on bounded weight codes the maximum size of a binary code is studied as a function of its length n minimum distance d and minimum codeword weight ssi w this function b n d w is first characterized in terms of its exponential growth rate in the limit n for fixed d n and w n the exponential growth rate of b n d w is shown to be equal to the exponential growth rate of a n d for 0 1 2 and equal to the exponential growth rate of a n d w for 1 2 1 second analytic and numerical upper bounds on b n d w are derived using the semidefinite programming sdp method these bounds yield a nonasymptotic improvement of the second johnson bound and are tight for certain values of the parameters

on the inequivalence of generalized preparata codes if m is odd and sigma in aut gf 2 m is such that x rightarrow x sigma 2 1 is 1 1 there is a 2 m 1 1 2 m l 2m 2 nonlinear binary code p sigma having minimum distance 5 all the codes p sigma have the same distance and weight enumerators as the usual preparata codes which rise as p sigma when x sigma x 2 it is shown that p sigma and p tau are equivalent if and only if tau sigma pm 1 and aut p sigma is determined

spherical codes generated by binary partitions of symmetric pointsets several constructions are presented by which spherical codes are generated from groups of binary codes in the main family of constructions the codes are generated from equally spaced symmetric pointsets on the real line the main ideas are code concatenation and set partitioning extensive tables are presented for spherical codes in dimension n spl les 24

variable transformation to obtain geometric ergodicity in the random walk metropolis algorithm a random walk metropolis sampler is geometrically ergodic if its equilibrium density is super exponentially light and satisfies a curvature condition stochastic process appl 85 2000 341 361 many applications including bayesian analysis with conjugate priors of logistic and poisson regression and of log linear models for categorical data result in posterior distributions that are not super exponentially light we show how to apply the change of variable formula for diffeomorphisms to obtain new densities that do satisfy the conditions for geometric ergodicity sampling the new variable and mapping the results back to the old gives a geometrically ergodic sampler for the original variable this method of obtaining geometric ergodicity has very wide applicability

new constructions of optimal cyclically permutable constant weight codes three new constructions for families of cyclic constant weight codes are presented all are asymptotically optimum in the sense that in each case as the length of the sequences within the family approaches infinity the ratio of family size to the maximum possible under the johnson upper bound approaches unity

on language equations with invertible operations the paper studies language equations of the type x l r and l y r where l and r are given languages and is an invertible binary word language operation for most of the considered insertion and deletion operations the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular l and r in case l is a context free language and r is a regular one the existence of a solution is generally undecidable the results can be extended to more complex linear equations systems of linear equations as well as for equations of higher degree

on group theoretic codes for asymmetric channels we study single error correcting codes for the asymmetric channel with input and output alphabets being 0 1 a 1 from an abelian group g of order n with elements g0 0 g1 gn 1 constantin and rao 1979 inform contr 40 20 36 define vg b1 b2 bn 1 o 1 a 1 n 1 n 1i 1 bigi 0 g and show that vg correct single errors we give explicit expressions for the size and weight distribution of these codes we further give a short discussion of some constant weight codes obtained by a similar construction

p systems with minimal insertion and deletion in this paper we consider insertion deletion p systems with priority of deletion over insertion we show that such systems with one symbol context free insertion and deletion rules are able to generate parikh sets of all recursively enumerable languages psre if a one symbol one sided context is added to the insertion or deletion rules then all recursively enumerable languages can be generated the same result holds if a deletion of two symbols is permitted we also show that the priority relation is very important and in its absence the corresponding class of p systems is strictly included in the family of matrix languages mat

