globally asymptotical stability of discrete time analog neural networks some globally asymptotical stability criteria for the equilibrium states of a general class of discrete time dynamic neural networks with continuous states are presented using a diagonal lyapunov function approach the neural networks are assumed to have the asymmetrical weight matrices throughout the paper the resulting criteria are described by the diagonal stability of some matrices associated with the network parameters some novel stability conditions represented by either the existence of the positive diagonal solutions of the lyapunov equations or some inequalities are given using the equivalence between the diagonal stability and the schur stability for a nonnegative matrix some simplified global stability conditions are also presented finally some examples are provided for demonstrating the effectiveness of the global stability conditions presented

an improved lower bound on the sensitivity complexity of graph properties turan 1984 11 initiated the study of the sensitivity complexity of graph properties he conjectured that for any non trivial graph properties on n vertices the sensitivity complexity is at least n 1 he proved an email protected lower bound for sensitivity in his paper turan 1984 11 wegener 1985 12 proved this conjecture for all monotone graph properties in this paper we improve turan s lower bound to 617n 0 35n we hope that this will shed some light on the proof of turan s conjecture

sensitivity block sensitivity and l block sensitivity of boolean functions sensitivity is one of the simplest and block sensitivity one of the most useful invariants of a boolean function nisan siam j comput 20 6 1991 999 and nisan and szegedy comput complexity 4 4 1994 301 have shown that block sensitivity is polynomially related to a number of measures of boolean function complexity the main open question is whether or not a polynomial relationship exists between sensitivity and block sensitivity we define the intermediate notion of l block sensitivity and show that for any fixed l this new quantity is polynomially related to sensitivity we then achieve an improved though still exponential upper bound on block sensitivity in terms of sensitivity as a corollary we also prove that sensitivity and block sensitivity are polynomially related when the block sensitivity is n

wyner ziv coding over broadcast channels digital schemes this paper addresses lossy transmission of a common source over a broadcast channel when there is correlated side information at the receivers with emphasis on the quadratic gaussian and binary hamming cases a digital scheme that combines ideas from the lossless version of the problem i e slepian wolf coding over broadcast channels and dirty paper coding is presented and analyzed this scheme uses layered coding where the common layer information is intended for both receivers and the refinement information is destined only for one receiver for the quadratic gaussian case a quantity characterizing the combined quality of each receiver is identified in terms of channel and side information parameters it is shown that it is more advantageous to send the refinement information to the receiver with better combined quality in the case where all receivers have the same overall quality the presented scheme becomes optimal unlike its lossless counterpart however the problem eludes a complete characterization

partial decode forward relaying for the gaussian two hop relay network the multicast capacity of the gaussian two hop relay network with one source n relays and l destinations is studied it is shown that a careful modification of the partial decode forward coding scheme whereby the relays recover and coherently transmit degraded sets of message parts achieves the cutset upper bound within 1 2 log n bits regardless of the channel gains and power constraints this scheme improves upon a previous scheme by chern and ozgur which is also based on partial decode forward yet has an unbounded gap from the cutset bound for l ge 2 destinations when restricted to noncoherent transmission among the relays the proposed partial decode forward scheme achieves a slightly larger gap of log n bits from the cutset bound the computation of this relaxed achievable rate involves evaluating mutual information across l n 1 cuts out of the total l 2 n possible cuts providing a very simple linear complexity algorithm to approximate the single source multicast capacity of the gaussian two hop relay network

stability analysis of neural net controllers using fuzzy neural networks neural networks can only be trained with a crisp and finite data set therefore the approximation quality of a trained network is hard to verify so a common way in proving stability of a trained neural net controller is to demonstrate the existence of a lyapunov function in this article we propose a new method how stability of a neural net controller used as a closed loop feedback controller can be proven instead of finding a lyapunov function conditions for a fuzzy training set are developed if a fuzzy neural net is trained using this training set special properties of fuzzy neural nets can be used for estimating the generalization error after defuzzification of the fuzzy net finite stability of the process can be concluded

crew prams and decision trees this paper gives a full characterization of the time needed to compute a boolean function on a crew pram with an unlimited number of processors the characterization is given in terms of a new compl

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

complexity measures and decision tree complexity a survey we discuss several complexity measures for boolean functions certificate complexity sensitivity block sensitivity and the degree of a representing or approximating polynomial we survey the relations and biggest gaps known between these measures and show how they give bounds for the decision tree complexity of boolean functions on deterministic randomized and quantum computers

stability analysis of dynamical neural networks in this paper we use the matrix measure technique to study the stability of dynamical neural networks testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given it shows how a few well known results can be unified and generalized in a straightforward way local exponential stability of a class of dynamical neural networks is also studied we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point from this some well known and new sufficient conditions for local exponential stability of neural networks are obtained

network simplification in half duplex building on submodularity this paper explores the network simplification problem in the context of gaussian half duplex diamond networks specifically given an n relay diamond network this problem seeks to derive fundamental guarantees on the capacity of the best k relay subnetwork as a function of the full network capacity simplification guarantees are presented in terms of a particular approximate capacity termed independent gaussian ig approximate capacity that characterizes the network capacity to within an additive gap which is independent of the channel coefficients and operating snr the main focus of this work is when k n 1 relays are selected out of n relays in a diamond network first a simple algorithm is proposed which selects all relays except the one with the minimum ig approximate half duplex capacity it is shown that the selected n 1 relay subnetwork has an ig approximate half duplex capacity that is at least 1 2 of the ig approximate half duplex capacity of the full network and that for the proposed algorithm this guarantee is tight furthermore this work proves the following tight fundamental guarantee there always exists a subnetwork of k n 1 relays that have an ig approximate half duplex capacity that is at least equal to n 1 n of the ig approximate half duplex capacity of the full network finally these results are extended to derive lower bounds on the fraction guarantee when k in 1 n relays are selected the key steps in the proofs lie in the derivation of properties of submodular functions which provide a combinatorial handle on the network simplification problem for gaussian half duplex diamond networks

can neural nets be universal approximators for fuzzy functions abstract we first argue that the extension principle is too computationally involved to be an efficient way for a computer to evaluate fuzzy functions we then suggest using cuts and interval arithmetic to compute the valued of fuzzy functions using the method of computing fuzzy functions we then show that neural nets are universal approximators for computable fuzzy functions when we only input non negative or non positive fuzzy numbers

on the sensitivity complexity of bipartite graph properties sensitivity complexity introduced by cook dwork and reischuk 1982 1986 in 2 3 is an important complexity measure of boolean functions turan 1984 7 initiated the study of sensitivity complexity for graph properties he conjectured that for any non trivial graph property on n vertices the sensitivity complexity is at least n 1 he proved that it is greater than n 4 in his paper wegener 1985 8 verified this conjecture for all monotone graph properties recently sun 2011 6 improved the lower bound to 617n for general graph properties we follow their steps and investigate the sensitivity complexity of bipartite graph properties in this paper we propose the following conjecture about the sensitivity of bipartite graph properties which can be considered as the bipartite analogue of turan s conjecture for any non trivial nxm bipartite graph property f s f max email protected email protected we prove this conjecture for all nx2 bipartite graph properties for general nxm bipartite graph properties we show a max n email protected m email protected lower bound we also prove this conjecture when the bipartite graph property can be written as a composite function

a learning algorithm of fuzzy neural networks with triangular fuzzy weights abstract in this paper first we propose an architecture of fuzzy neural networks with triangular fuzzy weights the proposed fuzzy neural network can handle fuzzy input vectors as well as real input vectors in both cases outputs from the fuzzy neural network are fuzzy vectors the input output relation of each unit of the fuzzy neural network is defined by the extension principle of zadeh next we define a cost function for the level sets i e cuts of fuzzy outputs and fuzzy targets then we derive a learning algorithm from the cost function for adjusting three parameters of each triangular fuzzy weight finally we illustrate our approach by computer simulations on numerical examples

an approach to stability criteria of neural network control systems this paper discusses stability of neural network nn based control systems using lyapunov approach first it is pointed out that the dynamics of nn systems can be represented by a class of nonlinear systems treated as linear differential inclusions ldi next stability conditions for the class of nonlinear systems are derived and applied to the stability analysis of single nn systems and feedback nn control systems furthermore a method of parameter region pr representation which graphically shows the location of parameters of nonlinear systems is proposed by introducing new concepts of vertex point and minimum representation from these concepts an important theorem which is useful for effectively finding a lyapunov function is derived stability criteria of single nn systems are illustrated in terms of pr representation finally stability of feedback nn control systems which consist of a plant represented by an nn and an nn controller is analyzed

the fuzzy neural network approximation lemma abstract it is well known that artificial neural networks are universal approximators but what about fuzzy neural networks only buckley and hayashi 1 presented a theoretical result for these networks they showed that there are fuzzy functions which cannot be approximated by a certain fuzzy neural network in this paper we answer the question for a special type of fuzzy neural networks especially with regard to the fuzzy arithmetic that is used it is simplified in order to minimize the computational expense as well as to simplify the theoretical examinations we prove that the class of fuzzy functions which is identical to the class of all continuous real functions extended by means of the extension principle can be approximated by certain fuzzy neural networks

efficient capacity computation and power optimization for relay networks the capacity or approximations to capacity of various single source single destination relay network models has been characterized in terms of the cut set upper bound in principle a direct computation of this bound requires evaluating the cut capacity over exponentially many cuts we show that the minimum cut capacity of a relay network under some special assumptions can be cast as a minimization of a submodular function and as a result can be computed efficiently we use this result to show that the capacity or an approximation to the capacity within a constant gap for the gaussian wireless erasure and avestimehr diggavi tse deterministic relay network models can be computed in polynomial time we present some empirical results showing that computing constant gap approximations to the capacity of gaussian relay networks with around 300 nodes can be done in order of minutes for gaussian networks cut set capacities are also functions of the powers assigned to the nodes we consider a family of power optimization problems and show that they can be solved in a polynomial time in particular we show that the minimization of the sum of powers assigned to the nodes subject to a minimum rate constraint measured in terms of cut set bounds can be computed in the polynomial time we propose a heuristic algorithm to solve this problem and measure its performance through simulations on random gaussian networks we observe that in the optimal allocations most of the power is assigned to a small subset of relays which suggests that network simplification may be possible without excessive performance degradation

amplify and forward in wireless relay networks rate diversity and network size a wireless network with fading and a single source destination pair is considered the information reaches the destination via multiple hops through a sequence of layers of single antenna relays at high signal to noise ratio snr the simple amplify and forward strategy is shown to be optimal in terms of degrees of freedom because it achieves the degrees of freedom equal to a point to point multiple input multiple output mimo system hence the lack of coordination in relay nodes does not reduce the achievable degrees of freedom the performance of this amplify and forward strategy degrades with increasing network size this phenomenon is analyzed by finding the tradeoffs between network size rate and diversity a lower bound on the diversity multiplexing tradeoff for concatenation of multiple random gaussian matrices is obtained also it is shown that achievable network size in the outage formulation short codes is a lot smaller than the ergodic formulation long codes

wireless network simplification the gaussian n relay diamond network we consider the gaussian n relay diamond network where a source wants to communicate to destination node through a layer of n relay nodes we investigate the following question what fraction of the capacity can we maintain using only k out of the n available relays we show that independent of the channel configurations and operating snr we can always find a subset of k relays which alone provide a rate k k 1 c over bar g where c over bar is the information theoretic cutset upper bound on the capacity of the whole network and g is independent of the channel coefficients and the snr and depends only on n and k logarithmic in n and linear in k in particular for k 1 this means that half of the capacity of any n relay diamond network can be approximately achieved by routing information over a single relay we also show that this fraction is tight there are configurations of the n relay diamond network where every subset of k relays alone can at most provide approximately a fraction k k 1 of the total capacity these high capacity k relay subnetworks can be also discovered efficiently we propose an algorithm that computes a constant gap approximation to the capacity of the gaussian n relay diamond network in o n log n running time and discovers a high capacity k relay subnetwork in o kn running time this result also provides a new approximation to the capacity of the gaussian n relay diamond network which is hybrid in nature it has both multiplicative and additive gaps in the intermediate snr regime this hybrid approximation is tighter than existing purely additive or purely multiplicative approximations to the capacity of this network

