Results 1  10
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98
Efficient power control via pricing in wireless data networks
 IEEE Transactions on Communication
, 2000
"... A major challenge in operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With increasing demand for wireless data servic ..."
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Cited by 201 (6 self)
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A major challenge in operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash equilibrium that is ine#cient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e. to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system.
On Projection Algorithms for Solving Convex Feasibility Problems
, 1996
"... Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of the ..."
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Cited by 142 (24 self)
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Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated . Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given. 1991 M.R. Subject Classification. Primary 47H09, 49M45, 6502, 65J05, 90C25; Secondary 26B25, 41A65, 46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65K05, 90C90, 92C55. Key words and phrases. Angle between two subspaces, averaged mapping, Cimmino's method, computerized tomography, convex feasibility problem, convex function, convex inequalities, convex programming, convex set, Fej'er monotone sequence, firmly nonexpansive mapping, H...
Entanglement of a pair of quantum bits
 Physical Review Letters
, 1997
"... The “entanglement of formation ” of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for the entanglement of formation for all mixed states of two qu ..."
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Cited by 34 (0 self)
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The “entanglement of formation ” of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two nonzero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system. PACS numbers: 03.65.Bz, 89.70.+c 1 Entanglement is the potential of quantum states to exhibit correlations that cannot be accounted for classically. For decades, entanglement has been the focus of much work in the foundations of quantum mechanics, being associated particularly with quantum nonseparability and the violation of Bell’s inequalities [1]. In recent years, however, it has begun to be viewed also as a potentially useful resource. The predicted capabilities of a quantum computer, for example, rely crucially on entanglement [2], and a proposed quantum cryptographic scheme achieves security by converting shared entanglement into a shared secret key [3]. For both theoretical and potentially practical reasons, it has become interesting to quantify entanglement, just as we quantify other resources such as energy and information. In this letter we adopt a recently proposed quantitative definition of entanglement and derive an explicit formula for the entanglement of a large class of states of a pair of binary quantum systems (qubits). The simplest kind of entangled system is a pair of qubits in a pure but nonfactorizable state. A pair of spin 1 particles in the singlet state 2 1 √ (  ↑↓ 〉 −  ↓↑〉) is perhaps the most familiar example, but one can also
Hopfield models as generalized random mean field models. Mathematical aspects of spin glasses and neural networks
 3–89, Progr. Probab., 41 Birkhäuser
, 1998
"... Abstract: We give a comprehensive selfcontained review on the rigorous analysis of the thermodynamics of a class of random spin systems of mean field type whose most prominent example is the Hopfield model. We focus on the low temperature phase and the analysis of the Gibbs measures with large devi ..."
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Cited by 30 (9 self)
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Abstract: We give a comprehensive selfcontained review on the rigorous analysis of the thermodynamics of a class of random spin systems of mean field type whose most prominent example is the Hopfield model. We focus on the low temperature phase and the analysis of the Gibbs measures with large deviation techniques. There is a very detailed and complete picture in the regime of “small α”; a particularly satisfactory result concerns a nontrivial regime of parameters in which we prove 1) the convergence of the local “mean fields ” to gaussian random variables with constant variance and random mean; the random means are from site to site independent gaussians themselves; 2) “propagation of chaos”, i.e. factorization of the extremal infinite volume Gibbs measures, and 3) the correctness of the “replica symmetric solution ” of Amit, Gutfreund and Sompolinsky [AGS]. This last result was first proven by M. Talagrand [T4], using different techniques.
A convergent incremental gradient method with constant step size
 SIAM J. OPTIM
, 2004
"... An incremental gradient method for minimizing a sum of continuously differentiable functions is presented. The method requires a single gradient evaluation per iteration and uses a constant step size. For the case that the gradient is bounded and Lipschitz continuous, we show that the method visits ..."
