Sharif Digital Repository

Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal's coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact... 

In this paper, a new on-line handwritten signature verification system using Hidden Markov Model (HMM) is presented. The proposed system segments each signature based on its perceptually important points and then computes for each segment a number of features that are scale and displacement invariant. The resulted sequence is then used for training an HMM to achieve signature verification. Our database includes 622 genuine signatures and 1010 forgery signatures that were collected from a population of 69 human subjects. Our verification system has achieved a false acceptance rate (FAR) of 4% and a false rejection rate (FRR) of 12%. © 2003 IEEE  

Consider a number of parallel queues, each having unlimited capacity and multiple identical exponential servers. The service discipline in each queue is first-come-first-served (FCFS). Customers arrive according to a state-dependent Poisson process with an arrival rate which is a function of the total number of customers in the system. Upon arrival, a customer joins a queue according to a state-dependent stationary policy, where the state of the system is taken to be the number of customers in each queue. No jockeying among queues is allowed. Each arriving customer has a generally distributed deadline until the beginning of its service, after which it must depart the system immediately. An... 

In this paper, we apply the stochastic dynamic programming to find the dynamic shortest path from the source node to the sink node in stochastic dynamic networks, in which the arc lengths are independent random variables with exponential distributions. In each node there is an environmental variable, which evolves in accordance with a continuous time Markov process. The parameter of the exponential distribution of the transition time of each arc is also a function of the state of the environmental variable of its initiative node. Upon arriving at each node, we can move toward the sink node through the best outgoing arc or wait. At the beginning, it is assumed that upon arriving at each node,... 

Statistical properties of interbeat intervals cascade in human hearts are evaluated by considering the joint probability distribution P(Δx 2, τ 2 Δx1, τ 1) for two interbeat increments Δx1 and Δx2 of different time scales τ 1 and τ 2. We present evidence that the conditional probability distribution P(Δx2, τ2|Δx1, τ 1 ) may be described by a Chapman-Kolmogorov equation. The corresponding Kramers-Moyal (KM) coefficients are evaluated. The analysis indicates that while the first and second KM coefficients take on well-defined and significant values, the higher-order coefficients in the KM expansion are small. As a result, the joint probability distributions of the increments in the interbeat... 

By applying shortest path analysis in stochastic networks, we introduce a new approach to obtain the reliability function of time-dependent systems. We assume that not all elements of the system are set to function from the beginning. Upon the failure of each element of the active path in the reliability graph, the system switches to the next path. Then, the corresponding elements are activated, and consequently, the connection between the input and the output is established. It is also assumed that each element exhibits a constant hazard rate and its lifetime is a random variable with exponential distribution. To evaluate the system reliability, we construct a directed stochastic network... 

In this chapter we provide mathematical tools to study the stochastic process from the physical point of view. © 2019, Springer Nature Switzerland AG  

In this chapter we provide mathematical tools to study the stochastic process from the physical point of view. © 2019, Springer Nature Switzerland AG  

In this paper we present a method for transient analysis of availability and survivability of a system with the identical components and identical repairmen. The considered system is supposed to consist of series of k-out-of-n or parallel components. We employed the Markov models, eigen vectors and eigenvalues for analyzing the transient availability and survivability of the system. The method is implemented through an algorithm which is tested in MATLAB programming environment. The new method enjoys a stronger mathematical foundation and more flexibility for analyzing the transient availability and survivability of the system. © 2006 Elsevier Inc. All rights reserved  

In this paper a reliability model for power transformer protection is proposed. The model is an extension of a previously proposed Markov model for transmission line protection. Optimum routine test and self checking intervals of the power transformer protection system are determined using the extended Markov model. © 2006 IEEE  

This paper introduces an analytical method for approximating the fraction of jobs that miss their deadlines in a real-time system when earliest-deadline-first scheduling policy (EDF) is used. In the system, jobs either all have deadlines until the beginning of service or deadlines until the end of service. In the former case, EDF is known to be optimal and, in the latter case, it will be optimal if preemption is allowed. In both cases, the system is modeled by an M/M/1/EDF+M queue, i.e., a single server queue with Poisson arrival, and service times and customer impatience, which are exponentially distributed. The optimality property of EDF is used for the estimation of a key parameter, γn... 

We investigate the Markov property of rough surfaces. Using stochastic analysis, we characterize the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation. The obtained Langevin equation enables us to regenerate surfaces with similar statistical properties compared with the observed morphology by atomic force microscopy. © 2003 The American Physical Society  

This paper presents a robust tracking approach to handle challenges such as occlusion and appearance change. Here, the target is partitioned into a number of patches. Then, the appearance of each patch is modeled using a dictionary composed of corresponding target patches in previous frames. In each frame, the target is found among a set of candidates generated by a particle filter, via a likelihood measure that is shown to be proportional to the sum of patch-reconstruction errors of each candidate. Since the target's appearance often changes slowly in a video sequence, it is assumed that the target in the current frame and the best candidates of a small number of previous frames, belong to... 

The simultaneous emergence of several abrupt disease outbreaks or the extinction of some serotypes of multistrain diseases are fingerprints of the interaction between pathogens spreading within the same population. Here, we propose a general and versatile benchmark to address the unfolding of both cooperative and competitive interacting diseases. We characterize the explosive transitions between the disease-free and the epidemic regimes arising from the cooperation between pathogens and show the critical degree of cooperation needed for the onset of such abrupt transitions. For the competing diseases, we characterize the mutually exclusive case and derive analytically the transition point... 

We consider a queuing loss system with heterogeneous skill based servers and Poisson arrivals. We first assume that each arrival has a vector (X1,…,Xn) of independent binary random variables with Xi=1 if server i is eligible to serve that arrival. The service time at server i is exponential with rate μi. Arrivals finding no servers that are both idle and eligible to serve them are lost. Assuming the system incurs a cost of one unit for each lost customer, our goal is to find the optimal policy for assigning arrivals to idle and eligible servers so as to minimize the expected discounted cost of the system. Later, we generalize our model by considering k server pools where each pool i is... 

In this study, a method for transient analysis of availability and survivability of a system with the standby components is presented. The availability and survivability of the standby systems is evaluated in two cases, the standby systems with the identical components and the standby systems with the non-identical components. In this study the Markov models, eigen vectors and eigen values for analyzing the transient availability and survivability of the system are employed. The method is implemented through an algorithm which is tested in MATLAB (matrix laboratory) programming environment. The new method enjoys a stronger mathematical foundation and more flexibility for analyzing the... 

In a deregulated electric power utility industry in which a competitive electricity market can influence system reliability, market risks cannot be ignored. This paper (1) proposes an analytical probabilistic model for reliability evaluation of competitive electricity markets and (2) develops a methodology for incorporating the market reliability problem into HLII reliability studies. A Markov state space diagram is employed to evaluate the market reliability. Since the market is a continuously operated system, the concept of absorbing states is applied to it in order to evaluate the reliability. The market states are identified by using market performance indices and the transition rates... 

In a deregulated electric power system in which a competitive electricity market can influence system reliability, system analysts are rapidly recognizing that they cannot ignore market risks. This paper first proposes an analytical probabilistic model for the reliable evaluation of competitive electricity markets and then develops a methodology for incorporating the market reliability problem into composite power system reliability studies. The market reliability is evaluated using the Markov state space diagram. Since the market is a continuously operated system, the concept of absorbing states is applied to it in order to evaluate reliability. The market states are identified using market...