algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

finite element approximation of a sixth order nonlinear degenerate parabolic equation we consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation equation here where generically equation here for any given equation here in addition to showing well posedness of our approximation we prove convergence in space dimensions d leq 3 furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed finally some numerical experiments in one and two space dimensions are presented

finite element approximation of surfactant spreading on a thin film we consider a fully practical finite element approximation of the following system of nonlinear degenerate parabolic equations begin alignat 2 textstyle frac partial u partial t textstyle frac 1 2 nabla u 2 nabla sigma v textstyle frac 1 3 nabla u 3 nabla w 0 quad mbox in omega t qquad hspace 2cm nonumber w c delta u a u 3 delta u nu nonumber textstyle frac partial v partial t nabla u v nabla sigma v rho delta v textstyle frac 1 2 nabla u 2 v nabla w 0 quad mbox in omega t nonumber end alignat the above models a surfactant driven thin film flow in the presence of both attractive a 0 and repulsive delta 0 with nu 3 van der waals forces where u is the height of the film v is the concentration of the insoluble surfactant monolayer and sigma v 1 v is the typical surface tension here rho geq 0 and c 0 are the inverses of t

a study on smoothing for particle filtered 3d human body tracking stochastic models have become the dominant means of approaching the problem of articulated 3d human body tracking where approximate inference is employed to tractably estimate the high dimensional 30d posture space of these approximate inference techniques particle filtering is the most commonly used approach however filtering only takes into account past observations almost no body tracking research employs smoothing to improve the filtered inference estimate despite the fact that smoothing considers both past and future evidence and so should be more accurate in an effort to objectively determine the worth of existing smoothing algorithms when applied to human body tracking this paper investigates three approximate smoothed inference techniques particle filtered backwards smoothing variational approximation and gibbs sampling results are quantitatively evaluated on both the humaneva dataset as well as a scene containing occluding clutter surprisingly it is found that existing smoothing techniques are unable to provide much improvement on the filtered estimate and possible reasons as to why are explored and discussed

finite element approximation of the cahn hilliard equation with degenerate mobility we consider a fully practical finite element approximation of the cahn hilliard equation with degenerate mobility textstyle frac partial u partial t del b u del gamma lap u psi u where b cdot geq 0 is a diffusional mobility and psi cdot is a homogeneous free energy in addition to showing well posedness and stability bounds for our approximation we prove convergence in one space dimension furthermore an iterative scheme for solving the resulting nonlinear discrete system is analyzed we also discuss how our approximation has to be modified in order to be applicable to a logarithmic homogeneous free energy finally some numerical experiments are presented

variational message passing bayesian inference is now widely established as one of the principal foundations for machine learning in practice exact inference is rarely possible and so a variety of approximation techniques have been developed one of the most widely used being a deterministic framework called variational inference in this paper we introduce variational message passing vmp a general purpose algorithm for applying variational inference to bayesian networks like belief propagation vmp proceeds by sending messages between nodes in the network and updating posterior beliefs using local operations at each node each such update increases a lower bound on the log evidence unless already at a local maximum in contrast to belief propagation vmp can be applied to a very general class of conjugate exponential models because it uses a factorised variational approximation furthermore by introducing additional variational parameters vmp can be applied to models containing non conjugate distributions the vmp framework also allows the lower bound to be evaluated and this can be used both for model comparison and for detection of convergence variational message passing has been implemented in the form of a general purpose inference engine called vibes variational inference for bayesian networks which allows models to be specified graphically and then solved variationally without recourse to coding

