discriminative feature selection for on line signature verification abstract on line handwritten signatures are collected as real time dynamical signals which are written on collective devices by users since individuals have different writing habits consistent and discriminative features should be selected to distinguish genuine signatures from forged signatures in this paper two methods which are based on full factorial experiment design and optimal orthogonal experiment design are proposed for selecting discriminative features among candidates to improve the robustness consistency of feature is analyzed at first and more consistent features are selected as candidates for discriminative feature selection to reduce the influences of fluctuations caused by internal and external writing environments changes before verification signatures are effectively aligned to their reference templates based on gaussian mixture model a modified dynamic time warping with signature curve constraint is presented for verification to improve the efficiency comprehensive experiments are implemented based on the data of the open access databases mcyt and svc2004 task2 experimental results verify the effectiveness and robustness of our proposed methods

on the bellman s principle of optimality abstract bellman s equation is widely used in solving stochastic optimal control problems in a variety of applications including investment planning scheduling problems and routing problems building on markov decision processes for stationary policies we present a new proof for bellman s equation of optimality our proof rests its case on the availability of an explicit model of the environment that embodies transition probabilities and associated costs

exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations we consider the problem of routing vehicles stationed at a central facility depot to supply customers with known demands in such a way as to minimize the total distance travelled the problem is referred to as the vehicle routing problem vrp and is a generalization of the multiple travelling salesman problem that has many practical applications we present tree search algorithms for the exact solution of the vrp incorporating lower bounds computed from i shortest spanning k degree centre tree k dct and ii q routes the final algorithms also include problem reduction and dominance tests computational results are presented for a number of problems derived from the literature the results show that the bounds derived from the q routes are superior to those from k dct and that vrps of up to about 25 customers can be solved exactly

the equivariant tamagawa number conjecture and modular symbols we show that for each elliptic curve e mathbb q with l e mathbb q 1 ne 0 there are infinitely many odd primes l and for each such l infinitely many abelian l extensions k mathbb q such that the l part of the equivariant tamagawa number conjecture holds for the pair h 1 e k 1 mathbb z text gal k mathbb q

legendre polynomials based feature extraction for online signature verification consistency analysis of feature combinations in this paper feature combinations associated with the most commonly used time functions related to the signing process are analyzed in order to provide some insight on their actual discriminative power for online signature verification a consistency factor is defined to quantify the discriminative power of these different feature combinations a fixed length representation of the time functions associated with the signatures based on legendre polynomials series expansions is proposed the expansion coefficients in these series are used as features to model the signatures two different signature styles namely western and chinese from a publicly available signature database are considered to evaluate the performance of the verification system two state of the art classifiers namely support vector machines and random forests are used in the verification experiments error rates comparable to the ones reported over the same signature datasets in a recent signature verification competition show the potential of the proposed approach the experimental results also show that there is a good correlation between the consistency factor and the verification errors suggesting that consistency values could be used to select the optimal feature combination highlightsa feature extraction approach based on legendre series representation of the time functions associated with the signatures is proposed a consistency factor is proposed to quantify the discriminative power of different combinations of the time functions the correlation between the proposed consistency factor and the verification performance of a feature combination is analyzed a recent signature database containing western and chinese signatures is used the verification performance is quantified based on log likelihood ratios

signature alignment based on gmm for on line signature verification on line handwritten signatures are collected as real time dynamical signals which are written on collective devices by users since writing environments are always changed fluctuations can be caused by signature size location and rotation angle which being various at each inputting signatures should be effectively aligned before verification which can diminish deviations caused by these fluctuations in this study we propose a method of signature alignment based on gaussian mixture model to obtain the best matching in verification a modified dynamic time warping with signature curve constraint is presented to improve the efficiency weight factors are dynamically assigned to features which depend on coefficient of variation to improve the robustness several experiments are implemente d on the open access on line signature databases mcyt and svc2004 task2 the best performances can be provided with equal error rates 2 15 and 2 63 respectively experimental results indicate the effectiveness and robustness of our proposed method signatures are aligned well to reference template based on gaussian mixture model before verification efficiency of verification is improved by modified dynamic time warping with signature curve constraint distance probability is presented to describe the dissimilarity between test signatures and references a strategy of dynamic weight factors being assigned to features depend on coefficient of variation

generalized stark formulae over function fields we establish formulae of stark type for the stickelberger elements in the function field setting our result generalizes a work of hayes and a conjecture of gross it is used to deduce a p adic version of rubin stark conjecture and burns conjecture

new hermite orthogonal polynomial kernel and combined kernels in support vector machine classifier support vector machine is a desired method for classification of different types of data but the main obstacle to using this method is the considerable reduction of classification speed upon increase in the size of problem in this paper a new kernel function is proposed for svm which is derived from hermite orthogonal polynomials this function improves classification accuracy as well as reduction in the number of support vectors and increases the classification speed the overall kernel performance has been evaluated on real world data sets from uci repository by the ten fold cross validation method the combinations of hermite function with common kernels are proposed in this paper experimental results reveal that the hermite chebyshev kernel which is obtained from combination of hermite and chebyshev kernel has the best performance in the number of support vectors and hermite gussian kernel that is produced from combination hermite and gussian kernel has the first rank in the error rate among all experimental kernels on the other hand the hermite proposed method has the least number of support vectors and best performance in the error rate in comparison with common kernels and lowest required time among all kernels a new kernel function has been proposed by using hermite orthogonal polynomial new combined kernels resulted by combining hermite and common kernels have been proposed the proposed methods have been compared with three common kernels on real and synthetic data sets hermite kernel function has the lowest required time for classification the proposed methods yield better error rate and they have the best support vectors reduction significantly

derived heights and generalized mazur tate regulators 2 algebraic preliminaries 4 2 1 notations and conventions 4 2 2 duality 5 2 2 1 local duality 5 2 2 2 global duality 6 2 3 assumptions 8 2 4 preliminary calculations 10

open loop routing of n arrivals to m parallel queues we consider the problem of routing n arrivals to m queues in parallel when no information other than the prior statistics are available for the decision process the work we present here differs from results in the literature in two significant ways 1 we address the nonstationary problem of open loop routing for n spl infin arrivals and 2 we do not decompose the problem into an allocation phase and a routing phase but look instead for an overall optimal policy exhaustive enumeration and dynamic programming turn out to be computationally infeasible approaches for realistic values of the parameters n and m examination of the necessary conditions for optimality as given by pontryagin s maximum principle leads to the formulation of a policy iteration algorithm convergence of the algorithm in a finite number of iterations as well as monotonicity results are established while only convergence to a local minimum is guaranteed extensive computational experimentation points to its near optimality some variants of the basic policy iteration algorithm are also discussed

p adic periods and modular symbols of elliptic curves of prime conductor under certain assumptions we prove a conjecture of mazur and tate describing a relation between the modular symbol attached to an elliptic curve with split multiplicative reduction atp and itsp adic period we generalize this relation to modular forms of weight 2 with coefficients not necessarily in

a novel formulation of orthogonal polynomial kernel functions for svm classifiers the gegenbauer family abstract orthogonal polynomial kernels have been recently introduced to enhance support vector machine classifiers by reducing their number of support vectors previous works have studied these kernels as isolated cases and discussed only particular aspects in this paper a novel formulation of orthogonal polynomial kernels that includes and improves previous proposals legendre chebyshev and hermite is presented two undesired effects that must be avoided in order to use orthogonal polynomial kernels are identified and resolved the annihilation and the explosion effects the proposed formulation is studied by means of introducing a new family of orthogonal polynomial kernels based on gegenbauer polynomials and comparing it against other kernels experimental results reveal that the gegenbauer family competes with the rbf kernel in accuracy while requiring fewer support vectors and overcomes other classical and orthogonal kernels

heegner points on mumford tate curves 1 shimura curves 417 2 heegner points 429 3 the regulator term 441 4 the conjecture 445 5 applications and re nements 447

on mordell weil groups and congruences between derivatives of twisted hasse weil l functions let a be an abelian variety defined over a number field k and let f be a finite galois extension of k let p be a prime number then under certain not too stringent conditions on a and f we compute explicitly the algebraic part of the p component of the equivariant tamagawa number of the pair h1 a f 1 z gal f k by comparing the result of this computation with the theorem of gross and zagier we are able to give the first verification of the p component of the equivariant tamagawa number conjecture for an abelian variety in the technically most demanding case in which the relevant mordell weil group has strictly positive rank and the relevant field extension is both non abelian and of degree divisible by p more generally our approach leads us to the formulation of certain precise families of conjectural p adic congruences between the values at s 1 of derivatives of the hasse weil l functions associated to twists of a normalised by a product of explicit equivariant regulators and periods and to explicit predictions concerning the galois structure of tate shafarevich groups in several interesting cases we provide theoretical and numerical evidence in support of these more general predictions

a center sliding bayesian binary classifier adopting orthogonal polynomials a center sliding bayesian design adopting orthogonal polynomials for binary pattern classification is studied in this paper essentially a bayesian weight solution is coupled with a center sliding scheme in feature space which provides an easy tuning capability for binary classification the proposed method is compared with several state of the art binary classifiers in terms of their solution forms decision thresholds and decision boundaries based on the center sliding bayesian framework a novel orthogonal polynomial classifier is subsequently developed the orthogonal polynomial classifier is evaluated using two representative orthogonal polynomials for feature mapping our experimental results show promising potential of the orthogonal polynomial classifier since it achieves both desired accuracy and computational efficiency highlightsproposed a center sliding bayesian classifier with deterministic solution proposed to adopt orthogonal polynomials for efficient feature expansion developed an easy tuning mechanism for the classification framework provided an extensive evaluation of the proposed classifier

congruences for critical values of higher derivatives of twisted hasse weil l functions let a be an abelian variety over a number field k and let f be a finite cyclic extension of k of p power degree for an odd prime p under certain technical hypotheses we obtain a reinterpretation of the equivariant tamagawa number conjecture etnc for a f k and p as an explicit family of p adic congruences involving values of derivatives of the hasse weil l functions of twists of a normalised by completely explicit twisted regulators this reinterpretation makes the etnc amenable to numerical verification and furthermore leads to explicit predictions which refine well known conjectures of mazur and tate

stickelberger elements and modular parametrizations of elliptic curves in the present paper we shall give evidence to support the claim conjecture i below and 1 3 that every elliptic curve a o which can be parametrized by modular functions admits a canonical modular parametrization whose properties can be related to intrinsic properties of a in particular we will see how such a parametrizat ion can be used to prove some rather pleasant integrality properties of stickelberger elements ad p adic l functions attached to a in addition if conjecture i is true then we can give an intrinsic characterization of the isomorphism class of a special elliptic curve in the q isogeny class of a distinguished by modular considerations for most of the paper we have opted for the concrete approach and defined modular parametrizations in terms of x i n definition 1 1 however to justify our view of these parametrizations as being canonical we begin here with a more intrinsic definition recall that shimura 19 chap 6 see w 1 of this paper has defined a compatible system of canonical models of modular curves xs ses where 5 p is a certain collection of open subgroups of the group gl 2 az over the finite adeles a i of q we define the adelic upper half plane to be the pro variety ll m xs and give the q structure induced by the s field of modular functions whose q expansions at the 0 cusp have coefficients in q a modular parametrization of a is a q morphism a which sends

sur la nature non cyclotomique des points d ordre fini des courbes elliptiques appendice par e kowalski et p michel