joint source channel coding with side information using hybrid digital analog codes we study the joint source channel coding problem of transmitting a gaussian source over a gaussian channel in two cases i the presence of interference known only to the transmitter and ii in the presence of side information about the source known only to the receiver we introduce hybrid digital analog forms of the costa and wyner ziv coding schemes we present the random coding counterpart of schemes based on lattices proposed by kochman and zamir then we discuss applications of the hybrid digital analog schemes in the case of channel signal to noise ratio mismatch and for lossy multicasting of a common source with bandwidth compression

a branch and cut decomposition algorithm for solving chance constrained mathematical programs with finite support we present a new approach for exactly solving chance constrained mathematical programs having discrete distributions with finite support and random polyhedral constraints such problems have been notoriously difficult to solve due to nonconvexity of the feasible region and most available methods are only able to find provably good solutions in certain very special cases our approach uses both decomposition to enable processing subproblems corresponding to one possible outcome at a time and integer programming techniques to combine the results of these subproblems to yield strong valid inequalities computational results on a chance constrained formulation of a resource planning problem inspired by a call center staffing application indicate the approach works significantly better than both an existing mixed integer programming formulation and a simple decomposition approach that does not use strong valid inequalities we also demonstrate how the approach can be used to efficiently solve for a sequence of risk levels as would be done when solving for the efficient frontier of risk and cost

an efficient trajectory method for probabilistic production inventory distribution problems we consider a supply chain operating in an uncertain environment the customers demand is characterized by a discrete probability distribution a probabilistic programming approach is adopted for constructing an inventory production distribution plan over a multiperiod planning horizon the plan does not allow the backlogging of the unsatisfied demand and minimizes the costs of the supply chain while enabling it to reach a prescribed nonstockout service level it is a strategic plan that hedges against undesirable outcomes and that can be adjusted to account for possible favorable realizations of uncertain quantities a modular integrated and computationally tractable method is proposed for the solution of the associated stochastic mixed integer optimization problems containing joint probabilistic constraints with dependent right hand side variables the concept of p efficiency is used to construct a finite number of demand trajectories which in turn are employed to solve problems with joint probabilistic constraints we complement this idea by designing a preordered set based preprocessing algorithm that selects a subset of promising p efficient demand trajectories finally to solve the resulting disjunctive mixed integer programming problem we implement a special column generation algorithm that limits the risk of congestion in the resources of the supply chain the methodology is validated on an industrial problem faced by a large chemical supply chain and turns out to be very efficient it finds a solution with a minimal integrality gap and provides substantial cost savings

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

the sample average approximation method for stochastic discrete optimization in this paper we study a monte carlo simulation based approach to stochastic discrete optimization problems the basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function the obtained sample average optimization problem is solved and the procedure is repeated several times until a stopping criterion is satisfied we discuss convergence rates stopping rules and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem

deconstructing hopf spaces we characterize hopf spaces with finitely generated cohomology as an algebra over the steenrod algebra we deconstruct the original space into an h space y with finite mod p cohomology and a finite number of p torsion eilenberg mac lane spaces we give a precise description of homotopy commutative h spaces in this setting

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

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

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

tcm ssma communication systems with cascaded sequences and pam qam signal sets an expression in matrix form for the multiple access interference mai in an asynchronous direct sequence spread spectrum multiple access ds ssma communication system with cascaded sequences cvs arbitrary chip waveforms and trellis coded modulation tcm with a pulse amplitude modulation pam or quadrature amplitude modulation qam signal set is obtained tcm provides significant coding gain while the cvs decrease the correlation between the mai of adjacent data intervals the expression is used to calculate arbitrarily accurate probability density functions pdfs of the mai in the tcm system and to derive an accurate approximation of the mai variance it also helps illustrate some properties of the mai by separating contributing parameters into different matrices we derive an approximation of the upper union bound on the bit error probability and investigate its applicability the results show that cv schemes can greatly reduce the pairwise error probabilities peps until the length of the cv becomes greater than that of the error weight sequence ews under consideration