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

new single error correcting codes a matrix construction of nonlinear error correcting codes is considered it is shown how this construction and some related theorems can be applied to old codes to get new codes with minimum distance 3 in total 13 new binary single error correcting codes of length at most 511 are obtained

a stochastic newton mcmc method for large scale statistical inverse problems with application to seismic inversion we address the solution of large scale statistical inverse problems in the framework of bayesian inference the markov chain monte carlo mcmc method is the most popular approach for sampling the posterior probability distribution that describes the solution of the statistical inverse problem mcmc methods face two central difficulties when applied to large scale inverse problems first the forward models typically in the form of partial differential equations that map uncertain parameters to observable quantities make the evaluation of the probability density at any point in parameter space very expensive and second the high dimensional parameter spaces that arise upon discretization of infinite dimensional parameter fields make the exploration of the probability density function prohibitive the challenge for mcmc methods is to construct proposal functions that simultaneously provide a good approximation of the target density while being inexpensive to manipulate here we present a so called stoch

bounded hairpin completion hairpin completion is a formal operation inspired from biochemistry here we consider a restricted variant of hairpin completion called bounded hairpin completion applied to a word encoding a single stranded molecule x such that either a suffix or a prefix of x is complementary to a subword of x hairpin completion produces a new word z which is a prolongation of x to the right or to the left by annealing although this operation is a purely mathematical one and the biological reality is just a source of inspiration it seems rather unrealistic to impose no restriction on the length of the prefix or suffix added by the hairpin completion the restriction considered here concerns the length of all prefixes and suffixes that are added to the current word by hairpin completion they cannot be longer than a given constant closure properties of some classes of formal languages under the non iterated and iterated bounded hairpin completion are investigated we consider the bounded hairpin completion distance between two words and generalize this distance to languages and discuss algorithms for computing them finally also the inverse operation namely bounded hairpin reduction as well as the set of all primitive bounded hairpin roots of a regular language are considered

finding a maximum clique in an arbitrary graph we describe a new type of branch and bound procedure for finding a maximum clique in an arbitrary graph g v e the two main ingredients both of o v e time complexity are i an algorithm for finding a maximal triangulated induced subgraph of g and ii an algorithm for finding a maximal k chromatic induced subgraph of g we discuss computational experience on randomly generated graphs with up to 400 vertices and 30 000 edges

existence and uniqueness of monotone measure preserving maps introduction given a pair of borel probability measures and v on rd it is natural to ask whether v can be obtained from by redistributing its mass in a canonical way in the case of the line d 1 the answer is clear as long as both measures are free from atoms x v x 0mthere is a map y x of the line to itself for which uniquely determined almost everywhere this map may be taken to be nondecreasing by a suitable choice of y x e rw o at the remaining points interpreting and v as the initial and final distribution of a one dimensional fluid the transformation y x gives a rearrangement of fluid particles yielding final state v from the initial state this rearrangement is characterized by the fact that it preserves particle ordering obviating any need for two particles to cross although the generalization of this construction to higher dimensions is the focus of this paper the one dimensional case will be pursued slightly further when the measures are absolutely continuous with respect to lebesgue d x f x dx and dr y g y dymthen formally at least neglecting regularity issues the fundamental theorem of calculus yields

an updated table of minimum distance bounds for binary linear codes in 1973 helgert and sfinaff published a table of upper and lower bounds on the maximum minimum distance for binary linear error correcting codes up to length 127 this article presents an updated table incorporating numerous improvements that have appeared since then to simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well known general code construction techniques this program also made it possible to check the original table furthermore it offers a quick and reliable update service for future improvements

quasi linear geostatistical theory for inversing a quasi linear theory is presented for the geostatistical solution to the inverse problem the archetypal problem is to estimate the log transmissivity function from observations of head and log transmissivity at selected locations the unknown is parameterized as a realization of a random field and the estimation problem is solved in two phases structural analysis where the random field is characterized followed by estimation of the log transmissivity conditional on all observations the proposed method generalizes the linear approach of kitanidis and vomvoris 1983 the generalized method is superior to the linear method in cases of large contrast in formation properties but informative measurements i e there are enough observations that the variance of estimation error of the log transmissivity is small the methodology deals rigorously with unknown drift coefficients and yields estimates of covariance parameters that are unbiased and grid independent the applicability of the methodology is demonstrated through an example that includes structural analysis determination of best estimates and conditional simulations

