the poset metrics that allow binary codes of codimension m to be m m 1 or m 2 perfect a binary poset code of codimension m of cardinality 2n m where n is the code length can correct maximum m errors all possible poset metrics that allow codes of codimension m to be m m 1 or m 2 perfect are described some general conditions on a poset which guarantee the nonexistence of perfect poset codes are derived as examples we prove the nonexistence of r perfect poset codes for some r in the case of the crown poset and in the case of the union of disjoint chains

convergence and stability of numerical solutions to sddes with markovian switching a class of linear stochastic delay differential equations with markovian switching is considered the main aim of this paper is to investigate the convergence and stability of the euler method of the equations it is proved that the euler method is convergent with strong order p 1 2 the ms stable properties of the euler scheme are also studied

symplectic conditions and stochastic generating functions of stochastic runge kutta methods for stochastic hamiltonian systems with multiplicative noise abstract this paper develops numerical approximate algorithms for the solutions of stochastic hamiltonian systems with multiplicative noise some conditions are captured to guarantee that a given stochastic runge kutta method is symplectic this paper also shows that stochastic symplectic runge kutta methods can be written in terms of stochastic generating functions based on the order and symplectic conditions some low stage stochastic symplectic runge kutta methods with strong global order 1 0 are constructed some numerical results are presented to demonstrate the efficiency of stochastic symplectic runge kutta methods

the αth moment stability for the stochastic pantograph equation in this paper we investigate the ath moment asymptotical stability of the analytic solution and the numerical methods for the stochastic pantograph equation by using the razumikhin technique especially the linear stochastic pantograph equations and the semi implicit euler method applying them are considered the convergence result of the semi implicit euler method is obtained the stability conditions of the analytic solution of those equations and the numerical method are given finally some experiments are given

computational experience with a bundle approach for semidefinite cutting plane relaxations of max cut and equipartition we propose a dynamic version of the bundle method to get approximate solutions to semidefinite programs with a nearly arbitrary number of linear inequalities our approach is based on lagrangian duality where the inequalities are dualized and only a basic set of constraints is maintained explicitly this leads to function evaluations requiring to solve a relatively simple semidefinite program our approach provides accurate solutions to semidefinite relaxations of the max cut and the equipartition problem which are not achievable by direct approaches based only on interior point methods

mean square stability of analytic solution and euler maruyama method for impulsive stochastic differential equations from the view of algebra the mean square stability of analytic solutions and numerical solutions for impulsive stochastic differential equations are considered by the logarithmic norm the conditions under which the analytic and numerical solutions for a linear impulsive stochastic differential equation are mean square stable ms stable respectively are obtained the conditions are simple and easy to use some numerical experiments are given to illustrate the results

on the isomorphism problem for helly circular arc graphs the isomorphism problem is known to be efficiently solvable for interval graphs while for the larger class of circular arc graphs its complexity status stays open we consider the intermediate class of intersection graphs for families of circular arcs that satisfy the helly property we solve the isomorphism problem for this class in logarithmic space if an input graph has a helly circular arc model then our algorithm constructs it canonically which means that the models constructed for isomorphic graphs are equal

computational complexity of computing a partial solution for the graph automorphism problems it is known that a nontrivial automorphism on a given graph is computed by using any oracle that computes a pair of vertices u v such that u is mapped to v by some nontrivial automorphism in this paper we consider a weaker oracle acting as follows for a given graph the oracle returns a pair v b of a vertex v and a bit email protected 0 1 with the promise that if it returns v 0 then the vertex v is fixed by some nontrivial automorphism but if it returns v 1 then the vertex v is moved by some nontrivial automorphism provided that the given graph has a nontrivial automorphism we here note that the oracle may return an arbitrary pair as its answer in case that the given graph has no nontrivial automorphism we then show a stronger result that such an oracle is still powerful enough to compute a nontrivial automorphism we also show that a similar result holds for rightga a ga complete problem we further investigate the computational complexity of computing a partial solution for prefixga which is known to be gi complete for this problem we show that when we consider any oracle similar to one mentioned above the oracle does not help us to solve prefixga unless gi t p ga

