on the observability of continuous time switched linear systems under partially unknown inputs this technical note addresses the problem of observability of continuous time switched linear systems sls subject to unknown disturbances unknown switching signals and unconstrained nonzero dwell time for this class of hybrid systems a geometric characterization of the observability properties is presented in particular attention is focused on the estimation of the sls state from the continuous measurements using the well known concept of a b invariant subspaces three main problems are addressed and solved namely the observability for every nonzero state trajectory the observability for almost every control input and the observability for almost every state trajectory it is also shown that the approach herein presented subsumes some of the classical results on observability of sls previously reported in the literature and allows expressing them in a common framework

approximate characterizations for the gaussian source broadcast distortion region we consider the joint source channel coding problem of sending a gaussian source on a k user gaussian broadcast channel with bandwidth mismatch a new outer bound to the achievable distortion region is derived using the technique of introducing more than one additional auxiliary random variable which was previously used to derive sum rate lower bound for the symmetric gaussian multiple description problem by combining this outer bound with the achievability result based on source channel separation we provide approximate characterizations of the achievable distortion region within constant multiplicative factors furthermore we show that the results can be extended to general broadcast channels and the performance of the source channel separation based approach is also within the same constant multiplicative factors of the optimum

state space reconstruction and spatio temporal prediction of lattice dynamical systems this paper addresses the problems of state space reconstruction and spatio temporal prediction for lattice dynamical systems it is shown that the state space of any finite lattice dynamical system can be embedded into a reconstruction space for almost every in the sense of prevalence smooth measurement mapping as long as the dimension of the reconstruction space is larger than twice the size of the lattice based on this result an input output spatio temporal dynamical relation for each site within the lattice is derived and used for spatio temporal prediction of the system in the case of infinite lattice dynamical systems an approach based on constructing local lattice dynamical systems is proposed it is shown that the finite dimensional results can be directly applied to the local modelling and spatio temporal prediction for infinite lattice dynamical systems two numerical examples are provided to demonstrate the proposed theory and approach

complexities of differentiable dynamical systems we define the notion of localizable property for a dynamical system then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems these notions are the fast growth of the number of periodic points the positive entropy and the high emergence we finally propose a dictionary between the previously explained theory on entropy and the ongoing one on emergence

prevalence an addendum to prevalence a translation invariant almost every on infinite dimensional spaces bull amer math soc n s 27 1992 no 2 217 238 mr1161274 93k 28018

regularity criteria for almost every function in sobolev spaces in this paper we determine the multifractal nature of almost every function in the prevalence setting in a given sobolev or besov space according to different regularity exponents these regularity criteria are based on local l p regularity or on wavelet coefficients and give a precise information on pointwise behavior

broadcasting correlated gaussians we study the transmission of a memoryless bivariate gaussian source over an average power constrained one to two gaussian broadcast channel the transmitter observes the source and describes it to the two receivers by means of an average power constrained signal each receiver observes the transmitted signal corrupted by a different additive white gaussian noise and wishes to estimate the source component intended for it receiver 1 wishes to estimate the first source component and receiver 2 wishes to estimate the second our interest is in the pairs of expected squared error distortions that are simultaneously achievable at the two receivers we prove that an uncoded transmission scheme that sends a linear combination of the source components achieves the optimal power versus distortion trade off whenever the signal to noise ratio is below a certain threshold the threshold is a function of the source correlation and the distortion at the receiver with the weaker noise

pattern formation in a nonlinear model for animal coats abstract several models have been proposed for describing the formation of animal coat patterns we consider reaction diffusion models due to murray which rely on a turing instability for the pattern selection in this paper we describe the early stages of the pattern formation process for large domain sizes this includes the selection mechanism and the geometry of the patterns generated by the nonlinear system on one two and three dimensional base domains these results are obtained by an adaptation of results explaining the occurrence of spinodal decomposition in materials science as modeled by the cahn hilliard equation we use techniques of dynamical systems viewing solutions of the reaction diffusion model in terms of nonlinear semiflows our results are applicable to any parabolic system exhibiting a turing instability

on the testability of identification in some nonparametric models with endogeneity this paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity the first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions these conditions are typically referred to as completeness conditions the second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions for each of these hypothesis testing problems we provide conditions under which any test will have power no greater than size against any alternative in this sense we conclude that no nontrivial tests for these hypothesis testing problems exist publication abstract

