rumors in a network who s the culprit we provide a systematic study of the problem of finding the source of a rumor in a network we model rumor spreading in a network with the popular susceptible infected si model and then construct an estimator for the rumor source this estimator is based upon a novel topological quantity which we term rumor centrality we establish that this is a maximum likelihood ml estimator for a class of graphs we find the following surprising threshold phenomenon on trees which grow faster than a line the estimator always has nontrivial detection probability whereas on trees that grow like a line the detection probability will go to 0 as the network grows simulations performed on synthetic networks such as the popular small world and scale free networks and on real networks such as an internet as network and the u s electric power grid network show that the estimator either finds the source exactly or within a few hops of the true source across different network topologies we compare rumor centrality to another common network centrality notion known as distance centrality we prove that on trees the rumor center and distance center are equivalent but on general networks they may differ indeed simulations show that rumor centrality outperforms distance centrality in finding rumor sources in networks which are not tree like

coding theorems for shannon s cipher system with correlated source outputs and common information source coding problems are treated for shannon s 1949 cipher system with correlated source outputs x y several cases are considered based on whether both x and y only x or only y must be transmitted to the receiver whether both x and y only x or only y must be kept secret or whether the security level is measured by sup 1 spl sol sub k h x sup k spl verbar w sup 1 spl sol sub k h y sup k spl verbar w or sup 1 spl sol sub k h x sup k y sup k spl verbar w where w is a cryptogram the admissible region of cryptogram rate and key rate for a given security level is derived for each case furthermore two new kinds of common information of x and y say c sub 1 x y and c sub 2 x y are considered c sub 1 x y is defined as the rate of the attainable minimum core of x sup k y sup k by removing each private information from x sup k y sup k as much as possible while c sub 2 x y is defined as the rate of the attainable maximum core v sub c such that if one loses v sub c then each uncertainty of x sup k and y sup k becomes h v sub c it is proved that c sub 1 x y i x y and c sub 2 x y min spl lcub h x h y spl rcub c sub 1 x y justifies the author s intuitive feeling that the mutual information represents a common information of x and y

a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

estimation efficiency under privacy constraints we investigate the problem of estimating a random variable y under a privacy constraint dictated by another correlated random variable x when x and y are discrete we express the underlying privacy utility tradeoff in terms of the privacy constrained guessing probability mathcal h p xy varepsilon and the maximum probability mathsf p mathsf c y z of correctly guessing y given an auxiliary random variable z where the maximization is taken over all p z y ensuring that mathsf p mathsf c x z leq varepsilon for a given privacy threshold varepsilon geq 0 we prove that mathcal h p xy cdot is concave and piecewise linear which allows us to derive its expression in closed form for any varepsilon when x and y are binary in the non binary case we derive mathcal h p xy varepsilon in the high utility regime i e for sufficiently large but nontrivial values of varepsilon under the assumption that y and z have the same alphabets we also analyze the privacy constrained guessing probability for two scenarios in which x y and z are binary vectors when x and y are continuous random variables we formulate the corresponding privacy utility tradeoff in terms of mathsf sensr p xy varepsilon the smallest normalized minimum mean squared error mmse incurred in estimating y from a gaussian perturbation z here the minimization is taken over a family of gaussian perturbations z for which the mmse of f x given z is within a factor 1 varepsilon from the variance of f x for any non constant real valued function f we derive tight upper and lower bounds for mathsf sensr when y is gaussian for general absolutely continuous random variables we obtain a tight lower bound for mathsf sensr p xy varepsilon in the high privacy regime i e for small varepsilon

stress constrained shape and topology optimization with fixed mesh a b spline finite cell method combined with level set function abstract in this paper we develop an efficient and flexible design method that integrates the b spline finite cell method b spline fcm and the level set function lsf for stress constrained shape and topology optimization any structure of complex geometry is embedded within an extended regular and fixed eulerian mesh no matter how the structure is optimized high order b spline shape functions are further implemented to ensure precisions of stress analysis and sensitivity analysis meanwhile level set functions i e implicit functions are used to enable topological changes of the considered structure through smooth boundary variations involved parameters rather than the conventional discrete form of lsf are directly taken as design variables to facilitate the numerical computing process to be specific the lsf is constructed by means of r functions that incorporate cubic splines as implicit functions to offer flexibilities for shape optimization within the framework of fixed mesh while the compactly supported radial basis functions cs rbfs are employed as implicit functions for stress constrained topology optimization it is shown the proposed fcm lsf method is a convenient approach that makes it possible to calculate stress and stress sensitivities with high precision representative examples of shape and topology optimization with and without stress constraints are solved with success demonstrating the advantages of the fcm lsf method

