Markov Random Process Research Articles

Diffusion approximation of the network with limited number of same type customers and time dependent service parameters

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Vector model of wind for performance analysis of stand-alone wind power systems

A statistical model of speed of horizontal wind in the atmosphere, intended for estimating the efficiency of stand-alone wind power systems treated as nonlinear stochastic dynamic systems, is developed. The model is based on the representation of wind as a two-dimensional Gaussian---Markov random process. The method of calculating model parameters by using observation results of the wind magnitude and direction on the land-based weather station is presented. The model parameters are calculated for several locations in Russia. More precise and simplified variants of the model are proposed. The model adequacy is analyzed by comparing the system's efficiency indexes with their reference values.

Distributed Secure Coordinated Control for Multiagent Systems Under Strategic Attacks.

This paper studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov's method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

A random graph model of density thresholds in swarming cells

Swarming behaviour is a type of bacterial motility that has been found to be dependent on reaching a local density threshold of cells. With this in mind, the process through which cell-to-cell interactions develop and how an assembly of cells reaches collective motility becomes increasingly important to understand. Additionally, populations of cells and organisms have been modelled through graphs to draw insightful conclusions about population dynamics on a spatial level. In the present study, we make use of analogous random graph structures to model the formation of large chain subgraphs, representing interactions between multiple cells, as a random graph Markov process. Using numerical simulations and analytical results on how quickly paths of certain lengths are reached in a random graph process, metrics for intercellular interaction dynamics at the swarm layer that may be experimentally evaluated are proposed.

Analysis of Decorrelation Transform Gain for Uncoded Wireless Image and Video Communication.

An uncoded transmission scheme called SoftCast has recently shown great potential for wireless video transmission. Unlike conventional approaches, SoftCast processes input images only by a series of transformations and modulates the coefficients directly to a dense constellation for transmission. The transmission is uncoded and lossy in nature, with its noise level commensurate with the channel condition. This paper presents a theoretical analysis for an uncoded visual communication, focusing on developing a quantitative measurements for the efficiency of decorrelation transform in a generalized uncoded transmission framework. Our analysis reveals that the energy distribution among signal elements is critical for the efficiency of uncoded transmission. A decorrelation transform can potentially bring a significant performance gain by boosting the energy diversity in signal representation. Numerical results on Markov random process and real image and video signals are reported to evaluate the performance gain of using different transforms in uncoded transmission. The analysis presented in this paper is verified by simulated SoftCast transmissions. This provide guidelines for designing efficient uncoded video transmission schemes.

Time-domain multi-state markov model for engine system reliability analysis

A novel reliability-based approach has been developed for multi-state engine systems. Firstly, the output power of the engine is discretized and modeled as a discrete-state continuous-time Markov random process. Secondly, the multi-state Markov model is established. According to the observed data, the transition intensity is determined. Thirdly, the proposed method is extended to compute the forced outage rate and the expected engine capacity deficiency based on time response. The proposed method can therefore be used for forecasting and monitoring the reliability of the multi-state engine utilizing time-domain response data. It is illustrated that the proposed method is practicable, feasible and gives reasonable prediction which conforms to the engineering practice.

Method of compression of digital halftone images on the basis of markov chains with several states

The paper presents a mathematical model (MM) of a digital halftone image (DHI) on the basis of a two-dimensional Markov chain with several states; its adequacy to real images is analyzed. On the basis of MM a method of DHI compression is developed. The method provides separation of DHI into binary images with subsequent combining of two digits in a plane. Each plane is considered as a two-dimensional random Markov process with several (N=4) states. On the basis of the theory of random Markov processes prediction of the plane elements is carried out. All incorrectly predicted elements are located in a bit stream and serve as a reference for the recovery of the image. Separation of areas containing background noise with a structure similar to the white gaussian noise (WGN) is carried out beforehand for the planes containing low- order bits, these areas are not stored, they are filled with WGN samples in case of restoration. The efficiencyof the method is no inferior to that of known methods of compression based on DCT or DWT, it does not involve computing operations and makes it possible to work with multidigital images (8 and more digits) without increase in the time of compression due to parallel processing of the planes.

Kindred Distributions: An Application to Wealth and Income Densities

We describe a simple method to obtain kindred stationary densities of random Markov processes with respect to an Ito transformation function. As applied to income and wealth densities, they are akin to one another because they share the income growth and income volatility shape parameters. The procedure first assumes a linear infinitesimal drift and a quadratic infinitesimal variance, which together with the stationary Kolmogorov forward equation gives rise to a power law income distribution. To find a kindred distribution we assume that the rate of change of wealth is a function of savings from income and the returns from accumulated wealth. Applying the Ito transformation, we then obtain an explicit wealth-income density, which turns out to be another power law density with an augmented exponential term. It shares certain shape parameters with the income density. Another objective of the paper is to learn how volatility affects the specific wealth-income prediction in Piketty-Zucman (2014).

Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension

Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered.

A new technique for testing professional skills and competencies and examples of its practical applications

A new technique for testing professional skills and competencies as well as its practical applications are presented. The approach in question uses modeling and analyzing the spatio-temporal peculiarities of subjects’ oculomotor activity, which are based on the representation of gaze movement on a stimulus surface with the aid of random continuous-time Markov processes with discrete states. The procedure of model parameters estimation provided with goodness-of-fit tests as well as the classifier-building technique, which makes it possible to assess a degree of correspondence between the observed gaze movement distribution and reference distributions identified for different diagnosed groups, were considered. Three examples of practical application of the suggested technique are given as illustrations: assessing a mathematical background level, studying differences in spatio-temporal gaze movement distributions identified for aircraft pilots with different flight proficiency, and assessing skill levels for dispatchers of building automatic control systems.

Quasioptimal nonlinear filtering of laser Doppler vibrometer signals

The problem of quasioptimal nonlinear filtering of heterodyne laser Doppler vibrometer signals is solved in the Gaussian approximation of a posteriori probability density of the vector of estimated parameters. A filtering algorithm is synthesized for the case of monoharmonic vibrations with a fluctuating vibration displacement amplitude model in the form of a normal Markov random process. Mathematical simulation is used to show the efficiency of the algorithm of tracking the unknown parameters of the laser Doppler vibrometer signal in the presence of additive monitoring noise and the deterministic trend of the information parameter.

Behavioral and Emotional Dynamics of Two People Struggling to Reach Consensus about a Topic on Which They Disagree

We studied the behavioral and emotional dynamics displayed by two people trying to resolve a conflict. 59 groups of two people were asked to talk for 20 minutes to try to reach a consensus about a topic on which they disagreed. The topics were abortion, affirmative action, death penalty, and euthanasia. Behavior data were determined from audio recordings where each second of the conversation was assessed as proself, neutral, or prosocial. We determined the probability density function of the durations of time spent in each behavioral state. These durations were well fit by a stretched exponential distribution, with an exponent, , of approximately 0.3. This indicates that the switching between behavioral states is not a random Markov process, but one where the probability to switch behavioral states decreases with the time already spent in that behavioral state. The degree of this “memory” was stronger in those groups who did not reach a consensus and where the conflict grew more destructive than in those that did. Emotion data were measured by having each person listen to the audio recording and moving a computer mouse to recall their negative or positive emotional valence at each moment in the conversation. We used the Hurst rescaled range analysis and power spectrum to determine the correlations in the fluctuations of the emotional valence. The emotional valence was well described by a random walk whose increments were uncorrelated. Thus, the behavior data demonstrated a “memory” of the duration already spent in a behavioral state while the emotion data fluctuated as a random walk whose steps did not have a “memory” of previous steps. This work demonstrates that statistical analysis, more commonly used to analyze physical phenomena, can also shed interesting light on the dynamics of processes in social psychology and conflict management.

Statistical characteristics of the magnitude and location of the greatest maximum of Markov random process with piecewise constant drift and diffusion coefficients

We considered a method for the determining of the statistical characteristics of the magnitude, location and first-passage time of Markov random process, with piecewise constant drift and diffusion coefficients. We found the closed analytical expressions for distribution functions of the specified random variables. We also analyzed the asymptotic behavior of probability density and ordinary moments of location of the greatest maximum of Markov random process and showed their coincidence with some known results for the particular cases.

Methods for Comprehensive Analysis of Heat Supply Reliability

The paper deals with the problem of comprehensive analysis of heat supply reliability for consumers. It implies a quantitative assessment of the impact of all stages of heat energy production and distribution on heat supply reliability for each consumer of the heat supply system. A short review of existing methods for the analysis of fuel and heat supply reliability is presented that substantiates the key approaches to solving the problem of comprehensive analysis of heat supply reliability. A methodological approach is suggested, in which mathematical models and methods for nodal evaluation of heat supply reliability for consumers are developed and the studies on the impact of different elements of fuel and heat supply systems on its level are described. Mathematical modeling is based on the Markov random processes, models of flow distribution in a heat network, deterministic dependences of thermal processes of heat energy consumption and some other models.

Maneuvering target tracking by adaptive statistics model

A good model can extract useful information about the target's state from observations effectively. There are many models used to tracking a, maneuvering target such as constant-velocity (CV) model, Singer acceleration model (zero-mean first-order Markov model) and current model (mean-adaptive acceleration model), etc. While due to the complexity of maneuvering target, to seek the target model which can get better performance is still a subject worthy of study. Based on statistics relation between the autocorrelation function and the covariance of Markov random processing, this paper develops a model which can adaptively adjust system parameters on line. Simulations show the good estimation performance get by the model developed here, and comparing CV, Singer and current models, the model can adaptively get the model parameter while tracking the trajectory and needn't doing several tests to obtain a priori parameter.