bayesian inverse problems with l_1 priors a randomize then optimize approach prior distributions for bayesian inference that rely on the l 1 norm of the parameters are of considerable interest in part because they promote parameter fields with less regularity than gaussian priors e g discontinuities and blockiness these l 1 type priors include the total variation tv prior and the besov space b 1 1 s prior and in general yield non gaussian posterior distributions sampling from these posteriors is challenging particularly in the inverse problem setting where the parameter space is high dimensional and the forward problem may be nonlinear this paper extends the randomize then optimize rto method an optimization based sampling algorithm developed for bayesian inverse problems with gaussian priors to inverse problems with l 1 type priors we use a variable transformation to convert an l 1 type prior to a standard gaussian prior such that the posterior distribution of the transformed parameters is amenable to metropolized sampling via rto we demonstrate thi

constructions for q ary constant weight codes this paper introduces a new combinatorial construction for q ary constant weight codes which yields several families of optimal codes and asymptotically optimal codes the construction reveals intimate connection between q ary constant weight codes and sets of pairwise disjoint combinatorial designs of various types

optimal ternary constant weight codes of weight four and distance six recently chee and ling constructions for q ary constant weight codes ieee trans inf theory vol 53 no 1 135 146 jan 2007 introduced a new combinatorial construction for q ary constant weight codes which reveals a close connection between q ary constant weight codes and sets of pairwise disjoint combinatorial designs in this paper we study the problem of constructing optimal ternary constant weight codes with hamming weight four and minimum distance six using this approach the construction here exploits completely reducible super simple designs and group divisible codes the problem is solved leaving only two cases undetermined previously the sizes of constant weight codes of weight four and distance six were known only for those of length no greater than 10

new bounds and constructions for granular media coding improved lower and upper bounds on the size and the rate of grain correcting codes are presented the lower bound is gilbert varshamov like combined with a construction by gabrys et al and it improves on the previously best known lower bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval 0 0 0668 one of the two newly presented upper bounds improves on the best known upper bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval tau in 0 1 8 and meets the lower bound of 1 2 for tau geq 1 8 moreover in a nonasymptotic regime both upper bounds improve on the previously best known results on the largest size of t grain correcting codes of length n for certain values of n and t constructions of 1 grain correcting codes based on a partitioning technique are presented for lengths up to 18 finally a lower bound of 1 2 log 2 n on the minimum redundancy of infty grain detecting codes of length n is presented

bounds and constructions for binary asymmetric error correcting codes corresp by use of known bounds on constant weight binary codes new uppper bounds are obtained on the cardinality of binary codes correcting asymmetric errors some constructions are exhibited that come close to these bounds for single error correcting codes some constructions are derived from the steiner system s 5 6 12 and for double error correcting codes some constructions are derived from the nordstrom robinson code

some new constant weight codes a n d w denotes the maximum cardinality of any binary code of length n minimum distance d and constant weight w the results of a search for good constant weight codes using a combinatorial optimization algorithm are reported a brief description of the algorithm is given the problem of constructing a constant weight code of length n minimum distance d and weight w containing m codewords is mapped to an optimization problem the algorithm is used to solve the optimization problem for given parameters n d w and m the application of the algorithm has led to some new constant weight codes their parameters are given

optimal ternary constant composition codes of weight four and distance five constant composition codes cccs are a generalization of constant weight codes and permutation codes the concept of group divisible codes an analog of group divisible designs in combinatorial design theory was first introduced by chee et al this new class of codes has been shown to be useful in recursive constructions of constant weight codes and constant composition codes in this paper we consider the problem of determining the maximal sizes of ternary constant composition codes of weight four and distance five using group divisible codes as the main tools we determine the exact values for these parameters the previously known results are those with code length no greater than 10

the sizes of optimal q ary codes of weight three and distance four a complete solution this correspondence introduces two new constructive techniques to complete the determination of the sizes of optimal q ary codes of constant weight three and distance four

