snake in the box codes for rank modulation motivated by the rank modulation scheme with applications to flash memory we consider gray codes capable of detecting a single error also known as snake in the box codes we study two error metrics kendall s metric which applies to charge constrained errors and the l metric which is useful in the case of limited magnitude errors in both cases we construct snake in the box codes with rate asymptotically tending to 1 we also provide efficient successor calculation functions as well as ranking and unranking functions finally we also study bounds on the parameters of such codes

generalized gray codes for local rank modulation we consider the local rank modulation scheme in which a sliding window going over a sequence of real valued variables induces a sequence of permutations local rank modulation is a generalization of the rank modulation scheme which has been recently suggested as a way of storing information in flash memory we study gray codes for the local rank modulation scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation unlike the limited scope of previous works we consider code constructions for the entire range of parameters including the code length sliding window size and overlap between adjacent windows we show that the presented codes have asymptotically optimal rate we also provide efficient encoding decoding and next state algorithms

effects of time integration schemes on discontinuous deformation simulations using the numerical manifold method numerical stability by using certain time integration scheme is a critical issue for accurate simulation of discontinuous deformations of solids to investigate the effects of the time integration schemes on the numerical stability of the numerical manifold method the implicit time integration schemes ie the newmark the hht alpha and the wbz alpha methods and the explicit time integration algorithms ie the central difference the zhai s and chung lee methods are implemented their performance is examined by conducting transient response analysis of an elastic strip subjected to constant loading impact analysis of an elastic rod with an initial velocity and excavation analysis of jointed rock masses respectively parametric studies using different time steps are conducted for different time integration algorithms and the convergence efficiency of the open close iterations for the contact problems is also investigated it is proved that the hilber hughes taylor alpha hht alpha wood bossak zienkiewicz alpha wbz alpha zhai s and chung lee methods are more attractive in solving discontinuous deformation problems involving nonlinear contacts it is also found that the examined explicit algorithms showed higher computational efficiency compared to those implicit algorithms within acceptable computational accuracy

infinity norm permutation covering codes from cyclic groups we study covering codes of permutations with the ell infty metric we provide a general code construction which combines short building block codes into a single long code we focus on cyclic transitive groups as building blocks determining their exact covering radius and showing a linear time algorithm for finding a covering codeword when used in the general construction we show that the resulting covering code asymptotically out performs the best known code while maintaining linear time decoding we also bound the covering radius of relabeled cyclic transitive groups under conjugation showing that the covering radius is quite robust while relabeling cannot reduce the covering radius by much the downside is that we prove the covering radius cannot be increased by more than 1 when using relabeling

a survey of full length nonlinear shift register cycle algorithms shift registers have been used to generate sequences of 0 s and 1 s for over thirty years a wide variety of applications has been made of these sequences principally communications have made use of the sequences generated one particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences these sequences are periodic and of length 2 n and all 2 n different binary n tuples appear exactly one time in a periodic portion of the sequence in this paper we discuss various algorithms which have been suggested for generating these sequences

explicit time integration algorithms for structural dynamics with optimal numerical dissipation abstract a new predictor corrector explicit time integration algorithm is presented for solving structural dynamics problems the basis of the algorithm is the implicit generalized method developed by the authors like its implicit parent the explicit generalized method is a one parameter family of algorithms in which the parameter defines the high frequency numerical dissipation for a given value of high frequency dissipation the explicit generalized method minimizes low frequency dissipation the algorithm can be utilized effectively for structural dynamics calculations in which numerical dissipation is needed to reduce spurious oscillations parameter values are given that enable physical damping to be treated explicitly while maintaining second order accuracy without the need for an expensive second corrector pass

local rank modulation for flash memories local rank modulation lrm scheme was suggested for representing the information in flash memories in order to overcome the drawbacks of rank modulation for 0 with s dividing n an s t n lrm scheme is a lrm scheme where the n cells are locally viewed cyclically through a sliding window of size t resulting in a sequence of small permutations which requires less comparisons and less distinct values the gap between two such windows equals to s in this paper encoding decoding and asymptotic enumeration of the 1 t n lrm scheme are studied

