Stochastic Dynamic Process Research Articles

Stochastic Modeling of Star Formation Histories. III. Constraints from Physically Motivated Gaussian Processes

Galaxy formation and evolution involve a variety of effectively stochastic processes that operate over different timescales. The extended regulator model provides an analytic framework for the resulting variability (or “burstiness”) in galaxy-wide star formation due to these processes. It does this by relating the variability in Fourier space to the effective timescales of stochastic gas inflow, equilibrium, and dynamical processes influencing giant molecular clouds' creation and destruction using the power spectral density (PSD) formalism. We use the connection between the PSD and autocovariance function for general stochastic processes to reformulate this model as an autocovariance function, which we use to model variability in galaxy star formation histories (SFHs) using physically motivated Gaussian processes in log star formation rate (SFR) space. Using stellar population synthesis models, we then explore how changes in model stochasticity can affect spectral signatures across galaxy populations with properties similar to the Milky Way and present-day dwarfs, as well as at higher redshifts. We find that, even at fixed scatter, perturbations to the stochasticity model (changing timescales vs. overall variability) leave unique spectral signatures across both idealized and more realistic galaxy populations. Distributions of spectral features including Hα and UV-based SFR indicators, Hδ and Ca H and K absorption-line strengths, D n (4000), and broadband colors provide testable predictions for galaxy populations from present and upcoming surveys with the Hubble Space Telescope, James Webb Space Telescope, and Nancy Grace Roman Space Telescope. The Gaussian process SFH framework provides a fast, flexible implementation of physical covariance models for the next generation of spectral energy distribution modeling tools. Code to reproduce our results can be found at https://github.com/kartheikiyer/GP-SFH.

Multistage reliability-constrained stochastic planning of diamond distribution network: An approximate dynamic programming approach

In this paper, a multistage reliability-constrained stochastic planning model is established for the diamond distribution network, a new type of distribution system grid structure, with the goal of optimizing the total cost of investment and operation. The uncertainty of load growth is simulated by generating multiple load growth scenarios, and the power supply loss caused by the reliability of components in the system is also considered. The multistage stochastic dynamic decision process is modeled by The Markov decision process. In order to solve the “curse of dimensionality” problem in multi-stage stochastic planning model, the approximate dynamic programming algorithm is used to solve it. The case study is based on the typical structure of the diamond distribution network and realistic data of an actual district in Shanghai, China. The planning results verify the effectiveness of the model and the solution algorithm, and demonstrate the reliability and economy of the diamond distribution network are superior to the traditional double-ring network.

Modeling Processes of Emergence and Growth of Fractal Structures and Chamber Defects of Thermal Power Units

The paper considers modeling the emergence and growth of possible fractal structures and defects on the inner surface of the chambers of thermal power units, which allow control and regulation of the development of such stochastic dynamic processes. We are talking about the use of modeling procedures for the given analysis, which are quite universal in the framework of certain approaches. A general qualitative consideration of the modeling of processes such as the deposition of materials on a solid surface of various complex configurations, and the occurrence of its fracturing and defects of fractal types, is given. In the first part, we consider an analogy between the processes of the emergence and growth of fractal structures and chamber defects with laser processes of controlled deposition of substances on the surface of a solid body and the growth of its fracturing. A number of models have been developed for the emergence and growth of fractal inhomogeneities of various types and configurations on a solid surface with identification of the possibility of their preliminary monitoring at the initial stage of their appearance. At the same time, both various surfaces in the form of coatings and the formation of fracturing and cluster zones of inhomogeneities and defects have been analyzed. The emphasis in the course of research has been made both on the analysis of their regulated structure, and also on the dynamics of the growth of fracturing and cluster zones of heterogeneities and defects in a certain direction. At the initial stage, the indicated process of formation of fractures and cluster zones of inhomogeneities and defects in space was monitored with different scaling: nano- and microscales. This study has been carried out within the framework of an analogy under the following conditions: firstly, given control over the cha-racteristics of similar objects in the corresponding laser experiment; secondly, the presence of a real possibility of ensuring their formation on the inner surfaces of the chambers in contact with the working substance; thirdly, the possibility of such structures influencing on the efficiency of various types of thermal power units in the context of achieving the desired direction and/or undesirability of changing the indicators and characteristics of units taking into account the laws of technical thermodynamics.

