Sharif Digital Repository

In this paper1 we consider higher isoperimetric numbers of a (finite directed) graph. In this regard we focus on the nth mean isoperimetric constant of a directed graph as the minimum of the mean outgoing normalized flows from a given set of n disjoint subsets of the vertex set of the graph. We show that the second mean isoperimetric constant in this general setting, coincides with (the mean version of) the classical Cheeger constant of the graph, while for the rest of the spectrum we show that there is a fundamental difference between the nth isoperimetric constant and the number obtained by taking the minimum over all n-partitions. In this direction, we show that our definition is the... 

In this paper. 11This article is a revised version of Daneshgar and Hajiabolhassan (2008) [19] distributed on arXiv.org (1'st, Jan. 2008). we consider higher isoperimetric numbers of a (finite directed) graph. In this regard we focus on the nth mean isoperimetric constant of a directed graph as the minimum of the mean outgoing normalized flows from a given set of n disjoint subsets of the vertex set of the graph. We show that the second mean isoperimetric constant in this general setting, coincides with (the mean version of) the classical Cheeger constant of the graph, while for the rest of the spectrum we show that there is a fundamental difference between the nth isoperimetric constant and... 

In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff–Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which also provides a generalization of a theorem of Mohar (1992) as a necessary condition for Hamiltonicity. In particular, in the case that the range is a Cayley graph or an edge-transitive graph, we obtain theorems with a corollary about the existence of homomorphisms to cycles. This, specially, provides... 

This study provides a stochastic dynamic programming model with a Markov chain that explicitly focuses on the customer as well as a new model for valuing the customers in the banking industry. The proposed framework calculates individual customer’s lifetime value dynamically. The study follows a stochastic dynamic programming model that is based on the Markov chain. The deduced findings are illustrated with supplementary context from an outstanding case study. The findings underline the importance of the stochastic model for calculating customer lifetime value based on customer behavior. The presented framework provides a beneficial way for future research and valuable insight for allocating... 

In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff-Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which also provides a generalization of a theorem of Mohar (1992) as a necessary condition for Hamiltonicity. In particular, in the case that the range is a Cayley graph or an edge-transitive graph, we obtain theorems with a corollary about the existence of homomorphisms to cycles. This, specially, provides... 

In this paper, we consider a cognitive radio network in which multiple Secondary Users (SUs) contend to access primary network's channels with a random access scheme. Our goal is to analyze SUs' queuing delay performance in terms of mean queue lengths and find a minimum buffer space for which the overflow probability is less than a desired threshold. In general, the considered network can be modeled as a multidimensional Markov chain. However, the enormous state space makes the numerical analysis intractable. Nevertheless, the state space can be reduced to a two-dimensional Markov chain in the symmetric channel condition. By this approach, the optimal contention probability that minimizes... 

While the main assumption of an economic model of a variable sample size and sampling interval (VSSI) X-Bar control chart is normality, some process data may not follow a normal distribution. In this paper, a model for an economic design of the VSSI X-Bar chart under non-normality of the process data is first developed. Then a parameter-tuned genetic algorithm is proposed to solve the model and compare its performances in terms of the expected loss per hour to the ones of a fixed sample size and sampling interval X-Bar control charts that works under the normality assumption. Finally, a numerical example is given to illustrate the applications of the proposed methodology and to perform a... 

While the main assumption of an economic model of a variable sample size and sampling interval (VSSI) X-Bar control chart is normality, some process data may not follow a normal distribution. In this paper, a model for an economic design of the VSSI X-Bar chart under non-normality of the process data is first developed. Then a parameter-tuned genetic algorithm is proposed to solve the model and compare its performances in terms of the expected loss per hour to the ones of a fixed sample size and sampling interval X-Bar control charts that works under the normality assumption. Finally, a numerical example is given to illustrate the applications of the proposed methodology and to perform a... 

One of the main tools in radar target recognition is high resolution range profile (HRRP). However, it is very sensitive to the aspect angle. One solution to this problem is to assume the consecutive samples of HRRP identically independently distributed (IID) in small frames of aspect angles, an assumption which is not true in reality. However, based on this assumption, some models have been developed to characterize the sequential information contained in the multi-aspect radar echoes. Therefore, they only consider the short dependency between consecutive samples. Here, we propose an alternative model, the segment model, to address the shortcomings of these assumptions. In addition, using a... 

This study presents a steady-state Markov chain model to predict the long-term probability of drought conditions. The research aims to propose a rigorous framework for statistical analysis of drought characteristics and its trends over time for a large area of aquifers and plains in Iran. For this purpose, two meteorological indicators called the Standardized Precipitation Index (SPI), and the Groundwater Resource Index (GRI) are examined. The groundwater drought study includes more than 26,000 wells in about 600 meteorological stations over 20 years being surveyed daily. This study discusses the spatial interpolation of drought steady-state probabilities based on recorded SPI and GRI data... 

Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the... 

In this paper, an analytical method is developed to compute the project completion time distribution in a dynamic PERT network, where the activity durations are exponentially distributed random variables. The projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. The authors' approach is to transform this dynamic PERT network into a stochastic network and, then, to obtain the project completion time distribution by constructing a proper continuous-time Markov chain. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities... 

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... 

Today's competitive market has witnessed a growing interest in improving the reliability of products in both service and industrial operations. A large number of monitoring schemes have been introduced to effectively control the reliability-related quality characteristics. These methods have focused on single-stage processes or considered quality variables which are independent. However, the main feature of multistage processes is the cascade property which needs to be justified for the sake of optimal process monitoring. The problem becomes complicated when the presence of censored observations is pronounced. Therefore, both the effects of influential covariates and censored data must be... 

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...