a probabilistic plan recognition algorithm based on plan tree grammars we present the phatt algorithm for plan recognition unlike previous approaches to plan recognition phatt is based on a model of plan execution we show that this clarifies several difficult issues in plan recognition including the execution of multiple interleaved root goals partially ordered plans and failing to observe actions we present the phatt algorithm s theoretical basis and an implementation based on tree structures we also investigate the algorithm s complexity both analytically and empirically finally we present phatt s integrated constraint reasoning for parametrized actions and temporal constraints

stable trace formula cuspidal tempered terms consider a connected reductive group g over a number field f for technical reasons we assume that the derived group of g is simply connected see l1 in l3 langlands partially stabilizes the trace formula for g after making certain assumptions he writes the elliptic regular part of the trace formula for g as a linear combination of the elliptic g regular parts of the stable trace formulas for the elliptic endoscopic groups h of g the function f used in the stable trace formula forh is obtained from the function f used in the trace formula for g by transferring orbital integrals

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

image segmentation with a unified graphical model we propose a unified graphical model that can represent both the causal and noncausal relationships among random variables and apply it to the image segmentation problem specifically we first propose to employ conditional random field crf to model the spatial relationships among image superpixel regions and their measurements we then introduce a multilayer bayesian network bn to model the causal dependencies that naturally exist among different image entities including image regions edges and vertices the crf model and the bn model are then systematically and seamlessly combined through the theories of factor graph to form a unified probabilistic graphical model that captures the complex relationships among different image entities using the unified graphical model image segmentation can be performed through a principled probabilistic inference experimental results on the weizmann horse data set on the voc2006 cow data set and on the msrc2 multiclass data set demonstrate that our approach achieves favorable results compared to state of the art approaches as well as those that use either the bn model or crf model alone

on interpolatory divergence free wavelets we construct interpolating divergence free multiwavelets based on cubic hermite splines we give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields we also show that the standard interpolatory wavelets based on the deslauriers dubuc interpolatory scheme or on interpolatory splines cannot be used to construct compactly supported divergence free interpolatory wavelets

composite wavelet bases for operator equations this paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit n cube these bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains this covers also elliptic boundary value problems although this study is primarily motivated by our previous analysis of wavelet methods for pseudo differential equations with special emphasis on boundary integral equations in this case it is natural to model the boundary surface as a union of parametric images of the unit cube it will be shown how to construct wavelet bases on the surface which are composed of wavelet bases defined on each surface patch here the relevant properties are the validity of norm equivalences in certain ranges of sobolev scales as well as appropriate moment conditions

extended picard complexes and linear algebraic groups for a smooth geometrically integral variety x over a field k of characteristic 0 we introduce and investigate the extended picard complex upic x it is a certain complex of galois modules of length 2 whose zeroth cohomology is k x k and whose first cohomology is pic x where k is a fixed algebraic closure of k and x is obtained from x by extension of scalars to k when x is a k torsor of a connected linear k group g we compute upic x upic g in the derived category in terms of the algebraic fundamental group 1 g as an application we compute the elementary obstruction for such x

a combined approach for goal oriented error estimation and adaptivity using operator customized finite element wavelets we describe how wavelets constructed out of finite element interpolation functions provide a simple and convenient mechanism for both goal oriented error estimation and adaptivity in finite element analysis this is done by posing an adaptive refinement problem as one of compactly representing a signal the solution to the governing partial differential equation in a multiresolution basis to compress the solution in an efficient manner we first approximately compute the details to be added to the solution on a coarse mesh in order to obtain the solution on a finer mesh the estimation step and then compute exactly the coefficients corresponding to only those basis functions contributing significantly to a functional of interest the adaptation step in this sense therefore the proposed approach is unified since unlike many contemporary error estimation and adaptive refinement methods the basis functions used for error estimation are the same as those used for adaptive refinement we illustrate the application of the proposed technique for goal oriented error estimation and adaptivity for second and fourth order linear elliptic pdes and demonstrate its advantages over existing methods copyright 2005 john wiley sons ltd

preconditioning in h div and applications we consider the solution of the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator i grad div the natural setting for such problems is in the hilbert space h div and the variational formulation is based on the inner product in h div we show how to construct preconditioners for these equations using both domain decomposition and multigrid techniques these preconditioners are shown to be spectrally equivalent to the inverse of the operator as a consequence they may be used to precondition iterative methods so that any given error reduction may be achieved in a finite number of iterations with the number independent of the mesh discretization we describe applications of these results to the efficient solution of mixed and least squares finite element approximations of elliptic boundary value problems

wavelets for the maxwell s equations an overview abstract in recent years wavelets decompositions have been widely used in computational maxwell s curl equations to effectively resolve complex problems in this paper we review different types of wavelets that we can consider the cohen daubechies feauveau biorthogonal wavelets the orthogonal daubechies wavelets and the deslauries dubuc interpolating wavelets we summarize the main features of these frameworks and we propose some possible future works

