common hypercyclic vectors for multiples of backward shift we prove that l 2 contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift oper ator by constants of absolute value greater than 1

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

on identification via multiway channels with feedback for the case of complete feedback a fairly unified theory of identification is presented its guiding principle is the discovery that communicators sender and receiver must set up a common random experiment with maximal entropy and use it as randomization for a suitable identification technique it is shown how this can be done in a constructive manner the proof of optimality weak converse is based on a novel entropy bound which can be viewed as a substitute for fano s lemma in the present context the single letter characterization of second order capacity regions now rests on an entropy characterization problem which often can be solved this is done for the multiple access channel with deterministic encoding strategies and for the broadcast channel with randomized encoding strategies

complete systems of partial derivatives of entire functions and frequently hypercyclic operators abstract we find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space h c d of all entire functions of d variables as an application of this result we describe new classes of frequently hypercyclic operators on h c d

improved lower bounds on the sizes of error correcting codes for list decoding elias 1991 derived upper and lower bounds on the sizes of error correcting codes for list decoding the asymptotic values of his lower bounds for linear codes and for nonlinear codes are separated the present authors derive improved lower bounds for linear and for nonlinear codes they conjecture their two bounds are identical however they were able to verify this only for small lists

universal detection of messages via finite state channels we propose a universal asymptotically optimum decision rule for deciding whether or not an observed sequence generated at the output of an unknown finite state channel corresponds to a given channel input message the hypothesized message is tested against a certain alternative message or several alternative messages under the neyman pearson criterion

distributional chaos for operators on banach spaces abstract four notions of distributional chaos namely dc1 dc2 dc 2 1 2 and dc3 are studied within the framework of operators on banach spaces it is known that for general dynamical systems dc1 dc2 dc 2 1 2 dc3 we show that dc1 and dc2 coincide in our context which answers a natural question in contrast there exist dc 2 1 2 operators which are not dc2 under the condition that there exists a dense set x 0 x such that t n x 0 for any x x 0 dc3 operators are shown to be dc1 moreover we prove that any upper frequently hypercyclic operator is dc 2 1 2 finally several examples are provided to distinguish between different notions of distributional chaos li yorke chaos and irregularity

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

the common randomness capacity of a pair of independent discrete memoryless channels we study the following problem two agents alice and bob are connected to each other by independent discrete memoryless channels they wish to generate common randomness i e agree on a common random variable by communicating interactively over the two channels assuming that alice and bob are allowed access to independent external random sources at rates in bits per step of communication of h sub a and h sub b respectively we show that they can generate common randomness at a rate of max min h sub a h w q i p v min h sub b h v p i q w bits per step by exploiting the noise on the two channels here v is the channel from alice to bob and w is the channel from bob to alice the maximum is over all probability distributions p and q on the input alphabets of v and w respectively we also prove a strong converse which establishes the above rate as the highest attainable in this situation

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

algebraic genericity of frequently universal harmonic functions on trees abstract we show that the set of frequently universal harmonic functions on a tree t contains a vector space except 0 which is dense in the space of harmonic functions on t seen as subset of c t in order to prove this we replace the complex plane c by any separable frechet space e and we repeat all the theory

genericity of wild holomorphic functions and common hypercyclic vectors abstract let t be the translation operator by in the space of entire functions h c defined by t f z f z we prove that there is a residual set g of entire functions such that for every f g and every c 0 the sequence t n f is dense in h c that is g is a residual set of common hypercyclic vectors functions for the family t c 0 also we prove similar results for many families of operators as multiples of differential operator multiples of backward shift weighted backward shifts

lineability criteria with applications lineability is a property enjoyed by some subsets within a vector space x a subset a of x is called lineable whenever a contains except for zero an infinite dimensional vector subspace if additionally x is endowed with richer structures then the more stringent notions of dense lineability maximal dense lineability and spaceability arise naturally in this paper several lineability criteria are provided and applied to specific topological vector spaces mainly function spaces sometimes such criteria furnish unified proofs of a number of scattered results in the related literature families of strict order integrable functions hypercyclic vectors non extendable holomorphic mappings riemann non lebesgue integrable functions sequences not satisfying the lebesgue dominated convergence theorem nowhere analytic functions bounded variation functions entire functions with fast growth and peano curves among others are analyzed from the point of view of lineability