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

on the equivariant tamagawa number conjecture for tate motives let l be a finite abelian extension of and let k be any subfield of l for each integer r with r 0 we prove the equivariant tamagawa number conjecture for the pair h0 spec l r gal l k

an elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup conjecturally for p an odd prime and r a certain ring of p integers the stable general linear group gl r and the etale model for its classifying space have isomorphic mod p cohomology rings in particular these two cohomology rings should have the same image with respect to the restriction map to the diagonal subgroup we show that a strong unstable version of this last property holds for any rank if p is regular and certain homology classes for sl 2 r vanish we check that this criterion is satisfied for p 3 as evidence for the conjecture

a cup product in the galois cohomology of number fields this paper is devoted to the consideration of a certain cup product in the galois cohomology of an algebraic number field with restricted ramification let n be a positive integer let k be a number field containing the group n of nth roots of unity and let s be a finite set of primes including those above n and all real archimedean places let gk s denote the galois group of the maximal extension of k unramified outside s inside a fixed algebraic closure of k we consider the cup product h gk s n h gk s n h gk s 2 n

a gaussian process guided particle filter for tracking 3d human pose in video in this paper we propose a hybrid method that combines gaussian process learning a particle filter and annealing to track the 3d pose of a human subject in video sequences our approach which we refer to as annealed gaussian process guided particle filter comprises two steps in the training step we use a supervised learning method to train a gaussian process regressor that takes the silhouette descriptor as an input and produces multiple output poses modeled by a mixture of gaussian distributions in the tracking step the output pose distributions from the gaussian process regression are combined with the annealed particle filter to track the 3d pose in each frame of the video sequence our experiments show that the proposed method does not require initialization and does not lose tracking of the pose we compare our approach with a standard annealed particle filter using the humaneva i dataset and with other state of the art approaches using the humaneva ii dataset the evaluation results show that our approach can successfully track the 3d human pose over long video sequences and give more accurate pose tracking results than the annealed particle filter

systems of cahn hilliard equations the phase separation of alloys with two or more components is studied with emphasis on more than two components particular attention is given to differences between multicomponent and binary alloys specific topics of the paper include equilibrium theory aspects of the dynamics and numerical simulations in the equilibrium theory it is found that there is an enriched equilibrium structure that allows for multiple coexisting phases and the presence of triple points in the solution dynamic results include the characterization of the spinodal region and of the concentration variations that lead to spinodal decomposition unlike the binary theory not all composition variations lead to separation and the compositions are not restricted to the convex hull of the equilibrium concentrations linear analysis is used to predict that a pseudo binary will initially result from spinodal decomposition numerical simulations of the dynamics for a ternary alloy verify this initially but more than two phases often

monte carlo smoothing for nonlinear time series we develop methods for performing smoothing computations in general state space models the methods rely on a particle representation of the filtering distributions and their evolution through time using sequential importance sampling and resampling ideas in particular novel techniques are presented for generation of sample realizations of historical state sequences this is carried out in a forward filtering backward smoothing procedure that can be viewed as the nonlinear non gaussian counterpart of standard kalman filter based simulation smoothers in the linear gaussian case convergence in the mean squared error sense of the smoothed trajectories is proved showing the validity of our proposed method the methods are tested in a substantial application for the processing of speech signals represented by a time varying autoregression and parameterized in terms of time varying partial correlation coefficients comparing the results of our algorithm with those from a simple smoother based on the filte

etale k theory and arithmetic remark the requirement that be an odd prime can be dropped if k is totally imaginary the groups on the right of 1 1 are continuous adic etale cohomology groups recall that z l denotes the sheaf of th roots of unity z p i z l and z 0 hmv z l i d quillen has conjectured the existence of isomorphisms of type 1 1 b harris and g segal 4 have shown that 1 1 is surjective on torsion if k 1 c soule 6 in many cases proved surjectivity for k 2 with i i the surjectivity of 1 1 together with a borel s computation of k 0 q 1 gives a new proof of the existence 7 of isomorphisms

a practical numerical scheme for the ternary cahn hilliard system with a logarithmic free energy abstract we consider a practically stable finite difference method for the ternary cahn hilliard system with a logarithmic free energy modeling the phase separation of a three component mixture the numerical scheme is based on a linear unconditionally gradient stable scheme by eyre and is solved by an efficient and accurate multigrid method the logarithmic function has a singularity at zero to remove the singularity we regularize the function near zero by using a quadratic polynomial approximation we perform a convergence test a linear stability analysis and a robustness test of the ternary cahn hilliard equation we observe that our numerical solutions are convergent consistent with the exact solutions of linear stability analysis and stable with practically large enough time steps using the proposed numerical scheme we also study the temporal evolution of morphology patterns during phase separation in one two and three dimensional spaces

on some exact sequences in the theory of cyclotomic fields abstract the purpose of this article is to show the existence of some exact sequences which relate the ideal class groups of cyclotomic fields to gauss sums these exact sequences imply the results of hachimori ichimura and beliaeva furthermore we study the relations between the etale cohomology groups and some conjectures on cyclotomic fields

some remarks concerning mod nk theory the spectral sequence predicted by a beilinson relating motivic cohomology to algebraic k theory has been established for smooth quasi projective varieties over a field cf fs l1 among other properties verified this spectral sequence has the expected multiplicative behavior involving cup product in motivic cohomology and product in algebraic k theory and a good multiplicative mod n reduction relating mod n motivic cohomology to mod n algebraic k theory the purpose of this short paper is to draw two simple conclusions concerning mod n algebraick theory of smooth quasi projective varieties over an algebraically closed field by comparing this spectral sequence to its localization which we show converges to mod n etale k theory in theorem 2 1 we verify that the map from mod n algebraic k theory to mod n etale k theory of a smooth quasi projective variety x over an algebraically closed field in which n is invertible is surjective in degrees greater than or equal to twice the dimension of x this refines the surjectivity result of dfst and extends an argument by a suslin in s1 then in example 3 4 we show that certain projective smooth 3 folds x constructed by s bloch and h esnault have non zero elements in k0 x z n which are killed by multiplication by a sufficiently high power of the bott element k2 x z n although the existence of such examples is perhaps not surprising there have been attempts to prove that multiplication by is always injective the authors gratefully acknowledge useful conversations with h esnault and a suslin

relative k_ 0 annihilators fitting ideals and stickelberger phenomena when g is abelian and l is a prime we show how elements of the relative k group k 0 bf z l g bf q l give rise to annihilator fitting ideal relations of certain associated bf z g modules examples of this phenomenon are ubiquitous particularly we give examples in which g is the galois group of an extension of global fields and the resulting annihilator fitting ideal relation is closely connected to stickelberger s theorem and to the conjectures of coates and sinnott and brumer higher stickelberger ideals are defined in terms of special values of l functions when these vanish we show how to define fractional ideals generalising the stickelberger ideals with similar annihilator properties the fractional ideal is constructed from the borel regulator and the leading term in the taylor series for the l function en route our methods yield new proofs in the case of abelian number fields of formulae predicted by lichtenbaum for the orders of k groups and etale cohomology groups of rings of algebraic integers

finite element approximation of a model reaction diffusion problem with a non lipschitz nonlinearity given 0 andp 0 1 we consider the following problem findu such that begin gathered delta u lambda u p 0in omega hfill u 1on partial omega hfill end gathered where 2 is a smooth convex domain we prove optimalh 1 andl error bounds for the standard continuous piecewise linear galerkin finite element approximation in addition we analyse a more practical approximation using numerical integration on the nonlinear term finally we consider a modified nonlinear sor algorithm which is shown to be globally convergent for solving the algebraic system derived from the more practical approximation

torsion algebraic cycles and etale cobordism we prove that the classical integral cycle class map from algebraic cycles to etale cohomology factors through a quotient of l adic etale cobordism over an algebraically closed field of positive characteristic this shows that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of atiyah hirzebruch and totaro also work in positive characteristic

