotically stable equilibrium of the deterministic system. Explicit mean square bounds for the linearized process are derived in terms of the spectral properties of a symmetric matrix, providing insight into the temporal validity of the linear approximation. To investigate global behavior, we relate the first exit time from the domain of interest to backward Kolmogorov equations and numerically solve the associated elliptic and parabolic PDEs with FreeFEM, obtaining estimates of expectations and survival probabilities. An application to the case of Mexico highlights nontrivial effects: while the spectral structure governs local stability, institutional volatility can non-monotonically accelerate global exit, showing that highly reactive interventions without effective sanctions increase uncertainty. Policy implications and possible extensions are discussed. Full article

Phase stability at low radio frequencies is severely impacted by ionospheric propagation delays. Radio interferometers such as the giant metrewave radio telescope (GMRT) are capable of detecting changes in the ionosphere’s total electron content (TEC) over larger spatial scales and with greater sensitivity compared to conventional tools like the global navigation satellite system (GNSS). Thanks to its unique design, featuring both a dense central array and long outer arms, and its strategic location, the GMRT is particularly well-suited for studying the sensitive ionospheric region located between the northern peak of the equatorial ionization anomaly (EIA) and the magnetic equator. In this study, we observe the bright flux calibrator 3C48 for ten hours to characterize and study the low-latitude ionosphere with the upgraded GMRT (uGMRT). We outline the methods used for wideband data reduction and processing to accurately measure differential TEC ($\delta \mathrm{TEC}$) between antenna pairs, achieving a precision of< mTECU (1 mTECU = ${10}^{-3}$ TECU) for central square antennas and approximately mTECU for arm antennas. The measured $\delta \mathrm{TEC}$ values are used to estimate the TEC gradient across GMRT arm antennas. We measure the ionospheric phase structure function and find a power-law slope of $\beta =1.72\pm 0.07$, indicating deviations from pure Kolmogorov turbulence. The inferred diffractive scale, the spatial separation over which the phase variance reaches $1{\mathrm{rad}}^2$, is ∼6.66 km. The small diffractive scale implies high phase variability across the field of view and reduced temporal coherence, which poses challenges for calibration and imaging. Full article

Markov chain perturbation theory is a rapidly developing subfield of the theory of stochastic processes. This review outlines emerging applications of this theory in the analysis of stochastic models of chemical reactions, with a particular focus on biochemistry and molecular biology. We begin by discussing the general problem of approximate modeling in stochastic chemical kinetics. We then briefly review some essential mathematical results pertaining to perturbation bounds for continuous-time Markov chains, emphasizing the relationship between robustness under perturbations and the rate of exponential convergence to the stationary distribution. We illustrate the use of these results to analyze stochastic models of biochemical reactions by providing concrete examples. Particular attention is given to fundamental problems related to approximation accuracy in model reduction. These include the partial thermodynamic limit, the irreversible-reaction limit, parametric uncertainty analysis, and model reduction for linear reaction networks. We conclude by discussing generalizations and future developments of these methodologies, such as the need for time-inhomogeneous Markov models. Full article

The aim of the research is to improve approaches to assessing and predicting the environmental sustainability of innovative enterprises (IEs) for their sustainable development. The concept of environmental sustainability is defined, and the mechanism for managing it at IEs is developed. To implement the system of methods, models, principles, functions, actions, stages, and operations of the proposed management mechanism of the IE’s environmentally sustainable development, intelligent environmental monitoring, and a set of indicators for assessing and forecasting the status of an IE’s environmental sustainability were developed. It is proposed to evaluate the statuses of environmental sustainability of IEs on the basis of expert assessments of indicators and the developed scoring system and to forecast them using Markov chains described by the system of Kolmogorov differential equations and the corresponding system of algebraic equations. The proposed methodology was tested on the environmental sustainability analysis of Enzym Company (Lviv, Ukraine) in 2017–2021. The results of the study allow us to objectively assess the statuses of environmental sustainability of the enterprise and determine their probability, as well as its directions of sustainable development and ways of introducing innovative eco-technologies. Full article