generic diffeomorphisms with superexponential growth of number of periodic orbits let m be a smooth compact manifold of dimension at least 2 and diff r m be the space of c r smooth diffeomorphisms of m associate to each diffeomorphism f 2 diff r m the sequence pn f of the number of isolated periodic points for f of period n in this paper we exhibit an open set n in the space of diffeomorphisms diff r m such for a baire generic diffeomorphism f 2 n the number of periodic points pnf grows with a period n faster than any following sequence of numbers fangn2zc along a subsequence i e pn f a ni for some ni 1 with i 1 in the cases of surface diffeomorphisms i e dim m d 2 an open set n with a supergrowth of the number of periodic points is a newhouse domain a proof of the man result is based on the gontchenko shilnikov turaev theorem gst a complete proof of that theorem is also presented

hausdorff and packing dimension of fibers and graphs of prevalent continuous maps abstract the notions of shyness and prevalence generalize the property of being zero and full haar measure to arbitrary not necessarily locally compact polish groups the main goal of the paper is to answer the following question what can we say about the hausdorff and packing dimension of the fibers of prevalent continuous maps let k be an uncountable compact metric space we prove that a prevalent f c k r d has many fibers with almost maximal hausdorff dimension this generalizes a theorem of dougherty and yields that a prevalent f c k r d has graph of maximal hausdorff dimension generalizing a result of bayart and heurteaux we obtain similar results for the packing dimension we show that for a prevalent f c 0 1 m r d the set of y f 0 1 m for which dim h f 1 y m contains a dense open set having full measure with respect to the occupation measure m f 1 where dim h and m denote the hausdorff dimension and the m dimensional lebesgue measure respectively we also prove an analogous result when 0 1 m is replaced by any self similar set satisfying the open set condition we cannot replace the occupation measure with lebesgue measure in the above statement we show that the functions f c 0 1 for which positively many level sets are singletons form a non shy set in c 0 1 in order to do so we generalize a theorem of antunovic burdzy peres and ruscher as a complementary result we prove that the functions f c 0 1 for which dim h f 1 y 1 for all y min f max f form a non shy set in c 0 1 we also prove sharper results in which large hausdorff dimension is replaced by positive measure with respect to generalized hausdorff measures which answers a problem of fraser and hyde

broadcasting correlated vector gaussians the problem of sending two correlated vector gaussian sources over a bandwidth matched two user scalar gaussian broadcast channel is studied in this paper where each receiver wishes to reconstruct its target source under a covariance distortion constraint we derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair our derivation is based on a new bounding technique which involves the introduction of appropriate remote sources furthermore it is shown that this lower bound is achievable by a class of hybrid schemes for the special case where the weak receiver wishes to reconstruct a scalar source under the mean squared error distortion constraint

outer bounds on the admissible source region for broadcast channels with correlated sources two outer bounds on the admissible source region for broadcast channels with correlated sources are presented the first one is strictly tighter than the existing outer bound by gohari and anantharam while the second one provides a complete characterization of the admissible source region in the case where the two sources are conditionally independent given the common part these outer bounds are deduced from the general necessary conditions established for the lossy source broadcast problem via suitable comparisons between the virtual broadcast channel induced by the source and the reconstructions and the physical broadcast channel

local behavior of traces of besov functions prevalent results let 1 d d and p q s satisfying 0 p 0 q 0 s d p in this article we study the global and local regularity properties of traces on affine subsets of rd of functions belonging to the besov space bp qs rd given a d dimensional subspace h rd for almost all functions in bp qs rd in the sense of prevalence we are able to compute the singularity spectrum of the traces fa of f on affine subspaces of the form a h for lebesgue almost every a rd d in particular we prove that for lebesgue almost every a rd d these traces fa are more regular than what could be expected from standard trace theorems and that fa enjoys a multifractal behavior

observing lyapunov exponents of infinite dimensional dynamical systems can lyapunov exponents of infinite dimensional dynamical systems be observed by projecting the dynamics into n using a typical nonlinear projection map we answer this question affirmatively by developing embedding theorems for compact invariant sets associated with c1 maps on hilbert spaces examples of such discrete time dynamical systems include time t maps and poincare return maps generated by the solution semigroups of evolution partial differential equations we make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite dimensional dynamical system in so doing we adopt an empirical approach and formulate checkable conditions under which a lyapunov exponent computed from experimental data will be a lyapunov exponent of the infinite dimensional dynamical system under study provided the nonlinear projection map producing the data is typical in the sense of prevalence