A purely data-driven framework for prediction, optimization, and control of networked processes

Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network structure and the underlying dynamical process, identifying stochastic nonlinear dynamical processes continues to be an outstanding problem. Here, we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks. The proposed approach requires no prior knowledge of the network structure and identifies the underlying dynamics solely using a collection of two-step snapshots of the states. This data-driven system identification is achieved by using the Koopman operator to find a low-dimensional representation of the dynamical patterns that evolve linearly. Further, we use the global linear Koopman model to solve critical control problems by applying to model predictive control (MPC)–typically, a challenging proposition when applied to large networks. We show that our proposed approach tackles this by converting the original nonlinear programming into a more tractable optimization problem that is both convex (quadratic programming) and with far fewer variables.

In a niche-neutral continuum, a set of theoretical models in a metacommunity operates simultaneously in patchy habitats.

This study investigated the origins and maintenance of biodiversity by integrating ecological and evolutionary mechanisms into a spatially-explicit synthesis between niche-based processes and neutral dynamics (ND). An individual-based model on a two-dimensional grid with periodic boundary conditions was used to compare a niche-neutral continuum induced in contrasting spatial and environmental settings while characterizing the operational scaling of deterministic-stochastic processes. The spatially-explicit simulations revealed three major findings. First, the number of guilds in a system approaches a stationary state and the species composition in a system converges to a dynamic equilibrium of ecologically-equivalent species generated by the speciation-extinction balance. This convergence of species composition can be argued under a point mutation mode of speciation and niche conservatism due to the duality of ND. Second, the dispersal modes of biota may affect how the influence of environmental filtering changes across ecological-evolutionary scales. This influence is greatest in compactly-packed areas within biogeographic units for large-bodied active dispersers, such as fish. Third, the species are filtered along the environmental gradient and the coexistence of ecologically-different species in each local community in a homogeneous environment is allowed by dispersals in a set of local communities. Therefore, the ND among the single-guild species, extinction-colonization trade-off among species of similar environmental optima and different levels of specialization, and mass effect, such as weak species-environment associations, operate simultaneously in patchy habitats. In spatially-explicit synthesis, characterizing where a metacommunity falls along a niche-neutral continuum is too superficial and involves an abstraction that any biological process is probabilistic; therefore, they are dynamic-stochastic processes. The general patterns observed in the simulations allowed a theoretical synthesis of a metacommunity and explained the complex patterns observed in the real world.

Rethinking statistical learning as a continuous dynamic stochastic process, from the motor systems perspective.

The brain integrates streams of sensory input and builds accurate predictions, while arriving at stable percepts under disparate time scales. This stochastic process bears different unfolding dynamics for different people, yet statistical learning (SL) currently averages out, as noise, individual fluctuations in data streams registered from the brain as the person learns. We here adopt a new analytical approach that instead of averaging out fluctuations in continuous electroencephalographic (EEG)-based data streams, takes these gross data as the important signals. Our new approach reassesses how individuals dynamically learn predictive information in stable and unstable environments. We find neural correlates for two types of learners in a visuomotor task: narrow-variance learners, who retain explicit knowledge of the regularity embedded in the stimuli. They seem to use an error-correction strategy steadily present in both stable and unstable environments. This strategy can be captured by current optimization-based computational frameworks. In contrast, broad-variance learners emerge only in the unstable environment. Local analyses of the moment-by-moment fluctuations, naïve to the overall outcome, reveal an initial period of memoryless learning, well characterized by a continuous gamma process starting out exponentially distributed whereby all future events are equally probable, with high signal (mean) to noise (variance) ratio. The empirically derived continuous Gamma process smoothly converges to predictive Gaussian signatures comparable to those observed for the error-corrective mode that is captured by current optimization-driven computational models. We coin this initially seemingly purposeless stage exploratory. Globally, we examine a posteriori the fluctuations in distributions' shapes over the empirically estimated stochastic signatures. We then confirm that the exploratory mode of those learners, free of expectation, random and memoryless, but with high signal, precedes the acquisition of the error-correction mode boasting smooth transition from exponential to symmetric distributions' shapes. This early naïve phase of the learning process has been overlooked by current models driven by expected, predictive information and error-based learning. Our work demonstrates that (statistical) learning is a highly dynamic and stochastic process, unfolding at different time scales, and evolving distinct learning strategies on demand.