multiple object identification coding in the case of ordinary identification coding a code is devised to identify a single object among n objects but in this paper we consider a coding problem to identify k objects at once among n objects in the both cases that k objects are ranked or not ranked by combining moulin koetter scheme with the varepsilon almost strongly universal class of hash functions used in kurosawa yoshida scheme an efficient and explicit coding scheme is proposed for k multiple object identification k moid coding furthermore it is shown that the k moid capacity c text k moid which is the maximum achievable coding rate in the k moid coding is equal to the ordinary channel capacity and the proposed scheme can attain c text k moid

strong transitivity properties for operators abstract given a furstenberg family f of subsets of n an operator t on a topological vector space x is called f transitive provided for each non empty open subsets u v of x the set n z t n u v belongs to f we classify the topologically transitive operators with a hierarchy of f transitive subclasses by considering families f that are determined by various notions of largeness and density in z

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

s linear and convex structures in function families abstract in this paper the notion of s lineability originally coined by vladimir i gurariy is introduced and developed in a general abstract setting this new notion is then applied to specific situations as for instance classes of differentiable nowhere monotone functions as well as families of vectors having dense orbit with respect to an operator large convex structures are also shown to exist inside the family of topologically mixing continuous selfmaps of a real compact interval

hypercyclic orbits intersect subspaces in wild ways abstract let t x x be a hypercyclic operator of an infinite dimensional separable banach space x by modifying a construction of grivaux we will show that the t orbit of a hypercyclic vector can intersect certain closed vector subspaces of x in many strange ways moreover the set of visiting times of the orbit to the subspace can also be quite exotic especially when the operator satisfies a stronger form of hypercyclicity as a by product we will improve and or supply new proofs to some of the recent results about subspace hypercyclicity

state estimation for discrete time markov jump linear systems with time correlated and mode dependent measurement noise abstract the state estimation problem for discrete time markov jump linear systems corrupted by time correlated and mode dependent measurement noise is considered where the time correlated and mode dependent measurement noise is described via a discrete time stochastic system with markov parameter and kronecker delta function by defining the measurement noise in this manner both time correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise a novel distributed measurement differencing method is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper the first algorithm is optimal in the sense of minimum mean square error which can exactly compute the minimum mean square error estimate of system state the second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some gaussian hypotheses the two proposed algorithms are recursive and the proposed suboptimal algorithm has a time independent complexity the performance of the proposed suboptimal algorithm is illustrated using computer simulations

on identification secret sharing schemes let p be a set of participants sharing a secret from a set of secrets a secret sharing scheme is a protocol such that any qualified subset of p can determine the secret by pooling their shares the messages which they receive without error whereas non qualified subsets of p cannot obtain any knowledge about the secret when they pool what they receive in optimal schemes the sizes of shared secrets depend on the sizes of shares given to the participants namely the former grow up exponentially as the latter increase exponentially in this paper instead of determining the secret we require the qualified subsets of participants to identify the secret this change would certainly make no difference from determining secret if no error for identification were allowed so here we relax the requirement to identification such that an error may occur with a vanishing probability as the sizes of the secrets grow up under relaxed condition this changing allows us to share a set of secrets with double exponential size as the sizes of shares received by the participants exponentially grow thus much longer secret can be shared on the other hand by the continuity of shannon entropy we have that the relaxation makes no difference for ordinary secret sharing schemes we obtain the characterizations of relations of sizes of secrets and sizes of the shares for identification secret sharing schemes without and with public message our idea originates from ahlswede dueck s awarded work in 1989 where the identification codes via channels were introduced

