non uniform bounds in the poisson approximation with applications to informational distances i we explore asymptotically optimal bounds for deviations of bernoulli convolutions from the poisson limit in terms of the shannon relative entropy and the pearson chi 2 distance the results are based on proper non uniform estimates for densities this part deals with the so called non degenerate case

asymptotic dimension and small cancellation for hierarchically hyperbolic spaces and groups we prove that all hierarchically hyperbolic groups have finite asymptotic dimension one application of this result is to obtain the sharpest known bound on the asymptotic dimension of the mapping class group of a finite type surface improving the bound from exponential to at most quadratic in the complexity of the surface we also apply the main result to various other hierarchically hyperbolic groups and spaces we also prove a small cancellation result namely if g is a hierarchically hyperbolic group h g is a suitable hyperbolically embedded subgroup and n h is sufficiently deep in h then g n is a relatively hierarchically hyperbolic group this new class provides many new examples to which our asymptotic dimension bounds apply along the way we prove new results about the structure of hhss for example the associated hyperbolic spaces are always obtained up to quasi isometry by coning off canonical coarse product regions in the original space generalizing a relation established by masur and minsky between the complex of curves of a surface and teichmuller space

explicit solution to the singular discrete time stationary linear filtering problem a closed form solution to the stationary discrete time linear filtering problem is obtained explicitly in terms of the system state space matrices in the limiting singular case where the measurement noise tends to zero simple expressions in closed form are obtained for the kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the kalman filter closed loop matrix is derived the minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure and a remarkably different behavior of the solution in the minimum and nonminimum phase cases is found

optimum asymptotic multiuser efficiency of randomly spread cdma this correspondence analyzes the high signal to noise ratio snr performance of optimum multiuser detectors for synchronous direct sequence spread spectrum with random spreading in an additive white gaussian noise channel under very general conditions on the received powers we show that the optimum asymptotic efficiency of a k user system with spreading gain n converges to 1 almost surely as k spl rarr spl infin and k n is kept equal to an arbitrary nonzero constant therefore the asymptotic behavior of the minimum bit error rate is equivalent to that of a single user system

design of signature sequences for overloaded cdma and bounds on the sum capacity with arbitrary symbol alphabets in this paper we explore some of the fundamentals of synchronous code division multiple access cdma as applied to wireless and optical communication systems under very general settings of any size for the user symbols and the signature matrix entries the channel is modeled by real complex additive noise of arbitrary distribution two problems are addressed the first problem concerns whether uniquely detectable overloaded matrices exist in the absence of additive noise under these general settings and if so whether there are any practical optimum detection algorithms the second one is about the bounds for the sum channel capacity when user data and signature matrices employ any real or complex alphabets finite or infinite in response to the first problem we have developed practical maximum likelihood detection algorithms for overloaded cdma systems for a large class of alphabets in response to the second problem a general theorem has been developed in which the sum capacity lower bounds with respect to the number of users spreading gain and signal to noise ratio can be derived to show the power and utility of the main theorem a number of sum capacity bounds for special cases are evaluated an important conclusion of this paper is that the lower and upper bounds of the sum capacity for small medium size cdma systems depend on both the input and the signature symbols this is contrary to the asymptotic results for large scale systems reported in the literature also confirmed in this paper where the signature symbols and statistics disappear for signature matrices and input vectors with i i d entries furthermore upper and asymptotic bounds are derived and compared to other derivations

spectral efficiency of random time hopping cdma traditionally paired with impulsive communications time hopping code division multiple access th cdma is a multiple access technique that separates users in time by coding their transmissions into pulses occupying a subset of n mathsf s chips out of the total n included in a symbol period in contrast with the traditional direct sequence cdma ds cdma where n mathsf s n this paper analyzes the th cdma with random spreading by determining whether peculiar theoretical limits are identifiable with both optimal and suboptimal receiver structures in particular in the archetypal case of sparse spreading that is n mathsf s 1 results indicate that the th cdma has a fundamentally different behavior than ds cdma where the crucial role played by energy concentration typical of th directly relates with its intrinsic uneven use of degrees of freedom

