gradient of mutual information in linear vector gaussian channels this paper considers a general linear vector gaussian channel with arbitrary signaling and pursues two closely related goals i closed form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system and ii fundamental connections between information theory and estimation theory generalizing the fundamental relationship recently unveiled by guo shamai and verdu spl acute we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output gradients and derivatives with respect to other parameters are then found via the differentiation chain rule

on existence of solutions for parabolic hemivariational inequalities abstract a class of parabolic hemivariational inequalities is considered in which the energy function is locally lipschitz not necessarily convex or differentiable and the nonlinear evolution operator is multivalued and generalized pseudomonotone using techniques of multivalued analysis and a surjectivity result for l generalized pseudomonotone operators we prove the existence for a cauchy problem and a periodic problem some applications to nonsmooth mechanics are also indicated

existence of solutions for wave type hemivariational inequalities with noncoercive viscosity damping abstract in this paper we prove the existence of solutions for a hyperbolic hemivariational inequality of the form u au bu j u f where b is a linear elliptic operator and a is linear and nonnegative not necessarily coercive

on minimal eigenvalues of a class of tridiagonal matrices it is known that the worst case near far resistance of optimum multiuser detectors for asynchronous gaussian multiple access channels can be expressed in terms of a class of block tridiagonal matrices and the minimal eigenvalues of such a class of block tridiagonal matrices serve as a good measure of the worst case near far resistance in this paper we focus on the two user scenario where each block tridiagonal matrix under consideration is a tridiagonal matrix we derive closed form expressions for the minimal eigenvalues of such a class of tridiagonal matrices in terms of the largest real solution of a trigonometric equation in 0 pi we also obtain lower bounds and upper bounds on the minimal eigenvalues which improve on previously known results in the literature

coercive and semicoercive hemivariational inequalities variational inequalities have a concrete mechanical meaning they are expressions of the principle of virtual work or power in its inequality form in the case of lack of monotonicity of the underlying stress strain or reaction displacement conditions or equivalently if the corresponding energy functionals are nonconvex the variational expressions are no longer variational inequalities another type of inequality expression arises as variational formulation of the problem these expressions have been introduced in mechanics by the author and are called hemivariational inequalities the aim of this paper is the formulation of an abstract mathematical theory for coercive and semicoercive hemivariational inequalities

existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities abstract in this paper we consider the problem of the existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities with a pseudomonotone operator using regularized approximating and first eigenfunction methods and the surjectivity result we prove the existence of solutions for quasilinear parabolic hemivariational inequalities

existence of solutions for hyperbolic hemivariational inequalities in this paper we study a hyperbolic hemivariational inequality with a nonlinear pseudomonotone operator depending on the derivative of an unknown function and a linear monotone operator depending on an unknown function using the surjectivity result for l pseudomonotone operators an existence result for such inequalities is proved

joint optimization of the transmit covariance and relay precoder in general gaussian amplify and forward relay channels the maximum data rate that can be achieved by the strictly causal full duplex amplify and forward af scheme in general gaussian relay channels is achieved by gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder this problem possesses an intricate nonconvex structure and is hence difficult to solve to circumvent this difficulty the relay precoder is assumed to be given and then the karush kuhn tucker conditions are used to obtain closed form expressions for the optimal input covariance corresponding to that precoder these expressions are used to show that subdiagonal precoders suffice to attain the maximum achievable rate of the af scheme at any source transmit power in addition to significantly reducing the effort expended in searching for the optimal relay precoder this observation enables us to find the optimal precoders at low and high source transmit powers for asymptotically low transmit powers the optimal relaying mechanism is shown to possess an interlacing structure thereby resembling half duplex operation in contrast for asymptotically high transmit powers it is optimal for the relay to be silent the asymptotic analysis enables us to develop an explicit formulation for a suboptimal precoder that at intermediate source transmit powers are shown numerically to outperform asymptotically optimal precoders

linear non regenerative multicarrier mimo relay communications based on mmse criterion in this letter we propose linear non regenerative multicarrier multiple input multiple output mimo relay technique that aims to minimize the mean squared error mse of the signal waveform estimation at the destination we generalize the existing result on the structure of the optimal relay amplifying matrix by considering the direct source destination link to minimize the mse a power loading algorithm is developed which has a significantly reduced computational complexity compared with existing techniques

convex multilevel decomposition algorithms for non monotone problems a convex multilevel decomposition algorithm is proposed in this paper for the solution of static analysis problems involving non monotone possibly multivalued laws the theory is developed here for a model structure with non monotone interface or boundary conditions first the non monotone laws are written in the form of a difference of two monotone functions under this decomposition the non linear elastostatic analysis problem is equivalent to a system of convex variational inequalities and to non convex min min problems for appropriately defined lagrangian functions the solution s of each one of the aforementioned problems describe the position s of static equilibrium of the considered structure in this paper a multilevel optimization scheme due to auchmuty 1 is used for the numerical solution of the problem the most interesting feature of this method from the computational mechanics standpoint is the fact that each one of the subproblems involved in the multilevel algorithm is a convex optimization problem or in terms of mechanics an appropriately modified monotone unilateral problem thus existing algorithms and software can be used for the numerical solution with minor modifications numerical results concerning the calculation of elastic and rigid stamp problems and of material inclusion problems with delamination and non monotone stick slip frictional effects illustrate the theory

