Information Geometry and Chaos on Negatively Curved Statistical Manifolds
Cafaro, Carlo
2007-01-01
A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying an ED Gaussian model describing an arbitrary system of 3N non-interacting degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.
Non-negatively curved 5-manifolds with almost maximal symmetry rank
Galaz-Garcia, Fernando
2011-01-01
We show that a closed, simply-connected, non-negatively curved 5-manifold admitting an effective, isometric $T^2$ action is diffeomorphic to one of $S^5$, $S^3\\times S^2$, $S^3\\tilde{\\times} S^2$ (the non-trivial $S^3$-bundle over $S^2$) or the Wu manifold $SU(3)/SO(3)$.
Principal Curves on Riemannian Manifolds.
Hauberg, Soren
2016-09-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only...... in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimize a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend...... from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls...
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Some connectedness problems in positively curved Finsler manifolds
Peter, Ioan Radu
2009-01-01
This paper studies some connectedness problems under the positivity hypothesis of various curvatures ( k-Ricci and flag curvature). Our approach uses Morse Theory for general end conditions (see [Ioan Radu Peter, The Morse index theorem where the ends are submanifolds in Finsler geometry, Houston J. Math. 32 (4) (2006) 995-1009]). Some previous results related to the flag curvature were obtained in [Ioan Radu Peter, A connectedness principle in positively curved Finsler manifolds, in: H. Shimada, S. Sabau (Eds.), Advanced Studies in Pure Mathematics, Finsler Geometry, Sapporo 2005-In Memory of Makoto Matsumoto, Mathematical Society of Japan, 2007]. Some results from Riemannian geometry are extended to the Finsler category also. The Finsler setting is much more complicated and the difference between Finsler and Riemann settings will be emphasized during the paper.
Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
Biswas, Indranil; 10.1016/j.difgeo.2009.09.003
2010-01-01
We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact K\\"ahler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.
Complete Formulas for the Volumes of Tubes about Curves in a Riemannian Manifold
Institute of Scientific and Technical Information of China (English)
Fa En WU
2001-01-01
By using the Taylor expansions of the solutions of Jacobi equations, we obtain the completeformulas for the volumes of tubes about curves in a Riemannian manifold. This unifies the known resultsand simplifies the computations involved in this direction. In the special case of surfaces, we also obtainthe corresponding complete formulas which generalize the known results.
Non-negative Ricci curvature on closed manifolds under Ricci flow
Maximo, Davi
2009-01-01
In this short note we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf in \\cite{K} for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result B\\"ohm and Wilking have for dimensions twelve and above, \\cite{BW}. Moreover, the manifolds constructed here are \\Kahler manifolds and relate to a question raised by Xiuxiong Chen in \\cite{XC}, \\cite{XCL}.
Geometrodynamics of Information on Curved Statistical Manifolds and its Applications to Chaos
Cafaro, C
2008-01-01
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of chaoticity is proposed. The general classical formalism is illustrated in a relatively simple example. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying an ED Gaussian model describing an arbitrary system of 3N degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively. An information-geometric analogue of the Zurek-Paz quantum chaos criterion in the classical reversible limit is proposed. This analogy is illustrated applying the IGAC to a set of n-uncoupled three-dimensional anisotropic inverted harmonic oscillators characterized by a Ohmic distributed frequency spectrum.
Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature
Directory of Open Access Journals (Sweden)
Arnaldo S. Nascimento
2010-05-01
Full Text Available We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N-dimensional Riemannian manifolds without boundary and non-negative Ricci curvature. Conversely, for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative, we prove the existence of nonconstant local minimizers for the same class of functionals.
Directory of Open Access Journals (Sweden)
Roman Urban
2004-12-01
Full Text Available We consider the Green functions for second-order left-invariant differential operators on homogeneous manifolds of negative curvature, being a semi-direct product of a nilpotent Lie group $N$ and $A=mathbb{R}^+$. We obtain estimates for mixed derivatives of the Green functions both in the coercive and non-coercive case. The current paper completes the previous results obtained by the author in a series of papers [14,15,16,19].
Non-positively curved graph manifolds are virtually fibered over the circle
2001-01-01
In this note we prove that any closed graph manifold admitting a metric of non-positive sectional curvature (NPC-metric) has a finite cover, which is fibered over the circle. An explicit criterion to have a finite cover, which is fibered over the circle, is presented for the graph manifolds of certain class.
Infinity Behavior of Bounded Subharmonic Functions on Ricci Non-negative Manifolds
Institute of Scientific and Technical Information of China (English)
Bao Qiang WU
2004-01-01
In this paper, we study the infinity behavior of the bounded subharmonic functions on a Ricci non-negative Riemannian manifold M. We first show that limr→∞r2/V(r) ∫B(r)△hdv = 0 if h is a bounded subharmonic function. If we further assume that the Laplacian decays pointwisely faster than quadratically we show that h approaches its supremun pointwisely at infinity, under certain auxiliary conditions on the volume growth of M. In particular, our result applies to the case when the Riemannian manifold has maximum volume growth. We also derive a representation formula in our paper, from which one can easily derive Yau's Liouville theorem on bounded harmonic functions.
ON COMPLETE SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE IN NEGATIVE PINCHED MANIFOLDS
Institute of Scientific and Technical Information of China (English)
Leng Yan; Xu Hongwei
2007-01-01
A rigidity theorem for oriented complete submanifolds with parallel mean curvature in a complete and simply connected Riemannian (n + p)-dimensional manifold Nn+p with negative sectional curvature is proved. For given positive integers n(≥ 2), p and for a constant H satisfying H ＞ 1 there exists a negative number τ(n,p, H) ∈ (-1, 0) with the property that if the sectional curvature of N is pinched in [-1, τ(n,p, H)], and if the squared length of the second fundamental form is in a certain interval, then Nn+p is isometric to the hyperbolic space Hn+p(-1). As a consequence, this submanifold M is congruent to Sn(1/ H2-1) or theVeronese surface in S4(1/√H2-1).
Directory of Open Access Journals (Sweden)
Roman Urban
2003-08-01
Full Text Available We consider the Green functions for second order non-coercive differential operators on homogeneous manifolds of negative curvature, being a semi-direct product of a nilpotent Lie group $N$ and $A=mathbb{R}^+$. We obtain estimates for the mixed derivatives of the Green functions that complements a previous work by the same author [17].
Barth, TIm
2002-01-01
This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.
Shiota, Masahiro
1987-01-01
A Nash manifold denotes a real manifold furnished with algebraic structure, following a theorem of Nash that a compact differentiable manifold can be imbedded in a Euclidean space so that the image is precisely such a manifold. This book, in which almost all results are very recent or unpublished, is an account of the theory of Nash manifolds, whose properties are clearer and more regular than those of differentiable or PL manifolds. Basic to the theory is an algebraic analogue of Whitney's Approximation Theorem. This theorem induces a "finiteness" of Nash manifold structures and differences between Nash and differentiable manifolds. The point of view of the author is topological. However the proofs also require results and techniques from other domains so elementary knowledge of commutative algebra, several complex variables, differential topology, PL topology and real singularities is required of the reader. The book is addressed to graduate students and researchers in differential topology and real algebra...
Ciliberto, Ciro
2012-01-01
In this paper we study the gonality of the normalizations of curves in the linear system $|H|$ of a general primitively polarized complex $K3$ surface $(S,H)$ of genus $p$. We prove two main results. First we give a necessary condition on $p, g, r, d$ for the existence of a curve in $|H|$ with geometric genus $g$ whose normalization has a $g^ r_d$. Secondly we prove that for all numerical cases compatible with the above necessary condition, there is a family of \\emph{nodal} curves in $|H|$ of genus $g$ carrying a $g^1_k$ and of dimension equal to the \\emph{expected dimension} $\\min\\{2(k-1),g\\}$. Relations with the Mori cone of the hyperk\\"ahler manifold $\\Hilb^ k(S)$ and with conjectures by Hassett-Tschinkel and by Huybrechts-Sawon are discussed. This is an improved version of the preprint arXiv:1202.2701 with stronger main result and simplified degeneration argument.
Joyce, Dominic
2009-01-01
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind. We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y. Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c. Our theory is tailored to future applications in Symplectic Geometry, and is part of a project to describe the geometric structure on moduli spaces of J-holomorphic curv...
