the dirichlet cauchy problem for nonlinear hyperbolic equations in a domain with edges abstract we study the dirichlet cauchy problem for nonlinear hyperbolic equation of second order in a domain with edges the aim of this paper is to prove the regularity of solution in weighted sobolev spaces

thermal effects in a two dimensional hybrid elastic structure in this paper we consider a two dimensional hybrid thermo elastic structure consisting of a thermo elastic plate which has a beam attached to its free end we show that the initial boundary value problem for the interactive system of partial differential equations which take account of the mechanical strains stresses and the thermal stresses in the plate and the beam can be associated with a uniformly bounded evolution operator it turns out that the interplay of parabolic dynamics due to the thermal effects in the hybrid structure and the hyperbolic dynamics associated with the elasticity of the structure yields analyticity for the entire system this result yields solvability for the problem under optimal initial freedom of the displacement velocity and temperature in the plate and the beam while uniform stability is readily available

enhanced local texture feature sets for face recognition under difficult lighting conditions making recognition more reliable under uncontrolled lighting conditions is one of the most important challenges for practical face recognition systems we tackle this by combining the strengths of robust illumination normalization local texture based face representations distance transform based matching kernel based feature extraction and multiple feature fusion specifically we make three main contributions 1 we present a simple and efficient preprocessing chain that eliminates most of the effects of changing illumination while still preserving the essential appearance details that are needed for recognition 2 we introduce local ternary patterns ltp a generalization of the local binary pattern lbp local texture descriptor that is more discriminant and less sensitive to noise in uniform regions and we show that replacing comparisons based on local spatial histograms with a distance transform based similarity metric further improves the performance of lbp ltp based face recognition and 3 we further improve robustness by adding kernel principal component analysis pca feature extraction and incorporating rich local appearance cues from two complementary sources gabor wavelets and lbp showing that the combination is considerably more accurate than either feature set alone the resulting method provides state of the art performance on three data sets that are widely used for testing recognition under difficult illumination conditions extended yale b cas peal r1 and face recognition grand challenge version 2 experiment 4 frgc 204 for example on the challenging frgc 204 data set it halves the error rate relative to previously published methods achieving a face verification rate of 88 1 at 0 1 false accept rate further experiments show that our preprocessing method outperforms several existing preprocessors for a range of feature sets data sets and lighting conditions

fourth order time stepping for stiff pdes a modification of the exponential time differencing fourth order runge kutta method for solving stiff nonlinear pdes is presented that solves the problem of numerical instability in the scheme as proposed by cox and matthews and generalizes the method to nondiagonal operators a comparison is made of the performance of this modified exponential time differencing etd scheme against the competing methods of implicit explicit differencing integrating factors time splitting and fornberg and driscoll s sliders for the kdv kuramoto sivashinsky burgers and allen cahn equations in one space dimension implementation of the method is illustrated by short matlab programs for two of the equations it is found that for these applications with fixed time steps the modified etd scheme is the best

blow up for quasi linear wave equations in three space dimensions we consider equations of the form u phi x t u u u 1a for a function u u x 1 x n t u x t here denotes the d alembertian square frac partial 2 partial t 2 vartriangle 1b and u represents the vector of first derivatives u that of second derivatives of u with respect to the x k and t on linearizing 1a shall go over into the classical wave equation u 0 this means that and its first derivatives with respect to u u u shall vanish for u u u 0

symmetric and arbitrarily high order birkhoff hermite time integrators and their long time behaviour for solving nonlinear klein gordon equations abstract the klein gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering its computation represents a major challenge the main theme of this paper is the construction of symmetric and arbitrarily high order time integrators for the nonlinear klein gordon equation by integrating birkhoff hermite interpolation polynomials to this end under the assumption of periodic boundary conditions we begin with the formulation of the nonlinear klein gordon equation as an abstract second order ordinary differential equation ode and its operator variation of constants formula we then derive a symmetric and arbitrarily high order birkhoff hermite time integration formula for the nonlinear abstract ode accordingly the stability convergence and long time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi definite matrix subject to suitable temporal and spatial smoothness a remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for pdes in the literature numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches

a non dominance based online stopping criterion for multi objective evolutionary algorithms a non dominance criterion based metric that tracks the growth of an archive of non dominated solutions over a few generations is proposed to generate a convergence curve for multi objective evolutionary algorithms moeas it was observed that similar to single objective optimization problems there were significant advances toward the pareto optimal front in the early phase of evolution while relatively smaller improvements were obtained as the population matured this convergence curve was used to terminate the moea search to obtain a good trade off between the computational cost and the quality of the solutions two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of the proposed metric

a statistical approach to texture classification from single images we investigate texture classification from single images obtained under unknown viewpoint and illumination a statistical approach is developed where textures are modelled by the joint probability distribution of filter responses this distribution is represented by the frequency histogram of filter response cluster centres textons recognition proceeds from single uncalibrated images and the novelty here is that rotationally invariant filters are used and the filter response space is low dimensional classification performance is compared with the filter banks and methods of leung and malik ijcv 2001 schmid cvpr 2001 and cula and dana ijcv 2004 and it is demonstrated that superior performance is achieved here classification results are presented for all 61 materials in the columbia utrecht texture database we also discuss the effects of various parameters on our classification algorithm such as the choice of filter bank and rotational invariance the size of the texton dictionary as well as the number of training images used finally we present a method of reliably measuring relative orientation co occurrence statistics in a rotationally invariant manner and discuss whether incorporating such information can enhance the classifier s performance

modifications of real code genetic algorithm for global optimization a series of modifications to the real coded genetic algorithm for the task of locating the global minimum of multidimensional functions are presented here these modifications include a new stopping rule a novel mutation mechanism and a periodically application of a local search procedure the proposed modifications are tested on a series of optimization problems and the results are reported

global classical solutions of nonlinear wave equations is a formally selfadjoint positive elliptic operator and f is a real c2 function with non negative primitive function we treat both the homogeneous initialboundary value problem over ir x f2 for a smooth open set 2clr and the cauchy problem over ir x 1r for the initial boundary value problem we show that any strong solution of 0 1 known to exist according to heinz and yon wahl 4 if 2rn f j u2 o lul 2j j 0 1 u oo

l c ℝn decay of classical solutions for nonlinear schrodinger equations on etudie le probleme aux valeurs initiales pour l equation de schrodinger non lineaire iu t u f u 2 u u o x x x r n t r 1 n 11 sous de bonnes hypotheses de regularite sur f et et des conditions de croissance et de signe sur f on montre que les normes maximum des solutions decroissent quand t au meme taux que celles des solutions de l equation de schrodinger libre

global existence and blow up of solutions for higher order viscoelastic wave equation with a nonlinear source term abstract the initial boundary value problem for some nonlinear higher order viscoelastic wave equation with a nonlinear source term in a bounded domain is studied the existence of global weak solutions for this problem is established by using the galerkin method meanwhile under suitable conditions on relaxation function g and the positive initial energy as well as non positive initial energy it is proved that the solution blows up in the finite time and the lifespan estimates of solutions are also given

a markov chain analysis of genetic algorithms with power of 2 cardinality alphabets abstract in this paper we model the run time behavior of gas using higher cardinality representations as markov chains define the states of the markov chain and derive the transition probabilities of the corresponding transition matrix we analyze the behavior of this chain and obtain bounds on its convergence rate and bounds on the runtime complexity of the ga we further investigate the effects of using binary versus higher cardinality representation of a search space