recurrence properties of hypercyclic operators we generalize the notions of hypercyclic operators mathfrak u frequently hypercyclic operators and frequently hypercyclic operators by introducing a new concept in linear dynamics namely mathcal a hypercyclicity we then state an mathcal a hypercyclicity criterion inspired by the hypercyclicity criterion and the frequent hypercyclicity criterion and we show that this criterion characterizes the mathcal a hypercyclicity for weighted shifts we also investigate which density properties can the sets n x u n in mathbb n t nx in u have for a given hypercyclic operator and we study the new notion of reiteratively hypercyclic operators

on identification capacity of infinite alphabets or continuous time channels two kinds of channels are considered 1 discrete time channel with additive noise and 2 poisson and white gaussian i e continuous time channels for the type 1 channel there are given some sufficient conditions when the shannon and identification capacities coincide it is shown that the identification capacity of poisson and gaussian channels without bandwidth constraint is infinite conversely for a white gaussian channel with bandwidth constraint the identification capacity coincides with the shannon capacity

ratio list decoding we extend the notion of list decoding to ratio list decoding which involves a list decoder whose list size is specified as a function of the number of messages m n and the block length n we present the necessary and sufficient conditions on m n for the existence of code sequences which enable reliable list decoding with respect to the desired list size l m n n it is shown that the ratio capacity defined as the supremum of achievable normalized logarithms of the ratio r m n n m n l m n n is equal to the shannon channel capacity c for both stochastic and deterministic encoding allowing for random list size we are able to deduce some properties of identification codes where the decoder s output can be viewed as a list of messages corresponding to decision regions that include the channel output we further address the regime of mismatched list decoding in which the list constitutes of the codewords that accumulate the highest score values jointly with the channel output according to some given function we study the case of deterministic encoding and mismatched ratio list decoding we establish similar necessary and sufficient conditions for the existence of code sequences which enable reliable mismatched list decoding with respect to the desired list size l m n n and we show that the ratio capacity with mismatched decoding is equal to the mismatch capacity focusing on the case of an exponential list size l n e n theta its comparison with ordinary mismatched decoding shows that the increase in capacity is by theta bits per channel used for all channels and decoding metrics several properties of the average error probability in the setup of mismatched list decoding with deterministic list size are provided

topologically transitive extensions of bounded operators let x be any banach space and t a bounded operator on x an extensionopen image in new window of the pair x t consists of a banach space open image in new window in which x embeds isometrically through an isometry i and a bounded operatoropen image in new window on open image in new window such that open image in new window when x is separable it is additionally required that open image in new window be separable we say that open image in new window is a topologically transitive extension of x t when open image in new window is topologically transitive on open image in new window i e for every pair open image in new window of non empty open subsets of open image in new window there exists an integer n such that open image in new window is non empty we show that any such pair x t admits a topologically transitive extension open image in new window and that when h is a hilbert space h t admits a topologically transitive extension open image in new window where open image in new window is also a hilbert space we show that these extensions are indeed chaotic

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

the specification property and infinite entropy for certain classes of linear operators abstract we study the specification property and infinite topological entropy for two specific types of linear operators translation operators on weighted lebesgue function spaces and weighted backward shift operators on sequence f spaces it is known from the work of bartoll martinez gimenez murillo arcila and peris that for weighted backward shift operators the existence of a single non trivial periodic point is sufficient for specification we show this also holds for translation operators on weighted lebesgue function spaces this implies in particular that for these operators the specification property is equivalent to devaney chaos we show that these forms of chaos unsurprisingly imply infinite topological entropy but that surprisingly the converse does not hold

the common randomness capacity of a network of discrete memoryless channels we generalize our previous results on generating common randomness at two terminals to a situation where any finite number of agents interconnected by an arbitrary network of independent point to point discrete memoryless channels wish to generate common randomness by interactive communication over the network our main result is an exact characterization of the common randomness capacity of such a network i e the maximum number of bits of randomness that all the agents can agree on per step of communication as a by product we also obtain a purely combinatorial result viz a characterization of the incidence vectors of the spanning arborescences rooted at a specified vertex in a digraph and having exactly one edge exiting the root as precisely the extreme points of a certain unbounded convex polyhedron described by a system of linear inequalities

