multiterminal source coding with high resolution we consider separate encoding and joint decoding of correlated continuous information sources subject to a difference distortion measure we first derive a multiterminal extension of the shannon lower bound for the rate region then we show that this shannon outer bound is asymptotically tight for small distortions these results imply that the loss in the sum of the coding rates due to the separation of the encoders vanishes in the limit of high resolution furthermore lattice quantizers followed by slepian wolf lossless encoding are asymptotically optimal we also investigate the high resolution rate region in the remote coding case where the encoders observe only noisy versions of the sources for the quadratic gaussian case we establish a separation result to the effect that multiterminal coding aimed at reconstructing the noisy sources subject to the rate constraints followed by estimation of the remote sources from these reconstructions is optimal under certain regularity conditions on the structure of the coding scheme

indirect and direct gaussian distributed source coding problems we consider the distributed source coding system of l correlated gaussian sources y l l 1 2 ldots l which are noisy observations of correlated gaussian remote sources x k k 1 2 ldots k we assume that y l t y 1 y 2 ldots y l is an observation of the source vector x k t x 1 x 2 ldots x k having the form y l ax k n l where a is a l times k matrix and n l t n 1 n 2 ldots n l is a vector of l independent gaussian random variables also independent of x k in this system l correlated gaussian observations are separately compressed by l encoders and sent to the information processing center we study the remote source coding problem where the decoder at the center attempts to reconstruct the remote source x k we consider three distortion criteria based on the covariance matrix of the estimation error on x k for each of those three criteria we derive explicit inner and outer bounds of the rate distortion region next in the case of k l and a i l we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation y l x l n l to investigate this problem we shall establish a result that provides a strong connection between the remote source coding problem and multiterminal source coding problem using this result we derive several new partial solutions to the multiterminal source coding problem

robustness of a network formed of spatially embedded networks we present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks we show results for a treelike and a random regular network of networks each with i unconstrained dependency links and ii dependency links restricted to a maximum euclidean length r analytic results are given for each network of networks with spatially unconstrained dependency links and compared to simulations for the case of two fully interdependent spatially embedded networks it was found li et al phys rev lett 108 228702 2012 that the system undergoes a first order phase transition only for r r c 8 we find here that for treelike networks of networks composed of n networks r c significantly decreases as n increases and rapidly n 11 reaches its limiting value of 1 for cases where the dependencies form loops such as in random regular networks we show analytically and confirm through simulations that there is a certain fraction of dependent nodes q max above which the entire network structure collapses even if a single node is removed the value of q max decreases quickly with m the degree of the random regular network of networks our results show the extreme sensitivity of coupled spatial networks and emphasize the susceptibility of these networks to sudden collapse the theory proposed here requires only numerical knowledge about the percolation behavior of a single network and therefore can be used to find the robustness of any network of networks where the profile of percolation of a singe network is known numerically

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

fractional maximal operator in orlicz spaces abstract this work studies the fractional maximal operator acting between orlicz spaces the necessary and sufficient conditions for the existence of optimal target and domain spaces are established and the explicit formulas for corresponding optimal young functions are presented also we characterize whether the operator is bounded between two given orlicz spaces

fine properties of functions with bounded deformation the paper is concerned with the fine properties of functions in the space of functions with bounded deformation we analyse the set of lebesgue points and the set where these functions have one sided approximate limits moreover following the analogy with we decompose the symmetric distributional derivative into an absolutely continuous part a jump part and a cantor part the main result of the paper is a structure theorem for functions showing that these parts of the derivative can be recovered from the corresponding ones of the one dimensional sections moreover we prove that functions are approximately differentiable in almost every point of their domain

on the sum rate of gaussian multiterminal source coding new proofs and results we show that the lower bound on the sum rate of the direct and indirect gaussian multiterminal source coding problems can be derived in a unified manner by exploiting the semidefinite partial order of the distortion covariance matrices associated with the minimum mean squared error mmse estimation and the so called reduced optimal linear estimation through which an intimate connection between the lower bound and the berger tung upper bound is revealed we give a new proof of the minimum sum rate of the indirect gaussian multiterminal source coding problem i e the gaussian ceo problem for the direct gaussian multiterminal source coding problem we derive a general lower bound on the sum rate and establish a set of sufficient conditions under which the lower bound coincides with the berger tung upper bound we show that the sufficient conditions are satisfied for a class of sources and distortion constraints in particular they hold for arbitrary positive definite source covariance matrices in the high resolution regime in contrast with the existing proofs the new method does not rely on shannon s entropy power inequality

