blind constant modulus equalization via convex optimization in this paper we formulate the problem of blind equalization of constant modulus cm signals as a convex optimization problem the convex formulation is obtained by performing an algebraic transformation on the direct formulation of the cm equalization problem using this transformation the original nonconvex cm equalization formulation is turned into a convex semidefinite program sdp that can be efficiently solved using interior point methods our sdp formulation is applicable to baud spaced equalization as well as fractionally spaced equalization performance analysis shows that the expected distance between the equalizer obtained by the sdp approach and the optimal equalizer in the noise free case converges to zero exponentially as the signal to noise ratio snr increases in addition simulations suggest that our method performs better than standard methods while requiring significantly fewer data samples

an algorithm for global minimization of linearly constrained concave quadratic functions we present an algorithm for the global minimization of a quadratic function x y xtqx htx dty over a polytope x y rn k ax by b x 0 y 0 where x h rn y d rk b rm and where a and b are m n and m k matrices respectively and q is an n n symmetric positive definite matrix we first consider the case where k 0 and construct a tight parallelpiped r containing by using an arbitrary set of q conjugate directions and by solving 2n linear programs we show that the convex envelope of with respect to r is linear and obtain an explicit formula for it we then describe a branch and bound algorithm in which the linearity of the convex envelope allows efficient lower bounding for the subproblems for each subproblem we obtain the linear convex envelope of over a smaller parallelepiped r with facets parallel to those of r then we obtain a lower bound by minimizing this convex envelope over r if is the optimal objective value for each e 0 the algorithm generates a sequence of feasible points zj with nonincreasing function values j and a nondecreasing sequence j of lower bounds to moreover if e 0 there exist j0 such that j j e for all j j0 and if e 0 j j converges to 0 the results are then generalized to the case where k is nonzero and possibly much larger than n preliminary computational results are also presented

universal property of the housekeeping entropy production the entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative the housekeeping entropy production which is a part of total entropy production is associated with the heat dissipation in maintaining a nonequilibrium steady state we derive a langevin type stochastic differential equation for the housekeeping entropy production the equation allows us to define a housekeeping entropic time ensuremath tau remarkably it turns out that the probability distribution of the housekeeping entropy production at a fixed value of ensuremath tau is given by the gaussian distribution regardless of system details the gaussian distribution is universal for any systems whether in the steady state or in the transient state and whether they are driven by time independent or time dependent driving forces we demonstrate the universal distribution numerically for model systems

a reflective newton method for minimizing a quadratic function subject to bounds on some of the variables we propose a new algorithm a reflective newton method for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables this method applies to a general indefinite quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem our new method exhibits strong convergence properties global and quadratic convergence and appears to have significant practical potential strictly feasible points are generated experimental results on moderately large and sparse problems support the claim of practicality for large scale problems

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

a fast linear programming algorithm for blind equalization a fast implementation of a special non mse cost function for blind equalization is presented here this baud rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters for a generic class of channels with persistently exciting quadrature amplitude modulation input signals this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery

fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium we present a general framework for systems which are prepared in a nonstationary nonequilibrium state in the absence of any perturbation and which are then further driven through the application of a time dependent perturbation by assumption the evolution of the system must be described by markovian dynamics we distinguish two different situations depending on the way the nonequilibrium state is prepared either it is created by some driving or it results from a relaxation following some initial nonstationary conditions our approach is based on a recent generalization of the hatano sasa relation for nonstationary probability distributions we also investigate whether a form of the second law holds for separate parts of the entropy production and for any nonstationary reference process a question motivated by the work of m esposito et al phys rev lett 104 090601 2010 we find that although the special structure of the theorems derived in this reference is not recovered in the general case detailed fluctuation theorems still hold separately for parts of the entropy production these detailed fluctuation theorems contain interesting generalizations of the second law of thermodynamics for nonequilibrium systems

optimizing improved hardy inequalities let be a bounded domain in rn n 3 containing the origin motivated by a question of brezis and vazquez we consider an improved hardy inequality with best constant b that we formally write as n 22 21 x 2 bv x we first give necessary conditions on the potential v under which the previous inequality can or cannot be further improved we show that the best constant b is never achieved in h01 and in particular that the existence or not of further correction terms is not connected to the nonachievement of b in h01 our analysis reveals that the original inequality can be repeatedly improved by adding on the right hand side specific potentials this leads to an infinite series expansion of hardy s inequality the series obtained is in some sense optimal in establishing these results we derive various sharp improved hardy sobolev inequalities

