on the quadratic finite element approximation to the obstacle problem in this paper we obtain the error bound o left h frac 32 epsilon right for any epsilon 0 for the piecewise quadratic finite element approximation to the obstacle problem without the hypothesis that the free boundary has finite length see 3

a two level algorithm for an obstacle problem abstract due to the inequality feature of the obstacle problem the standard quadratic finite element method for solving the problem can only achieve an error bound of the form o n 3 4 n being the total number of degrees of freedom and 0 arbitrary to achieve a better error bound the key lies in how to capture the free boundary accurately in this paper we propose a two level algorithm for solving the obstacle problem the first part of the algorithm is through the use of the linear elements on a quasi uniform mesh then information on the approximate free boundary from the linear element solution is used in the construction of a quadratic finite element method under some assumptions it is shown that the numerical solution from the two level algorithm is expected to have a nearly optimal error bound of o n 1 0 arbitrary such an expected convergence order is observed numerically in numerical examples

a fast iterative nearest point algorithm for support vector machine classifier design in this paper we give a new fast iterative algorithm for support vector machine svm classifier design the basic problem treated is one that does not allow classification violations the problem is converted to a problem of computing the nearest point between two convex polytopes the suitability of two classical nearest point algorithms due to gilbert and mitchell et al is studied ideas from both these algorithms are combined and modified to derive our fast algorithm for problems which require classification violations to be allowed the violations are quadratically penalized and an idea due to cortes and vapnik and friess is used to convert it to a problem in which there are no classification violations comparative computational evaluation of our algorithm against powerful svm methods such as platt s sequential minimal optimization shows that our algorithm is very competitive

log canonical models for the moduli space of curves the first divisorial contraction in this paper we initiate our investigation of log canonical models for m g as we decrease from 1 to 0 we prove that for the first critical value 9 11 the log canonical model is isomorphic to the moduli space of pseudostable curves which have nodes and cusps as singularities we also show that 7 10 is the next critical value i e the log canonical model stays the same in the interval 7 10 9 11 in the appendix we develop a theory of log canonical models of stacks that explains how these can be expressed in terms of the coarse moduli space

discontinuous galerkin methods for solving a quasistatic contact problem we consider the numerical solution of a nonlinear evolutionary variational inequality arising in the study of quasistatic contact problems we study spatially semi discrete and fully discrete schemes for the problem with several discontinuous galerkin discretizations in space and finite difference discretization in time under appropriate regularity assumptions on the solution a unified error analysis is established for the schemes reaching the optimal convergence order for linear elements numerical results are presented on a two dimensional test problem to illustrate numerical convergence orders

compact convex projections we study the usefulness of conditional gradient like methods for determining projections onto convex sets in particular projections onto naturally arising convex sets in reproducing kernel hilbert spaces our work is motivated by the recently introduced kernel herding algorithm which is closely related to the conditional gradient method cgm it is known that the herding algorithm converges with a rate of 1 t where t counts the number of iterations when a point in the interior of a convex set is approximated we generalize this result and we provide a necessary and sufficient condition for the algorithm to approximate projections with a rate of 1 t the cgm which is in general vastly superior to the herding algorithm achieves only an inferior rate of 1 t in this setting we study the usefulness of such projection algorithms further by exploring ways to use these for solving concrete machine learning problems in particular we derive non parametric regression algorithms which use at their core a slightly modified kernel herding algorithm to determine projections we derive bounds to control approximation errors of these methods and we demonstrate via experiments that the developed regressors are en par with state of the art regression algorithms for large scale problems

fast svm training using approximate extreme points applications of non linear kernel support vector machines svms to large data sets is seriously hampered by its excessive training time we propose a modification called the approximate extreme points support vector machine aesvm that is aimed at overcoming this burden our approach relies on conducting the svm optimization over a carefully selected subset called the representative set of the training data set we present analytical results that indicate the similarity of aesvm and svm solutions a linear time algorithm based on convex hulls and extreme points is used to compute the representative set in kernel space extensive computational experiments on nine data sets compared aesvm to libsvm chang and lin 2011 cvm tsang et al 2005 bvm tsang et al 2007 lasvm bordes et al 2005 svmperf joachims and yu 2009 and the random features method rahimi and recht 2007 our aesvm implementation was found to train much faster than the other methods while its classification accuracy was similar to that of libsvm in all cases in particular for a seizure detection data set aesvm training was almost 500 times faster than libsvm and lasvm and 20 times faster than cvm and bvm additionally aesvm also gave competitively fast classification times

on the maximum deviation between the histogram and the underlying density the limiting joint distribution of the location and size of the maximum deviation between the historgram and the underlying density is derived for smooth densities the location and size of the maximum are asymptotically independent the size has a limiting double exponential distribution and the location has a limiting normal distribution

