Sharif Digital Repository

This article considers the Marsaglia effect by proposing a new test of randomness for Lehmer random number generators. Our test is based on the Manhattan distance criterion between consecutive pairs of random numbers rather than the usually adopted Euclidian distance. We derive the theoretical distribution functions for the Manhattan distance for both overlapping (two dimensional) as well as non-overlapping cases. Extensive goodness-of-fit testing as well as empirical experimentation provides ample proof of the merits of the proposed criterion  

A Santha-Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for nonbinary sequences. We show that unlike the binary setup of Santha and Vazirani, deterministic randomness extraction in the generalized case is sometimes possible. In particular, if the adversary has access to s "nondegenerate" dice that are c-sided and can choose one die to throw based on the previous realizations of the dice, then deterministic randomness... 

We introduce a method by which stochastic processes are mapped onto complex networks. As examples, we construct the networks for such time series as those for free-jet and low-temperature helium turbulence, the German stock market index (the DAX), and white noise. The networks are further studied by contrasting their geometrical properties, such as the mean length, diameter, clustering, and average number of connections per node. By comparing the network properties of the original time series investigated with those for the shuffled and surrogate series, we are able to quantify the effect of the long-range correlations and the fatness of the probability distribution functions of the series... 

A Santha-Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for nonbinary sequences. We show that unlike the binary case, deterministic randomness extraction in the generalized case is sometimes possible. We present a necessary condition and a sufficient condition for the possibility of deterministic randomness extraction. These two conditions coincide in “non-degenerate” cases. Next, we turn to a distributed setting. In... 

In this paper, we study the problem of channel simulation via interactive communication, known as the coordination capacity, in a two-terminal network. We assume that two terminals observe i.i.d. copies of two random variables and would like to generate i.i.d. copies of two other random variables jointly distributed with the observed random variables. The terminals are provided with two-way communication links, and shared common randomness, all at limited rates. Two special cases of this problem are the interactive function computation studied by Ma and Ishwar, and the tradeoff curve between one-way communication and shared randomness studied by Cuff. The latter work had inspired Gohari and... 

Synchronization is a phenomenon that occurs in systems of interacting units, and is widespread in nature, society and technology. Recent studies have enlightened us regarding the interplay between synchronization dynamics and interaction structure. However, most of these studies neglect that real-world networks may actually be directed and disconnected. Here, we study the synchronization of directed networks with multiple leaders using the Kuramoto model. We found that in networks with high driving strength, the steady-state frequency of each node is determined by the linear combination of leaders natural frequencies, with structural coe?cients that can be calculated using the eigenvectors... 

Based on extensive new numerical simulations, we show that Chu's arguments and objections against our previous results are invalid. In addition, we explain the origin of the differences between our results and the previous ones, obtained based on a simple model of one-dimensional disordered materials. © 2008 The American Physical Society  

Propagation of acoustic waves in strongly heterogeneous elastic media is studied using renormalization group analysis and extensive numerical simulations. The heterogeneities are characterized by a broad distribution of the local elastic constants. We consider both Gaussian-white distributed elastic constants, as well as those with long-range correlations with a nondecaying power-law correlation function. The study is motivated in part by recent analysis of experimental data for the spatial distribution of the elastic moduli of rock at large length scales, which indicated that the distribution contains the same type of long-range correlations as what we consider in the present paper. The... 

We obtain an exact analytical expression for magnetoresistance using noncommutative geometry and quantum groups. We then show there is a deep relationship between magnetoresistance and the quantum group suq(2), from which we understand the quantum interpretation of the quantum corrections to the conductivity  

We obtain an exact analytical expression for magnetoresistance using noncommutative geometry and quantum groups. Then we will show that there is a deep relationship between magnetoresistance and the quantum group su q(2), from which we understand the quantum interpretation of the quantum corrections to the conductivity. © 2003 Elsevier B.V. All rights reserved  

In this paper, we will discuss two special classes of mathematical programming models with fuzzy random variables. In the first model, a linear programming problem with fuzzy decision variables and fuzzy random coefficients is introduced. Then an algorithm is developed to solve the model based on fuzzy optimization method and fuzzy ranking method. In the second model, a fuzzy random quadratic spanning tree problem is presented. Then the proposed problem is formulated and solved by using the scalar expected value of fuzzy random variables. Furthermore, illustrative numerical examples are also given to clarify the methods discussed in this paper  