optimum sequence multisets for synchronous code division multiple access channels it is shown that the sum capacity of the symbol synchronous code division multiple access channel with equal average input energy constraints is maximized precisely by those spreading sequence multisets that meet welch s lower bound on total squared correlation it is further shown that the symmetric capacity of the channel determined by these same sequence multisets is equal to the sum capacity

loop transfer recovery techniques for discrete time optimal regulators using prediction estimators for discrete time lqg optimal regulators using current estimators it has been shown that perfect recoveries of the loop transfer matrices at the input or at the output are possible for square minimum phase systems however current estimators cannot be used when the processing time of the controller is significant in this note the loop transfer recoveries using prediction estimators for square minimum phase systems are considered it is shown that although the perfect recoveries are impossible the feedback properties obtained by the recovery techniques are those that can be recovered best in the presence of the delay in the controller

monotonic convergence in an information theoretic law of small numbers an entropy increasing to the maximum result analogous to the entropic central limit theorem barron 1986 artstein 2004 is obtained in the discrete setting this involves the thinning operation and a poisson limit monotonic convergence in relative entropy is established for general discrete distributions while monotonic increase of shannon entropy is proved for the special class of ultra log concave distributions overall we extend the parallel between the information theoretic central limit theorem and law of small numbers explored by kontoyiannis 2005 and harremoeumls 2007 2008 2009 ingredients in the proofs include convexity majorization and stochastic orders

crame spl acute r rao and moment entropy inequalities for renyi entropy and generalized fisher information the moment entropy inequality shows that a continuous random variable with given second moment and maximal shannon entropy must be gaussian stam s inequality shows that a continuous random variable with given fisher information and minimal shannon entropy must also be gaussian the crame spl acute r rao inequality is a direct consequence of these two inequalities in this paper the inequalities above are extended to renyi entropy p sup th moment and generalized fisher information generalized gaussian random densities are introduced and shown to be the extremal densities for the new inequalities an extension of the crame spl acute r rao inequality is derived as a consequence of these moment and fisher information inequalities

rate of convergence to poisson law in terms of information divergence the precise bounds on the information divergence from a binomial distribution to the accompanying poisson law are obtained as a corollary an upper bound for the total variation distance between the distributions is established which in a large range of change of the parameters of the distributions is better than those already known

optimal sequences and sum capacity of synchronous cdma systems the sum capacity of a multiuser synchronous cdma system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed by rupf and massey see ibid vol 40 p 1261 6 1994 which had solved the equal power constraint case we identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them

applying discrete time proportional integral observers for state and disturbance estimations in this note we apply the proportional integral observer to simultaneously estimate system states and unknown disturbances for discrete time nonminimum phase systems conditions for providing the existence of such observer are given when the disturbances do not vary too much between two consecutive sampling instances the proposed method can render the estimation errors of system states and disturbances to be constrained in a small bounded region simulation results support the theoretical developments

entropy inequalities for stable densities and strengthened central limit theorems we consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function by showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a levy centered density of parameter lambda 1 this introduces a new information theoretic approach to the central limit theorem for stable laws in which the main argument is shown to be the relative fractional fisher information recently introduced in toscani ricerche mat 65 1 71 91 2016 in particular it is proven that with respect to the relative fractional fisher information the levy density satisfies an analogous of the logarithmic sobolev inequality which allows to pass from the monotonicity and decay to zero of the relative fractional fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate

density parameter estimation of skewed spl alpha stable distributions over the last few years there has been a great interest in spl alpha stable distributions for modeling impulsive data as a critical step in modeling with spl alpha stable distributions the problem of estimating the parameters of stable distributions have been addressed by several works in the literature however many of these works consider only the special case of symmetric stable random variables this is an important restriction however since most real life signals are skewed the existing techniques on estimating skewed distribution parameters are either computationally too expensive require lookup tables or have poor convergence properties we introduce three novel classes of estimators for the parameters of general stable distributions which are generalizations of the methods previously suggested for parameter estimation of symmetric stable distributions these estimators exploit expressions we develop for fractional lower order negative order and logarithmic moments and tail statistics we also introduce simple transformations that allow one to use existing symmetric stable parameter estimation techniques techniques suggested in this paper provide the only closed form solutions we are aware of for parameters that may be efficiently computed simulation results show that at least one of our new estimators has better performance than the existing techniques over most of the parameter space furthermore our techniques require substantially less computation