data compression and histograms in this paper the relationship between code length and the selection of the number of bins for a histogram density is considered for a sequence of iid observations on 0 1 first we use a shortest code length criterion to select the number of bins for a histogram a uniform almost sure asymptotic expansion for the code length is given and it is used to prove the asymptotic optimality of the selection rule in addition the selection rule is consistent if the true density is uniform 0 1 secondly we deal with the problem what is the best achievable average code length with underlying density functionf minimax lower bounds are derived for the average code length over certain smooth classes of underlying densitiesf for the smooth class with bounded first derivatives the rate in the lower bound is shown to be achieved by a code based on a sequence of histograms whose number of bins is changed predictively moreover this best code can be modified to ensure that the almost sure version of the code length has asymptotically the same behavior as its expected value i e the average code length

training a support vector machine in the primal most literature on support vector machines svms concentrates on the dual optimization problem in this letter we point out that the primal problem can also be solved efficiently for both linear and nonlinear svms and that there is no reason for ignoring this possibility on the contrary from the primal point of view new families of algorithms for large scale svm training can be investigated

morphisms and faces of pseudo effective cones let x y be a morphism of projective varieties and suppose that is a pseudo effective numerical cycle class satisfying 0 a conjecture of debarre jiang and voisin predicts that is a limit of classes of effective cycles contracted by we establish new cases of the conjecture for higher codimension cycles in particular we prove a strong version when x is a fourfold and has relative dimension one

a hybrid classification algorithm by subspace partitioning through semi supervised decision tree among data mining techniques the decision tree is one of the more widely used methods for building classification models in the real world because of its simplicity and ease of interpretation however the method has some drawbacks including instability the nonsmooth nature of the decision boundary and the possibility of overfitting to overcome these problems several works have utilized the relative advantages of other classifiers such as logistic regression support vector machine and neural networks in combination with a decision tree in hybrid models which avoid the drawbacks of other models some hybrid models have used decision trees to quickly and efficiently partition the input space and many studies have proved the effectiveness of the hybrid methods however there is room for further improvement by considering the topological properties of a dataset because typical decision trees split nodes based only on the target variable the proposed semi supervised decision tree splits internal nodes by utilizing both labels and the structural characteristics of data for subspace partitioning to improve the accuracy of classifiers applied to terminal nodes in the hybrid models experimental results confirm the superiority of the proposed algorithm and demonstrate the detailed characteristics of the algorithm highlightspropose the semi supervised split criterion for decision trees combine the semi supervised decision tree as subspace partitioning with other classifiers experiments on several datasets showed that the proposed method outperforms the existing ones

towards the ample cone of mg n in this paper we study the ample cone of the moduli space m g n of stable n pointed curves of genus g our motivating conjecture is that a divisor on m g n is ample iff it has positive intersection with all 1 dimensional strata the components of the locus of curves with at least 3g n 2 nodes this translates into a simple conjectural description of the cone by linear inequalities and as all the 1 strata are rational includes the conjecture that the mori cone is polyhedral and generated by rational curves our main result is that the conjecture holds iff it holds for g 0 more precisely there is a natural finite map r m0 2g n m g n whose image is the locus rg n of curves with all components rational any 1 strata either lies in rg n or is numerically equivalent to a family e of elliptic tails and we show that a divisor d is nef iff d e 0 and r d is nef we also give results on contractions i e morphisms with connected fibers to projective varieties of m g n for g 1 showing that any fibration factors through a tautological one given by forgetting points and that the exceptional locus of any birational contraction is contained in the boundary

the design of stable sparse wavefield extrapolators using projections onto convex sets abstractwe present the results of poststack explicit depth migration of the well known 2d seg eage salt model zero offset seismic data using sparse wavefield extrapolators the extrapolators are designed to be sparse by forcing some of the very small complex valued coefficients magnitude values to be zero the proposed extrapolators design method combines the previously reported modified projections onto convex sets mpocs for designing explicit depth frequency space f x wavefield extrapolation operators with hard thresholding of the small extrapolators coefficients magnitude the real and imaginary parts of the mpocs operators with small magnitudes are replaced by zeros during the mpocs algorithm iterations the migrated result of the seg eage salt model data using such sparse designed operators shows comparable migrated results using the nonsparse version of the mpocs extrapolation operators as well as the image obtained using the well known phase shift plus interpolation pspi migration techn

extremal effective divisors on overline mathcal m _ 1 n for every n ge 3 we exhibit infinitely many extremal effective divisors on overline mathcal m 1 n the deligne mumford moduli space parameterizing stable genus one curves with n ordered marked points

improving quality of sample entropy estimation for continuous distribution probability functions abstract entropy is a one of the key parameters characterizing state of system in statistical physics although the entropy is defined for systems described by discrete and continuous probability distribution function pdf in numerous applications the sample entropy is estimated by a histogram which in fact denotes that the continuous pdf is represented by a set of probabilities such a procedure may lead to ambiguities and even misinterpretation of the results within this paper two possible general algorithms based on continuous pdf estimation are discussed in the application to the shannon and tsallis entropies it is shown that the proposed algorithms may improve entropy estimation particularly in the case of small data sets

effective cones of quotients of moduli spaces of stable n pointed curves of genus zero let x n m 0 n the moduli space of n pointed stable genus zero curves and let x n m be the quotient of x n by the action of s n m on the last n m marked points the cones of effective divisors ne 1 x n m m 0 1 2 are calculated using this upper bounds for the cones mov x n m generated by divisors with moving linear systems are calculated m 0 1 along with the induced bounds on the cones of ample divisors of m g and m g 1 as an application the cone ne 1 m 2 1 is analyzed in detail

oversmoothed nonparametric density estimates abstract the optimal histogram for a sample of size n from a density defined on the entire real line requires at least 2n 1 3 bins under mild smoothness conditions similar bounds exist for the frequency polygon and kernel estimators values near these bounds give nearly optimal results for a variety of smooth densities providing good quick density estimates

towards mori s program for the moduli space of stable maps we introduce and compute the class of a number of effective divisors on the moduli space of stable maps overline scr m 0 0 bbb p r d which for small d provide a good understanding of the extremal rays and the stable base locus decomposition for the effective cone we also discuss various birational models that arise in mori s program including the hilbert scheme the chow variety the space of k stable maps the space of branchcurves and the space of semi stable sheaves

statistical inference for dea estimators of directional distances in productivity and efficiency analysis the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set the most familiar non parametric methods use farrell debreu shephard or hyperbolic radial measures these approaches require that inputs and outputs be non negative which can be problematic when using financial data recently chambers et al 1998 have introduced directional distance functions which can be viewed as additive rather than multiplicative measures efficiency directional distance functions are not restricted to non negative input and output quantities in addition the traditional input and output oriented measures are nested as special cases of directional distance functions consequently directional distances provide greater flexibility however until now only free disposal hull fdh estimators of directional distances and their conditional and robust extensions have known statistical properties simar and vanhems 2012 this paper develops the statistical properties of directional d estimators which are especially useful when the production set is assumed convex we first establish that the directional data envelopment analysis dea estimators share the known properties of the traditional radial dea estimators we then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance estimation of confidence intervals and bias correction the methods are illustrated in some empirical examples

linear time algorithms for linear programming in r 3 and related problems linear time algorithms for linear programming in r 2 and r 3 are presented the methods used are applicable for other graphic and geometric problems as well as quadratic programming for exam

tpmsvm a novel twin parametric margin support vector machine for pattern recognition a novel twin parametric margin support vector machine tpmsvm for classification is proposed in this paper this tpmsvm in the spirit of the twin support vector machine twsvm determines indirectly the separating hyperplane through a pair of nonparallel parametric margin hyperplanes solved by two smaller sized support vector machine svm type problems similar to the parametric margin email protected support vector machine email protected svm this tpmsvm is suitable for many cases especially when the data has heteroscedastic error structure that is the noise strongly depends on the input value but there is an advantage in the learning speed compared with the email protected svm the experimental results on several artificial and benchmark datasets indicate that the tpmsvm not only obtains fast learning speed but also shows good generalization

the essential histogram the histogram is widely used as a simple exploratory display of data but it is usually not clear how to choose the number and size of bins we construct a confidence set of distribution functions that optimally address the two main tasks of the histogram estimating probabilities and detecting features such as increases and modes in the distribution we define the essential histogram as the histogram in the confidence set with the fewest bins thus the essential histogram is the simplest visualization of the data that optimally achieves the main tasks of the histogram the only assumption we make is that the data are independent and identically distributed we provide a fast algorithm for the essential histogram and illustrate our methodology with examples an r package is available on cran

lagrangian support vector machines an implicit lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed this leads to the minimization of an unconstrained differentiable convex function in a space of dimensionality equal to the number of classified points this problem is solvable by an extremely simple linearly convergent lagrangian support vector machine lsvm algorithm lsvm requires the inversion at the outset of a single matrix of the order of the much smaller dimensionality of the original input space plus one the full algorithm is given in this paper in 11 lines of matlab code without any special optimization tools such as linear or quadratic programming solvers this lsvm code can be used as is to solve classification problems with millions of points for example 2 million points in 10 dimensional input space were classified by a linear surface in 82 minutes on a pentium iii 500 mhz notebook with 384 megabytes of memory and additional swap space and in 7 minutes on a 250 mhz ultrasparc ii processor with 2 gigabytes of memory other standard classification test problems were also solved nonlinear kernel classification can also be solved by lsvm although it does not scale up to very large problems it can handle any positive semidefinite kernel and is guaranteed to converge a short matlab code is also given for nonlinear kernels and tested on a number of problems

