dehn surgery on arborescent links this paper studies dehn surgery on a large class of links called arborescent links it will be shown that if an arborescent link l is sufficiently complicated in the sense that it is composed of at least 4 rational tangles t pl qi with all qj 2 and none of its length 2 tangles are of the form t 1 2ql 1 2q2 then all complete surgeries on l produce haken manifolds the proof needs some result on surgery on knots in tangle spaces let t r 2s p 2q b ti u t2 li k be a tangle with k a closed circle and let m b int n ti u t2 we will show that if s 1 and p 1 mod 2q then om remains incompressible after all nontrivial surgeries oln k two bridge links are a subclass of arborescent links for such a link l p q most dehn surgeries on it are non haken however it will be shown that all complete surgeries yield manifolds containing essential laminations unless p q has a partial fraction decomposition of the form 1 r 1 s in which case it does admit non laminar surgeries

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

ortho diffusion decompositions of graph based representation of images this paper proposes a new feature representation methodology for graph based data initially random walks on matrices of pairwise data similarities are considered a diffusion process is embedded into orthonormal decompositions of such matrices at various scales while enabling a data reduction mechanism as well at each scale the qr orthonormal decomposition algorithm alternating with diffusions and data reduction stages is applied recursively on the given graph based data representations the proposed methodology is used in extracting complex feature representations from images which are then used for image matching and in face recognition in the face recognition application both global appearance models and semantic representations of biometric features are considered both the correlation and the covariance of images of human faces are considered for the training stage when using global appearance models the proposed data representation is shown to be robust in face recognition applications when face images are represented in low resolution and when they are corrupted by noise highlightsthe ortho diffusion decompositions on graph representations of images are introduced correlation in the ortho diffusion space is used for optical flow estimation correlations covariance of ortho diffusion vectors is used for face recognition

graph characterization via ihara coefficients the novel contributions of this paper are twofold first we demonstrate how to characterize unweighted graphs in a permutation invariant manner using the polynomial coefficients from the ihara zeta function i e the ihara coefficients second we generalize the definition of the ihara coefficients to edge weighted graphs for an unweighted graph the ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph since the ihara zeta function has poles that give rise to infinities the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial moreover the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph to generalize the representation to edge weighted graphs we make use of the reduced bartholdi zeta function we prove that the computation of the ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights we also present a spectral analysis of the ihara coefficients and indicate their advantages over other graph spectral methods we apply the proposed graph characterization method to capturing graph class structure and clustering graphs experimental results reveal that the ihara coefficients are more effective than methods based on laplacian spectra

the distance between two separating reducing slopes is at most 4 let m be a simple 3 manifold such that one component of m say f has genus at least two for a slope on f we denote by m the manifold obtained by attaching a 2 handle to m along a regular neighborhood of on f if m is reducible then is called a reducing slope in this paper we shall prove that the distance between two separating reducing slopes on f is at most 4

qr factorization based blind channel identification with second order statistics most eigenstructure based blind channel identification and equalization algorithms with second order statistics need svd or evd of the correlation matrix of the received signal in this paper we address new algorithms based on qr factorization of the received signal directly without calculating the correlation matrix this renders the qr factorization based algorithms more robust against ill conditioned channels i e those channels with almost common zeros among the subchannels first we present a block algorithm that performs the qr factorization of the received data matrix as a whole then a recursive algorithm is developed based on the qr factorization by updating a rank revealing ulv decomposition compared with existing algorithms in the same category our algorithms are computationally more efficient the computation in each recursion of the recursive algorithm is on the order of o m sup 2 if only equalization is required where m is the dimension of the received signal vector our recursive algorithm preserves the fast convergence property of the subspace algorithms thus converging faster than other adaptive algorithms such as the super exponential algorithm with comparable computational complexities moreover our proposed algorithms do not require noise variance estimation numerical simulations demonstrate the good performance of the proposed algorithms

unlinking via simultaneous crossing changes given two distinct crossings of a knot or link projection we consider the question under what conditions can we obtain the unlink by changing both crossings simultaneously more generally for which simultaneous twistings at the crossings is the genus reduced though several examples show that the answer must be complicated they also suggest the correct necessary conditions on the twisting numbers let l be an oriented link in s3with a generic projection onto the plane r let a be a short arc in r2 transverse to both strands of l at a crossing so that the strands pass through a in opposite directions then the inverse image of a contains a disk punctured twice with opposite orientation by l define a crossing disk d for a link l in s3 to be a disk which intersects l in precisely two points of opposite orientation it is easy to see that any crossing disk arises in the manner described twisting the link q times as it passes through d is equivalent to doing llq surgery on dd in s3 and adds 29 crossings to this projection of l we say that this new link l q is obtained by adding q twists at d call dd a crossing circle for l a crossing disk d and its boundary do are essential if dd bounds no disk disjoint from l this is equivalent to the requirement that l cannot be isotoped off d in s3 od here we examine how a link can be turned into the unlink via simultaneous twists on disjoint crossing disks in particular we prove an analogue for pairs of crossing disks of the following theorem a much more general version of which is proven in st 1 41 see also gal

regularization on graphs with function adapted diffusion processes harmonic analysis and diffusion on discrete data has been shown to lead to state of the art algorithms for machine learning tasks especially in the context of semi supervised and transductive learning the success of these algorithms rests on the assumption that the function s to be studied learned interpolated etc are smooth with respect to the geometry of the data in this paper we present a method for modifying the given geometry so the function s to be studied are smoother with respect to the modified geometry and thus more amenable to treatment using harmonic analysis methods among the many possible applications we consider the problems of image denoising and transductive classification in both settings our approach improves on standard diffusion based methods

extended jordanian twists for lie algebras jordanian quantizations of lie algebras are studied using the factorizable twists for a restricted borel subalgebra b of sl n the explicit expressions are obtained for the twist element f universal r matrix and the corresponding canonical element t it is shown that the twisted hopf algebra uf b is self dual the cohomological properties of the involved lie bialgebras are studied to justify the existence of a contraction from the dinfeld jimbo quantization to the jordanian one the construction of the twist is generalized to a certain type of inhomogenious lie algebras

modified braid equations for soq 3 and noncommutative spaces general solutions of the rtt equation with a maximal number of free parameters in the specrtal decomposition of vector soq 3 r matrices are implemented to construct modified braid equations mbe these matrices conserve the given standard group relations of the nine elements of t but are not constrained to satisfy the standard braid equation be apart from q and a normalization factor our r contains two free parameters instead of only one such parameter for deformed unitary algebras studied in a previous paper math qa 0009178 where the nonzero right hand side of the mbe had a linear term proportional to r 12 r 23 in the present case the rhs is in general nonlinear several particular solutions are given sec ii and the general structure is analyzed appendix a our formulation of the problem in terms of projectors yields also two new solutions of standard nonmodified braid equation sec ii which are further discussed appendix b the noncommutative three spaces obtained by i

modified braid equations baxterizations and noncommutative spaces for the quantum groups glq n soq n and spq n modified braid equations satisfied by generalized r matrices for a given set of group relations obeyed by the elements of t matrices are constructed for q deformed quantum groups glq n soq n and spq n with arbitrary values of n the baxterization of r matrices treated as an aspect complementary to the modification of the braid equation is obtained for all these cases in particularly elegant forms a new class of braid matrices is discovered for the quantum groups soq n and spq n the r matrices of this class while being distinct from the restrictions of the universal r matrix to the corresponding vector representations satisfy the standard braid equation the modified braid equation and the baxterization are obtained for this new class of r matrices diagonalization of the generalized r matrices is studied the diagonalizers are obtained explicitly for some lower dimensional cases in a convenient way giving directly the eigenvalues of the corresponding r matrices applications of such

rtt relations a modified braid equation and noncommutative planes with the known group relations for the elements a b c d of a quantum matrix t as input a general solution of the rtt relations is sought without imposing the yang baxter yb constraint for r or the braid equation for r pr for three biparametric deformatios gl p q 2 gl g h 2 and gl q h 1 1 the standard the nonstandard and the hybrid one respectively r or r is found to depend apart from the two parameters defining the deformation in question on an extra free parameter k such that r 12 r 23 r 12 r 23 r 12 r 23 k k1 1 k k2 1 r 23 r 12 with k1 k2 1 p q 1 1 and 1 1 q respectively only for k k1 or k k2 one has the braid equation arbitray k corresponds to a class conserving the group relations independent of k of the mqybe or modified quantum yb equations studied by gerstenhaber giaquinto and schack various properties of the triparametric r k p q r k g h and r k q h are studied in the larger space of the modified braid equation mbe even r k p

metrics on the real quantum plane using the frame formalism we determine some possible metrics and metric compatible connections on the noncommutative differential geometry of the real quantum plane by definition a metric maps the tensor product of two 1 forms into a function on the quantum plane it is symmetric in a modified sense namely in the definition of symmetry one has to replace the permutator map with a deformed map fulfilling some suitable conditions correspondingly also the definition of the hermitian conjugate of the tensor product of two 1 forms is modified but reduces to the standard one if coincides with the permutator the metric is real with respect to such modified structure

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

robust processing of optical flow of fluids this paper proposes a new approach coupling physical models and image estimation techniques for modelling the movement of fluids the fluid flow is characterized by turbulent movement and dynamically changing patterns which poses challenges to existing optical flow estimation methods the proposed methodology which relies on navier stokes equations is used for processing fluid optical flow by using a succession of stages such as advection diffusion and mass conservation a robust diffusion step jointly considering the local data geometry and its statistics is embedded in the proposed framework the diffusion kernel is gaussian with the covariance matrix defined by the local second derivatives such an anisotropic kernel is able to implicitly detect changes in the vector field orientation and to diffuse accordingly a new approach is developed for detecting fluid flow structures such as vortices the proposed methodology is applied on artificially generated vector fields as well as on various image sequences

an efficient multimodal 2d 3d hybrid approach to automatic face recognition we present a fully automatic face recognition algorithm and demonstrate its performance on the frgc v2 0 data our algorithm is multimodal 2d and 3d and performs hybrid feature based and holistic matching in order to achieve efficiency and robustness to facial expressions the pose of a 3d face along with its texture is automatically corrected using a novel approach based on a single automatically detected point and the hotelling transform a novel 3d spherical face representation sfr is used in conjunction with the scale invariant feature transform sift descriptor to form a rejection classifier which quickly eliminates a large number of candidate faces at an early stage for efficient recognition in case of large galleries the remaining faces are then verified using a novel region based matching approach which is robust to facial expressions this approach automatically segments the eyes forehead and the nose regions which are relatively less sensitive to expressions and matches them separately using a modified iterative closest point icp algorithm the results of all the matching engines are fused at the metric level to achieve higher accuracy we use the frgc benchmark to compare our results to other algorithms that used the same database our multimodal hybrid algorithm performed better than others by achieving 99 74 percent and 98 31 percent verification rates at a 0 001 false acceptance rate far and identification rates of 99 02 percent and 95 37 percent for probes with a neutral and a nonneutral expression respectively

graph characteristics from the heat kernel trace graph structures have been proved important in high level vision since they can be used to represent structural and relational arrangements of objects in a scene one of the problems that arises in the analysis of structural abstractions of objects is graph clustering in this paper we explore how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering the heat kernel is the solution of the heat equation and is a compact representation of the path length distribution on a graph the trace of the heat kernel is given by the sum of the laplacian eigenvalues exponentiated with time we explore three different approaches to characterizing the heat kernel trace as a function of time our first characterization is based on the zeta function which from the mellin transform is the moment generating function of the heat kernel trace our second characterization is unary and is found by computing the derivative of the zeta function at the origin the third characterization is derived from the heat content i e the sum of the elements of the heat kernel we show how the heat content can be expanded as a power series in time and the coefficients of the series can be computed using the laplacian spectrum we explore the use of these characterizations as a means of representing graph structure for the purposes of clustering and compare them with the use of the laplacian spectrum experiments with the synthetic and real world databases reveal that each of the three proposed invariants is effective and outperforms the traditional laplacian spectrum moreover the heat content invariants appear to consistently give the best results in both synthetic sensitivity studies and on real world object recognition problems

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

immersed surfaces and seifert fibered surgery on montesinos knots we will use immersed surfaces to study seifert fibered surgery on montesinos knots and show that if 1 q1 1 1 q2 1 1 q3 1 1 then a montesinos knot k p q1 p2 q2 p3 q3 admits no atoroidal seifert fibered surgery

orthogonal laplacianfaces for face recognition following the intuition that the naturally occurring face data may be generated by sampling a probability distribution that has support on or near a submanifold of ambient space we propose an appearance based face recognition method called orthogonal laplacianface our algorithm is based on the locality preserving projection lpp algorithm which aims at finding a linear approximation to the eigenfunctions of the laplace beltrami operator on the face manifold however lpp is nonorthogonal and this makes it difficult to reconstruct the data the orthogonal locality preserving projection olpp method produces orthogonal basis functions and can have more locality preserving power than lpp since the locality preserving power is potentially related to the discriminating power the olpp is expected to have more discriminating power than lpp experimental results on three face databases demonstrate the effectiveness of our proposed algorithm

