on the existence of periodic solutions to p laplacian rayleigh differential equation with a delay abstract in this paper the authors study the existence of periodic solutions to a p laplacian rayleigh differential equation with a delay as follows p y t f y t g y t t e t where p 1 is a constant p r r p u u p 2 u f g e c r r t t t with t 0 t 0 t and e t t e t t 0 is a constant by using mawhin s continuation theorem some new results are obtained

the concavity of p renyi entropy power for doubly nonlinear diffusion equations and lp gagliardo nirenberg sobolev inequalities abstract we prove the concavity of p renyi entropy power for positive solutions to the doubly nonlinear diffusion equations on r n or compact riemannian manifolds with nonnegative ricci curvature as applications we give new proofs of the sharp l p sobolev inequality and l p gagliardo nirenberg inequalities on r n moreover two improvements of l p gagliardo nirenberg inequalities are derived

beyond the entropy power inequality via rearrangements a lower bound on the renyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements for the special case of boltzmann shannon entropy this lower bound is better than that given by the entropy power inequality several applications are discussed including a new proof of the classical entropy power inequality and an entropy inequality involving symmetrization of levy processes

existence and uniqueness of periodic solutions for a kind of lienard equation with two deviating arguments in this paper a kind of lienard equation with two deviating arguments of the formx t f x t x t g 1 t x email protected 1 t g 2 t x email protected 2 t p t is considered we derive some new sufficient conditions for checking uniqueness of t periodic solutions of this equation by using coincidence degree theory we also establish some new results on the existence and uniqueness of t periodic solutions for this equation which are new and complement previously known results

periodic solutions of a second order ordinary differential equation a necessary and sufficient condition for nonresonance the nonlinearity g in 1 1 is a continuous function from r to r and the forcing term h is taken in l o 27r nonresonance means that 1 1 admits at least one solution x for any given h integrating eq 1 1 over a period one immediately sees that a necessary condition for nonresonance is that the function g be unbounded from above and from below on r it will appear later cf 1 6 that this unboundedness can be looked at as a condition relating the behaviour at infinity of the nonlinearity g with respect to the first eigenvalue 1 0 of the associated linear problem xf ax in 0 27r x 0 x 27r x 0 x1 271 1 2

a new entropy power inequality for integer valued random variables the entropy power inequality epi yields lower bounds on the differential entropy of the sum of two independent real valued random variables in terms of the individual entropies versions of the epi for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy but no universal inequality is known beyond trivial ones more recently the sumset theory for the entropy function yields a sharp inequality h x x prime h x geq 1 over 2 o 1 when x x prime are independent identically distributed i i d with high entropy this paper provides the inequality h x x prime h x geq g h x where x x prime are arbitrary i i d integer valued random variables and where g is a universal strictly positive function on bbr satisfying g 0 0 extensions to nonidentically distributed random variables and to conditional entropies are also obtained

periodic solutions for p laplacian differential equation with multiple deviating arguments abstract by employing mawhin s continuation theorem the existence of periodic solutions of the p laplacian differential equation with multiple deviating arguments p x t f x t x t j 1 n j t g x t j t e t under various assumptions are obtained

a strengthened entropy power inequality for log concave densities we show that shannon s entropy power inequality admits a strengthened version in the case in which the densities are log concave in such a case in fact one can extend the blachman stam argument to obtain a sharp inequality for the second derivative of shannon s entropy functional with respect to the heat semigroup

ultrasonic texture motion analysis theory and simulation a theoretical model was previously developed to evaluate the relationship between the dynamics of ultrasonic speckle and its underlying tissue the model is divided into an instrumental part represented by the point spread function in the far field of the ultrasonic apparatus and a moving tissue component described by a collection of scatterers by computing the convolution of these terms and then the envelope one obtains a simulated ultrasonic speckle pattern sequence which shows speckle motions closely linked to the tissue dynamics when small motion amplitudes are involved here a theoretical study of the correlation between various linear transformations of the tissue and the corresponding ultrasonic speckle motions is performed based on a 2d extension of the envelope cross correlation analysis of a narrow band gaussian noise in the linear scan case obviously tissue translation generates an identical speckle translation however tissue speckle motion correlation decreases with increasing rotation and or biaxial deformation lateral deformation perpendicular to the beam propagation axis being much less sensitive with respect to the transducer frequency the rotation and the axial deformation of the tissue show a better relationship with their respective speckle motion at lower frequencies while lateral deformation correlation is independent of the pulse frequency with respect to beam pulse size parameters tissue speckle correlation decreases with rotation when a wide ultrasonic beam is used while the axial deformation correlation decreases with the axial duration of the pulse this study sets the ground for the development of an ultrasonic strain gauge particularly useful for the assessment of biomechanical soft tissue and fluid flow properties based on speckle tracking

