new techniques for constructing t ecd edaued and t ecd eds ued codes abstract this paper presents procedures for constructing systematic t error correcting d error detecting all unidirectional error detecting t ed d ed aued codes as well as t error correcting d error detecting and s unidirectional error detecting t ec d ed aued codes the technique proposed are similar to those recently reported to construct t ec aued codes a t ec d ed code is chosen and then a tail is appended in such a way that the new code can detect all or s errors when they are unidirectional interesting tail sequences are included in this paper the efficiency of the t ec d ed aued and t ec d ed s ued codes reported in this paper compares favorably to the existing methods in addition these procedures enable simple and fast encoding and decoding algorithms many useful codes are tabulated

optimal q ary error correcting all unidirectional error detecting codes codes that can correct up to t symmetric errors and detect all unidirectional errors known as t ec aued codes are studied in this paper given positive integers q a and t let n q a t 1 denote the length of the shortest q ary t ec aued code of size a we introduce combinatorial constructions for q ary t ec aued codes via one factorizations of complete graphs and concatenation of mds codes and codes from resolvable set systems consequently we determine the exact values of n q a t 1 for several new infinite families of q a and t

constant weight codes for correcting symmetric errors and detecting unidirectional errors proposes two classes of constant weight codes which can be used for correcting t symmetric errors and simultaneously detecting all unidirectional errors codes in the first class are in quasi systematic form and codes in the second class are in systematic form since each codeword of codes in both classes can be divided into a data part and a parity check part the proposed codes have the merit of easily mapping messages into codewords

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

test pattern generation based on reed muller coefficients reed muller coefficients are used to generate a test pattern selection procedure for detecting single stuck at faults this procedure is based on the heuristics deduced from the way in which the spectral coefficients are affected by such faults the changes that the spectral coefficients undergo are also compared with the fault models used most frequently to model defects in combinational circuits the proposed pattern generating procedure does not need a simulation of the circuit for each of the possible stuck at faults and its complexity is proportional to the number of gates in the circuit the proportionality constant increases exponentially as the number of inputs in the circuit increases to evaluate the performance of the proposed method its application to some benchmark circuits including the alu 74181 is presented

new lower bounds for asymmetric and unidirectional codes new lower bounds on the sizes of asymmetric codes and unidirectional codes are presented various methods are used three of them of special interest the first is a partitioning method that is a modification of a method used to construct constant weight codes the second is a combining codes method that is used to obtain a new code from a few others the third method is shortening by weights that is applied on symmetric codes or on codes generated by the combining codes method tables for the sizes of codes of length n

variational identities and applications to differential systems j serrin 1 introduction in the work of ponos p and in recent work of pucci serrin ps variational identities are discussed which are useful for solving various ques tions about elliptic differential equations and particular elliptic systems here we obtain a number of further applications of these identities to systems it was noted in ps that these identities are closely related to noether s theorem for variational problems by working out the divergence term arising in noether s theorem and making some simplifications one obtains a general identity for variational problems if a variational integral has a symmetry group g with the following infinitesimal generator

existence and multiplicity of positive solutions for multi parameter three point differential equations system abstract in this paper we study the existence and multiplicity of positive solutions for the differential equations system x a 1 t f 1 x t y t 0 0 t 1 y a 2 t f 2 x t y t 0 0 t 1 x 0 0 x 1 1 x 1 y 0 0 y 1 2 y 2 where 0 are parameters 0 2 1 1 1 2 0 1 a 1 c 0 1 0 and f 2 c 0 0 0 the system is a semi positone problem since the nonlinear term f 1 is allowed to take negative values and a 2 t may change sign on 0 1 the results are established via fixed point index theory

on the undetected error probability of nonlinear binary constant weight codes the undetected error probability uep of binary n 2 spl delta m nonlinear constant weight codes over the binary symmetric channel bsc is investigated where n is the blocklength m is the weight of codeword and 2 spl delta is the minimum distance of the codes the distance distribution of the n 2 m nonlinear constant weight codes is evaluated it is proven in this paper that the 5 2 2 code 5 2 3 code 6 2 3 code 7 2 4 code 7 2 3 code and 8 2 4 code are the only proper error detecting codes in the n 2 m nonlinear constant weight codes for n spl ges 5 in the sense that their uep is increased monotonically with the channel error rate p of course all these proper codes are m out of n codes furthermore it is conjectured that except for the cases of n spl les 4 spl delta there are no proper error detecting binary n 2 spl delta m nonlinear constant weight codes for n 8 and spl deltaspl ges 1

coherence thresholds in models of language change and evolution the effects of noise dynamics and network of interactions a simple model of language evolution proposed by komarova niyogi and nowak is characterized by a payoff in communicative function and by an error in learning that measure the accuracy in language acquisition the time scale for language change is generational and the model s equations in the mean field approximation are a particular case of the replicator mutator equations of evolutionary dynamics in well mixed populations this model exhibits a critical coherence threshold i e a minimal accuracy in the learning process is required to maintain linguistic coherence in this work we analyze in detail the effects of different fitness based dynamics driving linguistic coherence and of the network of interactions on the nature of the coherence threshold by performing numerical simulations and theoretical analyses of three different models of language change in finite populations with two types of structure fully connected networks and regular random graphs we find that although the threshold of the original replicator mutator evolutionary model is robust with respect to the structure of the network of contacts the coherence threshold of related fitness driven models may be strongly affected by this feature

uniqueness of the positive solution for a class of semilinear elliptic systems abstract we prove the uniqueness of the positive radially symmetric solution to the following problem u v p 1 0 x b 1 v w p 2 0 x b 1 w u p 3 0 x b 1 u v w 0 x b 1 where p i 0 i 1 2 3 and b 1 is the unit ball in r n

on the classification of standing wave solutions to a coupled schrodinger system in this paper we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear schrodinger equation we establish the existence and uniqueness of solutions to the dirichlet problem on the ball and entire space as the parameters within certain regions in addition a complete structure of different types of solutions for the radial case is also provided

existence of solutions to higher order lane emden type systems abstract we prove existence results for the lane emdentype system u v q v u p in b 1 r n r u r 0 r 0 1 on b 1 r v r 0 r 0 1 on b 1 where b 1 is the unitary ball in r n n max 2 2 is the outward pointing normal n 1 and 1 is the polyharmonic operator a continuation method together with a priori estimates will be exploited moreover we prove uniqueness for the particular case 2 1 and p q 1

comparison of voter and glauber ordering dynamics on networks we study numerically the ordering process of two very simple dynamical models for a two state variable on several topologies with increasing levels of heterogeneity in the degree distribution we find that the zero temperature glauber dynamics for the ising model may get trapped in sets of partially ordered metastable states even for finite system size and this becomes more probable as the size increases voter dynamics instead always converges to full order on finite networks even if this does not occur via coherent growth of domains the time needed for order to be reached diverges with the system size in both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale free

on the uniqueness and structure of solutions to a coupled elliptic system abstract in this paper we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear schrodinger equation we establish the existence and uniqueness of solutions to the dirichlet problem on the ball in addition the nonexistence of the ground state solutions under certain conditions on the nonlinearities and the complete structure of different types of solutions to the shooting problem are proved

some optimal binary and ternary t ec aued codes codes that can correct up to t symmetric errors and detect all unidirectional errors are studied boumlinck and van tilborg gave a bound on the length of binary such codes a generalization of this bound to arbitrary alphabet size is given this generalized boumlinck van tilborg bound combined with constructions is used to determine some optimal binary and ternary codes for correcting t symmetric errors and detecting all unidirectional errors

positive solutions for singular systems of three point boundary value problems this paper investigates the following singular systems of nonlinear second order three point boundary value problems u f t v email protected 0 1 v g t u email protected 0 1 u 0 v 0 0 u 1 email protected h v 1 email protected h where email protected 0 1 0 email protected 1 f and g may be singular at t 0 and or t 1 under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression two examples are then presented to demonstrate the application of our main results

constructions and bounds for systematic tec aued codes several methods of constructing systematic t error correcting all unidirectional error detecting codes are described these codes can be constructed by adding a tail to a linear t error correcting code but other constructions presented are more of an ad hoc nature these codes will often be found as suitably chosen subsets of nonsystematic tec aued codes further bounds on the word length of systematic tec aued codes are derived and extensive tables are given

consensus formation on coevolving networks groups formation and structure we study the effect of adaptivity on a social model of opinion dynamics and consensus formation we analyse how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state we find that while on static networks these properties are determined by percolation phenomena on adaptive networks the rewiring process leads to different behaviors adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion though it also makes possible the division of clusters we show how the convergence time is determined by the characteristic time of link rearrangement we finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents

a new class of symmetric error correcting unidirectional error detecting codes abstract a new class of symmetric error correcting unidirectional error detecting codes are developed they provide protection against both transient and permanent faults the codes are systematic in nature and hence the information bits are easy to retrieve the encoding decoding methods for these codes are discussed

uniqueness results for higher order lane emden systems abstract in this paper we develop a gidas ni nirenberg technique for polyharmonic equations and systems of lane emden type as far as we are concerned with dirichlet boundary conditions we prove uniqueness of solutions up to eighth order equations namely which involve the fourth iteration of the laplace operator then we can extend the result to arbitrary polyharmonic operators of any order provided some natural boundary conditions are satisfied but not for dirichlet s the obstruction is apparently a new phenomenon and seems due to some loss of information when the polyharmonic operator turns out to be a power of the laplacian and this is the case of navier s boundary conditions as byproduct uniqueness of solutions holds in a fairly general context new existence results for systems are also established

on symmetric error correcting and all unidirectional error detecting codes the design of binary block codes that are capable of correcting up to t symmetric errors and detecting all unidirectional errors is discussed a class of systematic t symmetric error correcting all unidirectional error detecting t syec aued codes are proposed when t 0 the proposed codes become berger codes for t 1 the proposed codes are shown to be of asymptotically optimal order methods to construct nonsystematic t syec aued codes for t 2 and 3 are also presented

symmetry properties of positive solutions for fully nonlinear elliptic systems abstract we investigate symmetry properties of positive solutions for fully nonlinear uniformly elliptic systems such as f i x d u i d 2 u i f i x u 1 u n d u i 0 1 i n in a bounded domain in r n with dirichlet boundary condition u 1 u n 0 on here f i s are nonincreasing with the radius r x and satisfy a cooperativity assumption in addition each f i is the sum of a locally lipschitz with a nondecreasing function in the variable u i and may have superlinear gradient growth we show that symmetry occurs for systems with nondifferentiable f i s by developing a unified treatment of the classical moving planes method in the spirit of gidas ni nirenberg we also present different applications of our results including uniqueness of positive solutions for lane emden systems in the subcritical case in a ball and symmetry for a class of systems with natural growth in the gradient

systematic t error correcting all unidirectional error detecting codes in this paper we give methods for the construction of systematic t random error correcting and all unidirectional error detecting codes also we give the encoding decoding algorithms and discuss their implementation

existence uniqueness and stability of positive solutions to sublinear elliptic systems reaction diffusion systems are used to model many chemical and biological phenomena in the natural world 25 26 and systems of coupled partial differential equations are also used in other physical models such as nonlinear schrodinger systems in multi component bose einstein condensates and nonlinear optics 19 23 the steady state solutions or standing wave solutions of such systems of nonlinear partial differential equations satisfy a nonlinear elliptic system with more than one equation much effort has been devoted to the existence of solutions of such systems see for example 4 8 10 11 13 15 17 24 30 33 34 but it is usually difficult to determine whether or not the solution is unique we consider the positive solutions of a semilinear elliptic system of the form

uniqueness of positive solutions for a class of elliptic systems abstract in this article we consider uniqueness of positive radial solutions to the elliptic system u a x f u v 0 v b x g u v 0 subject to the dirichlet boundary condition on the open unit ball in r n n 2 our uniqueness results applies to for instance f u v u q v p g u v u p v q p q 0 p q 1 or more general cases

voter model with non poissonian interevent intervals recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long tail distribution we investigate the effect of such a non poissonian nature of human behavior on dynamics of opinion formation we use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks compared with the exponential distribution of interevent intervals i e the standard voter model the power law distribution of interevent intervals slows down consensus on the ring this is because of the memory effect in the power law case the expected time until the next update event on a link is large if the link has not had an update event for a long time on the complete graph the consensus time in the power law case is close to that in the exponential case regular graphs bridge these two results such that the slowing down of the consensus in the power law case as compared to the exponential case is less pronounced as the degree increases

uniqueness of positive solutions for some nonlinear fourth order equations abstract in this paper we study the uniqueness question of positive solutions of the two point boundary value problem u 4 t f u t r 0 is fixed andf 0 0 is inc1 a uniqueness result is proved whenfsatisfies 0 0 some examples are also given

constructions and properties of block codes for partial response channels we report on block coding techniques for partial response channels with transfer function 1 spl mnplus d sup m m 1 2 we consider various constructions of block codes with prescribed minimum euclidean distance upper and lower bounds to the size of a code with minimum squared euclidean distance greater than unity are furnished a table is presented of cardinalities of codes of small length with prescribed minimum squared euclidean distance

voter model dynamics in complex networks role of dimensionality disorder and degree distribution we analyze the ordering dynamics of the voter model in different classes of complex networks we observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks we also find that when there is no ordering in the system the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity the existence of hubs i e highly connected nodes in the network modifies the linear system size scaling law of the survival time the size of an ordered domain is sensitive to the network disorder and the average degree decreasing with both however it seems not to depend on network size and on the heterogeneity of the degree distribution

an improvement on constructions of t ec aued codes a common method of constructing t error correcting all unidirectional error detecting t ec aued codes is to choose a t ec code and then to append a tail such that the new code can detect all unidirectional errors the tail is a function of the weight of the codeword we present a technique to reduce the weight distribution of the t ec code so that the tail needed will be shorter in some cases the weight distribution span of the code is reduced by eliminating the all zero codeword and replacing it with a codeword of weight greater than 2t 1

efficient encoding algorithm for second order spectral null codes using cyclic bit shift some efficient second order spectral null codes encoded an index of the random walk function recursively and ended with the short base second order spectral null codes all of these codes used the tallini bose random walk function that exchanges two consecutive bits in this paper we propose a new random walk function based on cyclic bit shift on which the redundancy can be improved moreover the bit shift can be implemented efficiently by either software or hardware

theory of unidirectional error correcting detecting codes in this paper we present some basic theory on unidirectional error correcting detecting codes we define symmetric asymmetric and unidirectional error classes and proceed to derive the necessary and sufficient conditions for a binary code to be unidirectional error correcting detecting

analytic treatment of consensus achievement in the single type zealotry voter model abstract we introduce zealots of one opinion in the voter model on a complete graph and examine how they affect consensus achievement using first step analysis for markov chains to obtain an exact solution we find that the mean consensus time scales with the population size n increasing the number of zealots z will decrease the consensus time in a power law fashion for large z the mean magnetization was also analytically obtained and was found to contain an exponential dependence on z the dynamics for the complete graph are qualitatively similar to those obtained in another study for the barabasi albert network in general the existence of zealots serves to hasten consensus except in the case where only a few zealots oppose the vast majority

existence of positive radial solutions for a semilinear elliptic system without variational structure in this article we consider component wise positive radial solutions of a weakly coupled semilinear elliptic system in a ball with homogeneous dirichlet data we deal with a nonvariational problem we show that the existence results recently obtained by zou while very general nevertheless do not include all cases where existence can be proved

positive solutions of three point boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we study the three point boundary value problems for systems of nonlinear second order ordinary differential equations of the form u f t v t 0 1 v g t u t 0 1 u 0 v 0 0 u u 1 v v 1 under some conditions we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones

lym type inequalities for tec aued codes some lym type inequalities are introduced to obtain a relationship between the parameters of t error correcting all unidirectional error detecting codes of length n as an application of these inequalities new lower bounds on the redundancies of systematic tec aued codes are derived and an extensive table is given

existence and uniqueness of positive radial solutions for the lane emden system in this article we consider component wise positive radial solutions of a weakly coupled system of elliptic equations in a ball with homogeneous nonlinearities the existence is well known in general we give a result for the remaining cases the uniqueness is less studied we complement the known results

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

bounds on the capacity of the unidirectional channels in the usual binary symmetric channel both 1 spl rarr 0 and 0 spl rarr 1 types of errors can occur in the binary asymmetric channel only 1 spl rarr 0 type of errors can occur whereas in the unidirectional channel both 1 spl rarr 0 and 0 spl rarr 1 types of errors can occur but unlike the binary symmetric channel for any particular transmitted word of length n all the errors are of the same type in general a symmetric unidirectional channel is a channel which shows the behavior of both the symmetric and unidirectional channel many practical systems such as semiconductor memories and circuits can be modeled as a unidirectional and or symmetric unidirectional channels this paper gives the formal definition of these last two channels and shows some interesting simple bounds on their information capacities

two batch search with lie cost we consider the problem of searching for an unknown number in the search space u 0 m 1 q ary questions can be asked and some of the answers may be wrong an arbitrary integer weighted bipartite graph gamma is given stipulating the cost gamma i j of each answer jnei when the correct answer is i i e the cost of a wrong answer correct answers are supposed to be cost less it is assumed that a maximum cost e for the sum of the cost of all wrong answers can be afforded by the responder during the whole search we provide tight upper and lower bounds for the largest size m m q e gamma n for which it is possible to find an unknown number x isinu with n q ary questions and maximum lie cost e our results improve the bounds of cicalese et al 2004 and ahlswede et al 2008 the questions in our strategies can be asked in two batches of nonadaptive questions finally we remark that our results can be further generalized to a wider class of error models including also unidirectional errors

another method for constructing t ec aued codes an improved method to construct t ec aued t error correcting and all unidirectional error detecting codes is presented in some cases the new method improves the best known t ec aued codes furthermore the construction does not require complementation of codewords except the all zero and the all ones words