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

efficient denoising algorithms for large experimental datasets and their applications in fourier transform ion cyclotron resonance mass spectrometry modern scientific research produces datasets of increasing size and complexity that require dedicated numerical methods to be processed in many cases the analysis of spectroscopic data involves the denoising of raw data before any further processing current efficient denoising algorithms require the singular value decomposition of a matrix with a size that scales up as the square of the data length preventing their use on very large datasets taking advantage of recent progress on random projection and probabilistic algorithms we developed a simple and efficient method for the denoising of very large datasets based on the qr decomposition of a matrix randomly sampled from the data this approach allows a gain of nearly three orders of magnitude in processing time compared with classical singular value decomposition denoising this procedure called urqrd uncoiled random qr denoising strongly reduces the computer memory footprint and allows the denoising algorithm to be applied to virtually unlimited data size the efficiency of these numerical tools is demonstrated on experimental data from high resolution broadband fourier transform ion cyclotron resonance mass spectrometry which has applications in proteomics and metabolomics we show that robust denoising is achieved in 2d spectra whose interpretation is severely impaired by scintillation noise these denoising procedures can be adapted to many other data analysis domains where the size and or the processing time are crucial

on combined standard nonstandard or hybrid q h deformations combined q h deformations proposed by kupershmidt and ballesteros herranz parashar are studied in each case a transformation is shown to lead to an equivalent standard q deformation we briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric p q deformations to nonhybrid but biparametric nonstandard g h ones finally a case of hybrid q h deformation is recalled related to the superalgebra gl 1 1

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

essential laminations in 3 manifolds it is a well established principle in manifold topology that by studying codimension 1 objects and their complementary pieces one obtains a great deal of topological and geometric information about the manifold itself this is particularly true for 3 dimensional manifolds using incompressible surfaces a great many advances have been made during the last 30 years the most spectacular results were obtained by haken ha waldhausen w and thurston t1 more recently work t2 g14 using taut foliations in 3 manifolds has proven fruitful unfortunately in some sense most closed 3 manifolds do not contain incompressible surfaces and it is currently not known exactly which 3 manifolds have taut foliations the purpose of this paper is to study another codimension 1 object the essential lamination which is a generalization of the incompressible surface as well as the taut foliation we will show that the existence of an essential lamination in a 3 manifold m implies that m has useful properties similar to those of manifolds having either an incompressible surface or a taut foliation we will also show that the universal cover of a manifold containing an essential lamination is r3 precise definitions of terms used in the following theorem will be given in section 1 here we give only a rough idea we begin with two alternative approximate definitions of essential lamination i an essential lamination in a 3 manifold m is a lamination satisfying four conditions the inclusion of leaves of the lamination into m should induce an injection on stj the complement of the lamination should be irreducible no leaf should be a sphere and the lamination should be end incompressible to say that a lamination is end incompressible means roughly that a folded leaf can be straightened using an isotopy there are no infinite folds ii alternatively

the gervais neveu felder equation for the jordanian quasi hopf uh y sl 2 algebra using a contraction procedure we construct a twist operator that satisfies a shifted cocycle condition and leads to the jordanian quasi hopf uh y sl 2 algebra the corresponding universal h y matrix obeys a gervais neveu felder equation associated with the uh y sl 2 algebra for a class of representations the dynamical yang baxter equation may be expressed as a compatibility condition for the algebra of the lax operators

the classification of punctured torus groups thurston s ending lamination conjecture proposes that a flnitely generated kleinian group is uniquely determined up to isometry by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends we present a proof of this conjecture for punctured torus groups these are free two generator kleinian groups with parabolic commutator which should be thought of as representations of the fundamental group of a punctured torus as a consequence we verify the conjectural topological description of the deformation space of punctured torus groups including bers conjecture that the quasi fuchsian groups are dense in this space and prove a rigidity theorem two punctured torus groups are quasi conformally conjugate if and only if they are topologically conjugate

