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

kazhdan projections random walks and ergodic theorems in this paper we investigate generalizations of kazhdan s property t to the setting of uniformly convex banach spaces we explain the interplay between the existence of spectral gaps and that of kazhdan projections our methods employ markov operators associated to a random walk on the group for which we provide new norm estimates and convergence results this construction exhibits useful properties and flexibility and allows to reclassify the existence of kazhdan projections from a c algebraic phenomenon to a natural object associated to random walks on groups we give a number of applications of these results in particular we address several open questions we give a direct comparison of properties te and fe with lafforgue s reinforced banach property t we obtain shrinking target theorems for orbits of kazhdan groups and apply them to a question of kleinbock and margulis finally we construct non compact ghost projections for warped cones answering a question of willett and yu in this last case we conjecture that such warped cones provide new counterexamples to the coarse baum connes conjecture

an information theoretic framework for deriving canonical decision feedback receivers in gaussian channels a framework is presented that allows a number of known results relating feedback equalization linear prediction and mutual information to be easily understood a lossless additive decomposition of mutual information in a general class of gaussian channels is introduced and shown to produce an information preserving canonical decision feedback receiver the approach is applied to intersymbol interference isi channels to derive the well known minimum mean square error mmse decision feedback equalizer dfe when applied to the synchronous code division multiple access cdma channel the result is the mmse or signal to interference ratio sir maximizing decision feedback detector which is shown to achieve the channel sum capacity at the vertices of the capacity region finally in the case of the asynchronous cdma channel we are able to give new connections between information theory decision feedback receivers and structured factorizations of multivariate spectra

exclusion and persistence in deterministic and stochastic chemostat models abstract we first introduce and analyze a variant of the deterministic single substrate chemostat model in this model microbe removal and growth rates depend on biomass concentration with removal terms increasing faster than growth terms using a comparison principle we show that persistence of all species is possible in this scenario then we turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation in particular we show that random effects may lead to extinction in scenarios where the deterministic model predicts persistence on the other hand we also establish some stochastic persistence results

operator norm localization property of metric spaces under finite decomposition complexity abstract the notions of operator norm localization property and finite decomposition complexity were recently introduced in metric geometry to study the coarse novikov conjecture and the stable borel conjecture in this paper we show that a metric space x has weak finite decomposition complexity with respect to the operator norm localization property if and only if x itself has the operator norm localization property it follows that any metric space with finite decomposition complexity has the operator norm localization property in particular we obtain an alternative way to prove a very recent result by e guentner r tessera and g yu that all countable linear groups have the operator norm localization property

achieving the gaussian rate distortion function by prediction the ldquowater fillingrdquo solution for the quadratic rate distortion function of a stationary gaussian source is given in terms of its power spectrum this formula naturally lends itself to a frequency domain ldquotest channelrdquo realization we provide an alternative time domain realization for the rate distortion function based on linear prediction the predictive test channel has some interesting implications including the optimality at all distortion levels of pre post filtered vector quantized differential pulse code modulation dpcm and a duality relationship with decision feedback equalization dfe for intersymbol interference isi channels

periodic solution for a non autonomous lotka volterra predator prey model with random perturbation abstract this paper studies a stochastic non autonomous lotka volterra predator prey model we prove that there exists at least one positive periodic solution under some simple and reasonable conditions in addition we obtain sufficient conditions for persistence in mean and extinction for the stochastic non autonomous system our method and results are new and the ideas could be used to study other types of non autonomous stochastic predator prey systems

joint wyner ziv dirty paper coding by modulo lattice modulation the combination of source coding with decoder side information the wyner ziv problem and channel coding with encoder side information the gel fand pinsker problem can be optimally solved using the separation principle in this work we show an alternative scheme for the quadratic gaussian case which merges source and channel coding this scheme achieves the optimal performance by applying a modulo lattice modulation to the analog source thus it saves the complexity of quantization and channel decoding and remains with the task of ldquoshapingrdquo only furthermore for high signal to noise ratio snr the scheme approaches the optimal performance using an snr independent encoder thus it proves for this special case the feasibility of universal joint source channel coding

higher index theory for certain expanders and gromov monster groups ii abstract in this paper the first of a series of two we continue the study of higher index theory for expanders we prove that if a sequence of graphs is an expander and the girth of the graphs tends to infinity then the coarse baum connes assembly map is injective but not surjective for the associated metric space x expanders with this girth property are a necessary ingredient in the construction of the so called gromov monster groups that coarsely contain expanders in their cayley graphs we use this connection to show that the baum connes assembly map with certain coefficients is injective but not surjective for these groups using the results of the second paper in this series we also show that the maximal baum connes assembly map with these coefficients is an isomorphism

