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In this paper, a kind of finite-step random walks with three absorption boundaries is studied. First, the general expression of absorption probability for the random dots being absorbed by the three absorption boundaries is obtained. Second, the related mathematical proofs are provided.
This paper applies the theory of stochastic processes to quantitatively study the dynamical behavior of mass mind under the influence of "group pressure" quantified by a submissive parameter. A finite state irreducible Markov chain whose transition probability matrix depends on the submissive parameter is introduced to describe the composition and evolution of mass attitudes. The microstructure...
This paper is to study nonparametric Bayesian estimation for a proportional hazards model with "long-term survivors". The cumulative hazards function is modeled by a beta process, and the priors of the cure rate and coefficient of covariates can be improper distributions under the proposed model. The posterior estimators of the cure rate, the coefficient for covariates and the survival function...
This paper proposes a data acquisition scheme which supports probabilistic data quality assurance in an error-prone wireless sensor network (WSN). Given a query and a statistical model of real-world data which is highly correlated, the aim of the scheme is to find a sensor selection scheme which is used to deal with inaccurate data and probabilistic guarantee on the query result. Since most sensor...
Automated analysis of fluorescence microscopy data relies on robust segmentation and tracking algorithms for sub-cellular structures in order to generate quantitative results. The accuracy of the image processing results is, however, frequently unknown or determined a priori on synthetic benchmark data. We present a particle filter framework based on Markov Chain Monte Carlo methods and adaptive annealing...
This article considers the issue of dynamic spectrum access in time domain, in which the secondary user seeks spectrum vacancy between bursty transmissions of the primary user to communicate. Since spectrum sensing and data transmission can not be done simultaneously in the same band, the secondary user should employ the sense-then-transmit strategy to detect the presence of primary user before accessing...
This paper provides a conceptually simple, memoryless-style proof to the capacity of the Anantharam and Verdu's exponential server timing channel (ESTC). The approach is inspired by Rubin's approach for characterizing the rate-distortion of a Poisson process with structured distortion measures. This approach obviates the need for using the information density to prove achievability, by exploiting:...
This paper introduces the problem of determining through distributed consensus the fastest mixing Markov chain with a desired sparsity pattern. In contrast to the centralized optimization-based problem formulation, we develop a novel distributed relaxation by constructing a dynamical system over the cross product of an appropriately patterned set of stochastic matrices. In particular, we define a...
This paper presents new results in observer-based robust fault reconstruction for uncertain systems using cascaded sliding mode observers. Signals from an observer are used as the output of a fictitious system whose input is the fault. Then an observer is implemented for the fictitious system. This process is repeated until the first Markov parameter of the fictitious system is full rank. The result...
We investigate the Gaussian, three-nodes relay channel with orthogonal receive components, i.e., the transmitted signals from the source and the relay do not interfere with each other. We develop and analyze low-complexity symbol-wise (as opposed to block-wise) relaying strategies based on a one-dimensional, parametric piecewiselinear (PL) mapping. We numerically compute and optimize the achievable...
Practical problems require the synthesis of a set of stabilizing controllers that guarantee transient performance specifications such as a bound on the overshoot of its closed loop step response. A majority of these specifications for linear time invariant (LTI) systems can be converted to the requirement of synthesizing a set of stabilizing controllers guaranteeing the non-negative impulse response...
This paper is concerned with an information-theoretic framework to aggregate a large-scale Markov chain to obtain a reduced order Markov model. The Kullback-Leibler (K-L) divergence rate is employed as a metric to measure the distance between two stationary Markov chains. Model reduction is obtained by considering an optimization problem with respect to this metric. The solution is just the optimal...
For stochastic hybrid systems, safety verification methods are very little supported mainly because of complexity and difficulty of the associated mathematical problems. The key of the methods that succeeded in solving various instances of this problem is to prove the equivalence of these instances with known problems. In this paper, we apply the same pattern to the most general model of stochastic...
We study the adaptive control problems of a class of discrete-time partially observed Markov decision processes whose transition kernels are parameterized by a unknown vector. Given a sequence of parameter estimates converging to the true value with probability 1, we propose an adaptive control policy and show that under some conditions this policy is self-optimizing in the long-run average sense.
High density probe-based storage devices use multiple, simultaneously accessed parallel channels for achieving high I/O data rates. This paper presents an analytical methodology for evaluating the performance of coding and interleaving schemes in such devices, when they are affected by burst errors. Markov processes are used to describe the burstiness of errors due to external disturbances and analytical...
In this work we study source coding problems where a helper provides rate-limited side information to the involved parties. We first consider the Wyner-Ziv problem, where in addition to the memoryless side information available to the decoder, a helper sends common, rate-limited side information to the encoder and decoder. A single letter characterization of the achievable rates is derived, under...
We introduce a new methodology to construct a Gaussian mixture approximation to the true filter density in hybrid Markovian switching systems. We relax the assumption that the mode transition process is a Markov chain and allow it to depend on the actual and unobservable state of the system. The main feature of the method is that the Gaussian densities used in the approximation are selected as the...
The pseudo self similar processes are quite attractive due to their simplicity but the question we are interested in this paper concerns the basic estimation of such models. How do the standard estimators (sample mean and variance) converge with time? This will give us an indication about the time we have to collect data in order to accurately model them. With no surprise we notice that this is dependant...
In this paper, we investigate the state preparation problem of quantum noiselsss subsystems for the quantum Markovian systems via quantum feedback control. The controlled dynamics we consider are given by the so-called stochastic master equation including the coupling terms with the environment. We formulate the problem as a stochastic stabilization problem of an invariant set. This formulation allows...
In this paper an optimal Kalman filter design problem is studied for networked stochastic linear discrete-time systems with random measurement delays, packet dropouts and missing measurements. Any of these three uncertainties in the measurement can occur in the network in the same run. Based on a Markov chain, we develop a unified/combined model to accommodate random delay, packet dropouts and missing...
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