Sharif Digital Repository

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  

Marton's region is the best known inner bound for a general discrete memoryless broadcast channel. We establish improved bounds on the cardinalities of the auxiliary random variables. We combine the perturbation technique along with a representation using concave envelopes to achieve this improvement. As a corollary of this result, we show that a randomized time division strategy achieves the entire Marton's region for binary input broadcast channels, extending the previously known result for the sum-rate and validating a previous conjecture due to the same authors  

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... 

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  

Hypercontractivity has had many successful applications in mathematics, physics, and theoretical computer science. In this work we use recently established properties of the hypercontractivity ribbon of a pair of random variables to study a recent conjecture regarding the mutual information between binary functions of the individual marginal sequences of a sequence of pairs of random variables drawn from a doubly symmetric binary source  

In this paper we study the problem of generation of dependent random variables, known as the coordination capacity [4], [5], in multiterminal networks. In this model m nodes of the network are observing i.i.d. repetitions of X (1), X (2),⋯, X (m) distributed according to q(x (1),⋯, x (m)). Given a joint distribution q(x (1),⋯,x (m), y (1), ⋯, y (m)), the final goal of the i th node is to construct the i.i.d. copies of Y (i) after the communication over the network where X (1), X (2),⋯, X (m), Y (1), Y (2),⋯, Y (m) are jointly distributed according to q(x (1), , x (m), y (1),⋯,y (m)). To do this, the nodes can exchange messages over the network at rates not exceeding the capacity constraints... 

Motivated by numerous applications in Monte Carlo techniques and as of late, in deriving non dominated solutions in multi-objective optimization problems, this article addresses generating uniform random variables (λi, λi ≥ 0, i = 1,..., n) over a simplex in ℝ2 (n ≥ 2), i.e., Σi=1 n λi = 1. In this article, first, conditional distribution of λi where Σi=1 n λi = 1 is derived and then inverse method is applied to generate random variables  

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley... 

The authors indicate the dependence between the inputs of the relay channel with one auxiliary random variable as Cover, El-Gamal and Salehi have done for the multiple access channel with arbitrarily correlated sources. Then, by considering broadcast and multiple access sub-channels in the relay channel, the authors describe the essential role of the relay with special Markovity conditions on the auxiliary random variable and channel input-outputs, and unify most of known capacity theorems into one capacity theorem. The capacity theorem potentially may be applicable to a more general class of relay channels including at least the relay channels with known capacity. © The Institution of... 

The total cost of earthquakes is in this paper modeled as a continuous random variable that includes the cost of damage and the cost of construction to prevent damage. Realizations of this variable are obtained by evaluating an array of probabilistic models that take many basic random variables as input. Consequently, analyses can be conducted to determine the mean cost, as well as cost exceedance probabilities and other measures of seismic risk. Such results are employed to address the underlying decision problem, namely to minimize the total cost of earthquakes when that cost is a continuous random variable. Applicable decision theories are outlined and several risk measures are... 

Marton's inner bound is the tightest known inner bound on the capacity region of the broadcast channel. It is not known, however, if this bound is tight in general. One approach to settle this key open problem in network information theory is to investigate the multiletter extension of Marton's bound, which is known to be tight in general. This approach has become feasible only recently through the development of a new method for bounding cardinalities of auxiliary random variables by Gohari and Anantharam. This paper undertakes this long overdue approach to establish several new results, including 1) establishing the optimality of Marton's bound for new classes of product broadcast... 

Cut-set bounds are not, in general, tight for all classes of network communication problems. In this paper, we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, which results in bounds that are tighter than the corresponding cut-set bounds. We also define the concept of 'uncertainty region' which might be of independent interest. We provide a full characterization of this region for the case of two correlated random variables. The bounding technique works as follows: on one hand, we show that if the communication problem is solvable, the uncertainty of certain random variables in the network with respect to imaginary parties... 

In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to... 

In this paper, we investigate the effect of applying an exponential window on the limiting spectral distribution (l.s.d.) of the exponentially windowed sample covariance matrix (SCM) of complex array data. We use recent advances in random matrix theory which describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We derive an explicit expression for the l.s.d. of the noise-only data. Simulations are performed to support our theoretical claims  

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... 

Cut-set bounds on achievable rates for network communication protocols are not in general tight. In this paper we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that results in bounds that are tighter than the corresponding cut-set bounds. We also define the concept of "uncertainty region" which might be of independent interest. We provide a full characterization of this region for the case of two correlated random variables. The bounding technique works as follows: on one hand we show that if the communication problem is solvable, the uncertainty of certain random variables in the network with respect to imaginary parties... 

Bell's theorem states that quantum mechanics is not a locally causal theory. This state is often interpreted as nonlocality in quantum mechanics. Toner and Bacon [Phys. Rev. Lett. 91, 187904 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.187904] have shown that a shared random-variable theory augmented by one bit of classical communication exactly simulates the Bell correlation in a singlet state. In this paper, we show that in Toner and Bacon protocol, one of the parties (Bob) can deduce another party's (Alice) measurement outputs, if she only informs Bob of one of her own outputs. Afterwards, we suggest a nonlocal version of Toner and Bacon protocol wherein classical communications is... 

In many wireless communication protocols, small and random delay, called jitter, is imposed before packet transmission so as to reduce packet collisions. Jitter is recommended for many routing protocols such as AODV and LOADng. Jitter can be exploited to change the order of routes about which destination is informed and, as a result, make better routes, regarding their metric, more likely to choose by the destination. However, to the best of our knowledge, there is only one mechanism, called adaptive jitter mechanism, proposed for metric-based routing protocols. In this paper, we aim to show feasibility of using different random variables for jittering and define some shaping functions to...