asymptotic recovery for discrete time systems an asymptotic recovery design procedure is proposed for square discrete time linear time invariant multivariable systems which allows a state feedback design to be approximately recovered by a dynamic output feedback scheme both the case of negligible processing time compared to the sampling interval and of significant processing time are discussed in the former case it is possible to obtain perfect recovery if the plant is minimum phase and has the smallest possible number of zeros at infinity in other cases good recovery is frequently possible new conditions are found which ensure that the return ratio being recovered exhibits good robustness properties

discrete time pi nonlinear cal h _ infty estimation in this technical note exact and approximate solutions of the discrete time suboptimal proportional integral h estimation problem for affine nonlinear systems using finite dimensional estimators filters are presented sufficient conditions for the solvability of the problem are given in terms of discrete time hamilton jacobi isaac s equations for linear systems it is shown that these equations reduce to a system of linear matrix inequalities simulation results are also presented to show the benefit of the new approach

maximum entropy versus minimum risk and applications to some classical discrete distributions the game which can be taken to lie behind the maximum entropy principle is studied refining previous techniques new theoretical results are obtained these results are illustrated by concrete examples pertaining to well known classical models

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

entropy bounds for discrete random variables via maximal coupling this paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions the derivation of the bounds relies on maximal coupling and they apply to discrete random variables which are defined over finite or countably infinite alphabets loosened versions of these bounds are demonstrated to reproduce some previously reported results the use of the new bounds is exemplified for the poisson approximation where bounds on the local and total variation distances follow from stein s method

integral controller design based on disturbance cancellation partial ltr approach for non minimum phase plants for non minimum phase plants the loop transfer recovery ltr design of integral controllers based on the disturbance cancellation is considered since the design requires an unstabilizable extended plant the standard ltr method cannot be applied a new partial ltr method is proposed to overcome the difficulty the target of the proposed design is a fictitious controller including a disturbance estimator based on the measurement of the minimum phase state it is shown that the riccati equation including the gain matrix of the disturbance estimator in the target can be used to recover the target feedback property in the output feedback controller a simple design example is presented to show the effectiveness of the proposed method

bounds on the sum capacity of synchronous binary cdma channels in this paper we obtain a family of lower bounds for the sum capacity of code division multiple access cdma channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution the envelope of this family gives a relatively tight lower bound in terms of the number of users spreading gain and the noise distribution the derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero the noisy channel bound approaches the noiseless case the behavior of the lower bound shows that for small noise power the number of users can be much more than the spreading gain without any significant loss of information overloaded cdma a conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution as the noise level increases and or the ratio of the number of users and the spreading gain increases the conjectured upper bound approaches the lower bound we have also derived asymptotic limits of our bounds that can be compared to a formula that tanaka obtained using techniques from statistical physics his bound is close to that of our conjectured upper bound for large scale systems

optimality of the myriad filter in practical impulsive noise environments linear filtering theory has been largely motivated by the characteristics of gaussian signals in the same manner the proposed myriad filtering methods are motivated by the need for a flexible filter class with high statistical efficiency in non gaussian impulsive environments that can appear in practice we introduce several important properties of the myriad filter and prove its optimality in the family of spl alpha stable distributions

sumset and inverse sumset inequalities for differential entropy and mutual information the sumset and inverse sumset theories of freiman plunnecke and ruzsa give bounds connecting the cardinality of the sumset a b fa b a2 a b2 bg of two discrete sets a b to the cardinalities or the ner structure of the original sets a b for example the sum dierence