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

lattices which are good for almost everything we define an ensemble of lattices and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings sphere coverings additive white gaussian noise awgn channel codes and mean squared error mse quantization codes these lattices are generated by applying construction a to a random linear code over a prime field of growing size i e by lifting the code to spl ropf sup n

linecast line based distributed coding and transmission for broadcasting satellite images in this paper we propose a novel coding and transmission scheme called linecast for broadcasting satellite images to a large number of receivers the proposed linecast matches perfectly with the line scanning cameras that are widely adopted in orbit satellites to capture high resolution images on the sender side each captured line is immediately compressed by a transform domain scalar modulo quantization without syndrome coding the transmission power is directly allocated to quantized coefficients by scaling the coefficients according to their distributions finally the scaled coefficients are transmitted over a dense constellation this line based distributed scheme features low delay low memory cost and low complexity on the receiver side our proposed line based prediction is used to generate side information from previously decoded lines which fully utilizes the correlation among lines the quantized coefficients are decoded by the linear least square estimator from the received data the image line is then reconstructed by the scalar modulo dequantization using the generated side information since there is neither syndrome coding nor channel coding the proposed linecast can make a large number of receivers reach the qualities matching their channel conditions our theoretical analysis shows that the proposed linecast can achieve shannon s optimum performance by using a high dimensional modulo lattice quantization experiments on satellite images demonstrate that it achieves up to 1 9 db gain over the state of the art 2d broadcasting scheme and a gain of more than 5 db over jpeg 2000 with forward error correction

stability of a stochastic sir system abstract we propose a stochastic sir model with or without distributed time delay and we study the stability of disease free equilibrium the numerical simulation of the stochastic sir model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found

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

embeddings of uniform roe algebras in this paper we study embeddings of uniform roe algebras generally speaking given metric spaces x and y we are interested in which large scale geometric properties are stable under embedding of the uniform roe algebra of x into the uniform roe algebra of y

exactness of locally compact groups we give some new characterizations of exactness for locally compact second countable groups in particular we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact hausdorff space this answers an open question by anantharaman delaroche

on invariant measures and the asymptotic behavior of a stochastic delayed sirs epidemic model abstract in this paper we consider a stochastic epidemic model with time delay and general incidence rate we first prove the existence and uniqueness of the global positive solution by using the krylov bogoliubov method we obtain the existence of invariant measures furthermore we study a special case where the incidence rate is bilinear with distributed time delay when the basic reproduction number r 0 1 the analysis of the asymptotic behavior around the disease free equilibrium e 0 is provided while when r 0 1 we prove that the invariant measure is unique and ergodic the numerical simulations also validate our analytical results

on the c algebra of matrix finite bounded operators abstract let h be a separable hilbert space with a fixed orthonormal basis let b k h denote the set of operators whose matrices have no more than k non zero entries in each line and in each column the closure of the union over k n of b k h is a c algebra we study some properties of this c algebra we show that this c algebra is not an a w algebra its group of invertibles is contractible and it gives rise to an example of a c algebra with a dense subalgebra and a maximal closed ideal with zero intersection

analysis of the deterministic and stochastic sirs epidemic models with nonlinear incidence abstract in this paper the deterministic and stochastic sirs epidemic models with nonlinear incidence are introduced and investigated for deterministic system the basic reproductive number r 0 is obtained furthermore if r 0 1 then the disease free equilibrium is globally asymptotically stable and if r 0 1 then there is a unique endemic equilibrium which is globally asymptotically stable for stochastic system to begin with we verify that there is a unique global positive solution starting from the positive initial value then when r 0 1 we prove that stochastic perturbations may lead the disease to extinction in scenarios where the deterministic system is persistent when r 0 1 a result on fluctuation of the solution around the disease free equilibrium of deterministic model is obtained under appropriate conditions at last if the intensity of the white noise is sufficiently small and r 0 1 then there is a unique stationary distribution to stochastic system

ghostbusting and property a abstract we show that the roe algebra of a bounded geometry metric space contains non compact ghosts if and only if the space does not have property a

qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity abstract in this paper we propose a stochastic delayed epidemic model with specific functional response the time delay represents temporary immunity period i e time from recovery to becoming susceptible again we first show that the proposed model is mathematically and biologically well posed moreover the extinction of the disease and the persistence in the mean are established in the terms of a threshold value r 0 s which is smaller than the basic reproduction number r 0 of the corresponding deterministic system