an efficient unconditionally energy stable local discontinuous galerkin scheme for the cahn hilliard brinkman system in this paper we present an efficient and unconditionally energy stable fully discrete local discontinuous galerkin ldg method for approximating the cahn hilliard brinkman chb system which is comprised of a cahn hilliard type equation and a generalized brinkman equation modeling fluid flow the semi discrete energy stability of the ldg method is proved firstly due to the strict time step restriction t o x 4 of explicit time discretization methods for stability we introduce a semi implicit scheme which consists of the implicit euler method combined with a convex splitting of the discrete cahn hilliard energy strategy for the temporal discretization the unconditional energy stability of this fully discrete convex splitting scheme is also proved obviously the fully discrete equations at the implicit time level are nonlinear and to enhance the efficiency of the proposed approach the nonlinear full approximation scheme fas multigrid method has been employed to solve this system of algebraic equations we also show the nearly optimal complexity numerically numerical experiments based on the overall solution method of combining the proposed ldg method convex splitting scheme and the nonlinear multigrid solver are given to validate the theoretical results and to show the effectiveness of the proposed approach for the chb system

on special elements in higher algebraic k theory and the lichtenbaum gross conjecture abstract we conjecture the existence of special elements in odd degree higher algebraic k groups of number fields that are related in a precise way to the values at strictly negative integers of the derivatives of artin l functions of finite dimensional irreducible complex representations we prove this conjecture for an important family of examples and also provide other evidence both theoretical and numerical in its support

k2of cyclic group rings over λ rings the theory developed in previous papers of the author is used to compute the algebraick2of group rings of cyclicp groups with coefficients in an arbitrary ring

an error bound for the finite element approximation of the cahn hilliard equation with logarithmic free energy an error bound is proved for a fully practical piecewise linear finite element approximation using a backward euler time discretization of the cahn hilliard equation with a logarithmic free energy

preconditioning for allen cahn variational inequalities with non local constraints the solution of allen cahn variational inequalities with mass constraints is of interest in many applications this problem can be solved both in its scalar and vector valued form as a pde constrained optimization problem by means of a primal dual active set method at the heart of this method lies the solution of linear systems in saddle point form in this paper we propose the use of krylov subspace solvers and suitable preconditioners for the saddle point systems numerical results illustrate the competitiveness of this approach

finite element approximation of the cahn hilliard equation with concentration dependent mobility we consider the cahn hilliard equation with a logarithmic free energy and non degenerate concentration dependent mobility in particular we prove that there exists a unique solution for sufficiently smooth initial data further we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions finally some numerical experiments are presented

finite element approximation of a model for phase separation of a multi component alloy with non smooth free energy a model for the phase separation of a multi component alloy with non smooth free energy is considered an error bound is proved for a fully practical piecewise linear finite element approximation using a backward euler time discretization an iterative scheme for solving the resulting nonlinear algebraic system is analysed finally numerical experiments with three components in one and two space dimensions are presented in the one dimensional case we compare some steady states obtained numerically with the corresponding stationary solutions of the continuous problem which we construct explicitly

stable etale realization and etale cobordism abstract we show that there is a stable homotopy theory of profinite spaces and use it for two main applications on the one hand we construct an etale topological realization of the stable a 1 homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero on the other hand we get a natural setting for etale cohomology theories in particular we define and discuss an etale topological cobordism theory for schemes it is equipped with an atiyah hirzebruch spectral sequence starting from etale cohomology finally we construct maps from algebraic to etale cobordism and discuss algebraic cobordism with finite coefficients over an algebraically closed field after inverting a bott element

multiphase allen cahn and cahn hilliard models and their discretizations with the effect of pairwise surface tensions in this paper the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an n component mixture are studied for the general choice of phase variables the unisolvent property of the coefficient matrix involved in the n phase models based on the pairwise surface tensions is established moreover the symmetric positive definite property of the coefficient matrix on an n 1 n 1 dimensional hyperplane which is of fundamental importance to the well posedness of the models can be proved equivalent to some physical condition for pairwise surface tensions the n phase allen cahn and n phase cahn hilliard equations can then be derived from the free energy functional a natural property is that the resulting dynamics of concentrations are independent of phase variables chosen finite element discretizations for n phase models can be obtained as a natural extension of the existing discretizations for the two phase model the discrete energy law of the numerical schemes can be proved and numerically observed under some restrictions pertaining to time step size numerical experiments including the spinodal decomposition and the evolution of triple junctions are described in order to investigate the effect of pairwise surface tensions

