a newton cg augmented lagrangian method for semidefinite programming we consider a newton cg augmented lagrangian method for solving semidefinite programming sdp problems from the perspective of approximate semismooth newton methods in order to analyze the rate of convergence of our proposed method we characterize the lipschitz continuity of the corresponding solution mapping at the origin for the inner problems we show that the positive definiteness of the generalized hessian of the objective function in these inner problems a key property for ensuring the efficiency of using an inexact semismooth newton cg method to solve the inner problems is equivalent to the constraint nondegeneracy of the corresponding dual problems numerical experiments on a variety of large scale sdp problems with the matrix dimension n up to 4 110 and the number of equality constraints m up to 2 156 544 show that the proposed method is very efficient we are also able to solve the sdp problem fap36 with n 4 110 and m 1 154 467 in the seventh dimacs implementation challenge much more accurately than in previous attempts

map estimation via agreement on trees message passing and linear programming we develop and analyze methods for computing provably optimal maximum a posteriori probability map configurations for a subclass of markov random fields defined on graphs with cycles by decomposing the original distribution into a convex combination of tree structured distributions we obtain an upper bound on the optimal value of the original problem i e the log probability of the map assignment in terms of the combined optimal values of the tree problems we prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common an important implication is that any such shared configuration must also be a map configuration for the original distribution next we develop two approaches to attempting to obtain tight upper bounds a a tree relaxed linear program lp which is derived from the lagrangian dual of the upper bounds and b a tree reweighted max product message passing algorithm that is related to but distinct from the max product algorithm in this way we establish a connection between a certain lp relaxation of the mode finding problem and a reweighted form of the max product min sum message passing algorithm

primal dual interior point methods for semidefinite programming convergence rates stability and numerical results primal dual interior point path following methods for semidefinite programming are considered several variants are discussed based on newton s method applied to three equations primal feasibility dual feasibility and some form of centering condition the focus is on three such algorithms called the xz xz zx and q methods for the xz zx and q algorithms the newton system is well defined and its jacobian is nonsingular at the solution under nondegeneracy assumptions the associated schur complement matrix has an unbounded condition number on the central path under the nondegeneracy assumptions and an additional rank assumption practical aspects are discussed including mehrotra predictor corrector variants and issues of numerical stability compared to the other methods considered the xz zx method is more robust with respect to its ability to step close to the boundary converges more rapidly and achieves higher accuracy

lifting and separation procedures for the cut polytope the max cut problem and the associated cut polytope on complete graphs have been extensively studied over the last 25 years however in comparison only little research has been conducted for the cut polytope on arbitrary graphs in particular separation algorithms have received only little attention in this study we describe new separation and lifting procedures for the cut polytope on general graphs these procedures exploit algorithmic and structural results known for the cut polytope on complete graphs to generate valid and sometimes facet defining inequalities for the cut polytope on arbitrary graphs in a cutting plane framework we report computational results on a set of well established benchmark problems

a nonlinear programming algorithm for solving semidefinite programs via low rank factorization in this paper we present a nonlinear programming algorithm for solving semidefinite programs sdps in standard form the algorithm s distinguishing feature is a change of variables that replaces the symmetric positive semidefinite variable x of the sdp with a rectangular variable r according to the factorization x rr t the rank of the factorization i e the number of columns of r is chosen minimally so as to enhance computational speed while maintaining equivalence with the sdp fundamental results concerning the convergence of the algorithm are derived and encouraging computational results on some large scale test problems are also presented

integral grothendieck riemann roch theorem we show that in characteristic zero the obvious integral version of the grothendieck riemann roch formula obtained by clearing the denominators of the todd and chern characters is true without having to divide the chow groups by their torsion subgroups the proof introduces an alternative to grothendieck s strategy we use resolution of singularities and the weak factorization theorem for birational maps