common randomness in information theory and cryptography ii cr capacity for pt i see ibid vol 39 p 1121 1993 the common randomness cr capacity of a two terminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model we determine cr capacity for several models including those whose statistics depend on unknown parameters the cr capacity is shown to be achievable robustly by common randomness of nearly uniform distribution no matter what the unknown parameters are our cr capacity results are relevant for the problem of identification capacity and also yield a new result on the regular transmission capacity of arbitrarily varying channels with feedback

mean li yorke chaos in banach spaces abstract we investigate the notion of mean li yorke chaos for operators on banach spaces we show that it differs from the notion of distributional chaos of type 2 contrary to what happens in the context of topological dynamics on compact metric spaces we prove that an operator is mean li yorke chaotic if and only if it has an absolutely mean irregular vector as a consequence absolutely cesaro bounded operators are never mean li yorke chaotic dense mean li yorke chaos is shown to be equivalent to the existence of a dense or residual set of absolutely mean irregular vectors as a consequence every mean li yorke chaotic operator is densely mean li yorke chaotic on some infinite dimensional closed invariant subspace a dense mean li yorke chaos criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained moreover we construct an example of an invertible hypercyclic operator t such that every nonzero vector is absolutely mean irregular for both t and t 1 several other examples are also presented finally mean li yorke chaos is also investigated for c 0 semigroups of operators on banach spaces

universal properties of harmonic functions on trees abstract we consider an infinite locally finite tree t equipped with nearest neighbor transition coefficients giving rise to a space of harmonic functions we show that except for trivial cases the generic harmonic function on t has dense range in c by looking at forward only transition coefficients we show that the generic harmonic function induces a boundary martingale that approximates in probability all measurable functions on the boundary of t we also study algebraic genericity spaceability and frequent universality of these phenomena

explicit construction of optimal constant weight codes for identification via channels the identification coding theorems of r ahlswede and g dueck 1981 have shown that for any nonzero probabilities of missed and false identification it is possible to transmit exp exp nr messages with n uses of a noisy channel where r is as close as desired to the shannon capacity of the channel that capability is achieved by the identification codes explicitly constructed with a three layer concatenated constant weight code used in conjunction with a channel transmission code of rate r

recurrence and topological entropy of translation operators abstract in this paper we provide several characterizations on weak recurrence of translation operators on weighted lebesgue spaces and on continuous function spaces it is shown that the translation operator admits a nonzero nonwandering point if and only if it has a nonzero recurrent point if and only if it is hypercyclic that the translation operator admits a nonzero almost periodic point if and only if it is devaney chaotic moreover every hypercyclic translation operator has infinite topological entropy but the converse is not true finally we remark that there exists a linear operator which has the specification property on the whole space

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

common hypercyclic functions for translation operators with large gaps abstract let h c be the set of entire functions endowed with the topology of local uniform convergence fix a sequence of non zero complex numbers n n which satisfies the following property for every m 0 there exists a subsequence n of n such that i n 1 n m for every n 1 2 and ii n 1 1 n we prove that there exists a residual set g h c such that for every f g and every non zero complex number a the set f z n a n 1 2 is dense in h c this answers in the affirmative question 1 in 29 and it also provides an extension of a theorem due to costakis and sambarino in 32

the role of the angle in supercyclic behavior abstract a bounded operator t acting on a hilbert space h is said to be supercyclic if there is a vector f h such that the projective orbit t n f n 0 and c is dense in h we use a new method based on a very simple geometric idea that allows us to decide whether an operator is supercyclic or not the method is applied to obtain the following result a composition operator acting on the hardy space whose inducing symbol is a parabolic linear fractional map of the disk onto a proper subdisk is not supercyclic this result finishes the characterization of the supercyclic behavior of composition operators induced by linear fractional maps and thus completes previous work of bourdon and shapiro

linear operators with infinite entropy abstract we examine the chaotic behavior of certain continuous linear operators on infinite dimensional banach spaces and provide several equivalent characterizations of when these operators have infinite topological entropy for example it is shown that infinite topological entropy is equivalent to non zero topological entropy for translation operators on weighted lebesgue function spaces in particular finite non zero entropy is impossible for this class of operators which answers a question raised by yin and wei

invariant gaussian measures for operators on banach spaces and linear dynamics we give conditions for an operator t on a complex separable banach space x with sufficiently many eigenvectors associated to eigenvalues of modulus 1 to admit a non degenerate invariant gaussian measure with respect to which it is weak mixing the existence of such a measure depends on the geometry of the banach space and on the possibility of parametrizing the mathbb t eigenvector fields of t in a regular way we also investigate the connection with frequent hypercyclicity