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

dimension independent likelihood informed mcmc many bayesian inference problems require exploring the posterior distribution of high dimensional parameters that represent the discretization of an underlying function this work introduces a family of markov chain monte carlo mcmc samplers that can adapt to the particular structure of a posterior distribution over functions two distinct lines of research intersect in the methods developed here first we introduce a general class of operator weighted proposal distributions that are well defined on function space such that the performance of the resulting mcmc samplers is independent of the discretization of the function second by exploiting local hessian information and any associated low dimensional structure in the change from prior to posterior distributions we develop an inhomogeneous discretization scheme for the langevin stochastic differential equation that yields operator weighted proposals adapted to the non gaussian structure of the posterior the resulting dimension independent and likelihood informed dili mcmc samplers may be useful for a large class of high dimensional problems where the target probability measure has a density with respect to a gaussian reference measure two nonlinear inverse problems are used to demonstrate the efficiency of these dili samplers an elliptic pde coefficient inverse problem and path reconstruction in a conditioned diffusion

semidefinite programming bounds for constant weight codes for nonnegative integers n d and w let a n d w be the maximum size of a code c subseteq mathbb f 2 n with a constant weight w and minimum distance at least d we consider two semidefinite programs based on quadruples of code words that yield several new upper bounds on a n d w the new upper bounds imply that a 22 8 10 616 and a 22 8 11 672 lower bounds on a 22 8 10 and a 22 8 11 are obtained from the n d 22 7 shortened golay code of size 2048 it can be concluded that the shortened golay code is a union of constant weight w codes of sizes a 22 8 w

spectral enumerators for certain additive error correcting codes over integer alphabets the paper contains a study of certain block codes with integer coordinate symbols devised for the correction of some types of additive errors the codes are defined by a check equation over a finite abelian group thus they appear as an extension of the varshamov and constantin rao codes the main results of the paper are concerned with the error correcting capability including a decoding method for generalized varshamov codes and principally with enumeration problems a general formula for spectral enumerators is obtained and applied to the varshamov and constantin rao codes

new lower bounds for constant weight codes some new lower bounds are given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance 4 and constant weight w in a number of cases the results significantly improve on the best bounds previously known

contextual insertions deletions and computability we investigate two generalizations of insertion and deletion of words that have recently become of interest in the context of molecular computing given a pair of words x y called a context the x y contextual insertion of a wordvinto a worduis performed as follows for each occurrence ofxyas a subword inu we include in the result of the contextual insertion the words obtained by insertingvintou betweenxandy the x y contextual deletion operation is defined in a similar way we study closure properties of the chomsky families under the defined operations contextual ins closed and del closed languages and decidability of existence of solutions to equations involving these operations moreover we prove that every turing machine can be simulated by a system based entirely on contextual insertions and deletions

cyclic constant weight codes upper bounds and new optimal constructions in this paper we consider optimal q ary cyclic constant weight codes of length n minimum distance d and weight w briefly cyclic n d w q codes we introduce the pure and mixed difference method to present a combinatorial description for a cyclic n d w q code and then obtain some tight upper bounds on the sizes of optimal cyclic n d w q codes finally by using skolem type sequences we completely determine the sizes of optimal cyclic n d 3 3 codes with minimum distance 1 leq d leq 6

multiply constant weight codes and the reliability of loop physically unclonable functions we introduce the class of multiply constant weight codes to improve the reliability of certain physically unclonable function response and extend classical coding methods to construct multiply constant weight codes from known q ary and constant weight codes we derive analogs of johnson bounds and give constructions showing these bounds to be asymptotically tight up to a constant factor under certain conditions we also examine the rates of multiply constant weight codes and demonstrate that these rates are the same as those of constant weight codes of corresponding parameters

insertion deletion correction with spectral nulls levenshtein 1966 proposed a class of single insertion deletion correcting codes based on the number theoretic construction due to varshamov and tenengolt s 1965 we present several interesting results on the binary structure of these codes and their relation to constrained codes with nulls in the power spectral density function one surprising result is that the higher order spectral null codes of immink and beenker 1987 are sub codes of balanced levenshtein codes other spectral null sub codes with similar coding rates may also be constructed we furthermore present some coding schemes and spectral shaping markers which alleviate the fundamental restriction on levenshtein s codes that the boundaries of each codeword should be known before insertion deletion correction can be effected

on the maximum weight clique problem we introduce several new classes of graphs on which the maximum weight clique problem is solvable in polynomial time their common feature and the central idea of our algorithms is that every clique of any of our graphs is contained in some member of a polynomial sized collection of induced subgraphs that are complements of bipartite graphs

optimal quaternary constant weight codes with weight four and distance five constant weight codes play an important role in coding theory the problem of determining the sizes for optimal quaternary constant weight codes with length n weight 4 and minimum hamming distance 5 n 5 4 4 codes has been investigated in several papers although some constructions and several infinite families for such codes with length n 0 1 mod 4 have been given the problem is still far from complete in this paper we determine the size of an optimal n 5 4 4 code for each integer n 4 leaving 55 lengths unsolved especially for length n 0 1 mod 4 the existence problem of the equivalent combinatorial object namely the generalized steiner system is solved leaving only seven values undetermined

a 16 9 6 5 4 error correcting dc free block code a 2n k l c d dc free binary block code is a code of length 2n constant weight n 2 sup k codewords maximum runlength of a symbol l maximum accumulated charge c and minimum distance d the purpose of this code is to achieve dc freeness and error correction at the same time the goal is to keep the rate k 2n and d large and l and c small of course these are conflicting goals h c ferreira ieee trans magn vol mag 20 no 5 p 881 3 1984 presented a 16 8 8 5 4 dc free code here a 16 9 6 5 4 dc free code is presented easy encoding and decoding algorithms are also given

orbit and coset analysis of the golay and related codes let b be a code of length n over a field f with automorphism group g b sub w denotes the subset of codewords of weight w the goal is to classify the vectors of f sup n into orbits under g and to determine their distances from the various subcodes b sub w this is done for the first order reed muller nordstrom robinson and hamming codes of length 16 the golay and shortened golay codes of lengths 22 23 24 and the ternary golay code of length 12

the covering radius of the leech lattice we investigate the points in 24 dimensional space that are at maximal distance from the leech lattice i e the deep holes in that lattice the distance of such a point from the leech lattice is 1 sqrt 2 times the minimal distance between the lattice points furthermore there are 23 inequivalent types of deep hole one for each of the 23 even unimodular 24 dimensional lattices found by niemeier

upper bounds on the number of columns in supersaturated designs we consider two level designs in this paper with the two levels denoted by 1 and 1 the run size n of a supersaturated design does not exceed its number of columns or factors m that is n m in a screening experiment although a large number of factors are studied the number of active factors is usually very small this assumption of effect sparsity box meyer 1986 is the rationale for using supersaturated designs booth cox 1962 was the first paper to consider deterministic construction of supersaturated designs three systematic construction methods were recently proposed and discussed in lin 1993 wu 1993 and tang wu 1997 and computer generation of supersaturated designs was considered by lin 1995 nguyen 1996 and li wu 1997 since n m supersaturated designs cannot be made orthogonal it is therefore desirable to have supersaturated designs which are as close to orthogonal as possible the most commonly used measure of non orthogonality among the columns of a supersaturated design is

bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6 upper bounds to the maximum number of codewords in a binary code of length n and asymmetric distance delta are derived for some values of n and delta a method is given in which a code of length n m and asymmetric distance at least t 1 is constructed by expurgating and puncturing a code of length n and hamming distance at least 2t 1 novel asymmetric error correcting codes are constructed by applying this method to some celebrated symmetric error correcting codes a table is presented on the size of optimal asymmetric error correcting codes of length less than 24 and asymmetric distance less than 6

lexicographic codes error correcting codes from game theory lexicographic codes or lexicodes are defined by various versions of the greedy algorithm the theory of these codes is closely related to the theory of certain impartial games which leads to a number of surprising properties for example lexicodes over an alphabet of size b 2 a are closed under addition while if b 2 2 a the lexicodes are closed under multiplication by scalars where addition and multiplication are in the nim sense explained in the text hamming codes and the binary golay codes are lexieodes remarkably simple constructions are given for the steiner systems s 5 6 12 and s 5 8 24 several record breaking constant weight codes are also constructed

randomize then optimize a method for sampling from posterior distributions in nonlinear inverse problems high dimensional inverse problems present a challenge for markov chain monte carlo mcmc type sampling schemes typically they rely on finding an efficient proposal distribution which can be dif

sufficient conditions for pure state n representability a simple scheme is presented allowing the construction of most of the known and a wide variety of new sufficient conditions for pure state n representability of reduced one electron density operators

a new parallel algorithm for the maximal independent set problem a new parallel algorithm for the maximal independent set problem is constructed it runs in o log 4 n time when implemented on a linear number of erew processors this is the first deterministic algorithm for the maximal independent set problem mis whose running time is polylogarithmic and whose processor time product is optimal up to a polylogarithmic factor

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

optimal binary one error correcting codes of length 10 have 72 codewords the maximum number of codewords in a binary code with length n and minimum distance d is denoted by a n d by construction it is known that a 10 3 spl ges 72 and a 11 3 spl ges 144 these bounds have long been conjectured to be the exact values this is here proved by classifying various codes of smaller length and lengthening these using backtracking and isomorphism rejection there are 562 inequivalent codes attaining a 10 3 72 and 7398 inequivalent codes attaining a 11 3 144

constructions for perfect mixed codes and other covering codes a construction for an infinite family of perfect mixed codes with covering radius 2 is presented these are the first known nontrivial perfect mixed codes with covering radius greater than 1 based on mixed codes constructions for binary covering codes that lead to a considerable improvement of upper bounds on the sizes of covering codes are presented these codes and some other codes can be obtained by the blockwise direct sum construction two infinite families of codes are of special interest they are quasi perfect nonlinear union of their disjoint translates covers the space and their density as covering codes is remarkably low

constructions of optimal and near optimal multiply constant weight codes multiply constant weight codes mcwcs have been recently studied to improve the reliability of certain physically unclonable function response in this paper we give combinatorial constructions for the mcwcs which yield several new infinite families of optimal mcwcs furthermore we demonstrate that the johnson type upper bounds of the mcwcs are asymptotically tight for fixed hamming weights and distances finally we provide bounds and constructions of the 2 d mcwcs

perfect constant weight codes in his pioneering work from 1973 delsarte conjectured that there are no nontrivial perfect codes in the johnson scheme many attempts were made during the years which followed to prove delsarte s conjecture but only partial results have been obtained we survey all these attempts and prove some new results having the same flavor we also present a new method taking a different approach which we hope can lead to the settling of this conjecture we show how this new method rules out sets of parameters as well as specific given parameters

on constant composition codes over z sub q a constant composition code is a special constant weight code under the restriction that each symbol should appear a given number of times in each codeword in this correspondence we give a lower bound for the maximum size of the q ary constant composition codes with minimum distance at least 3 this bound is asymptotically optimal and generalizes the graham sloane bound for binary constant weight codes in addition three construction methods of constant composition codes are presented and a number of optimum constant composition codes are obtained by using these constructions

bayesian inference with optimal maps we present a new approach to bayesian inference that entirely avoids markov chain simulation by constructing a map that pushes forward the prior measure to the posterior measure existence and uniqueness of a suitable measure preserving map is established by formulating the problem in the context of optimal transport theory we discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem exploiting gradient information from the forward model when possible the resulting algorithm overcomes many of the computational bottlenecks associated with markov chain monte carlo advantages of a map based representation of the posterior include analytical expressions for posterior moments and the ability to generate arbitrary numbers of independent posterior samples without additional likelihood evaluations or forward solves the optimization approach also provides clear convergence criteria for posterior approximation and facilitates model selection through automatic evaluation of the marginal likelihood we demonstrate the accuracy and efficiency of the approach on nonlinear inverse problems of varying dimension involving the inference of parameters appearing in ordinary and partial differential equations

