automorphisms of graph groups abstract given a graph v e the graph group on is the group generated by the vertex set v with the defining relations being that two adjacent vertices commute in the following the centralizer problem for graph groups is solved and it is shown that for some graph groups aut f is finitely generated by generators which are natural analogues to the nielsen automorphisms for a free group

small cancellation theory and automatic groups part ii the main results obtained in part i can be rephrased in the language of root systems and euclidean planar tessellations as saying that finite a1 x a1 and a 2 piecewise euclidean abbreviated pe complexes of non positive curvature have automatic fundamental groups a 2 dimensional complex is a a 1 a1 respectively a2 pe complex if every 2 cell can be identified with a unit square resp equilateral triangle in the euclidean plane in such a way that the induced metrics agree on intersections such a complex has non positive curvature if the link of each vertex contains no circuits without backtracking of length less than 2 n here we prove using similar techniques that finite 2 complexes modelled on the other two root systems b 2 and g2 corresponding to tessellations by 45 right angle triangles and by 30 60 right angle triangles also have automatic fundamental groups theorems 2 3 and 3 2 to be precise

garside families and garside germs garside families have recently emerged as a relevant context for extending results involving garside monoids and groups which themselves extend the classical theory of generalized braid groups here we establish various characterizations of garside families that is equivalently various criteria for establishing the existence of normal decompositions of a certain type

artin groups of euclidean type this article resolves several long standing conjectures about artin groups of euclidean type specifically we prove that every irreducible euclidean artin group is a torsion free centerless group with a decidable word problem and a finite dimensional classifying space we do this by showing that each of these groups is isomorphic to a subgroup of a group with an infinite type garside structure the garside groups involved are introduced here for the first time they are constructed by applying semi standard procedures to crystallographic groups that contain euclidean coxeter groups but which need not be generated by the reflections they contain

dismantlability of weakly systolic complexes and applications in this paper we investigate the structural properties of weakly systolic complexes introduced recently by the second author and of their 1 skeletons the weakly bridged graphs we present several characterizations of weakly systolic complexes and weakly bridged graphs then we prove that weakly bridged graphs are dismantlable using this we establish the fixed point theorem for weakly systolic complexes as a consequence we get results about conjugacy classes of finite subgroups and classifying spaces for finite subgroups of weakly systolic groups as immediate corollaries we obtain new results on systolic complexes and

hybrid prismatic tetrahedral grid generation for viscous flow applications a method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed the prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions whereas the tetrahedral grid covers the rest of the computational domain the delaunay approach for tetrahedral grid generation is used the proposed prismatic grid is structured in directions normal to the boundary faces but the number of prisms generated from one boundary face is variable from face to face unlike conventional prismatic grid generators this technique works well even in regions of cavities and gaps the delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms particular attention is given to the boundary constraining problem a robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

unstructured grid generation using iterative point insertion and local reconnection a procedure is presented for efficient generation of high quality two or three dimensional unstructured grids of triangular or tetrahedral elements the present procedure uses an iterative point creation and insertion scheme wherein points are created using advancing front type point placement initially the connectivity for these generated points is obtained by directly subdividing the elements which contain them without regard to quality this connectivity is then improved by iteratively using local reconnection subject to a quality criterion for two dimensions a min max criterion is used and for three dimensions a delaunay in sphere criterion followed by a min max type criterion is used the overall procedure is applied repetitively until a complete field grid is generated with a desired point distribution grid quality and performance statistics are presented for a variety of two and three dimensional configurations the combined quality and efficiency attributes of this procedure appear to be a substantial improvement over existing methods

development and verification of a coupled dsmc ns scheme using unstructured mesh an efficient and accurate parallel coupled dsmc ns method using three dimensional unstructured grid topology is proposed and verified for the simulation of high speed gas flows involving continuum and rarefied regimes a domain overlapping strategy taking advantage of unstructured data format with dirichlet dirichlet type boundary conditions based on two breakdown parameters is used iteratively to determine the choice of solvers in the spatial domain the selected breakdown parameters for this study include 1 a local maximum knudsen number defined as the ratio of the local mean free path and local characteristic length based on property gradient and 2 a thermal non equilibrium indicator defined as the ratio of the difference between translational and rotational temperatures to the translational temperature a supersonic flow m 4 over a quasi 2 d 25 wedge is employed as the first step in verifying the present coupled method the results of simulation using the coupled method are in excellent agreement with those of the pure dsmc method which is taken as the benchmark solution effects of the size of overlapping regions and the choice of breakdown parameters on the convergence history are discussed results show that the proposed iteratively coupled method predicts the results more accurately as compared to the one shot coupled method which has been often used in practice further a realistic 3 d nitrogen flow which two near continuum parallel orifice jets underexpand into a near vacuum environment is simulated using the present coupled method to demonstrate its capability finally developments in extending the present method are also outlined in this paper

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

proof of the k pi 1 conjecture for affine artin groups we prove the k pi 1 conjecture for affine artin groups the complexified complement of an affine reflection arrangement is a classifying space this is a long standing problem due to arnol d pham and thom our proof is based on recent advancements in the theory of dual coxeter and artin groups as well as on several new results and constructions in particular we show that all affine noncrossing partition posets are el shellable we use these posets to construct finite classifying spaces for dual affine artin groups we introduce new cw models for the orbit configuration spaces associated with arbitrary coxeter groups we construct finite classifying spaces for the braided crystallographic groups introduced by mccammond and sulway

artin groups and infinite coxeter groups if the associated coxeter group 7 is finite for the braid group b the associated coxeter group is the symmetric group s brieskorn and saito 4 and independently deligne 6 have investigated artin groups of finite type in 1969 garside 7 solved the conjugacy problem for braid groups brieskorn this work was supported by nsf grants mcs 7902512 and mcs 7703452 the authors would like to thank the referee for an extremely careful reading of the paper and many helpful sugges tions

a unifying review of linear gaussian models factor analysis principal component analysis mixtures of gaussian clusters vector quantization kalman filter models and hidden markov models can all be unified as variations of unsupervised learning under a single basic generative model this is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity through the use of other nonlinearities we show how independent component analysis is also a variation of the same basic generative model we show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term we introduce a new model for static data known as sensible principal component analysis as well as a novel concept of spatially adaptive observation noise we also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models

unsupervised state space modeling using reproducing kernels a novel framework for the design of state space models ssms is proposed whereby the state transition function of the model is parametrized using reproducing kernels the nature of ssms requires learning a latent function that resides in the state space and for which input output sample pairs are not available thus prohibiting the use of gradient based supervised kernel learning to this end we then propose to learn the mixing weights of the kernel estimate by sampling from their posterior density using monte carlo methods we first introduce an offline version of the proposed algorithm followed by an online version which performs inference on both the parameters and the hidden state through particle filtering the accuracy of the estimation of the state transition function is first validated on synthetic data next we show that the proposed algorithm outperforms kernel adaptive filters in the prediction of real world time series while also providing probabilistic estimates a key advantage over standard methods

flow simulation using generalized static and dynamic grids a new approach is presented for a e ow simulation system using generalized grids in a generalized grid the physical domain of interest is decomposed into cells with an arbitrary number of edges or faces the grid can be of structured unstructured or hanging node type or an arbitrary combination of the types a cell face based data structure is used to storethegrid information a e ow simulation system is developed forgeneralized gridsthat can handle static and dynamic grids the full navier stokes equations in the integral form are taken as the relations that govern the e uid e ow a cell centered e nite volume scheme is developed for solving these governing equations the numerical e ux across the cell faces is evaluated by an upwind scheme based on roe s approximate riemann solver a higher order scheme is formulated by utilizing taylor s series expansion and green s theorem limiter functions are used to preserve monotonocity the skin friction coefe cient is used to evaluate the accuracy of the limiterfunctions thegeneralized minimalresidualmethod isutilized tosolvethesparselinearsystem ofequations resulting from thelinearization of the e ux vectors thespalart allmaras one equation turbulence model has been implemented for the generalized grids and is used to evaluate the turbulent viscosity for dynamically moving bodies the equations of classical mechanics are used to predict the trajectory based on the external aerodynamic and body forces a variety of computational examples are presented to demonstratethe wide rangeof applications and the results are compared with experimental data whenever available