analysis and comparison of numerical methods for the klein gordon equation in the nonrelativistic limit regime we analyze rigourously error estimates and compare numerically temporal spatial resolution of various numerical methods for solving the klein gordon kg equation in the nonrelativistic limit regime involving a small parameter 0 varepsilon ll 1 which is inversely proportional to the speed of light in this regime the solution is highly oscillating in time i e there are propagating waves with wavelength of o varepsilon 2 and o 1 in time and space respectively we begin with four frequently used finite difference time domain fdtd methods and obtain their rigorous error estimates in the nonrelativistic limit regime by paying particularly attention to how error bounds depend explicitly on mesh size h and time step as well as the small parameter varepsilon based on the error bounds in order to compute correct solutions when 0 varepsilon ll1 the four fdtd methods share the same varepsilon scalability tau o varepsilon 3 then we propose new numerical methods by using either fourier pseudospectral or finite difference approximation for spatial derivatives combined with the gautschi type exponential integrator for temporal derivatives to discretize the kg equation the new methods are unconditionally stable and their varepsilon scalability is improved to o 1 and tau o varepsilon 2 for linear and nonlinear kg equations respectively when 0 varepsilon ll1 numerical results are reported to support our error estimates

a filon type asymptotic approach to solving highly oscillatory second order initial value problems abstract in this paper we analyze and design filon type asymptotic methods for solving highly oscillatory second order initial value problems q t mq t f t q t q t where m is a non singular and diagonalizable matrix having large eigenvalues and m 1 we first derive filon type asymptotic methods for highly oscillatory linear systems and then extend the methods to highly oscillatory nonlinear systems the integrators are a blend of the existing filon type methods and asymptotic methods based on the variation of constants formula it is shown that the new integrators are convergent and the accuracy of the new integrators is improved as m grows large this point is significant and powerful for effectively dealing with highly oscillatory systems numerical experiments are carried out and the numerical results show the advantage and efficiency of our new integrators as compared with existing numerical methods for highly oscillatory problems from the scientific literature

on space time means and strong global solutions of nonlinear hyperbolic equations on demontre l existence de solutions globales appartenant a l loc r 2 l 2 2 r n pour des equations non lineaires de la forme t u u b x d u f u 0 t x r r n u 0 x 0 x t u 0 x 1 x x r n

convergence criteria for genetic algorithms in this paper we discuss convergence properties for genetic algorithms by looking at the effect of mutation on convergence we show that by running the genetic algorithm for a sufficiently long time we can guarantee convergence to a global optimum with any specified level of confidence we obtain an upper bound for the number of iterations necessary to ensure this which improves previous results our upper bound decreases as the population size increases we produce examples to show that in some cases this upper bound is asymptotically optimal for large population sizes the final section discusses implications of these results for optimal coding of genetic algorithms

conservation of energy momentum and actions in numerical discretizations of non linear wave equations for classes of symplectic and symmetric time stepping methods trigonometric integrators and the stormer verlet or leapfrog method applied to spectral semi discretizations of semilinear wave equations in a weakly non linear setting it is shown that energy momentum and all harmonic actions are approximately preserved over long times for the case of interest where the cfl number is not a small parameter such results are outside the reach of standard backward error analysis here they are instead obtained via a modulated fourier expansion in time

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

classifying non uniformly sampled vector valued curves we propose a novel means of classifying vector valued curves using functional principal components this uses cross validation to select curve components the degree of smoothing and scores associated with the best classification performance our approach is well suited to data generated by sensors of different modalities and time varying sampling frequencies experimental comparisons show this approach has significant advantages over conventional techniques using non uniformly sampled data our approach also generates novel forms of derivative analysis a widely used technique for classifying spectral functions from contaminated data

a gautschi type method for oscillatory second order differential equations we study a numerical method for second order differential equations in which high frequency oscillations are generated by a linear part for example semilinear wave equations are of this type the numerical scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly we prove that the method admits second order error bounds which are independent of the product of the step size with the frequencies our analysis also provides new insight into the m ollified impulse method of garcia archilla sanz serna and skeel we include results of numerical experiments with the sine gordon equation

exponential time differencing for stiff systems we develop a class of numerical methods for stiff systems based on the method of exponential time differencing we describe schemes with second and higher order accuracy introduce new runge kutta versions of these schemes and extend the method to show how it may be applied to systems whose linear part is nondiagonal we test the method against other common schemes including integrating factor and linearly implicit methods and show how it is more accurate in a number of applications we apply the method to both dissipative and dispersive partial differential equations after illustrating its behavior using forced ordinary differential equations with stiff linear parts