randomly spread cdma asymptotics via statistical physics this paper studies randomly spread code division multiple access cdma and multiuser detection in the large system limit using the replica method developed in statistical physics arbitrary input distributions and flat fading are considered a generic multiuser detector in the form of the posterior mean estimator is applied before single user decoding the generic detector can be particularized to the matched filter decorrelator linear minimum mean square error mmse detector the jointly or the individually optimal detector and others it is found that the detection output for each user although in general asymptotically non gaussian conditioned on the transmitted symbol converges as the number of users go to infinity to a deterministic function of a hidden gaussian statistic independent of the interferers thus the multiuser channel can be decoupled each user experiences an equivalent single user gaussian channel whose signal to noise ratio snr suffers a degradation due to the multiple access interference mai the uncoded error performance e g symbol error rate and the mutual information can then be fully characterized using the degradation factor also known as the multiuser efficiency which can be obtained by solving a pair of coupled fixed point equations identified in this paper based on a general linear vector channel model the results are also applicable to multiple input multiple output mimo channels such as in multiantenna systems

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

efficient geodesics and an effective algorithm for distance in the complex of curves we give an algorithm for determining the distance between two vertices of the complex of curves while there already exist such algorithms for example by leasure shackleton and webb our approach is new simple and more effective for all distances accessible by computer our method gives a new preferred finite set of geodesics between any two vertices of the complex called efficient geodesics which are different from the tight geodesics introduced by masur and minsky

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

tight geodesics in the curve complex the curve graph mathcal g associated to a compact surface is the 1 skeleton of the curve complex defined by harvey masur and minsky showed that this graph is hyperbolic and defined the notion of a tight geodesic therein we prove some finiteness results for such geodesics for example we show that a slice of the union of tight geodesics between any pair of points has cardinality bounded purely in terms of the topological type of we deduce some consequences for the action of the mapping class group on mathcal g in particular we show that it satisfies an acylindricity condition and that the stable lengths of pseudoanosov elements are rational with bounded denominator

on the maximum entropy of the sum of two dependent random variables investigates the maximization of the differential entropy h x y of arbitrary dependent random variables x and y under the constraints of fixed equal marginal densities for x and y we show that max h x y h 2x under the constraints that x and y have the same fixed marginal density f if and only if f is log concave the maximum is achieved when x y if f is not log concave the maximum is strictly greater than h 2x as an example identically distributed gaussian random variables have log concave densities and satisfy max h x y h 2x with x y more general inequalities in this direction should lead to capacity bounds for additive noise channels with feedback

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

a semigroup approach to poisson approximation the aim of this paper is twofold first to show that poisson approximation problems for independent summands can in a natural way be treated in a suitable operator semigroup framework allowing at the same time for an asymptotically precise evaluation of the leading term with respect to the total variation distance second to determine asymptotically those poisson distributions which minimize this distance for given bernoulli summands besides semigroup methods coupling techniques as well as direct computations are used

binomial and poisson distributions as maximum entropy distributions the binomial and the poisson distributions are shown to be maximum entropy distributions of suitably defined sets poisson s law is considered as a case of entropy maximization and also convergence in information divergence is established

when the a contrario approach becomes generative the a contrario approach is a statistical hypothesis testing based approach to detect geometric meaningful events in images the general methodology consists in computing the probability of an observed geometric event under a noise model null hypothesis h 0 h0 and then declare the event meaningful when this probability is small enough generally the noise model is taken to be the independent uniform distribution on the considered elements our aim in this paper will be to question the choice of the noise model what happens if we enrich the noise model how to characterize the noise models such that there are no meaningful events against them among them what is the one that has maximum entropy what does a sample of it look like how is this noise model related to probability distributions on the elements that would produce with high probability the same detections all these questions will be formalized and answered in two different frameworks the detection of clusters in a set of points and the detection of line segments in an image the general idea is to capture the perceptual information contained in an image and then generate new images having the same visual content we believe that such a generative approach can have applications for instance in image compression or for clutter removal

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

on the entropy of compound distributions on nonnegative integers some entropy comparison results are presented concerning compound distributions on nonnegative integers the main result shows that under a log concavity assumption two compound distributions are ordered in terms of shannon entropy if both the ldquonumbers of claimsrdquo and the ldquoclaim sizesrdquo are ordered accordingly in the convex order several maximum minimum entropy theorems follow as a consequence most importantly two recent results of johnson 2008 on maximum entropy characterizations of compound poisson and compound binomial distributions are proved under fewer assumptions and with simpler arguments