mds poset codes satisfying the asymptotic gilbert varshamov bound in hamming weights we prove that mds linear poset codes satisfy gilbert varshamov bound for their hamming weights asymptotically we also construct mds linear poset codes on arbitrary poset metric spaces by using the dilworth s chain decomposition theorem and results about the hermite interpolation problem over a finite field we prove that there exist linear poset codes with large weights for both poset metrics and hamming metrics as well

numerical treatment of stochastic delay differential equations a global error bound abstract motivated by the error analysis of numerical solution for stochastic delay differential equations a new result indicating the dependency of convergence rate of the scheme on two separate quantities p and q where the former is the global order of underlying scheme and the latter is that of interpolation approximating the history of system is presented as an objective instance the stochastic runge kutta srk schemes of global order 0 5 1 and 1 5 in the strong convergence sense are utilized to formulate three one step schemes to approximate the solution of the problem moreover the mean square stability of these schemes will be asymptotically developed finally the theoretical results will be confirmed by some test problems

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

generalized hamming weights of linear codes the generalized hamming weight d sub r c of a binary linear code c is the size of the smallest support of any r dimensional subcode of c the parameter d sub r c determines the code s performance on the wire tap channel of type ii bounds on d sub r c and in some cases exact expressions are derived in particular a generalized griesmer bound for d sub r c is presented and examples are given of codes meeting this bound with equality

the volume algorithm revisited relation with bundle methods we revise the volume algorithm va for linear programming and relate it to bundle methods when first introduced va was presented as a subgradient like method for solving the original problem in its dual form in a way similar to the serious null steps philosophy of bundle methods va produces green yellow or red steps in order to give convergence results we introduce in va a precise measure for the improvement needed to declare a green or serious step this addition yields a revised formulation rva that is halfway between va and a specific bundle method that we call bva we analyze the convergence properties of both rva and bva finally we compare the performance of the modified algorithms versus va on a set of rectilinear steiner problems of various sizes and increasing complexity derived from real world vlsi design instances

convergence analysis of deflected conditional approximate subgradient methods subgradient methods for nondifferentiable optimization benefit from deflection i e defining the search direction as a combination of the previous direction and the current subgradient in the constrained case they also benefit from projection of the search direction onto the feasible set prior to computing the steplength that is from the use of conditional subgradient techniques however combining the two techniques is not straightforward especially if an inexact oracle is available which can only compute approximate function values and subgradients we present a convergence analysis of several different variants both conceptual and implementable of approximate conditional deflected subgradient methods our analysis extends the available results in the literature by using the main stepsize rules presented so far while allowing deflection in a more flexible way furthermore to allow for diminishing square summable rules where the stepsize is tightly controlled a priori we propose a new class of deflection restricted approaches where it is the deflection parameter rather than the stepsize which is dynamically adjusted using the target value of the optimization sequence for both polyak type and diminishing square summable stepsizes we propose a correction of the standard formula which shows that in the inexact case knowledge about the error computed by the oracle which is available in several practical applications can be exploited in order to strengthen the convergence properties of the method the analysis allows for several variants of the algorithm at least one of them is likely to show numerical performances similar to these of heavy ball subgradient methods popular within backpropagation approaches to train neural networks while possessing stronger convergence properties

primal convergence from dual subgradient methods for convex optimization when solving a convex optimization problem through a lagrangian dual reformulation subgradient optimization methods are favorably utilized since they often find near optimal dual solutions quickly however an optimal primal solution is generally not obtained directly through such a subgradient approach unless the lagrangian dual function is differentiable at an optimal solution we construct a sequence of convex combinations of primal subproblem solutions a so called ergodic sequence which is shown to converge to an optimal primal solution when the convexity weights are appropriately chosen we generalize previous convergence results from linear to convex optimization and present a new set of rules for constructing the convexity weights that define the ergodic sequence of primal solutions in contrast to previously proposed rules they exploit more information from later subproblem solutions than from earlier ones we evaluate the proposed rules on a set of nonlinear multicommodity flow problems and demonstrate that they clearly outperform the ones previously proposed

