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#### Fuzzy random minimum cost network problem [electronic resource]

, Article Journal of Industrial and Systems Engineering ; Vol. 6, No. 1, pp 34-47, 2012 ; Eshghi, Kourosh ; Sharif University of Technology
Abstract

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

#### A resource constrained project scheduling problem with fuzzy random duration [electronic resource]

, Article Journal of Uncertain Systems ; Vol.4, No.2, pp.123-132, 2010 ; Eshghi, Kourosh ; Eshragh Jahromi, Abdolhamid ; Sharif University of Technology
Abstract

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

#### Improved cardinality bounds on the auxiliary random variables in Marton's inner bound

, Article IEEE International Symposium on Information Theory - Proceedings ; 2013 , Pages 1272-1276 ; ISSN: 21578095 ; ISBN: 9781479904464 ; Gohari, A ; Nair, C ; Sharif University of Technology
2013

Abstract

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 of a more general class of relay channels

, Article 2008 International Symposium on Information Theory and its Applications, ISITA2008, Auckland, 7 December 2008 through 10 December 2008 ; April , 2008 ; 9781424420698 (ISBN) ; Aref, M. R ; Commemorative Organization for the Japan World; Exposition('70); Support Center for Advanced Telecommunications; Technology Research; REFEC Research Foundation for the; Electrotechnology of Chubu ; Sharif University of Technology
2008

Abstract

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 fuzzy random minimum cost network flow programming problem [electronic resource]

, Article Journal of Industrial and Systems Engineering (JISE)-Iranian Institute of Industrial Engineering ; Article 3, Volume 6, Issue 1, Spring 2012, Page 34-47 ; Eshghi, Kourosh ; Sharif University of Technology
Abstract

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

#### On hypercontractivity and the mutual information between Boolean functions

, Article 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013, Monticello, IL ; Oct , 2013 , Pages 13-19 ; 9781479934096 (ISBN) ; Gohari, A. A ; Kamath, S ; Nair, C ; Sharif University of Technology
IEEE Computer Society
2013

Abstract

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

#### Generating dependent random variables over networks

, Article 2011 IEEE Information Theory Workshop, ITW 2011 ; 2011 , Pages 698-702 ; 9781457704376 (ISBN) ; Anantharam, V ; Sharif University of Technology
Abstract

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...

#### Conditional distribution inverse method in generating uniform random vectors over a simplex

, Article Communications in Statistics: Simulation and Computation ; Volume 40, Issue 5 , Dec , 2011 , Pages 685-693 ; 03610918 (ISSN) ; Abbasi, B ; Mahlooji, H ; Sharif University of Technology
Abstract

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

#### On the evaluation of marton’s inner bound for two-receiver broadcast channels

, Article IEEE Transactions on Information Theory ; 2018 ; 00189448 (ISSN) ; Gohari, A ; Nair, C ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018

Abstract

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...

#### Unified approach to the capacity evaluation of the relay channel

, Article IET Communications ; Volume 3, Issue 7 , 2009 , Pages 1208-1215 ; 17518628 (ISSN) ; Aref, M. R ; Sharif University of Technology
2009

Abstract

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...

#### Risk measures for minimization of earthquake costs

, Article Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 ; 2013 , Pages 2619-2626 ; 9781138000865 (ISBN) ; Allahdadian, S ; Mahsuli, M ; Sharif University of Technology
2013

Abstract

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...

#### Defining a Correlation Measure for Random Variables Derived from SSP

, M.Sc. Thesis Sharif University of Technology ; Amini, Arash (Supervisor) ; Aminzadeh-Gohari, Amin (Co-Supervisor)
Abstract

Studying the statistical dependence of two or several random variables is the basis of statistical estimation and prediction. The correlation measures such as mutual information, Pearson correlation, and maximal correlation are common tools in quantifying the extent to which two random variables are dependent. While such measures are highly informative and computationally simple for jointly Gaussian random variables, it is not the case for general random variables. Infinitely divisible random variables are typical examples that are characterized in the Fourier domain (characteristic functions are known); except for a few special cases, no closed-form expressions are available for the...

#### On marton's inner bound and its optimality for classes of product broadcast channels

, Article IEEE Transactions on Information Theory ; Vol. 60, Issue. 1 , 2014 , pp. 22-41 ; ISSN: 0018-9448 ; Gohari, A ; Nair, C ; Yu, Y ; Sharif University of Technology
Abstract

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...

#### Beyond the cut-set bound: Uncertainty computations in network coding with correlated sources

, Article IEEE Transactions on Information Theory ; Volume 59, Issue 9 , 2013 , Pages 5708-5722 ; 00189448 (ISSN) ; Yang, S ; Jaggi, S ; Sharif University of Technology
2013

Abstract

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...

#### Limiting spectral distribution of the sample covariance matrix of the windowed array data

, Article Eurasip Journal on Advances in Signal Processing ; Volume 2013, Issue 1 , 2013 ; 16876172 (ISSN) ; Gazor, S ; Bastani, M. H ; Sharif University of Technology
2013

Abstract

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...

#### Spectral distribution of the exponentially windowed sample covariance matrix

, Article ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 25 March 2012 through 30 March 2012, Kyoto ; 2012 , Pages 3529-3532 ; 15206149 (ISSN) ; 9781467300469 (ISBN) ; Bastani, M. H ; Gazor, S ; Sharif University of Technology
IEEE
2012

Abstract

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

#### Channel simulation via interactive communications

, Article IEEE International Symposium on Information Theory - Proceedings ; 2012 , Pages 3053-3057 ; 9781467325790 (ISBN) ; Gohari, A ; Aref, M. R ; Sharif University of Technology
IEEE
2012

Abstract

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...

#### Beyond the cut-set bound: Uncertainty computations in network coding with correlated sources

, Article IEEE International Symposium on Information Theory - Proceedings, 31 July 2011 through 5 August 2011 ; July , 2011 , Pages 598-602 ; 21578104 (ISSN) ; 9781457705953 (ISBN) ; Yang, S ; Jaggi, S ; Sharif University of Technology
2011

Abstract

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...

#### Investigation of quantum-entanglement simulation in random-variable theories augmented by either classical communication or nonlocal effects

, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 92, Issue 5 , November , 2015 ; 10502947 (ISSN) ; Sharif University of Technology
American Physical Society
2015

Abstract

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...

#### Impact of jitter mechanisms on metric-based wireless routing protocols

, Article 2016 IEEE International Conference on Wireless Communications, Signal Processing and Networking, 23 March 2016 through 25 March 2016 ; 2016 , Pages 574-578 ; 9781467393379 (ISBN) ; Hemmatyar, A. M. A ; Cognizant; DRDO; et al.; IEEE; ISRO; SSN ; Sharif University of Technology
Presses Polytechniques Et Universitaires Romandes

Abstract

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...