the boundary element method applied to the analysis of two dimensional nonlinear sloshing problems this paper deals with an application of the boundary element method to the analysis of nonlinear sloshing problems namely nonlinear oscillations of a liquid in a container subjected to forced oscillations first the problem is formulated mathematically as a nonlinear initial boundary value problem by the use of a governing differential equation and boundary conditions assuming the fluid to be inviscid and incompressible and the flow to be irrotational next the governing equation laplace equation and boundary conditions except the dynamic boundary condition on the free surface are transformed into an integral equation by employing the galerkin method two dynamic boundary condition is reduced to a weighted residual equation by employing the galerkin method two equations thus obtained are discretized by the use of the finite element method spacewise and the finite difference method timewise collocation method is employed for the discretization of the integral equation due to the nonlinearity of the problem the incremental method is used for the numerical analysis numerical results obtained by the present boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory good agreements are obtained and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems

consistency and convergence rates of one class svms and related algorithms we determine the asymptotic behaviour of the function computed by support vector machines svm and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel hilbert space of the gaussian rbf kernel in the situation where the number of examples tends to infinity the bandwidth of the gaussian kernel tends to 0 and the regularization parameter is held fixed non asymptotic convergence bounds to this limit in the l2 sense are provided together with upper bounds on the classification error that is shown to converge to the bayes risk therefore proving the bayes consistency of a variety of methods although the regularization term does not vanish these results are particularly relevant to the one class svm for which the regularization can not vanish by construction and which is shown for the first time to be a consistent density level set estimator

on the estimation of a probability density function by the maximum penalized likelihood method abstract a class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density the limiting case of the estimates as the amount of smoothing increasing has a natural form which makes the method attractive for data analysis and which provides a rationale for a particular choice of roughness penalty the estimates are shown to be the solution of an unconstrained convex optimization problem and mild natural conditions are given for them to exist rates of consistency in various norms and conditions for asymptotic normality and approximation by a gaussian process are given thus breaking new ground in the theory of maximum penalized likelihood density estimation author

isogeometric boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

performance measures for neyman pearson classification in the neyman pearson np classification paradigm the goal is to learn a classifier from labeled training data such that the probability of a false negative is minimized while the probability of a false positive is below a user specified level alpha isin 0 1 this work addresses the question of how to evaluate and compare classifiers in the np setting simply reporting false positives and false negatives leaves some ambiguity about which classifier is best unlike conventional classification however there is no natural performance measure for np classification we cannot reject classifiers whose false positive rate exceeds a since among other reasons the false positive rate must be estimated from data and hence is not known with certainty we propose two families of performance measures for evaluating and comparing classifiers and suggest one criterion in particular for practical use we then present general learning rules that satisfy performance guarantees with respect to these criteria as in conventional classification the notion of uniform convergence plays a central role and leads to finite sample bounds oracle inequalities consistency and rates of convergence the proposed performance measures are also applicable to the problem of anomaly prediction

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

boundary element analysis of nonlinear water wave problems a new boundary element technique based on green s formula is applied to the analysis of nonlinear water wave problems the problems are formulated mathematically as two dimensional nonlinear initial boundary value problems in terms of a velocity potential assuming the fluid to be inviscid and incompressible and the flow to be irrotational in the present paper two kinds of wave making problems are analysed 1 a tsunami generated by sea bed elevation 2 generation propagation and run up on a vertical wall of a solitary wave numerical results obtained by the present method are compared with available experimental data and analytical solutions excellent agreements are obtained

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

an explicit expression for the minimum phase image of transfer function matrices a simple expression is obtained for the transfer function matrix of the minimum phase image of a left invertible continuous time invariant system with zeros in the right half plane that may be of multiplicities greater than one this expression is obtained by multiplying the system transfer function matrix from the right by a special inner matrix and it is explicitly given in terms of the input zero directions that correspond to the zeros of the system in the right half plane the result provides a simple expression for the inner outer factorization of transfer function matrices and it can thus be used in h sub infinity optimal control

nested support vector machines one class and cost sensitive support vector machines svms are state of the art machine learning methods for estimating density level sets and solving weighted classification problems respectively however the solutions of these svms do not necessarily produce set estimates that are nested as the parameters controlling the density level or cost asymmetry are continuously varied such nesting not only reflects the true sets being estimated but is also desirable for applications requiring the simultaneous estimation of multiple sets including clustering anomaly detection and ranking we propose new quadratic programs whose solutions give rise to nested versions of one class and cost sensitive svms furthermore like conventional svms the solution paths in our construction are piecewise linear in the control parameters although here the number of breakpoints is directly controlled by the user we also describe decomposition algorithms to solve the quadratic programs these methods are compared to conventional non nested svms on synthetic and benchmark data sets and are shown to exhibit more stable rankings and decreased sensitivity to parameter settings