on the congruence subgroup problem determination of the metaplectic kernel let f be a global field i e either a number field or a function field in one variable over a finite field and let oo be the set of its archimedean places let g be a finite non empty set of places of f containing oo let o o denote the ring of g integers of f let a denote the ring of g adeles i e the restricted direct product of the completions f v for r eg let f be an absolutely simple simply connected subgroup of sl defined over f recall that a subgroup f of c f is an g arithmetic subgroup if fnsl n o has finite index in f as well as in o fy f c sl n o an g arithmetic subgroup f is a congruence subgroup if there exists a non zero ideal a in o o g such that

an improved error bound for a finite element approximation of a model for phase separation of a multi component alloy with a concentration dependent mobility matrix using a slightly different discretization scheme in time and adapting the approach in nochetto et al 1998 for analysing the time discretization error in the backward euler method we improve on the error bounds derived in i barrett and blowley 1998 and ii barrett and blowey 1999c for a fully practical piecewise linear finite element approximation of a model for phase separation of a multi component alloy with a concentration dependent mobility matrix and i a logarithmic free energy and ii a non smooth free energy the deep quench limit respectively moreover the improved error bound in the deep quench limit is optimal numerical experiments with three components illustrating the above error bounds are also presented

unconditionally energy stable time stepping scheme for cahn morral equation an unconditionally energy stable time stepping scheme is introduced to solve cahn morral like equations in the present study it is constructed based on the combination of david eyre s time stepping scheme and schur complement approach although the presented method is general and independent of the choice of homogeneous free energy density function term logarithmic and polynomial energy functions are specifically considered in this paper the method is applied to study the spinodal decomposition in multi component systems and optimal space tiling problems a penalization strategy is developed in the case of later problem to avoid trivial solutions extensive numerical experiments demonstrate the success and performance of the presented method according to the numerical results the method is convergent and energy stable independent of the choice of time stepsize its matlab implementation is included in the appendix for the numerical evaluation of algorithm and reproduction of the presented results extension of eyre s convex concave splitting scheme to multiphase systems efficient solution of spinodal decomposition in multi component systems efficient solution of least perimeter periodic space partitioning problem developing a penalization strategy to avoid trivial solutions presentation of matlab implementation of the introduced algorithm

integral motives and special values of zeta functions for each field k we define a category of rationally decomposed mixed motives with z coefficients when k is finite we show that the category is tannakian and we prove formulas relating the behaviour of zeta functions near integers to certain ext groups

preconditioning for vector valued cahn hilliard equations the solution of vector valued cahn hilliard systems is of interest in many applications we discuss strategies for the handling of smooth and nonsmooth potentials as well as for different types of constant mobilities concerning the nonsmooth systems the necessary bound constraints are incorporated via the moreau yosida regularization technique we develop effective preconditioners for the efficient solution of the linear systems in saddle point form numerical results illustrate the efficiency of our approach in particular we numerically show mesh and phase independence of the developed preconditioner in the smooth case the results in the nonsmooth case are also satisfying and the preconditioned version always outperforms the unpreconditioned one

an efficient fully discrete local discontinuous galerkin method for the cahn hilliard hele shaw system in this paper we develop an efficient and energy stable fully discrete local discontinuous galerkin ldg method for the cahn hilliard hele shaw chhs system the semi discrete energy stability of the ldg method is proved firstly due to the strict time step restriction dt o dx 4 of explicit time discretization methods for stability we introduce a semi implicit time integration scheme which is based on a convex splitting of the discrete cahn hilliard energy the unconditional energy stability has been proved for this fully discrete ldg scheme the fully discrete equations at the implicit time level are nonlinear thus the nonlinear full approximation scheme fas multigrid method has been applied to solve this system of algebraic equations which has been shown the nearly optimal complexity numerically numerical results are also given to illustrate the accuracy and capability of the ldg method coupled with the multigrid solver