research in statistical graphics abstract three active areas of research in statistical graphics are methodology computing and graphical perception the five articles in this special section provide a good representation of these areas dynamic graphical methods which involve a tight weaving of methodological and computing issues are a particularly exciting topic of research dynamic graphics will soon have a major impact on how data are analyzed evaluation of graphical inventions is difficult certain visualization issues can be evaluated by studies in graphical perception at the moment however the performance of most graphical methods can be studied only by rigorous field testing in which the methods are used to analyze a large number of data sets a bibliography is provided to allow readers to begin a study of any of the major areas of statistical graphics

asymptotically optimal cells for a historgram on examine les proprietes de l histogramme lorsque les cellules sont arbitraires on obtient une expression asymptotique pour l infimum de l erreur quadratique moyenne integree mise sur toutes les partitions

mutual information identifies spurious hurst phenomena in resting state eeg and fmri data long range memory in time series is often quantified by the hurst exponent h a measure of the signal s variance across several time scales we analyze neurophysiological time series from electroencephalography eeg and functional magnetic resonance imaging fmri resting state experiments with two standard hurst exponent estimators and with the time lagged mutual information function applied to discretized versions of the signals a confidence interval for the mutual information function is obtained from surrogate markov processes with equilibrium distribution and transition matrix identical to the underlying signal for eeg signals we construct an additional mutual information confidence interval from a short range correlated tenth order autoregressive model we reproduce the previously described hurst phenomenon h 0 5 in the analytical amplitude of alpha frequency band oscillations in eeg microstate sequences and in fmri signals but we show that the hurst phenomenon occurs without long range memory in the information theoretical sense we find that the mutual information function of neurophysiological data behaves differently from fractional gaussian noise fgn for which the hurst phenomenon is a sufficient condition to prove long range memory two other well characterized short range correlated stochastic processes ornstein uhlenbeck cox ingersoll ross also yield h 0 5 whereas their mutual information functions lie within the markovian confidence intervals similar to neural signals in these processes which do not have long range memory by construction a spurious hurst phenomenon occurs due to slow relaxation times and heteroscedasticity time varying conditional variance in summary we find that mutual information correctly distinguishes long range from short range dependence in the theoretical and experimental cases discussed our results also suggest that the stationary fgn process is not sufficient to describe neural data which seem to belong to a more general class of stochastic processes in which multiscale variance effects produce hurst phenomena without long range dependence in our experimental data the hurst phenomenon and long range memory appear as different system properties that should be estimated and interpreted independently

shape fitting with outliers given a set mathcal h of n hyperplanes in bbb r d we present an algorithm that eps approximates the extent between the top and bottom k levels of the arrangement of mathcal h in time o n k eps c where c is a constant depending on d the algorithm relies on computing a subset of mathcal h of size o k eps d 1 in near linear time such that the k level of the arrangement of the subset approximates that of the original arrangement using this algorithm we propose efficient approximation algorithms for shape fitting with outliers for various shapes these are the first algorithms to handle outliers efficiently for the shape fitting problems considered

solvability of parabolic variational hemivariational inequalities involving space fractional laplacian abstract the paper is devoted to investigate a new kind of variational hemivariational inequality of parabolic type driven by a generalized space fractional laplace operator and two multivalued terms which are expressed by the clarke generalized gradient and convex subgradient respectively an existence theorem of weak solutions to the problem is established by applying a surjectivity theorem for the sum of operators combined with results from nonsmooth analysis

review papers recent developments in nonparametric density estimation abstract advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where re

estimating the false discovery rate using nonparametric deconvolution summary given a set of microarray data the problem is to detect differentially expressed genes using a false discovery rate fdr criterion as opposed to common procedures in the literature we do not base the selection criterion on statistical significance only but also on the effect size therefore we select only those genes that are significantly more differentially expressed than some f fold e g f 2 this corresponds to use of an interval null domain for the effect size based on a simple error model we discuss a naive estimator for the fdr interpreted as the probability that the parameter of interest lies in the null domain e g log2 2 1 given that the test statistic exceeds a threshold we improve the naive estimator by using deconvolution that is the density of the parameter of interest is recovered from the data we study performance of the methods using simulations and real data