research on the connection radius of dependency links in interdependent spatial networks against cascading failures abstract most of previous research on complex networks always concentrates on topology ignoring the coordinates of components however the spatial information of components may be a key factor influencing the invulnerability of actual networks for interdependent infrastructures considering space constraints dependency links may be established locally where only nodes within certain connection radius r c o n n e c t can be connected as dependent node pairs therefore based on the topology based cascading failure model the invulnerability of interdependent scale free networks is studied by introducing five coupling patterns in this paper including global and local random couplings gr and lr global and local degree degree inter similarity couplings gd and ld and nearest neighbor coupling nn under topological attacks the inter similarity couplings gd and ld have better performance and as r c o n n e c t increases the effect of ld will gradually approach to gd in order to ensure a good invulnerability and low construction cost a novel hybrid coupling pattern of nn and ld is proposed with numerical simulations we find that selecting nodes with large degree to establish ld coupling has significant effect and there is an optimal selection fraction under localized attacks the local couplings perform better and ld is better for small r c o n n e c t while nn is better for large r c o n n e c t in addition we also study a simplified localized attacking strategy analytically based on percolation theory which is proved to be consistent with the numerical results for ld coupling the effect will be influenced by r c o n n e c t and there are minimum and maximum invulnerability values for topological and localized attacks respectively these findings can help to understand the characteristics of spatially embedded interdependent infrastructures

solutions of the divergence operator on john domains if rn is a bounded domain the existence of solutions u w01 p of divu f for f lp with vanishing mean value and 1 p is a basic result in the analysis of the stokes equations it is known that the result holds when is a lipschitz domain and that it is not valid for domains with external cusps in this paper we prove that the result holds for john domains our proof is constructive the solution u is given by an explicit integral operator acting on f to prove that u w01 p we make use of the calderon zygmund singular integral operator theory and the hardy littlewood maximal function for domains satisfying the separation property introduced in s buckley p koskela sobolev poincare implies john math res lett 2 5 1995 577 593 and 1 p n we also prove a converse result thus characterizing in this case the domains for which a continuous right inverse of the divergence exists in particular our result applies to simply connected planar domains because they satisfy the separation property

vector gaussian two terminal source coding we derive a lower bound on each supporting line of the rate region of the vector gaussian two terminal ceo problem which is a special case of the indirect vector gaussian two terminal source coding problem the key technical ingredient is a new extremal inequality it is shown that the lower bound coincides with the berger tung upper bound in the high resolution regime similar results are derived for the direct vector gaussian two terminal source coding problem

on the sum rate loss of quadratic gaussian multiterminal source coding this work studies the sum rate loss of quadratic gaussian multiterminal source coding i e the difference between the minimum sum rates of distributed encoding and joint encoding both with joint decoding of correlated gaussian sources subject to mse distortion constraints on individual sources it is shown that under the nondegraded assumption i e all target distortions are simultaneously achievable by a gaussian berger tung scheme the supremum of the sum rate loss of distributed encoding over joint encoding of l jointly gaussian sources increases almost linearly in the number of sources l with an asymptotic slope of 0 1083 bit per sample per source as l goes to infinity this result is obtained even though we currently do not have the full knowledge of the minimum sum rate for the distributed encoding case the main idea is to upper bound the minimum sum rate of multiterminal source coding by that achieved by parallel gaussian test channels while lower bounding the minimum sum rate of joint encoding by a reverse water filling solution to a relaxed joint encoding problem of the same set of gaussian sources with a sum distortion constraint that equals the sum of the individual target distortions we show that under the nondegraded assumption the supremum difference between the upper bound for distributed encoding and the lower bound for joint encoding is achieved in the bi eigen equal variance with equal distortion case in which both bounds are known to be tight