The distributed delay rearranges the bimodal distribution at protein level

BackgroundIn bimodal distribution, we refer ON to the mode with a higher protein level and OFF to a lower protein level. The traditional wisdom of manipulating the population in each mode is done by adding an inducer or inhibitor to change the protein number. MethodsBy delay stochastic simulation algorithm, we applied transcriptional or translational delay to the gene expression system of toggle switches. We also incorporated distributed delay in the model. From a deterministic aspect, reaction delay does NOT alter the steady-state value. Thus, our approach is different from the conventional method. Significant FindingsThe transcriptional delay rearranged the bimodal distribution at the protein level and the influence of the translational delay is even higher. The increment of delay time pushes more cells to have the protein in the ON mode. Remarkably, the distributed delay of translation guides 98% of cells to have protein in the ON mode. We then displayed the time-course trajectories and discovered the cause leading to the rearrangement of bimodal distribution. We also exclude the possibility that rearrangement of bimodal distribution simply comes from the trivial reason, the change of the input distribution, and concluded that the change of dynamic stochastic processes is crucial.

Metastability, fractal scaling, and synergistic information processing: What phase relationships reveal about intrinsic brain activity

Dynamic functional connectivity (dFC) in resting-state fMRI holds promise to deliver candidate biomarkers for clinical applications. However, the reliability and interpretability of dFC metrics remain contested. Despite a myriad of methodologies and resulting measures, few studies have combined metrics derived from different conceptualizations of brain functioning within the same analysis - perhaps missing an opportunity for improved interpretability. Using a complexity-science approach, we assessed the reliability and interrelationships of a battery of phase-based dFC metrics including tools originating from dynamical systems, stochastic processes, and information dynamics approaches. Our analysis revealed novel relationships between these metrics, which allowed us to build a predictive model for integrated information using metrics from dynamical systems and information theory. Furthermore, global metastability - a metric reflecting simultaneous tendencies for coupling and decoupling - was found to be the most representative and stable metric in brain parcellations that included cerebellar regions. Additionally, spatiotemporal patterns of phase-locking were found to change in a slow, non-random, continuous manner over time. Taken together, our findings show that the majority of characteristics of resting-state fMRI dynamics reflect an interrelated dynamical and informational complexity profile, which is unique to each acquisition. This finding challenges the interpretation of results from cross-sectional designs for brain neuromarker discovery, suggesting that individual life-trajectories may be more informative than sample means.

Dynamic Optimization of on‐Grid Integrated Energy System Considering Peak‐Shaving Demand Via Learning Methods