amenability free subgroups and haar null sets in non locally compact groups the paper has two objectives on the one hand we study left haar null sets a measure theoretic notion of smallness on polish not necessarily locally compact groups on the other hand we introduce and investigate two classes of polish groups which are closely related to this notion and to amenability we show that left haar null sets form a sigma ideal and have the steinhaus property on polish groups which are amenable at the identity and that they lose these two properties in the presence of appropriately embedded free subgroups as an application we prove an automatic continuity result for universally measurable homomorphisms from inverse limits of sequences of amenable locally compact second countable groups to second countable groups

generalizations of srb measures to nonautonomous random and infinite dimensional systems we review some developments that are direct outgrowths of or closely related to the idea of srb measures as introduced by sinai ruelle and bowen in the 1970s these new directions of research include the emergence of strange attractors in periodically forced dynamical systems random attractors in systems defined by stochastic differential equations srb measures for infinite dimensional systems including those defined by large classes of dissipative pdes quasi static distributions for slowly varying time dependent systems and surviving distributions in leaky dynamical systems

detection of symmetry of attractors from observations i theory abstract barany et al 1993 proposed a method for determining the symmetries of attractors of equivariant systems by averaging certain classes of equivariant maps we use an idea in barany et al to re cast definitions of symmetry detectives assuming that we only have access to equivariant observations from the system detecting from observations allows one to perform averaging in spaces that may have much lower dimension than the phase space this paper generalises and develops their suggestion among the generalisations we consider is the use of nonpolynomial detectives and we show using the notion of prevalence of hunt et al 1992 that our detectives and the detectives of barany et al 1993 dellnitz et al 1994 and golubitsky and nicol 1995 give the correct symmetry of attractors almost certainly in a measure theoretic sense we show that detectives can persistently give incorrect symmetries at isolated points in parametrised systems and discuss how to overcome this we show how one can find the symmetry of an attractor from examination of a poincare section in part ii of this article ashwin and tomes apply these results to find symmetries of attractors in a physical system of four coupled electronic oscillators with s4 symmetry

how often do simple dynamical processes have infinitely many coexisting sinks this work concerns the nature of chaotic dynamical processes sheldon newhouse wrote on dynamical processes depending on a parameter xx 1 t xn wherex is in the plane such as might arise when studying poincare return maps for autonomous differential equations in ir3 he proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane and that such parameter values would be dense in some interval the fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes we prove for an apparently typical situation that newhouse s construction yields only a set of parameter values of measure zero

prevalence a translation invariant almost every on infinite dimensional spaces we present a measure theoretic condition for a property to hold almost everywhere on an infinite dimensional vector space with particularemphasis on function spaces such as c k and l p like the concept of lebesgue almost every on an infinite dimensional spaces our notion of prevalence is translation invariant instead of using a specific measure on the entire space we define prevalence in terms of the class of all probability measures with compact support prevalence is a more appropriate condition than the topological concepts of open and dense or generic when one desires a probabilistic result on the likelihood of a given property on a function space

basic control for the viscous moore greitzer partial differential equation the notions of basic controllability and basic control are defined a quadratic optimal control of the linearized viscous moore greitzer equation is presented and it is confirmed that stall is uncontrollable in this model a basic control is constructed for the nonlinear viscous moore greitzer equation which can control both surge and stall some extensions of this construction are discussed numerical simulations of the basic control are presented and its performance is compared to the performance of a backstepping control constructed by banaszuk hauksson and mezic siam j control optim 37 1999 pp 1503 1537 it is shown that the viscous moore greizer equation with throttle control is not basically controllable but under certain conditions adding air injection control will make the equation basically controllable

genericity and robustness of full surplus extraction we study whether priors that admit full surplus extraction fse are generic an issue that becomes a gauge to evaluate the validity of the current mechanism design paradigm we consider the space of priors on the universal type space and thereby relax the assumption of a fixed finite number of types made by cremer and mclean 1988 we show that fse priors are topologically generic contrary to the result of heifetz and neeman 2006 that fse is generically impossible both geometrically and measure theoretically instead of using the bdp approach or convex combinations of priors adopted in heifetz and neeman 2006 we prove our genericity results by showing a robustness property of cremer mclean mechanisms

a lower bound on the sum rate of multiple description coding with symmetric distortion constraints we derive a single letter lower bound on the minimum sum rate of multiple description coding with symmetric distortion constraints for the binary uniform source with the erasure distortion measure or hamming distortion measure this lower bound can be evaluated with the aid of certain minimax theorems a similar minimax theorem is established in the quadratic gaussian setting which is further leveraged to analyze the special case where the minimum sum rate subject to two levels of distortion constraints with the second level imposed on the complete set of descriptions is attained in particular we determine the minimum achievable distortions at the intermediate levels

