singular kahler einstein metrics we study degenerate complex monge ampere equations of the form omega dd c f n e t f mu where omega is a big semi kahler form on a compact kahler manifold x of dimension n t in r and mu f omega n is a positive measure with density f in l p x omega n p 1 we prove the existence and unicity of continuous o plurisubharmonic solutions in case x is projective and omega psi omega where psi x to v is a proper birational morphism to a normal projective variety omega in ns r v is an ample class and mu has only algebraic singularities we prove that the solution is smooth in the regular locus of the equation we use these results to construct singular kahler einstein metrics of non positive curvature on projective klt pairs in particular on canonical models of algebraic varieties of general type

research on the unbiased probability estimation of error correcting output coding supervised classification based on error correcting output codes ecoc is an efficient method to solve the problem of multi class classification and how to get the accurate probability estimation via ecoc is also an attractive research direction this paper proposed three kinds of ecoc to get unbiased probability estimates and investigated the corresponding classification performance in depth at the same time two evaluating criterions for ecoc that has better classification performance were concluded which are bayes consistence and unbiasedness of probability estimation experimental results on artificial data sets and uci data sets validate the correctness of our conclusion

multiclass data segmentation using diffuse interface methods on graphs we present two graph based algorithms for multiclass segmentation of high dimensional data on graphs the algorithms use a diffuse interface model based on the ginzburg landau functional related to total variation and graph cuts a multiclass extension is introduced using the gibbs simplex with the functional s double well potential modified to handle the multiclass case the first algorithm minimizes the functional using a convex splitting numerical scheme the second algorithm uses a graph adaptation of the classical numerical merriman bence osher mbo scheme which alternates between diffusion and thresholding we demonstrate the performance of both algorithms experimentally on synthetic data image labeling and several benchmark data sets such as mnist coil and webkb we also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph laplacian and take advantage of the sparsity of the matrix experiments indicate that the results are competitive with or better than the current state of the art in multiclass graph based segmentation algorithms for high dimensional data

n point deformation of algebraic k3 surfaces we construct a set of noncommutative geometries by performing n point deformation of algebraic k3 surfaces first we consider two point deformation of algebraic k3 surfaces by performing algebraic deformation of a pair of commutative algebraic k3 surfaces in this case the moduli space of the noncommutative deformations is of dimension 19 the same as the moduli dimension of the complex deformations of commutative algebraic k3 surfaces then we extend this method to the n point case in the n point case the dimension of deformation moduli space becomes 19n n 1 2

semi iterative methods for the approximate solution of ill posed problems we study semi iterative two step interative methods of the form x n 1 t t alpha x n gamma x n 1 beta x n 1 beta x n 1 alpha gamma t y for the approximate solution of ill posed or ill conditioned linear equationstx y in infinite or finite dimensional hilbert spaces we present results on convergence convergence rates the influence of perturbed data and on the comparison of different methods

on converse and saturation results for tikhonov regularization of linear ill posed problems in this paper we prove some new converse and saturation results for tikhonov regularization of linear ill posed problems tx y where t is a linear operator between two hilbert spaces

flexible discriminant analysis by optimal scoring abstract fisher s linear discriminant analysis is a valuable tool for multigroup classification with a large number of predictors one can find a reduced number of discriminant coordinate functions that are optimal for separating the groups with two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership and the decision boundaries are linear this article is about richer nonlinear classification schemes linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups in this paper we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method in this way any multiresponse regression technique such as mars or neural networks can be postprocessed to improve its classification performance

a likelihood mpec approach to target classification in this paper we develop a method for classifying an unknown data vector as belonging to one of several classes this method is based on the statistical methods of maximum likehood and borrowed strength estimation we develop an mpec procedure for mathematical program with equilibrium constraints for the classification of a multi dimensional observation using a finite set of observed training data as the inputs to a bilevel optimization problem we present a penalty interior point method for solving the resulting mpec and report numerical results for a multispectral minefield classification application related approaches based on conventional maximum likehood estimation and a bivariate normal mixture model as well as alternative surrogate classification objective functions are described

stopping criterion for boosting based data reduction techniques from binary to multiclass problem so far boosting has been used to improve the quality of moderately accurate learning algorithms by weighting and combining many of their weak hypotheses into a final classifier with theoretically high accuracy in a recent work sebban nock and lallich 2001 we have attempted to adapt boosting properties to data reduction techniques in this particular context the objective was not only to improve the success rate but also to reduce the time and space complexities due to the storage requirements of some costly learning algorithms such as nearest neighbor classifiers in that framework each weak hypothesis which is usually built and weighted from the learning set is replaced by a single learning instance the weight given by boosting defines in that case the relevance of the instance and a statistical test allows one to decide whether it can be discarded without damaging further classification tasks in sebban nock and lallich 2001 we addressed problems with two classes it is the aim of the present paper to relax the class constraint and extend our contribution to multiclass problems beyond data reduction experimental results are also provided on twenty three datasets showing the benefits that our boosting derived weighting rule brings to weighted nearest neighbor classifiers

new pocs algorithms for regularization of inverse problems abstract ill posed problems described by first kind fredholm equations appear in many interesting practical cases in engineering or mathematical physics such as deconvolution and require regularization techniques to get adequate solutions this paper presents under a projection operators onto convex sets pocs framework to introduce the needed regularization operations a series of non adaptive and adaptive pocs regularization algorithms which offer as main advantages besides including previously proposed methods a lower computational load and the possibility of including any kind of constraints linear and nonlinear a series of simulation examples serve to appreciate the high performance of the proposed techniques in a typical problem recovering the discontinuites of a sequence showing sharp edges

krylov subspace iterative methods for boundary element method based near field acoustic holography the reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods the solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements these methods will not require the calculation of the singular value decomposition which can be expensive when the matrix system is considerably large krylov subspace methods are iterative methods that have the phenomena known as semi convergence i e the optimal regularization solution is obtained after a few iterations if the iteration is not stopped the method converges to a solution that generally is totally corrupted by errors on the measurements for these methods the number of iterations play the role of the regularization parameter we will focus our attention to the study of the regularizing properties from the krylov subspace methods like conjugate gradients least squares qr and the recently proposed hybrid method a discussion and comparison of the available stopping rules will be included a vibrating plate is considered as an example to validate our results

mathcal y scale regularization many inverse problems are ill posed in the sense that their solution is unstable with respect to data perturbations and hence regularization methods have to be used for their stable solution two possible drawbacks of standard regularization methods are a saturation i e only suboptimal approximations can be found for smooth solutions this is the case e g for tikhonov regularization b numerical effort e g the large number of iterations of methods like landweber iteration a framework that allows us to overcome both effects at least for certain classes of inverse problems is regularization in hilbert scales where a solution is searched in a scale of spaces hilbert scale but convergence is achieved in the original space regularization methods in hilbert scales can be viewed as modified preconditioned versions of standard methods in order to make the advantages of the hilbert scale approach applicable to a new class of problems we propose to use a scale of spaces over the image space instead this results in a new family of methods which we call mathcal y scale regularization and whose optimal convergence properties are analyzed one of the key steps in the analysis is the formulation of an adequate a posteriori stopping rule and the proof of optimal convergence rates the theoretical results are illustrated in several numerical examples

humans in groups the importance of contextual information for understanding collective activities in this work we consider the problem of modeling and recognizing collective activities performed by groups of people sharing a common purpose for this aim we take into account the social contextual information of each person in terms of the relative orientation and spatial distribution of people groups we propose a method able to process a video stream and at each time instant associate a collective activity with each individual in the scene by representing the individual or target as a part of a group of nearby people the target group to generalize with respect to the viewpoint we associate each target with a reference frame based on his spatial orientation which we estimate automatically by semi supervised learning then we model the social context of a target by organizing a set of instantaneous descriptors capturing the essence of mutual positions and orientations within the target group in a graph structure classification of collective activities is achieved with a multi class svm endowed with a novel kernel function for graphs we report an extensive experimental analysis on benchmark datasets that validates the proposed solution and shows significant improvements with respect to state of art results

a multiclass classification method based on decoding of binary classifiers in this letter we present new methods of multiclass classification that combine multiple binary classifiers misclassification of each binary classifier is formulated as a bit inversion error with probabilistic models by making an analogy to the context of information transmission theory dependence between binary classifiers is incorporated into our model which makes a decoder a type of boltzmann machine we performed experimental studies using a synthetic data set data sets from the uci repository and bioinformatics data sets and the results show that the proposed methods are superior to the existing multiclass classification methods

regularization of inverse problems by two point gradient methods in banach spaces in this paper we propose and analyze a two point gradient method for solving inverse problems in banach spaces which is based on the landweber iteration and an extrapolation strategy the method allows to use non smooth penalty terms including the l 1 like and the total variation like penalty functionals which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy in practical applications the design of the method involves the choices of the step sizes and the combination parameters which are carefully discussed numerical simulations are presented to illustrate the effectiveness of the proposed method

combining predictions in pairwise classification an optimal adaptive voting strategy and its relation to weighted voting weighted voting is the commonly used strategy for combining predictions in pairwise classification even though it shows good classification performance in practice it is often criticized for lacking a sound theoretical justification in this paper we study the problem of combining predictions within a formal framework of label ranking and under some model assumptions derive a generalized voting strategy in which predictions are properly adapted according to the strengths of the corresponding base classifiers we call this strategy adaptive voting and show that it is optimal in the sense of yielding a map prediction of the class label of a test instance moreover we offer a theoretical justification for weighted voting by showing that it yields a good approximation of the optimal adaptive voting prediction this result is further corroborated by empirical evidence from experiments with real and synthetic data sets showing that even though adaptive voting is sometimes able to achieve consistent improvements weighted voting is in general quite competitive all the more in cases where the aforementioned model assumptions underlying adaptive voting are not met in this sense weighted voting appears to be a more robust aggregation strategy

preconditioning landweber iteration in hilbert scales in this paper we investigate convergence of landweber iteration in hilbert scales for linear and nonlinear inverse problems as opposed to the usual application of hilbert scales in the framework of regularization methods we focus here on the case s 0 which for tikhonov regularization corresponds to regularization in a weaker norm in this case the hilbert scale operator l 2 s appearing in the iteration acts as a preconditioner which significantly reduces the number of iterations needed to match an appropriate stopping criterion additionally we carry out our analysis under significantly relaxed conditions i e we only require inlinemediaobject not available see fulltext instead of inlinemediaobject not available see fulltext which is the usual condition for regularization in hilbert scales the assumptions needed for our analysis are verified for several examples and numerical results are presented illustrating the theoretical ones

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

on the convergence and singularities of the j flow with applications to the mabuchi energy the j flow of s k donaldson and x x chen is a parabolic flow on kahler manifolds with two kahler metrics it is the gradient flow of the j functional that appears in chen s formula for the mabuchi energy we find a positivity condition in terms of the two metrics that is both necessary and sufficient for the convergence of the j flow to a critical metric we use this result to show that on manifolds with ample canonical bundle the mabuchi energy is proper on all kahler classes in an open neighborhood of the canonical class defined by a positivity condition this improves previous results of chen and of the second author we discuss the implications of this for the problem of the existence of constant scalar curvature kahler metrics we also study the singularities of the j flow and under certain conditions which always hold for dimension 2 derive some estimates away from a subvariety we discuss the conjectural remark of donaldson that if the j flow does not converge on a kahler surface then it should blow up over some curves of negative self intersection 2007 wiley periodicals inc

accelerated landweber iterations for the solution of ill posed equations in this paper the potentials of so calledlinear semiiterative methods are considered for the approximate solution of linear ill posed problems and ill conditioned matrix equations several efficient two step methods are presented most of which have been introduced earlier in the literature stipulating certain conditions concerning the smoothness of the solution a notion of optimal speed of convergence may be formulated various direct and converse results are derived to illustrate the properties of this concept if the problem s right hand side data are contaminated by noise semiiterative methods may be used asregularization methods assuming optimal rate of convergence of the iteration for the unperturbed problem the regularized approximations will be of order optimal accuracy to derive these results specific properties of polynomials are used in connection with the basic theory of solving ill posed problems rather recent results onfast decreasing polynomials are applied to answer an open question of brakhage numerical examples are given including a comparison to the method of conjugate gradients

classification by pairwise coupling we discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes and then coupling the estimates together the coupling model is similar to the bradley terry method for paired comparisons we study the nature of the class probability estimates that arise and examine the performance of the procedure in real and simulated data sets classifiers used include linear discriminants nearest neighbors adaptive nonlinear methods and the support vector machine

an analysis of a multi level projected steepest descent iteration for nonlinear inverse problems in banach spaces subject to stability constraints we consider nonlinear inverse problems described by operator equations in banach spaces assuming conditional stability of the inverse problem that is assuming that stability holds on a compact convex subset of the domain of the operator we introduce a novel nonlinear projected steepest descent iteration and analyze its convergence to an approximate solution given limited accuracy data we proceed with developing a multi level algorithm based on a nested family of compact convex subsets on which stability holds and the stability constants are ordered growth of the stability constants is coupled to the increase in accuracy of approximation between neighboring levels to ensure that the algorithm can continue from level to level until the iterate satisfies a desired discrepancy criterion after a finite number of steps

incorporating prior probabilities into high dimensional classifiers in standard parametric classifiers or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities the prior probabilities of the respective populations play a key role however those probabilities are largely ignored in the construction of high dimensional classifiers partly because there are no likelihoods to be constructed or bayes risks to be estimated nevertheless including information about prior probabilities can reduce the overall error rate particularly in cases where doing so is most important i e when the classification problem is particularly challenging and error rates are not close to zero in this paper we suggest a general approach to reducing error rate in this way by using a method derived from breiman s bagging idea the potential improvements in performance are identified in theoretical and numerical work the latter involving both applications to real data and simulations the method is simple and explicit to apply and does not involve choice of any tuning parameters

on a class of fully nonlinear flows in kahler geometry in this paper we study a class of fully nonlinear metric flow on kahler manifolds which includes the j flow as a special case we provide a sufficient and necessary condition for the long time convergence of the flow generalizing the result of songweinkove as a consequence under the given condition we solved the corresponding euler equation which is fully nonlinear of monge ampere type as an application we also discuss a complex monge ampere type equation including terms of mixed degrees which was first posed by chen

a convergence analysis of the landweber iteration for nonlinear ill posed problems in this paper we prove that the landweber iteration is a stable method for solving nonlinear ill posed problems for perturbed data with noise level delta we propose a stopping rule that yields the convergence rate o delta 1 2 under appropriate conditions we illustrate these conditions for a few examples

characterizing the scale dimension of a high dimensional classification problem classi cation of high dimensional data is inherently di1cult we present an exploratory data analysis methodology for characterizing the scale dimension of a classi cation problem the idea is to characterize the support of one distinguished target class as a collection of balls covering the class with each ball centeredat an observation in that class such that the radius is maximal without containing observations from the other classes the scale dimension is de ned to be the number of distinct radii ball sizes required to cover the class without covering observations from the other class a greedy algorithm is used to t the balls the balls then provide a description of the support of the target class with information about the complexity of the classi cation problem implicit in the number radii adjacency and position of the balls clustering the balls by radius and pruning the cluster tree yields an estimate of the scale dimension for the problem we illustrate the methodology with pedagogical simulations anda chemical sensor data analysis application publishedby elsevier science ltdon behalf of pattern recognition society

a posteriori parameter choice strategies for some newton type methods for the regularization of nonlinearill posed problems this paper treats a class of newton type methods for the approximate solution of nonlinear ill posed operator equations that use so called filter functions for regularizing the linearized equation in each newton step for noisy data we derive an aposteriori stopping rule that yields convergence of the iterates to asolution as the noise level goes to zero under certain smoothness conditions on the nonlinear operator appropriate closeness and smoothness assumptions on the starting value and the solution are shown to lead to optimal convergence rates moreover we present an application of the newton type methods under consideration to a parameter identification problem together with some numerical results

dimension reduction method for ode fluid models we develop a new dimension reduction method for large size systems of ordinary differential equations odes obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow the method is also applicable to other large size classical particle systems with negligibly small variations of particle concentration we propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution to illustrate the computational advantages of the proposed reduction method we use it to solve a system of smoothed particle hydrodynamic odes describing single phase and two phase layered poiseuille flows driven by uniform and periodic in space body forces for the single phase poiseuille flow driven by the uniform force the coarse solution was obtained with the zero order deconvolution for the single phase flow driven by the periodic body force and for the two phase flows the higher order the first and second order deconvolutions were necessary to obtain a sufficiently accurate solution

on the acceleration of kaczmarz s method for inconsistent linear systems abstract let the linear system ax b be rectangular but solvable if a is a large sparse matrix then one possibility to solve the system is to use the iterative method of kaczmarz even in the case when the system is unsolvable this method is applicable if the relaxation parameters are kept fixed in a certain interval to get a meaningful result however one has to apply strong underrelaxation we give an interpretation of the limit in terms of a generalized inverse of a and derive bounds with respect to the least squares solution using a result of buoni and varga we estimate the speed of convergence it is further shown that the eigenvalues of the iteration matrix are nearly real numbers and we propose to use chebyshev acceleration this results in a significant speedup

the instability of some gradient methods for ill posed problems for the solution of linear ill posed problems some gradient methods like conjugate gradients and steepest descent have been examined previously in the literature it is shown that even though these methods converge in the case of exact data their instability makes it impossible to base a priori parameter choice regularization methods upon them

supersymmetric quantum theory and non commutative geometry classical differential geometry can be encoded in spectral data such as connes spectral triples involving supersymmetry algebras in this paper we formulate non commutative geometry in terms of supersymmetric spectral data this leads to generalizations of connes non commutative spin geometry encompassing non commutative riemannian symplectic complex hermitian and hyper kahler geometry a general framework for non commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples in particular the non commutative torus and the non commutative 3 sphere are studied in some detail

extended domain eigenfunction method edem a study of ill posedness and regularization the extended domain eigenfunction method edem proposed for solving elliptic boundary value problems on annular like domains requires an inversion process the procedure thus represents an ill posed problem whose numerical solution involves an ill conditioned system of equations in this paper the ill posed nature of edem is studied and numerical solutions based on regularization schemes are considered it is shown that the edem solution methodology lends itself naturally to a formulation in terms of the well known iterative landweber method and the more general and faster converging semi iterative regularization schemes theoretical details and numerical results of the regularization schemes are presented for the case of the two dimensional laplace operator on annular domains

r k type landweber method for nonlinear ill posed problems in this paper we propose the r k type landweber iteration and investigate the convergence of the method for nonlinear ill posed problem f x y where f h h is a nonlinear operator between hilbert space h moreover for perturbed data with noise level d we prove that the convergence rate is o d 2 3 under appropriate conditions finally the numerical performance of this r k type landweber iteration for a nonlinear convolution equation is compared with the landweber iteration

matrix theory compactification on noncommutative t4 z2 in this article we construct gauge bundles on a noncommutative toroidal orbifold t 4 z2 first we explicitly construct a bundle with constant curvature connections on a noncommutative t 4 following rieffel s method then applying the appropriate quotient conditions for its z2 orbifold we find a connes douglas schwarz type solution of matrix theory compactified on t 4 z2 when we consider two copies of a bundle on t 4 invariant under the z2 action the resulting higgs branch moduli space of equivariant constant curvature connections becomes an ordinary toroidal orbifold t4 z2

probability estimation for multi class classification using adaboost abstract it is a general viewpoint that adaboost classifier has excellent performance on classification problems but could not produce good probability estimations in this paper we put forward a theoretical analysis of probability estimation model and present some verification experiments which indicate that adaboost can be used for probability estimation with the theory we suggest some useful measures for using adaboost algorithms properly and then we deduce a probability estimation model for multi class classification by pairwise coupling unlike previous approximate methods we provide an analytical solution instead of a special iterative procedure moreover a new problem that how to get a robust prediction with classifier scores is proposed experiments show that the traditional predict framework which chooses one with the highest score from all classes as the prediction is not always good while our model performs well

fft based preconditioners for toeplitz block least squares problems discretized two dimensional deconvolution problems arising e g in image restoration and seismic tomography can be formulated as least squares computations min b tx 2 where t is often a large scale rectangular toeplitz block matrix the authors consider solving such block least squares problems by the preconditioned conjugate gradient algorithm using square nonsingular circulant block and related preconditioners constructed from the blocks of the rectangular matrix t preconditioning with such matrices allows efficient implementation using the one dimensional or two dimensional fast fourier transform fft two block preconditioners related to those proposed by t chan and j olkin for square nonsingular toeplitz block systems are derived and analyzed it is shown that for important classes of t the singular values of the preconditioned matrix are clustered around one this extends the authors earlier work on preconditioners for toeplitz least squares iterations for one dimensiona

theta functions on noncommutative t4 we construct the so called theta vectors on noncommutative t4 which correspond to the theta functions on commutative tori with complex structures following the method of dieng and schwarz we first construct holomorphic connections and then find the functions satisfying the holomorphic conditions the theta vectors the holomorphic structure in the noncommutative t4 case is given by a 2 2 complex matrix and the consistency requires its off diagonal elements to be the same we also construct the tensor product of these functions satisfying the consistency requirement

solving multi class problems with linguistic fuzzy rule based classification systems based on pairwise learning and preference relations this paper deals with multi class classification for linguistic fuzzy rule based classification systems the idea is to decompose the original data set into binary classification problems using the pairwise learning approach confronting all pair of classes and to obtain an independent fuzzy system for each one of them along the inference process each fuzzy rule based classification system generates an association degree for both of its corresponding classes and these values are encoded into a fuzzy preference relation our analysis is focused on the final step that returns the predicted class label specifically we propose to manage the fuzzy preference relation using a non dominance criterion on the different alternatives contrasting the behaviour of this model with both the classical weighted voting scheme and a decision rule that combines the fuzzy relations of preference conflict and ignorance by means of a voting strategy our experimental study is carried out using two different linguistic fuzzy rule learning methods for which we show that the non dominance criterion is a good alternative in comparison with the previously mentioned aggregation mechanisms this empirical analysis is supported through the corresponding statistical analysis using non parametrical tests

semi iterative regularization in hilbert scales in this paper we investigate the regularizing properties of semi iterative regularization methods in hilbert scales for linear ill posed problems and perturbed data it is well known that standard landweber iteration can be remarkably accelerated by polynomial acceleration methods leading to optimal speed of convergence which can be obtained by several efficient two step methods e g the nu methods by brakhage it was observed earlier that a similar speed of convergence i e similar iteration numbers yielding optimal convergence rates can be obtained if landweber iteration is performed in hilbert scales we show that a combination of both ideas allows for a further acceleration yielding optimal convergence rates with only the square root of iterations as compared to the nu methods or landweber iteration in hilbert scales the theoretical results are illustrated by several examples and numerical tests including a comparison to the method of conjugate gradients

on the discrepancy principle for iterative and parametric methods to solve linear ill posed equations for the numerical solution of non necessarily well posed linear equations in banach spaces we consider a class of iterative methods which contains well known methods like the richardson iteration if the associated resolvent operator fulfils a condition with respect to a sector it is the purpose of this paper to show that for given noisy right hand side the discrepancy principle being a stopping rule for the iteration methods belonging to the mentioned class defines a regularization method and convergence rates are proved under additional smoothness conditions on the initial error this extends similar results obtained for positive semidefinite problems in hilbert spaces then we consider a class of parametric methods which under the same resolvent condition contains the method of the abstract cauchy problem and under a weaker resolvent condition the iterated method of lavrentiev a modified discrepancy principle is formulated for them and finally numerical illustrations are presented

transverse fully nonlinear equations on sasakian manifolds and applications abstract we prove a priori estimates for a class of transverse fully nonlinear equations on sasakian manifolds and give some geometric applications such as the transversion calabi yau theorem for transverse balanced and strongly gauduchon metrics we also explain that similar results hold on compact oriented taut transverse hermitian foliated manifold of complex co dimension n and give some geometric applications such as the transverse calabi yau theorems for transverse hermitian and strongly gauduchon metrics

the kahler ricci flow on surfaces of positive kodaira dimension 4 estimates 9 4 1 the zeroth order and volume estimates 9 4 2 a partial second order estimate 13 4 3 gradient estimates 14 4 4 the second order estimates 18

online learning of complex prediction problems using simultaneous projections we describe and analyze an algorithmic framework for online classification where each online trial consists of multiple prediction tasks that are tied together we tackle the problem of updating the online predictor by defining a projection problem in which each prediction task corresponds to a single linear constraint these constraints are tied together through a single slack parameter we then introduce a general method for approximately solving the problem by projecting simultaneously and independently on each constraint which corresponds to a prediction sub problem and then averaging the individual solutions we show that this approach constitutes a feasible albeit not necessarily optimal solution of the original projection problem we derive concrete simultaneous projection schemes and analyze them in the mistake bound model we demonstrate the power of the proposed algorithm in experiments with synthetic data and with multiclass text categorization tasks

on the regularity theory of fully nonlinear parabolic equations ii recently m crandall and p l lions 3 developed a very successful method for proving the existence of solutions of nonlinear second order partial differential equations their method called the theory of viscosity solutions also applies to fully nonlinear equations in which even the second order derivatives can enter in nonlinear fashion solutions produced by the viscosity method are guaranteed to be continuous but not necessarily smooth here we announce smoothness results for viscosity solutions our methods extend those of 1 we obtain krylov safonov i e c estimates 8 c 1 schauder c and w estimates for viscosity solutions of uniformly parabolic equations in general form the results can be viewed as a priori estimates on the classical c solutions our method produces in particular regularity results for a broad new array of nonlinear heat equations including the bellman equation 6

an accelerated alternating procedure for the cauchy problem for the helmholtz equation in this paper we study the cauchy problem for the helmholtz equation this problem appears in various applications and is severely ill posed the modified alternating procedure has been proposed by

the fast fourier transform method and ill conditioned matrices we study the problem of finding numerical solutions of the linear algebraic equation a x b where a denotes an nxn ill conditioned coefficient matrix it is well known that gaussian elimination methods coupled with pivoting strategies are ineffective in this setting due to round off error we propose a new and simple application of the fast fourier transform fft method other viable methods such as the qr method qrm or the singular value decomposition method svdm have been proposed in the literature the goal of this paper is to investigate the performance of the proposed method and compare it to other popular methods the comparison is illustrated by computer simulation results using matlab

spectral algorithms for supervised learning we discuss how a large class of regularization methods collectively known as spectral regularization and originally designed for solving ill posed inverse problems gives rise to regularized learning algorithms all of these algorithms are consistent kernel methods that can be easily implemented the intuition behind their derivation is that the same principle allowing for the numerical stabilization of a matrix inversion problem is crucial to avoid overfitting the various methods have a common derivation but different computational and theoretical properties we describe examples of such algorithms analyze their classification performance on several data sets and discuss their applicability to real world problems

pointwise rational approximation and iterative methods for iii posed problems we study the connection between the pointwise approximation of the zero function by rational functions and iterative methods for the approximate solution of ill posed linear equations results are presented on convergence stability and saturation phenomena

learning from examples as an inverse problem many works related learning from examples to regularization techniques for inverse problems emphasizing the strong algorithmic and conceptual analogy of certain learning algorithms with regularization algorithms in particular it is well known that regularization schemes such as tikhonov regularization can be effectively used in the context of learning and are closely related to algorithms such as support vector machines nevertheless the connection with inverse problem was considered only for the discrete finite sample problem and the probabilistic aspects of learning from examples were not taken into account in this paper we provide a natural extension of such analysis to the continuous population case and study the interplay between the discrete and continuous problems from a theoretical point of view this allows to draw a clear connection between the consistency approach in learning theory and the stability convergence property in ill posed inverse problems the main mathematical result of the paper is a new probabilistic bound for the regularized least squares algorithm by means of standard results on the approximation term the consistency of the algorithm easily follows

a predictor corrector iterated tikhonov regularization for linear ill posed inverse problems many questions in science and engineering often give rise to linear ill posed inverse problems to enable meaningful approximate solutions of the inverse problems various regularization methods have subsequently been proposed to make these problems less sensitive to perturbations one of the most popular regularization techniques is iterated tikhonov regularization which has attracted considerable attention due to its interesting applications in practical however this regularization often suffers from inaccurate results and low computational efficiency in some situations in this paper we proposed an accelerated predictor corrector iterated tikhonov regularization this method combined the classical iterated tikhonov regularization with modified euler method which could improve computational efficiency without sacrificing numerical accuracy the convergence rate of the accelerated regularization was investigated theoretically when the right hand side was corrupted by noise in particular we derived an error estimate of optimal order for the convergence of the accelerated regularization both one and two dimensional numerical experiments were implemented to illustrate the accuracy and efficiency of the accelerated version of iterated tikhonov regularization

image reconstruction and restoration using the simplified topological e algorithm in order to compute meaningful approximations of the solutions of large scale linear inverse ill posed problems some form of regularization should be employed cimmino and landweber methods are well known iterative regularization methods that can be quite successfully applied for tomographic reconstruction and image restoration problems despite their usually slow convergence the goal of this paper is to explore the performance of a recent extrapolation algorithm when applied to accelerate the convergence of these iterative regularization methods in particular we provide insight and algorithmic details about the simplified topological e algorithm applied to slow converging iterative regularization methods the results of many numerical experiments and comparisons with other methods are also displayed

convergence analysis of the homotopy perturbation method for solving nonlinear ill posed operator equations the homotopy perturbation method is used to construct a new iteration algorithm for solving nonlinear ill posed operator equations numerical tests are given showing that the algorithm is more efficient than the well known landweber method

a regularization algorithm for decoding perceptual temporal profiles from fmri data in several biomedical fields researchers are faced with regression problems that can be stated as statistical learning problems one example is given by decoding brain states from functional magnetic resonance imaging fmri data recently it has been shown that the general statistical learning problem can be restated as a linear inverse problem hence new algorithms were proposed to solve this inverse problem in the context of reproducing kernel hilbert spaces in this paper we detail one iterative learning algorithm belonging to this class called method and test its effectiveness in a between subjects regression framework specifically our goal was to predict the perceived pain intensity based on fmri signals during an experimental model of acute prolonged noxious stimulation we found that using a linear kernel the psychophysical time profile was well reconstructed while pain intensity was in some cases significantly over underestimated no substantial differences in terms of accuracy were found between the proposed approach and one of the state of the art learning methods the support vector machines nonetheless adopting the method yielded a significant reduction in computational time an advantage that became more evident when a relevant feature selection procedure was implemented the method can be easily extended and included in typical approaches for binary or multiple classification problems and therefore it seems well suited to build effective brain activity estimators

a new approach for imbalanced data classification based on data gravitation imbalanced classification is an important machine learning research topic that troubles most general classification models because of the imbalanced class distribution a newly developed physical inspired classification method i e the data gravitation based classification dgc model performs well in many general classification problems however like other general classifiers the performance of dgc suffers in imbalanced tasks in this study we develop a specific dgc model namely imbalanced dgc idgc model for imbalanced problems the amplified gravitation coefficient agc is introduced for gravitation computing agc is a type of coefficient that contains class imbalance information which can strengthen and weaken the gravitational field of the minority and majority classes we also design a fitness evaluation function in the weight optimization procedure of the data distribution to ensure that the model parameters adapt to the imbalanced class distributions a total of 44 binary class data sets and 15 multiclass imbalanced data sets are used to test the performance of the proposed method experimental results show that the adapted dgc model is effective for imbalanced problems

a novel technique for subpixel image classification based on support vector machine this paper presents a novel support vector machine classifier designed for subpixel image classification pixel spectral unmixing the proposed classifier generalizes the properties of svms to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic this results in the definition of a fuzzy input fuzzy output support vector machine f2svm classifier that can 1 process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2 provide a fuzzy modeling of the classification results allowing a relation many to one between classes and pixels the presented binary f2svm can address multicategory problems according to two strategies the fuzzy one against all foaa and the fuzzy one against one foao strategies these strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems the effectiveness of the proposed f2svm classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics experimental results confirm the validity of the proposed subpixel classification method