principal inertia components and applications we explore properties and applications of the principal inertia components pics between two discrete random variables x and y the pics lie in the intersection of information and estimation theory and provide a fine grained decomposition of the dependence between x and y moreover the pics describe which functions of x can or cannot be reliably inferred in terms of mmse given an observation of y we demonstrate that the pics play an important role in information theory and they can be used to characterize information theoretic limits of certain estimation problems in privacy settings we prove that the pics are related to the fundamental limits of perfect privacy

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

comments on a source matching approach to finding minimax codes by davisson l d and leon garcia a in the above paper 1 davisson and leon garcia prove a result equating the minimax redundancy for universal codes to a channel capacity that is computable by standard techniques they point out that the result had been developed earlier in unpublished work by gallager i would like to point out an alternative development of this result and to compare this work with that of davisson and leon garcia

chebyshev polynomials moment matching and optimal estimation of the unseen we consider the problem of estimating the support size of a discrete distribution whose minimum non zero mass is at least 1 k using independent samples we show that the minimax sample complexity to achieve an additive error of k with probability at least 0 5 is within universal constant factors of k log k log 2 1 which improves the state of the art result k 2 log k due to valiant and valiant the optimal procedure is a linear estimator based on the chebyshev polynomial and its approximation theoretic properties we also study the closely related species problem where the goal is to estimate the number of distinct colors in an urn containing k balls from repeated draws while achieving an additive error proportional to k still requires k log k samples we show that with k samples one can strictly outperform a general support size estimator using interpolating polynomials

renyi s divergence and entropy rates for finite alphabet markov sources in this work we examine the existence and the computation of the renyi divergence rate lim sub n spl rarr spl infin 1 n d sub spl alpha p sup n spl par q sup n between two time invariant finite alphabet markov sources of arbitrary order and arbitrary initial distributions described by the probability distributions p sup n and q sup n respectively this yields a generalization of a result of nemetz 1974 where he assumed that the initial probabilities under p sup n and q sup n are strictly positive the main tools used to obtain the renyi divergence rate are the theory of nonnegative matrices and perron frobenius theory we also provide numerical examples and investigate the limits of the renyi divergence rate as spl alpha spl rarr 1 and as spl alpha spl darr 0 similarly we provide a formula for the renyi entropy rate lim sub n spl rarr spl infin 1 n h sub spl alpha p sup n of markov sources and examine its limits as spl alpha spl rarr 1 and as spl alpha spl darr 0 finally we briefly provide an application to source coding

renyi divergence measures for commonly used univariate continuous distributions abstract probabilistic distances also called divergences which in some sense assess how close two probability distributions are from one another have been widely employed in probability statistics information theory and related fields of particular importance due to their generality and applicability are the renyi divergence measures this paper presents closed form expressions for the renyi and kullback leibler divergences for nineteen commonly used univariate continuous distributions as well as those for multivariate gaussian and dirichlet distributions in addition a table summarizing four of the most important information measure rates for zero mean stationary gaussian processes namely renyi entropy differential shannon entropy renyi divergence and kullback leibler divergence is presented lastly a connection between the renyi divergence and the variance of the log likelihood ratio of two distributions is established thereby extending a previous result by song j stat plan infer 93 2001 on the relation between renyi entropy and the log likelihood function a table with the corresponding variance expressions for the univariate distributions considered here is also included

steady state analysis of the multistage constant modulus array the multistage constant modulus cm array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training we examine its steady state properties at convergence using a stochastic analysis and computer simulations based on a wiener model of convergence for the gradient adaptive algorithms closed form expressions are derived for the cm array and canceller weight vectors as well as the effective source direction vectors at all stages along the cascade system the signal capture and direction finding capabilities of the system are also discussed computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms

applications of cumulants to array processing iii blind beamforming for coherent signals for pt ii see ibid vol 43 no 7 p 1663 7 1995 we provide a cumulant based blind beamforming method for recovery of statistically independent narrowband source signals in the presence of coherent or perfectly correlated multipath propagation our method is based on the fact that for a blind beamformer the presence of coherent multipaths is equivalent to the case of independent sources with a different steering matrix our approach is applicable to any array configuration having unknown response signal sources must have nonzero fourth order cumulants there is no need to estimate the directions of arrival our method maximizes signal to interference plus noise ratio sinr a comparable result does not exist using just second order statistics

hellinger consistency of certain nonparametric maximum likelihood estimators consider a class mathscr p p theta theta in theta of probability measures on a measurable space mathscr x mathscr a dominated by a sigma finite measure mu let f theta dp theta d mu theta in theta and let theta n be a maximum likelihood estimator based on n independent observations from p theta 0 theta 0 in theta we use results from empirical process theory to obtain convergence for the hellinger distance h f hat theta n f theta 0 under certain entropy conditions on the class of densities f theta theta in theta the examples we present are a model with interval censored observations smooth densities monotone densities and convolution models in most examples the convexity of the class of densities is of special importance

parametric study and shape optimization of piezoelectric energy harvesters by isogeometric analysis and kriging metamodeling abstract piezo electric energy harvesters pehs are widely used to recycle waste vibrations for powering small electronic devices in this work the performance of pehs of non conventional shapes is studied with the aim to optimize their design a peh is modeled as a bimorph cantilever kirchhoff love plate subjected to base acceleration the shape is described by non uniform rational b splines nurbs and the problem is solved by the isogeometric analysis iga accuracy of the iga solutions is demonstrated on two benchmark problems then we conduct a parametric study to investigate the effect of shape perturbations on the fundamental frequency the peak amplitude of the frequency response function frf and the peak amplitude of the frf per unit of area next we build the kriging meta model to obtain the boundary shapes that maximize the peak amplitude of the frf and the peak amplitude of the frf per unit of area for a target frequency the optimization is performed for three cases with a fixed tip mass without a tip mass and with a tip mass being one of the design parameters

rate distortion theory for secrecy systems secrecy in communication systems is measured herein by the distortion that an adversary incurs the transmitter and receiver share secret key which they use to encrypt communication and ensure distortion at an adversary a model is considered in which an adversary not only intercepts the communication from the transmitter to the receiver but also potentially has side information in particular the adversary may have causal or noncausal access to a signal that is correlated with the source sequence or the receiver s reconstruction sequence the main contribution is the characterization of the optimal tradeoff among communication rate secret key rate distortion at the adversary and distortion at the legitimate receiver it is demonstrated that causal side information at the adversary plays a pivotal role in this tradeoff it is also shown that measures of secrecy based on normalized equivocation are a special case of the framework

from ɛ entropy to kl entropy analysis of minimum information complexity density estimation we consider an extension of e entropy to a kl divergence based complexity measure for randomized density estimation methods based on this extension we develop a general information theoretical inequality that measures the statistical complexity of some deterministic and randomized density estimators consequences of the new inequality will be presented in particular we show that this technique can lead to improvements of some classical results concerning the convergence of minimum description length and bayesian posterior distributions moreover we are able to derive clean finite sample convergence bounds that are not obtainable using previous approaches

cumulant based inverse filter criteria for mimo blind deconvolution properties algorithms and application to ds cdma systems in multipath tugnait 1995 and chi and chen proposed multi input multi output inverse filter criteria mimo ifc using higher order statistics for blind deconvolution of mimo linear time invariant systems this paper proposes three properties on the performance of the mimo linear equalizer associated with mimo ifc for any signal to noise ratio including p1 perfect phase equalization property p2 a relation to mimo minimum mean square error mimo mmse equalizer and p3 a connection with the one obtained by mimo super exponential algorithm mimo sea that usually converges fast but does not guarantee convergence for finite data based on p2 a fast algorithm for computing the theoretically optimum mimo equalizer is proposed moreover based on p3 a fast mimo ifc based algorithm with performance similar to that of the mimo sea and with guaranteed convergence is proposed as well as its application to suppression of multiple access interference and intersymbol interference isi for multiuser asynchronous ds cdma systems in multipath finally some simulation results are presented to support the analytic results and the proposed algorithms