a 3d isogeometric be fe analysis with dynamic remeshing for the simulation of a deformable particle in shear flows abstract a three dimensional isogeometric coupled boundary element and finite element approach based on analysis suitable t splines is developed for the simulation of deformable capsules suspended in shear flows boundary element analysis is used to solve the fluid stokes equation whereas the hydrodynamic membrane load is computed via isogeometric analysis under the assumption that the membrane is a hyper elastic thin shell with negligible bending resistance the smoothness of the t spline basis functions accommodate large deformations of the capsule without the need for additional smoothing techniques and can be used to accurately compute the membrane load a balanced distribution of membrane elements can be constructed using an unstructured locally refined mesh these properties are coupled with an adaptive temporal implicit integration scheme several benchmark examples are solved to illustrate the accuracy and potential of the method the approach is then applied to simulate the dynamics of a capsule in a real geometry of a brain capillary

sparseness of support vector machines support vector machines svms construct decision functions that are linear combinations of kernel evaluations on the training set the samples with non vanishing coefficients are called support vectors in this work we establish lower asymptotical bounds on the number of support vectors on our way we prove several results which are of great importance for the understanding of svms in particular we describe to which limit svm decision functions tend discuss the corresponding notion of convergence and provide some results on the stability of svms using subdifferential calculus in the associated reproducing kernel hilbert space

selective and reduced numerical integrations for nurbs based isogeometric analysis we propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on nurbs elements the notion of an approximation space that approximates the target space is introduced we explore the use of various approximation spaces associated with optimal patch wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points patch rules exploit the higher continuity of spline basis functions the tendency of smooth spline functions to exhibit numerical locking in nearly incompressible problems when using a full gauss legendre quadrature is alleviated with selective or reduced integration stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem we propose a local algorithm which is robust and computationally efficient to compute element by element the quadrature points and weights in patch rules the performance of the methods is assessed on several numerical examples in two dimensional elasticity and reissner mindlin shell structures

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

smooth discrimination analysis ties f and g can be based on the estimation of the set g x fx gx we consider applications where it is appropriate to assume that the region g has a smooth boundary or belongs to another nonparametric class of sets in particular this assumption makes sense if discrimination is used as a data analytic tool decision rules based on minimization of empirical risk over the whole class of sets and over sieves are considered their rates of convergence are obtained we show that these rules achieve optimal rates for estimation of g and optimal rates of convergence for bayes risks an interesting conclusion is that the optimal rates for bayes risks can be very fast in particular faster than the parametric root n rate these fast rates cannot be guaranteed for plug in rules

one class classification with gaussian processes detecting instances of unknown categories is an important task for a multitude of problems such as object recognition event detection and defect localization this article investigates the use of gaussian process gp priors for this area of research focusing on the task of one class classification we analyze different measures derived from gp regression and approximate gp classification we also study important theoretical connections to other approaches and discuss their underlying assumptions experiments are performed using a large number of datasets and different image kernel functions our findings show that our approaches can outperform the well known support vector data description approach indicating the high potential of gaussian processes for one class classification furthermore we show the suitability of our methods in the area of attribute prediction defect localization bacteria recognition and background subtraction these applications and experiments highlight the easy applicability of our method as well as its state of the art performance compared to established methods

an isogeometric analysis approach to gradient damage models continuum damage formulations are commonly used for the simulation of diffuse fracture processes implicit gradient damage models are employed to avoid the spurious mesh dependencies associated with local continuum damage models the c 0 continuity of traditional finite elements has hindered the study of higher order gradient damage approximations in this contribution we use isogeometric finite elements which allow for the construction of higher order continuous basis functions on complex domains we study the suitability of isogeometric finite elements for the discretization of higher order gradient damage approximations

on the bayes risk consistency of regularized boosting methods the probability of error of classification methods based on convex combinations of simple base classifiers by boosting algorithms is investigated the main result of the paper is that certain regularized boosting algorithms provide bayes risk consistent classifiers under the sole assumption that the bayes classifier may be approximated by a convex combination of the base classifiers nonasymptotic distribution free bounds are also developed which offer interesting new insight into how boosting works and help explain its success in practical classification problems