snake in the box codes for rank modulation under kendall s tau metric for a gray code in the scheme of rank modulation for flash memories the codewords are permutations and two consecutive codewords are obtained using a push to the top operation we consider the snake in the box code under kendall s tau metric which is a gray code capable of detecting one kendall s tau error we answer two open problems posed by horovitz and etzion first we prove the validity of a construction given by them resulting in a snake of size m 2n 1 2n 1 2 2n 1 second we come up with a different construction aiming at a larger snake of size m 2n 1 2n 1 2 2n 3 the construction is applied successfully to s 7

algorithms for the generation of full length shift register sequences two algorithms are presented for the generation of full length shift register cycles also referred to as de bruijn sequences the first algorithm generates 2 k cdot g n k full cycles of length 2 n using 3n k cdot g n k bits of storage where k is a free parameter in the range 1 leq k leq 2 n 4 2 and g n k is of the order of n 2 log k the second algorithm generates about 2 n 2 4 full cycles of length 2 n using about n 2 2 bits of storage in both algorithms the time required to produce the next bit from the last n bits is close to n a possible application to the construction of stream ciphers is indicated

snake in the box codes for rank modulation under kendall s tau metric in s_ 2n 2 snake in the box codes under kendall s tau metric are studied in the rank modulation scheme for flash memories where codewords are a subset of permutations in s n with minimal kendall s tau distance two and two cyclically consecutive codewords are connected via a push to the top operation studies so far restrict the push to the top operations only on odd indices resulting in a snake consisting of permutations with the same parity and thus the minimal distance constraint is easily satisfied asymptotically optimal snake codes have been constructed this way in s 2n 1 as for s 2n 2 this framework keeps the last element fixed and thus a snake in s 2n 2 is equivalent to a snake in s 2n 1 which is rather trivial if one wants to do better then it is inevitable to have some push to the top operations on even indices resulting in a combination of odd and even permutations in the snake which increases the difficulty to guarantee the minimal kendall s tau distance constraint thus horovitz and etzion pose the open problem to prove or disprove that the size of the largest snake in s 2n 2 is not larger than the size of the largest snake in s 2n 1 a first step toward this problem is a negative answer by wang and fu who construct a snake in s 2n 2 with exactly one more permutation than an optimal snake in s 2n 1 in this paper we give an explicit construction of a snake in s 2n 2 with size asymptotically approaching 1 4 s 2n 2

new strategies for some issues of numerical manifold method in simulation of crack propagation summary aiming to solve in a unified way continuous and discontinuous problems in geotechnical engineering the numerical manifold method introduces two covers namely the mathematical cover and the physical cover in order to reach the goal some issues in the simulation of crack propagation have to be solved among which are the four issues to be treated in this study 1 to reduce the rank deficiency induced by high degree polynomials as local approximation a new variational principle is formulated which suppresses the gradient dependent dofs 2 to evaluate the integrals with singularity of 1 r a new numerical quadrature scheme is developed which is simpler but more efficient than the existing duffy transformation 3 to analyze kinked cracks a sign convention for argument in the polar system at the crack tip is specified which leads to more accurate results in a simpler way than the existing mapping technique and 4 to demonstrate the mesh independency of numerical manifold method in handling strong singularity a mesh deployment scheme is advised which can reproduce all singular locations of the crack with regard to the mesh corresponding to the four issues typical examples are given to demonstrate the effectiveness of the proposed schemes copyright 2013 john wiley sons ltd

limited magnitude error correcting gray codes for rank modulation we construct error correcting codes over permutations under the infinity metric which are also gray codes in the context of rank modulation i e are generated as simple circuits in the rotator graph these errors model limited magnitude or spike errors for which only single error detecting gray codes are currently known surprisingly the error correcting codes we construct achieve a better asymptotic rate than that of presently known constructions not having the gray property and exceed the gilbert varshamov bound additionally we present efficient ranking and unranking procedures as well as a decoding procedure that runs in linear time finally we also apply our methods to solve an outstanding issue with error detecting rank modulation gray codes also known in this context as snake in the box codes under a different metric the kendall tau metric in the group of permutations over an even number of elements s 2n where we provide asymptotically optimal codes