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

analog matching of colored sources to colored channels analog uncoded transmission provides a simple and robust scheme for communicating a gaussian source over a gaussian channel under the mean squared error mse distortion measure unfortunately its performance is usually inferior to the all digital separation based source channel coding solution which requires exact knowledge of the channel at the encoder the loss comes from the fact that except for very special cases e g white source and channel of matching bandwidth bw it is impossible to achieve perfect matching of source to channel and channel to source by linear means we show that by combining prediction and modulo lattice operations it is possible to match any colored gaussian source to any colored gaussian noise channel of possibly different bw hence achieve shannon s optimum attainable performance r d c furthermore when the source and channel bws are equal but otherwise their spectra are arbitrary this scheme is asymptotically robust in the sense that for high signal to noise ratio snr a single encoder independent of the noise variance achieves the optimum performance the derivation is based upon a recent modulo lattice modulation scheme for transmitting a wyner ziv source over a dirty paper channel

asymptotic behavior of stochastic multi group epidemic models with distributed delays abstract in this paper we introduce stochasticity into multi group epidemic models with distributed delays and general kernel functions the stochasticity in the model is a standard technique in stochastic population modeling when the perturbations are small by using the method of stochastic lyapunov functions we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number r 0 if r 0 1 the solution of the stochastic system oscillates around the disease free equilibrium e 0 while if r 0 1 the solution of the stochastic model fluctuates around the endemic equilibrium e moreover we also establish sufficient conditions of these results

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

metric sparsification and operator norm localization abstract we study an operator norm localization property and its applications to the coarse novikov conjecture in operator k theory in particular we introduce a sufficient geometric condition called metric sparsification for the operator norm localization property this is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property we also show that a sequence of expanding graphs does not possess the operator norm localization property

operator norm localization property of relative hyperbolic group and graph of groups abstract in this article we study the spaces which have operator norm localization property we prove that a finitely generated group which is strongly hyperbolic with respect to a collection of finitely generated subgroups h 1 h n has operator norm localization property if and only if each h i i 1 2 n has operator norm localization property furthermore we prove the following result let be the fundamental group of a connected finite graph of groups with finitely generated vertex groups g p if g p has operator norm localization property for all vertices p then has operator norm localization property

fibred coarse embeddings a t menability and the coarse analogue of the novikov conjecture abstract the connection between the coarse geometry of metric spaces and analytic properties of topological groupoids is well known one of the main results of skandalis tu and yu is that a space admits a coarse embedding into hilbert space if and only if a certain associated topological groupoid is a t menable this groupoid characterisation then reduces the proof that the coarse baum connes conjecture holds for a coarsely embeddable space to known results for a t menable groupoids the property of admitting a fibred coarse embedding into hilbert space was introduced by chen wang and yu to provide a property that is sufficient for the maximal analogue to the coarse baum connes conjecture and in this paper we connect this property to the traditional coarse baum connes conjecture using a restriction of the coarse groupoid and homological algebra additionally we use this results to give a characterisation of the a t menability for residually finite discrete groups

joint unitary triangularization for mimo networks this paper considers communication networks where individual links can be described as those based on multiple input multiple output channels unlike orthogonal modulation methods such as the singular value decomposition we allow interference between subchannels which can be removed by the receivers via successive cancellation the degrees of freedom earned by this relaxation are used for obtaining a basis and corresponding decomposition which are simultaneously good for more than one link specifically we derive necessary and sufficient conditions for shaping the ratio vector of subchannel gains of two broadcast channel receivers we then apply this decomposition to two scenarios first in digital multicasting we present a practical capacity achieving scheme which uses only scalar codes and linear processing then we consider the joint source channel problem of transmitting a gaussian source over a two user multiple input multiple output channel where we show the existence of nontrivial cases where the optimal distortion pair which for high signal to noise ratios snrs equals the optimal point to point distortions of the individual users may be achieved by employing a hybrid digital analog scheme over the induced equivalent channel these scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network thus we coin the approach network modulation

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

a stochastic differential equation sis epidemic model incorporating ornstein uhlenbeck process abstract in this paper based on the results of gray et al 2011 we propose a new sde sis model incorporating mean reverting ornstein uhlenbeck process and prove that the stochastic basic reproduction number r 0 s can be used to identify the stochastic extinction and persistence for the sde mode if r 0 s 1 under mild extra conditions the disease will be extinct a s while if r 0 s 1 the disease will persist a s epidemiologically we find that smaller speed of reversion or bigger intensity of volatility can suppress the disease outbreak thus in order to control the spread of the disease we must decrease the speed of reversion or increase the intensity of volatility

a metric approach to limit operators we extend the limit operator machinery of rabinovich roch and silbermann from z n to bounded geometry strongly discrete metric spaces we do not assume the presence of any group structure or action on our metric spaces using this machinery and recent ideas of lindner and seidel we show that if a metric space x has yu s property a then a band dominated operator on x is fredholm if and only if all of its limit operators are invertible we also show that this always fails for metric spaces without property a

optimal linear joint source channel coding with delay constraint the problem of joint source channel coding is considered for a stationary remote noisy gaussian source and a gaussian channel the encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint it is shown that under the mean square error distortion metric an optimal encoder decoder pair from the linear and time invariant lti class can be found by minimization of a convex functional and a spectral factorization the functional to be minimized is the sum of the well known cost in a corresponding wiener filter problem and a new term which is induced by the channel noise and whose coefficient is the inverse of the channel s signal to noise ratio this result is shown to also hold in the case of vector valued signals assuming parallel additive white gaussian noise channels it is also shown that optimal lti encoders and decoders generally require infinite memory which implies that approximations are necessary a numerical example is provided which compares the performance to the lower bound provided by rate distortion theory less

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

uniform embeddability of relatively hyperbolic groups let be a finitely generated group which is hyperbolic relative to a finite family h1 hn of subgroups we prove that is uniformly embeddable in a hilbert space if and only if each subgroup hi is uniformly embeddable in a hilbert space

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

a stochastic sirs epidemic model with infectious force under intervention strategies abstract in this paper we extend a classical sirs epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation sde one through introducing random fluctuations the value of our study lies in two aspects mathematically by using the markov semigroups theory we prove that the reproduction number r 0 s can be used to govern the stochastic dynamics of sde model if r 0 s 1 under mild extra conditions the sde system has a disease free absorbing set which means the extinction of disease with probability one if r 0 s 1 under mild extra conditions it has an endemic stationary distribution which leads to the stochastical persistence of the disease epidemiologically we find that random fluctuations can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

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

a stochastic sirs epidemic model with nonlinear incidence rate a stochastic sirs model with ratio dependent incidence rate is developed the global dynamics of the deterministic model is shown the stochastic dynamics of the sde model is given the existence of a unique stationary distribution of the sde model is displayed in this paper we investigate the global dynamics of a general sirs epidemic model with a ratio dependent incidence rate and its corresponding stochastic differential equation version for the deterministic model we show that the basic reproduction number r0 determines whether there is an endemic outbreak or not if r0 1 the disease persists for the stochastic model we show that its related reproduction number r0s can determine whether there is a unique disease free stationary distribution or a unique endemic stationary distribution in addition we provide analytic results regarding the stochastic boundedness and permanence extinction one of the most interesting findings is that random fluctuations introduced in our stochastic model can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

the ergodicity and extinction of stochastically perturbed sir and seir epidemic models with saturated incidence abstract in this paper we include stochastic perturbations into sir and seir epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number r 0 the long time behavior of the two stochastic systems is studied mainly we utilize stochastic lyapunov functions to show under some conditions the solution has the ergodic property as r 0 1 while exponential stability as r 0 1 at last we make simulations to conform our analytical results

stability of sirs system with random perturbations epidemiological models with bilinear incidence rate si usually have an asymptotically stable trivial equilibrium corresponding to the disease free state or an asymptotically stable non trivial equilibrium i e interior equilibrium corresponding to the endemic state in this paper we consider an epidemiological model which is an sirs model with or without distributed time delay influenced by random perturbations we present the stability conditions of the disease free equilibrium of the associated stochastic sirs system

curves on a sphere shift map dynamics and error control for continuous alphabet sources we consider two codes based on dynamical systems for transmitting information from a continuous alphabet discrete time source over a gaussian channel the first code a homogeneous spherical code is generated by the linear dynamical system s spl dot as with a a square skew symmetric matrix the second code is generated by the shift map s sub n b sub n s sub n 1 mod 1 the performance of each of these codes is determined by the geometry of its locus or signal set specifically its arc length and minimum distance suitably defined we show that the performance analyses for these systems are closely related and derive exact expressions and bounds for relevant geometric parameters we also observe that the lattice spl zopf sup n underlies both modulation systems and we develop a fast decoding algorithm that relies on this observation analytic results show that for fixed bandwidth expansion good scaling behavior of the mean squared error is obtained relative to the channel signal to noise ratio snr particularly interesting is the resulting observation that sampled exponentially chirped modulation codes are good bandwidth expansion codes

stationary distribution and extinction of a stochastic sirs epidemic model with standard incidence abstract in this paper we consider a stochastic sirs epidemic model with standard incidence by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of ergodic stationary distribution of the model moreover we also establish sufficient conditions for extinction of the disease

a generalization of expander graphs and local reflexivity of uniform roe algebras abstract we introduce a generalization of expander graphs which is called a weak expander sequence it is proved that a uniform roe algebra of a weak expander sequence is not locally reflexive it follows that uniform roe algebras of expander graphs are not exact we introduce the notion of a generalized box space to discuss box spaces and expander sequences in a unified framework key tools for the proof are amenable traces and measured groupoids associated with generalized box spaces