fluctuation theorem for birth death or chemical master equations with time dependent rates for systems described by univariate birth death or chemical master equations driven out of equilibrium by externally controlled time dependent transition rates a nonlinear fluctuation theorem is derived for paradigmatic chemical reactions this theorem acquires a particularly transparent form

the explicit form of the rate function for semi markov processes and its contractions we derive the explicit form of the rate function for semi markov processes here the random time change trick plays an essential role also by exploiting the contraction principle of the large deviation theory to the explicit form we show that the fluctuation theorem gallavotti cohen symmetry holds for semi markov cases furthermore we elucidate that our rate function is an extension of the level 2 5 rate function for markov processes to semi markov cases

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

negatively curved manifolds elliptic operators and the martin boundary consider a riemannian manifold m of dimension n 2 and assume that m is complete simply connected and that its sectional curvatures are bounded between two negative constants in a recent paper 7 m anderson and r schoen have proved that the martin boundary of m with respect to the laplace beltrami operator a is naturally homeomorphic to soo m the sphere at infinity of m here we shall first establish a similar result for a wide class of elliptic operators on m giving at the same time a new proof of the theorem of anderson and schoen our proof relies heavily on several concepts of potential theory but on the other hand avoids the quite difficult calculations of 7 and perhaps makes the result more understandable roughly speaking we show that if y is a second order elliptic operator defined over m and has a uniformly nice behaviour on each ball of radius 1 in m then dq m the y martin boundary of m is s m provided that the following condition holds there is a positive y ci superharmonic function on m for some positive if instead we only assume the existence of the green function for y a minimal requirement when studying the y martin boundary then d m may be very different from so m even for a rotation invariant operator y on the unit ball of rn equipped

distribution of work in isothermal nonequilibrium processes diffusive motion in an externally driven potential is considered it is shown that the distribution of work required to drive the system from an initial equilibrium state to another is gaussian for slow but finite driving our result is obtained by projection method techniques exploiting a small parameter defined as the switching rate between the two states of the system the exact solution for a simple model system shows that such an expansion may fail in higher orders since the mean and the variance following from the exact distribution show nonanalytic behavior

universal interpretation of efficacy parameter in perturbed nonequilibrium systems abstract the fluctuation theorems have remained one of the cornerstones in the study of systems that are driven far out of equilibrium and they provide strong constraints on the fraction of trajectories that behave atypically in light of the second law they have mainly been derived for a predetermined external drive applied to the system however to improve the efficiency of a process one needs to incorporate protocols that are modified by receiving feedbacks about the recent state of the system during its evolution in such a case the forms of the conventional fluctuation theorems get modified the correction term involving terms that depend on the way the reverse conjugate process is defined namely the rules of using feedback in order to generate the exact time reversed conjugate protocols we show in this paper that this can be done in a large number of ways and in each case we would get a different expression for the correction terms this would in turn lead to several lower bounds on the mean work that must be performed on the system or on the entropy changes here we analyze a form of the extended fluctuation theorems that involves the efficacy parameter and find that this form retains a consistent physical meaning regardless of the design of feedback along the conjugate process as opposed to the case of the previously mentioned form of the modified fluctuation theorems

temperature measurement from perturbations the notion of configuration temperature is extended to discontinuous systems by identifying the temperature as the nontrivial root of several integral equations regarding the distribution of the energy change upon configuration perturbations the relations are generalized to pressure and a distribution mean force

optimal hardy inequalities for schrodinger operators on graphs for a given subcritical discrete schrodinger operator h on a weighted infinite graph x we construct a hardy weight w which is optimal in the following sense the operator h w is subcritical in x for all 1 our results rely on a criticality theory for schrodinger operators on general weighted graphs

integral fluctuation theorem for the housekeeping heat the housekeeping heat qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states by analysing the evolution of its probability distribution we prove an integral fluctuation theorem exp qhk 1 valid for arbitrary driven transitions between steady states we discuss gaussian limiting cases and the difference between the new theorem and both the hatano sasa and the jarzynski relation