Directory of Open Access Journals (Sweden)
Pąk Karol
2015-02-01
Full Text Available Let us recall that a topological space M is a topological manifold if M is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood that is homeomorphic to an open ball of E n for some n. However, if we would like to consider a topological manifold with a boundary, we have to extend this definition. Therefore, we introduce here the concept of a locally Euclidean space that covers both cases (with and without a boundary, i.e. where each point has a neighborhood that is homeomorphic to a closed ball of En for some n.
Kosinski, Antoni A
2007-01-01
The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho
Caloric curve of 8 GeV/c negative pion and antiproton + Au reactions
Ruangma, A; Martin, E; Ramakrishnan, E; Rowland, D J; Veselsky, M; Winchester, E M; Yennello, S J; Beaulieu, L; Hsi, W C; Kwiatkowski, K K; Lefort, T; Viola, V E; Botvina, A; Korteling, R G; Pienkowski, L; Breuer, H; Gushue, S; Remsberg, L P
2002-01-01
The relationship between nuclear temperature and excitation energy of hot nuclei formed by 8 GeV/c negative pion and antiproton beams incident on 197Au has been investigated with the ISiS 4-pidetector array at the BNL AGS accelerator. The double-isotope-ratio technique was used to calculate the temperature of the hot system. The two thermometers used (p/d-3He/4He) and (d/t-3He/4He) are in agreement below E*/A ~ 7 MeV when corrected for secondary decay. Comparison of these caloric curves to those from other experiments shows some differences that may be attributable to instrumentation and analysis procedures. The caloric curves from this experiment are also compared with the predictions from the SMM multifragmentation model.
Estimates for J-curves as submanifolds
Fish, Joel W
2009-01-01
Here we develop some basic analytic tools to study compactness properties of $J$-curves (i.e. pseudo-holomorphic curves) when regarded as submanifolds. Incorporating techniques from the theory of minimal surfaces, we derive an inhomogeneous mean curvature equation for such curves, we establish an extrinsic monotonicity principle for non-negative functions $f$ satisfying $\\Delta f\\geq -c^2 f$, we show that curves locally parameterized as a graph over a coordinate tangent plane have all derivatives a priori bounded in terms of curvature and ambient geometry, and we establish $\\epsilon$-regularity for the square length of their second fundamental forms. These results are all provided for $J$-curves either with or without Lagrangian boundary and hold in almost Hermitian manifolds of arbitrary even dimension (i.e. Riemannian manifolds for which the almost complex structure is an isometry).
Motion Planning via Manifold Samples
Salzman, Oren; Raveh, Barak; Halperin, Dan
2011-01-01
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generi...
Pro jective vector fields on Finsler manifolds
Institute of Scientific and Technical Information of China (English)
TIAN Huang-jia
2014-01-01
In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.
The Fibered Isomorphism Conjecture for Complex Manifolds
Institute of Scientific and Technical Information of China (English)
S. K. ROUSHON
2007-01-01
In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones,corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.
Spectral invariants of operators of Dirac type on partitioned manifolds
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Bleecker, D.
2004-01-01
We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators of Dirac type on closed manifolds and manifolds with bou...
Renteln, Paul
2013-11-01
Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.
Funar, L
1995-01-01
The aim of this note is to derive some invariants at infinity for open 3-manifolds in the framework of Topological Quantum Field Theories. These invariants may be used to test if an open manifold is simply connected at infinity as we done for Whitehead's manifold in case of the sl_{2}({\\bf C})-TQFT in level 4.
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories
Bonora, Loriano; Goncalves, Antonio E
2016-01-01
We derive formulas for the classical Chern-Simons invariant of irreducible $SU(n)$-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.
Calabi-Yau Manifolds Over Finite Fields, 1
Candelas, Philip; Rodríguez-Villegas, F; Candelas, Philip; Ossa, Xenia de la; Rodriguez-Villegas, Fernando
2000-01-01
We study Calabi-Yau manifolds defined over finite fields. These manifolds have parameters, which now also take values in the field and we compute the number of rational points of the manifold as a function of the parameters. The intriguing result is that it is possible to give explicit expressions for the number of rational points in terms of the periods of the holomorphic three-form. We show also, for a one parameter family of quintic threefolds, that the number of rational points of the manifold is closely related to as the number of rational points of the mirror manifold. Our interest is primarily with Calabi-Yau threefolds however we consider also the interesting case of elliptic curves and even the case of a quadric in CP_1 which is a zero dimensional Calabi-Yau manifold. This zero dimensional manifold has trivial dependence on the parameter over C but a not trivial arithmetic structure.
Quaternionic Kahler Manifolds, Constrained Instantons and the Magic Square: I
Dasgupta, Keshav; Wissanji, Alisha
2007-01-01
The classification of homogeneous quaternionic manifolds has been done by Alekseevskii, Wolf et al using transitive solvable group of isometries. These manifolds are not generically symmetric, but there is a subset of quaternionic manifolds that are symmetric and Einstein. A further subset of these manifolds are the magic square manifolds. We show that all the symmetric quaternionic manifolds including the magic square can be succinctly classified by constrained instantons. These instantons are mostly semilocal, and their constructions for the magic square can be done from the corresponding Seiberg-Witten curves for certain N = 2 gauge theories that are in general not asymptotically free. Using these, we give possible constructions, such as the classical moduli space metrics, of constrained instantons with exceptional global symmetries. We also discuss the possibility of realising the Kahler manifolds in the magic square using other solitonic configurations in the theory, and point out an interesting new sequ...
Holomorphic Cartan geometries and rational curves
Biswas, Indranil
2010-01-01
We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds
Liu, Chiu-Chu Melissa; Sheshmani, Artan
2017-07-01
An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.
Boots, Byron
2011-01-01
Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that sol...
Hadjoub, Zahia; Touati, Ibtissem; Doghmane, Malika; Doghmane, Abdellaziz
2008-10-01
This work concerns the investigation of loading layers/substrate structures in order to determine the critical thickness at which Rayleigh wave characteristics of layers can be completely distinguished from those of the substrates. To do so, we first calculate Rayleigh velocity dispersion curves of several thin film materials (about thirty) deposited on different slow and fast substrates (Be, Al 2O 3, AlN, Si, SiO 2, Mg, SiC, TiN, WC and Pyrex). Then, from the beginning of curve saturation (corresponding to the onset of intrinsic layer characteristics) we deduced normalized thickness transition for all layers/substrates combinations. Thus, we were able to deduce an analytical linear expression relating the critical thickness to combined effects of densities and velocities of both layers and substrates. Such a simple relation can be used, as an alternative method, to predict the transition critical thickness for any layer/substrate combination without the usual lengthy calculation of dispersion curves. To cite this article: Z. Hadjoub et al., C. R. Physique 9 (2008).
Borok, S.; Goldfarb, I.; Gol'dshtein, V.
2009-05-01
The paper concerns intrinsic low-dimensional manifold (ILDM) method suggested in [Maas U, Pope SB. Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space, combustion and flame 1992;88:239-64] for dimension reduction of models describing kinetic processes. It has been shown in a number of publications [Goldfarb I, Gol'dshtein V, Maas U. Comparative analysis of two asymptotic approaches based on integral manifolds. IMA J Appl Math 2004;69:353-74; Kaper HG, Kaper TJ, Asymptotic analysis of two reduction methods for systems of chemical reactions. Phys D 2002;165(1-2):66-93; Rhodes C, Morari M, Wiggins S. Identification of the low order manifolds: validating the algorithm of Maas and Pope. Chaos 1999;9(1):108-23] that the ILDM-method works successfully and the intrinsic low-dimensional manifolds belong to a small vicinity of invariant slow manifolds. The ILDM-method has a number of disadvantages. One of them is appearance of so-called "ghost"-manifolds, which do not have connection to the system dynamics [Borok S, Goldfarb I, Gol'dshtein V. "Ghost" ILDM - manifolds and their discrimination. In: Twentieth Annual Symposium of the Israel Section of the Combustion Institute, Beer-Sheva, Israel; 2004. p. 55-7; Borok S, Goldfarb I, Gol'dshtein V. About non-coincidence of invariant manifolds and intrinsic low-dimensional manifolds (ILDM). CNSNS 2008;71:1029-38; Borok S, Goldfarb I, Gol'dshtein V, Maas U. In: Gorban AN, Kazantzis N, Kevrekidis YG, Ottinger HC, Theodoropoulos C, editors. "Ghost" ILDM-manifolds and their identification: model reduction and coarse-graining approaches for multiscale phenomena. Berlin-Heidelberg-New York: Springer; 2006. p. 55-80; Borok S, Goldfarb I, Gol'dshtein V. On a modified version of ILDM method and its asymptotic analysis. IJPAM 2008; 44(1): 125-50; Bykov V, Goldfarb I, Gol'dshtein V, Maas U. On a modified version of ILDM approach: asymptotic analysis based on integral manifolds. IMA J Appl Math 2006
Energy Technology Data Exchange (ETDEWEB)
Spinler, E.A.; Baldwin, B.A. [Phillips Petroleum Co., Bartlesville, OK (United States)
1997-08-01
A method is being developed for direct experimental determination of capillary pressure curves from saturation distributions produced during centrifuging fluids in a rock plug. A free water level is positioned along the length of the plugs to enable simultaneous determination of both positive and negative capillary pressures. Octadecane as the oil phase is solidified by temperature reduction while centrifuging to prevent fluid redistribution upon removal from the centrifuge. The water saturation is then measured via magnetic resonance imaging. The saturation profile within the plug and the calculation of pressures for each point of the saturation profile allows for a complete capillary pressure curve to be determined from one experiment. Centrifuging under oil with a free water level into a 100 percent water saturated plug results in the development of a primary drainage capillary pressure curve. Centrifuging similarly at an initial water saturation in the plug results in the development of an imbibition capillary pressure curve. Examples of these measurements are presented for Berea sandstone and chalk rocks.