data driven techniques for smoothing histograms of local binary patterns local binary pattern histograms have proved very successful texture descriptors despite this success the description procedure bears some drawbacks that are still lacking solutions in the literature one of the problems arises when the number of extractable local patterns reduces while their dimension increases rendering the output histogram descriptions sparse and unstable finally showing up as a reduced recognition rate a smoothing method based on kernel density estimation was recently proposed as a means to tackle the aforementioned problem a constituent part of the method is to determine how much to smooth a histogram previously this was solved via trial and error in a problem specific manner in this paper the goal is to present data driven methods to determine this smoothing automatically in the end we present unsupervised and supervised methods for the given task and validate their performance with a representative set of local binary pattern variants in texture analysis problems covering material categorization and face recognition highlightsthis paper proposes data driven techniques for smoothing lbp histograms the proposed smoothing techniques cover unsupervised and supervised variants the techniques are evaluated on material categorization and face recognition histogram smoothing is beneficial especially in small sample size scenarios

on sor waveform relaxation methods waveform relaxation is a numerical method for solving large scale systems of ordinary differential equations on parallel computers it differs from standard iterative methods in that it computes the solution on many time levels or along a continuous time interval simultaneously this paper deals with the acceleration of the standard waveform relaxation method by successive overrelaxation sor techniques in particular different sor acceleration schemes based on multiplication with a scalar parameter or convolution with a time dependent function are described and theoretically analyzed the theory is applied to a one dimensional and two dimensional model problem and checked against results obtained by numerical experiments

on nonparametric multivariate binary discrimination aitchison aitken 1976 introduced a novel and ingenious nonparametric method for estimating probabilities in a multidimensional binary space the technique is designed for use in multivariate binary discrimination their estimator depends crucially on an unknown smoothing parameter a and aitchison aitken proposed a maximum likelihood method for determining a from the sample unfortunately this leads to an adaptive estimator which can behave very erratically when there are a number of empty or near empty cells present we demonstrate this both theoretically and by example to overcome these difficulties we introduce another method of estimating a which is designed to minimize a global function of the mean squared error

on error bounds for the gautschi type exponential integrator applied to oscillatory second order differential equations this paper studies a numerical method for second order oscillatory differential equations in which high frequency oscillations are generated by a linear time and or solution dependent part for constant linear part it is known that the method allows second order error bounds independent of the product of the step size with the frequencies and is therefore a long time step method most real world problems are not of that kind and it is important to study more general equations the analysis in this paper shows that one obtains second order error bounds even in the case of a time and or solution dependent linear part if the matrix is evaluated at averaged positions

a stopping criterion for multi objective optimization evolutionary algorithms this paper puts forward a comprehensive study of the design of global stopping criteria for multi objective optimization in this study we propose a global stopping criterion which is terms as mgbm after the authors surnames mgbm combines a novel progress indicator called mutual domination rate mdr indicator with a simplified kalman filter which is used for evidence gathering purposes the mdr indicator which is also introduced is a special purpose progress indicator designed for the purpose of stopping a multi objective optimization as part of the paper we describe the criterion from a theoretical perspective and examine its performance on a number of test problems we also compare this method with similar approaches to the issue the results of these experiments suggest that mgbm is a valid and accurate approach