exceptional sequences and clusters abstract we show that exceptional sequences for hereditary algebras are characterized by the fact that the product of the corresponding reflections is the inverse coxeter element in the weyl group we use this result to give a new combinatorial characterization of clusters tilting sets in the cluster category in the case where the hereditary algebra is of finite type

interval garside structures related to the affine artin groups of type a abstract garside theory emerged from the study of artin groups and their generalizations finite type artin groups admit two types of interval garside structures corresponding to their standard and dual presentations concerning affine artin groups digne established interval garside structures for two families of these groups by using their dual presentations recently mccammond established that none of the remaining dual presentations except for one additional case correspond to interval garside structures in this paper shifting attention from dual presentations to other nice presentations for the affine artin group of type a discovered by shi and corran lee lee i will construct interval garside structures related to this group this construction is the first successful attempt to establish interval garside structures not related to the dual presentations in the case of affine artin groups

unscented rauch tung striebel smoother this note considers the application of the unscented transform to optimal smoothing of nonlinear state space models in this note a new rauch tung striebel type form of the fixed interval unscented kalman smoother is derived the new smoother differs from the previously proposed two filter formulation based unscented kalman smoother in the sense that it is not based on running two independent filters forward and backward in time instead a separate backward smoothing pass is used which recursively computes corrections to the forward filtering result the smoother equations are derived as approximations to the formal bayesian optimal smoothing equations the performance of the new smoother is demonstrated with a simulation

solution adaptive mesh generation using feature aligned embedded surface meshes in this paper we present a technique for generating solution adaptive meshes that uses feature aligned surfaces embedded in the computational domain a feature detection algorithm is first employed to identify features of interest surfaces associated with these features are then meshed and a volume mesh that respects these embedded surface meshes is then generated this approach is promising because it provides a mechanism for controlling local grid quality as well as automatically aligning cell faces with the feature for flows that include topologically and or geometrically complex features we describe a mesh refinement technique that can be used in tandem with the embedded surface meshes to provide a mechanism for refining throughout the computational domain we include results from two cases to illustrate how the method works

robust filtering and smoothing with gaussian processes we propose a principled algorithm for robust bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non parametric gaussian process gp models gps are gaining increasing importance in signal processing machine learning robotics and control for representing unknown system functions by posterior probability distributions this modern way of system identification is more robust than finding point estimates of a parametric function representation our principled filtering smoothing approach for gp dynamic systems is based on analytic moment matching in the context of the forward backward algorithm our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state of the art gaussian filters and smoothers can fail

algorithms and geometry for graph products of groups recent work of gromov epstein cannon thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups see 16 17 and 14 many of these structures are preserved by taking graph products the graph product of groups not to be confused with the fundamental group of a graph of groups is a product mixing direct and free products whether the product between two groups in the graph product is free or direct is determined by a simplicial graph given a simplicial graph we say that two vertices are adjacent if they are joined by a single edge

dynamic unstructured method for flows past multiple objects in relative motion a new methodology is developed to simulate unsteady flows about objects in relative motion and compute the trajectory of their motion as determined by this flowfield the method couples the fluid dynamics and rigid body dynamics equations to capture the time dependent interference between stationary and moving boundaries the unsteady compressible inviscid euler equations are solved on dynamic unstructured grids by an explicit finite volume upwind method for efficiency the grid adaptation is perfomed within a window around the moving object the eulerian equations of the rigid body dynamics are solved by a runge kutta method in a noninertial frame of reference this dynamic unstructured flow solver is validated by computing the flow past a sinusoidally pitching airfoil and comparing these results with the experimental data the trajectory code is tested by computing the six degree of freedom trajectory of a store separating from a wing using the experimentally determined force and moment fields then comparing with the experimental trajectory finally the overall methodology is used for two two dimensional examples the flow past a pitching and plunging airfoil and the free call of a store after separation from a wing section