localization and periodicity in unstable homotopy theory in this paper we develop a hierarchy of natural localizations of spaces called the vn periodizations for n 0 which may be used to expose and study periodic phenomena in unstable homotopy theory these vn periodizations act less radically than the corresponding homological localizations 2 and respect fibrations to a very considerable extent a major part of this paper is devoted to developing the general theory of periodizations of spaces thereby providing a foundation for the study of the vn periodization and many others some of this general theory has been developed independently by dror farjoun 13 14 and we refer the reader to his work for an alternative approach with other interesting general results during the past decade remarkable progress was made by ravenel hopkins devinatz and smith 12 16 17 33 toward a global understanding of stable periodic phenomena and we hope that the present paper will help to prepare the way for a similar understanding of unstable periodic phenomena an excellent exposition of localization and periodicity in stable homotopy theory is now available in ravenel s book 35 major features of stable homotopy are understood chromatically as manifestations of more basic periodic phenomena these phenomena belong to a hierarchy starting with those detected rationally followed by those detected in classical k theory and in the successive morava k theories most fundamentally each finite cw spectrum has an intrinsic periodicity given by a vn self map which becomes a selfequivalence after suitable localization for simplicity we describe our results in the pointed homotopy category hoo of connected cw complexes for spaces w y e hoo we call y w periodic or w local when the pointed mapping space map w y is contractible or equivalently when xt w y for t 0 as shown more generally in 3 corollary 7 2 10 or 13 there is a natural initial example x pwx of a map from x to a w periodic space pwx in hoo and we call this the w periodization or w localization of x our notation is derived from the classical example where w sn l and pwx is the n th postnikov section

localizing with respect to self maps of the circle we describe a general procedure to construct idempotent functors on the pointed homotopy category of connected cw complexes some of which extend localization of nilpotent spaces at a set of primes p we focus our attention on one such functor whose local objects are cw complexes x for which the pth power map on the loop space qx is a self homotopy equiv alence if p p we study its algebraic properties its behaviour on certain spaces and its relation with other functors such as bousfield s homology local ization bousfield kan completion and quillen s plus construction

a model for dynamic chance constraints in hydro power reservoir management in this paper a model for joint dynamic chance constraints is proposed and applied to an optimization problem in water reservoir management the model relies on discretization of the decision variables but keeps the probability distribution continuous our approach relies on calculating probabilities of rectangles which is particularly useful in the presence of independent random variables but works for a moderate number of stages equally well in case of correlated variables numerical results are provided for two and three stages

the probabilistic set covering problem in a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability we analyze the structure of the set of probabilistically efficient points of binary random vectors develop methods for their enumeration and propose specialized branch and bound algorithms for probabilistic set covering problems

homotopical localizations of spaces for a map f of spaces dror farjoun and the author have constructed an f localization functor where a space y is called f local when map f y is an equivalence this very general construction gives all known idempotent homotopy functors of spaces the main theorem of this paper shows that f localization functors always preserve fiber sequences of connected h spaces up to small error terms for instance the localization with respect to the n th morava k theory preserves such fiber sequences up to error terms with at most three nontrivial homotopy groups this implies for example that a k 1 homology equivalence of h spaces must induce an isomorphism of v 1 periodic homotopy groups results are also obtained on the a nullification or a periodization functors which are just the f localization functors for the maps f from spaces a to points two spaces are said to have the same nullity when they give the same nullification functors and it is shown that arbitrary sets of nullity classes have both least upper bounds and greatest lower bounds the a nullifications of nilpotent postnikov spaces are completely determined

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

from cvar to uncertainty set implications in joint chance constrained optimization we review and develop different tractable approximations to individual chance constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional value at risk cvar measure we extend the idea to joint chance constrained problems and provide a new formulation that improves upon the standard approach our approach builds on a classical worst case bound for order statistics problems and is applicable even if the constraints are correlated we provide an application of the model on a network resource allocation problem with uncertain demand

on the telescopic homotopy theory of spaces in telescopic homotopy theory a space or spectrum x is approximated by a tower of localizations lnx n 0 taking account of vn periodic homotopy groups for progressively higher n for each n 1 we construct a telescopic kuhn functor n carrying a space to a spectrum with the same vn periodic homotopy groups and we construct a new functor n left adjoint to n using these functors we show that the nth stable monocular homotopy category comprising the nth fibers of stable telescopic towers embeds as a retract of the nth unstable monocular homotopy category in two ways one giving infinite loop spaces and the other giving infinite ln suspension spaces we deduce that ravenel s stable telescope conjectures are equivalent to unstable telescope conjectures in particular we show that the failure of ravenel s nth stable telescope conjecture implies the existence of highly connected infinite loop spaces with trivial johnson wilson e n homology but nontrivial vn periodic homotopy groups showing a fundamental difference between the unstable chromatic and telescopic theories as a stable chromatic application we show that each spectrum is k n equivalent to a suspension spectrum as an unstable chromatic application we determine the e n localizations and k n localizations of infinite loop spaces in terms of e n localizations of spectra under suitable conditions we also determine the e n localizations and k n localizations of arbitrary postnikov h spaces