stability analysis of numerical schemes for stochastic differential equations stochastic differential equations sdes represent physical phenomena dominated by stochastic processes as for deterministic ordinary differential equations odes various numerical schemes are proposed for sdes in this paper we study the stability of numerical schemes for scalar sdes with respect to the mean square norm which we call ms stability we will show some figures of the ms stability domain or regions for some numerical schemes and present numerical results which confirm it this notion is an extension of absolute stability in numerical methods for odes

dynamic bundle methods lagrangian relaxation is a popular technique to solve difficult optimization problems however the applicability of this technique depends on having a relatively low number of hard constraints to dualize when there are many hard constraints it may be preferable to relax them dynamically according to some rule depending on which multipliers are active from the dual point of view this approach yields multipliers with varying dimensions and a dual objective function that changes along iterations we discuss how to apply a bundle methodology to solve this kind of dual problems our framework covers many separation procedures to generate inequalities that can be found in the literature including but not limited to the most violated inequality we analyze the resulting dynamic bundle method giving a positive answer for its primal dual convergence properties and under suitable conditions show finite termination for polyhedral problems

two boundedness and monotonicity preserving methods for a generalized fisher kpp equation two finite difference methods are proposed for a generalized fisher kpp equation these methods are capable of preserving the skew symmetry of the equation these methods preserve the positivity boundedness and monotonicity of solutions these methods are solvable these methods are convergent a semi explicit finite difference method and an implicit finite difference method are proposed for a generalized fisher kpp equation with two space variables it is proved that these two methods could preserve the skew symmetry of this equation moreover under a condition on the step sizes the semi explicit method is capable of preserving the positivity the boundedness and the spatial and temporal monotonicity of initial approximations and the implicit method is able to preserve these properties with no restriction on the step sizes the stability and convergence of these two methods are also analyzed respectively finally some numerical simulations are provided to verify the validity of our analytical results

comparison of bundle and classical column generation when a column generation approach is applied to decomposable mixed integer programming problems it is standard to formulate and solve the master problem as a linear program seen in the dual space this results in the algorithm known in the nonlinear programming community as the cutting plane algorithm of kelley and cheney goldstein however more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard one of them is the bundle method our aim is to illustrate its differences with kelley s method in the process we review alternative stabilization techniques used in column generation comparing them from both primal and dual points of view numerical comparisons are presented for five applications cutting stock which includes bin packing vertex coloring capacitated vehicle routing multi item lot sizing and traveling salesman we also give a sketchy comparison with the volume algorithm

geometric approach to higher weights the notion of higher or generalized weights of codes is just as natural as that of the classical hamming weight the authors adopt the geometric point of view and always treat the q ary case some results and proofs being new the main goal is to present a clear picture of what is known on the subject

mean square and asymptotic stability of the stochastic theta method stability analysis of numerical methods for ordinary differential equations odes is motivated by the question for what choices of stepsize does the numerical method reproduce the characteristics of the test equation we study a linear test equation with a multiplicative noise term and consider mean square and asymptotic stability of a stochastic version of the theta method we extend some mean square stability results in saito and mitsui siam j numer anal 33 1996 pp 2254 2267 in particular we show that an extension of the deterministic a stability property holds we also plot mean square stability regions for the case where the test equation has real parameters for asymptotic stability we show that the issue reduces to finding the expected value of a parametrized random variable we combine analytical and numerical techniques to get insights into the stability properties for a variant of the method that has been proposed in the literature we obtain precise analytic expressions for the asymptotic stability region this allows us to prove a number of results the technique introduced is widely applicable and we use it to show that a fully implicit method suggested by kloeden and platen numerical solution of stochastic differential equations springer verlag 1992 has an asymptotic stability extension of the deterministic a stability property we also use the approach to explain some numerical results reported in milstein platen and schurz siam j numer anal 35 1998 pp 1010 1019