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

the classification of kleinian surface groups i models and bounds we give the first part of a proof of thurston s ending lamination conjecture in this part we show how to construct from the end invariants of a kleinian surface group a lipschitz model for the thick part of the corresponding hyperbolic manifold this enables us to describe the topological structure of the thick part and to give a priori geometric bounds

duality between equilibrium and growing networks in statistical physics any given system can be either at an equilibrium or away from it networks are not an exception most network models can be classified as either equilibrium or growing here we show that under certain conditions there exists an equilibrium formulation for any growing network model and vice versa the equivalence between the equilibrium and nonequilibrium formulations is exact not only asymptotically but even for any finite system size the required conditions are satisfied in random geometric graphs in general and causal sets in particular and to a large extent in some real networks

entropy and equilibrium via games of complexity abstract it is suggested that thermodynamical equilibrium equals game theoretical equilibrium aspects of this thesis are discussed the philosophy is consistent with maximum entropy thinking of jaynes but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle the games introduced are based on measures of complexity entropy is viewed as minimal complexity it is demonstrated that tsallis entropy q entropy and kaniadakis entropy entropy can be obtained in this way based on suitable complexity measures a certain unifying effect is obtained by embedding these measures in a two parameter family of entropy functions

divergence in lattices in semisimple lie groups and graphs of groups divergence functions of a metric space estimate the length of a path connecting two points a b at distance 3 s is a finite set of valuations of a number field k including all infinite valuations and o s is the corresponding ring of s integers

the classification of kleinian surface groups ii the ending lamination conjecture thurston s ending lamination conjecture states that a hyperbolic 3manifold n with nitely generated fundamental group is uniquely determined by its topological type and its end invariants in this paper we prove this conjecture for kleinian surface groups the general case when n has incompressible ends relative to its cusps follows readily the main ingredient is a uniformly bilipschitz model for the quotient of h 3 by a kleinian surface group

discrete time loop transfer recovery for systems with nonminimum phase zeros and time delays abstract the purpose of this paper is to study what happens when the discrete time loop transfer recovery ltr procedure is applied to plants with nonminimum phase zeros and with uniform time delay in all channels explicit expressions are given for the asymptotic behavior of the resulting sensitivity function and loop transfer function these results yield a better understanding of the mechanism of the discrete time loop transfer recovery procedure and the design limitations due to nonminimum phase zeros and time delays

on properties of the support of capacity achieving distributions for additive noise channel models with input cost constraints we study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion we derive a simple relation between three parameters the input output function the input cost function and the noise probability density function one which dictates the type of the optimal input in layman terms we prove that the support of the optimal input is bounded whenever the cost grows faster than a cutoff growth rate equal to the logarithm of the inverse of the noise probability density function evaluated at the input output function furthermore we prove a converse statement that says whenever the cost grows slower than the cutoff rate the optimal input has necessarily an unbounded support in addition we show how the discreteness of the optimal input is guaranteed whenever the triplet satisfy some analyticity properties we argue that a suitable cost function to be imposed on the channel input is one that grows similarly to the cutoff rate our results are valid for any cost function that is super logarithmic they summarize a large number of previous channel capacity results and give new ones for a wide range of communication channel models such as gaussian mixtures generalized gaussians and heavy tailed noise models that we state along with numerical computations

sharp bounds on the entropy of the poisson law and related quantities one of the difficulties in calculating the capacity of certain poisson channels is that h the entropy of the poisson distribution with mean is not available in a simple form in this paper we derive upper and lower bounds for h that are asymptotically tight and easy to compute the derivation of such bounds involves only simple probabilistic and analytic tools this complements the asymptotic expansions of knessl 1998 jacquet and szpankowski 1999 and flajolet 1999 the same method yields tight bounds on the relative entropy d n p between a binomial and a poisson thus refining the work of harremoe s and ruzankin 2004 bounds on the entropy of the binomial also follow easily