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

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

ranking the best instances we formulate a local form of the bipartite ranking problem where the goal is to focus on the best instances we propose a methodology based on the construction of real valued scoring functions we study empirical risk minimization of dedicated statistics which involve empirical quantiles of the scores we first state the problem of finding the best instances which can be cast as a classification problem with mass constraint next we develop special performance measures for the local ranking problem which extend the area under an roc curve auc criterion and describe the optimal elements of these new criteria we also highlight the fact that the goal of ranking the best instances cannot be achieved in a stage wise manner where first the best instances would be tentatively identified and then a standard auc criterion could be applied eventually we state preliminary statistical results for the local ranking problem

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

semi supervised novelty detection a common setting for novelty detection assumes that labeled examples from the nominal class are available but that labeled examples of novelties are unavailable the standard inductive approach is to declare novelties where the nominal density is low which reduces the problem to density level set estimation in this paper we consider the setting where an unlabeled and possibly contaminated sample is also available at learning time we argue that novelty detection in this semi supervised setting is naturally solved by a general reduction to a binary classification problem in particular a detector with a desired false positive rate can be achieved through a reduction to neyman pearson classification unlike the inductive approach semi supervised novelty detection ssnd yields detectors that are optimal e g statistically consistent regardless of the distribution on novelties therefore in novelty detection unlabeled data have a substantial impact on the theoretical properties of the decision rule we validate the practical utility of ssnd with an extensive experimental study we also show that ssnd provides distribution free learning theoretic solutions to two well known problems in hypothesis testing first our results provide a general solution to the general two sample problem that is the problem of determining whether two random samples arise from the same distribution second a specialization of ssnd coincides with the standard p value approach to multiple testing under the so called random effects model unlike standard rejection regions based on thresholded p values the general ssnd framework allows for adaptation to arbitrary alternative distributions in multiple dimensions

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

estimation variance and h sub infinity error minimization of stationary process with perfect measurements the singular estimation problem of linear continuous time stationary processes is solved both in the minimum error variance and the minimum h sub infinity norm sense simple explicit expressions for the resulting estimators and their corresponding minimum criteria are derived in terms of the system structure parameters these expressions enable an easy comparison between the two minimization procedures the theory is demonstrated by a simple example of fourth order which is solved by both minimization methods

bezier projection a unified approach for local projection and quadrature free refinement and coarsening of nurbs and t splines with particular application to isogeometric design and analysis abstract we introduce bezier projection as an element based local projection methodology for b splines nurbs and t splines this new approach relies on the concept of bezier extraction and an associated operation introduced here spline reconstruction enabling the use of bezier projection in standard finite element codes bezier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global l 2 projection bezier projection is used to develop a unified framework for spline operations including cell subdivision and merging degree elevation and reduction basis roughening and smoothing and spline reparameterization in fact bezier projection provides a quadrature free approach to refinement and coarsening of splines in this sense bezier projection provides the fundamental building block for h p k r adaptivity in isogeometric analysis

a generalized non linear transformation for evaluating singular integrals in this paper we propose a function which according to a parameter included therein generates a new sigmoidal transformation and converges to the well known sato polynomial transformation following well established procedures in the literature we employ the present transformation in the numerical evaluation of weakly singular integrals cauchy principal value integrals and hadamard finite part integrals by several numerical examples it is shown that the present transformation is available for all kinds of singular integrals mentioned above and in some cases gives better results compared with those of traditional non linear transformations copyright 2005 john wiley sons ltd

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

an effective method for numerical evaluation of general 2d and 3d high order singular boundary integrals in this paper a robust method is presented for numerical evaluation of weakly strongly hyper and super singular boundary integrals which exist in the cauchy principal value sense in two and three dimensional problems in this method the singularities involved in integration kernels are analytically removed by expressing the non singular parts of the integration kernels as power series in the local distance of the intrinsic coordinate system for three dimensional boundary integrals the radial integration method 1 is applied to transform the surface integral into a line integral over the contour of the surface and to remove various orders of singularities within the radial integrals some examples are provided to verify the correctness and robustness of the presented method

learning with sample dependent hypothesis spaces many learning algorithms use hypothesis spaces which are trained from samples but little theoretical work has been devoted to the study of these algorithms in this paper we show that mathematical analysis for these algorithms is essentially different from that for algorithms with hypothesis spaces independent of the sample or depending only on the sample size the difficulty lies in the lack of a proper characterization of approximation error to overcome this difficulty we propose an idea of using a larger function class not necessarily linear space containing the union of all possible hypothesis spaces varying with the sample to measure the approximation ability of the algorithm we show how this idea provides error analysis for two particular classes of learning algorithms in kernel methods learning the kernel via regularization and coefficient based regularization we demonstrate the power of this approach by its wide applicability

hierarchical t splines analysis suitability bezier extraction and application as an adaptive basis for isogeometric analysis abstract in this paper hierarchical analysis suitable t splines hasts are developed the resulting spaces are a superset of both analysis suitable t splines and hierarchical b splines the additional flexibility provided by the hierarchy of t spline spaces results in simple highly localized refinement algorithms which can be utilized in a design or analysis context a detailed theoretical formulation is presented bezier extraction is extended to hasts simplifying the implementation of hasts in existing finite element codes the behavior of a simple hasts refinement algorithm is compared to the local refinement algorithm for analysis suitable t splines demonstrating the superior efficiency and locality of the hasts algorithm finally hasts are utilized as a basis for adaptive isogeometric analysis

cluster validity measure and merging system for hierarchical clustering considering outliers clustering algorithms have evolved to handle more and more complex structures however the measures that allow to qualify the quality of such clustering partitions are rare and have been developed only for specific algorithms in this work we propose a new cluster validity measure cvm to quantify the clustering performance of hierarchical algorithms that handle overlapping clusters of any shape and in the presence of outliers this work also introduces a cluster merging system cms to group clusters that share outliers when located in regions of cluster overlap these outliers may be issued by a mixture of nearby cores the proposed cvm and cms are applied to hierarchical extensions of the support vector and gaussian process clustering algorithms both in synthetic and real experiments these results show that the proposed metrics help to select the appropriate level of hierarchy and the appropriate hyperparameters highlightscluster validity measure for arbitrary shaped clusters with outliers cluster merging system grouping cluster cores based on the outliers structure truly hierarchical variants of support vector and gaussian process clustering benefits for unsupervised change detection applications are presented

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

adaptive learning in cartesian product of reproducing kernel hilbert spaces we propose a novel adaptive learning algorithm based on iterative orthogonal projections in the cartesian product of multiple reproducing kernel hilbert spaces rkhss the objective is to estimate or track nonlinear functions that are supposed to contain multiple components such as i linear and nonlinear components and ii high and low frequency components in this case the use of multiple rkhss permits a compact representation of multicomponent functions the proposed algorithm is where two different methods of the author meet multikernel adaptive filtering and the algorithm of hyperplane projection along affine subspace hypass in a particular case the sum space of the rkhss is isomorphic under a straightforward correspondence to the product space and hence the proposed algorithm can also be regarded as an iterative projection method in the sum space the efficacy of the proposed algorithm is shown by numerical examples

consistency of support vector machines and other regularized kernel classifiers it is shown that various classifiers that are based on minimization of a regularized risk are universally consistent i e they can asymptotically learn in every classification task the role of the loss functions used in these algorithms is considered in detail as an application of our general framework several types of support vector machines svms as well as regularization networks are treated our methods combine techniques from stochastics approximation theory and functional analysis

on nonparametric estimation of density level sets let x 1 x n be independent identically distributed observations from an unknown probability density f consider the problem of estimating the level set g g f x r 2 f x from the sample x 1 x n under the assumption that the boundary of g has a certain smoothness we propose piecewise polynomial estimators of g based on the maximization of local empirical excess masses we show that the estimators have optimal rates of convergence in the asymptotically minimax sense within the studied classes of densities we find also the optimal convergence rates for estimation of convex level sets a generalization to the n dimensional case where n 2 is given

an improved exponential transformation for nearly singular boundary element integrals in elasticity problems abstract this paper presents an improved exponential transformation for nearly singular boundary element integrals in elasticity problems the new transformation is less sensitive to the position of the projection point compared with the original transformation in our work the conventional distance function is modified into a new form in the polar coordinate system based on the refined distance function an improved exponential transformation is proposed in the polar coordinate system moreover to perform integrations on irregular elements an adaptive integration scheme considering both the element shape and the projection point associated with the improved transformation is proposed furthermore when the projection point is located outside the integration element another nearest point is introduced to subdivide the integration elements into triangular or quadrilateral patches of fine shapes numerical examples are presented to verify the proposed method results demonstrate the accuracy and efficiency of our method

a two dimensional isogeometric boundary element method for elastostatic analysis the concept of isogeometric analysis where functions that are used to describe geometry in cad software are used to approximate the unknown fields in numerical simulations has received great attention in recent years the method has the potential to have profound impact on engineering design since the task of meshing which in some cases can add significant overhead has been circumvented much of the research effort has been focused on finite element implementations of the isogeometric concept but at present little has been seen on the application to the boundary element method the current paper proposes an isogeometric boundary element method bem which we term igabem applied to two dimensional elastostatic problems using non uniform rational b splines nurbs we find it is a natural fit with the isogeometric concept since both the nurbs approximation and bem deal with quantities entirely on the boundary the method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric bem implementation

an unsteady 3d isogeometrical boundary element analysis applied to nonlinear gravity waves abstract in this paper we describe a three dimensional isogeometric analysis based on the boundary element method iga bem in the time domain we show the capabilities and accuracy of the method for the simulation of non linear gravity waves the flow is assumed to be inviscid and irrotational and this leads to a mixed boundary value problem governed by the laplace s equation the boundary integral equation is solved at each time step and the time marching scheme is performed with a fourth order runge kutta method the hydrodynamic force is calculated with an auxiliary boundary equation in the simulations the analysis suitable t spline and nurbs basis are used to approximate both the geometry and the bem variables in the context of the bezier extraction framework the main advantages of this approach are 1 the control of the continuity and smoothness of the t spline and nurbs basis which makes the model numerically stable without the need of artificial smooth techniques 2 the high geometrical approximation of the non rational splines 3 the refinement capabilities without affecting the geometry and bem variables and 4 and the direct integration with computer aided geometrical design tools some numerical benchmark examples are analysed to demonstrate the accuracy and the stability of the method in addition we report simulations of waves generated by the movement of submerged foils which have implications in some wave generator systems installed in surf parks

least square regularized regression in sum space this paper proposes a least square regularized regression algorithm in sum space of reproducing kernel hilbert spaces rkhss for nonflat function approximation and obtains the solution of the algorithm by solving a system of linear equations this algorithm can approximate the low and high frequency component of the target function with large and small scale kernels respectively the convergence and learning rate are analyzed we measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic rkhss for sum space of rkhss with gaussian kernels by choosing appropriate parameters we tradeoff the sample error and regularization error and obtain a polynomial learning rate which is better than that in any single rkhs the utility of this method is illustrated with two simulated data sets and five real life databases

an explicit description of the reproducing kernel hilbert spaces of gaussian rbf kernels although gaussian radial basis function rbf kernels are one of the most often used kernels in modern machine learning methods such as support vector machines svms little is known about the structure of their reproducing kernel hilbert spaces rkhss in this work two distinct explicit descriptions of the rkhss corresponding to gaussian rbf kernels are given and some consequences are discussed furthermore an orthonormal basis for these spaces is presented finally it is discussed how the results can be used for analyzing the learning performance of svms

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

a classification framework for anomaly detection one way to describe anomalies is by saying that anomalies are not concentrated this leads to the problem of finding level sets for the data generating density we interpret this learning problem as a binary classification problem and compare the corresponding classification risk with the standard performance measure for the density level problem in particular it turns out that the empirical classification risk can serve as an empirical performance measure for the anomaly detection problem this allows us to compare different anomaly detection algorithms empirically i e with the help of a test set furthermore by the above interpretation we can give a strong justification for the well known heuristic of artificially sampling labeled samples provided that the sampling plan is well chosen in particular this enables us to propose a support vector machine svm for anomaly detection for which we can easily establish universal consistency finally we report some experiments which compare our svm to other commonly used methods including the standard one class svm

local rademacher complexities we propose new bounds on the error of learning algorithms in terms of a data dependent notion of complexity the estimates we establish give optimal rates and are based on a local and empirical version of rademacher averages in the sense that the rademacher averages are computed from the data on a subset of functions with small empirical error we present some applications to classification and prediction with convex function classes and with kernel classes in particular

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

estimation of a convex density contour in two dimensions abstract if a density in two dimensions has a convex contour containing probability the contour may be estimated from a sample by finding the convex polygon of smallest area containing a proportion of the sample points an algorithm for finding a particular contour is given that takes o n 2 space and o n 3 time for n sample points