geometric inequalities from phase space translations we establish a quantum version of the classical isoperimetric inequality relating the fisher information and the entropy power of a quantum state the key tool is a fisher information inequality for a state which results from a certain convolution operation the latter maps a classical probability distribution on phase space and a quantum state to a quantum state we show that this inequality also gives rise to several related inequalities whose counterparts are well known in the classical setting in particular it implies an entropy power inequality for the mentioned convolution operation as well as the isoperimetric inequality and establishes concavity of the entropy power along trajectories of the quantum heat diffusion semigroup as an application we derive a log sobolev inequality for the quantum ornstein uhlenbeck semigroup and argue that it implies fast convergence towards the fixed point for a large class of initial states

on the existence of a unique periodic solution to a lienard type p laplacian non autonomous equation abstract in this work we investigate the following lienard type p laplacian non autonomous equation p x t f x t x t g t x t e t some criteria for guaranteeing the existence and uniqueness of periodic solutions of this equation are given by using the manasevich mawhin continuation theorem and some new techniques our results are new and extend some known results from the literature in the last section two illustrative examples will be provided to demonstrate the applications of our results

intrinsic entropies of log concave distributions the entropy of a random variable is well known to equal the exponential growth rate of the volumes of its typical sets in this paper we show that for any log concave random variable x the sequence of the lfloor n theta rfloor text th intrinsic volumes of the typical sets of x in dimensions n geq 1 grows exponentially with a well defined rate we denote this rate by h x theta and call it the theta text th intrinsic entropy of x we show that h x theta is a continuous function of theta over the range 0 1 thereby providing a smooth interpolation between the values 0 and h x at the endpoints 0 and 1 respectively

maximum likelihood approach to strain imaging using ultrasound a maximum likelihood ml strategy for strain estimation is presented as a framework for designing and evaluating bioelasticity imaging systems concepts from continuum mechanics signal analysis and acoustic scattering are combined to develop a mathematical model of the ultrasonic waveforms used to form strain images the model includes three dimensional 3 d object motion described by affine transformations rayleigh scattering from random media and 3 d system response functions the likelihood function for these waveforms is derived to express the fisher information matrix and variance bounds for displacement and strain estimation the ml estimator is a generalized cross correlator for pre and post compression echo waveforms that is realized by waveform warping and filtering prior to cross correlation and peak detection experiments involving soft tissuelike media show the ml estimator approaches the cramer rao error bound for small scaling deformations at 5 mhz and 1 2 compression the predicted

correlation analysis of the beam angle dependence for elastography signal decorrelation is a major source of error in the displacements estimated using correlation techniques for elastographic imaging previous papers have addressed the variation in the correlation coefficient as a function of the applied compression for a finite window size and an insonification angle of zero degrees the recent use of angular beam steered radio frequency echo signals for spatial angular compounding and shear strain estimation have demonstrated the need for understanding signal decorrelation artifacts for data acquired at different beam angles in this paper we provide both numerical and closed form theoretical solutions of the correlation between pre and post compression radio frequency echo signals acquired at a specified beam angle the expression for the correlation coefficient obtained is a function of the beam angle and the applied compression for a finite duration window accuracy of the theoretical results is verified using tissue mimicking phantom experiments on a uniformly elastic phantom using beam steered data acquisitions on a linear array transducer the theory predicts a faster decorrelation with changes in the beam or insonification angle for longer radio frequency echo signal segments and at deeper locations in the medium theoretical results provide useful information for improving angular compounding and shear strain estimation techniques for elastography

a vector generalization of costa s entropy power inequality with applications this paper considers an entropy power inequality epi of costa and presents a natural vector generalization with a real positive semidefinite matrix parameter the new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean square error mmse estimate in linear vector gaussian channels as an application a new extremal entropy inequality is derived from the generalized costa epi and then used to establish the secrecy capacity regions of the degraded vector gaussian broadcast channel with layered confidential messages

