well posedness for nonlinear schrodinger equations with boundary forces in low dimensions by strichartz estimates abstract in this paper we study the well posedness of solutions for nonlinear schrodinger equations on one and two dimensional domains with boundary where the boundary is disturbed by an external inhomogeneous type of dirichlet or neumann force we first prove the local existence of solutions at the energy level for quadratic and superquadratic sources using the strichartz estimates on domains secondly we obtain conditional uniqueness and local stability then we prove the boundedness of solutions in the energy space to pass from the local theory to the global theory regarding subquadratic sources we appeal to classical methods and trudinger s inequality to prove the uniqueness which combined with the existence of weak energy solutions mass and energy inequalities eventually implies the continuity of solutions in time

smoothing effect for some schrodinger equations abstract we study the cauchy problem for the following schrodinger equation in r n n n i t u 1 2 u v 1 u v 2 u 2 u t x r r n u 0 x r n where v 1 v 1 x 1 x 1 v 2 v 2 x k 2 3 k x k k r 1 k 3 0 1 min 2 n 2 0 2 3 min 2 n we prove the existence uniqueness and smoothing effect of global solutions of with not necessarily in the sobolev space h1 rn

computing bit error probabilities for avalanche photodiode receivers by large deviations theory a bit error probability analysis of direct detection optical receivers is presented employing avalanche photodiodes an asymptotic analysis for large signal intensities is presented this analysis provides some useful insight into the balance between the poisson statistics the avalanche gain statistics and the gaussian thermal noise the conjugate distribution is developed it is obtained by applying the large deviation exponential twisting formula it is demonstrated that this conjugate distribution can be used to obtain numerically efficient monte carlo estimates of the bit error probability via the importance sampling method

inhomogeneous initial boundary value problem for the 2d nonlinear schrodinger equation we consider the inhomogeneous dirichlet initial boundary value problem for the nonlinear multidimensional schrodinger equation formulated on an upper right quarter plane we study traditionally important problems of the theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time also we are interested in the study of the influence of the dirichlet boundary data on the asymptotic behavior of solutions our approach to get well posedness of nonlinear problems is based on studying a linear theory and then using the fixed point argument to get a linear theory for the multidimensional model we proposed a general method based on the riemann hilbert approach and theory cauchy type integral equations to get smooth solutions in l we modify a method based on the factorization for the free schrodinger evolution group we consider the inhomogeneous dirichlet initial boundary value problem for the nonlinear multidimensional schrodinger equation formulated on an upper right quarter plane we study traditionally important problems of the theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time also we are interested in the study of the influence of the dirichlet boundary data on the asymptotic behavior of solutions our approach to get well posedness of nonlinear problems is based on studying a linear theory and then using the fixed point argument to get a linear theory for the multidimensional model we proposed a general method based on the riemann hilbert approach and theory cauchy type integral equations to get smooth solutions in l we modify a method based on the factorization for the free schrodinger evolution group

a class of optimum importance sampling strategies abstract the problem of estimating expectations of functionals of random vectors via simulation is investigated as an alternative to simple averaging an efficient form of monte carlo simulations known as importance sampling can be employed to produce arbitrarily accurate estimates of the expectation of interest the fundamental problem in importance sampling is to determine the appropriate statistics under which to conduct the simulation these statistics are typically determined from a constraint class by minimizing the variance of the importance sampling estimator over the class of admissible statistics in previous work the authors showed that minimizing the importance sampling variance is equivalent to finding the distribution which is closest to the unconstrained optimal distribution with respect to a specific information theoretic f divergence or ali silvey distance in this work the authors determine the optimal biasing density from a constraint class whose controlling parameter is fundamental in the performance analysis of importance sampling in addition it is shown that the constrained optimal distribution from this class minimizes every statistical distance measure to the global optimal distribution and as a consequence is optimal with respect to a large family of nonlinear cost functions salient features of this distribution are 1 unlike the unconstrained optimal solution this distribution can be made independent of the parameter to be estimated and thus can admit to implementation and 2 this distribution renders performance gains which can be made arbitrarily close to the optimal gains applications to estimating probabilities of rare events e g error rates in communication systems will be presented further analysis will show that in this case the savings over monte carlo simulations become unbounded as the probability of the rare event diminishes

nonexistence of asymptotically free solutions for a nonlinear schrodinger equation let u be a nontrivial smooth solution to iut u u p 1u if n 1 and 2 p 3 then there does not exist any finite energy free solution v such that u t v t 2 0 as t this extends a theorem of strauss in which the same result was proved for 1 p 2

nonexistence of the usual scattering states for the generalized ostrovsky hunter equation we consider the cauchy problem for the generalized ostrovsky hunter equation utx u u 1u xx we prove the nonexistence of the usual scattering states

nonparametric importance sampling abstract importance sampling is a widely used variance reduction simulation technique for the evaluation of high dimensional integrals a key step in the implementation of importance sampling is to choose a proper distribution function from which pseudorandom numbers are generated parametric sampling distributions if available at all are often inadequate for high dimensional integrals over irregular regions one possible remedy is to use a nonparametric method to estimate the unknown optimal sampling function we show that the nonparametric approach yields integral estimates that converge faster than estimates obtained from parametric approaches we also demonstrate that an adaptive method which has been used successfully in parametric settings does not yield better results than simple one step methods in the nonparametric setting

modified scattering for the critical nonlinear schrodinger equation abstract we consider the nonlinear schrodinger equation i u t u u 2 n u in all dimensions n 1 where c and 0 we construct a class of initial values for which the corresponding solution is global and decays as t like t n 2 if 0 and like t log t n 2 if 0 moreover we give an asymptotic expansion of those solutions as t we construct solutions that do not vanish so as to avoid any issue related to the lack of regularity of the nonlinearity at u 0 to study the asymptotic behavior we apply the pseudo conformal transformation and estimate the solutions by allowing a certain growth of the sobolev norms which depends on the order of regularity through a cascade of exponents

a large deviations perspective on the efficiency of multilevel splitting we analyze the performance of a multilevel splitting method for rare event simulation related to one recently proposed in the telecommunications literature this method splits promising paths into subpaths at intermediate levels to increase the number of observations of a rare event in our previous paper 1997 we gave sufficient conditions in specific classes of models for this method to be asymptotically optimal here we focus on necessary conditions in a general setting we show through a variety of results the importance of choosing the intermediate thresholds in a way consistent with the most likely path to a rare set both when the number of levels is fixed and when it increases with the rarity of the event in the latter case we give very general necessary conditions based on large deviations rate functions these indicate that even when the intermediate levels are chosen appropriately the method will frequently fail to be asymptotically optimal we illustrate the conditions with examples

on the choice of alternative measures in importance sampling with markov chains in the simulation of markov chains importance sampling involves replacing the original transition matrix say p with a suitably chosen transition matrix q that tends to visit the states of interest more frequently the likelihood ratio of p relative to q is an important random variable in the importance sampling method it always has expectation one and for any interesting pair of transition matrices p and q there is a sample path length that causes the likelihood ratio to be close to zero with probability close to one this may cause the variance of the importance sampling estimator to be larger than the variance of the traditional estimator we develop sufficient conditions for ensuring the tightness of the distribution of the logarithm of the likelihood ratio for all sample path lengths and we show that when these conditions are satisfied the likelihood ratio is approximately lognormally distributed with expected value one these conditions can be used to eliminate some choices of the alternative transition matrix q that are likely to result in a variance increase we also show that if the likelihood ratio is to remain well behaved for all sample path lengths the alternative transition matrix q has to approach the original transition matrix p as the sample path length increases the practical significance of this result is that importance sampling can be difficult to apply successfully in simulations that involve long sample paths

on large deviations theory and asymptotically efficient monte carlo estimation it is shown how large deviations theory can be applied to construct an asymptotically efficient simulation distribution for monte carlo simulation using the importance sampling technique a sufficient and necessary condition is given for the asymptotic efficiency of the candidate simulation distributions this is done in the multidimensional setting that is required by many practical simulation problems the result obtained is applied primarily in two areas first the generalization of previous work dealing with functionals of markov chains is discussed a second area of application is the simulation of nonlinear systems with gaussian inputs as an example of a system with gaussian inputs the simulation of a digital communication channel with nonlinear isi intersymbol interference characteristic of satellite data links is considered in the case of linear isi the asymptotically efficient exponentially twisted distribution turns out to agree with a method previously proposed by d lu and k yao 1988 the large deviations point of view provides some useful insight on how to extent the lu and yao method to nonlinear channels

texture classification and segmentation using wavelet packet frame and gaussian mixture model in this paper we propose a scheme for texture classification and segmentation the methodology involves an extraction of texture features using the wavelet packet frame decomposition this is followed by a gaussian mixture based classifier which assigns each pixel to the class each subnet of the classifier is modeled by a gaussian mixture model and each texture image is assigned to the class to which pixels of the image most belong this scheme shows high recognition accuracy in the classification of brodatz texture images it can also be expanded to an unsupervised texture segmentation using a kullback leibler divergence between two gaussian mixtures the proposed method was successfully applied to brodatz mosaic image segmentation and fabric defect detection

efficient simulation of value at risk with heavy tailed risk factors simulation of small probabilities has important applications in many disciplines the probabilities considered in value at risk var are moderately small however the variance reduction techniques developed in the literature for var computation are based on large deviations methods which are good for very small probabilities modeling heavy tailed risk factors using multivariate t distributions we develop a new method for var computation we show that the proposed method minimizes the variance of the importance sampling estimator exactly whereas previous methods produce approximations to the exact solution thus the proposed method consistently outperforms existing methods derived from large deviations theory under various settings the results are confirmed by a simulation study

a randomized bias technique for the importance sampling simulation of bayesian equalizers an importance sampling is simulation technique is presented for bayesian equalizers based on the large deviations theory approach developed by sadowsky and bucklew see ibid vol 36 no 5 p 579 1990 the resulting simulation density consists of a sum of exponentially twisted distributions for the additive gaussian channel this simulation density is equivalent to the conventional mean shift noise biasing is method but with the bias vector chosen from a fixed set in a random manner in order to properly select the bias vectors the asymptotic decision boundary of the bayesian equalizer is first determined it is shown that the boundary is formed by multiple hyperplanes and that the appropriate bias vectors are orthogonal to the hyperplanes the simulation technique is then extended to the recursive symbol by symbol detector of abend and fritchman a f algorithm proposed in 1970 and simulation results are presented for both recursive and non recursive equalizers

universal simulation distributions in this paper we present a new class of importance sampling simulation distributions the universal distributions we show that these distributions are universally efficient in the sense that they depend only on a single scalar parameter regardless of the dimensionality of the underlying system or of the error sets to be simulated

on the asymptotic efficiency of importance sampling techniques the asymptotic efficiency of importance sampling is techniques for the simulation of rare events in a multidimensional nonlinear setting was studied by j s sadowsky and j a bucklew see ibid vol 36 p 579 88 1990 fundamental results on the asymptotic efficiency of the mean value modification mm technique were derived additionally a statement was made that other is techniques cannot be asymptotically efficient it is shown that for the simulation of digital communication systems with gaussian input a broad class of asymptotically efficient is techniques exists necessary and sufficient conditions are provided for the asymptotic efficiency of five different is techniques including mm for one dimensional linear systems multidimensional generalizations of these is techniques are proposed a sufficient condition for the asymptotic efficiency of these techniques applied to multidimensional nonlinear systems is provided

clustering ellipses for anomaly detection comparing clustering and merging ellipsoids are problems that arise in various applications e g anomaly detection in wireless sensor networks and motif based patterned fabrics we develop a theory underlying three measures of similarity that can be used to find groups of similar ellipsoids in p space clusters of ellipsoids are suggested by dark blocks along the diagonal of a reordered dissimilarity image rdi the rdi is built with the recursive ivat algorithm using any of the three dis similarity measures as input and performs two functions i it is used to visually assess and estimate the number of possible clusters in the data and ii it offers a means for comparing the three similarity measures finally we apply the single linkage and clodd clustering algorithms to three two dimensional data sets using each of the three dissimilarity matrices as input two data sets are synthetic and the third is a set of real wsn data that has one known second order node anomaly we conclude that focal distance is the best measure of elliptical similarity ivat images are a reliable basis for estimating cluster structures in sets of ellipsoids and single linkage can successfully extract the indicated clusters

ellipsoidal decision regions for motif based patterned fabric defect detection this paper presents a study of using ellipsoidal decision regions for motif based patterned fabric defect detection the result of which is found to improve the original detection success using max min decision region of the energy variance values in our previous research max min decision region was found to be effective in distinct cases but ill detect the ambiguous false positive and false negative cases to alleviate this problem we first assume that the energy variance values can be described by a gaussian mixture model second we apply k means clustering to roughly identify the various clusters that make up the entire data population third convex hull of each cluster is employed as a basis for fitting an ellipsoidal decision region over it defect detection is then based on these ellipsoidal regions to validate the method three wallpaper groups are evaluated using the new ellipsoidal regions and compared with those results obtained using the max min decision region for the p2 group success rate improves from 93 43 to 100 for the pmm group success rate improves from 95 9 to 96 72 while the p4m group records the same success rate at 90 77 this demonstrates the superiority of using ellipsoidal decision regions in motif based defect detection

importance sampling simulation for evaluating lower bound symbol error rate of the bayesian dfe with multilevel signaling schemes for the class of equalizers that employs a symbol decision finite memory structure with decision feedback the optimal solution is known to be the bayesian decision feedback equalizer dfe the complexity of the bayesian dfe however increases exponentially with the length of the channel impulse response cir and the size of the symbol constellation conventional monte carlo simulation for evaluating the symbol error rate ser of the bayesian dfe becomes impossible for high channel signal to noise ratio snr conditions it has been noted that the optimal bayesian decision boundary separating any two neighboring signal classes is asymptotically piecewise linear and consists of several hyperplanes when the snr tends to infinity this asymptotic property can be exploited for efficient simulation of the bayesian dfe an importance sampling is simulation technique is presented based on this asymptotic property for evaluating the lower bound ser of the bayesian dfe with a multilevel pulse amplitude modulation m pam scheme under the assumption of correct decisions being fed back a design procedure is developed which chooses appropriate bias vectors for the simulation density to ensure asymptotic efficiency ae of the is simulation

direct evaluation of dynamical large deviation rate functions using a variational ansatz we describe a simple form of importance sampling designed to bound and compute large deviation rate functions for time extensive dynamical observables in continuous time markov chains we start with a model defined by a set of rates and a time extensive dynamical observable we construct a reference model a variational ansatz for the behavior of the original model conditioned on atypical values of the observable direct simulation of the reference model provides an upper bound on the large deviation rate function associated with the original model an estimate of the tightness of the bound and if the ansatz is chosen well the exact rate function the exact rare behavior of the original model does not need to be known in advance we use this method to calculate rate functions for currents and counting observables in a set of network and lattice models taken from the literature straightforward ansatze yield bounds that are tighter than bounds obtained from level 2 5 of large deviations via approximations that involve uniform scalings of rates we show how to correct these bounds in order to recover the rate functions exactly our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations

fractional nonlinear schrodinger equation of order α 0 1 abstract we consider the cauchy problem for the fractional nonlinear schrodinger equation i t u 1 x u u 2 u t 0 x r u 0 x u 0 x x r where r the order of the fractional derivative 0 1 we obtain the large time asymptoitic behavior of solutions which has a logarithmic phase modifications for large time comparing with the linear problem

efficient importance sampling for events of moderate deviations with applications summary we propose a method for finding the alternative distribution in importance sampling the alternative distribution is optimal in the sense that the asymptotic variance is mini mised for estimating tail probabilities of asymptotically normal statistics our contribution to importance sampling is three fold to begin with we obtain an explicit expression for the mean of the optimal alternative distribution and the expression motivates a recursive approximation algorithm secondly a new multi dimensional exponential tilting formula is presented lastly a conservative estimator of the variance is given to facilitate a quick comparison among different stratified sampling schemes in conjunction with importance sampling several numerical examples illustrating the efficacy of the proposed method are also included these results indicate that the proposed method is considerably more efficient than the method based on large deviations theory and the efficiency gain is more significant in higher dimensions

long range scattering for nonlinear schrodinger equations in one space dimension we consider the scattering problem for the nonlinear schrodinger equation in 1 1 dimensions open image in new window where x r 0 r p 3 we show that modified wave operators for exist on a dense set of a neighborhood of zero in the lebesgue spacel2 r or in the sobolev spaceh1 r the modified wave operators are introduced in order to control the long range nonlinearity u 2u

multidimensional inhomogeneous mixed initial boundary value problem for the nonlinear schrodinger equation abstract we consider the inhomogeneous mixed initial boundary value problem for the nonlinear multidimensional schrodinger equation formulated on upper right quarter plane we study traditionally important problems of the theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time also we are interested in the study of the influence of the mixta boundary data on the asymptotic behavior of solutions our approach to get well posedness of nonlinear problems is based on the studying a linear theory and then using the fixed point argument to get a linear theory for the multidimensional model we propose general method based on laplace approach and theory cauchy type integral equations to get smooth solutions in l we modify a method based on the factorization for the free schrodinger evolution group the advantage of our approach is that it can also be applied to non integrable equations and arbitrary boundary conditions this approach is new and it is not standard we believe that the results of this paper could be applicable to study a wide class of dissipative multidimensional nonlinear equations by the use of techniques of nonlinear analysis

global analysis of a model for capillary water waves in two dimensions in this paper we prove a global regularity result for a quadratic quasilinear model associated to the water waves system with surface tension and no gravity in dimension 2 the capillary waves system the model we consider here retains most of the difficulties of the full capillary water waves system including the delicate time resonance structure and modified scattering it is slightly simpler however at the technical level and our goal here is to present our method in this simplified situation the analysis of the full system is presented in a preprint by the authors 2014 2016 wiley periodicals inc

quadratic nonlinear klein gordon equation in one dimension we study the initial value problem for the quadratic nonlinear klein gordon equation vtt v vxx v2 t r x r with initial conditions v 0 x v0 x vt 0 x v1 x x r where v0 and v1 are real valued functions r using the method of normal forms of shatah normal forms and quadratic nonlinear klein gordon equations commun pure appl math 38 685 696 1985 we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous work of j m delort existence globale et comportement asymptotique pour l equation de klein gordon quasi lineaire a donnees petites en dimension 1 ann sci ec normale super 34 4 1 61 2001

active curve axis gaussian mixture models gaussian mixture models gmm have been broadly applied for the fitting of probability density function however due to the intrinsic linearity of gmm usually many components are needed to appropriately fit the data distribution when there are curve manifolds in the data cloud in order to solve this problem and represent data with curve manifolds better in this paper we propose a new nonlinear probability model called active curve axis gaussian model intuitively this model can be imagined as gaussian model being bent at the first principal axis for estimating parameters of mixtures of this model the em algorithm is employed experiments on synthetic data and chinese characters show that the proposed nonlinear mixture models can approximate distributions of data clouds with curve manifolds in a more concise and compact way than gmm does the performance of the proposed nonlinear mixture models is promising

adaptive threshold estimation via extreme value theory determining a detection threshold to automatically maintain a low false alarm rate is a challenging problem in a number of different applications the underlying parametric assumptions of most automatic target detection algorithms are invalid therefore thresholds derived using these incorrect distribution assumptions do not produce desirable results when applied to real sensor data monte carlo methods for threshold determination work well but tend to perform poorly when targets are present in order to mitigate these effects we propose an algorithm using extreme value theory through the use of the generalized pareto distribution gpd and a kolmogorov smirnov statistical test unlike previous work based on gpd estimates this algorithm incorporates a way to adaptively maintain low false alarm rates in the presence of targets both synthetic and real world detection results demonstrate the usefulness of this algorithm

stochastic systems with small noise analysis and simulation a phase locked loop example systems with wide bandwidth noise inputs are a common occurrence in stochastic control and communication theory and elsewhere e g tracking or synchronization systems such as phase locked loops pll one is often interested in calculating such quantities as the probability of escape from a desired error set in some time interval or the mean time for such escape diffusion approximations the system obtained in the limit bandwidth as the to infty are often used for this since they are easier to analyze when the noise effects in the physical system are small one is tempted to do an asymptotic analysis noise intensity to 0 on the diffusion approximation and use this for the desired estimates on the original system such a procedure does not work in general the double limit bandwidth to infty intensity to 0 is not always justified under quite broad conditions on the noise processes it is justified for the systems studied here we study a particular form of the pll owing to

conditional importance sampling estimators we give a unified presentation of the conditional importance sampling estimators we show that they are always better than their nonconditional counterparts we then present the large deviation theory associated with these estimators in particular we give conditional simulation distributions that are optimal in the sense that they are efficient interestingly enough these distributions will not in general be the usual exponential shifts we give examples showing how to use the theory developed

a system of quadratic nonlinear klein gordon equations in 2d abstract we consider the system of quadratic nonlinear klein gordon equations t 2 v 1 v 1 m 1 2 v 1 v 1 v 2 t 2 v 2 v 2 m 2 2 v 2 v 1 2 in two space dimensions under the mass condition such that 2 m 1 m 2 we construct the scattering operator in an almost natural weighted sobolev class h 1 1 or the scattering problem in lower order sobolev class h 4 3 1 h 1 where 0 is small

importance sampling for tanner trees this correspondence presents an importance sampling is simulation scheme for the soft iterative decoding on loop free multiple layer trees it is shown that this scheme is asymptotically efficient in that for an arbitrary tree and a given estimation precision the required number of samples is inversely proportional to the noise standard deviation this work has its application in the simulation of low density parity check ldpc codes

an inhomogeneous boundary value problem for nonlinear schrodinger equations abstract we consider a nonlinear schrodinger equation in a domain r n with the inhomegeneous dirichlet boundary condition u q where q is a given smooth function the nonlinear term contributes a positive term to the energy we prove the existence of global solutions of finite energy

inhomogeneous dirichlet boundary value problem for nonlinear schrodinger equations with a power nonlinearity on the upper half plane abstract we consider the inhomogeneous dirichlet boundary value problem for nonlinear schrodinger equations with a power nonlinearity in the upper half plane we present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to the problem by using the classical energy method and factorization techniques

critical nonlinear schrodinger equations with data in homogeneous weighted l2 spaces abstract we consider the initial value problem for nonlinear schrodinger equations with the critical nonlinearities 1 u 2 n u where im 1 0 when the space dimension n 1 2 we prove the global existence of small solutions in homogeneous weighted l 2 r n spaces it is shown that the small solutions decay uniformly like t n 2 for t 1 if im 1 0 the higher uniform time decay rates t n 2 log t n 2 for t 1 are obtained if im 1 0

direct sequence spread spectrum multiple access communications with random signature sequences a large deviations analysis a direct sequence spread spectrum multiple access bit error probability analysis is developed using large deviations theory let m denote the number of interfering spread spectrum signals and let n denote the signature sequence length then the large deviations limit is as n to infinity with m fixed a tight asymptotic expression for the bit error probability is proven and in addition recent large deviations results with the importance sampling monte carlo estimation technique are applied to obtain accurate and computationally efficient estimates of the bit error probability for finite values of m and n the large deviations point of view is compared also to the conventional asymptotics of central limit theory and the associated gaussian approximation the gaussian approximation is accurate and the ratio m n is moderately large and all signals have roughly equal power in the near far situation however the gaussian approximation is quite poor in contrast large deviations techniques are more accurate in the near far situation and it is here that these methods provide some important practical insight

large deviations theory and efficient simulation of excessive backlogs in a gi gi m queue the problem of using importance sampling to estimate the average time to buffer overflow in a stable gi gi m queue is considered using the notion of busy cycles estimation of the expected time to buffer overflow is reduced to the problem of estimating p sub n p buffer overflow during a cycle where n is the buffer size the probability p sub n is a large deviations probability p sub n vanishes exponentially fast as n to infinity a rigorous analysis of the method is presented it is demonstrated that the exponentially twisted distribution of s parekh and j walrand 1989 has the following strong asymptotic optimality property within the nonparametric class of all gi gi importance sampling simulation distributions as n to infinity the computational cost of the optimal twisted distribution of large deviations theory grows less than exponentially fast and conversely all other gi gi simulation distributions incur a computational cost that grows with strictly positive exponential rate

asymptotics for large time of solutions to the nonlinear schrodinger and hartree equations we study the asymptotic behavior in time of solutions to the cauchy problems for the nonlinear schrodinger equation with a critical power nonlinearity and the hartree equation we prove the existence of modified scattering states and the sharp time decay estimate in the uniform norm of solutions to the cauchy problem with small initial data this estimate is very important for the proof of the existence of modified scattering states to the nonlinear schrodinger equations with a critical nonlinearity and the hartree equation in order to derive the desired estimates we introduce a certain phase function since the previous methods based solely on a priori estimates of the operator x it acting on the solution without specifying any phase function do not work for the critical case under consideration the well known nonexistence of the usual l 2 scattering states shows that our result is sharp

constrained solutions in importance via robust statistics the problem of estimating estimating expectations of functions of random vectors via simulation is investigated monte carlo simulations also known as simple averaging have been used as a direct means of estimation a technique known as importance sampling can be used to modify the simulation via weighted averaging in the hope that the estimate will converge more rapidly to the expected value than standard monte carlo simulations a constrained optimal solution to the problem of minimizing the variance of the importance sampling estimator is derived this is accomplished by finding the distribution which is closest to the unconstrained optimal solution in the ali silvey sense s ali et al 1966 the solution from the constraint class is shown to be the least favorable density function in terms of bayes risk against the optimal density function examples of constraint classes which include epsilon mixture show that the constrained optimal solution can be made arbitrarily close to the optimal solution applications to estimating probability of error in communication systems are presented

optimal importance sampling for some quadratic forms of arma processes the determination of the asymptotically efficient importance sampling distribution for evaluating the tail probability p l sub n u for large n by monte carlo simulations is considered it is assumed that l sub n is the likelihood ratio statistic for the optimal detection of signal with spectral density s spl circ from noise with spectral density c spl circ l sub n 2n sup 1 x sub n sup t t sub n c spl circ sup 1 it sub n c spl circ s spl circ sup 1 x sub n c spl circ and s spl circ being both modeled as invertible gaussian arma processes and x sub n being a vector of n consecutive samples from the noise process by using large deviation techniques a sufficient condition for the existence of an asymptotically efficient importance sampling arma process whose coefficients are explicitly computed is given moreover it is proved that such an optimal process is unique

long range scattering for non linear schrodinger and hartree equations in space dimension n 2 we consider the scattering problem for the non linear schrodinger nls equation with a power interaction with critical powerp 1 2 n in space dimensionsn 2 and 3 and for the hartree equation with potential x 1 in space dimensionn 2 we prove the existence of modified wave operators in thel2 sense on a dense set of small and sufficiently regular asymptotic states

motif based defect detection for patterned fabric this paper proposes a generalized motif based method for detecting defects in 16 out of 17 wallpaper groups in 2d patterned texture it assumes that most patterned texture can be decomposed into lattices and their constituents motifs it then utilizes the symmetry property of motifs to calculate the energy of moving subtraction and its variance among different motifs by learning the distribution of these values over a number of defect free patterns boundary conditions for discerning defective and defect free patterns can be determined this paper presents the theoretical foundation of the method and defines the relations between motifs and lattice from which a new concept called energy of moving subtraction is derived using norm metric measurement between a collection of circular shift matrices of motif and itself it has been shown in this paper that the energy of moving subtraction amplifies the defect information of the defective motif together with its variance an energy variance space is further defined where decision boundaries are drawn for classifying defective and defect free motifs as the 16 wallpaper groups of patterned fabric can be transformed into three major groups the proposed method is evaluated over these three major groups from which 160 defect free lattices samples are used for defining the decision boundaries with 140 defect free and 113 defective samples used for testing an overall detection success rate of 93 32 is achieved for the proposed method no other generalized approach can achieve this success rate has been reported before and hence this result outperforms all other previously published approaches

smoothing effect for nonlinear schrodinger equations in exterior domains abstract we consider the following nonlinear schrodinger equations in exterior domains i t u 1 2 u u 2 u t x r x d u 0 x x x d u t x 0 or u t6v 0 t x r x d where d x rn x r d r 0 and v denotes the outward normal unit vector at x d in this paper we prove the radially symmetric solutions of have a smoothing property

modulation spaces and non linear hartree type equations abstract we study the cauchy problem for hartree equation with cubic convolution nonlinearity f u k u 2 u under a specified condition on potential k with cauchy data in modulation spaces m p q r n we establish global well posedness results in m p p r n with 1 p 2 n n when k x x r 0 m i n 2 n 2 in m p q r n with 1 q p 2 when k m 1 r n

asymptotic behavior of solutions to the short pulse equation with critical nonlinearity abstract we consider the cauchy problem for the short pulse equation u t x u u 3 x x x r t 0 u 0 x u 0 x x r where u 0 is a real valued function we prove the global existence of small solutions to the short pulse equation moreover we give the l time decay estimate u t l c 1 t 1 2 and the asymptotic behavior of solutions

uniformly efficient importance sampling for the tail distribution of sums of random variables successful efficient rare event simulation typically involves using importance sampling tailored to a specific rare event however in applications one may be interested in simultaneous estimation of many probabilities or even an entire distribution in this paper we address this issue in a simple but fundamental setting specifically we consider the problem of efficient estimation of the probabilities p sn na for large n for all a lying in an interval a where sn denotes the sum of n independent identically distributed light tailed random variables importance sampling based on exponential twisting is known to produce asymptotically efficient estimates when a reduces to a single point we show however that this procedure fails to be asymptotically efficient throughout a when a contains more than one point we analyze the best performance that can be achieved using a discrete mixture of exponentially twisted distributions and then present a method using a continuous mixture we show that a continuous mixture of exponentially twisted probabilities and a discrete mixture with a sufficiently large number of components produce asymptotically efficient estimates for all a a simultaneously

sharp asymptotic behavior of solutions for cubic nonlinear schrodinger equations with a potential we consider the cubic nonlinear schrodinger equation with a potential we obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions to the cauchy problem

a study of gaussian mixture models of color and texture features for image classification and segmentation the aims of this paper are two fold to define gaussian mixture models gmms of colored texture on several feature spaces and to compare the performance of these models in various classification tasks both with each other and with other models popular in the literature we construct gmms over a variety of different color and texture feature spaces with a view to the retrieval of textured color images from databases we compare supervised classification results for different choices of color and texture features using the vistex database and explore the best set of features and the best gmm configuration for this task in addition we introduce several methods for combining the color and structure information in order to improve the classification performances we then apply the resulting models to the classification of texture databases and to the classification of man made and natural areas in aerial images we compare the gmm model with other models in the literature and show an overall improvement in performance

uniform decay rates for the energy of weakly damped defocusing semilinear schrodinger equations with inhomogeneous dirichlet boundary control abstract in this paper we study the open loop stabilization as well as the existence and regularity of solutions of the weakly damped defocusing semilinear schrodinger equation with an inhomogeneous dirichlet boundary control first of all we prove the global existence of weak solutions at the h 1 energy level together with the stabilization in the same sense it is then deduced that the decay rate of the boundary data controls the decay rate of the solutions up to an exponential rate secondly we prove some regularity and stabilization results for the strong solutions in h 2 sense the proof uses the direct multiplier method combined with monotonicity and compactness techniques the result for weak solutions is strong in the sense that it is independent of the dimension of the domain the power of the nonlinearity and the smallness of the initial data however the regularity and stabilization of strong solutions are obtained only in low dimensions with small initial and boundary data

nonlinear schrodinger equations with exceptional potentials abstract we consider the cubic nonlinear schrodinger equation with an exceptional potential we obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions we prove the existence of modified scattering for this model that is linear scattering modulated by a phase our approach is based on the spectral theorem for the perturbed linear schrodinger operator and a factorization technique that allows us to control the resonant nonlinear term we make some parity assumptions in order to control the small energy behavior of the scattering coefficients and of the wave functions

neumann problem for the nonlinear klein gordon equation abstract the neumann initial boundary value problem for the nonlinear klein gordon equation 0 1 v t t v v x x v 3 t x r r v 0 x v 0 x v t 0 x v 1 x x r x v t 0 h t t r for real v 0 x v 1 x and h t is considered we prove the global well posedness for the initial boundary value problem 0 1 and we present a sharp time decay estimate of the solution in the uniform norm also we study the asymptotic behavior of the solution to 0 1 we show that the cubic nonlinearity in the neumann initial boundary value problem 0 1 is scattering critical

modified scattering and beating effect for coupled schrodinger systems on product spaces with small initial data in this paper we study a coupled nonlinear schrodinger system with small initial data in a product space we establish a modified scattering of the solutions of this system and we construct a modified wave operator the study of the resonant system which provides the asymptotic dynamics allows us to highlight a control of the sobolev norms and interesting dynamics with the beating effect the proof uses a recent work of hani pausader tzvetkov and visciglia for the modified scattering and a recent work of grebert paturel and thomann for the study of the resonant system