relationships between the constant modulus and wiener receivers the godard 1980 or the constant modulus algorithm cma is an effective technique for blind receiver design in communications however due to the complexity of the constant modulus cm cost function the performance of the cm receivers has primarily been evaluated using simulations theoretical analysis is typically based on either the noiseless case or approximations of the cost function the following question while resolvable numerically for a specific example remains unanswered in a generic manner in the presence of channel noise where are the cm local minima and what are their mean squared errors mse in this paper a geometrical approach is presented that relates the cm to wiener or minimum mse receivers given the mse and the intersymbol user interference of a wiener receiver a sufficient condition is given for the existence of a cm local minimum in the neighborhood of the wiener receiver the mse bounds on cm receiver performance are derived and shown to be tight in simulations the analysis shows that while in some cases the cm receiver performs almost as well as the nonblind wiener receiver it is also possible that due to its blind nature the cm receiver may perform considerably worse than a nonblind wiener receiver

a large deviations notion of perfect secrecy we consider the shannon cipher system with a variable key rate and study the necessary and sufficient conditions for perfect secrecy in the sense that the exponential rate of the probability of breaking into the system would not be improved by observing the cryptogram for a memoryless plain text source we derive achievable lower bounds on the number of key bits needed for almost every plain text sequence in every type class the corresponding minimum achievable average key rate turns out to be the negative logarithm of the probability of the most likely plain text letter which is in general smaller than the entropy

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

how to fool an unbounded adversary with a short key the symmetric encryption problem which manifests itself when two parties must securely transmit a message m with a short shared secret key is considered in conjunction with a computationally unbounded adversary as the adversary is unbounded any encryption scheme must leak information about m in particular the mutual information between m and its ciphertext cannot be zero despite this a family of encryption schemes is presented that guarantee that for any message space in 0 1 n with minimum entropy n lscr and for any boolean function h 0 1 n rarr 0 1 no adversary can predict h m from the ciphertext of m with more than 1 nomega 1 advantage this is achieved with keys of length lscr omega logn in general keys of length lscr s yield a bound of 2 theta s on the advantage these encryption schemes rely on no unproven assumptions and can be implemented efficiently applications of this to cryptosystems based on complexity theoretic assumptions are discussed and in addition a simplified proof of a fundamental elision lemma of goldwasser and micali is provided

maximal correlation secrecy this paper shows that the hirschfeld gebelein renyi maximal correlation between the message and the ciphertext provides good secrecy guarantees for cryptosystems that use short keys we first establish a bound on the eavesdropper s advantage in guessing functions of the message in terms of maximal correlation and the renyi entropy of the message this result implies that the maximal correlation is stronger than the notion of entropic security introduced by russell and wang we then show that a small maximal correlation rho can be achieved via a randomly generated cipher with key length approx 2 log 1 rho independent of the message length and by a stream cipher with key length 2 log 1 rho log n 2 for a message of length n we establish a converse showing that these ciphers are close to optimal this is in contrast with the entropic security for which there is a gap between the lower and upper bounds finally we show that a small maximal correlation implies secrecy with respect to several mutual information based criteria but is not necessarily implied by them hence maximal correlation is a stronger and more practically relevant measure of secrecy than the mutual information

a large deviations approach to secure lossy compression a shannon cipher system for memoryless sources in which distortion is allowed at the legitimate decoder is considered the source is compressed using a secured rate distortion code which satisfies a constraint on the compression rate as well as a constraint on the exponential rate of the excess distortion probability at the legitimate decoder secrecy is measured by the exponential rate of the exiguous distortion probability at the eavesdropper rather than by the traditional measure of equivocation the perfect secrecy exponent is defined as the maximal exiguous distortion exponent achievable when the key rate is unlimited the reproduction based estimate exponent is defined as the maximal exiguous distortion exponent achievable for a genie aided eavesdropper which knows the secret key under limited key rate it is proved that the maximal achievable exiguous distortion exponent is equal to the minimum between the key rate plus the reproduction based estimate exponent and the perfect secrecy exponent the result is generalized to a fairly general class of variable key rate and coding rate codes