an abstract existence theorem at resonance and its applications abstract by using brouwer degree theory and a continuation theorem based on mawhin s coincidence degree an abstract existence theorem at resonance for operator equations is developed as applications of this result some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension n n 2 the results due to nagle and sinkala are generalized improved and unified

a new entropy power inequality a strengthened version of shannon s entropy power inequality for the case where one of the random vectors involved is gaussian is proved in particular it is shown that if independent gaussian noise is added to an arbitrary multivariate random variable the entropy power of the resulting random variable is a concave function of the variance power of the added noise the strengthened inequality is shown to hold for the class of stable distributions

periodic solutions for p laplacian neutral functional differential equation with deviating arguments by using the theory of coincidence degree we study a kind of periodic solutions to p laplacian neutral functional differential equation with multiple deviating arguments a new result on the existence of periodic solutions is obtained

reverse brunn minkowski and reverse entropy power inequalities for convex measures we develop a reverse entropy power inequality for convex measures which may be seen as an anegeometric inverse of the entropy power inequality of shannon and stam the specialization of this inequality to log concave measures may be seen as a version of milman s reverse brunn minkowski inequality the proof relies on a demonstration of new relationships between the entropy of high dimensional random vectors and the volume of convex bodies and on a study of eective supports of convex measures both of which are of independent interest as well as on milman s deep technology of m ellipsoids and on certain information theoretic inequalities as a by product we also give a

existence and uniqueness of anti periodic solutions for a kind of rayleigh equation with two deviating arguments abstract in this paper we use the leray schauder degree theory to establish new results on the existence and uniqueness of anti periodic solutions for a kind of rayleigh equation with two deviating arguments of the form x f t x t g 1 t x t 1 t g 2 t x t 2 t e t

counterexample to the vector generalization of costa s entropy power inequality and partial resolution we give a counterexample to the vector generalization of costa s entropy power inequality due to liu et al in particular the claimed inequality can fail if the matrix valued parameter in the convex combination does not commute with the covariance of the additive gaussian noise conversely the inequality holds if these two matrices commute

on the existence of harmonic solutions of lie nard systems we discuss the existence of harmonic solutions of lienard systems of the form x d dtgradf x gradg x p t where f c 2 r n r g c 1 r n r p c 0 r r n and p t t p t for a constant t 0

the concavity of p entropy power and applications in functional inequalities abstract in this paper we prove the concavity of p entropy power of probability densities solving the p heat equation on closed riemannian manifold with nonnegative ricci curvature as applications we give new proofs of l p euclidean nash inequality and l p euclidean logarithmic sobolev inequality moreover an improvement of l p logarithmic sobolev inequality is derived

on the similarity of the entropy power inequality and the brunn minkowski inequality corresp the entropy power inequality states that the effective variance entropy power of the sum of two independent random variables is greater than the sum of their effective variances the brunn minkowski inequality states that the effective radius of the set sum of two sets is greater than the sum of their effective radii both these inequalities are recast in a form that enhances their similarity in spite of this similarity there is as yet no common proof of the inequalities nevertheless their intriguing similarity suggests that new results relating to entropies from known results in geometry and vice versa may be found two applications of this reasoning are presented first an isoperimetric inequality for entropy is proved that shows that the spherical normal distribution minimizes the trace of the fisher information matrix given an entropy constraint just as a sphere minimizes the surface area given a volume constraint second a theorem involving the effective radii of growing convex sets is proved

periodic solutions for higher order differential equations with deviating argument abstract by using the coincidence degree theory of mawhin we study the existence of periodic solutions for higher order differential equations with deviating argument x n t i 1 n 1 b i x i t f t x t x t 1 t x t m t p t some new results on the existence of periodic solutions of the equations are obtained meanwhile an example is given to illustrate our results

periodic solutions to a second order p laplacian neutral functional differential system abstract by analyzing some properties of the linear difference operator a a x t x t c x t first and then using an extension of mawhin s continuation theorem a second order p laplacian neutral functional differential system as follows d d t p x t c x t f t x t x t t x t is studied some new results on the existence of periodic solutions is obtained the result is related to the deviating arguments and meanwhile the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature

periodic solutions for nonlinear nth order differential equations with delays by applying the continuation theorem of coincidence degree theory we establish the existence of 2 periodic solutions for a class of nonlinear nth order differential equations with delays

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

periodic solutions for a kind of lienard equation with a deviating argument abstract by means of continuation theorem of coincidence degree theory we study a kind of lienard equation with a deviating argument as follows x t f x t x t g x t t x t e t some new results on the existence of periodic solutions are obtained

the concavity of renyi entropy power we associate to the pth renyi entropy a definition of entropy power which is the natural extension of shannon s entropy power and exhibits a nice behavior along solutions to the p nonlinear heat equation in rn we show that the renyi entropy power of general probability densities solving such equations is always a concave function of time whereas it has a linear behavior in correspondence to the barenblatt source type solutions this result extends costa s concavity inequality for shannon s entropy power to renyi entropies

a strong entropy power inequality when one of the random summands is gaussian we sharpen the entropy power inequality epi in terms of the strong data processing function for gaussian channels among other consequences this strong epi generalizes the vector extension of costa s epi to non gaussian channels in a precise sense this leads to a new reverse epi and as a corollary sharpens stam s uncertainty principle relating entropy power and fisher information or equivalently gross logarithmic sobolev inequality applications to network information theory are also given including a short self contained proof of the rate region for the two encoder quadratic gaussian source coding problem and a new outer bound for the one sided gaussian interference channel

information theoretic proofs of entropy power inequalities while most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information up to now shannon s entropy power inequality epi is an exception existing information theoretic proofs of the epi hinge on representations of differential entropy using either fisher information or minimum mean square error mmse which are derived from de bruijn s identity in this paper we first present an unified view of these proofs showing that they share two essential ingredients 1 a data processing argument applied to a covariance preserving linear transformation 2 an integration over a path of a continuous gaussian perturbation using these ingredients we develop a new and brief proof of the epi through a mutual information inequality which replaces stam and blachman s fisher information inequality fii and an inequality for mmse by guo shamai and verdu used in earlier proofs the result has the advantage of being very simple in that it relies only on the basic properties of mutual information these ideas are then generalized to various extended versions of the epi zamir and feder s generalized epi for linear transformations of the random variables takano and johnson s epi for dependent variables liu and viswanath s covariance constrained epi and costa s concavity inequality for the entropy power

information measures inequalities and performance bounds for parameter estimation in impulsive noise environments recent studies found that many channels are affected by additive noise that is impulsive in nature and is best explained by heavy tailed symmetric alpha stable distributions dealing with impulsive noise environments comes with an added complexity with respect to the standard gaussian environment the alpha stable probability density functions do not possess closed form expressions except in few special cases furthermore they have an infinite second moment and the nice hilbert space structure of the space of random variables having a finite second moment is lost along with its tools and methodologies this is indeed the case in estimation theory where classical tools to quantify the performance of an estimator are tightly related to the assumption of having finite variance variables in alpha stable environments expressions such as the mean square error and the cramer rao bound are hence problematic in this paper we tackle the parameter estimation problem in the impulsive noise environments and develop novel tools that are tailored to the alpha stable and heavy tailed noise environments tools that coincide with the standard ones adopted in the gaussian setup namely a generalized power measure and a generalized fisher information we generalize known information inequalities commonly used in the gaussian context the de bruijn identity the fisher information inequality the isoperimetric inequality for entropies and the cramer rao bound additionally we derive upper bounds on the differential entropy of independent sums having a stable component intermediately the new power measure is used to shed some light on the additive alpha stable noise channel capacity in a setup that generalizes the linear average power constrained additive white gaussian noise channel our theoretical findings are paralleled with numerical evaluations of various quantities and bounds using developed matlab packages

sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument abstract by means of mawhin s continuation theorem we study some second order differential equations with a deviating argument x t f t x t x t t x t e t some new results on the existence of periodic solutions are obtained the interest is that we allow the degree with respect to the variables x 0 x 1 x 2 of f t x 0 x 1 x 2 to be greater than 1 and also the result theorem 3 2 is related to the deviating argument t meanwhile we give an example to demonstrate our result

hessian and concavity of mutual information differential entropy and entropy power in linear vector gaussian channels within the framework of linear vector gaussian channels with arbitrary signaling the jacobian of the minimum mean square error and fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper capitalizing on prior research where the minimum mean square error and fisher information matrices were linked to information theoretic quantities through differentiation the hessian of the mutual information and the entropy are derived these expressions are then used to assess the concavity properties of mutual information and entropy under different channel conditions and also to derive a multivariate version of an entropy power inequality due to costa

convexity and regularity properties for entropic interpolations abstract in this paper we prove a convexity property of the relative entropy along entropic interpolations solutions of the schrodinger problem and a regularity property of the entropic cost along the heat flow then we derive a dimensional evi inequality and a contraction property for the entropic cost along the heat flow as a consequence we recover the equivalent results in the wasserstein space proved by erbar kuwada and sturm

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

monotonicity thinning and discrete versions of the entropy power inequality we consider the entropy of sums of independent discrete random variables in analogy with shannon s entropy power inequality where equality holds for normals in our case infinite divisibility suggests that equality should hold for poisson variables we show that some natural analogues of the epi do not in fact hold but propose an alternative formulation which does always hold the key to many proofs of shannon s epi is the behavior of entropy on scaling of continuous random variables we believe that renyi s operation of thinning discrete random variables plays a similar role to scaling and give a sharp bound on how the entropy of ultra log concave random variables behaves on thinning in the spirit of the monotonicity results established by artstein ball barthe and naor we prove a stronger version of concavity of entropy which implies a strengthened form of our discrete epi

positive almost periodic solutions for a class of lienard type systems with multiple deviating arguments this paper considers the lienard type systems with multiple deviating arguments sufficient conditions for the existence and exponential stability of positive almost periodic solutions are established which are new and complement previously known results

existence of periodic solutions to a p laplacian lienard differential equation with a deviating argument abstract by means of mawhin s continuation theorem a kind of p laplacian lienard differential equation with a deviating argument as follows p y t f y t y t h y t g y t t e t is studied a new result on the existence of periodic solutions is obtained the interest is that the relation between the existence of periodic solutions and the deviating argument t is investigated meanwhile the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature

capacity and rate regions of a class of broadcast interference channels in this paper a class of broadcast interference channels bic is investigated where one of the two broadcast receivers is subject to interference coming from a point to point transmission for a general discrete memoryless broadcast interference channel dm bic an achievable scheme based on message splitting superposition and binning is proposed and a concise representation of the corresponding achievable rate region mathcal r is obtained two partial order broadcast conditions interference oblivious less noisy and interference cognizant less noisy are defined thereby extending the usual less noisy condition for a regular broadcast channel by taking interference into account under these conditions a reduced form of mathcal r is shown to be equivalent to a rate region based on a simpler scheme where the broadcast transmitter uses only superposition furthermore if interference is strong for the interference oblivious less noisy dm bic the capacity region is given by the aforementioned two equivalent rate regions for the interference cognizant less noisy dm bic it is argued that the strong but not very strong interference condition does not exist and in this case the capacity region for the very strong interference is obtained for a gaussian broadcast interference channel channel parameters are categorized into three regimes for the first two regimes which are closely related to the two partial order broadcast conditions achievable rate regions are derived by specializing the corresponding achievable schemes of dm bics with gaussian input distributions the entropy power inequality based outer bounds are obtained by combining bounding techniques for a gaussian broadcast channel and a gaussian interference channel these inner and outer bounds lead to either exact or approximate characterizations of capacity regions and sum capacity under various conditions for the remaining complementing regime inner and outer bounds are also provided

periodic solutions to a second order nonlinear neutral functional differential equation in the critical case abstract in this paper the authors study the existence of periodic solutions for a second order neutral functional differential equation x t cx t f x t x t g t x t t e t in the critical case c 1 by employing mawhin s continuation theorem and some analysis techniques sufficient conditions are given for the existence of periodic solutions

anti periodic solutions for a class of nonlinear nth order differential equations with delays in this paper we use the leray schauder degree theory to establish new results on the existence and uniqueness of anti periodic solutions for a class of nonlinear nth order differential equations with delays of the form x n t f t x n 1 t g t x email protected t e t

a simple proof of the entropy power inequality this correspondence gives a simple proof of shannon s entropy power inequality epi using the relationship between mutual information and minimum mean square error mmse in gaussian channels

on the entropy power inequality for the renyi entropy of order 0 1 using a sharp version of the reverse young inequality and a renyi entropy comparison result due to fradelizi madiman and wang 2016 the authors derive renyi entropy power inequalities for log concave random vectors when renyi parameters belong to 0 1 furthermore the estimates are shown to be sharp up to absolute constants

periodic solutions to a kind of neutral functional differential equation in the critical case in this paper we consider a kind of neutral functional differential equation as follows x t cx t gt xt t e t in the critical case c 1 by employing the topological degree theory and some analysis techniques we obtain some new results on the existence of periodic solutions

simple proof of the concavity of the entropy power with respect to added gaussian noise a very simple proof of m h costa s result see ibid vol it 31 p 751 60 1985 that the entropy power of x sub t x n o ti is concave in t is derived as an immediate consequence of an inequality concerning fisher information this relationship between fisher information and entropy is found to be useful for proving the central limit theorem thus one who seeks new entropy inequalities should try first to find new equalities about fisher information or at least to exploit the existing ones in new ways

capacity bounds via duality with applications to multiple antenna systems on flat fading channels a technique is proposed for the derivation of upper bounds on channel capacity it is based on a dual expression for channel capacity where the maximization of mutual information over distributions on the channel input alphabet is replaced with a minimization of average relative entropy over distributions on the channel output alphabet we also propose a technique for the analysis of the asymptotic capacity of cost constrained channels the technique is based on the observation that under fairly mild conditions capacity achieving input distributions escape to infinity the above techniques are applied to multiple antenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown or only partially known at the receiver it is demonstrated that for high signal to noise ratio snr the capacity of such channels typically grows only double logarithmically in the snr to better understand this phenomenon and the rates at which it occurs we introduce the fading number as the second order term in the high snr asymptotic expansion of capacity and derive estimates on its value for various systems it is suggested that at rates that are significantly higher than the fading number communication becomes extremely power inefficient thus posing a practical limit on practically achievable rates upper and lower bounds on the fading number are also presented for single input single output siso systems the bounds coincide thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes we also demonstrate that for memoryless multiple input single output miso channels the fading number is achievable using beam forming and we derive an expression for the optimal beam direction this direction depends on the fading law and is in general not the direction that maximizes the snr on the induced siso channel using a new closed form expression for the expectation of the logarithm of a noncentral chi square distributed random variable we provide some closed form expressions for the fading number of some systems with gaussian fading including siso systems with circularly symmetric stationary and ergodic gaussian fading the fading number of the latter is determined by the fading mean fading variance and the mean squared error in predicting the present fading from its past it is not directly related to the doppler spread for the rayleigh ricean and multiple antenna rayleigh fading channels we also present firm nonasymptotic upper and lower bounds on channel capacity these bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high snr and their ratio to capacity approaches one at low snr

a concavity property for the reciprocal of fisher information and its consequences on costa s epi abstract we prove that the reciprocal of fisher information of a log concave probability density x in r n is concave in t with respect to the addition of a gaussian noise z t n 0 t i n as a byproduct of this result we show that the third derivative of the entropy power of a log concave probability density x in r n is nonnegative in t with respect to the addition of a gaussian noise z t for log concave densities this improves the well known costa s concavity property of the entropy power costa 1985

contractivity properties of a quantum diffusion semigroup we consider a quantum generalization of the classical heat equation and study contractivity properties of its associated semigroup we prove a nash inequality and a logarithmic sobolev inequality the former leads to an ultracontractivity result this in turn implies that the largest eigenvalue and the purity of a state with positive wigner function evolving under the action of the semigroup decrease at least inverse polynomially in time while its entropy increases at least logarithmically in time

on the equivalence between stein and de bruijn identities this paper focuses on illustrating 1 the equivalence between stein s identity and de bruijn s identity and 2 two extensions of de bruijn s identity first it is shown that stein s identity is equivalent to de bruijn s identity under additive noise channels with specific conditions second for arbitrary but fixed input and noise distributions under additive noise channels the first derivative of the differential entropy is expressed by a function of the posterior mean and the second derivative of the differential entropy is expressed in terms of a function of fisher information several applications over a number of fields such as signal processing and information theory are presented to support the usefulness of the developed results in this paper