adaptive multiscale wavelet galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization the multiscale galerkin formulation of two dimensional elasticity problems is presented for easy interpolation and boundary handlings as well as efficient adaptive analysis two dimensional interpolation wavelets are used as the multiscale trial functions in the galerkin formulation after the validity of the present multiscale adaptive method is verified with some benchmark problems the present wavelet based method is applied to the multiscale topology optimization that progresses design resolution levels dyadically from low to high levels by this application we show the potential of the multiscale method and the possibility of developing a fully integrated analysis and topology design optimization in the multiscale multiresolution setting

the elementary obstruction and homogeneous spaces let k be a field of characteristic zero and let k be an algebraic closure of k for a geometrically integral variety x over k we write k x for the function field of x x k k if x has a smooth k point the natural embedding of multiplicative groups k k x admits a galois equivariant retraction in the first part of this article equivalent conditions to the existence of such a retraction are given over local and then over global fields those conditions are expressed in terms of the brauer group of x in the second part of the article we restrict attention to varieties that are homogeneous spaces of connected but otherwise arbitrary algebraic groups with connected geometric stabilizers for k local or global and for such a variety x in many situations but not all the existence of a galois equivariant retraction to k k x ensures the existence of a k rational point on x for homogeneous spaces of linear algebraic groups the technique also handles the case where k is the function field of a complex surface resume soient k un corps de caracteristique nulle et k une cloture algebrique de k pour une k variete x geometriquement integre on note k x le corps des fonctions de x x k k si x possede un k point lisse le plongement naturel de groupes multiplicatifs k k x admet une retraction equivariante pour l action du groupe de galois de k sur k dans la premiere partie de l article sur les corps locaux puis sur les corps globaux on donne des conditions equivalentes a l existence d une telle retraction equivariante ces conditions s expriment en terme du groupe de brauer de la variete x dans la seconde partie de l article on considere le cas des espaces homogenes de groupes algebriques connexes non necessairement lineaires avec groupes d isotropie duke mathematical journal vol 141 no 2 c 2008 received 6 november 2006 revision received 23 april 2007 2000 mathematics subject classification primary 14g05 11g99 12g05 secondary 11e72 14f22 14k15

wavelet methods for second order elliptic problems preconditioning and adaptivity wavelet methods allow us to combine high order accuracy efficient preconditioning techniques and adaptive approximations in order to solve efficiently elliptic operator equations many difficulties remain in particular related to the adaptation of wavelet decompositions to bounded domains with prescribed boundary conditions leading to possibly high constants in the cal o 1 preconditioning in this paper we consider the framework of conforming domain decomposition to generate our wavelet bases and second order operators we emphasize the choice of the wavelets near the boundary of the tensor product reference domain in order to optimize the efficiency of the diagonal preconditioning of elliptic operators in order to improve the constants obtained by such diagonal preconditionings we propose to take into account interactions between the scales through the computation of a sparse approximate inverse spai on a set of nonzero entries obtained from the compression of the operator itself in the wavelet basis the efficiency of these methods is illustrated by solving elliptic second order problems with variable or constant coefficients and homogeneous boundary conditions on a uniform discretization finally we propose a coupling of the iterative solver with an adaptive space refinement technique on the laplacian model problem our experiments show that this algorithm generates an optimal nonlinear approximation of the solution

une formule pour le groupe de brauer algebrique dʼun torseur abstract given a homogeneous space x of a connected algebraic group g with connected stabilizers over a field k of characteristic zero we construct a complex of galois modules of length 3 and a canonical isomorphism between a hypercohomology group of this complex and an explicit subgroup of the brauer group of x this result is obtained as a consequence of a formula describing the algebraic brauer group of a torsor and it generalizes recent results by borovoi and van hamel by considering non linear groups g and by taking into account some transcendental elements in the brauer group of x

local global principles for 1 motives building upon our arithmetic duality theorems for 1 motives we prove that the manin obstruction related to a finite subquotient x of the brauer group is the only obstruction to the hasse principle for rational points on torsors under semiabelian varieties over a number field assuming the finiteness of the tate shafarevich group of the abelian quotient this theorem answers a question by skorobogatov in the semiabelian case and is a key ingredient of recent work on the elementary obstruction for homogeneous spaces over number fields we also establish a cassels tate type dual exact sequence for 1 motives and give an application to weak approximation