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

absolute stability conditions for discrete time recurrent neural networks an analysis of the absolute stability for a general class of discrete time recurrent neural networks rnn s is presented a discrete time model of rnn s is represented by a set of nonlinear difference equations some sufficient conditions for the absolute stability are derived using ostrowski s theorem and the similarity transformation approach for a given rnn model these conditions are determined by the synaptic weight matrix of the network the results reported in this paper need fewer constraints on the weight matrix and the model than in previously published studies

direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete unbounded distributed delays and markovian jumping parameters in this paper the problem of synchronization of chaotic fuzzy cellular neural networks fcnns with discrete unbounded distributed delays and markovian jumping parameters mjps is investigated sufficient delay dependent stability criteria are obtained in terms of linear matrix inequalities lmis to ensure the chaotic delayed fcnns to be stochastic asymptotically synchronous with the help of free weighting matrix and some inequality techniques the information of the delayed plant states can be taken into full consideration here the delay interval is decomposed into two subintervals by using the tuning parameter such that 0 1 by developing a delay decomposition approach and constructing suitable lyapunov krasovskii functional lkf sufficient conditions for synchronization are established for each subinterval numerical example and its simulations are provided to demonstrate the effectiveness and less conservatism of the derived results

on the modulo degree complexity of boolean functions abstract for each integer m 2 every boolean function f can be expressed as a unique multilinear polynomial modulo m and the degree of this multilinear polynomial is called its modulo m degree in this paper we investigate the modulo degree complexity of total boolean functions initiated by parikshit gopalan et al 9 in which they asked the following question whether the degree complexity of a boolean function is polynomially related with its modulo m degree for m be a power of primes it is already known that the module m degree can be arbitrarily smaller compare to the degree complexity see section 2 for details when m has at least two distinct prime factors the question remains open towards this question our results include 1 we obtain some nontrivial equivalent forms of this question 2 we affirm this question for some special classes of functions 3 we prove a no go theorem explaining why this problem is difficult to attack from the computational complexity point of view 4 we show a super linear separation between the degree complexity and the modulo m degree

slepian wolf coding over cooperative relay networks this paper deals with the problem of multicasting a set of discrete memoryless correlated sources dmcs over a cooperative relay network necessary conditions with cut set interpretation are presented a joint source wyner ziv encoding sliding window decoding scheme is proposed in which decoding at each receiver is done with respect to an ordered partition of other nodes for each ordered partition a set of feasibility constraints is derived then utilizing the submodular property of the entropy function and a novel geometrical approach the results of different ordered partitions are consolidated which lead to sufficient conditions for our problem the proposed scheme achieves operational separation between source coding and channel coding it is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks namely aref network and finite field deterministic network also in gaussian cooperative networks it is shown that reliable transmission of all dmcs whose slepian wolf region intersects the cut set bound region within a constant number of bits is feasible in particular all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two way relay networks

strong converse theorems for classes of multimessage multicast networks a renyi divergence approach this paper establishes that the strong converse holds for some classes of discrete memoryless multimessage multicast networks dm mmns whose corresponding cut set bounds are tight i e coincide with the corresponding sets of achievable rate tuples our strong converse result implies that for any dm mmn of these classes the average error probabilities of any sequence of codes operated at a rate tuple belonging to the exterior of the cut set bound must tend to one and are not simply bounded away from zero as the block length grows examples in the classes of dm mmns include wireless erasure networks dm mmns consisting of independent discrete memoryless channels dmcs as well as single destination dm mmns consisting of independent dmcs with destination feedback our elementary proof technique leverages properties of the renyi divergence

existence and stability of a unique equilibrium in continuous valued discrete time asynchronous hopfield neural networks it is shown that the assumption of d stability of the interconnection matrix together with the standard assumptions on the activation functions guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes for the synchronous mode these assumptions are also shown to imply local asymptotic stability of the equilibrium for the asynchronous mode of operation two results are derived first it is shown that symmetry and stability of the interconnection matrix guarantee local asymptotic stability of the equilibrium under a class of asynchronous modes this is referred to as local absolute asymptotic stability second it is shown that under the standard assumptions if the nonnegative matrix whose elements are the absolute values of the corresponding elements of the interconnection matrix is stable then the equilibrium is globally absolutely asymptotically stable under a class of asynchronous modes the results obtained are discussed from the points of view of their applications robustness and their relationship to earlier results

stability and the fuzzy controller abstract this paper corrects a part of the main result theorem 1 in buckley fuzzy sets and systems 77 1996 167 173

can fuzzy neural nets approximate continuous fuzzy functions abstract we first argue that regular fuzzy neural nets based on standard fuzzy arithmetic and the extension principle cannot be universal approximators this negative result is surprising since regular neural nets are universal approximators we then argue that hybrid fuzzy neural nets not necessarily based on standard fuzzy arithmetic can be universal approximators