exponential stability in p th mean of solutions and of convergent euler type solutions of stochastic delay differential equations one concept of the stability of a solution of an evolutionary equation relates to the sensitivity of the solution to perturbations in the initial data there are other stability concepts notably those concerned with persistent perturbations results are presented on the stability in p th mean of solutions of stochastic delay differential equations with multiplicative noise and of stochastic delay difference equations the difference equations are of a type found in numerical analysis and we employ our results to obtain mean square stability criteria for the solution of the euler maruyama discretization of stochastic delay differential equations the analysis proceeds as follows we show that an inequality of halanay type derivable via comparison theory can be employed to derive conditions for p th mean stability of a solution we then produce a discrete analogue of the halanay type theory that permits us to develop a p th mean stability analysis of analogous stochastic difference equations the application of the theoretical results is illustrated by deriving mean square stability conditions for solutions and numerical solutions of a constant coefficient linear test equation

weighted posets and digraphs admitting the extended hamming code to be a perfect code recently etzion et al introduced metrics on mathbb f 2 n based on directed graphs on n vertices and developed some basic coding theory on directed graph metric spaces in this paper we consider the problem of classifying directed graphs which admit the extended hamming codes to be a perfect code we first consider weighted poset metrics as a natural generalization of poset metrics and investigate interrelation between the weighted poset metrics and the directed graph based metrics in the next we classify weighted posets on a set with eight elements and directed graphs on eight vertices which admit the extended hamming code tilde mathcal h 3 to be a two perfect code we also construct some families of such structures for any k geq 3 which can be viewed as generalizations of some results presented by etzion et al and hyun and kim those families enable us to construct packing or covering codes of radius 2 under certain maps

exponential stability in mean square of neutral stochastic differential functional equations abstract the aim of this paper is to investigate the exponential stability in mean square for a neutral stochastic differential functional equation of the form d x t g xt f t x t g t xt dt t xt dw t where xt x t s s 0 with 0 is the past history of the solution several interesting examples are a given for illustration

an analysis of stability of milstein method for stochastic differential equations with delay this paper deals with the adapted milstein method for solving linear stochastic delay differential equations it is proved that the numerical method is mean square ms stable under suitable conditions the obtained result shows that the method preserves the stability property of a class of linear constant coefficient problems this is also verified by several numerical examples

exponential stability of euler maruyama solutions for impulsive stochastic differential equations with delay this paper establishes a method to study the exponential stability of euler maruyama em method for impulsive stochastic differential equations with delay by using the properties of m matrix and stochastic analysis technique some conditions under which the em solution is exponentially mean square stable are obtained some examples are provided to illustrate the results

graph animals subgraph sampling and motif search in large networks we generalize a sampling algorithm for lattice animals connected clusters on a regular lattice to a monte carlo algorithm for graph animals i e connected subgraphs in arbitrary networks as with the algorithm in n kashtan et al bioinformatics 20 1746 2004 it provides a weighted sample but the computation of the weights is much faster linear in the size of subgraphs instead of superexponential this allows subgraphs with up to ten or more nodes to be sampled with very high statistics from arbitrarily large networks using this together with a heuristic algorithm for rapidly classifying isomorphic graphs we present results for two protein interaction networks obtained using the tandem affinity purification tap method one of escherichia coli with 230 nodes and 695 links and one for yeast saccharomyces cerevisiae with roughly ten times more nodes and links we find in both cases that most connected subgraphs are strong motifs z scores 10 or antimotifs z scores 10 when the null model is the ensemble of networks with fixed degree sequence strong differences appear between the two networks with dominant motifs in e coli being nearly bipartite graphs and having many pairs of nodes that connect to the same neighbors while dominant motifs in yeast tend towards completeness or contain large cliques we also explore a number of methods that do not rely on measurements of z scores or comparisons with null models for instance we discuss the influence of specific complexes like the 26s proteasome in yeast where a small number of complexes dominate the k cores with large k and have a decisive effect on the strongest motifs with 6 8 nodes we also present zipf plots of counts versus rank they show broad distributions that are not power laws in contrast to the case when disconnected subgraphs are included

on the isomorphism of graphs having some eigenvalues of moderate multiplicity abstract graph isomorphism is one of the most prominent problems in computer science which is not known to be np complete or polynomial time solvable babai grigoryev and mount stoc 1982 showed that for graphs which only have eigenvalues of bounded multiplicity except at most one eigenvalue this problem is in p evdokimov and ponomarenko combinatorica 1999 extended the result of babai et al to graphs for which all eigenvalues have multiplicity o log n log log n where n is the number of vertices in this paper we present an elementary proof that if for two graphs the sum of squares of the multiplicities corresponding to the eigenvalues with unbounded multiplicity is o log n log log n then isomorphism testing can be solved in polynomial time although our result is completely covered by evdokimov and ponomarenko and hence it is not new our proof only uses elementary methods and is completely different from their considerably more demanding approach

on the generalized hamming weights of product codes the rth generalized hamming weight of a linear code is the minimum support size of any r dimensional subcode it has been found useful in the studies of cryptography and trellis coding the authors derive several results on expressing the generalized hamming weights of a product code in terms of those of its component codes they also formulate a general conjecture

metrics based on finite directed graphs and coding invariants given a finite directed graph with n vertices we define a metric d g on mathbb f q n where mathbb f q is the finite field with q elements the weight of a word is defined as the number of vertices that can be reached by a directed path from a vertex within the support of the vector two canonical forms which do not affect the metric are given to each graph based on these forms we characterize each such metric we further use these forms to prove that two graphs with different canonical forms yield different metrics efficient algorithms to check if a set of metric weights define a metric based on a graph are given we provide tight bounds on the number of metric weights required to reconstruct the metric furthermore we give a complete description of the group of linear isometries of the graph metrics and a characterization of the graphs for which every linear code admits a g canonical decomposition considering those graphs we are able to derive an expression of the packing radius of linear codes in such metric spaces finally given a directed graph which determines a hierarchical poset we present sufficient and necessary conditions to ensure the validity of the macwilliams identity and the macwilliams extension property

ms stability of the euler maruyama method for stochastic differential delay equations the aim of this paper is to investigate the stability of the euler maruyama method for the stochastic differential equations with time delay the definition of ms stability of numerical methods is established the condition of the mean square stability of analytical solution is obtained for a linear scalar system with multiplicative noise and the ms stability of the numerical scheme is proved

stochastic symplectic partitioned runge kutta methods for stochastic hamiltonian systems with multiplicative noise a new class of sprk methods and their order conditions are given symplectic conditions of the sprk methods are obtained stochastic generating functions of the ssprk methods are obtained it is proved that the ssprk methods can preserve the quadratic invariants some low stage ssprk methods are constructed some new stochastic partitioned runge kutta sprk methods are proposed for the strong approximation of partitioned stochastic differential equations sdes the order conditions up to strong global order 1 0 are calculated the sprk methods are applied to solve stochastic hamiltonian systems with multiplicative noise some conditions are captured to guarantee that a given sprk method is symplectic it is shown that stochastic symplectic partitioned runge kutta ssprk methods can be written in terms of stochastic generating functions in addition this paper also proves that the ssprk methods can conserve the quadratic invariants of original stochastic systems based on the order and symplectic conditions some low stage ssprk methods with strong global order 1 0 are constructed finally some numerical results are presented to demonstrate the efficiency of the ssprk methods

on the hardness of graph isomorphism we show that the graph isomorphism problem is hard under dlogtime uniform ac 0 many one reductions for the complexity classes nl pl probabilistic logarithmic space for every logarithmic space modular class mod k l and for the class det of problems nc 1 reducible to the determinant these are the strongest known hardness results for the graph isomorphism problem and imply a randomized logarithmic space reduction from the perfect matching problem to graph isomorphism we also investigate hardness results for the graph automorphism problem

a classification of posets admitting the macwilliams identity in this paper all poset structures that admit the macwilliams identity are classified and the macwilliams identities for poset weight enumerators corresponding to such posets are derived it is proved that being a hierarchical poset is a necessary and sufficient condition for a poset to admit the macwilliams identity an explicit relation is also derived between the p weight distribution of a hierarchical poset code and the p weight distribution of the dual code

classification of poset block spaces admitting macwilliams type identity in this paper we prove that a poset block space admits a macwilliams type identity if and only if the poset is hierarchical and at any level of the poset all the blocks have the same dimension when the poset block admits the macwilliams type identity we explicitly state the relation between the weight enumerators of a code and its dual