An integrated energy system (IES) is combined with electricity, gas and heating subnetworks to satisfy various loads, which results in a complicated energy coupling. Considering the power interaction between IES and power grid, the real-time dynamic optimal dispatch policies for the on-grid IES are proposed and compared by learning methods to improve the operation economic and peak-shaving performances in this study. Owing to the uncertainties of the load demands and real-time peak-shaving demand and renewable energy, together with the sequential operation of the controllable sources, the energy dispatch optimization problem of the IES is described as a stochastic dynamic optimization process. A source-load collaborative operation mode is proposed as the coupling of thermal energy and electrical power in the IES and compared with different energy dispatching mode. And reinforcement learning methods are adopted to achieve the dynamic optimal policy. Since the multiple systems with energy coupling would result in modeling difficulty and dimension curse during the optimization, a deep reinforcement learning method (DDQN) is used to solve this problem. A numerical analysis is performed by comprehensively comparing the different learning algorithms and operation modes, and the simulation results show that the derived dispatch policy achieved by DDQN method with source-load collaboration can effectively improve the performance of the IES in the stochastic environment. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Hidden dependence of spreading vulnerability on topological complexity.

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time-commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its "spreading vulnerability," is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the "entropy of temporal entanglement" as a quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological, and engineered systems.

A dynamic stochastic search algorithm for high-dimensional optimization problems and its application to feature selection

As the number of dimensions of an optimization problem increases, the process of deriving the solution becomes more complicated and difficult. Metaheuristic algorithms are effective methods for solving many optimization problems, whereas most of these algorithms perform poorly on high-dimensional problems. In this paper, a novel metaheuristic algorithm called Dynamic Stochastic Search (DSS) is proposed for high-dimensional optimization problems. To effectively execute the exploration (diversification) and exploitation (intensification) processes of DSS, a dynamic stochastic search process is designed by defining a stochastic search control factor, a search process based on the Gaussian distribution, two shrink modes inspired by the Whale Optimization Algorithm, and a balance mechanism derived from the Bat Algorithm. The proposed algorithm has the following advantages: no specific control parameters other than the population size and the maximum number of iterations, a simple structure, and less computational effort in the implementation. Analyzing the computational complexity of DSS demonstrates its simplicity. To evaluate the performance of DSS, twenty 300-dimensional and 3000-dimensional classical benchmark functions as well as thirty 100-dimensional CEC2014 benchmark functions are utilized. The statistical results prove the effectiveness and feasibility of DSS for high-dimensional optimization problems because it shows better convergence performance and higher efficiency than various advanced optimization algorithms. Moreover, the superiority of DSS in solving high-dimensional real-world optimization problems is validated by applying it to feature selection for ten real-world benchmark classification datasets from the UCI machine learning repository.

A Novel Ferroelectric FET-Based Adaptively-Stochastic Neuron for Stimulated-Annealing Based Optimizer With Ultra-Low Hardware Cost

In this work, based on ferroelectric FET (FeFET), a novel capacitor-less and bio-inspired adaptively-stochastic neuron is proposed and experimentally demonstrated for the first time for solving optimization problems in spiking neural network with remarkably reduced hardware cost. By exploiting the physics of inherent stochastic dynamic process of ferroelectric domains nucleation, the proposed FeFET-based neuron with only three transistors can realize adaptively stochastic spike firing behavior, where its stochasticity gradually decreases during operation. The adaptive stochasticity is experimentally demonstrated for the hardware implementation of stochastic simulated annealing algorithm for optimization, providing a promising ultralow-hardware-cost solution for solving optimization problems.

Methods for predicting the negative impact on the environment during the operation of vehicles in agricultural production

Modern agriculture is characterized by a continuous increase in production, which is inextricably linked with the growth of consumption of fuel and energy resources (FER). The consumption of motor fuel for agricultural enterprises is about 40% of the total consumption of fuel and energy resources. The use of motor fuel inevitably leads to emissions of pollutants. Predicting the negative impact on the environment depends on the quantity and quality of these emissions. The purpose of the research is: analysis of forecasting methods; selection and justification of the most attractive forecasting method; planning of measures to reduce emissions into the environment. The statistical method of forecasting, which uses the theory of multidimensional dynamic stochastic processes, is the most attractive. The development and implementation of measures developed taking into account the analysis of the forecast of the negative impact on the environment of vehicles of agricultural enterprises will reduce the negative impact on the environment by introducing energy-efficient technologies into the energy balance of the enterprise.