the kodaira dimension of moduli spaces of curves with marked points the purpose of this paper is to generalize the methods and results due to eisenbud harris and mumford on the moduli space of curves of genus g to the moduli space of curves of genus g with n marked points the main result is the determination for each g with 4 g 23 of an n such that the moduli space is of general type 1 introduction in the early 1980s eisenbud harris and mumford stud ied mg the moduli space of curves of a given genus and succeeded in proving that if the genus is at least 24 the moduli space is of general type this was contrary to many people s expectations as it had been known for some time that moduli spaces of curves of small genus were rational or unirational briefly what is involved in their proof is the computation of the canonical divisor of mg the exhibition of certain effective divisors and the determination of their classes and the verification that the canonical divisor is the sum of an ample and an effective divisor in the other direction it is known that mg has kodaira dimension when g 13 or g 15 one can generalize the definition of mg by asking for a parametrization of the curves of genus g together with n distinct nonsingular points on them this amounts to studying instead of families of curves families of curves with n disjoint sections as before it turns out that one obtains a noncompact moduli space which is compactified by replacing nonsingular curve by stable curve in the definitions in order to be considered stable an n pointed curve is required only to have finitely many automorphisms that fix all the marked points the space can still be compact even when the marked points are required to be distinct and nonsingular because coincident or singular marked points can be blown up on the total space of the family

fisher information and criticality in the kuramoto model of nonidentical oscillators we use the fisher information to provide a lens on the transition to synchronization of the kuramoto model of nonidentical frequencies on a variety of undirected graphs we numerically solve the equations of motion for a n 400 complete graph and n 1000 small world scale free uniform random and random regular graphs for large but finite graphs of small average diameter the fisher information f as a function of coupling shows a peak closely coinciding with the critical point as determined by kuramoto s order parameter or synchronization measure r however for graphs of larger average diameter the position of the peak in f differs from the critical point determined by estimates of r on the one hand this is a finite size effect even at n 1000 however we show across a range of topologies that the fisher information peak points to a transition for smaller graphs that indicates structural changes in the numbers of locally phase synchronized clusters often directly from metastable to stable frequency synchronization solving explicitly for a two cluster ansatz subject to gaussian noise shows that the fisher infomation peaks at such a transition we discuss the implications for fisher information as an indicator for edge of chaos phenomena in finite coupled oscillator systems

multinomial approximations for nonparametric experiments which minimize the maximal loss of fisher information certain nonparametric product experimentsp n n can asymptotically be approximated by multinomial experiments obtained by a finite interval partition of the sample space the real line for specific familiesp n defined in terms of bounded fisher information and monotone likelihood ratios with bounded derivatives we study the problem to calculate a partition which is optimal in the sense that it minimizes the maximal loss of fisher information caused by the discretization this leads to a minimax problem by considering partitions of the sample space intok intervals which have equal probability under a densityh and then lettingk we obtain an expansion for the quantity loss of fisher information which is of orderk 2 under regularity conditions the corresponding minimax problem for the first order term of this expansion is shown to be the unique solution of a free boundary problem

on stochastic complexity and nonparametric density estimation summary we use the concepts of stochastic complexity description length and model selection to develop data based methods for choosing smoothing parameters in nonparametric density estimation in the case of histogram estimators we derive a simple exact formula for stochastic complexity when the prior distribution of cell probabilities is uniform over the class of all possible choices the formula depends only on the data and the smoothing parameter which is readily chosen according to the criterion of minimum stochastic complexity approaches based on stochastic complexity and description length are shown to be asymptotically equivalent in certain circumstances they produce a degree of smoothing which is almost optimal from the viewpoint of minimizing l or supremum distance but which smooths a little more than is optimal in the sense of minimizing l distance for any finite value of r

optimal bandwidth selection for re substitution entropy estimation abstract a new fusion approach of selecting an optimal bandwidth for re substitution entropy estimator re is presented in this study when approximating the continuous entropy with density estimation two types of errors will be generated entropy estimation error type i error and density estimation error type ii error these two errors are all strongly dependent on the undetermined bandwidths firstly an experimental conclusion based on 24 typical probability distributions is demonstrated that there is some inconsistency between the optimal bandwidths associated with these two errors secondly two different error measures for type i and type ii errors are derived a trade off between type i and type ii errors is a fundamental and potential property of our proposed method called re i ii thus the fusion of these two errors is conducted and an optimal bandwidth for re i ii is solved finally the experimental comparisons are carried out to verify the estimation performance of our proposed strategy the discretization method is deemed to be the necessary preprocessing technology for the calculation of continuous entropy traditionally so the nine mostly used unsupervised discretization methods are introduced to give comparison of their computational performances with that of re i ii and five most popular estimators for entropy approximation are also plugged into our comparisons splitting data estimator sde cross validation estimator cve m spacing estimator mse m n spacing estimator mnse and nearest neighbor distance estimator nnde the simulation studies on 24 different typical density distributions show that re i ii can obtain the better estimation performance among the involved methods meanwhile the estimation behaviors of different entropy estimation methods are also revealed based on the comparative results the empirical analysis demonstrates that re i ii is more insensitive to data and a better generalizable way for the estimation of continuous entropy re i ii makes it possible for a handy optimal bandwidth to be derived from a given dataset

infinite max margin factor analysis via data augmentation this paper addresses the bayesian estimation of the discriminative probabilistic latent models especially the mixture models we develop the max margin factor analysis mmfa model which utilizes the latent variable support vector machine lvsvm as the classification criterion in the latent space to learn a discriminative subspace with max margin constraint furthermore to deal with multimodally distributed data we further extend mmfa to infinite gaussian mixture model and develop the infinite max margin factor analysis immfa model via the consideration of dirichlet process mixtures dpm it jointly learns clustering max margin classifiers and the discriminative latent space in a united framework to improve the prediction performance moreover both of mmfa and immfa are natural to handle outlier rejection problem since the observations are described by a single or a mixture of gaussian distributions additionally thanks to the conjugate property the parameters in the two models can be inferred efficiently via the simple gibbs sampler finally we implement our models on synthesized and real world data including multimodally distributed datasets and measured radar echo data to validate the classification and rejection performance of the proposed models jointly learning fa and svm mmfa is proposed to get a discriminative subspace clustering the dataset in the subspace by dpm mmfa is extended to immfa thanks to the jointly learning framework they gain good prediction performance having the data description ability the proposed models can reject outlier samples in bayesian framework parameters can be inferred efficiently by the gibbs sampler

on the histogram as a density estimator l 2 theory let f be a probability density on an interval i finite or infinite i includes its finite endpoints if any and f vanishes outside of i let x1 x k be independent random variables with common density f the empirical histogram for the x s is often used to estimate f to define this object choose a reference point xosi and a cell width h let nj be the number of x s falling in the j th class interval

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

log minimal model program for the moduli space of stable curves the first flip we give a geometric invariant theory git construction of the log canonical model m g a of the pairs m g ad for a 7 10 7 10 for small q we show that m g 7 10 is isomorphic to the git quotient of the chow variety of bicanonical curves m g 7 10 is isomorphic to the git quotient of the asymptotically linearized hilbert scheme of bicanonical curves in each case we completely classify the semi stable curves and their orbit closures chow semistable curves have ordinary cusps and tacnodes as singularities but do not admit elliptic tails hilbert semistable curves satisfy further conditions e g they do not contain elliptic chains we show that there is a small contraction m g 7 10 m g 7 10 that contracts the locus of elliptic bridges moreover by using the git interpretation of the log canonical models we construct a small contraction m g 7 10 m g 7 10 that is the mori flip of

hypertrees projections and moduli of stable rational curves we give a conjectural description for the cone of effective divisors of the grothendieck knudsen moduli space m 0 n of stable ra tional curves with n marked points namely we introduce new combi natorial structures called hypertrees and show that they give exceptional divisors onm 0 n with many remarkable properties x1 introduction a major open problem inspired by the pioneering work of harris and mumford hm on the kodaira dimension of the moduli space of stable curves is to understand geometry of its birational models and in particular to describe its cone of effective divisors and a decomposition of this cone into mori chambers hk encoding ample divisors on birational models here we study the genus zero case the moduli spaces m 0 n parame trize stable rational curves i e nodal trees of p 1 s with n marked points and without automorphisms for any subseti of marked points m 0 n has a natural boundary divisor i whose general element parametrizes stable rational curves with two irreducible components one marked by points in i and another marked by points ini c we will introduce new combinatorial objects called hypertrees with an eye towards the following 1 1 conjecture the effective cone of m 0 n is generated by boundary divisors and by divisorsd defined below parametrized by irreducible hypertrees

multifractal diffusion entropy analysis optimal bin width of probability histograms abstract in the framework of multifractal diffusion entropy analysis we propose a method for choosing an optimal bin width in histograms generated from underlying probability distributions of interest the method presented uses techniques of renyi s entropy and the mean squared error analysis to discuss the conditions under which the error in the multifractal spectrum estimation is minimal we illustrate the utility of our approach by focusing on a scaling behavior of financial time series in particular we analyze the s p500 stock index as sampled at a daily rate in the time period 1950 2013 in order to demonstrate a strength of the method proposed we compare the multifractal spectrum for various bin widths and show the robustness of the method especially for large values of q for such values other methods in use e g those based on moment estimation tend to fail for heavy tailed data or data with long correlations connection between the spectrum and renyi s q parameter is also discussed and elucidated on a simple example of multiscale time series

intersection theory of moduli space of stable n pointed curves of genus zero we give a new construction of the moduli space via a composition of smooth codimension two blowups and use our construction to determine the chow ring

on the distribution of spacings between zeros of the zeta function etude numerique de la distribution des espacements des zeros de la fonction zeta de riemann observation de certains phenomenes inatendus

discontinuous galerkin methods for solving elliptic variational inequalities we study discontinuous galerkin methods for solving elliptic variational inequalities of both the first and second kinds analysis of numerous discontinuous galerkin schemes for elliptic boundary value problems is extended to the variational inequalities we establish a priori error estimates for the discontinuous galerkin methods which reach optimal order for linear elements results from some numerical examples are reported

moduli spaces of weighted pointed stable curves abstract a weighted pointed curve consists of a nodal curve and a sequence of marked smooth points each assigned a number between zero and one a subset of the marked points may coincide if the sum of the corresponding weights is no greater than one we construct moduli spaces for these objects using methods of the log minimal model program and describe the induced birational morphisms between moduli spaces as the weights are varied in the genus zero case we explain the connection to geometric invariant theory quotients of points in the projective line and to compactifications of moduli spaces studied by kapranov keel and losev manin

loci of curves with subcanonical points in low genus inside the moduli space of curves of genus three with one marked point we consider the locus of hyperelliptic curves with a marked weierstrass point and the locus of non hyperelliptic curves with a marked hyperflex these loci have codimension two we compute the classes of their closures in the moduli space of stable curves of genus three with one marked point similarly we compute the class of the closure of the locus of curves of genus four with an even theta characteristic vanishing with order three at a certain point these loci naturally arise in the study of minimal dimensional strata of abelian differentials

generalized core vector machines kernel methods such as the support vector machine svm are often formulated as quadratic programming qp problems however given m training patterns a naive implementation of the qp solver takes o m 3 training time and at least o m2 space hence scaling up these qps is a major stumbling block in applying kernel methods on very large data sets and a replacement of the naive method for finding the qp solutions is highly desirable recently by using approximation algorithms for the minimum enclosing ball meb problem we proposed the core vector machine cvm algorithm that is much faster and can handle much larger data sets than existing svm implementations however the cvm can only be used with certain kernel functions and kernel methods for example the very popular support vector regression svr cannot be used with the cvm in this paper we introduce the center constrained meb problem and subsequently extend the cvm algorithm the generalized cvm algorithm can now be used with any linear nonlinear kernel and can also be applied to kernel methods such as svr and the ranking svm moreover like the original cvm its asymptotic time complexity is again linear in m and its space complexity is independent of m experiments show that the generalized cvm has comparable performance with state of the art svm and svr implementations but is faster and produces fewer support vectors on very large data sets

efficient svm training using low rank kernel representations svm training is a convex optimization problem which scales with the training set size rather than the feature space dimension while this is usually considered to be a desired quality in large scale problems it may cause training to be impractical the common techniques to handle this difficulty basically build a solution by solving a sequence of small scale subproblems our current effort is concentrated on the rank of the kernel matrix as a source for further enhancement of the training procedure we first show that for a low rank kernel matrix it is possible to design a better interior point method ipm in terms of storage requirements as well as computational complexity we then suggest an efficient use of a known factorization technique to approximate a given kernel matrix by a low rank matrix which in turn will be used to feed the optimizer finally we derive an upper bound on the change in the objective function value based on the approximation error and the number of active constraints support vectors this bound is general in the sense that it holds regardless of the approximation method

extremal higher codimension cycles on moduli spaces of curves we show that certain geometrically defined higher codimension cycles are ex tremal in the effective cone of the moduli space mg n of stable genus g curves with n ordered marked points in particular we prove that codimension two boundary strata are extremal and exhibit extremal boundary strata of higher codimension we also show that the locus of hyperelliptic curves with a marked weierstrass point in m3 1 and the locus of hyperel liptic curves in m4 are extremal cycles in addition we exhibit infinitely many extremal codimension two cycles in m1 n for n 5 and in m2 n for n 2

frequency polygons theory and application abstract in this article i investigate the theoretical properties and applications of the frequency polygon which is constructed by connecting with straight lines the mid bin values of a histogram for estimating an unknown probability density function using a random sample the frequency polygon is shown to dominate the histogram with respect to the criterion of integrated mean squared error achieving the same rate of convergence to zero of the integrated mean squared error as non negative kernel estimators data based algorithms for constructing frequency polygons are discussed and illustrated one is based on a histogram with bin width equal to 2 15sn 1 5 where s is an estimate of the standard deviation from a sample of size n another approach is based on the method of generalized crossvalidation the bivariate frequency polygon is also investigated comparisons are made between the frequency polygon and other density estimators examples with data in one and two dimensions are presented

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

decomposition methods for linear support vector machines in this letter we show that decomposition methods with alpha seeding are extremely useful for solving a sequence of linear support vector machines svms with more data than attributes this strategy is motivated by keerthi and lin 2003 who proved that for an svm with data not linearly separable after c is large enough the dual solutions have the same free and bounded components we explain why a direct use of decomposition methods for linear svms is sometimes very slow and then analyze why alpha seeding is much more effective for linear than nonlinear svms we also conduct comparisons with other methods that are efficient for linear svms and demonstrate the effectiveness of alpha seeding techniques in model selection

asymptotic maximum order statistic for sir in kappa mu shadowed fading using tools from extreme value theory evt it is proved that when the user signal and the interferer signals undergo independent and non identically distributed i n i d kappa mu shadowed fading the limiting distribution of the maximum of l independent and identically distributed i i d signal to interference ratio sir random variables rvs is a frechet distribution it is observed that this limiting distribution is close to the true distribution of maximum for maximum sir evaluated over moderate l furthermore moments of the maximum rv is shown to converge to the moments of the frechet rv in addition the rate of convergence of the actual distribution of the maximum to the frechet distribution is derived and analyzed for different kappa and mu parameters finally results from the stochastic ordering are used to analyze the variation in the limiting distribution with respect to the variation in source fading parameters these results are then used to derive upper bound for the rate in full array selection fas schemes for the antenna selection and the asymptotic outage probability and the ergodic rate in maximum sum capacity msc scheduling systems

a counterexample to fulton s conjecture on formula 0 n abstract we describe an elementary counterexample to a conjecture of fulton on the set of effective divisors on the space formula 0 n of marked rational curves

akaike s information criterion and kullback leibler loss for histogram density estimation we take a detailed look at akaike s information criterion aic and kullback leibler cross validation klcv in the problem of histogram density estimation two different definitions of number of unknown parameters inaic are considered a careful description is given of the influence of density tail properties on performance of both types ofaic and onklcv a number of practical conclusions emerge in particular we find thataic will often give problems when used with heavy tailed unbounded densities but can perform quite well with compactly supported densities in the latter case both types ofaic produce similar results and those results will sometimes be asymptotically equivalent to the ones obtained fromklcv however depending on the shape of the true density theklcv method can fail to balance bias and variance components of loss with the result thatklcv andaic may produce very different results

chow rings of moduli spaces of curves ii some results on the chow ring of overline mathscr m _4 ring of the moduli space of stable curves of genus 4 these results are not complete we find generators for the chow ring of 4 and for the chow groups in codimension 1 and 2 of w4 for a2 g 4 we find fourteen generators using test surfaces we prove that the dimension of a 2 4 4 is at least 13 and explicitly determine the single relation between the fourteen generators which still can exist finally we have two proofs that this relation does indeed hold so that the dimension of a2 4 4 equals 13 this enables us to determine the chow ring of 4 4 our original proof is based on a rather delicate argument the second proof uses a result of ran see r and is much simpler

estimating model discrepancy a quantity 2 is defined as the discrepancy between an actual and an assumed statistical model an estimator is developed for the case in which data are grouped the estimator is based on pearson

on the effective cone of higher codimension cycles in overline mathcal m _ g n m g n we exhibit infinitely many extremal effective codimension k cycles in overline mathcal m g n in the cases hence in these cases the effective cone is not rational polyhedral

core vector machines fast svm training on very large data sets standard svm training has o m3 time and o m2 space complexities where m is the training set size it is thus computationally infeasible on very large data sets by observing that practical svm implementations only approximate the optimal solution by an iterative strategy we scale up kernel methods by exploiting such approximateness in this paper we first show that many kernel methods can be equivalently formulated as minimum enclosing ball meb problems in computational geometry then by adopting an efficient approximate meb algorithm we obtain provably approximately optimal solutions with the idea of core sets our proposed core vector machine cvm algorithm can be used with nonlinear kernels and has a time complexity that is linear in m and a space complexity that is independent of m experiments on large toy and real world data sets demonstrate that the cvm is as accurate as existing svm implementations but is much faster and can handle much larger data sets than existing scale up methods for example cvm with the gaussian kernel produces superior results on the kddcup 99 intrusion detection data which has about five million training patterns in only 1 4 seconds on a 3 2ghz pentium 4 pc