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

vector gaussian multiple description with two levels of receivers the problem of l multiple descriptions of a stationary and ergodic gaussian source with two levels of receivers is investigated each of the first level receivers receive an arbitrary subset k of the l descriptions k l the second level receiver receives all l descriptions all the receivers both at the first level and the second level reconstruct the source using the subset of descriptions they receive the corresponding reconstructions are subject to quadratic distortion constraints our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met we show that an analog digital separation architecture involving joint gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios these scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k 2 and l 3

some analogies between haar meager sets and haar null sets in abelian polish groups abstract in the paper we would like to pay attention to some analogies between haar meager sets and haar null sets among others we show that 0 int a a for each borel non haar meager set a in an abelian polish group moreover we define d measurability as a topological analog of christensen measurability and prove that each d measurable homomorphism is continuous finally we show easy constructions of a haar meager non haar null set and conversely a meager haar null set which is not haar meager in spaces of sequences our results refer to the papers 1 2 4

avoiding σ porous sets in hilbert spaces abstract we give a constructive proof that any porous subset of a hilbert space has lebesgue measure zero on typical c 1 curves further we discover that this result does not extend to all forms of porosity we find that even power p porous sets may meet many c 1 curves in positive measure

probability of local bifurcation type from a fixed point a random matrix perspective results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems real random matrices time delay dynamical systems companion matrices and a set of mappings known for their properties as universal approximators neural networks the eigenvalue spectrum is considered both numerically and analytically using previous work of edelman et al based upon the numerical evidence various conjectures are presented the conclusion is that in many circumstances most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues nevertheless surprising situations are presented for which the aforementioned conclusion does not hold e g real random matrices with gaussian elements with a large positive mean and finite variance

numerical analysis of generalized regularized long wave equation using the element free kp ritz method abstract a numerical analysis of the generalized regularized long wave grlw equation by application of the element free kp ritz method is performed to approximate the displacement field an element free kernel particle estimation is employed and a system of nonlinear discrete equations is achieved by using the ritz minimization procedure to the energy expressions validation of the present numerical solutions with the exact results has been conducted by numerical examples and evidenced a good agreement

on the generic im possibility of full surplus extraction in mechanism design a number of studies most notably cremer and mclean 1985 1988 have shown that in harsanyi type spaces of a fixed finite size it is generically possible to design mechanisms that extract all the surplus from players and as a consequence implement any outcome as if the players private information were commonly known in contrast we show that within the set of common priors on the universal type space the subset of priors that permit the extraction of the players full surplus is shy shyness is an otion of smallness for convex subsets of infinite dimensional topological vector spaces in our case the set of common priors which generalizes the usual notion of zero lebesgue measure in finite dimensional spaces

optimality and approximate optimality of source channel separation in networks we consider the source channel separation architecture for lossy source coding in communication networks it is shown that the separation approach is optimal in two general scenarios and is approximately optimal in a third scenario the two scenarios for which separation is optimal complement each other the first is when the memoryless sources at source nodes are arbitrarily correlated each of which is to be reconstructed at possibly multiple destinations within certain distortions but the channels in this network are synchronized orthogonal and memoryless point to point channels the second is when the memoryless sources are mutually independent each of which is to be reconstructed only at one destination within a certain distortion but the channels are general including multi user channels such as multiple access broadcast interference and relay channels possibly with feedback the third scenario for which we demonstrate approximate optimality of source channel separation generalizes the second scenario by allowing each source to be reconstructed at multiple destinations with different distortions for this case the loss from optimality using the separation approach can be upper bounded when a difference distortion measure is taken and in the special case of quadratic distortion measure this leads to universal constant bounds