general approach to poset and additive metrics let p n leq p be a poset on n 1 2 ldots n mathbb f q n be the linear space of n tuples over a finite field mathbb f q and w be a weight on mathbb f q in this paper we consider metrics on mathbb f q n which are induced by posets over n and weights over mathbb f q such family of metrics extend both the additive metric induced by the weight w when the poset is an anti chain and the poset metrics when the weight is the hamming weight furthermore the pomset metrics is also a particular case of our construction consequently we provide a simpler approach to these metrics without using the multiset structure originally proposed for the general case we provide a complete description of the groups of linear isometries of these metric spaces in terms of a semi direct product which turns out to be similar to the case of poset metric spaces in particular we re obtain the groups of linear isometries of the poset pomset and additive metric spaces when considering a chain order we develop for codes on these spaces several of the invariants and properties found in the classical coding theory our construction of metrics based on partial orders and any weight over the base field highlights the dependence of the poset metric over mathbb f q n with the hamming metric on mathbb f q and the additive property of its extension on mathbb f q n

introduction to the numerical analysis of stochastic delay differential equations abstract we consider the problem of the numerical solution of stochastic delay differential equations of ito form d x t f x t x t d t g x t x t d w t t 0 t and x t t for t 0 with given f g wiener noise w and given 0 with a prescribed initial function we indicate the nature of the equations of interest and give a convergence proof for explicit single step methods some illustrative numerical examples using a strong euler maruyama scheme are provided

piecewise quadratic approximations in convex numerical optimization we present a bundle method for convex nondifferentiable minimization where the model is a piecewise quadratic convex approximation of the objective function unlike standard bundle approaches the model only needs to support the objective function from below at a properly chosen small subset of points as opposed to everywhere we provide the convergence analysis for the algorithm with a general form of master problem which combines features of trust region stabilization and proximal stabilization taking care of all the important practical aspects such as proper handling of the proximity parameters and the bundle of information numerical results are also reported

mean square stability of semi implicit euler method for linear stochastic differential equations with multiple delays and markovian switching in this paper we study the mean square ms stability and general mean square gms stability of semi implicit euler method for linear stochastic differential equations with multiple delays and markovian switching it is proved that semi implicit euler method is ms stable and gms stable under suitable conditions a numerical example is provided to illustrate the theoretical results

exponential stability of the split step θ method for neutral stochastic delay differential equations with jumps abstract the exponential mean square stability of the split step method for neutral stochastic delay differential equations nsddes with jumps is considered new conditions for jumps are proposed to ensure the exponential mean square stability of the trivial solution if the drift coefficient satisfies the linear growth condition it is shown that the split step method can reproduce the exponential mean square stability of the trivial solution for the constrained stepsize then by applying the chebyshev inequality and the borel cantelli lemma the almost sure exponential stability of both the trivial solution and the numerical solution can be obtained since split step method covers euler maruyama em method and split step backward euler ssbe method the conclusions are valid for these two methods moreover they can adapt to the nsddes and the sddes with jumps finally a numerical example illustrates the effectiveness of the theoretical results

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

duality and support weight distributions we show how to compute the support weight distribution a sub i sup r for r spl ges k d sub 2 sup spl perp 3 where d sub 2 sup spl perp is the second minimum support weight of a code provided the weight enumerator of the dual code is known

chains demi matroids and profiles it is shown that each chain of linear codes has an associated demi matroid a combinatorial structure that extends the notion of a vector matroid of a linear code these demi matroids are proven to determine important properties of the chain and it is shown that linear code chain duality is represented by demi matroid duality in a natural and yet surprising way profiles are defined for arbitrary demi matroids and thus for linear code chains which generalizes previous results in the literature and provides simple and transparent proofs thereof finally applications are given to encryption of messages through wire tap channels of type ii

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

s rock methods for stochastic delay differential equations with one fixed delay abstract we propose stabilized explicit stochastic runge kutta methods of strong order one half for ito stochastic delay differential equations with one fixed delay the family of the methods is constructed by embedding runge kutta chebyshev methods of order one for ordinary differential equations the values of a damping parameter of the methods are determined appropriately in order to obtain excellent mean square stability properties numerical experiments are carried out to confirm their order of convergence and stability properties

the volume algorithm producing primal solutions with a subgradient method we present an extension to the subgradient algorithm to produce primal as well as dual solutions it can be seen as a fast way to carry out an approximation of dantzig wolfe decomposition this gives a fast method for producing approximations for large scale linear programs it is based on a new theorem in linear programming duality we present successful experience with linear programs coming from set partitioning set covering max cut and plant location

new approaches for optimizing over the semimetric polytope the semimetric polytope is an important polyhedral structure lying at the heart of several hard combinatorial problems therefore linear optimization over the semimetric polytope is crucial for a number of relevant applications building on some recent polyhedral and algorithmic results about a related polyhedron the rooted semimetric polytope we develop and test several approaches based over lagrangian relaxation and application of non differentiable optimization algorithms for linear optimization over the semimetric polytope we show that some of these approaches can obtain very accurate primal and dual solutions in a small fraction of the time required for the same task by state of the art general purpose linear programming technology in some cases good estimates of the dual optimal solution but not of the primal solution can be obtained even quicker

convergence and stability of numerical solutions to a class of index 1 stochastic differential algebraic equations with time delay in this paper we study the convergence and stability of the stochastic theta method stm for a class of index 1 stochastic delay differential algebraic equations first in the case of constrained mesh i e the stepsize is a submultiple of the delay it is proved that the method is strongly consistent and convergent with order 1 2 in the mean square sense then the result is further extended to the case of non constrained mesh where we employ linear interpolation to approximate the delay argument later under a sufficient condition for mean square stability of the analytical solution it is proved that when the stepsizes are sufficiently small the stm approximations reproduce the stability of the analytical solution finally some numerical experiments are presented to illustrate the theoretical findings

weights which respect support and nn decoding in this work we explore a family of metrics over a finite field mathbb f q which respect the support of vectors we show how these metrics can be obtained from the edge labeled hamming cube and based on this representation we give a description of the group of linear isometries for q 2 next we introduce the concept of conditional sum of metrics and determine what are the conditions that out of two metrics respecting the support give rise to a new such metric finally we introduce the labeled poset block metrics a new family of metrics which respects support of vectors filling a gap existing in the known universe of such metrics for this family we give a full description of the group of linear isometries and determine sufficient conditions to ensure the existence of a macwilliams identity

split step theta method for stochastic delay integro differential equations with mean square exponential stability abstract in this paper we propose the split step theta method for stochastic delay integro differential equations by the lagrange interpolation technique and investigate the mean square exponential stability of the proposed scheme it is shown that the split step theta method can inherit the mean square exponential stability of the continuous model under the linear growth condition and the proposed stability condition by the delayed differential and difference inequalities established in the paper a numerical example is given at the end of the paper to illustrate the method and conclusion of the paper in addition the convergence of the split step theta method is proved in the appendix

the pricing of european options on two underlying assets with delays abstract in the paper the pricing of european options on two underlying assets with delays is discussed by using the approach of equivalent martingale measure transformation the market is proved to be complete with exchange option as a particular example we obtain the explicit pricing formula in a subinterval of option period the robust euler maruyama method is combined with the monte carlo simulation to compute exchange option prices within the whole option period numerical experiments indicate that there is an increasing possibility of the difference between the delayed and black scholes option prices with the increase of delay

lagrangian heuristic for a class of the generalized assignment problems a lagrangian based heuristic is proposed for many to many assignment problems taking into account capacity limits for task and agents a modified lagrangian bound studied earlier by the authors is presented and a greedy heuristic is then applied to get a feasible lagrangian based solution the latter is also used to speed up the subgradient scheme to solve the modified lagrangian dual problem a numerical study is presented to demonstrate the efficiency of the proposed approach

lagrangian relaxation via ballstep subgradient methods we exhibit useful properties of ballstep subgradient methods for convex optimization using level controls for estimating the optimal value augmented with simple averaging schemes they asymptotically find objective and constraint subgradients involved in optimality conditions when applied to lagrangian relaxation of convex programs they find both primal and dual solutions and have practicable stopping criteria up until now similar results have only been known for proximal bundle methods and for subgradient methods with divergent series stepsizes whose convergence can be slow encouraging numerical results are presented for large scale nonlinear multicommodity network flow problems

