the novikov conjecture for algebraic k theory of the group algebra over the ring of schatten class operators abstract in this paper we prove the algebraic k theory novikov conjecture for group algebras over the ring of schatten class operators the main technical tool in the proof is an explicit construction of the connes chern character

low distortion embeddings of graphs with large girth the main purpose of the paper is to construct a sequence of graphs of constant degree with indefinitely growing girths admitting embeddings into l1 with uniformly bounded distortions this result solves the problem posed by n linial a magen and a naor 2002

ideal structure of uniform roe algebras of coarse spaces abstract let c u x e be the uniform roe algebra of a coarse space x e with uniformly locally finite coarse structure by a controlled truncation technique we show that the controlled propagation operators in an ideal i of c u x e are exactly the controlled truncations of elements in i it follows that the lattice of the ideals of the uniform roe algebra c u x e in which controlled propagation operators are dense the lattice of the invariant open subsets in the unit space of the groupoid g x introduced by skandalis tu and yu the lattice of the ideals of the coarse structure e and the lattice of the ideals of the coarse space x are mutually isomorphic these lattices also give rise to a type of classification for the ideals of c u x e

marginal likelihood estimation via power posteriors model choice plays an increasingly important role in statistics from a bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model however this is typically a difficult task since it amounts to integrating over all model parameters the aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling we show how the marginal likelihood can be computed via markov chain monte carlo methods on modified posterior distributions for each model this then allows bayes factors or posterior model probabilities to be calculated we show that this approach requires very little tuning and is straightforward to implement the new method is illustrated in a variety of challenging statistical settings

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

operator norm localization for linear groups and its application to k theory abstract we prove the operator norm localization property for linear groups as an application we prove the coarse novikov conjecture for box spaces of a linear group

a new method for a class of linear variational inequalities in this paper we introduce a new iterative scheme for the numerical solution of a class of linear variational inequalities each iteration of the method consists essentially only of a projection to a closed convex set and two matrix vector multiplications both the method and the convergence proof are very simple

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

uniformly bounded representations of sl 2 r abstract we compute the norm of irreducible uniformly bounded representations of sl 2 r we show that the kunze stein version of the uniformly bounded representations has minimal norm in its similarity class of uniformly bounded representations

solving a class of asymmetric variational inequalities by a new alternating direction method abstract the augmented lagrangian method also referred to as an alternating direction method solves a class of variational inequalities vi via solving a series of sub vi problems the method is effective whenever the subproblems can be solved efficiently however the subproblem to be solved in each iteration of the augmented lagrangian method itself is still a vi problem it is essentially as difficult as the original one the only difference is that the dimension of the subproblems is lower in this paper we propose a new alternating direction method for solving a class of monotone variational inequalities in each iteration the method solves a convex quadratic programming with simple constrains and a well conditioned system of nonlinear equations for such easier subproblems existing efficient numerical softwares are applicable the effectiveness of the proposed method is demonstrated with an illustrative example

large riemannian manifolds which are flexible for each k z we construct a uniformly contractible metric on euclidean space which is not mod k hypereuclidean we also construct a pair of uniformly contractible riemannian metrics on r n n 11 so that the resulting manifolds z and z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism we show that for these spaces the c algebra assembly map k lf z k c z from locally finite k homology to the k theory of the bounded propagation algebra is not a monomorphism this shows that an integral version of the coarse novikov conjecture fails for real operator algebras if we allow a single cone like singularity a similar construction yields a counterexample for complex c algebras

a globally convergent newton method for solving strongly monotone variational inequalities variational inequality problems have been used to formulate and study equilibrium problems which arise in many fields including economics operations research and regional sciences for solving variational inequality problems various iterative methods such as projection methods and the nonlinear jacobi method have been developed these methods are convergent to a solution under certain conditions but their rates of convergence are typically linear in this paper we propose to modify the newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length the purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate it is then shown that under the strong monotonicity assumption the method is globally convergent and under some additional assumptions the rate of convergence is quadratic limited computational experience indicates the high efficiency of the proposed method