sk 1 of finite abelian groups i g which can be used both for specific computations and to prove general theo rems for certain classes of groups d st2 in collaboration with oliver we have greatly extended the power of our computational methods the results of all computations as well as the ad ditional methods leading to them will appear in the sequel a d o s to this paper in a future issue of inventiones there we derive a very efficient algo rithm for computing

algebraic k theory eventually surjects onto topological k theory background for x a smooth scheme over k t x 2g is isomorphic to the usual rood topological k theory of x as a complex manifold 6 in this case theorem 1 essentially answers a question of fulton 9 w 5 for many such x the mapp ko x k ot x cannot be a surjection as non trivial hodge conditions on the chern classes prevent some topological bundles from being stably algebraic nevertheless theorem 1 shows that the existence of these non algebraic topological bundles is reflected in the higher dimensional algebraic k groups of x there are several conjectures in this area which are part of the lichten

harmonic localization of algebraic k theory spectra the lichtenbaum quillen conjectures hold for the harmonic localization of the k theory spectrum of a nice scheme various consequences of this fact are explored for example the harmonic localization of the k theory of the integers at a regular prime is explicitly identified

a time adaptive finite volume method for the cahn hilliard and kuramoto sivashinsky equations this paper presents a complete finite volume method for the cahn hilliard and kuramoto sivashinsky type of equations the spatial discretization is high order accurate and suitable for general unstructured grids the time integration is addressed by means of implicit an implicit explicit fourth order runge kutta schemes with error control and adaptive time stepping the outcome is a practical accurate and efficient simulation tool which has been successfully applied to accuracy tests and representative simulations the use of adaptive time stepping is of paramount importance in problems governed by the cahn hilliard model an adaptive method may be several orders of magnitude more efficient than schemes using constant or heuristic time steps in addition to driving the simulations efficiently the time adaptive procedure provides a quantitative not just qualitative characterization of the rich temporal scales present in phase separation processes governed by the cahn hilliard phase field model

on the algebraic k theory of the complex k theory spectrum let p 5 be a prime let ku be the connective complex k theory spectrum and let k ku be the algebraic k theory spectrum of ku in this paper we study the p primary homotopy type of the spectrum k ku by computing its mod p v1 homotopy groups we show that up to a finite summand these groups form a finitely generated free module over the polynomial algebra mathbb f p b where b is a class of degree 2p 2 defined as a higher bott element

error analysis of a mixed finite element method for the cahn hilliard equation we propose and analyze a semi discrete and a fully discrete mixed finite element method for the cahn hilliard equation ut u 1f u 0 where 0 is a small parameter error estimates which are quasi optimal order in time and optimal order in space are shown for the proposed methods under minimum regularity assumptions on the initial data and the domain in particular it is shown that all error bounds depend on only in some lower polynomial order for small the cruxes of our analysis are to establish stability estimates for the discrete solutions to use a spectrum estimate result of alikakos and fusco 2 and chen 15 to prove a discrete counterpart of it for a linearized cahn hilliard operator to handle the nonlinear term on a stretched time grid the ideas and techniques developed in this paper also enable us to prove convergence of the fully discrete finite element solution to the solution of the hele shaw mullins sekerka problem as 0 in 29

higher relative class number formulae let e be a totally complex abelian number field with maximal real subfield f and let chi denote the non trivial character of gal e f similar to the classical case n 1 the value of the artin l function l e f chi 1 n at 1 n for odd n geq 3 is given by a relative class number formula of the form

local discontinuous galerkin methods for the cahn hilliard type equations in this paper we develop local discontinuous galerkin ldg methods for the fourth order nonlinear cahn hilliard equation and system the energy stability of the ldg methods is proved for the general nonlinear case numerical examples for the cahn hilliard equation and the cahn hilliard system in one and two dimensions are presented and the numerical results illustrate the accuracy and capability of the methods