sequential convex approximations to joint chance constrained programs a monte carlo approach when there is parameter uncertainty in the constraints of a convex optimization problem it is natural to formulate the problem as a joint chance constrained program jccp which requires that all constraints be satisfied simultaneously with a given large probability in this paper we propose to solve the jccp by a sequence of convex approximations we show that the solutions of the sequence of approximations converge to a karush kuhn tucker kkt point of the jccp under a certain asymptotic regime furthermore we propose to use a gradient based monte carlo method to solve the sequence of convex approximations

nullification and cellularization of classifying spaces of finite groups in this note we discuss the effect of the bz p nullification p bz p and the bz p cellularization cw bz p over classifying spaces of finite groups and we relate them with the corresponding functors with respect to moore spaces that have been intensively studied in the last years we describe p bz p bg by means of a covering fibration and we classify all finite groups g for which bg is bz p cellular we also carefully study the analogous functors in the category of groups and their relationship with the fundamental groups of p bz p bg and cw bz p bg

mathematical programs with cardinality constraints reformulation by complementarity type conditions and a regularization method optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discrete optimization here we introduce a mixed integer formulation whose standard relaxation still has the same solutions in the sense of global minima as the underlying cardinality constrained problem the relation between the local minima is also discussed in detail since our reformulation is a minimization problem in continuous variables it allows us to apply ideas from that field to cardinality constrained problems here in particular we therefore also derive suitable stationarity conditions and suggest an appropriate regularization method for the solution of optimization problems with cardinality constraints this regularization method is shown to be globally convergent to a mordukhovich stationary point extensive numerical results are given to illustrate the behavior of this method

an integer programming approach for linear programs with probabilistic constraints linear programs with joint probabilistic constraints pclp are difficult to solve because the feasible region is not convex we consider a special case of pclp in which only the right hand side is random and this random vector has a finite distribution we give a mixed integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint we obtain two strengthened formulations as a byproduct of this analysis we obtain new results for the previously studied mixing set subject to an additional knapsack inequality we present computational results which indicate that by using our strengthened formulations instances that are considerably larger than have been considered before can be solved to optimality

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

a sequential algorithm for solving nonlinear optimization problems with chance constraints an algorithm is presented for solving nonlinear optimization problems with chance constraints i e those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability in particular the algorithm is designed to solve cardinality constrained nonlinear optimization problems that arise in sample average approximations of chance constrained problems as well as in other applications in which it is only desired to enforce a minimum number of constraints the algorithm employs a novel exact penalty function which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented and convergence of the proposed algorithm to stationarity with respect to the penalty function is proved the effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear ca

convex approximations of chance constrained programs we consider a chance constrained problem where one seeks to minimize a convex objective over solutions satisfying with a given close to one probability a system of randomly perturbed convex constraints this problem may happen to be computationally intractable our goal is to build its computationally tractable approximation i e an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem we construct a general class of such convex conservative approximations of the corresponding chance constrained problem moreover under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables we build a large deviation type approximation referred to as bernstein approximation of the chance constrained problem this approximation is convex and efficiently solvable we propose a simulation based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the bernstein and well known scenario approximation approaches finally we extend our construction to the case of ambiguous chance constrained problems where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly while the chance constraint should be satisfied for every distribution given by this set

a sample approximation approach for optimization with probabilistic constraints we study approximations of optimization problems with probabilistic constraints in which the original distribution of the underlying random vector is replaced with an empirical distribution obtained from a random sample we show that such a sample approximation problem with a risk level larger than the required risk level will yield a lower bound to the true optimal value with probability approaching one exponentially fast this leads to an a priori estimate of the sample size required to have high confidence that the sample approximation will yield a lower bound we then provide conditions under which solving a sample approximation problem with a risk level smaller than the required risk level will yield feasible solutions to the original problem with high probability once again we obtain a priori estimates on the sample size required to obtain high confidence that the sample approximation problem will yield a feasible solution to the original problem finally we present numerical illustrations of how these results can be used to obtain feasible solutions and optimality bounds for optimization problems with probabilistic constraints

systematic lossy source channel coding the fundamental limits of systematic communication are analyzed in systematic transmission the decoder has access to a noisy version of the uncoded raw data analog or digital the coded version of the data is used to reduce the average reproduced distortion d below that provided by the uncoded systematic link and or increase the rate of information transmission unlike the case of arbitrarily reliable error correction d spl rarr 0 for symmetric sources channels where systematic codes are known to do as well as nonsystematic codes we demonstrate that the systematic structure may degrade the performance for nonvanishing d we characterize the achievable average distortion and we find necessary and sufficient conditions under which systematic communication does not incur loss of optimality the wyner ziv 1976 rate distortion theorem plays a fundamental role in our setting the general result is applied to several scenarios for a gaussian bandlimited source and a gaussian channel the invariance of the bandwidth signal to noise ratio snr in decibels product is established and the optimality of systematic transmission is demonstrated bernoulli sources transmitted over binary symmetric channels and over certain gaussian channels are also analyzed it is shown that if nonnegligible bit error rate is tolerated systematic encoding is strictly suboptimal

on mixing sets arising in chance constrained programming the mixing set with a knapsack constraint arises in deterministic equivalent of chance constrained programming problems with finite discrete distributions we first consider the case that the chance constrained program has equal probabilities for each scenario we study the resulting mixing set with a cardinality constraint and propose facet defining inequalities that subsume known explicit inequalities for this set we extend these inequalities to obtain valid inequalities for the mixing set with a knapsack constraint in addition we propose a compact extended reformulation with polynomial number of variables and constraints that characterizes a linear programming equivalent of a single chance constraint with equal scenario probabilities we introduce a blending procedure to find valid inequalities for intersection of multiple mixing sets we propose a polynomial size extended formulation for the intersection of multiple mixing sets with a knapsack constraint that is stronger than the original mixing formulation we also give a compact extended linear program for the intersection of multiple mixing sets and a cardinality constraint for a special case we illustrate the effectiveness of the proposed inequalities in our computational experiments with probabilistic lot sizing problems

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

on the convergence of successive linear quadratic programming algorithms the global convergence properties of a class of penalty methods for nonlinear programming are analyzed these methods include successive linear programming approaches and more specifically the successive linear quadratic programming approach presented by byrd et al math program 100 2004 pp 27 48 every iteration requires the solution of two trust region subproblems involving piecewise linear and quadratic models respectively it is shown that for a fixed penalty parameter the sequence of iterates approaches stationarity of the penalty function a procedure for dynamically adjusting the penalty parameter is described and global convergence results for it are established

central extensions and generalized plus constructions we describe the effect of homological plus constructions on the homotopy groups of eilenberg maclane spaces in terms of universal central extensions

conditions for convergence of trust region algorithms for nonsmooth optimization this paper discusses some properties of trust region algorithms for nonsmooth optimization the problem is expressed as the minimization of a functionh f x whereh is convex andf is a continuously differentiable mapping from to bounds for the second order derivative approximation matrices are discussed it is shown that powel s 7 8 results hold for nonsmooth optimization

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

implications of large cardinal principles in homotopical localization the existence of arbitrary cohomological localizations on the homotopy category of spaces has remained unproved since bousfield settled the same problem for homology theories in the decade of 1970 this is related with another open question namely whether or not every homotopy idempotent functor on spaces is an f localization for some map f we prove that both questions have an affirmative answer assuming the validity of a suitable large cardinal axiom from set theory vop nka s principle we also show that it is impossible to prove that all homotopy idempotent functors are f localizations using the ordinary zfc axioms of set theory zermelo fraenkel axioms with the axiom of choice since a counterexample can be displayed under the assumption that all cardinals are nonmeasurable which is consistent with zfc