sobolev inequalities for the symmetric gradient in arbitrary domains abstract a form of sobolev inequalities for the symmetric gradient of vector valued functions is proposed which allows for arbitrary ground domains in r n in the relevant inequalities boundary regularity of domains is replaced with information on boundary traces of trial functions the inequalities so obtained exhibit the same exponents as in classical inequalities for the full gradient of sobolev functions in regular domains furthermore they involve constants independent of the geometry of the domain and hence yield novel results yet for smooth domains our approach relies upon a pointwise estimate for the functions in question via a riesz potential of their symmetric gradient and an unconventional potential depending on their boundary trace

interdependent networks with identical degrees of mutually dependent nodes we study a problem of failure of two interdependent networks in the case of identical degrees of mutually dependent nodes we assume that both networks a and b have the same number of nodes n connected by the bidirectional dependency links establishing a one to one correspondence between the nodes of the two networks in a such a way that the mutually dependent nodes have the same number of connectivity links i e their degrees coincide this implies that both networks have the same degree distribution p k we call such networks correspondently coupled networks ccns we assume that the nodes in each network are randomly connected we define the mutually connected clusters and the mutual giant component as in earlier works on randomly coupled interdependent networks and assume that only the nodes that belong to the mutual giant component remain functional we assume that initially a 1 p fraction of nodes are randomly removed because of an attack or failure and find analytically for an arbitrary p k the fraction of nodes p that belong to the mutual giant component we find that the system undergoes a percolation transition at a certain fraction p p c which is always smaller than p c for randomly coupled networks with the same p k we also find that the system undergoes a first order transition at p c 0 if p k has a finite second moment for the case of scale free networks with 2 0 finally we find that the robustness of ccn increases with the broadness of their degree distribution

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

bounds on the extreme eigenvalues of positive definite toeplitz matrices easily computable bounds on the extreme eigenvalues of positive semidefinite psd toeplitz matrices are presented the bounds are especially suitable for matrices of relatively small dimension the bounds are derived for the wider class of psd hermitian matrices and interpreted via the levinson durbin algorithm for toeplitz matrices as a by product of this derivation an order recursive algorithm for the eigenvector eigenvalue decomposition is obtained and certain properties of the eigenvalues distribution are revealed

a new approach to counterexamples to l 1 estimates korn s inequality geometric rigidity and regularity for gradients of separately convex functions the derivation of counterexamples to l1 estimates can be reduced to a geometric decomposition procedure along rank one lines in matrix space we illustrate this concept in two concrete applications firstly we recover a celebrated and rather complex counterexample by ornstein proving the failure of korn s inequality and of the corresponding geometrically nonlinear rigidity result in l1 secondly we construct a function f 2 which is separately convex but whose gradient is not in bvloc in the sense that the mixed derivative 2f x1 x2 is not a bounded measure

negative orlicz sobolev norms and strongly nonlinear systems in fluid mechanics abstract we prove a version of the negative norm theorem in orlicz sobolev spaces a study of boundedness properties of the bogovski operator between orlicz spaces is a crucial step of independent interest in our approach applications to the problem of pressure reconstruction for non newtonian fluids governed by constitutive laws which are not necessarily of power type are presented a key inequality for a numerical analysis of the underlying elliptic system is also derived

a new sufficient condition for sum rate tightness in quadratic gaussian multiterminal source coding this paper considers the quadratic gaussian multiterminal mt source coding problem and provides a new sufficient condition for the berger tung bt sum rate bound to be tight the converse proof utilizes a set of virtual remote sources given which the observed sources are block independent with a maximum block size of 2 the given mt source coding problem is then related to a set of two terminal problems with matrix distortion constraints for which a new lower bound on the sum rate is given by formulating a convex optimization problem over all distortion matrices a sufficient condition is derived for the optimal bt scheme to satisfy the subgradient based karush kuhn tucker condition the subset of the quadratic gaussian mt problem satisfying our new sufficient condition subsumes all previously known tight cases and our proof technique opens a new direction for more general partial solutions