spectrally similar incommensurable 3 manifolds reid has asked whether hyperbolic manifolds with the same geodesic length spectrum must be commensurable building toward a negative answer to this question we construct examples of hyperbolic 3 manifolds that share an arbitrarily large portion of the length spectrum but are not commensurable more precisely for every n 0 we construct a pair of incommensurable hyperbolic 3 manifolds nn and nn whose volume is approximately n and whose length spectra agree up to length n both nn and nn are built by gluing two standard submanifolds along a complicated pseudo anosov map ensuring that these manifolds have a very thick collar about an essential surface the two gluing maps differ by a hyper elliptic involution along this surface our proof also involves a new commensurability criterion based on pairs of pants

multilinear discriminant analysis for face recognition there is a growing interest in subspace learning techniques for face recognition however the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma in this paper we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order first we propose a discriminant tensor criterion whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction then a novel approach called k mode optimization is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions we call this algorithm multilinear discriminant analysis mda which has the following characteristics 1 multiple interrelated subspaces can collaborate to discriminate different classes 2 for classification problems involving higher order tensors the mda algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem and 3 the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k mode optimization we provide extensive experiments on orl cmu pie and feret databases by encoding face images as second or third order tensors to demonstrate that the proposed mda algorithm based on higher order tensors has the potential to outperform the traditional vector based subspace learning algorithms especially in the cases with small sample sizes

angled decompositions of arborescent link complements this paper describes a way to subdivide a 3 manifold into angled blocks namely polyhedral pieces that need not be simply connected when the individual blocks carry dihedral angles that fit together in a consistent fashion we prove that a manifold constructed from these blocks must be hyperbolic the main application is a new proof of a classical unpublished theorem of bonahon and siebenmann that all arborescent links except for three simple families of exceptions have hyperbolic complements in the 1990s andrew casson introduced a powerful technique for constructing and studying cusped hyperbolic 3 manifolds his idea was to subdivide a manifold m into angled ideal tetrahedra that is tetrahedra whose vertices are removed and whose edges carry prescribed dihedral angles when the dihedral angles of the tetrahedra add up to 2 around each edge of m the triangulation is called an angled triangulation casson proved that every orientable cusped 3 manifold that admits an angled triangulation must also admit a hyperbolic metric and outlined a possible way to find the hyperbolic metric by studying the volumes of angled tetrahedra an idea also developed by rivin 17 the power of casson s approach lies in the fact that the defining equations of an angled triangulation are both linear and local making angled triangulations relatively easy to find and deform much easier than to study an actual hyperbolic triangulation as in 14 20 or in some aspects of thurston s seminal approach 22 the aim of this paper is to extend this approach to larger and more complicated building blocks these blocks can be ideal polyhedra instead of tetrahedra but they may also have nontrivial topology in general an angled block will be a 3 manifold whose boundary is subdivided into faces looking locally like the faces of an ideal polyhedron in a sense to be defined the edges between adjacent faces carry prescribed dihedral angles in section 2 we will describe the precise combinatorial conditions that the dihedral angles must satisfy these conditions will imply the following generalization of a result by lackenby 11 corollary 4 6

histogram of gabor phase patterns hgpp a novel object representation approach for face recognition a novel object descriptor histogram of gabor phase pattern hgpp is proposed for robust face recognition in hgpp the quadrant bit codes are first extracted from faces based on the gabor transformation global gabor phase pattern ggpp and local gabor phase pattern lgpp are then proposed to encode the phase variations ggpp captures the variations derived from the orientation changing of gabor wavelet at a given scale frequency while lgpp encodes the local neighborhood variations by using a novel local xor pattern lxp operator they are both divided into the nonoverlapping rectangular regions from which spatial histograms are extracted and concatenated into an extended histogram feature to represent the original image finally the recognition is performed by using the nearest neighbor classifier with histogram intersection as the similarity measurement the features of hgpp lie in two aspects 1 hgpp can describe the general face images robustly without the training procedure 2 hgpp encodes the gabor phase information while most previous face recognition methods exploit the gabor magnitude information in addition fisher separation criterion is further used to improve the performance of hgpp by weighing the subregions of the image according to their discriminative powers the proposed methods are successfully applied to face recognition and the experiment results on the large scale feret and cas peal databases show that the proposed algorithms significantly outperform other well known systems in terms of recognition rate

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

reducing and annular dehn fillings if two dehn fillings on a simple manifold create a reducible manifold and an annular manifold respectively then the distance between those filling slopes is known to be at most two moreover eudave munoz and wu gave infinitely many examples of manifolds admitting reducing and annular dehn fillings at distance two in this paper we complement their examples to establish a complete list of simple manifolds admitting such a pair of dehn fillings