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

fast computation of exact confidence limits for the common odds ratio in a series of 2 2 tables abstract the odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials we consider calculation of exact confidence limits for the common odds ratio in a series of independent 2 2 tables and propose three modifications of the network algorithm of mehta patel and gray 1 formulating and dealing with the problem in algebraic instead of graph theoretic terms 2 performing convolutions on the natural scale instead of the logarithmic scale and 3 using the secant method instead of binary search to compute roots of polynomial equations enhancement of computational efficiency exceeding an order of magnitude afforded by these modifications is empirically demonstrated we also compare the modified method with one based on the fast fourier transform fft further we show that the fft method can also result in considerable loss of numerical accuracy the modifications proposed in this article yield an algorithm that is not only fast and accurate but that combine

on implementing a primal dual interior point method for conic quadratic optimization based on the work of the nesterov and todd on self scaled cones an implementation of a primal dual interior point method for solving large scale sparse conic quadratic optimization problems is presented the main features of the implementation are it is based on a homogeneous and self dual model it handles rotated quadratic cones directly it employs a mehrotra type predictor corrector extension and sparse linear algebra to improve the computational efficiency finally the implementation exploits fixed variables which naturally occurs in many conic quadratic optimization problems this is a novel feature for our implementation computational results are also presented to document that the implementation can solve very large problems robustly and efficiently

on the cut polytope the cut polytopep c g of a graphg v e is the convex hull of the incidence vectors of all edge sets of cuts ofg we show some classes of facet defining inequalities ofp c g we describe three methods with which new facet defining inequalities ofp c g can be constructed from known ones in particular we show that inequalities associated with chordless cycles define facets of this polytope moreover for these inequalities a polynomial algorithm to solve the separation problem is presented we characterize the facet defining inequalities ofp c g ifg is not contractible tok 5 we give a simple characterization of adjacency inp c g and prove that for complete graphs this polytope has diameter one and thatp c g has the hirsch property a relationship betweenp c g and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied

the homotopy type of the cobordism category the embedded cobordism category under study in this paper generalizes the category of conformal surfaces introduced by g segal in s2 in order to formalize the concept of field theories our main result identifies the homotopy type of the classifying space of the embedded d dimensional cobordism category for all d for d 2 our results lead to a new proof of the generalized mumford conjecture somewhat different in spirit from the original one presented in mw

finite sample properties and asymptotic efficiency of monte carlo tests on donne une approche unifiee qui couvre le cas d une distribution nulle arbitraire afin d etudier les proprietes statistiques des tests de monte carlo

computing distributions for exact logistic regression abstract logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables usually this analysis is performed using large sample approximations when the sample size is small or the data structure sparse the accuracy of the asymptotic approximations is in question on other occasions singularity of the covariance matrix of parameter estimates precludes asymptotic analysis under these circumstances use of exact inferential procedures would seem to be a prudent alternative cox 1970 showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters to date however resorting to the exact method has not been computationally feasible except in a few special situations this article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient

solving quadratic 0 1 problems by semidefinite programs and cutting planes we present computational experiments for solving quadratic 0 1 problems our approach combines a semidefinite relaxation with a cutting plane technique and is applied in a branch and bound setting our experiments indicate that this type of approach is very robust and allows to solve many moderately sized problems having say less than 100 binary variables in a routine manner 1998 the mathematical programming society inc published by elsevier science b v

efficient semidefinite branch and cut for map mrf inference we propose a branch and cut b c method for solving general map mrf inference problems the core of our method is a very efficient bounding procedure which combines scalable semidefinite programming sdp and a cutting plane method for seeking violated constraints in order to further speed up the computation several strategies have been exploited including model reduction warm start and removal of inactive constraints we analyze the performance of the proposed method under different settings and demonstrate that our method either outperforms or performs on par with state of the art approaches especially when the connectivities are dense or when the relative magnitudes of the unary costs are low we achieve the best reported results experiments show that the proposed algorithm achieves better approximation than the state of the art methods within a variety of time budgets on challenging non submodular map mrf inference problems

