on weierstrass semigroups and the redundancy of improved geometric goppa codes improved geometric goppa codes have a smaller redundancy and the same bound on the minimum distance as ordinary algebraic geometry codes for an asymptotically good sequence of function fields we give a formula for the redundancy

the order bound on the minimum distance of the one point codes associated to the garcia stichtenoth tower garcia and stichtenoth discovered a tower of function fields that meets the drinfeld vladut bound on the ratio of the number of points to the genus for this tower pellikaan stichtenoth and torres derived a recursive description of the weierstrass semigroups associated to a tower of points on the associated curves in this correspondence a nonrecursive description of the semigroups is given and from this the enumeration of each of the semigroups is derived as well as its inverse this enables us to find an explicit formula for the order feng rao bound on the minimum distance of the associated one point codes

on the generalized feng rao numbers of numerical semigroups generated by intervals we give some general results concerning the computation of the generalized feng rao numbers of numerical semigroups in the case of a numerical semigroup generated by an interval a formula for the rth feng rao number is obtained

a note on numerical semigroups this correspondence is a short extension to the previous article bras amoroacutes 2004 in that work some results were given on one point codes related to numerical semigroups one of the crucial concepts in the discussion was the so called nu sequence of a semigroup this sequence has been used in the literature to derive bounds on the minimum distance as well as for defining improvements on the dimension of existing codes it was proven in that work that the nu sequence of a semigroup uniquely determines it here this result is extended to another object related to a semigroup the oplus operation this operation has also been important in the literature for defining other classes of improved codes it is also proven here that although the infinite set of values in the nu sequence resp the oplus values uniquely determines the associated semigroup no finite part of it can determine it because it is shared by infinitely many semigroups in that reference the proof of the fact that the nu sequence of a numerical semigroup uniquely determines it is constructive the result here presented shows that however that construction can not be performed as an algorithm with finite input

estimation of non normalized statistical models by score matching one often wants to estimate statistical models where the probability density function is known only up to a multiplicative normalization constant typically one then has to resort to markov chain monte carlo methods or approximations of the normalization constant here we propose that such models can be estimated by minimizing the expected squared distance between the gradient of the log density given by the model and the gradient of the log density of the observed data while the estimation of the gradient of log density function is in principle a very difficult non parametric problem we prove a surprising result that gives a simple formula for this objective function the density function of the observed data does not appear in this formula which simplifies to a sample average of a sum of some derivatives of the log density given by the model the validity of the method is demonstrated on multivariate gaussian and independent component analysis models and by estimating an overcomplete filter set for natural image data

the weight hierarchy of some reducible cyclic codes the generalized hamming weights ghws of linear codes are fundamental parameters the knowledge of which is of great interest in many applications however to determine the ghws of linear codes is difficult in general in this paper we study the ghws for a family of reducible cyclic codes and obtain the complete weight hierarchy in several cases this is achieved by extending the idea of yang et al into higher dimension and by employing some interesting combinatorial arguments it shall be noted that these cyclic codes may have arbitrary number of nonzeros

network generalized hamming weight in this work we extend the notion of generalized hamming weight for classical linear block codes to linear network codes by introducing the network generalized hamming weight nghw for a given network with respect to a fixed linear network code the basic properties of nghw are studied we further show that nghw can be used as a tool to characterize the security performance of a linear network code on a wiretap network we also introduce the notion of network maximum distance separable code nmds code by extending the notion of maximum distance separable code in classical algebraic coding theory we prove that nmds codes play an important role in minimizing the information that an eavesdropper can obtain from the network

the minimum distance of codes in an array coming from telescopic semigroups the concept of an error correcting array gives a new bound on the minimum distance of linear codes and a decoding algorithm which decodes up to half this bound this gives a unified point of view which explains several improvements on the minimum distance of algebraic geometric codes moreover it is explained in terms of linear algebra and the theory of semigroups only

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

list decoding from erasures bounds and code constructions we consider the problem of list decoding from erasures we establish lower and upper bounds on the rate of a binary linear code that can be list decoded with list size l when up to a fraction p of its symbols are adversarially erased such bounds already exist in the literature albeit under the label of generalized hamming weights and we make their connection to list decoding from erasures explicit our bounds show that in the limit of large l the rate of such a code approaches the capacity 1 p of the erasure channel such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate spl omega spl epsiv sup 2 log 1 spl epsiv that can be efficiently list decoded using lists of size o 1 spl epsiv when an adversarially chosen 1 spl epsiv fraction of symbols are erased for arbitrary spl epsiv 0 this improves previous results in this vein which achieved a rate of spl omega spl epsiv sup 3 log 1 spl epsiv

some polynomials over q t and their galois groups examples of polynomials with galois group over q t corresponding to every transitive group through degree eight are calculated constructively demonstrating the existence of an infinity of extensions with each galois group over q through degree eight the methods used which for the most part have not appeared in print are briefly discussed

levels of positive definite ternary quadratic forms the level n and squarefree character q of a positive definite ternary quadratic form are defined so that its associated modular form has level n and character xq we define a collection of correspondences between classes of quadratic forms having the same level and different discriminants this makes practical a method for finding representatives of all classes of ternary forms having a given level we also give a formula for the number of genera of ternary forms with a given level and character

acute semigroups the order bound on the minimum distance and the feng rao improvements we introduce a new class of numerical semigroups which we call the class of acute semigroups and we prove that they generalize symmetric and pseudosymmetric numerical semigroups arf numerical semigroups and the semigroups generated by an interval for a numerical semigroup spl lambda spl lambda sub 0 i spl nu sub i 1 for all i spl ges m we prove that the only numerical semigroups for which the sequence spl nu sub i is always nondecreasing are ordinary numerical semigroups furthermore we show that a semigroup can be uniquely determined by its sequence spl nu sub i

on the embedding problem for 2 s_4 representations let 2 s 4 denote the double cover of s 4 corresponding to the element in h 2 s 4 z 2z where transpositions lift to elements of order 2 and the product of two disjoint transpositions to elements of order 4 given an elliptic curve e let e 2 denote its 2 torsion points under some conditions on e elements in h 1 gal q e 2 0 correspond to galois extensions n of q with galois group isomorphic to s 4 in this work we give an interpretation of the addition law on such fields and prove that the obstruction for n having a galois extension n with gal n q 2 s 4 gives a homomorphism s 4 h 1 gal q e 2 h 2 gal q z 2z as a corollary we can prove if e has conductor divisible by few primes and high rank the existence of 2 dimensional representations of the absolute galois group of q attached to e and use them in some examples to construct 3 2 modular forms mapping via the shimura map to the modular form of weight 2 attached to e

the second feng rao number for codes coming from inductive semigroups the second feng rao number of every inductive numerical semigroup is explicitly computed this number determines the asymptotical behavior of the order bound for the second hamming weight of one point algebraic geometry codes in particular this result is applied for the codes defined by asymptotically good towers of function fields whose weierstrass semigroups are inductive in addition some properties of inductive numerical semigroups are studied the involved apery sets are computed in a recursive way and some tests to check whether given numerical semigroups are inductive or not are provided

phase coupling estimation from multivariate phase statistics coupled oscillators are prevalent throughout the physical world dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real world systems and are compelling models of neural systems however these formulations usually deal with the forward problem simulating a system from known coupling parameters here we provide a solution to the inverse problem determining the coupling parameters from measurements starting from the dynamic equations of a system of symmetrically coupled phase oscillators given by a nonlinear langevin equation we derive the corresponding equilibrium distribution this formulation leads us to the maximum entropy distribution that captures pairwise phase relationships to solve the inverse problem for this distribution we derive a closed form solution for estimating the phase coupling parameters from observed phase statistics through simulations we show that the algorithm performs well in high dimensions d 100 and in cases with limited data as few as 100 samples per dimension in addition we derive a regularized solution to the estimation and show that the resulting procedure improves performance when only a limited amount of data is available because the distribution serves as the unique maximum entropy solution for pairwise phase statistics phase coupling estimation can be broadly applied in any situation where phase measurements are made under the physical interpretation the model may be used for inferring coupling relationships within cortical networks

learning intermediate level representations of form and motion from natural movies we present a model of intermediate level visual representation that is based on learning invariances from movies of the natural environment the model is composed of two stages of processing an early feature representation layer and a second layer in which invariances are explicitly represented invariances are learned as the result of factoring apart the temporally stable and dynamic components embedded in the early feature representation the structure contained in these components is made explicit in the activities of second layer units that capture invariances in both form and motion when trained on natural movies the first layer produces a factorization or separation of image content into a temporally persistent part representing local edge structure and a dynamic part representing local motion structure consistent with known response properties in early visual cortex area v1 this factorization linearizes statistical dependencies among the first layer units making them learnable by the second layer the second layer units are split into two populations according to the factorization in the first layer the form selective units receive their input from the temporally persistent part local edge structure and after training result in a diverse set of higher order shape features consisting of extended contours multiscale edges textures and texture boundaries the motion selective units receive their input from the dynamic part local motion structure and after training result in a representation of image translation over different spatial scales and directions in addition to more complex deformations these representations provide a rich description of dynamic natural images and testable hypotheses regarding intermediate level representation in visual cortex

on the weight hierarchy of geometric goppa codes the weight hierarchy of a linear code is the set of generalized hamming weights of the code in the paper the authors consider geometric goppa codes and provide a lower bound on their generalized hamming weights similar to goppa s lower bound on their minimum distance in the particular case of hermitian codes exact results on the second and third generalized hamming weights are given for any m except a few cases where m is a parameter that governs the dimension of these codes in many instances the authors are able to provide considerably more information on their generalized hamming weights an upper bound relating the generalized hamming weights of hermitian codes to the pole numbers at a special point on the curve is also provided similar results are given in the case of codes from some subfields of the hermitian function fields which are also maximal finally a nontrivial family of codes is also presented whose weight hierarchy is completely determined

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

on the parameters of algebraic geometry codes related to arf semigroups we compute the order or feng rao 1994 bound on the minimum distance of one point algebraic geometry codes c sub spl omega p spl rho sub t q when the weierstrass semigroup at the point q is an arf 91949 semigroup the results developed to that purpose also provide the dimension of the improved geometric goppa codes related to these c sub spl omega p spl rho sub t q

new lower bounds on the generalized hamming weights of ag codes a sharp upper bound for the maximum integer not belonging to an ideal of a numerical semigroup is given and the ideals attaining this bound are characterized then the result is used through the so called feng rao numbers to bound the generalized hamming weights of algebraic geometry codes this is further developed for hermitian codes and the codes on one of the garcia stichtenoth towers as well as for some more general families

the fisher bingham distribution on the sphere abstract the fisher distribution is the analogue on the sphere of the isotropic bivariate normal distribution in the plane the purpose of this paper is to propose and analyze a spherical analogue of the general bivariate normal distribution estimation hypothesis testing and confidence regions are also discussed author

sampling properties of the spectrum and coherency of sequences of action potentials the spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes this article begins with a review of these quantities their interpretation and how they may be estimated a discussion of how to assess the statistical significance of features in these measures is included in addition new work is presented that builds on the framework established in the review section this work investigates how the estimates and their error bars are modified by finite sample sizes finite sample corrections are derived based on a doubly stochastic inhomogeneous poisson process model in which the rate functions are drawn from a low variance gaussian process it is found that in contrast to continuous processes the variance of the estimators cannot be reduced by smoothing beyond a scale set by the number of point events in the interval alternatively the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented corresponding to the detection of a periodic modulation of the underlying rate this work demonstrates that a known statistical test applicable to continuous processes applies with little modification to point process spectra and is of utility in studying a point process driven by a continuous stimulus although the material discussed is of general applicability to point processes attention will be confined to sequences of neuronal action potentials spike trains the motivation for this work

protein bioinformatics and mixtures of bivariate von mises distributions for angular data summary a fundamental problem in bioinformatics is to characterize the secondary structure of a protein which has traditionally been carried out by examining a scatterplot ramachandran plot of the conformational angles we examine two natural bivariate von mises distributions referred to as sine and cosine models which have five parameters and for concentrated data tend to a bivariate normal distribution these are analyzed and their main properties derived conditions on the parameters are established which result in bimodal behavior for the joint density and the marginal distribution and we note an interesting situation in which the joint density is bimodal but the marginal distributions are unimodal we carry out comparisons of the two models and it is seen that the cosine model may be preferred mixture distributions of the cosine model are fitted to two representative protein datasets using the expectation maximization algorithm which results in an objective partition of the scatterplot into a number of components our results are consistent with empirical observations new insights are discussed

on the weight hierarchy of codes coming from semigroups with two generators the weight hierarchy of one point algebraic geometry codes can be estimated by means of the generalized order bounds which are described in terms of a certain weierstrass semigroup the asymptotical behavior of such bounds for r 2 differs from that of the classical feng rao distance r 1 by the so called feng rao numbers this paper is addressed to compute the feng rao numbers for numerical semigroups of embedding dimension two with two generators obtaining a closed simple formula for the general case by using numerical semigroup techniques these involve the computation of the apery set with respect to an integer of the semigroups under consideration the formula obtained is applied to lower bounding the generalized hamming weights improving the bound given by kirfel and pellikaan in terms of the classical feng rao distance we also compare our bound with a modification of the griesmer bound improving this one in many cases

on semigroups generated by two consecutive integers and improved hermitian codes analysis of the berlekamp massey sakata algorithm for decoding one point codes leads to two methods for improving code rate one method due to feng and rao removes parity checks that may be recovered by their majority voting algorithm the second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic in this work formulae are given for the redundancies of hermitian codes optimized with respect to these criteria as well as the formula for the order bound on the minimum distance the results proceed from an analysis of numerical semigroups generated by two consecutive integers

a note on hermitian codes over gf q sup 2 properties of codes defined by goppa s algebraic geometric method using hermitian curves are discussed generator and parity check matrices for such codes are derived explicitly results concerning the minimum distance and the weight distribution of the codes are provided