a new inexact alternating directions method for monotone variational inequalities the alternating directions method adm is an effective method for solving a class of variational inequalities vi when the proximal and penalty parameters in sub vi problems are properly selected in this paper we propose a new adm method which needs to solve two strongly monotone sub vi problems in each iteration approximately and allows the parameters to vary from iteration to iteration the convergence of the proposed adm method is proved under quite mild assumptions and flexible parameter conditions

enhanced negative type for finite metric trees abstract a finite metric tree is a finite connected graph that has no cycles endowed with an edge weighted path metric finite metric trees are known to have strict 1 negative type in this paper we introduce a new family of inequalities 1 that encode the best possible quantification of the strictness of the non trivial 1 negative type inequalities for finite metric trees these inequalities are sufficiently strong to imply that any given finite metric tree t d must have strict p negative type for all p in an open interval 1 1 where 0 may be chosen so as to depend only upon the unordered distribution of edge weights that determine the path metric d on t in particular if the edges of the tree are not weighted then it follows that depends only upon the number of vertices in the tree we also give an example of an infinite metric tree that has strict 1 negative type but does not have p negative type for any p 1 this shows that the maximal p negative type of a metric space can be strict

uniformly bounded representations and exact groups abstract we characterize groups with guoliang yu s property a i e exact groups by the existence of a family of uniformly bounded representations which approximate the trivial representation

quantitative geometry rather than describing a traditional field of mathematics quantitative geometry refers to a modern way of thinking about geometry and its applications that occur in a wide range of mathematical disciplines the overarching theme here is that certain geometric problems can only be formulated after the introduction of auxiliary quantitative parameters and asking for their asymptotic or approximate behavior this leads to meaningful questions that do not necessarily have counterparts in classical qualitative geometric investigations a viewpoint that allows one to uncover deep and useful structural information that appears only in the quantitative regime quantitative reasoning allows one to tame complicated objects and phenomena that are unwieldy if one insists on exact measurements it is often the case that a rich yet structured picture emerges only if one asks the correct questions by allowing for controlled errors

property a and affine buildings abstract yu s property a is a non equivariant generalisation of amenability introduced in his study of the coarse baum connes conjecture in this paper we show that all affine buildings of type a 2 b 2 and g 2 have property a together with results of guentner higson and weinberger this completes a programme to show that all affine building have property a in passing we use our technique to obtain a new proof for groups acting on a n buildings

maximal and reduced roe algebras of coarsely embeddable spaces in 7 gong wang and yu introduced a maximal or universal version of the roe c algebra associated to a metric space we study the relationship between this maximal roe algebra and the usual version in both the uniform and non uniform cases the main result is that if a uniformly discrete bounded geometry metric space x coarsely embeds into a hilbert space then the canonical map between the maximal and usual uniform roe algebras induces an isomorphism on k theory we also give a simple proof that if x has property a then the maximal and usual uniform roe algebras are the same these two results are natural coarse geometric analogues of certain well known implications of a t menability and amenability for group c algebras the techniques used are e theoretic building on work of higson kasparov and trout 11 12 and yu 28

solving a class of linear projection equations many interesting and important constrained optimization problems in mathematical programming can be translated into an equivalent linear projection equation u p omega u mu q here p omega cdot is the orthogonal projection on some convex set omega e g omega bbb r n and m is a positive semidefinite matrix this paper presents some new methods for solving a class of linear projection equations the search directions of these methods are straighforward extensions of the directions in traditional methods for unconstrained optimization based on the idea of a projection and contraction method 7 we get a simple step length rule and are able to obtain global linear convergence