Hildebrand, Richard J.; Wozniak, John J.
2001-01-01
A compressed gas storage cell interconnecting manifold including a thermally activated pressure relief device, a manual safety shut-off valve, and a port for connecting the compressed gas storage cells to a motor vehicle power source and to a refueling adapter. The manifold is mechanically and pneumatically connected to a compressed gas storage cell by a bolt including a gas passage therein.
Low-loss single-mode negatively curved square-core hollow fibers.
Chen, Yang; Saleh, Mohammed F; Joly, Nicolas Y; Biancalana, Fabio
2017-04-01
We introduce a novel design of anti-resonant fibers with negative-curvature square cores to be employed in 1.55 and 2.94 μm transmission bands. The fibers have low losses and single-mode operation via optimizing the negative curvature of the guiding walls. The first proposed fiber shows a broadband transmission window spanning 0.9-1.7 μm, with losses of 0.025 and 0.056 dB/m at 1.064 and 1.55 μm, respectively. The second proposed fiber has approximately a 0.023 dB/m guiding loss at 2.94 μm with a small cross-sectional area, useful for laser micromachining applications.
Zhang, Zhenyue; Wang, Jing; Zha, Hongyuan
2012-02-01
Manifold learning algorithms seek to find a low-dimensional parameterization of high-dimensional data. They heavily rely on the notion of what can be considered as local, how accurately the manifold can be approximated locally, and, last but not least, how the local structures can be patched together to produce the global parameterization. In this paper, we develop algorithms that address two key issues in manifold learning: 1) the adaptive selection of the local neighborhood sizes when imposing a connectivity structure on the given set of high-dimensional data points and 2) the adaptive bias reduction in the local low-dimensional embedding by accounting for the variations in the curvature of the manifold as well as its interplay with the sampling density of the data set. We demonstrate the effectiveness of our methods for improving the performance of manifold learning algorithms using both synthetic and real-world data sets.
Ensemble manifold regularization.
Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng
2012-06-01
We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.
Institute of Scientific and Technical Information of China (English)
Xiuxiong CHEN; Haozhao LI
2008-01-01
The authors show that the 2-non-negative traceless bisectional curvature is preserved along the K(a)hler-Ricci flow.The positivity of Ricci curvature is also preserved along the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature.As a corollary,the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a K(a)hler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n≥3.
The variation of G in a negatively curved space-time
Mimoso, José P
2011-01-01
Scalar-tensor (ST) gravity theories provide an appropriate theoretical framework for the variation of Newton's fundamental constant, conveyed by the dynamics of a scalar-field non-minimally coupled to the space-time geometry. The experimental scrutiny of scalar-tensor gravity theories has led to a detailed analysis of their post-newtonian features, and is encapsulated into the so-called parametrised post-newtonian formalism (PPN). Of course this approach can only be applied whenever there is a newtonian limit, and the latter is related to the GR solution that is generalized by a given ST solution under consideration. This procedure thus assumes two hypothesis: On the one hand, that there should be a weak field limit of the GR solution; On the other hand that the latter corresponds to the limit case of given ST solution. In the present work we consider a ST solution with negative spatial curvature. It generalizes a general relativistic solution known as being of a degenerate class (A) for its unusual propertie...
Munkres, James R
1997-01-01
A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.
Hierarchical manifold learning.
Bhatia, Kanwal K; Rao, Anil; Price, Anthony N; Wolz, Robin; Hajnal, Jo; Rueckert, Daniel
2012-01-01
We present a novel method of hierarchical manifold learning which aims to automatically discover regional variations within images. This involves constructing manifolds in a hierarchy of image patches of increasing granularity, while ensuring consistency between hierarchy levels. We demonstrate its utility in two very different settings: (1) to learn the regional correlations in motion within a sequence of time-resolved images of the thoracic cavity; (2) to find discriminative regions of 3D brain images in the classification of neurodegenerative disease,
Gupta, Sanju; Saxena, Avadh
2012-12-01
Soft, polymeric and biological systems are self-assembled and hierarchical that involves a multitude of length scales, geometrical shapes and topological variation besides being elastically soft and easily deformable unlike their inorganic solid counterparts. Within the framework of topology and geometry applied to nanocarbons in our recent work [Gupta and Saxena, J. Appl. Phys. 109, 074316 (2011)], we invoke a similar approach to understanding soft/bio-macromolecular systems having structural diversity specifically within the context of minimal surfaces (i.e., mean curvature H = 0 and Gaussian curvature K surfaces such as catenoids (synthetic or natural ion-channel membrane proteins), helicoids (β-sheet proteins), and Schwarzites, respectively, which are analyzed within the framework of differential geometry to obtain the information about Gaussian curvature variation, Gaussian bending rigidity, elastic bending energy, and corresponding topological features. Specifically, we study the negative Gaussian curvature distribution providing surface structure of membrane proteins and Schwarzites and corresponding bending energy cost. We focus on ion-channel membrane proteins approximated as a symmetric catenoid, biological sheets as a helicoid and negatively curved carbons and certain mixed di- or triblock copolymers as periodic minimal surfaces, e.g., gyroids. Through these analyses, we identify the role of geometry (shape) and topology in energy storage and catalysis, nanomedicine and drug delivery applications and derive an overarching geometry/topology → property → functionality relationship paradigm.
Lin, Tong; Zha, Hongbin
2008-05-01
Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, i.e., how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low-dimensional space. Experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings.
Liu, Yang; Liu, Yan; Chan, Keith C C; Hua, Kien A
2014-12-01
In this brief, we present a novel supervised manifold learning framework dubbed hybrid manifold embedding (HyME). Unlike most of the existing supervised manifold learning algorithms that give linear explicit mapping functions, the HyME aims to provide a more general nonlinear explicit mapping function by performing a two-layer learning procedure. In the first layer, a new clustering strategy called geodesic clustering is proposed to divide the original data set into several subsets with minimum nonlinearity. In the second layer, a supervised dimensionality reduction scheme called locally conjugate discriminant projection is performed on each subset for maximizing the discriminant information and minimizing the dimension redundancy simultaneously in the reduced low-dimensional space. By integrating these two layers in a unified mapping function, a supervised manifold embedding framework is established to describe both global and local manifold structure as well as to preserve the discriminative ability in the learned subspace. Experiments on various data sets validate the effectiveness of the proposed method.
Manifolds, sheaves, and cohomology
Wedhorn, Torsten
2016-01-01
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples. Content Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis Readership Graduate Students in Mathematics / Master of Science in Mathematics About the Author Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany.
Convex functions and optimization methods on Riemannian manifolds
Udrişte, Constantin
1994-01-01
This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...
Manifold Learning by Graduated Optimization.
Gashler, M; Ventura, D; Martinez, T
2011-12-01
We present an algorithm for manifold learning called manifold sculpting , which utilizes graduated optimization to seek an accurate manifold embedding. An empirical analysis across a wide range of manifold problems indicates that manifold sculpting yields more accurate results than a number of existing algorithms, including Isomap, locally linear embedding (LLE), Hessian LLE (HLLE), and landmark maximum variance unfolding (L-MVU), and is significantly more efficient than HLLE and L-MVU. Manifold sculpting also has the ability to benefit from prior knowledge about expected results.