This paper presents a novel approach to modeling the repertoire of the immune system and its adaptation in response to the evolutionary dynamics of pathogens associated with their genetic variability. It is based on application of a dynamic programming-based framework to model the antigen-driven immune repertoire synthesis. The processes of formation of new receptor specificity of lymphocytes (the growth of their affinity during maturation) are described by an ordinary differential equation (ODE) with a piecewise-constant right-hand side. Optimal control synthesis is based on the solution of the Hamilton–Jacobi–Bellman equation implementing the dynamic programming approach for controlling Gaussian random processes generated by a stochastic differential equation (SDE) with the noise in the form of the Wiener process. The proposed description of the clonal repertoire of the immune system allows us to introduce an integral characteristic of the immune repertoire completeness or the integrative fitness of the whole immune system. The quantitative index for characterizing the immune system fitness is analytically derived using the Feynman–Kac–Kolmogorov equation. Full article

The surgical robots currently used in cardiac surgery are equipped with a remote center of motion (RCM) mechanism that enables the required spherical workspace. The dynamics model of the surgical robot’s RCM mechanism presented in this work includes a direct current (DC) motor, an optimal proportional–integral–derivative (PID) controller, and a LuGre friction model that takes into account the Stribeck effect and surface deformation. A finite element method (FEM) analysis of transients was carried out using the energy hypothesis of von Mises with an optimal input signal from the mechatronic system with a PID controller obtained using the Runge–Kutta differentiation method in the Dormand–Prince ordinary differential equations variant (ODE45). Five criteria were adopted for the objective function: the safety factor related to the stress function in the time-varying strength problem, the first natural frequency related to stiffness and the resonance phenomenon, the buckling coefficient in the statics problem related to stability, the static factor of safety, and the displacement of the operating tip. The force inputs to the dynamics model were derived from in vitro force measurements on cardiovascular tissue using a force sensor. The normality of the statistical distribution of the experimental data was confirmed using the Kolmogorov–Smirnov statistical test. The problem of multi-criteria optimization was solved using the non-sorter genetic algorithm (NSGA-II), the finite element method, and the von Mises distortion energy hypothesis. Velocity input signals for the transient dynamics model were obtained from a second in vitro experiment on cardiovascular tissue using the minimally robotic invasive surgery (MIRS) technique. An experienced cardiac surgeon conducted the experiment in a modern method using the Robin Heart Vision surgical robot, and a system of four complementary metal–oxide–semiconductor (CMOS) optical sensors and ariel performance analysis system (APAS-XP 2002) software were used to obtain the endoscopic tool trajectory signal. The trajectory signal was accurate to ±2 [mm] in relation to the adopted standard, and it was smoothed using the Savitzky–Golay (SG) polynomial smoothing, whose parameters were optimally selected using the Durbin–Watson (DW) statistical test. Full article

In many physical systems, it is important to know the exact trajectory of a solution. Relevant applications include celestial mechanics, fluid mechanics, robotics, etc. For cases where analytical methods cannot be applied, one can use computer-assisted proofs or rigorous computations. One can obtain a guaranteed bound for the solution trajectory in the phase space. The application of rigorous computations poses few problems for low-dimensional systems of ordinary differential equations (ODEs) but is a challenging problem for large-scale systems, for example, systems of ODEs obtained from the discretization of the PDEs. A large-scale system size for rigorous computations can be as small as about a hundred ODE equations because computational complexity for rigorous algorithms is much larger than that for simple computations. We are interested in the application of rigorous computations to the problem of proving the existence of a periodic orbit in the Kolmogorov problem for the Navier–Stokes equations. One of the key issues, among others, is the computation complexity, which increases rapidly with the growth of the problem dimension. In previous papers, we showed that 79 degrees of freedom are needed in order to achieve convergence of the rigorous algorithm only for the system of ordinary differential equations. Here, we wish to demonstrate the application of the proper orthogonal decomposition (POD) in order to approximate the attracting set of the system and reduce the dimension of the active degrees of freedom. Full article

The article develops the conceptual foundations of natural and artificial intellectualization of the enterprise, as well as the combination of artificial and natural intelligence in managing business processes in the context of modern challenges of the business environment. Based on the methods of structural design, a system model of the enterprise is developed as the basis for intelligent management. Quantitative and qualitative effects of human–cyber–physical systems, which are the result of management intellectualization, are highlighted. The possibilities of using deviation and perturbation management methods in managing the state of enterprise development with the support of decision-making and implementation of an intelligent information system are considered. The features of making managerial decisions during intelligent enterprise management are considered. The place of the human factor in such intellectual management is highlighted, in particular, in terms of improving the intelligence of employees and the natural intellectualization of the enterprise. The problem of assessing and forecasting the state of enterprise development in the context of intellectual management is highlighted. In this context, the expediency of using mathematical methods of Markov process theory, using systems of Kolmogorov differential equations and their solutions, using numerical methods and applied software products is justified. This made it possible to study the dynamics of probabilities of states and stability of development of enterprises and their employees; the dynamics of probabilities of states of innovative and technological processes; scientific and technological, environmental, social and economic efficiency of a business. To test the proposed mathematical models for assessing and predicting the state of development of enterprises and their employees, appropriate studies were conducted on the sanatorium–resort complex in Truskavets (Ukraine). Full article

The numerical analysis for the controllability assessment of a new design nuclear reactor is typically carried out by means of complex multiphysics codes, solving high fidelity partial differential equations governing the system neutronics as well as the fluid dynamics. Multiphysics codes deliver very accurate solutions at the expense of high computational times, which could be of several hours depending on the specific case study. In this work, to efficiently reduce runtimes, a sensitivity analysis (SA) is carried out to identify the most important input parameters affecting the solution of a multiphysics model developed for the controllability assessment of molten salt reactors (MSRs). The numerical modeling of these innovative systems is fundamental to allow for a safer and more sustainable power production (e.g., due to the lower radiotoxicity of the actinide inventory in MSRs and to the possibility of operation at atmospheric pressure). In this paper, four global sensitivity measures are calculated first, including the Pearson correlation coefficient, δ, Kolmogorov–Smirnov and Kuiper indices, whose results are aggregated by an ensemble strategy and confirmed by the CUmulative SUm of NOrmalized Reordered Output (CUSUNORO) plot. The results of the SA point out that the fuel density is the most important parameter yielding the largest variations in the system reactivity, fundamental for guaranteeing the MSR controllability. In light of this result, a simplified, surrogate model is then developed, which uses density as the only input parameter to determine reactivity, guaranteeing runtime reductions from several hours to a few seconds and, at the same time, a comparable level of accuracy of the multiphysics model. This result demonstrates the capability of global sensitivity analysis approaches to effectively identify the most relevant parameters in MSR systems, supporting the development of simplified, control-oriented models for these innovative reactors. Full article

In this paper, we consider an autonomous two-dimensional ODE Kolmogorov-type system with three parameters, which is a particular system of the general predator–prey systems with a Holling type II. By reformulating this system as a set of two second-order differential equations, we investigate the nonlinear dynamics of the system from the Jacobi stability point of view using the Kosambi–Cartan–Chern (KCC) geometric theory. We then determine the nonlinear connection, the Berwald connection, and the five KCC invariants which express the intrinsic geometric properties of the system, including the deviation curvature tensor. Furthermore, we obtain the necessary and sufficient conditions for the parameters of the system in order to have the Jacobi stability near the equilibrium points, and we point these out on a few illustrative examples. Full article

We provide a detailed description of a numerical approach that makes use of the shifted Chebyshev polynomials of the sixth kind to approximate the solution of some fractional order differential equations. Specifically, we choose the fractional Fisher–Kolmogorov–Petrovskii–Piskunov equation (FFKPPE) to describe this method. We write our approximate solution in the product form, which consists of unknown coefficients and shifted Chebyshev polynomials. To compute the numerical values of coefficients, we use the initial and boundary conditions and the collocation technique to create a system of equations whose number matches the unknowns. We test the applicability and accuracy of this numerical approach using two examples. Full article

This paper investigates the randomness assignment problem for a class of continuous-time stochastic nonlinear systems, where variance and entropy are employed to describe the investigated systems. In particular, the system model is formulated by a stochastic differential equation. Due to the nonlinearities of the systems, the probability density functions of the system state and system output cannot be characterised as Gaussian even if the system is subjected to Brownian motion. To deal with the non-Gaussian randomness, we present a novel backstepping-based design approach to convert the stochastic nonlinear system to a linear stochastic process, thus the variance and entropy of the system variables can be formulated analytically by the solving Fokker–Planck–Kolmogorov equation. In this way, the design parameter of the backstepping procedure can be then obtained to achieve the variance and entropy assignment. In addition, the stability of the proposed design scheme can be guaranteed and the multi-variate case is also discussed. In order to validate the design approach, the simulation results are provided to show the effectiveness of the proposed algorithm. Full article