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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...
Relations between belief propagation on erasure and symmetric channels
, Article Proceedings - 2004 IEEE International Symposium on Information Theory, Chicago, IL, 27 June 2004 through 2 July 2004 ; 2004 , Pages 209- ; 21578097 (ISSN) ; Sharif University of Technology
2004
Abstract
We give an upper bound on the performance of the belief propagation algorithm in decoding a code over a binary-input output-symmetric channel in terms of the decoding threshold of the code over the erasure channel. Using this upper bound, we obtain the overhead of fountain codes on the erasure channel, provided that they are capacity-achieving on a symmetric channel. The upper bound is similar to a lower bound proved by Khandekar. The lower bound will be used to bound from above the reception overhead of fountain codes on symmetric channels
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...
On group-characterizability of homomorphic secret sharing schemes
, Article Theoretical Computer Science ; Volume 891 , 2021 , Pages 116-130 ; 03043975 (ISSN) ; Khazaei, S ; Parviz, M ; Sharif University of Technology
Elsevier B. V
2021
Abstract
A group-characterizable (GC) random variable is induced by a finite group, called main group, and a collection of its subgroups. The notion extends directly to secret sharing schemes (SSSs). It is known that linear and abelian SSSs can be equivalently described in terms of GC SSSs. In this paper, we present a necessary and sufficient condition for a SSS to be equivalent to a GC one. Using this result, we show that homomorphic SSSs (HSSSs) are equivalent to GC SSSs whose subgroups are normal in the main group. We also present two applications for this equivalent description of HSSSs. One concerns lower bounding the information ratio of access structures for the class of HSSSs, and the other...
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...
Proof of humanity: a tax-aware society-centric consensus algorithm for blockchains
, Article Peer-to-Peer Networking and Applications ; Volume 14, Issue 6 , 2021 , Pages 3634-3646 ; 19366442 (ISSN) ; Fotuhi Firuzabad, M ; Dorri, A ; Dehghanian, P ; Sharif University of Technology
Springer
2021
Abstract
Blockchain technology brings about an opportunity to maintain decentralization in several applications, such as cryptocurrency. With the agents of a decentralized system operating independently, it calls for a consensus protocol that helps all nodes to agree on the state of the ledger. Most of the existing blockchains rely on Proof of Work (PoW) as the underlying consensus algorithm, resulting in a significant amount of electricity power consumption. Furthermore, it demands the miner to buy specific computation devices. Besides, a protocol to gather the society-related taxes such as public education funding and charities is lacking in existing consensus algorithms. In response, this paper...
On the PDF of the sum of random vectors
, Article IEEE Transactions on Communications ; Volume 48, Issue 1 , 2000 , Pages 7-12 ; 00906778 (ISSN) ; Hashemi, H ; Nader Esfahani, S ; Sharif University of Technology
2000
Abstract
There are various cases in physics and engineering sciences (especially communications) where one requires the envelope probability density function (pdf) of the sum of several random sinusoidal signals. According to the correspondence between a random sinusoidal signal and a random vector, the sum of random vectors can be considered as an abstract mathematical model for the above sum. Now it is desired to obtain the pdf of the length of the resulting vector. Considering the common and reasonable assumption of uniform distributions for the angles of vectors, many researchers have obtained the pdf of the length of the resulting vector only for special cases. However in this paper, the pdf is...
Compressibility measures for affinely singular random vectors
, Article IEEE Transactions on Information Theory ; Volume 68, Issue 9 , 2022 , Pages 6245-6275 ; 00189448 (ISSN) ; Amini, A ; Rini, S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2022
Abstract
The notion of compressibility of a random measure is a rather general concept which find applications in many contexts from data compression, to signal quantization, and parameter estimation. While compressibility for discrete and continuous measures is generally well understood, the case of discrete-continuous measures is quite subtle. In this paper, we focus on a class of multi-dimensional random measures that have singularities on affine lower-dimensional subsets. We refer to this class of random variables as affinely singular. Affinely singular random vectors naturally arises when considering linear transformation of component-wise independent discrete-continuous random variables. To...
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...