norm product belief propagation primal dual message passing for approximate inference inference problems in graphical models can be represented as a constrained optimization of a free energy function in this paper we treat both forms of probabilistic inference estimating marginal probabilities of the joint distribution and finding the most probable assignment through a unified message passing algorithm architecture in particular we generalize the belief propagation bp algorithms of sum product and max product and tree reweighted trw sum and max product algorithms trbp and introduce a new set of convergent algorithms based on convex free energy and linear programming lp relaxation as a zero temperature of a convex free energy the main idea of this work arises from taking a general perspective on the existing bp and trbp algorithms while observing that they all are reductions from the basic optimization formula of f ihi where the function f is an extended valued strictly convex but nonsmooth and the functions hi are extended valued functions not necessarily convex we use tools from convex duality to present the primal dual ascent algorithm which is an extension of the bregman successive projection scheme and is designed to handle optimization of the general type f ihi we then map the fractional free energy variational principle for approximate inference onto the optimization formula above and introduce the norm product message passing algorithm special cases of the norm product include sum product and max product bp algorithms trbp and nmplp algorithms when the fractional free energy is set to be convex convex free energy the norm product is globally convergent for the estimation of marginal probabilities and for approximating the lp relaxation we also introduce another branch of the norm product which arises as the zero temperature of the convex free energy which we refer to as the convex max product the convex max product is convergent unlike max product and aims at solving the lp relaxation

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

the partition problem in this paper we describe several forms of thek partition problem and give integer programming formulations of each case the dimension of the associated polytopes and some basic facets are identified we also give several valid and facet defining inequalities for each of the polytopes

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

clique web facets for multicut polytopes let g v e be a graph an edge set uv e u si v sj i j where s1 sk is a partition of v is called a multicut with k shores we investigate the polytopes mck n and mck n that are defined as the convex hulls of the incidence vectors of all multicuts with at most k shores and at least k shores respectively of the complete graph kn we introduce a large class of inequalities called clique web inequalities valid for these polytopes and provide a quite complete characterization of those clique web inequalities that define facets of mck n and mck n using general facet manipulation techniques like collapsing and node splitting we construct further new classes of facets for these multicut polytopes we also exhibit a class of clique web facets for which the separation problem can be solved in polynomial time

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

improved semidefinite bounding procedure for solving max cut problems to optimality we present an improved algorithm for finding exact solutions to max cut and the related binary quadratic programming problem both classic problems of combinatorial optimization the algorithm uses a branch and cut and bound paradigm using standard valid inequalities and nonstandard semidefinite bounds more specifically we add a quadratic regularization term to the strengthened semidefinite relaxation in order to use a quasi newton method to compute the bounds the ratio of the tightness of the bounds to the time required to compute them can be controlled by two real parameters we show how adjusting these parameters and the set of strengthening inequalities gives us a very efficient bounding procedure embedding our bounding procedure in a generic branch and bound platform we get a competitive algorithm extensive experiments show that our algorithm dominates the best existing method

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

the effect of simulation order on level accuracy and power of monte carlo tests we discuss the effect of simulation order on level accuracy and power of monte carlo tests in a very general setting both parametric problems with or without nuisance parameters and nonparametric problems are treated by a single unifying argument it is shown that if the level of a monte carlo test is known only nominally not precisely then the level error of a monte carlo test is an order of magnitude less than that of the corresponding asymptotic test this result is available whenever the test statistic is asymptotically pivotal even if the number of simulations is held fixed as the sample size n increases it implies that monte carlo methods are a real alternative to asymptotic methods we also show that even if the number of simulations is held fixed a monte carlo test is able to distinguish between the null hypothesis and alternative hypotheses distant n 12 from the null

confidence intervals from monte carlo tests abstract monte carlo tests have exact level when the distribution of the test statistic is free of nuisance parameters confidence sets obtained by inverting such tests are also exact but may have a complicated structure the sets reduce to intervals if the sampling can be organized in a special way a sufficient condition is that the test statistic is monotone in the parameter of interest when all random drawings are kept fixed examples given include models from the one parameter exponential class a simple theory quantifying the impact of monte carlo uncertainty is also developed

a finite branch and bound algorithm for nonconvex quadratic programming via semidefinite relaxations existing global optimization techniques for nonconvex quadratic programming qp branch by recursively partitioning the convex feasible set and thus generate an infinite number of branch and bound nodes an open question of theoretical interest is how to develop a finite branch and bound algorithm for nonconvex qp one idea which guarantees a finite number of branching decisions is to enforce the first order karush kuhn tucker kkt conditions through branching in addition such an approach naturally yields linear programming lp relaxations at each node however the lp relaxations are unbounded a fact that precludes their use in this paper we propose and study semidefinite programming relaxations which are bounded and hence suitable for use with finite kkt branching computational results demonstrate the practical effectiveness of the method with a particular highlight being that only a small number of nodes are required