Design and research on the simulation platform of Oscillating Flapping-Wing Wave Energy Converter based on AMESim

It is a stochastic dynamic process for conversion of wave energy, which includes the coupling of multiphysics. Energy conversion efficiency and stable output are important objectives. In order to explore the mechanism of wave energy efficient conversion, a wave energy generation scheme of oscillating-flapping wing was proposed. Taking the conversion system of wave power generation device as the research object, the mechanical-hydraulic-circuit simulation platform of the system is established by the software AMESim. The proposed scheme is tested and verified. The results show that the wave energy conversion system can effectively convert wave energy, realize the stable output of electric energy and store it in the battery pack, which provides a theoretical basis for the development of wave energy generation converter of oscillating-flapping wing.

Predictive Analysis of Mutual Fund Investment Using Sustainability Index Evidence from Indian Stock Market

This study is an attempt to predict the price movement between S & P BSE GREENEX and selected open ended equity mutual fund categories traded at stock exchanges in India. Daily data over the last 5 years were taken and the sample period is from January 1, 2016 to January 1, 2021. The authors use a set of econometric models such as dynamic lag vector auto regression stochastic process model, Cointegration, Granger causality test and Variance Decomposition to substantiate the existence of long run and short run association between the dependent and independent variables selected. The study shows clear evidences of cointegration between S & P BSE GREENEX and selected mutual fund categories, which is an indication of the existence of long run equilibrium relationship between the variables. The empirical investigation also proved the traces of bi-directional and uni-directional Granger- casual effect between the variables. The findings of the study show that S & P BSE GREENEX and large cap mutual fund categories have strong price movement relationship compared to mid-cap funds, which shows a marginal relationship and relatively very weak relationship with small cap funds.

Cooperation emergence in group population with unequal competitions

Groups are the basic unit of organization in our society. It is important to investigate how groups compete and cooperation evolves in the population composed of groups. In this paper, based on the celebrated multi-player public goods game, we propose a general theoretical framework of the stochastic dynamic process to study how inequalities among groups affect the evolution of cooperation in a group population. We find that cooperation can be promoted if enhancement factors of every group are not equivalent and constant, but are dynamic adjusted according to the group reputation which is defined as the fraction of cooperators in the last public goods game. Furthermore, we introduce the inequality in social roles of groups by means of heterogeneous graph and find that, under the influence of dynamic adjustment of enhancement factors, central groups can always own more cooperators compared to peripheral groups during game dynamics. Moreover, a highly heterogeneous group connecting patterns can help cooperators to survive in the population when the enhancement factor is small, but prevents the spread of cooperation more widely even if the enhancement factor increases.

Stochastic Model of Pore Nucleation when the Sample is Irradiates with Inert Gas Ions

Abstract—Non-point vacancy-gas defects (VGD) (pores, blisters) in the crystal lattice arise as a result of its irradiation with an inert gas Xe++, the process is considered as the formation of first-order phase transition nuclei by means of computational mathematics, kinetic theory, and the theory of stochastic dynamic variables and Wiener random processes. The characteristics of disordered porosity in samples consisting of layers (“dielectric/metal”) at various layer thicknesses are calculated. The formation of spherical shape defects in materials at times of the order of 10–4 s, when the porosity of the material nucleates, is preceded or accompanied by the appearance of microcracks. Irradiation of surfaces with an inert gas with ion energies of 5–10 keV refers to low-temperature blistering; in the model, the constancy of the influence of radiation fluxes stimulating a phase transition creates the condition of an “open” physical system in which it is possible to combine lattice defects into structures that cause local stresses, and the constancy of the temperature of the sample, the pressure of the implantable “monomers” of the gas, and supersaturation (similar to the parameters of vapor condensation) are characteristic of the fluctuation unstable stage of the phase transition move. Partial kinetic equations with nonlinear coefficients (Kolmogorov–Feller and Einstein–Smoluchowski) are solved by the method of stochastic molecular dynamics, which establishes a connection between the solution of Ito stochastic equations in the sense of Stratonovich and kinetic equations; stable numerical methods are used. The conditions for the formation of VGD are determined taking into account the influence of the elastic properties of the lattice, and the porosity and local stresses in thin layers of irradiated materials are calculated.

Application of videogrammetry in the mechanics of multi-phase systems

This paper is a description of the evolution of long-term research work on two-phase flows using parallel studies of dynamic image analysis and stochastic processes analysis. The state of current knowledge on the research of gas-solid and gas-liquid systems as well as a review of research relating to these issues are also presented. The work grants the principles of videogrammetric surveys based on stochastic analysis for a series of photographs taken with video techniques. The method applies the analysis of changes in selected features and parameters in the time domain. Especially in application to multiphase gas-liquid and solid-gas mixture flows, which are characterized by strong variabilities. Parameters such as flow patterns of the mixture were determined as time-space distributions of phase concentration, displacement velocities of separated two-phase structures, volume partitions of phases, and velocity field distributions are evaluated. The changes of certain parameters characterizing the flow in the time domain often hide more useful information. The subject of this study covers the basics of videogrammetry with a description of two-phase mixture motion for co-current flow in channels, mapping of the phase velocity field, also across the tube bundle in shell-and-tube apparatus, phase motion at the flow of a two-phase gas-liquid mixture in mini-channels, transport of liquids in air-lift pump and fluidization of solid particles.

New Optimization Model for Multi-Period Multi-Product Production Planning System with Uncertainty

The focus of this study is to develop a multi-period multi-product (MPMP) production planning system with uncertainty, and products demand (seasonal demand) uncertainty. Mainly, the problem aims reach the production levels of each product according to the uncertain demand for various periods, which depend on constraints of capacity, inventory, and resources. An analytical model proposed for this problem that can be categorized into two classes: non-linear and stochastic. The objective is to minimize the summation of variable production costs. As uncertain demand is a dynamic stochastic data process in the planning horizon, it is considered as a tree model. Each stage in the demand tree model is related to a cluster of a period time. Hence, depending on the tree model for the fluctuation demand; Two-Stage Stochastic Programming (TSP) model is presented as an alternative for all demand scenarios. In some of the reviewed articles validation of the analytical model were missing, while other studies were missing either manufacturing set up costs or assumptions of seasonal demand. Therefore, this study proposes TSP model using Sampling Average Approximation method (SAA) that is suitable for a production planning system in any manufacturing environment considering seasonal demand using optimization program (Lingo 16) to solve the mathematical model. Further, investigation of seasonal demand is performed using the multiplicative seasonal method, and the model validation was checked using Mathworks Matlab R2015a (64-Bit) considering manufacturing set up costs. Finally, some recommendations for future research are suggested.

Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter

In this paper, a novel hybrid control method is proposed to enhance the tracking performance of the Proportional–Integral (PI) based control system for a class of nonlinear and non-Gaussian stochastic dynamic processes with unmeasurable states. The system performance is presented by tracking error entropy as the system is nonlinear and subjected to non-Gaussian noises. The well-known kernel density estimation (KDE) technique is employed to estimate the entropy because the precise statistical property of noises is not available for many industrial processes. Since in many industrial cases gains of PI controllers are fixed, a compensative controller is designed without changing the existing closed loop PI controller. Moreover, the compensative signal is formed using the estimated states from the extended Kalman filter (EKF) and a nonlinear compensation realized by the radial basis function (RBF) neural network. The weights of RBF are trained to minimize the entropy of the closed loop tracking error. The convergence of RBF network is discussed and the stability of the resulting closed-loop control system is analysed in mean square sense. Finally, two numerical examples and a practical system simulation are given to illustrate the effectiveness of the proposed control method.