local properties of j complex curves in lipschitz continuous structures we prove the existence of primitive curves and positivity of intersections of j complex curves for lipschitz continuous almost complex structures these results are deduced from the comparison theorem for j holomorphic maps in lipschitz structures previously known for j of class mathcal c 1 lip we also give the optimal regularity of curves in lipschitz structures it occurs to be mathcal c 1 lnlip i e the first derivatives of a j complex curve for lipschitz j are log lipschitz continuous a simple example that nothing better can be achieved is given further we prove the genus formula for j complex curves and determine their principal puiseux exponents all this for lipschitz continuous j s

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

simultaneous supervised clustering and feature selection over a graph in this article we propose a regression method for simultaneous supervised clustering and feature selection over a given undirected graph where homogeneous groups or clusters are estimated as well as informative predictors with each predictor corresponding to one node in the graph and a connecting path indicating a priori possible grouping among the corresponding predictors the method seeks a parsimonious model with high predictive power through identifying and collapsing homogeneous groups of regression coefficients to address computational challenges we present an efficient algorithm integrating the augmented lagrange multipliers coordinate descent and difference convex methods we prove that the proposed method not only identifies the true homogeneous groups and informative features consistently but also leads to accurate parameter estimation a gene network dataset is analysed to demonstrate that the method can make a difference by exploring dependency structures among the genes

singularities of j holomorphic curves let v j be an almost complex manifold recall that a map from a riemann surface to v is j holomorphic if its derivative is complex linear a j holomorphic curve or j curve for short is the image of such a map nowhere locally constant the study of singularities of j holomorphic curves began with the statement of m gromov g about the positivity of intersections in the case when v is of dimension 4 the homological intersection of two compact j curves is a sum of positive local contributions and a similar property holds for the self intersection of one curve adjunction formula this property is crucial for applications of the theory to symplectic topology in dimension 4 and contact topology in dimension 3 gromov mcduff eliashberg hofer the positivity of intersections was proved by d mcduff mcd1 see also chapter vi in al then in mcd2 she proved that in any dimension a germ of j holomorphic map c 0 v v0 is topologically equivalent to a standard holomorphic germ from c 0 to cn 0 this was then strengthened to a c 1equivalence by m micallef and b white mw as a special case of a much more general result on singularities of generalized minimal surfaces they proved also that it applies to reducible germs

learning a mahalanobis distance metric for data clustering and classification distance metric is a key issue in many machine learning algorithms this paper considers a general problem of learning from pairwise constraints in the form of must links and cannot links as one kind of side information a must link indicates the pair of the two data points must be in a same class while a cannot link indicates that the two data points must be in two different classes given must link and cannot link information our goal is to learn a mahalanobis distance metric under this metric we hope the distances of point pairs in must links are as small as possible and those of point pairs in cannot links are as large as possible this task is formulated as a constrained optimization problem in which the global optimum can be obtained effectively and efficiently finally some applications in data clustering interactive natural image segmentation and face pose estimation are given in this paper experimental results illustrate the effectiveness of our algorithm

the hartogs type extension theorem for meromorphic maps into compact kahler manifolds extension theorems of this type are often called hartogs type extension theorems the above result was conjectured by griffiths see problem 1 in gr who proved it in the special case when d p o i n t and f d x is holomorphic important contributions towards the proof of this conjecture were made by b shiffman y t siu n sibony see sh sil sb3 in particular y t siu proved a thullen type extension theorem for meromorphic maps into compact kfihler manifolds see w 1 the above theorem can be applied to the study of covering maps of zariski open subsets in compact kfihler manifolds recall that a subdomain d of a complex manifold m is called levi pseudoconvex if for any peod there exists a neighbourhood u of p in m such that u c d is stein we say that d covers a complex manifold x if there is a subgroup g c aut d acting properly discontinuously and freely on d with d g x

discriminant adaptive nearest neighbor classification nearest neighbour classification expects the class conditional probabilities to be locally constant and suffers from bias in high dimensions we propose a locally adaptive form of nearest neighbour classification to try to ameliorate this curse of dimensionality we use a local linear discriminant analysis to estimate an effective metric for computing neighbourhoods we determine the local decision boundaries from centroid information and then shrink neighbourhoods in directions orthogonal to these local decision boundaries and elongate them parallel to the boundaries thereafter any neighbourhood based classifier can be employed using the modified neighbourhoods the posterior probabilities tend to be more homogeneous in the modified neighbourhoods we also propose a method for global dimension reduction that combines local dimension information in a number of examples the methods demonstrate the potential for substantial improvements over nearest neighbour classification

automorphismes reels d un fibre et operateurs de cauchy riemann soit n c n un fibre vectoriel complexe muni d une structure reelle au dessus d une courbe reelle sigma g c sigma de genre g in mathbb n nous etudions le signe de l action des automorphismes de n c n relevant l identite de sigma g sur les orientations du fibre determinant au dessus de l espace des operateurs de cauchy riemann reels de n c n ce signe s obtient comme le produit de deux termes le premier calcule la signature des permutations induite par les automorphismes sur les structures pin pm de la partie reelle de n c n le second provient de l action des automorphismes du fibre sur les classes de bordisme de structures spin reelles de sigma g c sigma

an obstruction bundle relating gromov witten invariants of curves and kahler surfaces in a previous paper the authors defined symplectic local gromov witten invariants associated to spin curves and showed that the gw invariants of a k ahler surface x with p g 0 are a sum of such local gw invariants this paper describes how the local gw invariants arise from an obstruction bundle in the sense of taubes over the space of stable maps into curves together with the results of our earlier paper this reduces the calculation of the gw invariants of elliptic and general type complex surfaces to computations in the gw theory of curves with additional classes the euler classes of the real obstruction bundles

almost kahler forms on rational 4 manifolds we study nakai moishezon type question and donaldson s tamed to compatible question for almost complex structures on rational four manifolds by extending taubes subvarieties current form technique to j nef genus 0 classes we give affirmative answers of these two questions for all tamed almost complex structures on s 2 bundles over s 2 as well as for many geometrically interesting tamed almost complex structures on other rational four manifolds including the del pezzo ones

continuous solutions of nonlinear cauchy riemann equations and pseudoholomorphic curves in normal coordinates we establish elliptic regularity for nonlinear inhomogeneous cauchy riemann equations under weak assumptions and give a counterexample in a borderline case in some cases where the inhomogeneous term has a separable factorization the solution set can be explicitly calculated the methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost complex structures

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

finite time singularities in ideal fluids with swirl three dimensional ideal incompressible fluids with swirl are studied numerically using two different methods standard finite differences and a projection method based on upwind differencing both methods give quantitatively similar results leading to the conclusion that singularities form in finite time in a manner consistent with known theoretical criteria the effect of singularities in incompressible flows on nearby compressible flows is discussed

semi supervised affinity propagation with soft instance level constraints soft constraint semi supervised affinity propagation scssap adds supervision to the affinity propagation ap clustering algorithm without strictly enforcing instance level constraints constraint violations lead to an adjustment of the ap similarity matrix at every iteration of the proposed algorithm and to addition of a penalty to the objective function this formulation is particularly advantageous in the presence of noisy labels or noisy constraints since the penalty parameter of scssap can be tuned to express our confidence in instance level constraints when the constraints are noiseless scssap outperforms unsupervised ap and performs at least as well as the previously proposed semi supervised ap and constrained expectation maximization in the presence of label and constraint noise scssap results in a more accurate clustering than either of the aforementioned established algorithms finally we present an extension of scssap which incorporates metric learning in the optimization objective and can further improve the performance of clustering

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

evidence for the development of singularities in euler flow abstract this paper is about the problem of determining whether singularities can develop from analytic initial conditions in the euler flow of three dimensional hydrodynamics the evidence is supplied by previous numerical simulations to provide a guide for interpreting this numerical output a theory based on renormalization is outlined here we conclude that it appears that the numerical results can be satisfactorily explained by this theory and that together theory and simulation support the verdict that singularities exist thus a more detailed and rigorous development of the application of the renormalization theory to this system is warranted

invariants of real symplectic 4 manifolds and lower bounds in real enumerative geometry we first build the moduli spaces of real rational pseudo holomorphic curves in a given real symplectic 4 manifold then following the approach of gromov and witten 3 19 11 we define invariants under deformation of real symplectic 4 manifolds these invariants provide lower bounds for the number of real rational j holomorphic curves which realize a given homology class and pass through a given real configuration of points

metric and kernel learning using a linear transformation metric and kernel learning arise in several machine learning applications however most existing metric learning algorithms are limited to learning metrics over low dimensional data while existing kernel learning algorithms are often limited to the transductive setting and do not generalize to new data points in this paper we study the connections between metric learning and kernel learning that arise when studying metric learning as a linear transformation learning problem in particular we propose a general optimization framework for learning metrics via linear transformations and analyze in detail a special case of our framework that of minimizing the logdet divergence subject to linear constraints we then propose a general regularized framework for learning a kernel matrix and show it to be equivalent to our metric learning framework our theoretical connections between metric and kernel learning have two main consequences 1 the learned kernel matrix parameterizes a linear transformation kernel function and can be applied inductively to new data points 2 our result yields a constructive method for kernelizing most existing mahalanobis metric learning formulations we demonstrate our learning approach by applying it to large scale real world problems in computer vision text mining and semi supervised kernel dimensionality reduction

geometric statistics in turbulence the author presents results regarding certain average properties of incompressible fluids derived from the equations of motion the author estimates the average dissipation rate the average dimension of level sets the role played by the field of direction of vorticity in the three dimensional euler and navier stokes equations is discussed and a class of two dimensional equations that are useful models of incompressible dynamics is described the author presents results concerning scaling exponents in turbulence