on the optimality of solutions of the max product belief propagation algorithm in arbitrary graphs graphical models such as bayesian networks and markov random fields mrfs represent statistical dependencies of variables by a graph the max product belief propagation algorithm is a local message passing algorithm on this graph that is known to converge to a unique fixed point when the graph is a tree furthermore when the graph is a tree the assignment based on the fixed point yields the most probable values of the unobserved variables given the observed ones good empirical performance has been obtained by running the max product algorithm or the equivalent min sum algorithm on graphs with loops for applications including the decoding of turbo codes except for two simple graphs cycle codes and single loop graphs there has been little theoretical understanding of the max product algorithm on graphs with loops here we prove a result on the fixed points of max product on a graph with arbitrary topology and with arbitrary probability distributions discrete or continuous valued nodes we show that the assignment based on a fixed point is a neighborhood maximum of the posterior probability the posterior probability of the max product assignment is guaranteed to be greater than all other assignments in a particular large region around that assignment the region includes all assignments that differ from the max product assignment in any subset of nodes that form no more than a single loop in the graph in some graphs this neighborhood is exponentially large we illustrate the analysis with examples

a linear programming approach to max sum problem a review the max sum labeling problem defined as maximizing a sum of binary i e pairwise functions of discrete variables is a general np hard optimization problem with many applications such as computing the map configuration of a markov random field we review a not widely known approach to the problem developed by ukrainian researchers schlesinger et al in 1976 and show how it contributes to recent results most importantly those on the convex combination of trees and tree reweighted max product in particular we review schlesinger et al s upper bound on the max sum criterion its minimization by equivalent transformations its relation to the constraint satisfaction problem the fact that this minimization is dual to a linear programming relaxation of the original problem and the three kinds of consistency necessary for optimality of the upper bound we revisit problems with boolean variables and supermodular problems we describe two algorithms for decreasing the upper bound we present an example application for structural image analysis

balanced simultaneous confidence sets abstract suppose that t tu is a family of parametric functions indexed by the variable u for each u an approximate confidence set cn u for tu may be obtained by referring a function of tu and the sample to an estimated quantile dn u of that function s sampling distribution this approach is sometimes called the pivotal method for constructing a confidence set even when it is not based on a true pivot a simultaneous confidence set cn for t is then obtained by simultaneously asserting the individual confidence sets cn u the problem is to choose the critical values for the cn u in such a way that the overall coverage probability of cn is correct and the coverage probabilities of the individual confidence sets cn u are equal the second property is termed balance it means that the simultaneous confidence set cn treats each constituent confidence statement cn u fairly aside from a few special cases the problem just described is too difficult for analytical approaches whe

correctness of local probability propagation in graphical models with loops graphical models such as bayesian networks and markov networks represent joint distributions over a set of variables by means of a graph when the graph is singly connected local propagation rules of the sort proposed by pearl 1988 are guaranteed to converge to the correct posterior probabilities recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops but a theoretical understanding of this performance has yet to be achieved for graphical models with a single loop we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments although the computed marginals will be incorrect we also show how nodes can use local information in the messages they receive in order to correct their computed marginals we discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single loop graphs may hold for a larger class of graphs specifically we discuss the implication of our results for understanding a class of recently proposed error correcting codes known as turbo codes

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

regularization methods for semidefinite programming we introduce a new class of algorithms for solving linear semidefinite programming sdp problems our approach is based on classical tools from convex optimization such as quadratic regularization and augmented lagrangian techniques we study the theoretical properties and we show that practical implementations behave very well on some instances of sdp having a large number of constraints we also show that the boundary point method from povh rendl and wiegele computing 78 2006 pp 277 286 is an instance of this class

the stable moduli space of riemann surfaces mumford s conjecture d mumford conjectured in 30 that the rational cohomology of the stable moduli space of riemann surfaces is a polynomial algebra generated by certain classes i of di mension 2i for the purpose of calculating rational cohomology one may replace the stable moduli space of riemann surfaces by b 1 where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus tillmann s insight 41 that the plus construction makes b 1 into an infinite loop space led to a stable homo topy version of mumford s conjecture stronger than the original 22 we prove the stronger version relying on harer s stability theorem 15 vassiliev s theorem concerning spaces of functions with moderate singularities 43 42 and methods from homotopy theory

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

an analysis of convex relaxations for map estimation of discrete mrfs the problem of obtaining the maximum a posteriori estimate of a general discrete markov random field i e a markov random field defined using a discrete set of labels is known to be np hard however due to its central importance in many applications several approximation algorithms have been proposed in the literature in this paper we present an analysis of three such algorithms based on convex relaxations i lp s the linear programming lp relaxation proposed by schlesinger 1976 for a special case and independently in chekuri et al 2001 koster et al 1998 and wainwright et al 2005 for the general case ii qp rl the quadratic programming qp relaxation of ravikumar and lafferty 2006 and iii socp ms the second order cone programming socp relaxation first proposed by muramatsu and suzuki 2003 for two label problems and later extended by kumar et al 2006 for a general label set we show that the socp ms and the qp rl relaxations are equivalent furthermore we prove that despite the flexibility in the form of the constraints objective function offered by qp and socp the lp s relaxation strictly dominates i e provides a better approximation than qp rl and socp ms we generalize these results by defining a large class of socp and equivalent qp relaxations which is dominated by the lp s relaxation based on these results we propose some novel socp relaxations which define constraints using random variables that form cycles or cliques in the graphical model representation of the random field using some examples we show that the new socp relaxations strictly dominate the previous approaches

a comparative study of energy minimization methods for markov random fields with smoothness based priors among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel labeling tasks such as depth or texture computation it has been known for decades that such problems can be elegantly expressed as markov random fields yet the resulting energy minimization problems have been widely viewed as intractable algorithms such as graph cuts and loopy belief propagation lbp have proven to be very powerful for example such methods form the basis for almost all the top performing stereo methods however the trade offs among different energy minimization algorithms are still not well understood in this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and runtime of several common energy minimization algorithms we investigate three promising methods graph cuts lbp and tree reweighted message passing in addition to the well known older iterated conditional mode icm algorithm our benchmark problems are drawn from published energy functions used for stereo image stitching interactive segmentation and denoising we also provide a general purpose software interface that allows vision researchers to easily switch between optimization methods the benchmarks code images and results are available at http vision middlebury edu mrf

message passing for graph structured linear programs proximal methods and rounding schemes the problem of computing a maximum a posteriori map configuration is a central computational challenge associated with markov random fields there has been some focus on tree based linear programming lp relaxations for the map problem this paper develops a family of super linearly convergent algorithms for solving these lps based on proximal minimization schemes using bregman divergences as with standard message passing on graphs the algorithms are distributed and exploit the underlying graphical structure and so scale well to large problems our algorithms have a double loop character with the outer loop corresponding to the proximal sequence and an inner loop of cyclic bregman projections used to compute each proximal update we establish convergence guarantees for our algorithms and illustrate their performance via some simulations we also develop two classes of rounding schemes deterministic and randomized for obtaining integral configurations from the lp solutions our deterministic rounding schemes use a re parameterization property of our algorithms so that when the lp solution is integral the map solution can be obtained even before the lp solver converges to the optimum we also propose graph structured randomized rounding schemes applicable to iterative lp solving algorithms in general we analyze the performance of and report simulations comparing these rounding schemes

an integral riemann roch theorem for surface bundles abstract this paper is a response to a conjecture by t akita about an integral riemann roch theorem for surface bundles

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

solving k cluster problems to optimality with semidefinite programming this paper deals with the computation of exact solutions of a classical np hard problem in combinatorial optimization the k cluster problem this problem consists in finding a heaviest subgraph with k nodes in an edge weighted graph we present a branch and bound algorithm that applies a novel bounding procedure based on recent semidefinite programming techniques we use new semidefinite bounds that are less tight than the standard semidefinite bounds but cheaper to get the experiments show that this approach is competitive with the best existing ones

string structures and trivialisations of a pfaffian line bundle the present paper is a contribution to categorial index theory its main result is the calculation of the pfaffian line bundle of a certain family of real dirac operators as an object in the category of line bundles furthermore it is shown how string structures give rise to trivialisations of that pfaffian