a source channel separation theorem with application to the source broadcast problem a converse method is developed for the source broadcast problem specifically it is shown that the separation architecture is optimal for a variant of the source broadcast problem and the associated source channel separation theorem can be leveraged via a reduction argument to establish a necessary condition for the original problem which unifies several existing results in the literature somewhat surprisingly this method albeit based on the source channel separation theorem can be used to prove the optimality of non separation based schemes and determine the performance limits in certain scenarios where the separation architecture is suboptimal

advanced topology on the multiscale sequence spaces s nu abstract we pursue the study of the multiscale spaces s introduced by jaffard in the context of multifractal analysis we give the necessary and sufficient condition for s to be locally p convex and exhibit a sequence of p norms that defines its natural topology the strong topological dual of s is identified to another sequence space depending on endowed with an inductive limit topology as a particular case we describe the dual of a countable intersection of besov spaces

a lower bound on the expected distortion of joint source channel coding we consider the classic joint source channel coding problem of transmitting a memoryless source over a memoryless channel the focus of this work is on the long standing open problem of finding the rate of convergence of the smallest attainable expected distortion to its asymptotic value as a function of the blocklength n our main result is that in general the convergence rate is not faster than n 1 2 in particular we show that for the problem of transmitting i i d uniform bits over a binary symmetric channels with hamming distortion the smallest attainable distortion bit error rate is at least omega n 1 2 above the asymptotic value if the bandwidth expansion ratio is above 1

rate region of gaussian multiple description coding with individual and central distortion constraints the rate region of gaussian multiple description coding with individual and central distortion constraints is completely characterized specifically a lower bound and an upper bound are derived for each supporting hyperplane of the rate region where the lower bound is associated with a max min game while the upper bound is associated with a min max game furthermore it is shown that these two bounds coincide due to the existence of a saddle point

vector gaussian multiple description with individual and central receivers t multiple descriptions of a vector gaussian source for individual and central receivers are investigated the sum rate of the descriptions with covariance distortion measure constraints in a positive semidefinite ordering is exactly characterized for two descriptions the entire rate region is characterized the key component of the solution is a novel information theoretic inequality that is used to lower bound the achievable multiple description rates jointly gaussian descriptions are optimal in achieving the limiting rates we also show the robustness of this description scheme the distortions achieved are no larger when used to describe any non gaussian source with the same covariance matrix

an extremal inequality motivated by multiterminal information theoretic problems we prove a new extremal inequality motivated by the vector gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems as a corollary this inequality yields a generalization of the classical entropy power inequality epi as another corollary this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables

abundance of fast growth of the number of periodic points in 2 dimensional area preserving dynamics we prove that there exists an open subset of the set of real analytic hamiltonian diffeomorphisms of the two dimensional torus in which diffeomorphisms exhibiting fast growth of the number of periodic points are dense we also prove that there exists an open subset of the set of smooth area preserving diffeomorphisms of a closed surface in which typical diffeomorphisms exhibit fast growth of the number of periodic points

global theory of one frequency schrodinger operators we study schrodinger operators with a one frequency analytic potential focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials from the dynamical point of view the transition signals the emergence of non uniform hyperbolicity so the dependence of the lyapunov exponent with respect to parameters plays a central role in the analysis though often ill behaved by conventional measures we show that the lyapunov exponent is in fact remarkably regular in a stratified sense which we define the irregularity comes from the matching of nice analytic or smooth functions along sets with complicated geometry this result allows us to establish that the critical set for the transition lies within countably many codimension one subvarieties of the infinite dimensional parameter space a more refined renormalization based analysis shows that the critical set is rather thin within those subvarieties and allows us to conclude that a typical potential has no critical energies such acritical potentials also form an open set and have several interesting properties only finitely many phase transitions may happen but never at any specific point in the spectrum and the lyapunov exponent is minorated in the region of the spectrum where it is positive on the other hand we do show that the number of phase transitions can be arbitrarily large

wild hyperbolic sets yet no chance for the coexistence of infinitely many klus simple newhouse attracting sets the phenomenon of the coexistence of infinitely many sinks for two dimensional dissipative diffeomorphisms is a result due to newhouse ne1 ne2 in fact for each parameter value at which a homoclinic tangency is formed nondegenerately there exist intervals in the parameter space containing dense sets of parameter values for which there are infinitely many coexisting sinks robinson r the structure of the sinks constructed by newhouse is limited simple newhouse parameter values are values at which there are infinitely many sinks having some special well defined property concerning the structure a result due to tedeschini lalli and yorke ty says that the lebesgue measure of the set of simple newhouse parameter values is zero when the tangencies are due to the standard affine horseshoe map it is argued in ty and pr that a more general derivation of this measure zero result would be desirable the main result of this paper is that the lebesgue measure of the set of klus simple parameter values including the simple newhouse parameter values is zero for saddle hyperbolic basic sets forming tangencies