correcting charge constrained errors in the rank modulation scheme we investigate error correcting codes for a the rank modulation scheme with an application to flash memory devices in this scheme a set of n cells stores information in the permutation induced by the different charge levels of the individual cells the resulting scheme eliminates the need for discrete cell levels overcomes overshoot errors when programming cells a serious problem that reduces the writing speed and mitigates the problem of asymmetric errors in this paper we study the properties of error correcting codes for charge constrained errors in the rank modulation scheme in this error model the number of errors corresponds to the minimal number of adjacent transpositions required to change a given stored permutation to another erroneous one a distance measure known as kendall s distance we show bounds on the size of such codes and use metric embedding techniques to give constructions which translate a wealth of knowledge of codes in the lee metric to codes over permutations in kendall s metric specifically the one error correcting codes we construct are at least half the ball packing upper bound

perfect snake in the box codes for rank modulation for odd n the alternating group on n elements is generated by the permutations that jump an element from an odd position to position 1 we prove hamiltonicity of the associated directed cayley graph for all odd n neq 5 a result of rankin implies that the graph is not hamiltonian for n 5 this solves a problem arising in rank modulation schemes for flash memory our result disproves a conjecture of horovitz and etzion and proves another conjecture of yehezkeally and schwartz

constant weight gray codes for local rank modulation we consider the local rank modulation lrm scheme in which a sliding window going over a sequence of real valued variables induces a sequence of permutations lrm is a generalization of the rank modulation scheme which has been recently suggested as a way of storing information in flash memory we study constant weight gray codes for the lrm scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation we present a practical construction of codes with asymptotically optimal rate and weight asymptotically half the length thus having an asymptotically optimal charge difference between adjacent cells next we turn to examine the existence of optimal codes by specifically studying codes of weight 2 and 3 in the former case we upper bound the code efficiency proving that there are no such asymptotically optimal cyclic codes in contrast for the latter case we construct codes which are asymptotically optimal we conclude by providing necessary conditions for the existence of cyclic and cyclic optimal gray codes

a survey of combinatorial gray codes the term combinatorial gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified small way this notion generalizes the classical binary reflected gray code scheme for listing n bit binary numbers so that successive numbers differ in exactly one bit position as well as work in the 1960s and 1970s on minimal change listings for other combinatorial families including permutations and combinations the area of combinatorial gray codes was popularized by herbert wilf in his invited address at the siam conference on discrete mathematics in 1988 and his subsequent siam monograph combinatorial algorithms an update 1989 in which he posed some open problems and variations on the theme this resulted in much recent activity in the area and most of the problems posed by wilf are now solved in this paper we survey the area of combinatorial gray codes describe recent results variations and trends and highlight some open problems

ising n fold integrals as diagonals of rational functions and integrality of series expansions we show that the n fold integrals n of the magnetic susceptibility of the ising model as well as various other n fold integrals of the ising class or n fold integrals from enumerative combinatorics like lattice green functions correspond to a distinguished class of functions generalizing algebraic functions they are actually diagonals of rational functions as a consequence the power series expansions of the analytic at x 0 solutions of these linear differential equations derived from geometry are globally bounded which means that after just one rescaling of the expansion variable they can be cast into series expansions with integer coefficients we also give several results showing that the unique analytical solution of calabi yau odes and more generally picard fuchs linear odes with solutions of maximal weights are always diagonals of rational functions besides in a more enumerative combinatorics context generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions we finally address the question of the relations between the notion of integrality series with integer coefficients or more generally globally bounded series and the modularity of odes

complementarity problem arising from static growth of multiple cracks and mls based numerical manifold method abstract the full response of a brittle structure containing multiple cracks to loading under the servo control is of vital importance in the evaluation of properties of the structure during crack growth the fracture toughness condition at all the crack tips as well as the equilibrium condition should be obeyed leading to a nonlinear complementarity problem ncp the vector valued function in the ncp depends implicitly on the cracking increments which in turn determine the stress field the stress field can be obtained through solving a mixed variational problem since the degrees of freedom in the discrete variational problem vary with cracking not only in magnitude but also in number the jacobian matrix of the ncp is hard to compute and it cannot be expected to be solved by the newton methods that involve the calculation of jacobian matrices therefore a well scaled projection contraction algorithm is designed the proposed procedure is able to simulate growth of multiple cracks in a natural way allowing the crack tips to stop anywhere with no sensitivity to node configuration or cracking increments through the analysis of some examples that have been widely tested many interesting and profound phenomena are found which have never been revealed