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

a remark on the equation of a vibrating plate on considere les equations de von karman decrivant une plaque vibrante a bord encastree ou completement libre on obtient dans les deux cas une solution classique unique on utilise un ensemble d equations integrales obtenues a partir de la formule des variations des constantes

long time energy conservation of numerical methods for oscillatory differential equations we consider second order differential systems where high frequency oscillations are generated by a linear part we present a frequency expansion of the solution and we discuss two invariants of the system that determine the coefficients of the frequency expansion these invariants are related to the total energy and the oscillatory harmonic energy of the original system for the numerical solution we study a class of symmetric methods that discretize the linear part without error we are interested in the case where the product of the step size with the highest frequency can be large in the sense of backward error analysis we represent the numerical solution by a frequency expansion where the coefficients are the solution of a modified system this allows us to prove the near conservation of the total and the oscillatory energy over very long time intervals

the global cauchy problem for the critical non linear wave equation abstract we study the global cauchy problem for the non linear wave equation p 1 0 for the critical value p n 2 n 2 in space dimension n 3 we identify a weak space time integrability property stip of the solutions and prove that it is sufficient to ensure the uniqueness of weak solutions the global existence of finite energy solutions with the naturally associated stip and the global existence of regular solutions with some n dependent restrictions on the regularity for spherically symmetric solutions we prove that the previous crucial stip follows from the morawetz inequality actually in a much stronger form than necessary thereby proving that all the previous results hold in the spherically symmetric case

new stopping criterion for genetic algorithms abstract genetic algorithms have been successfully applied in a wide variety of problems although widely used there are few theoretical guidelines for determining when to terminate the search one result by aytug and koehler provides a loose bound on the number of ga generations needed to see all populations and hence an optimal solution with a specified probability in this paper we derive a tighter bound this new bound is on the number of iterations required to achieve a level of confidence to guarantee that a genetic algorithm has seen all strings and hence an optimal solution

subset selection in multiple linear regression models a hybrid of genetic and simulated annealing algorithms the question of variable selection in a multiple linear regression model is a major open research topic in statistics the subset selection problem in multiple linear regression deals with the selection of a minimal subset of input variables without loss of explanatory power in this paper we adapt the genetic and simulated annealing algorithms for variable selection in multiple linear regression the performance of this hybrid heuristic method is compared to those obtained by forward selection backward elimination and classical genetic algorithm search a comparative analysis on the literature data sets and simulation data shows that our hybrid heuristic method may suggest efficient alternative to traditional subset selection methods for the variable selection problem in multiple linear regression models

an application of chain code based local descriptor and its extension to face recognition local descriptors are widely used technique of feature extraction to obtain information about both local and global properties of an object here we discuss an application of the chain code based local descriptor to face recognition by focusing on various datasets and considering different variants of this description method we augment the generic form of the descriptor by adding a possibility of grouping pixels into blocks i e effectively describing larger neighborhoods the results of experiments show the efficiency of the approach we demonstrate that the obtained results are comparable or even better than those delivered by other important algorithms in the class of methods based on the bag of visual words paradigm an extension of chain code based local descriptor ccbld is proposed ccbld is applied to face recognition task bag of visual words paradigm is realized through the dictionary of chain codes test results show that ccbld is comparable or outperforms other local descriptors the approach is tested using cas peal colorferet fg net and other datasets

genetic algorithm for constrained global optimization in continuous variables we present a stochastic global optimization algorithm referred to as a genetic algorithm ga for solving constrained optimization problems over a compact search domain it is a real coded ga that converges in probability to the optimal solution the constraints are treated through a repair operator a specific repair operator is included for linear inequality constraints

spectral methods for partial differential equations in irregular domains the spectral smoothed boundary method in this paper we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no flux boundary conditions the idea is to embed the domain into a box and use a smoothing term to encode the boundary conditions into a modified equation that can be approached by standard spectral methods the main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via fast fourier transform routines we discuss several examples of practical interest and test the results against standard numerical methods

finite difference calculus invariant structure of a class of algorithms for the nonlinear klein gordon equation in a previous work the authors have presented a formalism for deriving systematically invariant symmetric finite difference algorithms for nonlinear evolution differential equations that admit conserved quantities this formalism is herein cast in the context of exact finite difference calculus the algorithms obtained from the proposed formalism are shown to derive exactly from discrete scalar potential functions using finite difference calculus in the same sense as that of the corresponding differential equation being derivable from its associated energy function a conserved quantity a clear ramification of this result is that the derived algorithms preserve certain discrete invariant quantities which are the consistent counterpart of the invariant quantities in the continuous case results on the nonlinear stability of a class of algorithms that are derived using the proposed formalism and that preserve energy or linear momentum are discussed in the context of finite difference calculus some

