on a class of rearrangeable networks benes networks are nonblocking rearrangeable networks that can realize arbitrary permutations without conflict a class of 2 log sub b n stage networks which are equivalent to the benes networks is introduced networks in this class can be either symmetric or asymmetric in their structure regular or irregular in their interstage connections and even 2 log sub b n or 2 log sub b n 1 stages all networks in this class are nonblocking rearrangeable a switch labeling scheme is proposed to provide testing of the topological and functional equivalency for this class of networks this switch labeling scheme can also provide a novel matrix representation for network configuration this representation introduces a portability concept for the routing scheme on this class of networks with this representation a general routing scheme is also developed this routing scheme can realize arbitrary permutation for the whole class of 2 log sub b n stage networks

immersing almost geodesic surfaces in a closed hyperbolic three manifold let m 3 be a closed hyperbolic three manifold we construct closed surfaces that map by immersions into m 3 so that for each one the corresponding mapping on the universal covering spaces is an embedding or in other words the corresponding induced mapping on fundamental groups is an injection

a harmonic retrieval framework for discontinuous motion estimation motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities in this paper we show that discontinuous or multiple motion estimation can be viewed as a multicomponent harmonic retrieval problem from this viewpoint a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous or multiple motion compared with existing techniques the resulting algorithm is not iterative which not only implies computational efficiency but also obviates concerns regarding convergence or local minima it also adds flexibility to spatio temporal techniques which have suffered from lack of explicit modeling of discontinuous motion experimental verification of our framework on both synthetic data as well as real image data is provided

the kr benes network a control optimal rearrangeable permutation network the benes network has been used as a rearrangeable network for over 40 years yet the uniform n 2 log n 1 control complexity of the n spl times n benes is not optimal for many permutations in this paper we present a novel o log n depth rearrangeable network called kr benes that is permutation specific control optimal the kr benes routes every permutation with the minimal control complexity specific to that permutation and its worst case complexity for arbitrary permutations is bounded by the benes thus it replaces the benes when considering control complexity latency we design the kr benes by first constructing a restricted 2log k 2 depth rearrangeable network called k benes for routing k bounded permutations with control 2n log k 0 spl les k spl les n 4 we then show that the n spl times n benes network itself with one additional stage contains every kr benes network as a subgraph and use this property to construct the kr benes network with regard to the control optimality of the kr benes we show that any optimal network for rearrangeably routing k bounded permutations must have depth 2log k 2 and therefore the k benes and hence the kr benes is optimal

right angled coxeter polytopes hyperbolic six manifolds and a problem of siegel by gluing together the sides of eight copies of an all right angled hyperbolic six dimensional polytope two orientable hyperbolic six manifolds with euler characteristic 1 are constructed they are the first known examples of orientable hyperbolic six manifolds having the smallest possible volume

shrinkwrapping and the taming of hyperbolic 3 manifolds we introduce a new technique for finding cat 1 surfaces in hyperbolic 3 manifolds we use this to show that a complete hyperbolic 3 manifold with finitely generated fundamental group is geometrically and topologically tame

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

euclidean decompositions of noncompact hyperbolic manifolds on introduit une methode pour diviser une variete hyperbolique non compacte de volume fini en morceaux euclidiens canoniques

a new routing algorithm for a class of rearrangeable networks this paper presents a routing algorithm for a class of multistage interconnection networks specifically the concatenation of two omega networks which has 2 log sub 2 n stages is treated it is shown that this kind of asymmetric omega omega network can be converted into a symmetric omega sup 1spl times omega network or a symmetric omega spl times omega sup 1 network however they have butterfly connections between the two center stages a general algorithm is developed which routes a class of symmetric networks the algorithm routes the network from center stages to outer stages at both the input and the output sides simultaneously the algorithm presented is simpler and more flexible than the well known looping algorithm in that it can be applied adaptively according to the structure of the network it can be applied to routing the omega based networks regardless of the center stage connection patterns i e straight skewed straight simple butterfly or skewed butterfly as long as the networks are symmetric the sufficient conditions for proper routing are shown and proved in addition an example is shown to demonstrate the algorithm

a self routing benes network and parallel permutation algorithms a benes permutation network capable of setting its own switches dynamically is presented the total switch setting and delay time for the n input utput self routing network is o log n it is shown that the network is capable of performing a rich class of permutations the self routing scheme leads to efficient o log n parallel algorithms to perform the same class of permutations on cube connected and perfect shuffle computers

on the correctness of inside out routing algorithm recently a new routing algorithm called inside out routing algorithm was proposed for routing an arbitrary permutation in the omega based 2log sub 2 n stage networks this paper discusses the problems of the inside out routing algorithm and shows that the suggested condition for proper routing in the omega omega network is insufficient an extended necessary and sufficient condition for proper routing in the omega omega network is also suggested however it is unknown if any permutation can be successfully routed by a heuristic algorithm which follows the condition thus the rearrangeability of the omega omega network still remains an open problem

residual finiteness growths of virtually special groups let g be a virtually special group then the residual finiteness growth of g is at most linear this result cannot be found by embedding g into a special linear group indeed the special linear group mathrm sl k mathbb z for k 2 has residual finiteness growth n k 1

estimation of multiple accelerated motions using chirp fourier transform and clustering motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed which however cannot handle both time varying and multiple motions extending previously published ideas we present an efficient method for estimating multiple linearly time varying motions it is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals from this viewpoint one can exploit established signal processing tools such as the chirp fourier transform it is shown that accelerated motion results in energy concentration along planes in the 4 d space spatial frequencies temporal frequency chirp rate using fuzzy c planes clustering we estimate the plane motion parameters the effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

the bianchi groups are separable on geometrically finite subgroups let d be a square free positive integer and od the ring of integers in q p id the main result of this paper is that the groups psl 2 od are

recognition and velocity computation of large moving objects in images two one dimensional time sequences are generated from the projections of the two dimensional sequence on the x and y axes then the two dimensional fast fourier transform for the generated time sequences is computed a peak in the spectrum for the selected spatial frequency is detected the temporal frequency at which the peak is detected gives an estimate of the velocity of the moving object analytical formulations for large moving objects in a time sequence with zero background are presented an algorithm is given for velocity formulation

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

quantifying residual finiteness abstract we introduce the notion of quantifying the extent to which a finitely generated group is residually finite we investigate this behavior for examples that include free groups the first grigorchuk group finitely generated nilpotent groups and certain arithmetic groups such as sl n z in the context of finite nilpotent quotients we find a new characterization of finitely generated nilpotent groups

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