Fast Tracking for Video Target Tracking

Fast video tracking can result in irregular sampling tracking problem. This paper transforms the irregular sampling measurement to the time-varying parameters and develops a model with adaptive parameters on line by the autocorrelation function of Markov random processing. Simulations and experiments show the good fast-tracking performance can be get by the model developed here even at very high irregular rate of measurement sampling time.

A Cultural Immune Quantum Evolutionary Algorithm and Its Application

This paper proposes to integrate immune quantum evolutionary algorithm into cultural algorithms frame to develop a more efficient cultural immune quantum evolutionary algorithm (CIQEA). The computing model consists of a population space based on quantum-inspired evolutionary algorithm and a belief space based on immune vaccination, the population space and belief space have their own population evolved independently and parallel. The population space contributes vaccines to the belief population periodically, and the belief space continually evolve these vaccines which are used to provide better evolutionary direction to the population space, to constitute the dual-evolution and dual-improvement mechanism that can improve the global optimization abilities and convergence speed greatly. The convergence of CIQEA is proved based on markov random process and its superiority is shown by the experimental results on the knapsack problem.

COMBINE MARKOV RANDOM FIELDS AND MARKED POINT PROCESSES TO EXTRACT BUILDING FROM REMOTELY SENSED IMAGES

Abstract. Automatic building extraction from remotely sensed images is a research topic much more significant than ever. One of the key issues is object and image representation. Markov random fields usually referring to the pixel level can not represent high-level knowledge well. On the contrary, marked point processes can not represent low-level information well even though they are a powerful model at object level. We propose to combine Markov random fields and marked point processes to represent both low-level information and high-level knowledge, and present a combined framework of modelling and estimation for building extraction from single remotely sensed image. At high level, rectangles are used to represent buildings, and a marked point process is constructed to represent the buildings on ground scene. Interactions between buildings are introduced into the the model to represent their relationships. At the low level, a MRF is used to represent the statistics of the image appearance. Histograms of colours are adopted to represent the building's appearance. The high-level model and the low-level model are combined by establishing correspondences between marked points and nodes of the MRF. We adopt reversible jump Markov Chain Monte Carlo (RJMCMC) techniques to explore the configuration space at the high level, and adopt a Graph Cut algorithm to optimize configuration at the low level. We propose a top-down schema to use results from high level to guide the optimization at low level, and propose a bottom-up schema to use results from low level to drive the sampling at high level. Experimental results demonstrate that better results can be achieved by adopting such hybrid representation.

Markovian geology prediction approach and its application in mountain tunnels

A geology prediction approach based on Markov random process and Bayesian updating procedure is presented in this article. It can dynamically predict the ground conditions ahead of tunnel face in a probabilistic way with very low cost, when the tunnel face advances and new geological information is revealed. The application case study on Chuangshi Tunnel project shows that the prediction results fit the real grounds condition well, especially for the short range ahead of face. This approach can be regarded as a good complement to the geophysical prospecting approach during the construction of mountain tunnels.

Mobility prediction in mobile wireless networks

In realistic mobile ad-hoc network scenarios, the hosts usually travel to the pre-specified destinations, and often exhibit non-random motion behaviors. In such mobility patterns, the future motion behavior of the mobile is correlated with its past and current mobility characteristics. Therefore, the memoryless mobility models are not capable of realistically emulating such a mobility behavior. In this paper, an adaptive learning automata-based mobility prediction method is proposed in which the prediction is made based on the Gauss–Markov random process, and exploiting the correlation of the mobility parameters over time. In this prediction method, using a continuous-valued reinforcement scheme, the proposed algorithm learns how to predict the future mobility behaviors relying only on the mobility history. Therefore, it requires no a prior knowledge of the distribution parameters of the mobility characteristics. Furthermore, since in realistic mobile ad hoc networks the mobiles move with a wide variety of the mobility models, the proposed algorithm can be tuned for duplicating a wide spectrum of the mobility patterns with various randomness degrees. Since the proposed method predicts the basic mobility characteristics of the host (i.e., speed, direction and randomness degree), it can be also used to estimate the various ad-hoc network parameters like link availability time, path reliability, route duration and so on. In this paper, the convergence properties of the proposed algorithm are also studied and a strong convergence theorem is presented to show the convergence of the algorithm to the actual characteristics of the mobility model. The simulation results conform to the theoretically expected convergence results and show that the proposed algorithm precisely estimates the motion behaviors.