Stochastic Dynamic Process Research Articles

Mean-field models in swarm robotics: a survey

We present a survey on the application of fluid approximations, in the form of mean-field models, to the design of control strategies in swarm robotics. Mean-field models that consist of ordinary differential equations, partial differential equations, and difference equations have been used in the swarm robotics literature, depending on whether the state of each agent and the time variable take values from a discrete or continuous set. These macroscopic models are independent of the number of agents in the swarm, and hence can be used to synthesize robot control strategies in a scalable manner, in contrast to individual-based microscopic models of swarms that represent finite numbers of discrete agents. Moreover, mean-field models are amenable to rigorous investigation using tools from dynamical systems theory, control theory, stochastic processes, and analysis of partial differential equations, enabling new insights and provable guarantees on the dynamics of collective behaviors. In this paper, we survey the applications of these models to problems in swarm robotics that include coverage, task allocation, self-assembly, consensus, and environmental mapping.

Life-Cycle Modeling of Structural Defects via Computational Geometry and Time-Series Forecasting.

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segments from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, two-dimensional (2D) point clouds analogous to information derived from point clouds were firstly generated over simulated life cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements; however, assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.

Stochastic dynamics in nonequilibrium phase transitions of multiple totally asymmetric simple exclusion processes coupled with strong and weak interacting effects

Totally asymmetric simple exclusion process (TASEP) is an important stochastic dynamic process in the area of statistical physics, which can be used to model microscopic transport in nonequilibrium processes. Due to its rich stochastic dynamics and nonequilibrium phase transition mechanisms, the importance of TASEP in statistical physics is similar with that of Ising model, which has attracted many attentions. In this paper, multiple TASEPs are introduced and coupled with various strong and weak interacting effects of self-driven particles. Both strong and weak couplings are calculated by means of mean-field analyses and Monte Carlo simulations. Tremendous cluster dynamics, evolution law of topological structures of phase diagrams and mechanisms of shock evolution are found in thermodynamic limit of proposed particle system. Monte Carlo simulation results like phase boundaries are found to be a good match with mean-field analyses, which reflect the validity of the research. The research work will be conducive to exploring the mechanisms of stochastic dynamics in the process of nonequilibrium phase transitions of multi-body interacting particle systems.

A novel motion platform system for testing prosthetic knees

The principle of a novel motion platform system (NMPS) for testing prosthetic knees (PKs) is proposed to imitate the stochastic dynamic processes. The NMPS is realized by commanding a thigh simulator to imitate thigh motions of a tester in real time. The NMPS includes a motion platform, a bio-guided unit, a posture sensing unit, and a control and data collection unit. An indirect approach to obtain the vertical motion of the tester’s hip joint is proposed and experimentally validated. The prototype of the NMPS is fabricated. The prototype’s ability to imitate the tester’s thigh motions is experimentally tested at an accelerated/decelerated walking speed. Correspondingly, the swing angle of the developed four-bar linkage prosthetic knee based on magnetorheological effect (FLPKME) is experimentally tested and analyzed. The experimental results indicate that the developed NMPS can accurately imitate the amplitudes and speeds changing in the stochastic dynamic processes of the healthy un-amputated individual’s thigh.

Lamb Wave-Minimum Sampling Variance Particle Filter-Based Fatigue Crack Prognosis.

Fatigue cracks are one of the common failure types of key aircraft components, and they are the focus of prognostics and health management (PHM) systems. Monitoring and prediction of fatigue cracks show great application potential and economic benefit in shortening aircraft downtime, prolonging service life, and enhancing maintenance. However, the fatigue crack growth process is a non-linear non-Gaussian dynamic stochastic process, which involves a variety of uncertainties. Actual crack initiation and growth sometimes deviate from the results of fracture mechanics analysis. The Lamb wave-particle filter (LW-PF) fatigue-crack-life prediction based on piezoelectric transducer (PZT) sensors has the advantages of simple modeling and on-line prediction, making it suitable for engineering applications. Although the resampling algorithm of the standard particle filter (PF) can solve the degradation problem, the discretization error still exists. To alleviate the accuracy decrease caused by the discretization error, a Lamb wave-minimum sampling variance particle filter (LW-MSVPF)-based fatigue crack life prediction method is proposed and validated by fatigue test of the attachment lug in this paper. Sampling variance (SV) is used as a quantitative index to analyze the difference of particle distribution before and after resampling. Compared with the LW-PF method, LW-MSVPF can increase the prediction accuracy with the same computational cost. By using the minimum sampling variance (MSV) resampling method, the original particle distribution is retained to a maximum degree, and the discretization error is significantly reduced. Furthermore, LW-MSVPF maintains the characteristic of dimensional freedom, which means a broader application in on-line prognosis for more complex structures.

The multi-stage dynamic stochastic decision process with unknown distribution of the random utilities

We consider a decision maker who performs a stochastic decision process over a multiple number of stages, where the choice alternatives are characterized by random utilities with unknown probability distribution. The decisions are nested each other, i.e. the decision taken at each stage is affected by the subsequent stage decisions. The problem consists in maximizing the total expected utility of the overall multi-stage stochastic dynamic decision process. By means of some results of the extreme values theory, the probability distribution of the total maximum utility is derived and its expected value is found. This value is proportional to the logarithm of the accessibility of the decision maker to the overall set of alternatives in the different stages at the start of the decision process. It is also shown that the choice probability to select alternatives becomes a Nested Multinomial Logit model.