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

stationary points of a kurtosis maximization algorithm for blind signal separation and antenna beamforming blind source separation has been the subject of extensive research in particular blind antenna beamforming is an effective signal separation technique for communication systems to combat co channel interference among many potential candidate approaches the simple constant modulus algorithm cma has been widely studied and used in practice the cma is designed to capture and separate signals with negative kurtosis however when some signals have positive kurtoses the cma is unable to capture and separate these sources we show that the kurtosis maximum algorithm kma can capture signals with both the positive and negative kurtoses its global convergence proof is presented for noiseless systems with multiple signals sources and for systems with a single source and zero kurtosis such as gaussian additive noise

on convergence analysis of fractionally spaced adaptive blind equalizers in this paper we study the convergence analysis of fractionally spaced adaptive blind equalizers we show that based on the trivial and nontrivial nullspaces of a channel convolution matrix all equilibria can be classified as channel dependent equilibria cde or algorithm dependent equilibria ade because oversampling provides channel diversity the nullspace of the channel convolution matrix is affected we show that fractionally spaced equalizers fses do not possess any cde if a length zero condition is satisfied the convergence behavior of these fse are clearly determined by the specific choice of cost function alone we characterize the global convergence ability of several popular algorithms simply based on their ade we also present an fse implementation of the super exponential algorithm we show that the fse implementation does not introduce any nonideal approximation simulation results are also presented to illustrate the robustness and the improved performance of fse under the super exponential algorithm

on families of optimal hardy weights for linear second order elliptic operators abstract we construct families of optimal hardy weights for a subcritical linear second order elliptic operator using a one dimensional reduction more precisely we first characterize all optimal hardy weights with respect to one dimensional subcritical sturm liouville operators on a b a b and then apply this result to obtain families of optimal hardy inequalities for general linear second order elliptic operators in higher dimensions as an application we prove a new rellich inequality

equivalence of two bochkov kuzovlev equalities in quantum two level systems we present two kinds of bochkov kuzovlev work equalities in a two level system that is described by a quantum markovian master equation one is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint we show that these two equalities are indeed equivalent importantly this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function we use a numerical model to verify these results

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

structure of positive solutions to δ v u 0 in rn on etudie la structure de toutes les solutions positives d une equation de schrodinger stationnaire ou le potentiel v est suppose etre une fonction a valeur reelle appartenant a l p loc r n avec p n 2 pour n 2 et p 1 pour n 1 on considere une formule de representation explicite pour des solutions positives leurs asymptotes a l infini et le probleme de dirichlet avec une condition aux limites a l infini

thermodynamic formula for the cumulant generating function of time averaged current the cumulant generating function of time averaged current is studied from an operational viewpoint specifically for interacting brownian particles under nonequilibrium conditions we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added where the modified system is characterized by a variational principle the formula reminds us of einstein s fluctuation theory in equilibrium statistical mechanics furthermore since the formula leads to the fluctuation dissipation relation when the linear response regime is focused on it is regarded as an extension of the linear response theory to that valid beyond the linear response regime the formula is also related to previously known theories such as the donsker varadhan theory the additivity principle and the least dissipation principle but it is not derived from them examples of its application are presented for a driven brownian particle on a ring subject to a periodic potential

global minimization of large scale constrained concave quadratic problems by separable programming the global minimization of a large scale linearly constrained concave quadratic problem is considered the concave quadratic part of the objective function is given in terms of the nonlinear variablesx r n while the linear part is in terms ofy r k for large scale problems we may havek much larger thann the original problem is reduced to an equivalent separable problem by solving a multiple cost row linear program with 2n cost rows the solution of one additional linear program gives an incumbent vertex which is a candidate for the global minimum and also gives a bound on the relative error in the function value of this incumbent ana priori bound on this relative error is obtained which is shown to be 0 25 in important cases if the incumbent is not a satisfactory approximation to the global minimum a guaranteede approximate solution is obtained by solving a single liner zero one mixed integer programming problem this integer problem is formulated by a simple piecewise linear underestimation of the separable problem

maximum likelihood parameter and rank estimation in reduced rank multivariate linear regressions this paper considers the problem of maximum likelihood ml estimation for reduced rank linear regression equations with noise of arbitrary covariance the rank reduced matrix of regression coefficients is parameterized as the product of two full rank factor matrices this parameterization is essentially constraint free but it is not unique which renders the associated ml estimation problem rather nonstandard nevertheless the problem turns out to be tractable and the following results are obtained an explicit expression is derived for the ml estimate of the regression matrix in terms of the data covariances and their eigenelements furthermore a detailed analysis of the statistical properties of the ml parameter estimate is performed additionally a generalized likelihood ratio test glrt is proposed for estimating the rank of the regression matrix the paper also presents the results of some simulation exercises which lend empirical support to the theoretical findings

blind digital signal separation using successive interference cancellation iterative least squares blind separation of instantaneous linear mixtures of digital signals is a basic problem in communications when little or nothing can be assumed about the mixing matrix signal separation may be achieved by exploiting structural properties of the transmitted signals e g finite alphabet or coding constraints we propose a monotonically convergent and computationally efficient iterative least squares ils blind separation algorithm based on an optimal scaling lemma the signal estimation step of the proposed algorithm is reminiscent of successive interference cancellation sic ideas for well conditioned data and moderate snr the proposed sic ils algorithm provides a better performance complexity tradeoff than competing ils algorithms coupled with blind algebraic digital signal separation methods sic ils offers a computationally inexpensive true least squares refinement option we also point out that a widely used ils finite alphabet blind separation algorithm can exhibit limit cycle behavior

splitting of the rate matrix as a definition of time reversal in master equation systems motivated by recent progress in nonequilibrium fluctuation relations we present a generalized time reversal for stochastic master equation systems with discrete states which is defined as a splitting of the rate matrix into irreversible and reversible parts an immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splittings additionally we find that the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the reversible rate part which was previously ignored

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

a subspace interior and conjugate gradient method for large scale bound constrained minimization problems a subspace adaptation of the coleman li trust region and interior method is proposed for solving large scale bound constrained minimization problems this method can be implemented with either sparse cholesky factorization or conjugate gradient computation under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its full space version computational performance on various large test problems is reported advantages of our approach are demonstrated our experience indicates that our proposed method represents an efficient way to solve large bound constrained minimization problems

general approach to blind source separation this paper identifies and studies two major issues in the blind source separation problem separability and separation principles we show that separability is an intrinsic property of the measured signals and can be described by the concept of m row decomposability introduced in this paper we also show that separation principles can be developed by using the structure characterization theory of random variables in particular we show that these principles can be derived concisely and intuitively by applying the darmois skitovich theorem which is well known in statistical inference theory and psychology some new insights are gained for designing blind source separation filters

optimal hardy weight for second order elliptic operator an answer to a problem of agmon abstract for a general subcritical second order elliptic operator p in a domain r n or noncompact manifold we construct hardy weight w which is optimal in the following sense the operator p w is subcritical in for all 1 null critical in for 1 and supercritical near any neighborhood of infinity in for any 1 moreover if p is symmetric and w 0 then the spectrum and the essential spectrum of w 1 p are equal to 1 and the corresponding agmon metric is complete our method is based on the theory of positive solutions and applies to both symmetric and nonsymmetric operators the constructed hardy weight is given by an explicit simple formula involving two distinct positive solutions of the equation p u 0 the existence of which depends on the subcriticality of p in

a fractionally spaced blind equalizer based on linear programming we formulate the blind fractionally spaced equalization fse problem as one that minimizes a piecewise linear convex function subject to some linear constraints on the equalizer parameters we show that this formulation achieves both the interference removal and the carrier phase recovery when the input signal possesses a certain quadrature amplitude modulation qam type symmetry a fast linear programming implementation is presented to solve the convex minimization problem computer simulation results indicate the new linear programming based fse is able to accurately equalize channels that are known to be not equalizable by t spaced or baud rate blind equalizers and yields superior performance to other blind fse methods

stochastic thermodynamics with odd controlling parameters stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations the definitions of work and heat and the microscopically reversible condition are two key concepts in the current framework of stochastic thermodynamics herein we apply stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible such a contradiction also leads to a revision to the fluctuation theorems and nonequilibrium work relations by introducing adjoint dynamics we find that the total entropy production can be separated into three parts with two of them satisfying the integral fluctuation theorem revising the definitions of work and heat and the microscopically reversible condition allows us to derive two sets of modified nonequilibrium work relations including the jarzynski equality the detailed crooks work relation and the integral crooks work relation we consider the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation for the jarzynski like equality derived from shortcuts to isothermality