matched multiuser gaussian source channel communications via uncoded schemes we investigate whether uncoded schemes are optimal for gaussian sources on multiuser gaussian channels particularly we consider two problems the first is to send correlated gaussian sources on a gaussian broadcast channel where each receiver is interested in reconstructing only one source component or one specific linear function of the sources under the mean squared error distortion measure the second is to send correlated gaussian sources on a gaussian multiple access channel where each transmitter observes a noisy combination of the sources and the receiver wishes to reconstruct the individual source components or individual linear functions under the mean squared error distortion measure it is shown that when the channel parameters satisfy certain general conditions the induced distortion tuples are on the boundary of the achievable distortion region and thus optimal instead of following the conventional approach of attempting to characterize the achievable distortion region we ask the question whether and how a match can be effectively determined this decision problem formulation helps to circumvent the difficult optimization problem often embedded in region characterization problems and it also leads us to focus on the critical conditions in the outer bounds that make the inequalities become equalities which effectively decouple the overall problem into several simpler sub problems optimality results previously unknown in the literature are obtained using this novel approach explicit and novel outer bounds are derived for the two problems as the byproducts of our investigation

finite dimensional bounds on bbz _m and binary ldpc codes with belief propagation decoders this paper focuses on finite dimensional upper and lower bounds on decodable thresholds of zopfm and binary low density parity check ldpc codes assuming belief propagation decoding on memoryless channels a concrete framework is presented admitting systematic searches for new bounds two noise measures are considered the bhattacharyya noise parameter and the soft bit value for a maximum a posteriori probability map decoder on the uncoded channel for zopf m ldpc codes an iterative m dimensional bound is derived for m ary input symmetric output channels which gives a sufficient stability condition for zopfm ldpc codes and is complemented by a matched necessary stability condition introduced herein applications to coded modulation and to codes with nonequiprobably distributed codewords are also discussed for binary codes two new lower bounds are provided for symmetric channels including a two dimensional iterative bound and a one dimensional noniterative bound the latter of which is the best known bound that is tight for binary symmetric channels bscs and is a strict improvement over the existing bound derived by the channel degradation argument by adopting the reverse channel perspective upper and lower bounds on the decodable bhattacharyya noise parameter are derived for nonsymmetric channels which coincides with the existing bound for symmetric channels

smoothness of projections bernoulli convolutions and the dimension of exceptions erd s 1939 1940 studied the distribution of the random series p 0 n and showed that is singular for infinitely many 1 2 1 and absolutely continuous for a e in a small interval 1 1 solomyak 1995 proved a conjecture made by garsia 1962 that is absolutely continuous for a e 1 2 1 in order to sharpen this result we have developed a general method that can be used to estimate the hausdorff dimension of exceptional parameters in several contexts in particular we prove for any 0 1 2 the set of 0 1 such that is singular has hausdorff dimension strictly less than 1 for any borel set a rd with hausdorff dimension dim a d 1 2 there are points x a such that the pinned distance set x y y a has positive lebesgue measure moreover the set of x where this fails has hausdorff dimension at most d 1 dim a let k denote the middle cantor set for 1 2 and let k r be any compact set peres and solomyak 1998 showed that for a e 0 1 2 such that dim k dimk 1 the sum k k has positive length we show that the set of exceptional in this statement has hausdorff dimension at most 2 dim k dimk 0 for any borel set e rd with dim e 2 almost all orthogonal projections of e onto lines through the origin have nonempty interior and the exceptional set of lines where this fails has dimension at most d 1 dim e if is a borel probability measure on rd with correlation dimension greater than m 2 then for a prevalent set of c1 maps f rd rm in the sense described by hunt sauer and yorke 1992 the image of under f has a density with at least fractional derivatives in l2 rm