Hidden Markov Model (HMM)-based synthesis (HTS) has recently been confirmed to be the most effective method in generating natural speech. However, it lacks adequate context generalization when the training data is limited. As a solution, current study provides a new context-dependent speech modeling framework based on the Gaussian Conditional Random Field (GCRF) theory. By applying this model, an innovative speech synthesis system has been developed which can be viewed as an extension of Context-Dependent Hidden Semi Markov Model (CD-HSMM). A novel Viterbi decoder along with a stochastic gradient ascent algorithm was applied to train model parameters. Also, a fast and efficient parameter... 

Generation of random numbers is one of the most important steps in cryptographic algorithms. High endurance, high performance and low energy consumption are the attractive features offered by the Magnetic Tunnel Junction (MTJ) devices. Therefore, they have been considered as one of the promising candidates for next-generation digital integrated circuits. In this paper, a new circuit design for true random number generation using MTJs is proposed. Our proposed circuit offers a high speed, low power and a truly random number generation. In our design, we employed two MTJs that are configured in special states. Generated random bit at the output of the proposed circuit is returned to the write... 

How can we remove some interactions (generate shorter clauses) in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e., random K -satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will directly provide the solutions of the original problem. © 2006... 

Capacity has been found for degraded, reversely degraded, full feedback, semi-deterministic, orthogonal relay channels, also for a class of deterministic relay channels and a class of modulo sum relay channels. We indicate what the relay decodes and forwards with one auxiliary random variable having bounded cardinality and attempt to define a more general class of relay channels in order to unify most of known capacity theorems into one capacity theorem by considering additional assumptions imposed to the definition of those channels. In other words, the relay channel inputs are dependent as in multiple access channel with arbitrarily correlated sources and here we do for the relay channel... 

A known theorem in probability is adopted and through a probabilistic approach, it is generalized to develop a method for generating random deviates from the distribution of any continuous random variable. This method, which may be considered as an approximate version of the Inverse Transform algorithm, takes two random numbers to generate a random deviate, while maintaining all the other advantages of the Inverse Transform method, such as the possibility of generating ordered as well as correlated deviates and being applicable to all density functions, regardless of their parameter values. © Sharif University of Technology, October 2008  

In this paper, a fuzzy random minimum cost flow problem is presented. In this problem, cost parameters and decision variables are fuzzy random variables and fuzzy numbers respectively. The object of the problem is to find optimal flows of a capacitated network. Then, two algorithms are developed to solve the problem based on Er-expected value of fuzzy random variables and chance-constrained programming. Furthermore, the results of two algorithms will be compared. An illustrative example is also provided to clarify the concept  

In this paper, first a fuzzy random resource-constrained project scheduling problem is presented. The object of the problem is to find the optimal scheduling of project activities. In this model, duration of project activities is a fuzzy random variable. Then, the proposed model is formulated by using the expected value of fuzzy random variables as an IP model. An illustrative example is also provided to clarify the concept. © 2010 World Academic Press, UK. All rights reserved  

In this paper, a special class of redundancy optimization problem with fuzzy random variables is presented. In this model, fuzzy random lifetimes are considered as basic parameters and the Er-expected of system lifetime is used as a major type of system performance. Then a redundancy optimization problem is formulated as a binary integer programming model. Furthermore, illustrative numerical examples are also given to clarify the methods discussed in this paper  

Disruptions rarely occur in supply chains, but their negative financial and technical impacts make the recovery process very slow. In this paper, we propose a capacitated supply chain network design (SCND) model under random disruptions both in facility and transportation, which seeks to determine the optimal location and types of distribution centers (DC) and also the best plan to assign customers to each opened DC. Unlike other studies in the extent literature, we use new concepts of reliability to model the strategic behavior of DCs and customers at the network: (1) Failure of DCs might be partial, i.e. a disrupted DC might still be able to serve with a portion of its initial capacity (2)...