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

isogeometric shape optimization of shells using semi analytical sensitivity analysis and sensitivity weighting abstract we present isogeometric shape optimization for shell structures applying sensitivity weighting and semi analytical analysis we use a rotation free shell formulation and all involved geometry models i e initial design analysis model optimization model and final design use the same geometric basis in particular nurbs a sensitivity weighting scheme is presented which eliminates certain effects of the chosen discretization on the design update a multilevel design approach is applied such that the design space can be chosen independently from the analysis space the use of semi analytical sensitivities allows having different polynomial degrees for design and analysis model different numerical examples are performed which confirm the applicability of the proposed method furthermore a shape optimization example with an exact solution is presented which can serve as general benchmark for shape optimization methods

zero rate reliability of the exponential server timing channel we determine the reliability function of the exponential server timing channel estc in the limit as the data rate approaches zero the limit shows that at low rates the estc is strictly more reliable than the poisson channel without dark current answering a question arikan posed in these transactions the proof employs a distance metric over inputs to timing channels that parallels euclidean and hamming distance for conventional channels a consequence of the proof is that bounded distance decoding with distance measured according to this metric is exponentially optimum for the estc in the low rate regime we also prove the straight line bound for the channel and a bound on the reliability of timing channels with general service distributions in the limit as the data rate approaches zero

weakening the tight coupling between geometry and simulation in isogeometric analysis from sub and super geometric analysis to geometry independent field approximation gift this paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field the method inherits the main advantage of isogeometric analysis ie preserves the original exact computer aided design geometry for example given by nonuniform rational b splines but allows pairing it with an approximation space which is more suitable flexible for analysis for example t splines lr splines truncated hierarchical b splines and pht splines this generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain and therefore without weakening the link with the computer aided design model we demonstrate the use of the method with different choices of geometry and field spaces and show that despite the failure of the standard patch test the optimum convergence rate is achieved for nonnested spaces

super exponential algorithms for multichannel blind deconvolution multichannel blind deconvolution has been receiving increasing attention shalvi and weinstein proposed an attractive approach to single channel blind deconvolution called the super exponential methods the objective of this correspondence is to extend the shalvi and weinstein 1993 1994 approach to the multichannel case and present super exponential algorithms for multichannel blind deconvolution we propose three approaches to multichannel blind deconvolution in the first one we present a multichannel super exponential algorithm in the second one we present a super exponential deflation algorithm in the third one we present a two stage super exponential algorithm

interpretations of renyi entropies and divergences abstract in this paper a new operational definition of renyi divergence and renyi entropy is presented other operational definitions are mentioned

an operational approach to information leakage given two random variables x and y an operational approach is undertaken to quantify the leakage of information from x to y the resulting measure mathcal l left x to y right is called maximal leakage and is defined as the multiplicative increase upon observing y of the probability of correctly guessing a randomized function of x maximized over all such randomized functions a closed form expression for mathcal l left x to y right is given for discrete x and y and it is subsequently generalized to handle a large class of random variables the resulting properties are shown to be consistent with an axiomatic view of a leakage measure and the definition is shown to be robust to variations in the setup moreover a variant of the shannon cipher system is studied in which performance of an encryption scheme is measured using maximal leakage a single letter characterization of the optimal limit of normalized maximal leakage is derived and asymptotically optimal encryption schemes are demonstrated furthermore the sample complexity of estimating maximal leakage from data is characterized up to subpolynomial factors finally the guessing framework used to define maximal leakage is used to give operational interpretations of commonly used leakage measures such as shannon capacity maximal correlation and local differential privacy

super exponential blind adaptive beamforming the objective of the beamforming with the exploitation of a sensor array is to enhance the signals of the sources from desired directions suppress the noises and the interfering signals from other directions and or simultaneously provide the localization of the associated sources in this paper we present a higher order cumulant based beamforming algorithm namely the super exponential blind adaptive beamforming algorithm which is extended from the super exponential algorithm sea and the inverse filter criteria ifc while both sea and ifc assume noise free conditions this requirement is no longer needed and all the noise components are taken into account in the proposed algorithm two special conditions are derived under which the proposed blind beamforming algorithm achieves the performance of the corresponding optimal nonblind beamformer in the sense of minimum mean square error mmse simulation results show that the proposed algorithm is effective and robust to diverse initial weight vectors its performance with the use of the fourth order cumulants is close to that of the nonblind optimal mmse beamformer