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

wavelet bases in h div and h curl some years ago compactly supported divergence free wavelets have been constructed which also give rise to a stable biorthogonal wavelet splitting of h div these bases have successfully been used both in the analysis and numerical treatment of the stokes and navier stokes equations in this paper we construct stable wavelet bases for the stream function spaces h curl moreover curl free vector wavelets are constructed and analysed the relationship between h div and h curl are expressed in terms of these wavelets we obtain discrete orthogonal hodge decompositions our construction works independently of the space dimension but in terms of general assumptions on the underlying wavelet systems in l 2 omega that are used as building blocks we give concrete examples of such bases for tensor product and certain more general domains omega subset er n as an application we obtain wavelet multilevel preconditioners in h div and h curl email urban dragon ian pv cnr it keywords h div h curl stream function spaces wavelets

wavelet adaptive method for second order elliptic problems boundary conditions and domain decomposition summary wavelet methods allow to combine high order accuracy multilevel preconditioning techniques and adaptive approximation in order to solve efficiently elliptic operator equations one of the main difficulty in this context is the efficient treatment of non homogeneous boundary conditions in this paper we propose a strategy that allows to append such conditions in the setting of space refinement i e adaptive discretizations of second order problems our method is based on the use of compatible multiscale decompositions for both the domain and its boundary and on the possibility of characterizing various function spaces from the numerical properties of these decompositions in particular this allows the construction of a lifting operator which is stable for a certain range of smoothness classes and preserves the compression of the solution in the wavelet basis an explicit construction of the wavelet bases and the lifting is proposed on fairly general domains based on c 0 conforming domain decomposition techniques

multigrid in h div and h curl summary we consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the hilbert spaces bf h div and bf h curl in three dimensions we show that if appropriate finite element spaces and appropriate additive or multiplicative schwarz smoothers are used then the multigrid v cycle is an efficient solver and preconditioner for the discrete operator all results are uniform with respect to the mesh size the number of mesh levels and weights on the two terms in the inner products

the sensitivity of belief networks to imprecise probabilities an experimental investigation abstract bayesian belief networks are being increasingly used as a knowledge representation for reasoning under uncertainty some researchers have questioned the practicality of obtaining the numerical probabilities with sufficient precision to create belief networks for large scale applications in this work we investigate how precise the probabilities need to be by measuring how imprecision in the probabilities affects diagnostic performance we conducted a series of experiments on a set of real world belief networks for medical diagnosis in liver and bile disease we examined the effects on diagnostic performance of 1 varying the mappings from qualitative frequency weights into numerical probabilities 2 adding random noise to the numerical probabilities 3 simplifying from quaternary domains for diseases and findings absent mild moderate and severe to binary domains absent and present and 4 using test cases that contain diseases outside the network we found that even extreme differences in the probability mappings and large amounts of noise lead to only modest reductions in diagnostic performance we found no significant effect of the simplification from quaternary to binary representation we also found that outside diseases degraded performance modestly overall these findings indicate that even highly imprecise input probabilities may not impair diagnostic performance significantly and that simple binary representations may often be adequate these findings of robustness suggest that belief networks are a practical representation without requiring undue precision

interactive construction of graphical decision models based on causal mechanisms abstract we propose a framework for building graphical decision models from individual causal mechanisms our approach is based on the work of simon simon h a 1953 causal ordering and identifiability in hood w c koopmans t c eds studies in econometric method cowles commission for research in economics monograph no 14 john wiley and sons inc new york ny pp 49 74 ch iii who proposed a causal ordering algorithm for explicating causal asymmetries among variables in a self contained set of structural equations we extend the causal ordering algorithm to under constrained sets of structural equations common during the process of problem structuring we demonstrate that the causal ordering explicated by our extension is an intermediate representation of a modeler s understanding of a problem and that the process of model construction consists of assembling mechanisms into self contained causal models we describe i ma g e ni e an interactive modeling tool that supports mechanism based model construction and demonstrate empirically that it can effectively assist users in constructing graphical decision models

parallel preconditioning with sparse approximate inverses a parallel preconditioner is presented for the solution of general sparse linear systems of equations a sparse approximate inverse is computed explicitly and then applied as a preconditioner to an iterative method the computation of the preconditioner is inherently parallel and its application only requires a matrix vector product the sparsity pattern of the approximate inverse is not imposed a priori but captured automatically this keeps the amount of work and the number of nonzero entries in the preconditioner to a minimum rigorous bounds on the clustering of the eigenvalues and the singular values are derived for the preconditioned system and the proximity of the approximate to the true inverse is estimated an extensive set of test problems from scientific and industrial applications provides convincing evidence of the effectiveness of this approach

effective construction of divergence free wavelets on the square we present an effective construction of divergence free wavelets on the square with suitable boundary conditions since 2d divergence free vector functions are the curl of scalar stream functions we simply derive divergence free multiresolution spaces and wavelets by considering the curl of standard biorthogonal multiresolution analyses bmras on the square the key point of the theory is that the derivative of a 1d bmra is also a bmra as established by jouini and lemarie rieusset 1993 16 we propose such construction in the context of generic compactly supported wavelets which allows fast algorithms examples illustrate the practicality of the method