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Cited by 26 (2 self)
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An incremental gradient method for minimizing a sum of continuously differentiable functions is presented. The method requires a single gradient evaluation per iteration and uses a constant step size. For the case that the gradient is bounded and Lipschitz continuous, we show that the method visits regions in which the gradient is small infinitely often. Under certain unimodality assumptions, global convergence is established. In the quadratic case, a global linear rate of convergence is shown. The method is applied to distributed optimization problems arising in wireless sensor networks, and numerical experiments compare the new method with the standard incremental gradient method.
A New Framework For Power Control In Wireless Data Networks: Games, Utility, And Pricing
, 1999
"... We develop a new framework for distributed power control for wireless data based on the economic principles of utility and pricing. Utility is defined as the measure of satisfaction that a user derives from accessing the wireless data network. Properties of utility functions are introduced and a spe ..."
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Cited by 22 (1 self)
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We develop a new framework for distributed power control for wireless data based on the economic principles of utility and pricing. Utility is defined as the measure of satisfaction that a user derives from accessing the wireless data network. Properties of utility functions are introduced and a specific function, based on throughput per terminal battery lifetime including forward error control, is presented and shown to conform to those properties. Users enter into a noncooperative game to maximize their individual utilities by adjusting their transmitter powers. A unique Nash equilibrium for the above game is shown to exist but is not Pareto efficient. A pricing function is then introduced which leads to Pareto improvements for the noncooperative game.
Extremal Eigenvalue Problems For Composite Membranes, I
, 1990
"... : Given an open bounded connected set\Omega ae R N and a prescribed amount of two homogeneous materials of different density, for small k we characterize the distribution of the two materials in\Omega that extremizes the kth eigenvalue of the resulting clamped membrane. We show that these extrem ..."
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Cited by 12 (3 self)
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: Given an open bounded connected set\Omega ae R N and a prescribed amount of two homogeneous materials of different density, for small k we characterize the distribution of the two materials in\Omega that extremizes the kth eigenvalue of the resulting clamped membrane. We show that these extremizers vary continuously with the proportion of the two constituents. The characterization of the extremizers in terms of level sets of associated eigenfunctions provides geometric information on their respective interfaces. Each of these results generalizes to N dimensions the now classical one dimensional work of M.G. Krein. 1 1. INTRODUCTION Within the class of fixed endpoint strings on the interval (0; 1) with density between ff and fi and mass equal to fffl + fi(1 \Gamma fl), M.G. Krein [19] was able to isolate those with the largest or smallest kth natural frequency. More precisely, denoting by k (ae) the kth Dirichlet eigenvalue of the string with density ae, and by ae fl k (ae ...
Computing Population Variance and Entropy under Interval Uncertainty: LinearTime Algorithms
, 2006
"... In statistical analysis of measurement results it is often necessary to compute the range [V, V] of the population variance V = 1 n · n∑ (xi − E) 2 where E = 1 n · n∑ xi when we only know the intervals i=1 [˜xi − ∆i, ˜xi + ∆i] of possible values of the xi. While V can be computed efficiently, the pr ..."
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Cited by 11 (7 self)
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In statistical analysis of measurement results it is often necessary to compute the range [V, V] of the population variance V = 1 n · n∑ (xi − E) 2 where E = 1 n · n∑ xi when we only know the intervals i=1 [˜xi − ∆i, ˜xi + ∆i] of possible values of the xi. While V can be computed efficiently, the problem of computing V is, in general, NPhard. In our previous paper “Population Variance under Interval Uncertainty: A New Algorithm ” (Reliable Computing, 2006, Vol. 12, No. 4, pp. 273–280) we showed that in
The Constraint Rule of the Maximum Entropy Principle
, 1995
"... The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability distri ..."
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Cited by 11 (0 self)
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The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability distributions. In practical applications, however, the information consists of empirical data. A constraint rule is then employed to construct constraints on probability distributions out of these data. Usually one adopts the rule to equate the expectation values of certain functions with their empirical averages. There are, however, various other ways in which one can construct constraints from empirical data, which makes the maximum entropy principle lead to very different probability assignments. This paper shows that an argument by Jaynes to justify the usual constraint rule is unsatisfactory and investigates several alternative choices. The choice of a constraint rule is also show...