a hybrid genetic algorithm with the baldwin effect here we present a new hybrid genetic algorithm hga with the baldwin effect in the hga a local search is employed to change the fitness of individuals but the acquired improvements do not change the individual itself this local search step exploits the baldwin effect some numerical applications show that this algorithm can yield the global optimum more efficiently than commonly used hgas a theorem is presented that guarantees the convergence in probability of the new hga

a general steady state distribution based stopping criteria for finite length genetic algorithms we propose two general stopping criteria for finite length simple genetic algorithms based on steady state distributions and empirically investigate the impact of mutation rate string length crossover rate and population size on their convergence our first stopping criterion is based on the second largest eigenvalue of the genetic algorithm transition matrix and the second stopping criterion is based on minorization conditions

the effect of multiple optima on the simple ga run time complexity genetic algorithms are stochastic search algorithms that have been applied to optimization problems in this paper we analyze the run time complexity of a genetic algorithm when we are interested in one of a set of distinguished solutions one such case occurs when multiple optima exist we define the worst case scenario and derive a probabilistic worst case bound on the number of iterations required to find one of these multiple solutions of interest

an efficient high order explicit scheme for solving hamiltonian nonlinear wave equations in this work we propose and analyze a novel high order explicit scheme for efficiently solving hamiltonian nonlinear wave equations the new explicit scheme is based on the blend of a fourth order finite difference scheme for spatial discretization and a multidimensional extended runge kutta nystrom erkn method for time integration respectively the conservation law of the semi discrete energy is established the stability and convergence of the semidiscretization are examined the results of numerical experiments show that the blend of the finite difference approximation and multidimensional erkn method gives an efficient high order explicit scheme for hamiltonian nonlinear wave equations in comparison with some existing methods

arbitrarily high order time stepping schemes based on the operator spectrum theory for high dimensional nonlinear klein gordon equations abstract in this paper we explore arbitrarily high order lagrange collocation type time stepping schemes for effectively solving high dimensional nonlinear klein gordon equations with different boundary conditions we begin with one dimensional periodic boundary problems and first formulate an abstract ordinary differential equation ode on a suitable infinity dimensional function space based on the operator spectrum theory we then introduce an operator variation of constants formula which is essential for the derivation of our arbitrarily high order lagrange collocation type time stepping schemes for the nonlinear abstract ode the nonlinear stability and convergence are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi definite matrix under some suitable smoothness assumptions with regard to the two dimensional dirichlet or neumann boundary problems our new time stepping schemes coupled with discrete fast sine cosine transformation can be applied to simulate the two dimensional nonlinear klein gordon equations effectively all essential features of the methodology are present in one dimensional and two dimensional cases although the schemes to be analysed lend themselves with equal to higher dimensional case the numerical simulation is implemented and the numerical results clearly demonstrate the advantage and effectiveness of our new schemes in comparison with the existing numerical methods for solving nonlinear klein gordon equations in the literature

asymptotic preserving schemes for the klein gordon equation in the non relativistic limit regime we consider the klein gordon equation in the non relativistic limit regime i e the speed of light c c tending to infinity we construct an asymptotic expansion for the solution with respect to the small parameter depending on the inverse of the square of the speed of light as the first terms of this asymptotic can easily be simulated our approach allows us to construct numerical algorithms that are robust with respect to the large parameter c c producing high oscillations in the exact solution

numerical solution of the nonlinear klein gordon equation using radial basis functions the nonlinear klein gordon equation is used to model many nonlinear phenomena in this paper we propose a numerical scheme to solve the one dimensional nonlinear klein gordon equation with quadratic and cubic nonlinearity our scheme uses the collocation points and approximates the solution using thin plate splines tps radial basis functions rbf the implementation of the method is simple as finite difference methods the results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme