a multiple hyper ellipsoidal subclass model for an evolutionary classifier abstract a pattern classification scheme in which the classifier is able to grow and evolve during the operation process is presented the evolutionary property of the classifier is made possible by modeling the pattern vectors in multiple hyper ellipsoidal subclass distributions learning of the classifier takes place at the subclass levels only this property allows the classifier to retain its previously learned patterns while accepting and learning new pattern classes the classifier is suitable to operate in dynamical environments where continuous updating of the pattern class distributions is needed

robust multiple classification of known signals in additive noise an asymptotic weak signal approach the problem of extracting one out of a finite number of possible signals of known form given observations in an additive noise model is considered two approaches are studied either the signal with shortest distance to the observed data or the signal having maximal correlation with some transformation of the observed data is chosen with a weak signal approach the limiting error probability is a monotone function of the pitman efficacy and it is the same for both the distance based and correlation based detectors using the minimax theory of huber it is possible to derive robust choices of distance correlation when the limiting error probability is used as performance criterion this generalizes previous work in the area from two signals to an arbitrary number of signals considered are m type and r type distances and also one dimensional and two dimensional signals some monte carlo simulations are performed to compare the finite sample size error probabilities with the asymptotic error probabilities

large time asymptotics for the fourth order nonlinear schrodinger equation abstract we consider the cauchy problem for the fourth order nonlinear schrodinger equation in the super critical case i t u 1 4 x 4 u x u 1 u where 4 c we prove the global existence and the large time asymptotics of solutions for small initial data u 0 h 1 h 1 2 1 when the order of the nonlinearity 4

a wreath product group approach to signal and image processing ii convolution correlation and applications for pt i see ibid vol 48 no 1 p 102 32 2000 this paper continues the investigation of the use of spectral analysis on certain noncommutative finite groups wreath product groups in digital signal processing we describe the generalization of discrete cyclic convolution in convolution over these groups and show how it reduces to multiplication in the spectral domain finite group based convolution is defined in both the spatial and spectral domains and its properties established we pay particular attention to wreath product cyclic groups and further describe convolution properties from a geometric view point in terms of operations with specific signals and filters group based correlation is defined in a natural way and its properties follow from those of convolution the detection of similarity of perceptually similar signals and an application of correlation the detection of similarity of group transformed signals several examples using images are included to demonstrate the ideas pictorially

multiple subclass pattern recognition a maximin correlation approach this paper addresses a correlation based nearest neighbor pattern recognition problem where each class is given as a collection of subclass templates the recognition is performed in two stages in the first stage the class is determined templates for this stage are created using the subclass templates assignment into subclasses occurs in the second stage this two stage approach may be used to accelerate template matching in particular the second stage may be omitted when only the class needs to be determined the authors present a method for optimal aggregation of subclass templates into class templates for each class the new template is optimal in that it maximizes the worst case i e minimum correlation with its subclass templates an algorithm which solves this maximin optimization problem is presented and its correctness is proved in addition test results are provided indicating that the algorithm s execution time is polynomial in the number of subclass templates the authors show tight bounds on the maximin correlation the bounds are functions only of the number of original subclass templates and the minimum element in their correlation matrix the algorithm is demonstrated on a multifont optical character recognition problem

data compression and harmonic analysis in this paper we review some recent interactions between harmonic analysis and data compression the story goes back of course to shannon s r d theory in the case of gaussian stationary processes which says that transforming into a fourier basis followed by block coding gives an optimal lossy compression technique practical developments like transform based image compression have been inspired by this result in this paper we also discuss connections perhaps less familiar to the information theory community growing out of the field of harmonic analysis recent harmonic analysis constructions such as wavelet transforms and gabor transforms are essentially optimal transforms for transform coding in certain settings some of these transforms are under consideration for future compression standards we discuss some of the lessons of harmonic analysis in this century typically the problems and achievements of this field have involved goals that were not obviously related to practical data compression and have used a language not immediately accessible to outsiders nevertheless through an extensive generalization of what shannon called the sampling theorem harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations we explain why harmonic analysis has interacted with data compression and we describe some interesting recent ideas in the field that may affect data compression in the future

wellposedness for the fourth order nonlinear schrodinger equations abstract we study the local smoothing effects and wellposedness of cauchy problem for the fourth order nonlinear schrodinger equations in 1d i t u x 4 u p x u 2 x u 2 t x r where p is a polynomial excluding constant or linear terms

global solution for a sixth order nonlinear schrodinger equation abstract in this paper we are concerned with a sixth order nonlinear schrodinger equation by applying the factorization formula and an analytical method we prove the existence and uniqueness of global solution for the cauchy problem of the sixth order nonlinear schrodinger equation

maximin projection learning for optimal treatment decision with heterogeneous individualized treatment effects a saline feature of data from clinical trials and medical studies is inhomogeneity patients not only differ in baseline characteristics but also the way they respond to treatment optimal individualized treatment regimes are developed to select effective treatments based on patient s heterogeneity however the optimal treatment regime might also vary for patients across different subgroups in this paper we mainly consider patient s heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups we propose a new maximin projection learning for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation based on estimated optimal treatment regimes for all subgroups the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming qclp problem which can be efficiently computed by interior point methods consistency and asymptotic normality of the estimator is established numerical examples show the reliability of the proposed methodology

nonlinear fourth order schrodinger equations with radial data abstract we prove the small data scattering and large data local well posedness for the nonlinear fourth order schrodinger equation with radial data in critical h s c space and in particular for some s c 0 the new ingredient is the improved strichartz estimates for fourth order schrodinger equations with radial initial data

stability of solitons described by nonlinear schrodinger type equations with higher order dispersion abstract steady solitons described by the fourth order nonlinear schrodinger type equations in one two and three dimensions with power law nonlinearities are studied conditions of existence and stability of such solitons are found numerical results demonstrating soliton existence stability and instability are described they agree with the developed theory

the cauchy problem for the fourth order nonlinear schrodinger equation related to the vortex filament abstract the cauchy problem of one dimensional fourth order nonlinear schrodinger equation related to the vortex filament is studied local well posedness for initial data in h s r s 1 2 is obtained by the fourier restriction norm method under certain coefficient condition

global existence and asymptotic behavior of solutions to the fourth order nonlinear schrodinger equation in the critical case abstract we consider the cauchy problem for the nonlinear fourth order nonlinear schrodinger equation i t u 1 4 x 4 u i x u 3 u t 0 x r u 0 x u 0 x x r with critical nonlinearity where r we assume that the initial data are such that u 0 h 1 1 with sufficiently small norm u 0 h 1 1 we prove that there exists a unique global solution e i t 4 x 4 u c 0 h 1 1 of the cauchy problem for the nonlinear fourth order nonlinear schrodinger equation such that u t l c 1 t 1 4 moreover we show that if the total mass 1 2 r u 0 x d x 0 then the large time asymptotics is determined by the self similar solution

asymptotics for the fourth order nonlinear schrodinger equation in the critical case abstract we consider the cauchy problem for the fourth order nonlinear schrodinger equation i t u 1 4 x 4 u u 4 u t x r r u 0 x u 0 x x r we prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions u 0 x d x 0 0

embeddings for a weakly differentiable functions on domains abstract we prove that the inhomogeneous estimate of vector fields on balls in r n b d k 1 u n n 1 d x n 1 n c b a u u d x for all u c b r n holds if and only if the linear constant coefficient differential operator a of order k has finite dimensional null space fdn this generalizes the gagliardo nirenberg sobolev inequality on domains and provides the local version of the analogous homogeneous embedding in full space r n d k 1 u n n 1 d x n 1 n c r n a u d x for all u c c r n r n proved by van schaftingen precisely for elliptic and cancelling ec operators building on fundamental l 1 estimates from the works of bourgain and brezis we prove that fdn strictly implies ec and discuss the contrast between homogeneous and inhomogeneous estimates on both algebraic and analytic level

a two stage cross correlation approach to template matching two stage template matching with sum of absolute differences as the similarity measure has been developed by vanderburg and rosenfeld 1 2 this correspondence shows the development of two stage template matching with cross correlation as the similarity measure the threshold value of the first stage is derived analytically and its validity is verified experimentally considerable speed up over the one stage process can be obtained by introducing only a small false dismissal probability

an optimal global nearest neighbor metric a quadratic metric dao x y x y t ao x y is proposed which minimizes the mean squared error between the nearest neighbor asymptotic risk and the finite sample risk under linearity assumptions a heuristic argument is given which indicates that this metric produces lower mean squared error than the euclidean metric a nonparametric estimate of ao is developed if samples appear to come from a gaussian mixture an alternative parametrically directed distance measure is suggested for nearness decisions within a limited region of space examples of some two class gaussian mixture distributions are included