information cascade with marginal stability in a network of chaotic elements abstract a newly discovered cascade process of clusters is studied in a network of chaotic elements it is shown that the splitting of clusters and the synchronization of elements are balanced in a class of partially ordered states where marginal stability is sustained over an interval of the bifurcation parameters the partition information creation in bit space shows an avalanche process of information which leads to the anomalous behavior of power spectra roughly fitted by a power law form of the wavenumber lyapunov spectra have accumulation at null exponents analogous with those studied in fluid turbulence models

gauss curvature flow the fate of the rolling stones we prove firey s 1974 conjecture that convex surfaces moving by their gauss curvature become spherical as they contract to points

fast rates for support vector machines using gaussian kernels for binary classification we establish learning rates up to the order of n 1 for support vector machines svms with hinge loss and gaussian rbf kernels these rates are in terms of two assumptions on the considered distributions tsybakov s noise assumption to establish a small estimation error and a new geometric noise condition which is used to bound the approximation error unlike previously proposed concepts for bounding the approximation error the geometric noise assumption does not employ any smoothness assumption 1 introduction in recent years support vector machines svms have been the subject of many theoretical considerations despite this effort their learning performance on restricted classes of distributions is still widely unknown in particular it is unknown under which nontrivial circumstances svms can guarantee fast learning rates the aim of this work is to use concepts like tsybakov s noise assumption and local rademacher averages to establish learning rates up to the order of n 1 for nontrivial distributions in addition to these concepts that are used to deal with the stochastic part of the analysis we also introduce a geometric assumption for distributions that allows us to estimate the approximation properties of gaussian rbf kernels unlike many other concepts introduced for bounding the approximation error our geometric assumption is not in terms of smoothness but describes the concentration and the noisiness of the data generating distribution near the decision boundary let us formally introduce the statistical classification problem to this end let us fix a subset x r d we write y 1 1 given a finite training set

multilabel predictions with sets of probabilities in this paper we study how multilabel predictions can be obtained when our uncertainty is described by a convex set of probabilities such predictions typically consisting of a set of potentially optimal decisions are hard to make in large decision spaces such as the one considered in multilabel problems however we show that when considering the hamming or the ranking loss outer approximating predictions can be efficiently computed from label wise information as in the precise case we also perform some first experiments showing the behaviour of the partial predictions obtained through these approximations such experiments also confirm that predictions become partial on those labels where the precise prediction is likely to make an error highlightswe consider the problem of multilabel prediction with probability sets we show that efficient approximations can be obtained for the hamming loss we show that efficient approximations can be obtained for the ranking loss we perform first experiments confirming the expected behaviour of the approximations

a unified view of class selection with probabilistic classifiers the possibility of selecting a subset of classes instead of one unique class for assignation is of great interest in many decision making systems selecting a subset of classes instead of singleton allows to reduce the error rate and to propose a reduced set to another classifier or an expert this second step provides additional information and therefore increases the quality of the result in this paper a unified view of the problem of class selection with probabilistic classifiers is presented the proposed framework based on the evaluation of the probabilistic equivalence allows to retrieve class selective frameworks that have been proposed in the literature we also describe an approach in which the decision rules are compared by the help of a normalized area under the error selection curve it allows to get a relative independence of the performance of a classifier without reject option and thus a reliable class selection decision rule evaluation the power of this generic proposition is demonstrated by evaluating and comparing it to several state of the art methods on nine real world datasets and four different probabilistic classifiers a unified framework of class selection by the use of probabilistic equivalence is presented a learning procedure for adapting the probabilistic equivalence is proposed a normalized performance measure for class selection is described experiments on real world datasets using different classifiers show the statistical significance of the proposition

capacity of reproducing kernel spaces in learning theory the capacity of reproducing kernel hilbert spaces rkhs plays an essential role in the analysis of learning theory covering numbers and packing numbers of balls of these reproducing kernel spaces are important measurements of this capacity we first present lower bound estimates for the packing numbers by means of nodal functions then we show that if a mercer kernel is c sup s for some s 0 being not an even integer the rkhs associated with this kernel can be embedded into c sup s 2 this gives upper bound estimates for the covering number concerning sobolev smooth kernels examples and applications to v sub spl gamma dimension and tikhonov 1977 regularization are presented to illustrate the upper and lower bound estimates

towards a statistical test for functional connectivity dynamics abstract sliding window correlation is an emerging method for mapping time resolved resting state functional connectivity to avoid mapping spurious connectivity fluctuations false positives leonardi and van de ville recently recommended choosing a window length exceeding the longest wavelength composing the bold signal usually assumed to be 100 s here we provide further statistical support for this rule of thumb however we demonstrate that non stationary fluctuations in functional connectivity can in theory be detected with much shorter window lengths e g 40 s while maintaining nominal control of false positives we find that statistical power is near maximal for window lengths chosen according to leonardi and van de ville s rule of thumb furthermore we lay some foundations for a parametric test to identify non stationary fluctuations in functional connectivity also noting limitations of the sinusoidal model upon which our work and the work of leonardi and van de ville is based most notably our analytical results pertain to covariances as does our statistical test whereas functional connectivity is more commonly measured using correlations

on reject and refine options in multicategory classification abstractin many real applications of statistical learning a decision made from misclassification can be too costly to afford in this case a reject option which defers the decision until further investigation is conducted is often preferred in recent years there has been much development for binary classification with a reject option yet little progress has been made for the multicategory case in this article we propose margin based multicategory classification methods with a reject option in addition and more importantly we introduce a new and unique refine option for the multicategory problem where the class of an observation is predicted to be from a set of class labels whose cardinality is not necessarily one the main advantage of both options lies in their capacity of identifying error prone observations moreover the refine option can provide more constructive information for classification by effectively ruling out implausible classes efficient implementations have been developed

optimal aggregation of classifiers in statistical learning classification can be considered as nonparametric estimation of sets where the risk is defined by means of a specific distance between sets associated with misclassification error it is shown that the rates of convergence of classifiers depend on two parameters the complexity of the class of candidate sets and the margin parameter the dependence is explicitly given indicating that optimal fast rates approaching o n 1 can be attained where n is the sample size and that the proposed classifiers have the property of robustness to the margin the main result of the paper concerns optimal aggregation of classifiers we suggest a classifier that automatically adapts both to the complexity and to the margin and attains the optimal fast rates up to a logarithmic factor

cautious label ranking with label wise decomposition abstract in this paper we are interested in the label ranking problem we are more specifically interested in the recent trend consisting in predicting partial but more accurate i e making less incorrect statements orders rather than complete ones to do so we propose a ranking method based on label wise decomposition we estimate an imprecise probabilistic model over each label rank and we infer a partial order from it using optimization techniques this leads to new results concerning a particular bilinear assignment problem finally we provide some experiments showing the feasibility of our method

the multiscale character of evoked cortical activity abstract both the architecture and the dynamics of the brain have characteristic features at different spatial scales however the existence nature and function of dynamical interdependencies between such scales have not been investigated we studied the multiscale properties of functional magnetic resonance imaging fmri data acquired while human subjects viewed a visual image traditional region of interest analysis of this data set revealed evoked activity in primary and extrastriate visual cortex wavelet transform in the spatial domain provides a multiscale representation of this evoked brain activity studying the correlation structure of this representation revealed strong and novel interdependencies in these data within and between different spatial scales we found that such correlations are stronger than those evident in the original data and comparable in magnitude to those obtained after gaussian smoothing however analysis of the data in the wavelet domain revealed additional structure such as positive correlations strong anti correlations and phase lagged interdependencies statistical significance of these effects was inferred through nonparametric bootstrap techniques we conclude that the spatial analysis of functional neuroimaging data in the wavelet domain provides novel information which may reflect complex spatiotemporal neuronal activity and information encoding it also affords a quantitative means of testing hierarchical and multiscale models of cortical activity

statistical performance of support vector machines the support vector machine svm algorithm is well known to the computer learning community for its very good practical results the goal of the present paper is to study this algorithm from a statistical perspective using tools of concentration theory and empirical processes our main result builds on the observation made by other authors that the svm can be viewed as a statistical regularization procedure from this point of view it can also be interpreted as a model selection principle using a penalized criterion it is then possible to adapt general methods related to model selection in this framework to study two important points 1 what is the minimum penalty and how does it compare to the penalty actually used in the svm algorithm 2 is it possible to obtain oracle inequalities in that setting for the specific loss function used in the svm algorithm we show that the answer to the latter question is positive and provides relevant insight to the former our result shows that it is possible to obtain fast rates of convergence for svms

test your surrogate data before you test for nonlinearity the schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis in particular we pinpoint some important caveats of the prominent algorithm of amplitude adjusted fourier transform surrogates aaft and compare it to the iterated aaft which is more consistent in representing the null hypothesis it turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be reinvestigated taking into account the inaccuracies in the aaft algorithm mainly concerning the mismatching of the linear correlations in order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics the application of this setup to some well known real data sets cautions against the use of the aaft algorithm

reliable detection of nonlinearity in experimental time series with strong periodic components abstract testing with phase randomised surrogate signals has been used extensively to search for interesting nonlinear dynamical structure in experimental time series in this paper we argue that in the case of experimental time series with strong periodic components the method of phase randomised surrogate data may not be particularly suitable to test for nonlinearity since construction of such surrogates by fft requires a time series whose length is a power of 2 we demonstrate that in the case of nearly periodic signals this approach will almost always produce spurious detection of nonlinearity this error can be fixed by adjusting the length of the time series such that it becomes an integer multiple of the dominant periodicity the resulting time series will not be a power of 2 and requires the use of a dft to generate surrogate data dft based surrogates no longer detect spurious nonlinearity but cannot be used to detect periodic nonlinearity we propose a new test nonlinear cross prediction nlcp which avoids some of the problems associated with phase randomised surrogate data and which allows reliable detection of both periodic and aperiodic nonlinearity in the test the original data are used to construct a nonlinear model to predict the original data set as well as amplitude inverted and time reversed versions of the original data lower predictability of the amplitude inverted or time reversed copies reflect respectively an asymmetric amplitude distribution and time irreversibility both of these indicate nonlinearity in the data set

statistical behavior and consistency of classification methods based on convex risk minimization we study how closely the optimal bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function the measurement of closeness is characterized by the loss function used in the estimation we show that such a classification scheme can be generally regarded as a nonmaximum likelihood conditional in class probability estimate and we use this analysis to compare various convex loss functions that have appeared in the literature furthermore the theoretical insight allows us to design good loss functions with desirable properties another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization this study sheds light on the good performance of some recently proposed linear classification methods including boosting and support vector machines it also shows their limitations and suggests possible improvements

curvature contraction of convex hypersurfaces by nonsmooth speeds the research of the second author was supported by an australian postgraduate award the research of the first third fourth and fifth authors was supported by discovery project grant dp120100097 of the australian research council

convexity classification and risk bounds many of the classification algorithms developed in the machine learning literature including the support vector machine and boosting can be viewed as minimum contrast methods that minimize a convex surrogate of the 0 1 loss function the convexity makes these algorithms computationally efficient the use of a surrogate however has statistical consequences that must be balanced against the computational virtues of convexity to study these issues we provide a general quantitative relationship between the risk as assessed using the 0 1 loss and the risk as assessed using any nonnegative surrogate loss function we show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function that it satisfies a pointwise form of fisher consistency for classification the relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications we also present a refined version of this result in the

covering numbers for support vector machines support vector sv machines are linear classifiers that use the maximum margin hyperplane in a feature space defined by a kernel function previously the only bounds on the generalization performance of sv machines within valiant s probably approximately correct framework took no account of the kernel used except in its effect on the margin and radius it has been shown that one can bound the relevant covering numbers using tools from functional analysis in this paper we show that the resulting bound can be greatly simplified the new bound involves the eigenvalues of the integral operator induced by the kernel it shows that the effective dimension depends on the rate of decay of these eigenvalues we present an explicit calculation of covering numbers for an sv machine using a gaussian kernel which is significantly better than that implied by previous results

pinching estimates and motion of hypersurfaces by curvature functions second derivative pinching estimates are proved for a class of elliptic and parabolic equations including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature the estimates imply convergence of convex hypersurfaces to spheres under these flows improving earlier results of b chow and the author the result is obtained via a detailed analysis of gradient terms in the equations satisfied by second derivatives

design of reject rules for ecoc classification systems ecoc is a widely used and successful technique which implements a multi class classification system by decomposing the original problem into several two class problems in this paper we study the possibility to provide ecoc systems with a tailored reject option carried out through different schemes that can be grouped under two different categories an external and an internal approach the first one is based on the reliability of the entire system output and does not require any change in its structure the second scheme instead estimates the reliability of the internal dichotomizers and implies a slight modification in the decoding stage experimental results on popular benchmark data sets are reported to show the behavior of the different schemes

active learning via perfect selective classification we discover a strong relation between two known learning models stream based active learning and perfect selective classification an extreme case of classification with a reject option for these models restricted to the realizable case we show a reduction of active learning to selective classification that preserves fast rates applying this reduction to recent results for selective classification we derive exponential target independent label complexity speedup for actively learning general non homogeneous linear classifiers when the data distribution is an arbitrary high dimensional mixture of gaussians finally we study the relation between the proposed technique and existing label complexity measures including teaching dimension and disagreement coefficient

a moment bound for multi hinge classifiers the success of support vector machines in binary classification relies on the fact that hinge loss employed in the risk minimization targets the bayes rule recent research explores some extensions of this large margin based method to the multicategory case we show a moment bound for the socalled multi hinge loss minimizers based on two kinds of complexity constraints entropy with bracketing and empirical entropy obtaining such a result based on the latter is harder than finding one based on the former we obtain fast rates of convergence that adapt to the unknown margin

classification with a reject option using a hinge loss we consider the problem of binary classification where the classifier can for a particular cost choose not to classify an observation just as in the conventional classification problem minimization of the sample average of the cost is a difficult optimization problem as an alternative we propose the optimization of a certain convex loss function analogous to the hinge loss used in support vector machines svms its convexity ensures that the sample average of this surrogate loss can be efficiently minimized we study its statistical properties we show that minimizing the expected surrogate loss the risk also minimizes the risk we also study the rate at which the risk approaches its minimum value we show that fast rates are possible when the conditional probability p y 1 x is unlikely to be close to certain critical values

wavelets and functional magnetic resonance imaging of the human brain the discrete wavelet transform dwt is widely used for multiresolution analysis and decorrelation or whitening of nonstationary time series and spatial processes wavelets are naturally appropriate for analysis of biological data such as functional magnetic resonance images of the human brain which often demonstrate scale invariant or fractal properties we provide a brief formal introduction to key properties of the dwt and review the growing literature on its application to fmri we focus on three applications in particular i wavelet coefficient resampling or wavestrapping of 1 d time series 2 to 3 d spatial maps and 4 d spatiotemporal processes ii wavelet based estimators for signal and noise parameters of time series regression models assuming the errors are fractional gaussian noise fgn and iii wavelet shrinkage in frequentist and bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps we conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fmri data

flow of pinched convex hypersurfaces by powers of curvature functions in hyperbolic space abstract this paper concerns closed h convex hypersurfaces of dimension n 2 in the hyperbolic space h n 1 of constant sectional curvature evolving in direction of its normal vector where the speed equals a power 1 of a curvature function f which is monotone symmetric homogeneous of degree 1 it is shown that if the initial h convex hypersurface is pinched then this is maintained under the flow and the hypersurfaces shrink to a round point in h n 1 in finite time as a consequence when rescaling appropriately the evolving hypersurfaces converge smoothly and exponentially to the unit sphere of r n 1

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

learning nondeterministic classifiers nondeterministic classifiers are defined as those allowed to predict more than one class for some entries from an input space given that the true class should be included in predictions and the number of classes predicted should be as small as possible these kind of classifiers can be considered as information retrieval ir procedures in this paper we propose a family of ir loss functions to measure the performance of nondeterministic learners after discussing such measures we derive an algorithm for learning optimal nondeterministic hypotheses given an entry from the input space the algorithm requires the posterior probabilities to compute the subset of classes with the lowest expected loss from a general point of view nondeterministic classifiers provide an improvement in the proportion of predictions that include the true class compared to their deterministic counterparts the price to be paid for this increase is usually a tiny proportion of predictions with more than one class the paper includes an extensive experimental study using three deterministic learners to estimate posterior probabilities a multiclass support vector machine svm a logistic regression and a naive bayes the data sets considered comprise both uci multi class learning tasks and microarray expressions of different kinds of cancer we successfully compare nondeterministic classifiers with other alternative approaches additionally we shall see how the quality of posterior probabilities measured by the brier score determines the goodness of nondeterministic predictions

asymptotic analysis of penalized likelihood and related estimators a general approach to the first order asymptotic analysis ofpenalized likelihood and related estimators is described the method gives expansions for the systematic and random error asymptotic convergence rates in a family of spectral norms are obtained the theory applies to a broad range of function estimation prob erns including non paxametric dellsity hazard and generalized regression curve estimation some examples are provided ams 1980 subject classifications primary 62 g05 secondary 62j05 41 a35 41 a25 47 a53 45 llo 45 m05

using distance covariance for improved variable selection with application to learning genetic risk models variable selection is of increasing importance to address the difficulties of high dimensionality in many scientific areas in this paper we demonstrate a property for distance covariance which is incorporated in a novel feature screening procedure together with the use of distance correlation the approach makes no distributional assumptions for the variables and does not require the specification of a regression model and hence is especially attractive in variable selection given an enormous number of candidate attributes without much information about the true model with the response the method is applied to two genetic risk problems where issues including uncertainty of variable selection via cross validation subgroup of hard to classify cases and the application of a reject option are discussed

anisotropic flow of convex hypersurfaces by the square root of the scalar curvature abstract we show the existence of a smooth solution for the flow deformed by the square root of the scalar curvature multiplied by a positive anisotropic factor when the strictly convex initial hypersurface in euclidean space is suitably pinched we also prove the convergence of rescaled surfaces to a smooth limit manifold which is a round sphere for a general case in dimension two it is shown that with a volume preserving rescaling the limit profile satisfies a soliton equation

towards a comprehensive theory of brain activity coupled oscillator systems under external forces abstract recently jirsa et al and haken discussed a theory comprising the brain wave equation proposed by nunez the wilson cowan ermentrout cowan model and hopfield networks this theory was applied to model findings obtained in an experiment that relates brain activity and behavior the so called julliard experiment in previous works of jirsa et al and frank et al the focus was on the brain wave aspect recently we conducted similar experiments the results obtained are modeled in this paper in terms of coupled oscillator systems coupled oscillator systems are considered to represent the wilson cowan ermentrout cowan model aspect of the unifying theory building on a model proposed by haken kelso and bunz and the theory of weakly coupled oscillators established by winfree and by kuramoto we derive a nonlinear fokker planck equation whose stationary solutions mimic the neocortical brain activity observed in our experiments

how fast elements can affect slow dynamics a chain of coupled chaotic elements with different time scales is studied in contrast with the adiabatic approximation we find that correlations between elements are transferred from faster to slower elements when the differences in the time scales of the elements lie within a certain range for such correlations to occur three features are essential strong correlations among the elements a bifurcation in the dynamics of the fastest element by changing its control parameter and cascade propagation of the bifurcation by studying coupled rossler equations we demonstrate that fast elements can affect the dynamics of slow elements when these conditions are satisfied the relevance of our results to biological memory is briefly discussed

classification methods with reject option based on convex risk minimization in this paper we investigate the problem of binary classification with a reject option in which one can withhold the decision of classifying an observation at a cost lower than that of misclassification since the natural loss function is non convex so that empirical risk minimization easily becomes infeasible the paper proposes minimizing convex risks based on surrogate convex loss functions a necessary and sufficient condition for infinite sample consistency both risks share the same minimizer is provided moreover we show that the excess risk can be bounded through the excess surrogate risk under appropriate conditions these bounds can be tightened by a generalized margin condition the impact of the results is illustrated on several commonly used surrogate loss functions

multicategory angle based large margin classification large margin classifiers are popular methods for classification among existing simultaneous multicategory large margin classifiers a common approach is to learn k different functions for a k class problem with a sum to zero constraint such a formulation can be inefficient we propose a new multicategory angle based large margin classification framework the proposed angle based classifiers consider a simplex based prediction rule without the sum to zero constraint and enjoy more efficient computation many binary large margin classifiers can be naturally generalized for multicategory problems through the angle based framework theoretical and numerical studies demonstrate the usefulness of the angle based methods

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

a comparative evaluation of wavelet based methods for hypothesis testing of brain activation maps wavelet based methods for hypothesis testing are described and their potential for activation mapping of human functional magnetic resonance imaging fmri data is investigated in this approach we emphasise convergence between methods of wavelet thresholding or shrinkage and the problem of hypothesis testing in both classical and bayesian contexts specifically our interest will be focused on the trade off between type i probability error control and power dissipation estimated by the area under the roc curve we describe a technique for controlling the false discovery rate at an arbitrary level of error in testing multiple wavelet coefficients generated by a 2d discrete wavelet transform dwt of spatial maps of fmri time series statistics we also describe and apply change point detection with recursive hypothesis testing methods that can be used to define a threshold unique to each level and orientation of the 2d dwt and bayesian methods incorporating a formal model for the anticipated sparseness of wavelet coefficients representing the signal or true image the sensitivity and type i error control of these algorithms are comparatively evaluated by analysis of null images acquired with the subject at rest and an experimental data set acquired from five normal volunteers during an event related finger movement task we show that all three wavelet based algorithms have good type i error control the fdr method being most conservative and generate plausible brain activation maps the bayesian method being most powerful we also generalise the formal connection between wavelet based methods for simultaneous multiresolution denoising hypothesis testing and methods based on monoresolution gaussian smoothing followed by statistical testing of brain activation maps

integrated wavelet processing and spatial statistical testing of fmri data we introduce an integrated framework for detecting brain activity from fmri data which is based on a spatial discrete wavelet transform unlike the standard wavelet based approach for fmri analysis we apply the suitable statistical test procedure in the spatial domain for a desired significance level this scheme has one remaining degree of freedom characterizing the wavelet processing which is optimized according to the principle of minimal approximation error this allows us to determine the threshold values in a way that does not depend on data while developing our framework we make only conservative assumptions consequently the detection of activation is based on strong evidence we have implemented this framework as a toolbox wspm for the spm2 software taking advantage of multiple options and functions of spm such as the setup of the linear model and the use of the hemodynamic response function we show by experimental results that our method is able to detect activation patterns the results are comparable to those obtained by spm even though statistical assumptions are more conservative

volume preserving flow by powers of symmetric polynomials in the principal curvatures we study a volume preserving curvature flow of convex hypersurfaces driven by a power of the k th elementary symmetric polynomial in the principal curvatures unlike most of the previous works on related problems we do not require assumptions on the curvature pinching of the initial datum we prove that the solution exists for all times and that the speed remains bounded and converges to a constant in an integral norm in the case of the volume preserving scalar curvature flow we can prove that the hypersurfaces converge smoothly to a round sphere

a family of measures for best top n class selective decision rules when classes strongly overlap in the feature space or when some classes are not known in advance the performance of a classifier heavily decreases to overcome this problem the reject option has been introduced it simply consists in withdrawing the decision and let another classifier or an expert take the decision whenever exclusively classifying is not reliable enough the classification problem is then a matter of class selection from none to all classes in this paper we propose a family of measures suitable to define such decision rules it is based on a new family of operators that are able to detect blocks of similar values within a set of numbers in the unit interval the soft labels of an incoming pattern to be classified using a single threshold experiments on synthetic and real datasets available in the public domain show the efficiency of our approach

spatiotemporal wavelet analysis for functional mri characterizing the spatiotemporal behavior of the bold signal in functional magnetic resonance imaging fmri is a central issue in understanding brain function while the nature of functional activation clusters is fundamentally heterogeneous many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal furthermore few analysis approaches use true spatiotemporal continuity in their statistical formulations to address these issues we present a novel spatiotemporal wavelet procedure that uses a stimulus convolved hemodynamic signal plus correlated noise model the wavelet fits computed by spatially constrained maximum likelihood estimation provide efficient multiscale representations of heterogeneous brain structures and give well identified parsimonious spatial activation estimates that are modulated by the temporal fmri dynamics in a study of both simulated data and actual fmri memory task experiments our new method gave lower mean squared error and seemed to result in more localized fmri activation maps compared to models using standard wavelet or smoothing techniques our spatiotemporal wavelet framework suggests a useful tool for the analysis of fmri studies

analysis of error reject trade off in linearly combined multiple classifiers in this paper a theoretical and experimental analysis of the error reject trade off achievable by linearly combining the outputs of an ensemble of classifiers is presented to this aim the theoretical framework previously developed by tumer and ghosh for the analysis of the simple average rule without the reject option has been extended analytical results that allow to evaluate the improvement of the error reject trade off achievable by simple averaging their outputs under different assumptions about the distributions of the estimation errors affecting a posteriori probabilities are provided the conditions under which the weighted average can provide a better error reject trade off than the simple average are then determined from the theoretical results obtained under the assumption of unbiased and uncorrelated estimation errors simple guidelines for the design of multiple classifier systems using linear combiners are given finally an experimental evaluation and comparison of the error reject trade off of the simple and weighted averages is reported for five real data sets the results show the practical relevance of the proposed guidelines in the design of linear combiners

convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature we consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity we prove that the ratio of circumradius to inradius is bounded by a function of the circumradius with limit 1 at zero we apply this result to the motion of hypersurfaces by arbitrary speeds which are smooth homogeneous functions of the principal curvatures of degree greater than one for smooth strictly convex initial hypersurfaces with ratio of principal curvatures sufficiently close to one at each point we prove that solutions remain smooth and strictly convex and become spherical in shape while contracting to points in finite time recently several papers have considered the flow of convex hypersurfaces by speeds which are homogeneous functions of the principal curvatures of degree 1 under suitable pinching conditions on the curvature of the initial hypersurface the aim is to prove that solutions become spherical as they contract to points this behaviour has been established for a wide range of flows where the speed is homogeneous of degree 1 in the principal curvatures including the mean curvature flow h1 the flow by nth root of gauss curvature ch1 square root of scalar curvature ch2 and a large family of other speeds a1 a3 a4 the first such result with degree of homogeneity higher than 1 was due to ben chow ch1 and concerned flow by powers of the gauss curvature he proved that flow by k with 1 n produces a spherical limiting shape provided the initial hypersurface is sufficiently pinched i n the sense that hij c hgij later such results were proved by schulze s3 for powers of the mean curvature by alessandroni and sinestrari for powers of the scalar curvature a as and by cabezas rivas and sinestrari crs for normalized flows by powers of elementary symmetric functions a feature of the results mentioned above is that the flows all have some divergence structure a point which is used crucially in deriving sufficient regularity of solutions to deduce the existence of a smooth limiting hypersurface in ch1 the divergence structure was used to deduce pinching of the principal curvatures using integral estimates in a manner similar to h1 in s3 a and as the curvature pinching was proved using maximum principle arguments but the divergence structure was still needed because higher regularity of solutions was established using results for divergence form porous medium equations to date we are not aware of any work which provides holder continuity for solutions of porous medium equations in non divergence form without assuming regularity of the coefficients in this paper we provide a geometric estimate which circumvents this difficulty we prove in section 3 that if the ratios of principal curvatures at each point are bounded in terms of the maximum principal curvature by a function which approaches one at infinity then the ratio of circumradius to inradius is as close to one as desired if the circumradius is sufficiently small using