a new family of explicit time integration methods for linear and non linear structural dynamics a new family of explicit single step time integration methods with controllable high frequency dissipation is presented for linear and non linear structural dynamic analyses the proposed methods are second order accurate and completely explicit with a diagonal mass matrix even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non linear structural dynamics stability and accuracy of the new explicit methods are analysed for the linear undamped damped cases furthermore the new methods are compared with other explicit methods

prediction of rank deficiency in partition of unity based methods with plane triangular or quadrilateral meshes in the partition of unity pu based methods the global approximation is built by multiplying a partition of unity by local approximations within this framework high order approximations are achieved by directly adopting high order polynomials as local approximations and therefore nodes along sides or inside elements which are usually adopted in the conventional finite element methods are no more required however the pu based approximation constructed in this way may suffer from rank deficiency due to the linear dependence of the global degrees of freedom in this paper the origin of the rank deficiency in the pu based approximation space is first dissected at an element level and then an approach to predict the rank deficiency for a mesh is proposed together with the principle of the increase of rank deficiency finally examples are investigated to validate the present approach the current work indicates such a fact that the rank deficiency is an unrelated issue to the nullity of the global matrix it can be resolved in its own manner

on vanishing coefficients of algebraic power series over fields of positive characteristic let k be a field of characteristic p 0 and let f t1 td be a power series in d variables with coefficients in k that is algebraic over the field of multivariate rational functions k t1 td we prove a generalization of both derksen s recent analogue of the skolem mahler lech theorem in positive characteristic and a classical theorem of christol by showing that the set of indices n1 nd d for which the coefficient of t 1 n 1 cdots t d n d in f t1 td is zero is a p automatic set applying this result to multivariate rational functions leads to interesting effective results concerning some diophantine equations related to s unit equations and more generally to the mordell lang theorem over fields of positive characteristic

numerical manifold space of hermitian form and application to kirchhoff s thin plate problems summary for second order problems where the behavior is described by second order partial differential equations the numerical manifold method nmm has gained great success because of difficulties in the construction of the h 2 regular lagrangian partition of unity subordinate to the finite element cover however few applications of the nmm have been found to fourth order problems such as kirchhoff s thin plate problems parallel to the finite element methods this study constructs the numerical manifold space of the hermitian form to solve fourth order problems from the minimum potential principle meanwhile the mixed primal formulation and the penalized formulation fitted to the nmm for kirchhoff s thin plate problems are derived the typical examples indicate that by the proposed procedures even those earliest developed elements in the finite element history such as zienkiewicz s plate element regain their vigor copyright 2013 john wiley sons ltd

rational points over finite fields for regular models of algebraic varieties of hodge type geq 1 let r be a discrete valuation ring of mixed characteristics 0 p with finite residue field k and fraction field k let k be a finite extension of k and let x be a regular proper and flat r scheme with generic fibre x k and special fibre x k assume that x k is geometrically connected and of hodge type geq 1 in positive degrees then we show that the number of k rational points of x satisfies the congruence x k equiv 1 mod k thanks to cite bbe07 we deduce such congruences from a vanishing theorem for the witt cohomology groups h q x k w so x k q for q 0 in our proof of this last result a key step is the construction of a trace morphism between the witt cohomologies of the special fibres of two flat regular r schemes x and y of the same dimension defined by a surjective projective morphism f y to x

constructions of snake in the box codes for rank modulation snake in the box code is a gray code which is capable of detecting a single error gray codes are important in the context of the rank modulation scheme which was suggested recently for representing information in flash memories for a gray code in this scheme the codewords are permutations two consecutive codewords are obtained using the push to the top operation and distance measure is defined on permutations in this paper the kendall s metric is used as the distance measure we present a general method for constructing such gray codes we apply the method recursively to obtain a snake of length m2n 1 2n 1 2n 1 m2n 1 for permutations of s2n 1 from a snake of length m2n 1 for permutations of s2n 1 thus we have lim n m2n 1 s2n 1 0 4338 improving on the previous known ratio of lim n 1 n using the general method we also present a direct construction this direct construction is based on necklaces and it might yield snakes of length 2n 1 2 2n 1 for permutations of s2n 1 the direct construction was applied successfully for s7 and s9 and hence lim n m2n 1 s2n 1 0 4743