Mean Field Equilibria for Resource Competition in Spatial Settings

We study a model of competition among nomadic agents for time-varying and location-specific resources arising in crowdsourced transportation services, online communities, and traditional location-based economic activity. This model comprises a group of agents and a single location endowed with a dynamic stochastic resource process. Periodically, each agent derives a reward determined by the location’s resource level and the number of other agents there and has to decide whether to stay at the location or move. On moving, the agent arrives at a different location whose dynamics are independent of and identical to the original location. Using the methodology of mean field equilibrium, we study the equilibrium behavior of the agents as a function of the dynamics of the stochastic resource process and the nature of the competition among colocated agents. We show that an equilibrium exists in which each agent decides whether to switch locations based only on the agent’s current location’s resource level and the number of other agents there. We additionally show that when an agent’s payoff is decreasing in the number of other agents at the agent’s location, equilibrium strategies obey a simple threshold structure. We show how to exploit this structure to compute equilibria numerically and use these numerical techniques to study how system structure affects the agents’ collective ability to explore their domain to find and effectively utilize resource-rich areas.

Fault detection and diagnosis based on particle filters combined with interactive multiple-model estimation in dynamic process systems

A new approach to fault detection and diagnosis (FDD) is developed for nonlinear stochastic dynamic process systems in this paper. It is called PFs-IMM, which combines particle filters (PFs) and the interactive multiple model (IMM) estimation. In this method, a multiple-model estimation scheme is first formulated to describe the complex process system poorly represented by a single model. The IMM algorithm can deal with abrupt changes in the behavior of operating processes. The residuals of the multiple models are examined for the likelihood of each model. A decision rule is employed to adaptively determine which model is the most appropriate one at each time step. Then based on IMM, a set of PFs run in parallel is used to estimate the states and the reconciled measurements even when the operating mode changes. Each of the PFs utilizes a particular mode to derive the estimation of the state variables as well as the reconciliation of the measured variables based on the probabilistic weighting scheme. From the multiple filters, the interaction among PFs allows the fusing of dynamic estimates. To achieve higher sensitivity to faults and more robustness to disturbances and noises, a new fault index function is developed for FDD. The proposed PFs-IMM approach provides an integrated framework. It can estimate the current operational or faulty mode of the system and derive the overall state estimation and the measurement reconciliation as well. The simulation solutions to the problems are obtained to demonstrate the effectiveness of the proposed method in highly nonlinear dynamic processes.

The finite volume method for two-dimensional Burgers’ equation

The Burgers' equation as a useful mathematical model is applied in many fields such as fluid dynamic, heat conduction, and continuous stochastic processes. Although this equation can be solved analytically, it is only based on the restricted set of initial-boundary value conditions. So the numerical method for solving the Burgers' equation is necessary. In this paper, a finite volume method is presented for the two-dimensional Burgers' equation on a triangular mesh. We give a semi-discrete finite volume scheme and drive the optimal error estimate in H1 norm.

Reaction Networks and Population Dynamics

Reaction systems and population dynamics constitute two highly developed areas of research that build on well-defined model classes, both in terms of dynamical systems and stochastic processes. Despite a significant core of common structures, the two fields have largely led separate lives. The workshop brought the communities together and emphasised concepts, methods and results that have, so far, appeared in one area but are potentially useful in the other as well.

Development of dynamic Bayesian models for web application test management

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics.

We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages-conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

Anticipating the emergence of infectious diseases.

In spite of medical breakthroughs, the emergence of pathogens continues to pose threats to both human and animal populations. We present candidate approaches for anticipating disease emergence prior to large-scale outbreaks. Through use of ideas from the theories of dynamical systems and stochastic processes we develop approaches which are not specific to a particular disease system or model, but instead have general applicability. The indicators of disease emergence detailed in this paper can be classified into two parallel approaches: a set of early-warning signals based around the theory of critical slowing down and a likelihood-based approach. To test the reliability of these two approaches we contrast theoretical predictions with simulated data. We find good support for our methods across a range of different model structures and parameter values.

Models with Time-Varying Mean and Variance: A Robust Analysis of U.S. Industrial Production

Many seasonal macroeconomic time series are subject to changes in their means and variances over a long time horizon. In this paper we propose a general treatment for the modelling of time-varying features in economic time series. We show that time series models with mean and variance functions depending on dynamic stochastic processes can be sufficiently robust against changes in their dynamic properties. We further show that the implementation of the treatment is relatively straightforward. An illustration is given for monthly U.S. Industrial Production. The empirical results including estimates of time-varying means and variances are discussed in detail.

Dynamical complexity of short and noisy time series

Shannon entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two such Compression-Complexity Measures namely Lempel-Ziv complexity (LZ) and Effort-To-Compress (ETC) on short time series from chaotic dynamical systems in the presence of noise. Both LZ and ETC outperform Shannon entropy (H) in accurately characterizing the dynamical complexity of such systems. For very short binary sequences (which arise in neuroscience applications), ETC has higher number of distinct complexity values than LZ and H, thus enabling a finer resolution. For two-state ergodic Markov chains, we empirically show that ETC converges to a steady state value faster than LZ. Compression-Complexity measures are promising for applications which involve short and noisy time series.

Discussion

Discussion

Simulation and Calibration of Options Prices under a Levy-Type Stochastic Dynamic and Semi Markov Market Switching Regimes Processes

This work mainly highlights the benefits of derivative pricing in a semi Markov switching market. We explore the main differences between Markov and Semi Markov regime switching models. The three main problems we deal with are, (1) historical parameter calibration through the recently developed LLGMM method, (2) effects of semi Markov parameters on option prices and (3) comparison of Heston model, semi Markov regime model and Markov regime model calibration performances over both sequential option price calibration and the overall implied volatility surface of the market. Employing the LLGMM method, parameters of the spot price process described by a linear Levy-type stochastic differential equation under semi-Markov structural perturbations are calibrated to observed prices. From Fourier space time stepping and Carr and Madan methods, risk neutral parameters of the spot price are calibrated and interpreted. American and European style vanilla and exotic option prices are simulated. The presented results are shown in the context of a piecewise constant semi-Markov intensity matrix approximating a Weibull intensity matrix. We obtain that under the conditional minimum entropy martingale measure, option prices predictably increase as the regime risk increases through the intensity matrix of the semi Markov process. Calibration and simulation results demonstrate noticeable effects of semi-Markov parameters on option prices and a demonstrably better calibration fit of the Black Scholes model over the entire volatility surface, in a market with semi Markov regimes.

Jamming-Resistant Multiradio Multichannel Opportunistic Spectrum Access in Cognitive Radio Networks

For achieving optimized spectrum usage, most existing opportunistic spectrum sensing and access protocols model the spectrum sensing and access problem as a partially observed Markov decision process by assuming that the information states and/or the primary users' (PUs) traffic statistics are known a priori to the secondary users (SUs). While theoretically sound, the existing solutions may not be effective in practice due to two main concerns. First, the assumptions are not practical, as before the communication starts, PUs' traffic statistics may not be readily available to the SUs. Second and more serious, existing approaches are extremely vulnerable to malicious jamming attacks. By leveraging the same statistic information and stochastic dynamic decision-making process that the SUs would follow, a cognitive attacker with sensing capability can sense and jam the channels to be accessed by SUs, while not interfering PUs. To address these concerns, we formulate the antijamming, multichannel access problem as a nonstochastic multi-armed bandit problem. By leveraging probabilistically shared information between the sender and the receiver, our proposed protocol enables them to hop to the same set of channels with high probability while gaining resilience to jamming attacks without affecting PUs' activities. We analytically show the convergence of the learning algorithms and derive the performance bound based on regret . We further discuss the problem of tracking the best adaptive strategy and characterize the performance bound based on a new regret . Extensive simulation results show that the probabilistic spectrum sensing and access protocol can overcome the limitation of existing solutions and is highly resilient to various jamming attacks even with jammed acknowledgment (ACK) information.

Introductory Physics for the Life Sciences (IPLS)

Teaching materials have been developed for introductory physics for the life sciences. They are written as self-contained self-study guides. The first chapter introduces students to using Excel using an authentic computational model of diffusion that introduces students to equilibrium as a dynamic stochastic process in the context of the oxygen cascade. Students discover that Fick's law is a consequence of Brownian motion in an active learning exercise using a kinetic Monte Carlo simulation of their own construction. Subsequent chapters introduce students to: algorithms and computational thinking; exponential decay in drug elimination and radioactive decay; half-life and semi-log plots; finite difference methods (and calculus); the principles of scientific modeling; model validation and residual analysis; and osmosis. Analysis of published clinical data and Nobel Prize winning research is featured. Because the materials are self-contained they can be used in a flipped-classroom approach. The chapters are available for free at http://circle4.com/biophysics/chapters/ and have been listed as curricular resources in the recent American association of Physics Teachers (AAPT) report on Introductory Physics for the Life Sciences (IPLS).

Discovery Through Gossip

AbstractWe study randomized gossip‐based processes in dynamic networks that are motivated by information discovery in large‐scale distributed networks such as peer‐to‐peer and social networks. A well‐studied problem in peer‐to‐peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self‐stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network — new edges are added to the network — and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications.This paper studies and analyzes two natural gossip‐based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., “pushes” their mutual information to each other). In the pull discovery process or the two‐hop walk, each node repeatedly requests or “pulls” a random contact from a random neighbor and connects itself to this two‐hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip.Our main result is an almost‐tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n‐node graph both processes take rounds to connect every node to all other nodes with high probability, whereas is a lower bound. We also study the two‐hop walk in directed graphs, and show that it takes time with high probability, and that the worst‐case bound is tight for arbitrary directed graphs, whereas Ω(n2) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 565–587, 2016