unidirectional covering codes a code c spl sube z sup n sub 2 where z sub 2 0 1 has unidirectional covering radius r if r is the smallest integer so that any word in z sup n sub 2 can be obtained from at least one codeword c spl isin c by replacing either 1s by 0s in at most r coordinates or 0s by 1s in at most r coordinates the minimum cardinality of such a code is denoted by e n r upper bounds on this function are here obtained by constructing codes using tabu search lower bounds on the other hand are mainly obtained by integer programming and exhaustive search best known bounds on e n r for n spl les 13 and r spl les 6 are tabulated

outfix guided insertion abstract motivated by work on bio operations on dna strings we consider an outfix guided insertion operation that can be viewed as a generalization of the overlap assembly operation on strings studied previously as the main result we construct a finite language l such that the outfix guided insertion closure of l is non regular we consider also the closure properties of regular and deterministic context free languages under the outfix guided insertion operation and decision problems related to outfix guided insertion deciding whether a language recognized by a deterministic finite automaton is closed under outfix guided insertion can be done in polynomial time the complexity of the corresponding question for nondeterministic finite automata remains open

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

on the weight of universal insertion grammars we study the computational power of pure insertion grammars we show that pure insertion grammars of weight 3 can characterize all recursively enumerable languages this is achieved by either applying an inverse morphism and a weak coding or a left right quotient with a regular language we also study an application in dna computing and improve some known results concerning the power of insertion deletion dna systems

constructions of binary constant weight cyclic codes and cyclically permutable codes a general theorem is proved showing how to obtain a constant weight binary cyclic code from a p ary linear cyclic code where p is a prime by using a representation of gf p as cyclic shifts of a binary p tuple based on this theorem constructions are given for four classes of binary constant weight codes the first two classes are shown to achieve the johnson upper bound on minimum distance asymptotically for long block lengths the other two classes are shown similarly to meet asymptotically the low rate plotkin upper bound on minimum distance a simple method is given for selecting virtually the maximum number of cyclically distinct codewords with full cyclic order from reed solomon codes and from berlekamp justesen maximum distance separable codes two correspondingly optimum classes of constant weight cyclically permutable codes are constructed it is shown that cyclically permutable codes provide a natural solution to the problem of constructing protocol sequence sets for the m active out of t users collision channel without feedback

optimal ternary constant weight codes with weight 4 and distance 5 constant weight codes cwcs play an important role in coding theory the problem of determining the sizes for optimal ternary cwcs with length n weight 4 and minimum hamming distance 5 n 5 4 3 code has been settled for all positive integers n 10 or n 10 and n 1 mod 3 with n 13 52 58 undetermined in this paper we investigate the problem of constructing optimal n 5 4 3 codes for all lengths n with the tool of group divisible codes we determine the size of an optimal n 5 4 3 code for each integer n 4 leaving the lengths n 12 13 21 27 33 39 45 52 unsolved

constructions of error correcting dc free block codes two dc free codes are presented with distance 2d b or 1 length 2n 2r d 1 for d 3 where r is the least integer or log sub 2 2n 1 for the first code l 4 c 2 and the asymptotic rate of this code is 0 7925 for the second code l 6 c 3 and the asymptotic rate of this code is 0 8858 asymptotically these rates achieve the channel capacity for small values of n these codes do not achieve the best rate as an example of codes of short length with good rate the author presents a 30 10 6 4 dc free block code with 2 sup 21 codewords a construction is presented for which from a given code c sub 1 of length n even weight and distance 4 the author obtains a 4n l c 4 dc free block code c sub 2 where l is 4 5 or 6 and c is not greater than n 1 but usually significantly smaller the codes obtained by this method have good rates for small lengths the encoding and decoding procedures for all the codes are discussed

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

on the size of optimal three error correcting binary codes of length 16 let a n d denote the maximum size of a binary code with length n and minimum distance d it has been known for decades that a 16 7 a 17 8 36 or 37 that is that the size of optimal 3 error correcting binary codes of length 16 is either 36 or 37 by a recursive classification via subcodes and a clique search in the final stage it is shown that the size of optimal such codes is 36

two new binary codes with minimum distance three the author obtains a binary code of length 18 which has 164 2 sup 6 10496 codewords the minimum distance of this code is three therefore a 18 3 or 10496 shortening the author obtains find a binary code of length 17 and minimum distance 3 which has 5248 codewords showing that a 17 3 or 5248

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

cyclotomic constructions of zero difference balanced functions with applications based on a recent work of ding wang and xiong we present some cyclotomic constructions of zero difference balanced zdb functions which interpret the previous construction proposed by cai zeng helleseth tang and yang the resulted zdb functions can be used to generate optimal constant composition codes and perfect difference systems of sets with new parameters

implicit sampling for hierarchical bayesian inversion and applications in fractional multiscale diffusion models abstract this paper presents an implicit sampling method for hierarchical bayesian inverse problems a widely used approach for sampling posterior distribution is markov chain monte carlo mcmc however the samples generated by mcmc are usually strongly correlated which may lead to a small size of effective samples the implicit sampling method proposed in chorin and tu 2009 can generate independent samples and capture inherent non gaussian features of the posterior in implicit sampling method the posterior samples are generated by a map and distribution around the maximum a posterior map point for practical applications some parameters in prior density are often unknown and the hierarchical bayesian formulation is used to estimate the map point effectively it is applied to the bayesian inverse problems of multi term time fractional diffusion models in heterogeneous media to effectively capture the heterogeneity effect we present a mixed generalized multiscale finite element method mixed gmsfem to substantially speed up the bayesian inversion finally we carry out a few numerical examples to effectively identify various unknown inputs

universal insertion grammars of size two abstract in this paper we show that pure insertion grammars of size 2 i e inserting two symbols in a left and right context each consisting of two symbols can characterize all recursively enumerable languages this is achieved by either applying an inverse morphism and a weak coding or a left right quotient with a regular l o c 2 language or an intersection with a l o c 2 language and a weak coding the obtained results improve the descriptional complexity of insertion grammars and complete the picture of known results on insertion deletion systems that are motivated from the dna computing area

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

on the computational completeness of graph controlled insertion deletion systems with binary sizes abstract a graph controlled insertion deletion gcid system is a regulated extension of an insertion deletion system such a system has several components and each component has some insertion deletion rules the transition is performed by any applicable rule in the current component on a string and the resultant string is then moved to the target component specified in the rule the language of the system is the set of all terminal strings collected in the final component the parameters in the size k n i i m j j of a gcid system denote from left to right the maximum number of components the maximal length of the insertion string the maximal length of the left context for insertion the maximal length of the right context for insertion the last three parameters follow a similar representation with respect to deletion in this paper we discuss the computational completeness of the families of gcid systems of size k 1 i i 1 j j with k 3 5 and for nearly all values of i i j j 0 1 all proofs are based on the simulation of type 0 grammars given in special geffert normal form sgnf the novelty in our proof presentation is that the context free and the non context free rules of the given sgnf grammar are simulated by gcid systems of different sizes and finally we combine them by stitching and overlaying to characterize the recursive enumerable languages this proof presentation greatly simplifies and unifies the proof of such characterization results we also connect some of the obtained gcid simulations to the domain of insertion deletion p systems

a lower bound for ternary constant weight codes we derive a lower bound for ternary constant weight codes with minimum hamming distance three the bound is similar to a bound for binary constant weight codes with minimum distance four described by graham and sloane 1980 it improves upon the gilbert 1952 bound and coincides asymptotically with the johnson 1962 bound for fixed weight as the codeword length tends to infinity

a lower bound for a n 4 w corresp an explicit lower bound is given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance four and constant weight w

morphic characterizations with insertion systems controlled by a context of length one among the variety of representation theorems for context free languages the chomsky schutzenberger theorem is unique in that it consists of dyck languages regular languages and simple operations in the present paper we obtain some characterizations of and representation theorems for languages in the chomsky hierarchy by using insertion systems strictly locally testable languages and morphisms in the framework of the chomsky schutzenberger theorem for instance each context free language l can be represented in the form l h l c r where c is an insertion system of weight 1 1 r is a strictly 2 testable language and h is a morphism in contrast if r is instead a strictly 1 testable language the class of languages generated is a proper subclass of context free languages and incomparable with the class of regular languages