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

linear subsets of nonlinear sets in topological vector spaces for the last decade there has been a generalized trend in mathematics on the search for large algebraic structures linear spaces closed subspaces or infinitely generated algebras composed of mathematical objects enjoying certain special properties this trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis operator theory summability theory polynomials in banach spaces hypercyclicity and chaos and general functional analysis this expository paper is devoted to providing an account on the advances and on the state of the art of this trend nowadays known as lineability and spaceability

brief paper a convex optimization approach to filtering in jump linear systems with state dependent transitions we introduce a new methodology to construct a gaussian mixture approximation to the true filter density in hybrid markovian switching systems we relax the assumption that the mode transition process is a markov chain and allow it to depend on the actual and unobservable state of the system the main feature of the method is that the gaussian densities used in the approximation are selected as the solution of a convex programming problem which trades off sparsity of the solution with goodness of fit a meaningful example shows that the proposed method can outperform the widely used interacting multiple model imm filter and gpb2 in terms of accuracy at the expenses of an increase in computational time

sums of hypercyclic operators abstract every bounded operator on a complex infinite dimensional separable hilbert space can be written as the sum of two hypercyclic operators and also as the sum of two chaotic operators

secure multiplex coding attaining channel capacity in wiretap channels it is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so called secrecy capacity cs which is usually smaller than the channel capacity c in order to remove the loss c cs we propose a multiplex coding scheme with plural independent messages in this paper it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each massage several bounds of achievable multiplex coding rate region are derived for general wiretap channels in the sense of information spectral methods by extending hayashi s proof in which the coding of the channel resolvability is applied to wiretap channels furthermore the exact region for deterministic coding is determined for stationary memoryless full rank wiretap channels

on random frequent universality abstract we give a probabilistic construction of frequently hypercyclic or universal entire functions using birkhoff s ergodic theorem we apply the same ideas to construct random frequently universal vectors for the polynomials of the weighted backward shift on the classical real or complex l p space

new directions in the theory of identification via channels studies two problems in the theory of identification via channels the first problem concerns the identification via channels with noisy feedback whereas for shannon s transmission problem the capacity of a discrete memoryless channel does not change with feedback it is known that the identification capacity is affected by feedback the authors study its dependence on the feedback channel they prove both a direct and a converse coding theorem although a gap exists between the upper and lower bounds provided by these two theorems the known result for channels without feedback and the known result for channels with complete feedback are both special cases of these two new theorems because in these cases the bounds coincide the second problem is the identification via wiretap channels a secrecy identification capacity is defined for the wiretap channel a dichotomy theorem is proved which says that the second order secrecy identification capacity is the same as shannon s capacity for the main channel as long as the secrecy transmission capacity of the wiretap channel is not zero and zero otherwise equivalently one can say that the identification capacity is not lowered by the presence of a wiretapper as long as 1 bit can be transmitted or identified correctly with arbitrarily small error probability this is in strong contrast to the case of transmission

identification via channels the authors main finding is that any object among doubly exponentially many objects can be identified in blocklength n with arbitrarily small error probability via a discrete memoryless channel dmc if randomization can be used for the encoding procedure a novel doubly exponential coding theorem is presented which determines the optimal r that is the identification capacity of the dmc as a function of its transmission probability matrix this identification capacity is a well known quantity namely shannon s transmission capacity for the dmc

inverse of u frequently hypercyclic operators abstract we show that there exists an invertible u frequently hypercyclic operator on l p n 1 p whose inverse is not u frequently hypercyclic

frequently hypercyclic operators with irregularly visiting orbits abstract we prove that a bounded operator t on a separable banach space x satisfying a strong form of the frequent hypercyclicity criterion which implies in particular that the operator is universal in the sense of glasner and weiss admits frequently hypercyclic vectors with irregularly visiting orbits i e vectors x x such that the set n t x u n 1 t n x u of return times of x into u under the action of t has positive lower density for every non empty open set u x but there exists a non empty open set u 0 x such that n t x u 0 has no density

resolvability theory for the multiple access channel we study the randomness needed for approximating the output distribution of a multiple access channel where the original input processes are independent of each other the approximation is achieved by simulating possibly alternative input processes at each of the entries where the sources of randomness available for the simulators are independent of each other and the simulators do not cooperate the resolvability region of a multiple access channel is defined as the set of all random bit rate pairs at which accurate output approximation is possible where the simulation accuracy is measured by the variational distance between finite dimensional output distributions inner and outer bounds on the resolvability region are derived and close relations between the concepts of resolvability region and capacity region are demonstrated

two remarks on frequent hypercyclicity abstract we show that if t x x is a continuous linear operator on an f space x 0 then the set of frequently hypercyclic vectors of t is of first category in x and this answers a question of a bonilla and k g grosse erdmann we also show that if t x x is a bounded linear operator on a banach space x 0 and if t is frequently hypercyclic or more generally syndetically transitive then the t orbit of every non zero element of x is bounded away from 0 and in particular t is not hypercyclic

good codes can be produced by a few permutations our main result is that good codes even those meeting the random coding bound can be produced with relatively few linear in the block length permutations from a single codeword this cutdown in complexity may be of practical importance the motivation for looking at such codes came from ahlswede s covering lemma which makes it possible to build correlated source codes from channel codes via permutations in appendix i we show that the problem of finding the best error exponents for coding sources with full side information at the decoder which has received attention in the recent literature can easily be reduced to the familiar one for the discrete memoryless channel dmc finally in appendices ii and iii we give rather precise double exponentially small bounds on the probabilities that a randomly chosen code will fail to meet the random coding or expurgated bound for the dmc according to these results good codes are hard to miss if selected at random this also explains why good codes of a iow complexity such as those produced by

hypercyclicity and unimodular point spectrum abstract we show that an operator on a separable complex banach space with sufficiently many eigenvectors associated to eigenvalues of modulus 1 is hypercyclic we apply this result to construct hypercyclic operators with prescribed k unimodular point spectrum we show how eigenvectors associated to unimodular eigenvalues can be used to exhibit common hypercyclic vectors for uncountable families of operators and prove that the family of composition operators c on h 2 d where is a disk automorphism having 1 as attractive fixed point has a residual set of common hypercyclic vectors

identification in the presence of feedback a discovery of new capacity formulas a study is made of the identification problem in the presence of a noiseless feedback channel and the second order capacity c sub f resp c sub f for deterministic resp randomized encoding strategies is determined several important phenomena are encountered 1 although feedback does not increase the transmission capacity of a discrete memoryless channel dmc it does increase the second order identification capacity 2 noise increases c sub f 3 the structure of the new capacity formulas is simpler than c e shannon s 1948 familiar formula this has the effect that proofs of converses become easier than in the authors previous work

linear structure of hypercyclic vectors abstract a vector x in a banach space b is called hypercyclic for a bounded linear operator t b b if the orbit t n x n 1 is dense in b our main result states that if t is a compact perturbation of an operator of norm 1 and satisfies an appropiate extra hypothesis then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t in particular the result applies to compact perturbations of the identity we also include applications to some weighted backward shifts and compact perturbations of the identity by weighted backward shifts this last result in combination with a recent one that states that every banach space admits an operator with a hypercyclic vector proves that in all banach space there is an operator t with an infinite dimensional closed subspace consisting except for zero of hypercyclic vectors the main result also applies to the differentiation operator and the translation operator t f z f z 1 on certain hilbert spaces consisting of entire functions