Beyond Sentiment: The Manifold of Human Emotions
Kim, Seungyeon; Lebanon, Guy; Essa, Irfan
2012-01-01
Sentiment analysis predicts the presence of positive or negative emotions in a text document. In this paper we consider higher dimensional extensions of the sentiment concept, which represent a richer set of human emotions. Our approach goes beyond previous work in that our model contains a continuous manifold rather than a finite set of human emotions. We investigate the resulting model, compare it to psychological observations, and explore its predictive capabilities. Besides obtaining significant improvements over a baseline without manifold, we are also able to visualize different notions of positive sentiment in different domains.
Manifold Regularized Reinforcement Learning.
Li, Hongliang; Liu, Derong; Wang, Ding
2017-01-27
This paper introduces a novel manifold regularized reinforcement learning scheme for continuous Markov decision processes. Smooth feature representations for value function approximation can be automatically learned using the unsupervised manifold regularization method. The learned features are data-driven, and can be adapted to the geometry of the state space. Furthermore, the scheme provides a direct basis representation extension for novel samples during policy learning and control. The performance of the proposed scheme is evaluated on two benchmark control tasks, i.e., the inverted pendulum and the energy storage problem. Simulation results illustrate the concepts of the proposed scheme and show that it can obtain excellent performance.
Function theory on symplectic manifolds
Polterovich, Leonid
2014-01-01
This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...
Ding, Yiting; Zhang, Yanxiang; Zheng, Quan-Shui; Tyree, Melvin T
2014-07-01
The Scholander-Hammel pressure chamber has been used in thousands of papers to measure osmotic pressure, πc , turgor pressure, Pt , and bulk modulus of elasticity, ε, of leaf cells by pressure-volume (PV) curve analysis. PV analysis has been questioned in the past. In this paper we use micromechanical analysis of leaf cells to examine the impact on PV curve analysis of negative turgor in living cells (Pt ). Models predict negative Pt (-0.1 to -1.8 MPa) depending on leaf cell size and shape in agreement with experimental values reported by J. J. Oertli. Modeled PV curves have linear regions even when Pt is quite negative, contrary to the arguments of M.T. Tyree. Negative Pt is totally missed by PV curve analysis and results in large errors in derived πc and Pt but smaller errors in ε. A survey of leaf cell sizes vs habitat (arid, temperate, and rainforest), suggests that the majority of published PV curves result in errors of 0.1-1.8 MPa in derived πc and Pt , whereby the error increases with decreasing cell size. We propose that small cell size in leaves is an ecological adaptation that permits plants to endure negative values of water potential with relatively little water loss. © 2014 The Authors. New Phytologist © 2014 New Phytologist Trust.
Yamabe flow on Berwald manifolds
Azami, Shahroud; Razavi, Asadollah
2015-12-01
Studying the geometric flow plays a powerful role in mathematics and physics. We introduce the Yamabe flow on Finsler manifolds and we will prove the existence and uniqueness for solution of Yamabe flow on Berwald manifolds.
Gómez, Gerard; Barrabés Vera, Esther
2011-01-01
The term Space Manifold Dynamics (SMD) has been proposed for encompassing the various applications of Dynamical Systems methods to spacecraft mission analysis and design, ranging from the exploitation of libration orbits around the collinear Lagrangian points to the design of optimal station-keeping and eclipse avoidance manoeuvres or the determination of low energy lunar and interplanetary transfers
Eigenvalue pinching on spinc manifolds
Roos, Saskia
2017-02-01
We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.
Manifold Insulation for Solar Collectors
1982-01-01
Results of computer analysis of effects of various manifold insulation detailed in 23-page report show that if fluid is distributed to and gathered from array of solar collectors by external rather than internal manifold, effectiveness of manifold insulation has major influence on efficiency. Report describes required input data and presents equations that govern computer model. Provides graphs comparing collector efficiencies for representative manifold sizes and insulations.
Pulse Distributing Manifold; Pulse Distributing Manifold
Energy Technology Data Exchange (ETDEWEB)
Schutting, Eberhard [Technische Univ. Graz (Austria); Sams, Theodor [AVL List GmbH, Graz (Austria); Glensvig, Michael [Forschungsgesellschaft mbH, Graz (AT). Kompetenzzentrum ' ' Das virtuelle Fahrzeug' ' (VIF)
2011-07-01
The Pulse Distributing Manifold is a new charge exchange method for turbocharged diesel engines with exhaust gas recirculation (EGR). The method is characterized in that the EGR mass flow is not diverted from the exhaust gas mass flow continuously, but over time broken into sub-streams. The temporal interruption is achieved by two phase-shifted outlet valves which are connected via separate manifolds only with the turbocharger or only with the EGR path. The time points of valve opening are chosen such that the turbocharger and the aftertreatment process of exhaust gas is perfused by high-energy exhaust gas of the blowdown phase while cooler and less energy-rich exhaust gas of the exhaust period is used for the exhaust gas recirculation. This increases the enthalpy for the turbocharger and the temperature for the exhaust gas treatment, while the cooling efficiency at the EGR cooler is reduced. The elimination of the continuous EGR valve has a positive effect on pumping losses. The principle functioning and the potential of this system could be demonstrated by means of a concept study using one-dimensional simulations. Without disadvantages in fuel consumption for the considered commercial vehicle engine, a reduction the EGR cooler performance by 15 % and an increase in exhaust temperature of 35 K could be achieved. The presented charge exchange method was developed, evaluated and patented within the scope of the research program 'K2-mobility' of the project partners AVL (Mainz, Federal Republic of Germany) and University of Technology Graz (Austria). The research project 'K2-Mobility' is supported by the competence center 'The virtual vehicle' Forschungsgesellschaft mbH (Graz, Austria).
Hashing on nonlinear manifolds.
Shen, Fumin; Shen, Chunhua; Shi, Qinfeng; van den Hengel, Anton; Tang, Zhenmin; Shen, Heng Tao
2015-06-01
Learning-based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes preserving the Euclidean similarity in the original space. Manifold learning techniques, in contrast, are better able to model the intrinsic structure embedded in the original high-dimensional data. The complexities of these models, and the problems with out-of-sample data, have previously rendered them unsuitable for application to large-scale embedding, however. In this paper, how to learn compact binary embeddings on their intrinsic manifolds is considered. In order to address the above-mentioned difficulties, an efficient, inductive solution to the out-of-sample data problem, and a process by which nonparametric manifold learning may be used as the basis of a hashing method are proposed. The proposed approach thus allows the development of a range of new hashing techniques exploiting the flexibility of the wide variety of manifold learning approaches available. It is particularly shown that hashing on the basis of t-distributed stochastic neighbor embedding outperforms state-of-the-art hashing methods on large-scale benchmark data sets, and is very effective for image classification with very short code lengths. It is shown that the proposed framework can be further improved, for example, by minimizing the quantization error with learned orthogonal rotations without much computation overhead. In addition, a supervised inductive manifold hashing framework is developed by incorporating the label information, which is shown to greatly advance the semantic retrieval performance.
Dynamics and zeta functions on conformally compact manifolds
Rowlett, Julie; Tapie, Samuel
2011-01-01
In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces, we obtain optimal meromorphic extensions of weighted dynamical zeta functions and asymptotic counting estimates for the number of weighted closed geodesics. A meromorphic extension of the standard dynamical zeta function and the prime orbit theorem follow as corollaries. Finally, we investigate interactions between the dynamics and spectral theory of these spaces.
Gobet, F; Carré, M; Farizon, B; Farizon, M; Gaillard, M J; Maerk, T D; Scheier, P
2002-01-01
By (i) selecting specific decay reactions in high energy collisions (60 keV/amu) of hydrogen cluster ions with a helium target (utilizing event-by-event data of a recently developed multi-coincidence experiment) and by (ii) deriving corresponding temperatures for these microcanonical cluster ensembles (analyzing the respective fragment distributions) we are able to construct caloric curves for ii sub 3 sup + (ii sub 2) sub m cluster ions (6 <= m <= 14). All individual curves and the mean of these curves show a backbending in the plateau region thus constituting direct evidence for a negative microcanonical heat capacity in the liquid-to-gas like transition of these finite systems.
Akbulut, Selman
2010-01-01
It is known that every compact Stein 4-manifolds can be embedded into a simply connected, minimal, closed, symplectic 4-manifold. Using this property, we give simple constructions of various cork structures of 4-manifolds. We also give an example of infinitely many disjoint embeddings of a fixed cork into a non-compact 4-manifold which produce infinitely many exotic smooth structures (recall that [7] gives examples arbitrarily many disjoint imbeddings of different corks in a closed manifold inducing mutually different exotic structures). Furthermore, here we construct arbitrary many simply connected compact codimention zero submanifolds of S^4 which are mutually homeomorphic but not diffeomorphic.
Canonical metrics on complex manifold
Institute of Scientific and Technical Information of China (English)
YAU Shing-Tung
2008-01-01
@@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Canonical metrics on complex manifold
Institute of Scientific and Technical Information of China (English)
YAU; Shing-Tung(Yau; S.-T.)
2008-01-01
Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.
Aytuna, Aydin
2011-01-01
An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the first part of this note we compile these notions of parabolicity and give some immediate relations among them. In section 3 we relate some of these notions to the linear topological type of the Fr\\'echet space of analytic functions on the given manifold. In sections 4 and 5 we look at some examples and show, for example, that the complement of the zero set of a Weierstrass polynomial possesses a continuous plurisubharmonic exhaustion function that is maximal off a compact subset.
An alternative to wave mechanics on curved spaces
Tomaschitz, Roman
1992-02-01
Geodesic motion in infinite spaces of constant negative curvature provides for the first time an example where a basically quantum mechanical quantity, a ground-state energy, is derived from Newtonian mechanics in a rigorous, nonsemiclassical way. The ground state energy emerges as the Hausdorff dimension of a quasi-self-similar curve at infinity of three-dimensional hyperbolic space H 3 in which our manifolds are embedded and where their universal covers are realized. This curve is just the locus of the limit set λ(γ) of the Kleinian group γ of covering transformations, which determines the bounded trajectories in the manifold; all of them lie in the quotient C(λ)γ, C(λ) being the hyperbolic convex hull of λ(γ). The three-dimensional hyperbolic manifolds we construct can be visualized as thickened surfaces, topological products I× S, I a finite open interval, the fibers S compact Riemann surfaces. We give a short derivation of the Patterson formula connecting the ground-state energy with the Hausdorff dimension δ of λ, and give various examples for the calculation of δ from the tessellations of the boundary of H 3, induced by the universal coverings of the manifolds.
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
Institute of Scientific and Technical Information of China (English)
张振跃; 查宏远
2004-01-01
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
Learning Smooth Pattern Transformation Manifolds
Vural, Elif
2011-01-01
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals. In order to construct a manifold, we build a representative pattern whose transformations accurately fit various input images. We examine two objectives of the manifold building problem, namely, approximation and classification. For the approximation problem, we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold. We present a DC (Difference-of-Convex) optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to transformation manifolds generated by rotation, translation and anisotropic scaling of a reference pattern. Then, we generalize this approach to a s...
Holonomy groups of Lorentzian manifolds
Galaev, Anton S
2016-01-01
In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker metrics and the classification of 2-symmetric Lorentzian manifolds are considered.
Quantum manifolds with classical limit
Hohmann, Manuel; Wohlfarth, Mattias N R
2008-01-01
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the manifold structure of spacetime. In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value. We speculate on the possible relevance of this geometry to quantum field theory and gravity.
Analysis, manifolds and physics
Choquet-Bruhat, Y
2000-01-01
Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.
Daverman, Robert J
2007-01-01
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve
On f-Eikonal Helices And f-Eikonal Slant Helices In Riemannian Manifolds
Şenol, Ali; Ziplar, Evren; Yayli, Yusuf
2012-01-01
In this paper, we define f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Also, we give the definition of harmonic curvature functions related to f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Moreover, we give characterizations for f-eikonal helix curves and f-eikonal V_{n}-slant helix curves by making use of the harmonic curvature functions.
Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds
Barreto, Yadira; Verjovsky, Alberto
2013-01-01
We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.
Incremental Alignment Manifold Learning
Institute of Scientific and Technical Information of China (English)
Zhi Han; De-Yu Meng; Zong-Sen Xu; Nan-Nan Gu
2011-01-01
A new manifold learning method, called incremental alignment method (IAM), is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire dataset. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects: high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.
Manifold statistics for essential matrices
Dubbelman, G.; Dorst, L.; Pijls, H.; Fitzgibbon, A.; et al.,
2012-01-01
Riemannian geometry allows for the generalization of statistics designed for Euclidean vector spaces to Riemannian manifolds. It has recently gained popularity within computer vision as many relevant parameter spaces have such a Riemannian manifold structure. Approaches which exploit this have been
On the Kobayashi-Royden pseudonorm for almost complex manifolds
Kruglikov, Boris S.
1997-01-01
In this paper we define Kobayashi-Royden pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. We prove that the pseudodistance induced by this pseudonorm coincides with the Kobayashi pseudodistance defined for the almost complex case earlier. We also consider a geometric application for moduli spaces of pseudoholomorphic curves.
Electromagnetic Field in Lyra Manifold: A First Order Approach
Casana, R.; de Melo, C. A. M.; Pimentel, B. M.
2005-12-01
We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.
Electromagnetic Field in Lyra Manifold: A First Order Approach
Casana, R; Pimentel, B M
2016-01-01
We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.
Dimensionality reduction of collective motion by principal manifolds
Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.
2015-01-01
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.
Hyperbolic spaces are of strictly negative type
DEFF Research Database (Denmark)
Hjorth, Poul G.; Kokkendorff, Simon L.; Markvorsen, Steen
2002-01-01
We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative....... The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type....
Cohomotopy sets of 4-manifolds
Kirby, Robion; Teichner, Peter
2012-01-01
Elementary geometric arguments are used to compute the group of homotopy classes of maps from a 4-manifold X to the 3-sphere, and to enumerate the homotopy classes of maps from X to the 2-sphere. The former completes a project initiated by Steenrod in the 1940's, and the latter provides geometric arguments for and extensions of recent homotopy theoretic results of Larry Taylor. These two results complete the computation of all the cohomotopy sets of closed oriented 4-manifolds and provide a framework for the study of Morse 2-functions on 4-manifolds, a subject that has garnered considerable recent attention.
Geometry of Cyclic Quotients; 1, Knotted Totally Geodesic Submanifolds in Positively Curved Spheres
Reznikov, A G
1994-01-01
We prove that there exists a metric of positive curvature in a three-sphere which admits a given torus knot as a closed geodesic.We also sketch a construction of a metric in a four sphere, very likely of positive curvature, which admits a totally geodesic projective plane with Euler number four. Surpisingly, the technique borrows a lot from the Mostow-Siu-Gromov-Thurston constuction of exotic negatively curved manifolds.
Haantjes Manifolds and Integrable Systems
Tempesta, Piergiulio
2014-01-01
A general theory of integrable systems is proposed, based on the theory of Haantjes manifolds. We introduce the notion of symplectic-Haantjes manifold (or $\\omega \\mathcal{H}$ manifold), as the natural setting where the notion of integrability can be formulated. We propose an approach to the separation of variables for classical systems, related to the geometry of Haantjes manifolds. A special class of coordinates, called Darboux-Haantjes coordinates, will be constructed from the Haantjes structure associated with an integrable systems. They enable the additive separation of variables of the Hamilton-Jacobi equation. We also present an application of our approach to the study of some finite-dimensional integrable models, as the H\\'enon-Heiles systems and a stationary reduction of the KdV hierarchy.
An introduction to differential manifolds
Lafontaine, Jacques
2015-01-01
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
Invariant Manifolds and Collective Coordinates
Papenbrock, T
2001-01-01
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.
An Explicit Nonlinear Mapping for Manifold Learning
Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo
2010-01-01
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have...
Nonlinear manifold representations for functional data
Chen, Dong; Müller, Hans-Georg
2012-01-01
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which...
An Alternative to Wave Mechanics on Curved Spaces
Tomaschitz, R
1992-01-01
Geodesic motion in infinite spaces of constant negative curvature provides for the first time an example where a basically quantum mechanical quantity, a ground-state energy, is derived from Newtonian mechanics in a rigorous, non-semiclassical way. The ground state energy emerges as the Hausdorff dimension of a quasi-self-similar curve at infinity of three-dimensional hyperbolic space H in which our manifolds are embedded and where their universal covers are realized. This curve is just the locus of the limit set L(G) of the Kleinian group G of covering transformations, which determines the bounded trajectories in the manifold; all of them lie in the quotient C(L)/G, C(L) being the hyperbolic convex hull of L(G). The three-dimensional hyperbolic manifolds we construct can be visualized as thickened surfaces, topological products I x S, I a finite open interval, the fibers S compact Riemann surfaces. We give a short derivation of the Patterson formula connecting the ground-state energy with the Hausdorff dimen...
Conjectures on counting associative 3-folds in $G_2$-manifolds
Joyce, Dominic
2016-01-01
There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\\varphi,*\\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\\omega)$. We can also generalize $(X,\\varphi,*\\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\\varphi,\\psi)$, where we compare $\\varphi$ with $\\omega$ and $\\psi$ with $J$. Associative 3-folds in $X$, a special kind of minimal submanifold, are analogous to $J$-holomorphic curves in $Y$. Several areas of Symplectic Geometry -- Gromov-Witten theory, Quantum Cohomology, Lagrangian Floer cohomology, Fukaya categories -- are built using 'counts' of moduli spaces of $J$-holomorphic curves in $Y$, but give an answer depending only on the symplectic manifold $(Y,\\omega)$, not on the (almost) complex structure $J$. We investigate whether it may be possible to define interesting invariants of tamed almost $G_2$-manifolds $(X,\\varphi,\\psi)$ by 'counting' compact associative 3-folds $N\\subset X$, such that the invariants depend only on $\\varphi$, and are independent of the 4-form $\\psi$ used to def...
Fivebranes and 3-manifold homology
Gukov, Sergei; Vafa, Cumrun
2016-01-01
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[M_3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.
Lattice QCD on nonorientable manifolds
Mages, Simon; Tóth, Bálint C.; Borsányi, Szabolcs; Fodor, Zoltán; Katz, Sándor D.; Szabó, Kálmán K.
2017-05-01
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a nonorientable manifold and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is that translational invariance is preserved up to exponentially small corrections. A Dirac fermion on a nonorientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.
Parallel spinors on flat manifolds
Sadowski, Michał
2006-05-01
Let p(M) be the dimension of the vector space of parallel spinors on a closed spin manifold M. We prove that every finite group G is the holonomy group of a closed flat spin manifold M(G) such that p(M(G))>0. If the holonomy group Hol(M) of M is cyclic, then we give an explicit formula for p(M) another than that given in [R.J. Miatello, R.A. Podesta, The spectrum of twisted Dirac operators on compact flat manifolds, Trans. Am. Math. Soc., in press]. We answer the question when p(M)>0 if Hol(M) is a cyclic group of prime order or dimM≤4.
Fivebranes and 3-manifold homology
Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun
2017-07-01
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[ M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.
Schobeiri, M. T.; John, J.
1996-01-01
The turbomachinery wake flow development is largely influenced by streamline curvature and streamwise pressure gradient. The objective of this investigation is to study the development of the wake under the influence of streamline curvature and streamwise pressure gradient. The experimental investigation is carried out in two phases. The first phase involves the study of the wake behind a stationary circular cylinder (steady wake) in curved channels at positive, zero, and negative streamwise pressure gradients. The mean velocity and Reynolds stress components are measured using a X-hot-film probe. The measured quantities obtained in probe coordinates are transformed to a curvilinear coordinate system along the wake centerline and are presented in similarity coordinates. The results of the steady wakes suggest strong asymmetry in velocity and Reynolds stress components. However, the velocity defect profiles in similarity coordinates are almost symmetrical and follow the same distribution as the zero pressure gradient straight wake. The results of Reynolds stress distributions show higher values on the inner side of the wake than the outer side. Other quantities, including the decay of maximum velocity defect, growth of wake width, and wake integral parameters, are also presented for the three different pressure gradient cases of steady wake. The decay rate of velocity defect is fastest for the negative streamwise pressure gradient case and slowest for the positive pressure gradient case. Conversely, the growth of the wake width is fastest for the positive streamwise pressure gradient case and slowest for the negative streamwise pressure gradient. The second phase studies the development of periodic unsteady wakes generated by the circular cylinders of the rotating wake generator in a curved channel at zero streamwise pressure gradient. Instantaneous velocity components of the periodic unsteady wakes, measured with a stationary X-hot-film probe, are analyzed by the
Killing Symmetry on Finsler Manifold
Ootsuka, Takayoshi; Ishida, Muneyuki
2016-01-01
Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\\delta K^\\flat =0$ by using the Killing non-linear 1-form $K^\\flat$ and the spray operator $\\delta$ with the Finsler non-linear connection. $K^\\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $\\delta K^\\flat =0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian gravity.
Invariant manifolds and collective coordinates
Energy Technology Data Exchange (ETDEWEB)
Papenbrock, T. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Institute for Nuclear Theory, University of Washington, Seattle, WA (United States); Seligman, T.H. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Centro de Ciencias Fisicas, University of Mexico (UNAM), Cuernavaca (Mexico)
2001-09-14
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction. (author)
Stein Manifolds and Holomorphic Mappings
Forstneric, Franc
2011-01-01
The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. This book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applicat
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
On timelike surfaces in Lorentzian manifolds
Hasse, Wolfgang
2008-01-01
We discuss the geometry of timelike surfaces (two-dimensional submanifolds) in a Lorentzian manifold and its interpretation in terms of general relativity. A classification of such surfaces is presented which distinguishes four cases of special algebraic properties of the second fundamental form from the generic case. In the physical interpretation a timelike surface can be viewed as the worldsheet of a ``track'', and timelike curves in this surface can be viewed as the worldlines of observers who are bound to the track, like someone sitting in a roller-coaster car. With this interpretation, our classification turns out to be closely related to (i) the visual appearance of the track, (ii) gyroscopic transport along the track, and (iii) inertial forces perpendicular to the track. We illustrate our general results with timelike surfaces in the Kerr-Newman spacetime.
Cone fields and topological sampling in manifolds with bounded curvature
Turner, Katharine
2011-01-01
Often noisy point clouds are given as an approximation of a particular compact set of interest. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of {\\mu}-critical points in an annular region. Since an offset of a set deformation retracts to the set itself provided that there are no critical points of the distance function nearby, we can use this theorem to show when the offset of a point cloud is homotopy equivalent to the set it is sampled from. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature. In the process, we prove stability theorems for {\\mu}-critical points when the ambient space is a manifold.
Layered models for closed 3-manifolds
Johnson, Jesse
2010-01-01
We define a combinatorial structure on 3-manifolds that combines the model manifolds constructed in Minsky's proof of the ending lamination conjecture with the layered triangulations defined by Jaco and Rubinstein.
Holomorphic flexibility properties of complex manifolds
2004-01-01
We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic manifolds.
Nonlinear manifold representations for functional data
Chen, Dong; 10.1214/11-AOS936
2012-01-01
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which we modify to address functional data settings. In simulations and applications, we study examples of functional data which lie on a manifold and validate the superior behavior of manifold mean and functional manifold components over traditional cross-sectional mean and functional principal components. We also include consistency proofs for our estimators under certain assumptions.
Periodic solutions and slow manifolds
Verhulst, F.
2006-01-01
After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we disc
Melnikov Vector and Heteroclinic Manifolds
Institute of Scientific and Technical Information of China (English)
朱德明
1994-01-01
Using the exponential dichotomies,the transversality theory and the generalized Melnikov method,we consider the conditions for the persistence and the transversality of the singular orbit,with high degeneracy,situated on the heteroclinic or homoclinic manifold under perturbation.The results obtained extend,include and improve the corresponding ones given in certain papers well known in this area.
Cobordism Independence of Grassmann Manifolds
Indian Academy of Sciences (India)
Ashish Kumar Das
2004-02-01
This note proves that, for $F=\\mathbb{R},\\mathbb{C}$ or $\\mathbb{H}$, the bordism classes of all non-bounding Grassmannian manifolds $G_k(F^{n+k})$, with < and having real dimension , constitute a linearly independent set in the unoriented bordism group $\\mathfrak{N}_d$ regarded as a $\\mathbb{Z}_2$-vector space.
Fluid delivery manifolds and microfluidic systems
Energy Technology Data Exchange (ETDEWEB)
Renzi, Ronald F.; Sommer, Gregory J.; Singh, Anup K.; Hatch, Anson V.; Claudnic, Mark R.; Wang, Ying-Chih; Van de Vreugde, James L.
2017-02-28
Embodiments of fluid distribution manifolds, cartridges, and microfluidic systems are described herein. Fluid distribution manifolds may include an insert member and a manifold base and may define a substantially closed channel within the manifold when the insert member is press-fit into the base. Cartridges described herein may allow for simultaneous electrical and fluidic interconnection with an electrical multiplex board and may be held in place using magnetic attraction.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
Softening the Complexity of Entropic Motion on Curved Statistical Manifolds
Cafaro, Carlo; Lupo, Cosmo; Mancini, Stefano
2011-01-01
We study the information geometry and the entropic dynamics of a 3D Gaussian statistical model. We then compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We show that the chaoticity (temporal complexity) of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE) and the Jacobi vector field intensity, is softened with respect to the chaoticity of the 3D Gaussian statistical model.
Quantization of Presymplectic Manifolds and Circle Actions
Silva, A C; Tolman, S; Silva, Ana Canas da; Karshon, Yael; Tolman, Susan
1997-01-01
We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.
Natural Connections on Riemannian Product Manifolds
Gribacheva, Dobrinka
2011-01-01
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
Invariant manifolds for flows in Banach Spaces
Energy Technology Data Exchange (ETDEWEB)
Lu Kening.
1989-01-01
The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.
Local Schrodinger flow into Kahler manifolds
Institute of Scientific and Technical Information of China (English)
丁伟岳; 王友德
2001-01-01
In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.
HOLOMORPHIC MANIFOLDS ON LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
Tsoy-Wo Ma
2005-01-01
Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.
On the manifold-mapping optimization technique
Echeverria, D.; Hemker, P.W.
2006-01-01
In this paper, we study in some detail the manifold-mapping optimization technique introduced in an earlier paper. Manifold mapping aims at accelerating optimal design procedures that otherwise require many evaluations of time-expensive cost functions. We give a proof of convergence for the manifold
Singular reduction of generalized complex manifolds
Goldberg, Timothy E
2010-01-01
In this paper, we develop the analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for reduction of Hamiltonian generalized Kaehler manifolds.
Manifold seal structure for fuel cell stack
Collins, William P.
1988-01-01
The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.
Minimal Webs in Riemannian Manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... theorems together with the comparison techniques for distance functions in Riemannian geometry and obtain bounds for the first Dirichlet eigenvalues, the exit times and the capacities as well as isoperimetric type inequalities for so-called extrinsic $R-$webs of minimal webs in ambient Riemannian manifolds...
Symmetries from the solution manifold
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Rigid subsets of symplectic manifolds
Entov, Michael
2007-01-01
We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of intersections involving, in particular, specific fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds (following the previous work of P.Albers) as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions. In addition, we get some geometric obstructions to semi-simplicity of the quantum homology of symplectic manifolds. The proofs are based on the Floer-theoretical machinery of partial symplectic quasi-states.
Torsions of 3-dimensional manifolds
Wurzbacher, T
2002-01-01
From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews
Koppelman formulas on flag manifolds
Samuelsson, Håkan
2010-01-01
We construct Koppelman formulas on manifolds of flags in $\\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding $\\debar$-equation. We also construct reproducing kernels for harmonic $(p,q)$-forms in the case of Grassmannians.
Polynomial Regression on Riemannian Manifolds
Hinkle, Jacob; Fletcher, P Thomas; Joshi, Sarang
2012-01-01
In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein as well as the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.
Deformations of extremal toric manifolds
Rollin, Yann
2012-01-01
Let $X$ be a compact toric extremal K\\"ahler manifold. Using the work of Sz\\'ekelyhidi, we provide a simple criterion on the fan describing $X$ to ensure the existence of complex deformations of $X$ that carry extremal metrics. As an example, we find new CSC metrics on 4-points blow-ups of $\\C\\P^1\\times\\C\\P^1$.
The Operator Manifold Formalism, 1
Ter-Kazarian, G T
1998-01-01
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the spacetime continuum and internal worlds, where the subquarks are defined implying the Confinement and Gauge principles. This formalism in Part II (hep-th/9812182) is used to develop further the microscopic approach to some key problems of particle physics.
Coincidence classes in nonorientable manifolds
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We study Nielsen coincidence theory for maps between manifolds of same dimension regardless of orientation. We use the definition of semi-index of a class, review the definition of defective classes, and study the occurrence of defective root classes. We prove a semi-index product formula for lifting maps and give conditions for the defective coincidence classes to be the only essential classes.
Manifolds of interconvertible pure states
Sinolecka, Magdalena M.; Zyczkowski, Karol; Kus, Marek
2001-01-01
Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1) dimensional, while the manifold of maximally entangled states has N^2-1 dimensions.
Manifolds of interconvertible pure states
Sinolecka, M M; Kus, M; Sinolecka, Magdalena M.; Zyczkowski, Karol; Kus, Marek
2002-01-01
Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1) dimensional, while the manifold of maximally entangled states has N^2-1 dimensions.
On Einstein, Hermitian 4-Manifolds
LeBrun, Claude
2010-01-01
Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2 # (-CP2), or the Einstein metric on CP2 # 2 (-CP2) constructed in Chen-LeBrun-Weber.
Model Reduction by Manifold Boundaries
Transtrum, Mark K.; Qiu, Peng
2015-01-01
Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce “black boxes” disconnected from the microscopic physics. We propose a new approach by translating the model reduction problem for an arbitrary statistical model into a geometric problem of constructing a low-dimensional, submanifold approximation to a high-dimensional manifold. When models are overly complex, we use the observation that the model manifold is bounded with a hierarchy of widths and propose using the boundaries as submanifold approximations. We refer to this approach as the manifold boundary approximation method. We apply this method to several models, including a sum of exponentials, a dynamical systems model of protein signaling, and a generalized Ising model. By focusing on parameters rather than physical degrees of freedom, the approach unifies many other model reduction techniques, such as singular limits, equilibrium approximations, and the renormalization group, while expanding the domain of tractable models. The method produces a series of approximations that decrease the complexity of the model and reveal how microscopic parameters are systematically “compressed” into a few macroscopic degrees of freedom, effectively building a bridge between the microscopic and the macroscopic descriptions. PMID:25216014
Geometric Hamilton-Jacobi theory on Nambu-Poisson manifolds
de León, M.; Sardón, C.
2017-03-01
The Hamilton-Jacobi theory is a formulation of classical mechanics equivalent to other formulations as Newtonian, Lagrangian, or Hamiltonian mechanics. The primordial observation of a geometric Hamilton-Jacobi theory is that if a Hamiltonian vector field XH can be projected into the configuration manifold by means of a 1-form dW, then the integral curves of the projected vector field XHd Wcan be transformed into integral curves of XH provided that W is a solution of the Hamilton-Jacobi equation. Our aim is to derive a geometric Hamilton-Jacobi theory for physical systems that are compatible with a Nambu-Poisson structure. For it, we study Lagrangian submanifolds of a Nambu-Poisson manifold and obtain explicitly an expression for a Hamilton-Jacobi equation on such a manifold. We apply our results to two interesting examples in the physics literature: the third-order Kummer-Schwarz equations and a system of n copies of a first-order differential Riccati equation. From the first example, we retrieve the original Nambu bracket in three dimensions and from the second example, we retrieve Takhtajan's generalization of the Nambu bracket to n dimensions.
Null eikonal helices and Null eikonal slant helices in the 4-dimensional Lorentzian manifold
Zıplar, Evren
2014-01-01
In this paper, we define the notion of eikonal helix and eikonal slant helix for null curves in the 4-dimensional Lorentzian manifold M 1 4 and give a characterization for the null curve to be the null eikonal helix. Moreover, we indicate an important relation between the null eikonal helix and null eikonal slant helix and find the axis of the null eikonal helix. We obtain some relationships between the curvatures of these curves.
A new construction of Calabi–Yau manifolds: Generalized CICYs
Directory of Open Access Journals (Sweden)
Lara B. Anderson
2016-05-01
Full Text Available We present a generalization of the complete intersection in products of projective space (CICY construction of Calabi–Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a ‘configuration matrix’, a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi–Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi–Yau manifolds are complete intersections in (not necessarily Fano ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.
A new construction of Calabi–Yau manifolds: Generalized CICYs
Energy Technology Data Exchange (ETDEWEB)
Anderson, Lara B., E-mail: lara.anderson@vt.edu [Physics Department, Robeson Hall, Virginia Tech, Blacksburg, VA 24061 (United States); Apruzzi, Fabio, E-mail: fabio.apruzzi@itp.uni-hannover.de [Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, D-30167 Hannover (Germany); Gao, Xin, E-mail: xingao@vt.edu [Physics Department, Robeson Hall, Virginia Tech, Blacksburg, VA 24061 (United States); Gray, James, E-mail: jamesgray@vt.edu [Physics Department, Robeson Hall, Virginia Tech, Blacksburg, VA 24061 (United States); Lee, Seung-Joo, E-mail: seungsm@vt.edu [Physics Department, Robeson Hall, Virginia Tech, Blacksburg, VA 24061 (United States)
2016-05-15
We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi–Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a ‘configuration matrix’, a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi–Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi–Yau manifolds are complete intersections in (not necessarily Fano) ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.