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

on instantaneous relaying the gaussian three node relay channel with orthogonal receive components i e the transmitted signals from the source and the relay do not interfere with each other is investigated for such channels linear relaying is a suboptimal strategy in general this is because a linear scheme merely repeats the received noisy signal and does not utilize the available degrees of freedom efficiently at this background nonlinear symbol wise as opposed to block wise relaying strategies are developed to compensate for the shortcomings of the linear strategy optimal strategies are presented for two special cases of the general scenario and it is shown that memoryless relaying can achieve the capacity furthermore for the general gaussian relay channel a parametric piecewise linear pl mapping is proposed and analyzed the achievable rates obtained by the pl mapping are computed numerically and optimized for a certain number of design parameters it is concluded that optimized pl relaying always outperforms conventional instantaneous linear relaying amplify and forward it is also illustrated that the proposed pl relaying scheme can improve on sophisticated block markov encoding i e decode and forward when the source relay link is ill conditioned relative to other links furthermore pl relaying can work at rates close to those achieved by side information encoding i e compress and forward but at a much lower complexity

bounds on capacity and minimum energy per bit for awgn relay channels upper and lower bounds on the capacity and minimum energy per bit for general additive white gaussian noise awgn and frequency division awgn fd awgn relay channel models are established first the max flow min cut bound and the generalized block markov coding scheme are used to derive upper and lower bounds on capacity these bounds are never tight for the general awgn model and are tight only under certain conditions for the fd awgn model two coding schemes that do not require the relay to decode any part of the message are then investigated first it is shown that the side information coding scheme can outperform the block markov coding scheme it is also shown that the achievable rate of the side information coding scheme can be improved via time sharing in the second scheme the relaying functions are restricted to be linear the problem is reduced to a single letter nonconvex optimization problem for the fd awgn model the paper also establishes a relationship between the minimum energy per bit and capacity of the awgn relay channel this relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy per bit that do not differ by more than a factor of 1 45 for the fd awgn relay channel model and 1 7 for the general awgn model

log determinant relaxation for approximate inference in discrete markov random fields graphical models are well suited to capture the complex and non gaussian statistical dependencies that arise in many real world signals a fundamental problem common to any signal processing application of a graphical model is that of computing approximate marginal probabilities over subsets of nodes this paper proposes a novel method applicable to discrete valued markov random fields mrfs on arbitrary graphs for approximately solving this marginalization problem the foundation of our method is a reformulation of the marginalization problem as the solution of a low dimensional convex optimization problem over the marginal polytope exactly solving this problem for general graphs is intractable for binary markov random fields we describe how to relax it by using a gaussian bound on the discrete entropy and a semidefinite outer bound on the marginal polytope this combination leads to a log determinant maximization problem that can be solved efficiently by interior point methods thereby providing approximations to the exact marginals we show how a slightly weakened log determinant relaxation can be solved even more efficiently by a dual reformulation when applied to denoising problems in a coupled mixture of gaussian model defined on a binary mrf with cycles we find that the performance of this log determinant relaxation is comparable or superior to the widely used sum product algorithm over a range of experimental conditions

three dimensional adhesive contact laws with debonding a nonconvex energy bundle method abstract in the present paper we develop a new numerical approach to the problem of structures having two or more parts of them adhesively bonded together like e g in sandwich structures the adhesive material is idealized by a nonmonotone possibly multivalued stress strain law which is three dimensional 3d and introduces a nonconvex nonsmooth energy function in the problem the problem is formulated as a hemivariational inequality whose solution s must render the potential energy substationary we apply here the proximal bundle method and more specifically the optimization programme nsolib based on first order polyhedral approximations of the locally lipschitz continuous objective function this algorithm permits the determination of at least one substasionarity point e g of an equilibrium problem an example of a 3d finite element model illustrates the effectiveness of the proposed mehod

high order adi scheme for option pricing in stochastic volatility models we propose a new high order alternating direction implicit adi finite difference scheme for the solution of initial boundary value problems of convection diffusion type with mixed derivatives and non constant coefficients as they arise from stochastic volatility models in option pricing our approach combines different high order spatial discretisations with hundsdorfer and verwer s adi time stepping method to obtain an efficient method which is fourth order accurate in space and second order accurate in time numerical experiments for the european put option pricing problem using heston s stochastic volatility model confirm the high order convergence

a joint time invariant filtering approach to the linear gaussian relay problem in this paper the linear gaussian relay problem is considered under the linear time invariant lti model the rate maximization problem in the linear gaussian relay channel is formulated in the frequency domain based on the toeplitz distribution theorem under the further assumption of realizable input spectra the rate maximization problem is converted to the problem of joint source and relay filter design with two power constraints one at the source and the other at the relay and a practical solution to this problem is proposed based on the adaptive projected sub gradient method numerical results show that the proposed method yields a considerable gain over the instantaneous amplify and forward af scheme in inter symbol interference isi channels also the optimality of the af scheme within the class of one tap relay filters is established in flat fading channels