frequently hypercyclic operators we investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators t on separable complex f spaces t is frequently hypercyclic if there exists a vector x such that for every nonempty open subset u of x the set of integers n such that t n x belongs to u has positive lower density we give several criteria for frequent hypercyclicity and this leads us in particular to study linear transformations from the point of view of ergodic theory several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting

operators with the specification property abstract we study a version of the specification property for linear dynamics operators having the specification property are investigated and relationships with other well known dynamical notions such as mixing devaney chaos and frequent hypercyclicity are obtained

strongly universal hashing and identification codes via channels this article shows that spl epsiv almost strongly universal classes of hash functions can yield better explicit constructions of identification codes via channels id codes and identification plus transmission codes it codes than the previous explicit constructions of verdu and wei 1993

optimal growth of entire functions frequently hypercyclic for the differentiation operator we solve a problem posed by bonilla and grosse erdmann 2007 7 by constructing an entire function f which is frequently hypercyclic with respect to the differentiation operator and satisfies mf r cerr 1 4 where c 0 may be chosen arbitrarily small this growth rate is sharp we also obtain optimal results for minimal growth in terms of average lp norms among other tools the proof uses the rudin shapiro polynomials and heat kernel estimates

strong converse for identification via quantum channels we present a simple proof of the strong converse for identification via discrete memoryless quantum channels based on a novel covering lemma the new method is a generalization to quantum communication channels of ahlswede s 1979 1992 approach to classical channels it involves a development of explicit large deviation estimates to the case of random variables taking values in self adjoint operators on a hilbert space this theory is presented separately in an appendix and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems

a bridge between u frequent hypercyclicity and frequent hypercyclicity abstract given a the family of weights a a n n decreasing to 0 such that the series n 0 a n diverges we show that the supremum on a of lower weighted densities coincides with the unweighted upper density and that the infimum on a of upper weighted densities coincides with the unweighted lower density we then investigate the notions of u frequent hypercyclicity and frequent hypercyclicity associated to these weighted densities we show that there exists an operator which is u frequently hypercyclic for each weight in a but not frequently hypercyclic although the set of frequently hypercyclic vectors always coincides with the intersection of sets of u frequently hypercyclic vectors for each weight in a

converse coding theorems for identification via channels in identification via channels the sum of two types of error probabilities of identification goes to one as the block length of transmission tends to infinity at rates above capacity when channels satisfy some stochastic properties this is well known as a strong converse theorem for the identification via channels in this paper we prove that the sum of two error probabilities tends to one exponentially and derive an explicit lower bound of this exponent function

identification plus transmission over channels with perfect feedback we determine the region of all identification and transmission rate pairs achievable over a discrete memoryless channel dmc with perfect and instantaneous feedback for both randomized and deterministic encoding as a by product we also have a new proof of kemperman s 1973 strong converse to shannon s coding theorem for dmc s with feedback

invertible composition operators on hp abstract the weakly closed algebras generated by certain sets of composition operators are shown to be reflexive a structure theorem for invertible composition operators on h2 is obtained and used to show that such operators are reflexive the structure theorem shows that invertible hyperbolic composition operators are similar to cosubnormal operators built up from bilateral weighted shifts another consequence of the structure theorem is that the composition operators induced by hyperbolic disc automorphisms are universal thus the general invariant subspace problem for hilbert space operators is contained in the problem of determining the invariant subspace lattices of these operators

strong mixing measures for linear operators and frequent hypercyclicity abstract we construct strongly mixing invariant measures with full support for operators on f spaces which satisfy the frequent hypercyclicity criterion for unilateral backward shifts on sequence spaces a slight modification shows that one can even obtain exact invariant measures

identification without randomization in the theory of identification via noisy channels randomization in the encoding has a dramatic effect on the optimal code size namely it grows double exponentially in the blocklength whereas in the theory of transmission it has the familiar exponential growth we consider now instead of the discrete memoryless channel dmc more robust channels such as the familiar compound cc and arbitrarily varying channels avc they can be viewed as models for jamming situations we make the pessimistic assumption that the jammer knows the input sequence before he acts this forces communicators to use the maximal error concept and also makes randomization in the encoding superfluous now for a dmc w by a simple observation made by ahlswede and dueck 1989 in the absence of randomization the identification capacity say c sub nri w equals the logarithm of the number of different row vectors in w we generalize this to compound channels a formidable problem arises if the dmc w is replaced by the avc w in fact for 0 1 matrices only in w we are exactly as for transmission led to the equivalent zero error capacity of shannon but for general w the identification capacity c sub nri w is quite different from the transmission capacity c w an observation is that the separation codes of ahlswede 1989 are also relevant here we present a lower bound on c sub nri w it implies for instance for w sub 0 1 sup 1 0 sub spl delta 1 spl delta 1 0 spl delta spl isin 0 1 2 that c sub nri w 1 which is obviously tight it exceeds c w which is known to exceed 1 h spl delta where h is the binary entropy function we observe that a separation code with worst case average list size l which we call an nra code can be partitioned into l 2 sup ne transmission codes this gives a nonsingle letter characterization of the capacity of avc with maximal probability of error in terms of the capacity of codes with list decoding we also prove that randomization in the decoding does not increase c sub i w and c sub nri w finally we draw attention to related work on source coding

optimal selling rules in a regime switching model in this note we derive optimal selling rules under a regime switching model the optimal stopping rule is of a threshold type for each state derived via the modified smooth fit the proof is via the martingale theory numerical examples are reported to demonstrate the dependence of threshold levels with various parameters and to compare our result with some suboptimal selling rules

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

general nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel several nonasymptotic formulas are established in channel resolvability and identification capacity and they are applied to the wiretap channel by using these formulas the epsi capacities of the above three problems are considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel as a result we solve an open problem proposed by han and verduacute moreover we obtain lower bounds of the exponents of error probability and the wiretapper s information in the wiretap channel

weak decoupling duality and quantum identification if a quantum system is subject to noise it is possible to perform quantum error correction reversing the action of the noise if and only if no information about the system s quantum state leaks to the environment in this paper we develop an analogous duality in the case that the environment approximately forgets the identity of the quantum state a weaker condition satisfied by randomizing maps and approximate unitary designs specifically we show that the environment approximately forgets quantum states if and only if the original channel approximately preserves pairwise fidelities of pure inputs an observation we call weak decoupling duality using this tool we then go on to study the task of using the output of a channel to simulate restricted classes of measurements on a space of input states the case of simulating measurements that test whether the input state is an arbitrary pure state is known as equality testing or quantum identification an immediate consequence of weak decoupling duality is that the ability to perform quantum identification cannot be cloned we furthermore establish that the optimal amortized rate at which quantum states can be identified through a noisy quantum channel is equal to the entanglement assisted classical capacity of the channel despite the fact that the task is quantum not classical and entanglement assistance is not allowed in particular this rate is strictly positive for every nonconstant quantum channel including classical channels

the principal measure of a quantum harmonic oscillator at the end of his paper oprocha 2006 j phys a math gen 39 14 559 65 oprocha said that it is difficult and interesting to know the exact value of the principal measure of an annihilation operator of the unforced quantum harmonic oscillator motivated by this in this paper we prove that this exact value is equal to 1 besides we point out that exhibits distributional chaos for any 0 2

unequal error protection an information theoretic perspective an information theoretic framework for unequal error protection is developed in terms of the exponential error bounds the fundamental difference between the bit wise and message wise unequal error protection uep is demonstrated for fixed length block codes on discrete memoryless channels dmcs without feedback effect of feedback is investigated via variable length block codes it is shown that feedback results in a significant improvement in both bit wise and message wise ueps except the single message case for missed detection the distinction between false alarm and missed detection formalizations for message wise uep is also considered all results presented are at rates close to capacity

notes on subspace hypercyclic operators a bounded linear operator t on a banach space x is called subspace hypercyclic for a subspace m if orb t x m is dense in m for a vector x m in this case we show that p t has a relatively dense range for every real or complex polynomial p which in turn answers a question posed in madore and martinez avendano 2011 8 as a consequence the algebraic structure of the set of subspace hypercyclic vectors can be described