distortion bounds for broadcasting with bandwidth expansion we consider the problem of broadcasting a single gaussian source to two listeners over a gaussian broadcast channel with rho channel uses per source sample where rho 1 a distortion pair d1 d2 is said to be achievable if one can simultaneously achieve a mean squared error mse d1 at receiver 1 and d2 at receiver 2 the main result of this correspondence is an outer bound for the set of all achievable distortion pairs that is we find necessary conditions under which d1 d2 is achievable we then apply this result to the problem of point to point transmission over a gaussian channel with unknown signal to noise ratio snr and rho 1 we show that if a system must be optimal at a certain snrmin then asymptotically the system distortion cannot decay faster than o 1 snr as for achievability we show that a previously reported scheme due to mittal and phamdo 2002 is optimal at high snr we introduce two new schemes for broadcasting with bandwidth expansion combining digital and analog transmissions we finally show how a system with a partial feedback returning from the bad receiver to the transmitter and to the good receiver achieves a distortion pair that lies on the outer bound derived here

analog computation with dynamical systems a b s t r a c t physical systems exhibit various levels of complexity their long term dynamics may converge to fixed points or exhibit complex chaotic behavior this paper presents a theory that enables to interpret natural processes as special purpose analog computers since physical systems are naturally described in continuous time a definition of computational complexity for continuous time systems is required in analogy with the classical discrete theory we develop fundamentals of computational complexity for dynamical systems discrete or continuous in time on the basis of an intrinsic time scale of the system dissipative dynamical systems are classified into the computational complexity classes pd co rpd npd and exp t corresponding to their standard counterparts according to the complexity of their long term behavior the complexity of chaotic attractors relative to regular ones leads to the conjecture pa fi npj continuous time flows have been proven useful in solving various practical problems our theory provides the tools for an algorithmic analysis of such flows as an example we analyze the continuous hopfield network 1998 elsevier science b v all rights reserved

on the role of the refinement layer in multiple description coding and scalable coding we clarify the relationship among several existing achievable multiple description rate distortion regions by investigating the role of refinement layer in multiple description coding specifically we show that the refinement layer in the el gamal cover egc scheme and the venkataramani kramer goyal vkg scheme can be removed as a consequence the egc region is equivalent to the egc region an antecedent version of the egc region while the vkg region when specialized to the 2 description case is equivalent to the zhang berger zb region moreover we prove that for multiple description coding with individual and hierarchical distortion constraints the number of layers in the vkg scheme can be significantly reduced when only certain weighted sum rates are concerned the role of refinement layer in scalable coding a special case of multiple description coding is also studied

energy distortion exponents in lossy transmission of gaussian sources over gaussian channels lossy transmission of gaussian sources over energy limited gaussian point to point and broadcast channels is studied under the infinite bandwidth regime i e when the number of channel uses is unlimited using previously known asymptotic achievability and converse results the energy distortion exponent defined as the rate of decay of the square error distortion as the available energy to noise ratio increases without bound is completely characterized for both the point to point and broadcast channel cases turning then to the scenario of zero delay transmission where outage events with arbitrarily small probability are allowed it is shown that the same energy distortion exponent as in the infinite delay case can be achieved in all the studied scenarios

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

the achievable distortion region of sending a bivariate gaussian source on the gaussian broadcast channel we provide a complete characterization of the achievable distortion region for the problem of sending a bivariate gaussian source over bandwidth matched gaussian broadcast channels where each receiver is interested in only one component of the source this setting naturally generalizes the simple single gaussian source bandwidth matched broadcast problem for which the uncoded scheme is known to be optimal we show that a hybrid scheme can achieve the optimum for the bivariate case but neither an uncoded scheme alone nor a separation based scheme alone is sufficient we further show that in this joint source channel coding setting the gaussian scenario is the worst scenario among the sources and channel noises with the same covariances

bifurcation to infinitely many sinks this paper considers one parameter families of diffeomorphisms ft in two dimensions which have a curve of dissipative saddle periodic pointspt i e ftn pt pt and detdftn pt 1 the family is also assumed to create new homoclinic intersections of the stable and unstable manifolds ofpt as the parameter varies throught0 gavirlov and silnikov proved that if the new homoclinic intersections are created nondegenerately att0 then there is an infinite cascade of periodic sinks i e there are parameter valuestn accumulating att0 for which there is a sink of periodn gs2 sect 4 we show that this result is true for real analytic diffeomorphisms even if the homoclinic intersection is created degenerately we give computer evidence to show that this latter result is probably applicable to the henon map fora near 1 392 andb equal 0 3