dual euclidean artin groups and the failure of the lattice property abstract the irreducible euclidean coxeter groups that naturally act geometrically on euclidean space are classified by the well known extended dynkin diagrams and these diagrams also encode the modified presentations that define the irreducible euclidean artin groups these artin groups have remained mysterious with some exceptions until very recently craig squier clarified the structure of the three examples with three generators more than twenty years ago and francois digne more recently proved that two of the infinite families can be understood by constructing a dual presentation for each of these groups and showing that it forms an infinite type garside structure in this article i establish that none of the remaining dual presentations for irreducible euclidean artin groups correspond to garside structures because their factorization posets fail to be lattices these are the first known examples of artin groups where all of their dual presentations fail to form garside structures nevertheless the results presented here about the cause of this failure form the foundation for a subsequent article in which the structure of euclidean artin groups is finally clarified

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

variational inference for latent variables and uncertain inputs in gaussian processes the gaussian process latent variable model gp lvm provides a flexible approach for non linear dimensionality reduction that has been widely applied however the current approach for training gp lvms is based on maximum likelihood where the latent projection variables are maximised over rather than integrated out in this paper we present a bayesian method for training gp lvms by introducing a non standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a gp lvm by maximising an analytic lower bound on the exact marginal likelihood we apply this method for learning a gp lvm from i i d observations and for learning non linear dynamical systems where the observations are temporally correlated we show that a benefit of the variational bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the non linear latent space the resulting framework is generic flexible and easy to extend for other purposes such as gaussian process regression with uncertain or partially missing inputs we demonstrate our method on synthetic data and standard machine learning benchmarks as well as challenging real world datasets including high resolution video data

metric systolicity and two dimensional artin groups we introduce the notion of metrically systolic simplicial complexes we study geometric and large scale properties of such complexes and of groups acting on them geometrically we show that all two dimensional artin groups act geometrically on metrically systolic complexes as direct corollaries we obtain new results on two dimensional artin groups and all their finitely presented subgroups we prove that the conjugacy problem is solvable and that the dehn function is quadratic we also show several large scale features of finitely presented subgroups of two dimensional artin groups lying background for further studies concerning their quasi isometric rigidity

an advancing front delaunay triangulation algorithm designed for robustness abstract a new algorithm is described for generating an unstructured mesh about an arbitrary two dimensional configuration mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements and the resulting triangulation constitutes the delaunay triangulation of these points the algorithm combines the mathematical elegance and efficiency of delaunay triangulation algorithms with the desirable point placement features boundary integrity and robustness that are traditionally associated with advancing front type mesh generation strategies the method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow field

gaussian process quadrature moment transform computation of moments of transformed random variables is a problem appearing in many engineering applications the current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors our aim is to design a method for moment transformation of gaussian random variables which accounts for the error in the numerically computed mean we employ an instance of bayesian quadrature called gaussian process quadrature gpq which allows us to treat the integral itself as a random variable where the integral variance informs us about the incurred integration error experiments on the coordinate transformation and nonlinear filtering examples show that the proposed gpq moment transform performs better than the classical transforms

gaussian groups and garside groups two generalisations of artin groups it is known that a number of algebraic properties of the braid groups extend to arbitrary finite coxeter type artin groups here we show how to extend the results to more general groups that we call garside groups define a gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths and where left and right lowest common multiples exist a garside monoid is a gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition a gaussian group is the group of fractions of a gaussian monoid and a garside group is the group of fractions of a garside monoid braid groups and more generally finite coxeter type artin groups are garside groups we determine algorithmic criteria in terms of presentations for recognizing gaussian and garside monoids and groups and exhibit infinite families of such groups we describe simple algorithms that solve the word problem in a gaussian group show that these algorithms have a quadratic complexity if the group is a garside group and prove that garside groups have quadratic isoperimetric inequalities we construct normal forms for gaussian groups and prove that in the case of a garside group the language of normal forms is regular symmetric and geodesic has the 5 fellow traveller property and has the uniqueness property this shows in particular that garside groups are geodesically fully biautomatic finally we consider an automorphism of a finite coxeter type artin group derived from an automorphism of its defining coxeter graph and prove that the subgroup of elements fixed by this automorphism is also a finite coxeter type artin group that can be explicitly determined 1991 mathematics subject classification primary 20f05 20f36 secondary 20b40 20m05