abelian gauge theory on riemann surfaces and new topological invariants an abelian gauge field theory framed on a complex line bundle l over a compact riemann surface m is developed which allows the coexistence simultaneously in the same model of magnetic vortices and antivortices represented by the n zeros and p poles of a section of l the quantized minimum energy e is given in terms of the first chern class c 1 l and by a certain intersection number obtained from the multivortices we show that e 2 n p to realize such topological invariants as minimum energies an existence and uniqueness theorem is established under the necessary and sufficient condition that c 1 l n p

on the schrodinger equation for the interaction x2 λx2 1 gx2 the method of obtaining the explicit expressions of all the even odd parity exact solutions of the schrodinger equation for the interaction x2 lambda x2 1 gx2 is discussed when the couplings lambda and g satisfy some specific relations in the general case a simple equation for approximating the energy eigenvalues has been developed

scaling generator coordinate method and the eigensolutions of the schrodinger equation an extremely simple approximate variational method for the study of the eigensolutions of the one dimensional schrodinger equation is introduced based upon the idea of employing scaled eigenstates of the harmonic oscillator as generating functions for the generator coordinate method the approach is successfully applied to a variety of situations

vortices in holomorphic line bundles over closed kahler manifolds we apply a modified yang mills higgs functional to unitary bundles over closed kahler manifolds and study the equations which govern the global minima the solutions represent vortices in holomorphic bundles and are direct analogs of the vortices overr2 we obtain a complete description of the moduli space of these new vortices where the bundle is of rank one the description is in terms of a class of divisors in the base manifold there is also a dependence on a real valued parameter which can be attributed to the compactness of the base manifold

on the schrodinger equation for the interaction x2 λx2 1 gx2 the lowest even and odd parity energy levels of schrodinger s equation for the interaction x2 lambda x2 1 gx2 for arbitrary positive values of lambda and g are obtained accurately from a first order variational perturbation treatment

multiple instantons representing higher order chern pontryagin classes ii this paper is a continuation of an earlier study on the generalized yang mills instantons over 4m dimensional spheres we will first present a discussion on the generalized yang mills equations the higher order chern pontryagin classes c 2m and the self dual or anti self dual equations we will then obtain some sharp asymptotic estimates for the self dual or anti self dual equations within the witten tchrakian framework which relates the integer value of c 2m to the number of vortices of the solution to a reduced 2 dimensional abelian higgs system over the poincare half plane we will prove that indeed for any integer n there exists a 2 n parameter family of the generalized self dual or anti self dual instantons realizing the topology c 2m n furthermore for the purpose of accommodating more general solutions we establish a removable singularity theorem which enables us to extend the solutions obtained on a 4m dimensional euclidean space with an integral bound to the holder continuous solutions on a 4m dimensional sphere

eigenvalues from power series expansions an alternative approach an appropriate rational approximation to the eigenfunction of the schrodinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of hankel determinants the convergence rate of this approach is greater than that for a well established method based on power series expansions weighted by a gaussian factor with an adjustable parameter the so called hill determinant method

dynamical systems that sort lists diagonalize matrices and solve linear programming problems abstract we establish a number of properties associated with the dynamical system h h h n where h and n are symmetric n by n matrices and a b ab ba the most important of these come from the fact that this equation is equivalent to a certain gradient flow on the space of orthogonal matrices we are especially interested in the role of this equation as an analog computer for example we show how to map the data associated with a linear programming problem into h 0 and n in such a way as to have h h h n evolve to a solution of the linear programming problem this result can be applied to find systems which solve a variety of genetic combinatorial optimization problems and it even provides an algorithm for diagonalizing symmetric matrices

texture classification by wavelet packet signatures this correspondence introduces a new approach to characterize textures at multiple scales the performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classification of twenty five natural textures both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations where each wavelet packet channel reflected a specific scale and orientation sensitivity wavelet packet representations for twenty five natural textures were classified without error by a simple two layer network classifier an analyzing function of large regularity d sub 20 was shown to be slightly more efficient in representation and discrimination than a similar function with fewer vanishing moments d sub 6 in addition energy representations computed from the standard wavelet decomposition alone 17 features provided classification without error for the twenty five textures included in our study the reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are beneficial for accomplishing segmentation classification and subtle discrimination of texture

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

shifted 1 n expansion approach to the interaction v r r2 λr2 1 gr2 the authors use the shifted 1 n expansion method to calculate the energy eigenvalues of the non polynomial oscillator v r r2 r2 1 gr2 the results thus obtained are in excellent agreement with exact numerical results it is also shown that the non polynomial interaction can be made supersymmetric and in this case also the results obtained by the shifted 1 n method matches extremely well with the exact analytic results given by supersymmetry

a necessary and sufficient condition for the existence of multisolitons in a self dual gauged sigma model this paper presents a resolution of the gaugedo 3 sigma model proposed by b j schroers in which the matter field o mapsr2 intos2 while the vector gauge potential gives rise to a magnetic field it is shown that for each natural numbern there are solutions to saturate the classical energy lower bounde 4 n for the field configurations in the topological family deg o n if and only ifn 1 furthermore the solutions obtained depend on at least 4n 3 continuous parameters the associated magnetic flux can assume its value in an open interval and the decay rates of the field strengths may be specified in a suitable range these solutions are multisolitons represented byn prescribed lumps of the magnetic field simulatingn identical particles in equilibrium and are governed by a nonlinear elliptic equation with both vortex and anti vortex source terms

study of a class of non polynomial oscillator potentials we develop a variational method to obtain accurate bounds for the eigenenergies of h v in arbitrary dimensions n 1 where v r is the nonpolynomial oscillator potential the variational bounds are compared with results previously obtained in the literature an infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues

on the x2 λx2 1 gx2 interaction presents an infinite set of exact solutions of odd parity for the one dimensional schrodinger equation with the interaction x2 lambda x2 1 gx2 these complement the exact solutions of even parity that have been obtained recently by flessas phys lett a vol 84 p 121 1981

greedy function approximation a gradient boosting machine function estimation approximation is viewed from the perspective of numerical optimization in function space rather than parameter space a connection is made between stagewise additive expansions and steepest descent minimization a general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion specific algorithms are presented for least squares least absolute deviation and huber m loss functions for regression and multiclass logistic likelihood for classification special enhancements are derived for the particular case where the individual additive components are regression trees and tools for interpreting such treeboost models are presented gradient boosting of regression trees produces competitive highly robust interpretable procedures for both regression and classification especially appropriate for mining less than clean data connections between this approach and the boosting methods of freund and shapire and friedman hastie and tibshirani are discussed

yang mills higgs theory on a compact riemann surface jaffe and taubes vortices and monopoles birkhauser boston 1980 have shown the existence and uniqueness of n vortex solutions on the complex plane in this paper their results are generalized to an arbitrary u 1 bundle over a compact riemann surface with a hermitian metric berger s nonlinear analysis nonlinearity and functional analysis academic new york 1977 has provided an effective method to prove the existence part of the main theorem of this paper

functional dissipation microarrays for classification in this article we describe a new method of extracting information from signals called functional dissipation that proves to be very effective for enhancing classification of high resolution texture rich data our algorithm bypasses to some extent the need to have very specialized feature extraction techniques and can potentially be used as an intermediate feature enhancement step in any classification scheme functional dissipation is based on signal transforms but uses the transforms recursively to uncover new features we generate a variety of masking functions and extract features with several generalized matching pursuit iterations in each iteration the recursive process modifies several coefficients of the transformed signal with the largest absolute values according to the specific masking function in this way the greedy pursuit is turned into a slow controlled dissipation of the structure of the signal that for some masking functions enhances separation among classes our case study in this paper is the classification of crystallization patterns of amino acids solutions affected by the addition of small quantities of proteins

large order shifted 1 n expansions through the asymptotic iteration method the perturbation technique within the framework of the asymptotic iteration method is used to obtain large order shifted 1 n expansions where n is the number of spatial dimensions this method is contrary to the usual rayleigh schrodinger perturbation theory no matrix elements need to be calculated the method is applied to the schrodinger equation and the non polynomial oscillator potential is discussed as an illustrative example

vortex equations in abelian gauged σ models we consider nonlinear gauged models with kahler domain and target for a special choice of potential these models admit bogomolny or self duality equations the so called vortex equations here we describe the space of solutions and energy spectrum of the vortex equations when the gauge group is a torus tn the domain is compact and the target is open image in new window we also obtain a large family of solutions when the target is a compact kahler toric manifold