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

robust optimization methodology and applications robust optimization ro is a modeling methodology combined with computational tools to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set the paper surveys the main results of ro as applied to uncertain linear conic quadratic and semidefinite programming for these cases computationally tractable robust counterparts of uncertain problems are explicitly obtained or good approximations of these counterparts are proposed making ro a useful tool for real world applications we discuss some of these applications specifically antenna design truss topology design and stability analysis synthesis in uncertain dynamic systems we also describe a case study of 90 lps from the netlib collection the study reveals that the feasibility properties of the usual solutions of real world lps can be severely affected by small perturbations of the data and that the ro methodology can be successfully used to overcome this phenomenon

chance constrained problems and rare events an importance sampling approach we study chance constrained problems in which the constraints involve the probability of a rare event we discuss the relevance of such problems and show that the existing sampling based algorithms cannot be applied directly in this case since they require an impractical number of samples to yield reasonable solutions we argue that importance sampling is techniques combined with a sample average approximation saa approach can be effectively used in such situations provided that variance can be reduced uniformly with respect to the decision variables we give sufficient conditions to obtain such uniform variance reduction and prove asymptotic convergence of the combined saa is approach as it often happens with is techniques the practical performance of the proposed approach relies on exploiting the structure of the problem under study in our case we work with a telecommunications problem with bernoulli input distributions and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the is distributions although some of the results are specific to this problem we are able to draw general insights that can be useful for other classes of problems we present numerical results to illustrate our findings

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

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

localization of andre quillen goodwillie towers and the periodic homology of infinite loopspaces abstract let k n be the n th morava k theory at a prime p and let t n be the telescope of a v n self map of a finite complex of type n in this paper we study the k n homology of x the 0th space of a spectrum x and many related matters we give a sampling of our results let p x be the free commutative s algebra generated by x it is weakly equivalent to the wedge of all the extended powers of x we construct a natural map s n x l t n p x l t n x of commutative algebras over the localized sphere spectrum l t n s the induced map of commutative cocommutative k n hopf algebras s n x k n p x k n x satisfies the following properties it is always monic it is an isomorphism if x is n connected n 1 x is torsion and t i x 0 for 1 i n 1 it is an isomorphism only if k i x 0 for 1 i n 1 it is universal the domain of s n x preserves k n isomorphisms and if f is any functor preserving k n isomorphisms then any natural transformation f x k n x factors uniquely through s n x the construction of our natural transformation uses the telescopic functors constructed and studied previously by bousfield and the author and thus depends heavily on the nilpotence theorem of devanitz hopkins and smith our proof that s n x is always monic uses topological andre quillen homology and goodwillie calculus in nonconnective settings

joint source channel coding of a gaussian mixture source over the gaussian broadcast channel suppose that we want to send a description of a single source to two listeners through a gaussian broadcast channel where the channel is used once per source sample the problem of joint source channel coding is to design a communication system to minimize the distortion d sub 1 at receiver 1 and at the same time minimize the distortion d sub 2 at receiver 2 if the source is gaussian the optimal solution is well known and it is achieved by an uncoded analog scheme we consider a gaussian mixture source we derive inner and outer bounds for the distortion region of all d sub 1 d sub 2 pairs that are simultaneously achievable the outer bound is based on the entropy power inequality while the inner bound is attained by a digital over analog encoding scheme which we present we also show that if the modes of the gaussian mixture are highly separated our bounds are tight and hence our scheme attains the entire distortion region this optimal region exceeds the region attained by separating source and channel coding although it does not contain the ideal point d sub 1 d sub 2 r sup 1 c sub 1 r sup 1 c sub 2

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

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

on stable maps from eilenberg maclane spaces to classifying spaces 0 introduction in recent years there has been a general interest in the problem of understanding the homotopy type of function spaces map x y where x is an infinite complex the special case where x is the classifying space of a finite group gives the celebrated segal s conjecture 4 when y lim fqnn qs and sullivan s conjecture 10 when y is a finite complex one would like to know whether the affirmative solution to these conjectures can also be applied to the study of map x y for other infinite complexes x the philosophy behind this approach to the problem has already manifested itself in 5 6 7 and 8 among others to give interesting results in this note we will utilize the solution to segal s conjecture to compute stable maps from eilenberg maclane spaces to classifying spaces as an application we will also describe the homotopy type of map x y at a prime p where x k 1t n wt finite n 2 and y q g g 0 u sp the original motivation behind this paper was due to anderson hodgkin 1 there they proved vanishing results on the topological k theory of higher eilenberg maclane spaces using atyiah s theorem on the k theory of the classifying spaces of compact lie groups we shall prove that the same result holds for stable cohomotopy groups the author is especially grateful to professor gunnar carlsson for pointing out 1 and how segal s conjecture comes into play

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