a projection based prediction correction method for structured monotone variational inequalities in this paper we propose a modified prediction correction method for structured monotone variational inequalities this method is based on a reformulation of the normal prediction correction method each iteration of the new method contains two predictions and a correction at each iteration a new strategy is applied to obtain a proper step length all the computing processes are easily implemented and the global convergence is also presented under mild assumptions numerical experiments for traffic equilibrium problems indicate that the new method is effectively applicable in practice

a bott periodicity theorem for infinite dimensional euclidean space abstract we formulate and prove an equivariant bott periodicity theorem for infinite dimensional euclidean vector spaces the main features of our argument are i the construction of a non commutative c algebra to play the role of the algebra of functions on infinite dimensional euclidean space and ii the construction of a certain index one elliptic partial differential operator which provides the basis for an inverse to the bott periodicity map these tools have applications to index theory and the novikov conjecture notably a proof of the novikov conjecture for amenable groups the applications will be considered elsewhere

a proximal decomposition algorithm for variational inequality problems in this paper we propose a new decomposition algorithm for solving monotone variational inequality problems with linear constraints the algorithm utilizes the problem s structure conductive to decomposition at each iteration the algorithm solves a system of nonlinear equations which is structurally much easier to solve than variational inequality problems the subproblems of classical decomposition methods and then performs a projection step to update the multipliers we allow to solve the subproblems approximately and we prove that under mild assumptions on the problem s data the algorithm is globally convergent we also report some preliminary computational results which show that the algorithm is encouraging

a metric approach to limit operators we extend the limit operator machinery of rabinovich roch and silbermann from z n to bounded geometry strongly discrete metric spaces we do not assume the presence of any group structure or action on our metric spaces using this machinery and recent ideas of lindner and seidel we show that if a metric space x has yu s property a then a band dominated operator on x is fredholm if and only if all of its limit operators are invertible we also show that this always fails for metric spaces without property a

a notion of geometric complexity and its application to topological rigidity we introduce a geometric invariant called finite decomposition complexity fdc to study topological rigidity of manifolds we prove for instance that if the fundamental group of a compact aspherical manifold m has fdc and if n is homotopy equivalent to m then m n is homeomorphic to n n for n large enough this statement is known as the stable borel conjecture on the other hand we show that the class of fdc groups includes all countable subgroups of gl n k for any field k

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

a marginal moment matching approach for fitting endemic epidemic models to underreported disease surveillance counts count data are often subject to underreporting especially in infectious disease surveillance we propose an approximate maximum likelihood method to fit count time series models from the endemic epidemic class to underreported data the approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class moreover the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed notably we show that this leads to a downward bias in model based estimates of the effective reproductive number a marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease the good performance of the proposed methodology is demonstrated in simulation studies an extension to time varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in berlin germany

bayesian parameter inference for dynamic infectious disease modelling rotavirus in germany understanding infectious disease dynamics using epidemic models based on ordinary differential equations requires the calibration of model parameters from data a commonly used approach in practice to simplify this task is to fix many parameters on the basis of expert or literature information however this not only leaves the corresponding uncertainty unexamined but often also leads to biased inference for the remaining parameters because of dependence structures inherent in any given model in the present work we develop a bayesian inference framework that lessens the reliance on such external parameter quantifications by pursuing a more data driven calibration approach this includes a novel focus on residual autocorrelation combined with model averaging techniques in order to reduce these estimates dependence on the underlying model structure we applied our methods to the modelling of age stratified weekly rotavirus incidence data in germany from 2001 to 2008 using a complex susceptible infectious susceptible type model complemented by the stochastic reporting of new cases as a result we found the detection rate in the eastern federal states to be more than four times higher compared with that of the western federal states 19 0 vs 4 3 and also the infectiousness of symptomatically infected individuals was estimated to be more than 10 times higher than that of asymptomatically infected individuals 95 credibility interval 8 1 19 6 not only do these findings give valuable epidemiological insight into the transmission processes we were also able to examine the considerable impact on the model predicted transmission dynamics when fixing parameters beforehand

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension