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Vector Space (vector + space)
Selected AbstractsReanimating Faces in Images and VideoCOMPUTER GRAPHICS FORUM, Issue 3 2003V. Blanz This paper presents a method for photo-realistic animation that can be applied to any face shown in a single imageor a video. The technique does not require example data of the person's mouth movements, and the image to beanimated is not restricted in pose or illumination. Video reanimation allows for head rotations and speech in theoriginal sequence, but neither of these motions is required. In order to animate novel faces, the system transfers mouth movements and expressions across individuals, basedon a common representation of different faces and facial expressions in a vector space of 3D shapes and textures. This space is computed from 3D scans of neutral faces, and scans of facial expressions. The 3D model's versatility with respect to pose and illumination is conveyed to photo-realistic image and videoprocessing by a framework of analysis and synthesis algorithms: The system automatically estimates 3D shape andall relevant rendering parameters, such as pose, from single images. In video, head pose and mouth movements aretracked automatically. Reanimated with new mouth movements, the 3D face is rendered into the original images. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation [source] Discrete modeling of the air-gap field of synchronous machines for computation of torque and radial forcesEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 2 2008Marc Bekemans Abstract In this paper, we exploit the multiple symmetries and the discrete character of the current distribution to express the torque and the radial forces in a PM synchronous machine. Under some assumptions, the magnetic field can be built with a limited number of discrete functions. These functions can constitute an orthogonal base of a vector space for the representation of the machine magnetic state. The representation of the stator and rotor fields as vectors of this space makes it possible to interpret the torque and the radial forces from the concept of distance between these vectors. The proposed method for torque and radial forces computation is well suited for a real-time evaluation and can be used for a generalization of the Field-Oriented Control to machines with non-sinusoidal flux distribution. Copyright © 2007 John Wiley & Sons, Ltd. [source] On the complexity of Rocchio's similarity-based relevance feedback algorithmJOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 10 2007Zhixiang Chen Rocchio's similarity-based relevance feedback algorithm, one of the most important query reformation methods in information retrieval, is essentially an adaptive learning algorithm from examples in searching for documents represented by a linear classifier. Despite its popularity in various applications, there is little rigorous analysis of its learning complexity in literature. In this article, the authors prove for the first time that the learning complexity of Rocchio's algorithm is O(d + d2(log d + log n)) over the discretized vector space {0,,, n , 1}d, when the inner product similarity measure is used. The upper bound on the learning complexity for searching for documents represented by a monotone linear classifier over {0,,, n , 1}d can be improved to, at most, 1 + 2k (n , 1) (log d , log(n , 1)), where k is the number of nonzero components in q. Several lower bounds on the learning complexity are also obtained for Rocchio's algorithm. For example, the authors prove that Rocchio's algorithm has a lower bound on its learning complexity over the Boolean vector space {0, 1}d. [source] Invariance and factorial modelsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2000P. McCullagh Two factors having the same set of levels are said to be homologous. This paper aims to extend the domain of factorial models to designs that include homologous factors. In doing so, it is necessary first to identify the characteristic property of those vector spaces that constitute the standard factorial models. We argue here that essentially every interesting statistical model specified by a vector space is necessarily a representation of some algebraic category. Logical consistency of the sort associated with the standard marginality conditions is guaranteed by category representations, but not by group representations. Marginality is thus interpreted as invariance under selection of factor levels (I -representations), and invariance under replication of levels (S -representations). For designs in which each factor occurs once, the representations of the product category coincide with the standard factorial models. For designs that include homologous factors, the set of S -representations is a subset of the I -representations. It is shown that symmetry and quasi-symmetry are representations in both senses, but that not all representations include the constant functions (intercept). The beginnings of an extended algebra for constructing general I -representations is described and illustrated by a diallel cross design. [source] Bases, spanning sets, and the axiom of choiceMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 3 2007Paul Howard Abstract Two theorems are proved: First that the statement "there exists a field F such that for every vector space over F, every generating set contains a basis" implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ,2 has a basis implies that every well-ordered collection of two-element sets has a choice function. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Spin dependent distribution and Fermi surface of the perovskite manganite compound La0.7Sr0.3MnO3 via 2D-ACAR measurements,PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2004A. S. Hamid Abstract Using 2D angular correlation of positron annihilation radiation (ACAR) experiment, we have performed a systematic study of the spin dependent and Fermi surface of the colossal magneto-resistance CMR La0.7Sr0.3MnO3. The measurements have been carried out using a re-versal magnetic field direction (parallel and anti-parallel to the direction of motion of the polarized posi-trons). The measured spectra have been investigated in the momentum space as well as in the wave vector space. They revealed information about the hybridization effect of Mn(3d eg1) and O(2p) like states. Further, the results showed that the majority spin electrons predominated at the Fermi level. From another perspective, the Fermi surface of La0.7Sr0.3MnO3 revealed a cuboids hole surface centered on R point and a spheroid electron surface centered on , point. A comparison with the earlier results showed qualitative agreement. However, the current results could reveal the dimension of the electron surface centered on , point that was predicted in the earlier 2D-ACAR measurements. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Energy consistent time integration of planar multibody systemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Stefan Uhlar The planar motion of rigid bodies and multibody systems can be easily described by coordinates belonging to a linear vector space. This is due to the fact that in the planar case finite rotations commute. Accordingly, using this type of generalized coordinates can be considered as canonical description of planar multibody systems. However, the extension to the three-dimensional case is not straightforward. In contrast to that, employing the elements of the direction cosine matrix as redundant coordinates makes possible a straightforward treatment of both planar and three-dimensional multibody systems. This alternative approach leads in general to differential-algebraic equations (DAEs) governing the dynamics of rigid body systems. The main purpose of the present paper is to present a comparison of the two alternative descriptions. In both cases energy-consistent time integration schemes are applied. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Central moments in quantum chemistryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2008David W. Small Abstract We define central moments of operators on finite-dimensional vector spaces and study some of their basic aspects. Central moments may be viewed as generalizations of the dispersion of a Hermitian operator. We show how eigenvalues may be represented by central moments, and how central moments may be used to obtain Krylov subspace approximations for operators on inner product spaces. We show that central-moments approximations are compatible with the concepts of size-consistency in quantum chemistry, and we use this to suggest a foundation for central-moments approximations in Coupled Cluster theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Isomorphism criterion for monomial graphsJOURNAL OF GRAPH THEORY, Issue 4 2005Vasyl Dmytrenko Abstract Let q be a prime power, ,,q be the field of q elements, and k,,m be positive integers. A bipartite graph G,=,Gq(k,,m) is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over ,,q, with two vertices (p1,,p2) , P and [ l1,,l2] , L being adjacent if and only if p2,+,l2,=,pl. We prove that graphs Gq(k,,m) and Gq,(k,,,m,) are isomorphic if and only if q,=,q, and {gcd,(k,,q,,,1), gcd,(m,,q,,,1)},=,{gcd,(k,,,q,,,1),gcd,(m,,,q,,,1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322,328, 2005 [source] Invariance and factorial modelsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2000P. McCullagh Two factors having the same set of levels are said to be homologous. This paper aims to extend the domain of factorial models to designs that include homologous factors. In doing so, it is necessary first to identify the characteristic property of those vector spaces that constitute the standard factorial models. We argue here that essentially every interesting statistical model specified by a vector space is necessarily a representation of some algebraic category. Logical consistency of the sort associated with the standard marginality conditions is guaranteed by category representations, but not by group representations. Marginality is thus interpreted as invariance under selection of factor levels (I -representations), and invariance under replication of levels (S -representations). For designs in which each factor occurs once, the representations of the product category coincide with the standard factorial models. For designs that include homologous factors, the set of S -representations is a subset of the I -representations. It is shown that symmetry and quasi-symmetry are representations in both senses, but that not all representations include the constant functions (intercept). The beginnings of an extended algebra for constructing general I -representations is described and illustrated by a diallel cross design. [source] Approximation of vector valued smooth functionsMATHEMATISCHE NACHRICHTEN, Issue 1 2004Eva C. Farkas Abstract A real locally convex space is said to be convenient if it is separated, bornological and Mackey-complete. These spaces serve as underlying objects for a whole theory of differentiation and integration (see [4]) upon which infinite dimensional differential geometry is based (cf. [8]). We investigate the question of density of the subspaces C,(E) , F and ,,f (E) , F of smooth (polynomial) decomposable functions in the space C,(E, F) of smooth functions between convenient vector spaces E, F with respect to various natural structures. A characterization is given for density with respect to the c, -topology and also some classical locally convex topologies on C,(E, F). It is shown furthermore, that for the space ,(,) the convenient analogon of the Schwartz kernel theorem for C, -functions holds. Spaces of C, -functions on both separable and non-separable manifolds are considered and an example of a non-separable manifold is given failing the above property of approximability by decomposable functions. Those notions and features of the theory of convenient vector spaces which are essential for the results of this paper are explained in the introductory section below and where needed. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Differential geometry: a natural tool for describing symmetry operationsACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2009Philippe Kocian Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group operation is a one-to-one map acting on the manifold, whereas a point-group operation is a linear map acting between two tangent spaces of the manifold. Manifold theory proves particularly powerful as a unified formalism describing symmetry operations of conventional as well as modulated crystals without requiring a higher-dimensional space. We show, in particular, that a modulated structure recovers a three-dimensional periodicity in any tangent space and that its point group consists of linear applications. [source] The Large-Scale Structure of Semantic Networks: Statistical Analyses and a Model of Semantic GrowthCOGNITIVE SCIENCE - A MULTIDISCIPLINARY JOURNAL, Issue 1 2005Mark Steyvers Abstract We present statistical analyses of the large-scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small-world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale-free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These regularities have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high-dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small-world statistics and power-law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. [source] Linear system solution by null-space approximation and projection (SNAP)NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2007M. Ili Abstract Solutions of large sparse linear systems of equations are usually obtained iteratively by constructing a smaller dimensional subspace such as a Krylov subspace. The convergence of these methods is sometimes hampered by the presence of small eigenvalues, in which case, some form of deflation can help improve convergence. The method presented in this paper enables the solution to be approximated by focusing the attention directly on the ,small' eigenspace (,singular vector' space). It is based on embedding the solution of the linear system within the eigenvalue problem (singular value problem) in order to facilitate the direct use of methods such as implicitly restarted Arnoldi or Jacobi,Davidson for the linear system solution. The proposed method, called ,solution by null-space approximation and projection' (SNAP), differs from other similar approaches in that it converts the non-homogeneous system into a homogeneous one by constructing an annihilator of the right-hand side. The solution then lies in the null space of the resulting matrix. We examine the construction of a sequence of approximate null spaces using a Jacobi,Davidson style singular value decomposition method, called restarted SNAP-JD, from which an approximate solution can be obtained. Relevant theory is discussed and the method is illustrated by numerical examples where SNAP is compared with both GMRES and GMRES-IR. Copyright © 2006 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||