distributed source coding of correlated gaussian remote sources we consider the distributed source coding system for l correlated memoryless gaussian remote sources specified with l correlated gaussian random variables xi i 1 2 l we deal with the case where each of l distributed encoders cannot directly observe the source xi but its noisy version yi xi ni here ni i 1 2 l are independent additive l gaussian noises also independent of xi i 1 2 l on this coding system the determination problem of the rate distortion region remains open in general in this paper we derive explicit outer and inner bounds of the rate distortion region we further find an explicit sufficient condition for those two bounds to match we also study the sum rate part of the rate distortion region when the correlation has some symmetrical property we derive an explicit upper bound of the sum rate part from the inner bounds of the rate distortion region on a lower bound we derive a new explicit bound by making full use of the symmetrical property of the correlation we further derive an explicit necessary and sufficient condition for the lower bound to coincide with the upper bound

korn type inequalities in orlicz spaces abstract we exhibit balance conditions between a young function a and a young function b for a korn type inequality to hold between the l b norm of the gradient of vector valued functions and the l a norm of its symmetric part in particular we extend a standard form of the korn inequality in l p with 1 p and an orlicz version involving a young function a satisfying both the 2 and the 2 condition

multiterminal source encoding with one distortion criterion the authors unify earlier investigations concerning the encoding of two correlated sources x sub k y sub k by means of separate encoders decoding is done by a single decoder which receives the outputs from both encoders the reconstruction of x sub k is required to be perfect in the usual shannon sense the authors determine the admissible rate region r d where d is the distortion of the reconstruction of y sub k the binary hamming case is investigated explicitly

lattices for distributed source coding jointly gaussian sources and reconstruction of a linear function consider a pair of correlated gaussian sources x 1 x 2 two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder the decoder is interested in reconstructing a linear combination of x 1 and x 2 to within a mean square distortion of d we obtain an inner bound to the optimal rate distortion region for this problem a portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components x 1 and x 2 first this results in a better rate region for certain parameter values our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory we then consider the case of linear reconstruction of k sources and provide an inner bound to the optimal rate distortion region some parts of the inner bound are achieved using the following coding structure lattice vector quantization followed by ldquocorrelatedrdquo lattice structured binning

new integral estimates for deformations in terms of their nonlinear strains if u is a bi lipschitzian deformation of a bounded lipschitz domain in ln n 2 we show that the lp norm p 1 p n of a certain nonlinear strain function e u associated with u dominates the distance in lq q np n p if p n from u to a suitably chosen rigid motion of n this work extends that of f john who proved corresponding estimates for p 1 under the hypothesis that u has uniformly small strain we also obtain a bound for the oscillation of du in l2 these estimates are apparently the first to apply with no a priori pointwise hypotheses upon the strain of u in 3 the integral int limits omega e u 2d 3 is dominated by typical hyperelastic energy functionals proposed in the literature for modeling the behavior of rubber thus the case n 3 p 2 gives the first general bound for the deformations of such materials in terms of the associated nonlinear elastic work

distributed compression of linear functions partial sum rate tightness and gap to optimal sum rate we consider the problem of distributed compression of the difference z y1 cy2 of two jointly gaussian sources y1 and y2 under an mse distortion constraint d on z the rate region for this problem is unknown if the correlation coefficient and the weighting factor c satisfy c 0 inspired by ahlswede and han s scheme for the problem of distributed compression of the modulo 2 sum of two binary sources we first propose a hybrid random structured coding scheme that is capable of saving the sum rate over both the random quantize and bin qb coding scheme and krithivasan and pradhan s structured lattice coding scheme the main idea is to use a random coding component in the first layer to adjust the source correlation so that the structured coding component in the second layer can be more efficient with the outputs from the first layer as decoder side information we then provide a new sum rate lower bound for the problem in hand by connecting it to the gaussian two terminal source coding problem with covariance matrix distortion constraint our lower bound not only improves existing bounds in many cases but also allows us to prove sum rate tightness of the qb scheme when c is either relatively small or large and d is larger than some threshold furthermore our lower bound enables us to show that our new hybrid scheme performs within two b s from the optimal sum rate for all values of c and d

the rate distortion function for the quadratic gaussian ceo problem a new multiterminal source coding problem called the ceo problem was presented and investigated by berger zhang and viswanathan recently viswanathan and berger have investigated an extension of the ceo problem to gaussian sources and call it the quadratic gaussian ceo problem they considered this problem from a statistical viewpoint deriving some interesting results in this paper we consider the quadratic gaussian ceo problem from a standpoint of multiterminal rate distortion theory we regard the ceo problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given this viewpoint leads us to a complete solution to the problem we determine the tradeoff between the total amount of rate and squared distortion deriving an explicit formula of the rate distortion function the derived function has the form of a sum of two nonnegative functions one is a classical rate distortion function for single gaussian source and the other is a new rate distortion function which dominates the performance of the system for a relatively small distortion it follows immediately from our result that the conjecture of viswanathan and berger on the asymptotic behavior of minimum squared distortion for large rates is true

on the generalized gaussian ceo problem this paper considers a distributed source coding dsc problem where l encoders observe noisy linear combinations of k correlated remote gaussian sources and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum distortion constraint this dsc problem is referred to as the generalized gaussian ceo problem since it can be viewed as a generalization of the quadratic gaussian ceo problem where the number of remote source k 1 first we provide a new outer region obtained using the entropy power inequality and an equivalent argument in the sense of having the same rate distortion region and berger tung inner region among a certain class of generalized gaussian ceo problems we then give two sufficient conditions for our new outer region to match the inner region achieved by berger tung schemes where the second matching condition implies that in the low distortion regime the berger tung inner rate region is always tight while in the high distortion regime the same region is tight if a certain condition holds the sum rate part of the outer region is also studied and shown to meet the berger tung sum rate upper bound under a certain condition which is obtained using the karush kuhn tucker conditions of the underlying convex semidefinite optimization problem and is in general weaker than the aforesaid two for rate region tightness

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

vector gaussian multiterminal source coding we derive an outer bound of the rate region of the vector gaussian l terminal ceo problem by establishing a lower bound on each supporting hyperplane of the rate region to this end we prove a new extremal inequality by exploiting the connection between differential entropy and fisher information as well as some fundamental estimation theoretic inequalities it is shown that the outer bound matches the berger tung inner bound in the high resolution regime we then derive a lower bound on each supporting hyperplane of the rate region of the direct vector gaussian l terminal source coding problem by coupling it with the ceo problem through a limiting argument the tightness of this lower bound in the high resolution regime and the weak dependence regime is also proved

a simple proof of the entropy power inequality this correspondence gives a simple proof of shannon s entropy power inequality epi using the relationship between mutual information and minimum mean square error mmse in gaussian channels

the rate loss in the wyner ziv problem the rate distortion function for source coding with side information at the decoder the wyner ziv problem is given in terms of an auxiliary random variable which forms a markov chain with the source and the side information this markov chain structure typical to the solution of multiterminal source coding problems corresponds to a loss in coding rate with respect to the conditional rate distortion function i e to the case where the encoder is fully informed we show that for difference or balanced distortion measures this loss is bounded by a universal constant which is the minimax capacity of a suitable additive noise channel furthermore in the worst case this loss is equal to the maximin redundancy over the rate distortion function of the additive noise test channel for example the loss in the wyner ziv problem is less than 0 5 bit sample in the squared error distortion case and it is less than 0 22 bit for a binary source with hamming distance these results have implications also in universal quantization with side information and in more general multiterminal source coding problems

solenoidal lipschitz truncation and applications in fluid mechanics abstract we extend the lipschitz truncation method to the setting of solenoidal functions in particular we approximate a solenoidal sobolev function by a solenoidal lipschitz function which differs from the original function only on a small set our main application is the existence of weak solutions to the two dimensional prandtl eyring fluid model which has almost linear growth in this situation a correction via bogovski operators does not work furthermore we extend the concept of almost a harmonicity to the fluid context in the pressure free formulation

rate distortion for correlated sources with partially separated encoders we resolve some open problems concerning the encoding of a pair of correlated sources with respect to a fidelity criterion two encoders are used one encoder observes only the output of the first source while the other is supplied both with the second source output and with partial information about the first source at some predetermined rate a general coding theorem is proved which established that cal s ast a certain region defined in terms of single letter information theoretic quantities is an inner bound to the region of all attainable vectors of rates and distortions for certain cases of interest the converse is proved too thereby establishing the rate distortion region for these cases

the regularity of minima for the dirichlet problem on bd we establish that the dirichlet problem for linear growth functionals on text bd the functions of bounded deformation gives rise to the same unconditional sobolev and partial text c 1 alpha regularity theory as presently available for the full gradient dirichlet problem on text bv functions of bounded deformation play an important role in for example plasticity however by ornstein s non inequality contain text bv as a proper subspace thus techniques to establish regularity by full gradient methods for variational problems on bv do not apply here in particular applying to all generalised minima that is minima of a suitably relaxed problem despite their non uniqueness and reaching the ellipticity ranges known from the text bv case this paper extends previous sobolev regularity results by gmeineder and kristensen in j calc var 58 56 2019 in an optimal way

a rearranged good inequality let tf be a maximal calderon zygmund singular integral mf the hardy littlewood maximal function and w an aoo weight we replace the good a inequality w x tf x 2r and mf x a by the rearrangement inequality tf t c mt t 2 tf 2t and show that it gives better estimates for tf in particular we obtain best possible weighted lp bounds previously unknown exponential integrability estimates and simplified derivations of known unweighted estimates for tf

variational inequality with almost history dependent operator for frictionless contact problems abstract we study two quasistatic contact problems which describe the frictionless contact between a body and deformable foundation on an infinite time interval the contact is modelled by the normal compliance condition with limited penetration and memory the first problem deals with evolution of a body made of a viscoplastic material and in the second problem the material is viscoelastic with long memory the constitutive functions of these materials have a non polynomial growth for each problem we derive a variational formulation that has the form of an almost history dependent variational inequality for the displacement field we demonstrate existence and uniqueness results of abstract almost history dependent inclusion and variational inequality in the reflexive orlicz sobolev space finally we apply the abstract results to prove existence of the unique weak solution to the contact problems

social significance of community structure statistical view community structure analysis is a powerful tool for social networks that can simplify their topological and functional analysis considerably however since community detection methods have random factors and real social networks obtained from complex systems always contain error edges evaluating the significance of a partitioned community structure is an urgent and important question in this paper integrating the specific characteristics of real society we present a framework to analyze the significance of a social community the dynamics of social interactions are modeled by identifying social leaders and corresponding hierarchical structures instead of a direct comparison with the average outcome of a random model we compute the similarity of a given node with the leader by the number of common neighbors to determine the membership vector an efficient community detection algorithm is proposed based on the position of the nodes and their corresponding leaders then using a log likelihood score the tightness of the community can be derived based on the distribution of community tightness we establish a connection between p value theory and network analysis and then we obtain a significance measure of statistical form finally the framework is applied to both benchmark networks and real social networks experimental results show that our work can be used in many fields such as determining the optimal number of communities analyzing the social significance of a given community comparing the performance among various algorithms etc

the sum rate bound for a new class of quadratic gaussian multiterminal source coding problems in this paper we show tightness of the berger tung bt sum rate bound for a new class of quadratic gaussian multiterminal mt source coding problems dubbed bi eigen equal variance with equal distortion beev ed where the l l source covariance matrix has equal diagonal elements with two distinct eigenvalues and the l target distortions are equal let k k l be the number of repetitions of the larger eigenvalue the beev covariance structure allows us to connect k i i d virtual gaussian sources with the l given mt sources via an l k semiorthogonal transform whose rows have equal euclidean norm plus additive i i d gaussian noises resulting in the two sets of sources being mutually conditional i i d by relating the given mt source coding problem to a generalized gaussian ceo problem with the k virtual sources as remote sources and the l mt sources as observations we obtain a lower bound on the mt sum rate and show its achievability by bt schemes under the equal distortion constraints our beev ed class of quadratic gaussian mt source coding problems subsumes both the positive symmetric case considered by wagner et al and the negative symmetric case other examples including a subclass of sources with be circulant symmetric covariance matrices and equal distortion constraints are also provided to highlight tightness of the sum rate bound