mutual information metric entropy and cumulative relative entropy risk assume p theta theta epsilon theta is a set of probability distributions with a common dominating measure on a complete separable metric space y a state theta epsilon theta is chosen by nature a statistician obtains n independent observations y 1 dots y n from y distributed according to p theta for each time t between 1 and n based on the observations y 1 dots y t 1 the statistician produces an estimated distribution hat p t for p theta and suffers a loss l p theta hat p t the cumulative risk for the statistician is the average total loss up to time n of special interest in information theory data compression mathematical finance computational learning theory and statistical mechanics is the special case when the loss l p theta hat p t is the relative entropy between the true distribution p theta and the estimated distribution hat p t here the cumulative bayes risk from time 1 to n is the mutual information between the random parameter theta and the observations y 1 dots y n new bounds on this mutual information are given in terms of the laplace transform of the hellinger distance between pairs of distributions indexed by parameters in theta from these bounds on the cumulative minimax risk are given in terms of the metric entropy of theta with respect to the hellinger distance the assumptions required for these bounds are very general and do not depend on the choice of the dominating measure they apply to both finite and infinite dimensional theta they apply in some cases where y is infinite dimensional in some cases where y is not compact in some cases where the distributions are not smooth and in some parametric cases where asymptotic normality of the posterior distribution fails

on pinsker s and vajda s type inequalities for csiszar s f divergences let d and v denote respectively information divergence and total variation distance pinsker s and vajda s inequalities are respectively d 1 2 v2 and d log 2 v 2 v 2v 2 v in this paper several generalizations and improvements of these inequalities are established for wide classes of f divergences first conditions on f are determined under which an f divergence df will satisfy df cf v2 or df c2 f v2 c4 f v4 where the constants cf c2 f and c4 f are best possible as a consequence lower bounds in terms of v are obtained for many well known distance and divergence measures including the 2 and hellinger s discrimination and the families of tsallis and renyi s divergences for instance if d p q 1 1 p q1 d 1 and p q 1 1 log p q1 d are respectively the relative information of type and the renyi s information gain of order it is shown that d 1 2 v2 1 72 1 2 v4 whenever 1 2 0 1 and that 2 v2 1 36 1 5 5 2 v4 for 0 1 in a somewhat different direction and motivated by the fact that these pinsker s type lower bounds are accurate only for small variation v close to zero lower bounds for df which are accurate for both small and large variation v close to two are also obtained in the special case of the information divergence they imply that d log 2 2 v 2 v 2 log 2 v 2 which uniformly improves vajda s inequality

identification and deconvolution of multichannel linear non gaussian processes using higher order statistics and inverse filter criteria this paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple input multiple output mimo system given only the measurements of the vector output of the system the system is assumed to be driven by a temporally i i d and spatially independent non gaussian vector sequence which is not observed an iterative inverse filter criteria based approach is developed using the third order or the fourth order normalized cumulants of the inverse filtered data at zero lag stationary points of the proposed cost functions are investigated the approach is input iterative i e the input sequences are extracted and removed one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed the strong consistency of the proposed approach is also briefly discussed computer simulation examples are presented to illustrate the proposed approaches

a general minimax result for relative entropy suppose nature picks a probability measure p sub spl theta on a complete separable metric space x at random from a measurable set p sub spl theta p spl theta spl theta spl isin spl theta then without knowing spl theta a statistician picks a measure q on s finally the statistician suffers a loss d p sub 0 spl par q the relative entropy between p sub spl theta and q we show that the minimax and maximin values of this game are always equal and there is always a minimax strategy in the closure of the set of all bayes strategies this generalizes previous results of gallager 1979 and davisson and leon garcia 1980

coding theorems for the shannon cipher system with a guessing wiretapper and correlated source outputs the security level of the shannon cipher system is traditionally measured by equivocation where is a secret plaintext with length and is its cryptogram but merhav and arikan have considered another security criterion which is measured by the number of guesses needed for a wiretapper to uncover from merhav has also considered the third security criterion which measured by the probability of correct guess of a wiretapper on the other hand in the case of the traditional security criterion yamamoto has treated a coding problem for correlated source outputs and such that only is secret against wiretappers and only must be transmitted to a legitimate receiver in this correspondence coding theorems are proved for the case that yamamoto s coding problem is applied to merhav arikan s security criterion or merhav s security criterion

tunable measures for information leakage and applications to privacy utility tradeoffs we introduce a tunable measure for information leakage called maximal alpha leakage this measure quantifies the maximal gain of an adversary in inferring any potentially random function of a dataset from a release of the data the inferential capability of the adversary is in turn quantified by a class of adversarial loss functions that we introduce as alpha loss alpha in 1 infty cup infty the choice of alpha determines the specific adversarial action and ranges from refining a belief about any function of the data for alpha 1 to guessing the most likely value for alpha infty while refining the alpha text th moment of the belief for alpha in between maximal alpha leakage then quantifies the adversarial gain under alpha loss over all possible functions of the data in particular for the extremal values of alpha 1 and alpha infty maximal alpha leakage simplifies to mutual information and maximal leakage respectively for alpha in 1 infty this measure is shown to be the arimoto channel capacity of order alpha we show that maximal alpha leakage satisfies data processing inequalities and a sub additivity property thereby allowing for a weak composition result building upon these properties we use maximal alpha leakage as the privacy measure and study the problem of data publishing with privacy guarantees wherein the utility of the released data is ensured via a hard distortion constraint unlike average distortion hard distortion provides a deterministic guarantee of fidelity we show that under a hard distortion constraint for alpha 1 the optimal mechanism is independent of alpha and therefore the resulting optimal tradeoff is the same for all values of alpha 1 finally the tunability of maximal alpha leakage as a privacy measure is also illustrated for binary data with average hamming distortion as the utility measure

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

fundamental aspects of shape optimization in the context of isogeometric analysis we develop a mathematical foundation for shape optimization problems under state equation constraints where both state and control are discretized by b splines or nurbs in other words we use isogeometric analysis iga for solving the partial differential equation and a nodal approach to change domains where control points take the place of nodes and where thus a quite general class of functions for representing optimal shapes and their boundaries becomes available the minimization problem is solved by a gradient descent method where the shape gradient will be defined in isogeometric terms this gradient is obtained following two schemes optimize first discretize then and reversely discretize first optimize then we show that for isogeometric analysis the two schemes yield the same discrete system moreover we also formulate shape optimization with respect to nurbs in the optimize first ansatz which amounts to finding optimal control points and weights simultaneously numerical tests illustrate the theory

point processes and queues martingale dynamics i martingales 1 histories and stopping times 2 martingales 3 predictability 4 square integrable martingales references solutions to exercises chapter i ii point processes queues and intensities 1 counting processes and queues 2 watanabe s characterization 3 stochastic intensity general case 4 predictable intensities 5 representation of queues 6 random changes of time 7 cryptographic point processes references solutions to exercises chapter ii iii integral representation of point process martingales 1 the structure of internal histories 2 regenerative form of the intensity 3 the representation theorem 4 hilbert space theory of poissonian martingales 5 useful extensions references solutions to exercises chapter iii iv filtering 1 the theory of innovations 2 state estimates for queues and markov chains 3 continuous states and nontrivial prehistory references solutions to exercises chapter iv v flows in markovian networks of queues 1 single station the historical results and the filtering method 2 jackson s networks 3 burke s output theorem for networks 4 cascades and loops in jackson s networks 5 independence and poissonian flows in markov chains references solutions to exercises chapter v vi likelihood ratios 1 radon nikodym derivatives and tests of hypotheses 2 changes of intensities a la girsanov 3 filtering by the method of the probability of reference 4 applications 5 the capacity of a point process channel 6 detection formula187 references189 solutions to exercises chapter vi vii optimal control 1 modeling intensity controls 2 dynamic programming for intensity controls complete observation case 3 input regulation a case study in impulsive control 4 attraction controls 5 existence via likelihood ratio references solutions to exercises chapter vii viii marked point processes 1 counting measure and intensity kernels 2 martingale representation and filtering 3 radon nikodym derivatives 4 towards a general theory of intensity references solutions to exercises chapter viii a1 background in probability and stochastic processes 1 introduction 2 monotone class theorem 3 random variables 4 expectations 5 conditioning and independence 6 convergence 7 stochastic processes 8 markov processes references a2 stopping times and point process histories 1 stopping times 2 changes of time and meyer dellacherie s integration formula 3 point process histories references a3 wiener driven dynamical systems 1 ito s stochastic integral 2 square integrable brownian martingales 3 girsanov s theorem references a4 stieltjes lebesgue calculus 1 the stieltjes lebesgue integral 2 the product and exponential formulas references general bibliography