remote source coding under gaussian noise dueling roles of power and entropy power the distributed remote source coding the so called ceo problem is studied in the case where the underlying source not necessarily gaussian has finite differential entropy and the observation noise is gaussian the main result is a new lower bound for the sum rate distortion function under arbitrary distortion measures when specialized to the case of mean squared error it is shown that the bound exactly mirrors a corresponding upper bound except that the upper bound has the source power variance whereas the lower bound has the source entropy power bounds exhibiting this pleasing duality of power and entropy power have been well known for direct and centralized source coding since shannon s work while the bounds hold generally their value is most pronounced when interpreted as a function of the number of agents in the ceo problem

periodic solutions of lienard differential equations with subquadratic potential conditions abstract in this paper we study the second order forced lienard equation x f x x g x e t we obtain the existence of periodic solutions under some subquadratic conditions

existence and uniqueness of periodic solutions for a kind of rayleigh equation with finitely many deviating arguments abstract in this paper we consider a kind of rayleigh equation with finitely many deviating arguments of the form x f t x t k 1 n g k t x t k t p t by using the coincidence degree theory we establish the results on the existence and uniqueness of periodic solutions for the above equation the results we obtained include and improve the results existing in the literature

nonlinear diffusions extremal properties of barenblatt profiles best matching and delays abstract in this paper we consider functionals based on moments and nonlinear entropies which have a linear growth in time in case of source type solutions to the fast diffusion or porous medium equations that are also known as barenblatt solutions as functions of time these functionals have convexity properties for generic solutions so that their asymptotic slopes are extremal for barenblatt profiles the method relies on scaling properties of the evolution equations and provides a simple and direct proof of sharp gagliardo nirenberg sobolev inequalities in scale invariant form the method also gives refined estimates of the growth of the second moment and as a consequence establishes the monotonicity of the delay corresponding to the best matching barenblatt solution compared to the barenblatt solution with same initial second moment here the notion of best matching is defined in terms of a relative entropy

existence and uniqueness of periodic solutions for a kind of rayleigh equation with two deviating arguments in this paper we consider a kind of rayleigh equation with two deviating arguments of the form x f t x t g 1 t x email protected 1 t g 2 t x email protected 2 t p t by using the coincidence degree theory we establish new results on the existence and uniqueness of periodic solutions for the above equation

existence and multiplicity results for periodic solutions of semilinear duffing equations we obtain existence an multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear duffing s equation x g x p t in the semi linear case 0 a g x x b for x large we introduce new conditions of nonresonance with respect to the spectrum of the associated linear differential operator x x and show by some nonlinear counterexamples that the results are sharp

periodic solutions for a kind of lienard equation using inequality techniques and coincidence degree theory new results are provided concerning the existence and uniqueness of t periodic solutions for a lienard equations with delay an illustrative example is provided to demonstrate that the results in this paper hold under weaker conditions than existing results and are more effective

wasserstein continuity of entropy and outer bounds for interference channels it is shown that under suitable regularity conditions differential entropy is o sqrt n lipschitz as a function of probability distributions on mathbb r n with respect to the quadratic wasserstein distance under similar conditions discrete shannon entropy is shown to be o n lipschitz in distributions over the product space with respect to ornstein s bar d distance wasserstein distance corresponding to the hamming distance these results together with talagrand s and marton s transportation information inequalities allow one to replace the unknown multi user interference with its independent identically distributed approximations as an application a new outer bound for the two user gaussian interference channel is proved which in particular settles the missing corner point problem of costa 1985

on renyi entropy power inequalities this paper gives improved renyi entropy power inequalities r epis consider a sum s n sum k 1 n x k of n independent continuous random vectors taking values on mathbb r d and let alpha in 1 infty an r epi provides a lower bound on the order alpha renyi entropy power of s n that up to a multiplicative constant which may depend in general on n alpha d is equal to the sum of the order alpha renyi entropy powers of the n random vectors x k k 1 n for alpha 1 the r epi coincides with the well known entropy power inequality by shannon the first improved r epi is obtained by tightening the recent r epi by bobkov and chistyakov which relies on the sharpened young s inequality a further improvement of the r epi also relies on convex optimization and results on rank one modification of a real valued diagonal matrix

periodic solutions for p laplacian rayleigh equations with a deviating argument abstract by using the generalized borsuk theorem in coincidence degree theory some new criteria for guaranteeing the existence of periodic solutions for p laplacian rayleigh equations with a deviating argument are derived