a proof of the fisher information inequality via a data processing argument the fisher information j x of a random variable x under a translation parameter appears in information theory in the classical proof of the entropy power inequality epi it enters the proof of the epi via the de bruijn identity where it measures the variation of the differential entropy under a gaussian perturbation and via the convolution inequality j x y sup 1 spl ges j x sup 1 j y sup 1 for independent x and y known as the fisher information inequality fii the fii is proved in the literature directly in a rather involved way we give an alternative derivation of the fii as a simple consequence of a data processing inequality for the cramer rao lower bound on parameter estimation

ltr design of discrete time proportional integral observers applies the proportional integral pi observer in connection with loop transfer recovery ltr design for discrete time systems both the prediction and the filtering versions of the pi observer are considered we show that a pi observer makes it possible to obtain time recovery i e exact recovery for t spl rarr spl infin under mild conditions two systematic ltr design methods one based on an extension of the linear quadratic gaussian loop transfer recovery lqg ltr and the other based on linear matrix inequality lmi are derived for the discrete time pi observer case explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given

maximizing the entropy of a sum of independent bounded random variables let x1 xn be n independent symmetric random variables supported on the interval 1 1 and let sn sigmai 1 nxi be their sum we show that the differential entropy of sn is maximized when x1 xn 1 are bernoulli taking on 1 or 1 with equal probability and xn is uniformly distributed

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

entropy power inequality for the renyi entropy the classical entropy power inequality is extended to the renyi entropy we also discuss the question of the existence of the entropy for sums of independent random variables

algorithms detecting stability and morseness for finitely generated groups abstract the notions of stable and morse subgroups of finitely generated groups generalize the concept of a quasiconvex subgroup of a word hyperbolic group for a word hyperbolic group g kapovich 31 provided a partial algorithm which on input a finite set s of g halts if s generates a quasiconvex subgroup of g and runs forever otherwise in this paper we give various detection and decidability algorithms for stability and morseness of a finitely generated subgroup of mapping class groups right angled artin groups toral relatively hyperbolic groups and finitely generated groups discriminated by a locally quasiconvex torsion free hyperbolic group for example ordinary limit groups

parameter estimation and blind channel identification in impulsive signal environments new methods for parameter estimation and blind channel identification in impulsive signal environments are presented where the signals noise are modeled as symmetric spl alpha stable s spl alpha s processes first we present methods for estimating the parameters characteristic exponent spl alpha and dispersion spl gamma of a s spl alpha s distribution from a time series the fractional lower order moments with both positive and negative orders and their applications to signal processing are introduced then we present a new algorithm for blind channel identification using the output fractional lower order moments and the spl alpha spectrum a new spectral representation for impulsive signals is introduced from the spl alpha spectrum we establish the blind identifiability conditions of any fir channel mixed phase unknown order with i i d s spl alpha s spl alpha 1 input as a byproduct a simple algorithm for recovering the phase of any type of a signal from the magnitude of its z transform is presented the novelty of our paper is in parameter estimation and blind identification of the fir channel based on fractional lower order moments of its output data monte carlo simulations clearly demonstrate the performance of the new methods

on the maximum entropy properties of the binomial distribution it is shown that the binomial n p distribution maximizes the entropy in the class of ultra log concave distributions of order n with fixed mean np this result which extends a theorem of shepp and olkin 1981 is analogous to that of johnson 2007 who considers the poisson case the proof constructs a markov chain whose limiting distribution is binomial n p and shows that the entropy never decreases along the iterations of this markov chain

thinning entropy and the law of thin numbers renyi s thinning operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables the properties of thinning are investigated in an information theoretic context especially in connection with information theoretic inequalities related to poisson approximation results the classical binomial to poisson convergence sometimes referred to as the law of small numbers is seen to be a special case of a thinning limit theorem for convolutions of discrete distributions a rate of convergence is provided for this limit and nonasymptotic bounds are also established this development parallels in part the development of gaussian inequalities leading to the information theoretic version of the central limit theorem in particular a thinning markov chain is introduced and it is shown to play a role analogous to that of the ornstein uhlenbeck process in connection to the entropy power inequality