a stabilized structured dantzig wolfe decomposition method we discuss an algorithmic scheme which we call the stabilized structured dantzig wolfe decomposition method for solving large scale structured linear programs it can be applied when the subproblem of the standard dantzig wolfe approach admits an alternative master model amenable to column generation other than the standard one in which there is a variable for each of the extreme points and extreme rays of the corresponding polyhedron stabilization is achieved by the same techniques developed for the standard dantzig wolfe approach and it is equally useful to improve the performance as shown by computational results obtained on an application to the multicommodity capacitated network design problem

two well known properties of subgradient optimization the subgradient method is both a heavily employed and widely studied algorithm for non differentiable optimization nevertheless there are some basic properties of subgradient optimization that while well known to specialists seem to be rather poorly known in the larger optimization community this note concerns two such properties both applicable to subgradient optimization using the divergent series steplength rule the first involves convergence of the iterative process and the second deals with the construction of primal estimates when subgradient optimization is applied to maximize the lagrangian dual of a linear program the two topics are related in that convergence of the iterates is required to prove correctness of the primal construction scheme

duality for poset codes in this paper we extend wei s duality theorem relating the generalized hamming weight hierarchy of a code to the hierarchy of the dual code to the scope of codes with poset metrics as a consequence of this duality theorem we prove some results concerning discrepancy of codes and chain condition for generalized weights

bundle methods for sum functions with easy components applications to multicommodity network design we propose a version of the bundle scheme for convex nondifferentiable optimization suitable for the case of a sum function where some of the components are easy that is they are lagrangian functions of explicitly known compact convex programs this corresponds to a stabilized partial dantzig wolfe decomposition where suitably modified representations of the easy convex subproblems are inserted in the master problem as an alternative to iteratively inner approximating them by extreme points thus providing the algorithm with exact information about a part of the dual objective function the resulting master problems are potentially larger and less well structured than the standard ones ruling out the available specialized techniques and requiring the use of general purpose solvers for their solution this strongly favors piecewise linear stabilizing terms as opposed to the more usual quadratic ones which in turn may have an adverse effect on the convergence speed of the algorithm so that the overall performance may depend on appropriate tuning of all these aspects yet very good computational results are obtained in at least one relevant application the computation of tight lower bounds for fixed charge multicommodity min cost flow problems

on the exponential stability in mean square of neutral stochastic functional differential equations in 1 2 some efforts have been devoted to the investigation of exponential stability in mean square of neutral stochastic functional differential equations however the results derived there are either difficult to demonstrate in a straightforward way for practical situations or somewhat too restricted to be applied to general neutral stochastic functional differential equations for instance nonautonomous cases in this paper we shall establish some results which are more effective and relatively easy to verify to obtain the required stability

characterization of metrics induced by hierarchical posets in this paper we consider metrics determined by hierarchical posets and give explicit formulas for the main parameters of a linear code the minimum distance and the packing covering and chebyshev radii of a code we also present ten characterizations of hierarchical poset metrics including new characterizations and simple new proofs to the known ones

the isomorphism problem for k trees is complete for logspace we show that for k constant k tree isomorphism can be decided in logarithmic space by giving an o klogn space canonical labeling algorithm the algorithm computes a unique tree decomposition uses colors to fully encode the structure of the original graph in the decomposition tree and invokes lindell s tree canonization algorithm as a consequence the isomorphism the automorphism as well as the canonization problem for k trees are all complete for deterministic logspace completeness for logspace holds even for simple structural properties of k trees we also show that a variant of our canonical labeling algorithm runs in time o k 1 n where n is the number of vertices yielding the fastest known fpt algorithm for k tree isomorphism

a dual ascent approach for steiner tree problems on a directed graph the steiner tree problem on a directed graph stdg is to find a directed subtree that connects a root node to every node in a designated node setv we give a dual ascent procedure for obtaining lower bounds to the optimal solution value the ascent information is also used in a heuristic procedure for obtaining feasible solutions to the stdg computational results indicate that the two procedures are very effective in solving a class of stdg s containing up to 60 nodes and 240 directed 120 undirected arcs