Unobstructedness of deformations of holomorphic maps onto Fano manifolds of Picard number 1
Hwang, Jun-Muk
2009-01-01
We show that deformations of a surjective morphism onto a Fano manifold of Picard number 1 are unobstructed and rigid modulo the automorphisms of the target, if the variety of minimal rational tangents of the Fano manifold is non-linear or finite. The condition on the variety of minimal rational tangents holds for practically all known examples of Fano manifolds of Picard number 1, except the projective space. When the variety of minimal rational tangents is non-linear, the proof is based on an earlier result of N. Mok and the author on the birationality of the tangent map. When the varieties of minimal rational tangents of the Fano manifold is finite, the key idea is to factorize the given surjective morphism, after some transformation, through a universal morphism associated to the minimal rational curves.
$\\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
Aprile, Francesco
2016-01-01
General half-BPS A-type boundary conditions are formulated for N=2 supersymmetric field theories on compact 3-manifolds with boundary. We observe that under suitable conditions manifolds of the real A-type admitting two complex supersymmetries (related by charge conjugation) possess, besides a contact structure, a natural integrable toric foliation. A boundary, or a general co-dimension-1 defect, can be inserted along any leaf of this preferred foliation to produce manifolds with boundary that have the topology of a solid torus. We show that supersymmetric field theories on such manifolds can be endowed with half-BPS A-type boundary conditions. We specify the natural curved space generalization of the A-type projection of bulk supersymmetries and analyze the resulting A-type boundary conditions in generic 3d non-linear sigma models and YM/CS-matter theories.
Smooth Maps of a Foliated Manifold in a Symplectic Manifold
Indian Academy of Sciences (India)
Mahuya Datta; Md Rabiul Islam
2009-06-01
Let be a smooth manifold with a regular foliation $\\mathcal{F}$ and a 2-form which induces closed forms on the leaves of $\\mathcal{F}$ in the leaf topology. A smooth map $f:(M,\\mathcal{F})\\longrightarrow(N, )$ in a symplectic manifold $(N, )$ is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the restriction of $f^∗$ is the same as the restriction of on each leaf of the foliation. If is a foliated symplectic immersion then the derivative map $Df$ gives rise to a bundle morphism $F:TM\\longrightarrow TN$ which restricts to a monomorphism on $T\\mathcal{F}\\subseteq TM$ and satisfies the condition $F^∗=$ on $T\\mathcal{F}$. A natural question is whether the existence of such a bundle map ensures the existence of a foliated symplectic immersion . As we shall see in this paper, the obstruction to the existence of such an is only topological in nature. The result is proved using the ℎ-principle theory of Gromov.
Differential Calculus on N-Graded Manifolds
Sardanashvily, G.; W. Wachowski
2017-01-01
The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on Z2-graded manifolds. We follow the notion of an N-graded manifold as a local-ringed space whose body is a s...
Discrete equations and the singular manifold method
Estévez, P G
1999-01-01
The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painleve type equations for which auto-Backlund transformations are obtained. These auto-Backlund transformations can be used to obtain discrete equations.
OBJECTORIENTED NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The design and management of the objects about the numerical manifold method are studied by abstracting the finite cover system of numerical manifold method as independent data classes and the theoretical basis for the researching and expanding of numerical manifold method is also put forward. The Hammer integration of triangular area coordinates is used in the integration of the element. The calculation result shows that the program is accuracy and effective.
Homology group on manifolds and their foldings
Directory of Open Access Journals (Sweden)
M. Abu-Saleem
2010-03-01
Full Text Available In this paper, we introduce the definition of the induced unfolding on the homology group. Some types of conditional foldings restricted on the elements of the homology groups are deduced. The effect of retraction on the homology group of a manifold is dicussed. The unfolding of variation curvature of manifolds on their homology group are represented. The relations between homology group of the manifold and its folding are deduced.
Similarity Learning of Manifold Data.
Chen, Si-Bao; Ding, Chris H Q; Luo, Bin
2015-09-01
Without constructing adjacency graph for neighborhood, we propose a method to learn similarity among sample points of manifold in Laplacian embedding (LE) based on adding constraints of linear reconstruction and least absolute shrinkage and selection operator type minimization. Two algorithms and corresponding analyses are presented to learn similarity for mix-signed and nonnegative data respectively. The similarity learning method is further extended to kernel spaces. The experiments on both synthetic and real world benchmark data sets demonstrate that the proposed LE with new similarity has better visualization and achieves higher accuracy in classification.
Hidden torsion, 3-manifolds, and homology cobordism
Cha, Jae Choon
2011-01-01
This paper continues our exploration of homology cobordism of 3-manifolds using our recent results on Cheeger-Gromov rho-invariants associated to amenable representations. We introduce a new type of torsion in 3-manifold groups we call hidden torsion, and an algebraic approximation we call local hidden torsion. We construct infinitely many hyperbolic 3-manifolds which have local hidden torsion in the transfinite lower central subgroup. By realizing Cheeger-Gromov invariants over amenable groups, we show that our hyperbolic 3-manifolds are not pairwise homology cobordant, yet remain indistinguishable by any prior known homology cobordism invariants.
Differential Calculus on N-Graded Manifolds
Directory of Open Access Journals (Sweden)
G. Sardanashvily
2017-01-01
Full Text Available The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on Z2-graded manifolds. We follow the notion of an N-graded manifold as a local-ringed space whose body is a smooth manifold Z. A key point is that the graded derivation module of the structure ring of graded functions on an N-graded manifold is the structure ring of global sections of a certain smooth vector bundle over its body Z. Accordingly, the Chevalley–Eilenberg differential calculus on an N-graded manifold provides it with the de Rham complex of graded differential forms. This fact enables us to extend the differential calculus on N-graded manifolds to formalism of nonlinear differential operators, by analogy with that on smooth manifolds, in terms of graded jet manifolds of N-graded bundles.
Stability of Strongly Gauduchon Manifolds under Modifications
Popovici, Dan
2010-01-01
In our previous works on deformation limits of projective and Moishezon manifolds, we introduced and made crucial use of the notion of strongly Gauduchon metrics as a reinforcement of the earlier notion of Gauduchon metrics. Using direct and inverse images of closed positive currents of type $(1, \\, 1)$ and regularisation, we now show that compact complex manifolds carrying strongly Gauduchon metrics are stable under modifications. This stability property, known to fail for compact K\\"ahler manifolds, mirrors the modification stability of balanced manifolds proved by Alessandrini and Bassanelli.
Manifold knowledge extraction and target recognition
Chao, Cai; Hua, Zhou
2009-10-01
Advanced mammalian target identification derived from the perception of target's manifold and measurement manifolddistance. It does not rely on object's segmented accuracy, not depend on target's variety model, and adapt to a range of changes on targets. In this paper, based on the existed manifold learning algorithm, set up a new bionic automatic target recognition model, discussed the targets manifold knowledge acquisition and the knowledge expression architecture, gave a manifold knowledge-based new method for automatic target recognition. Experiments show that the new method has a strong adaptability to targets various transform, and has a very high correctly identification probability.
Spectral gaps, inertial manifolds and kinematic dynamos
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es
2005-10-17
Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.
Manifold learning in protein interactomes.
Marras, Elisabetta; Travaglione, Antonella; Capobianco, Enrico
2011-01-01
Many studies and applications in the post-genomic era have been devoted to analyze complex biological systems by computational inference methods. We propose to apply manifold learning methods to protein-protein interaction networks (PPIN). Despite their popularity in data-intensive applications, these methods have received limited attention in the context of biological networks. We show that there is both utility and unexplored potential in adopting manifold learning for network inference purposes. In particular, the following advantages are highlighted: (a) fusion with diagnostic statistical tools designed to assign significance to protein interactions based on pre-selected topological features; (b) dissection into components of the interactome in order to elucidate global and local connectivity organization; (c) relevance of embedding the interactome in reduced dimensions for biological validation purposes. We have compared the performances of three well-known techniques--kernel-PCA, RADICAL ICA, and ISOMAP--relatively to their power of mapping the interactome onto new coordinate dimensions where important associations among proteins can be detected, and then back projected such that the corresponding sub-interactomes are reconstructed. This recovery has been done selectively, by using significant information according to a robust statistical procedure, and then standard biological annotation has been provided to validate the results. We expect that a byproduct of using subspace analysis by the proposed techniques is a possible calibration of interactome modularity studies. Supplementary Material is available online at www.libertonlinec.com.
Characterizing humans on Riemannian manifolds.
Tosato, Diego; Spera, Mauro; Cristani, Marco; Murino, Vittorio
2013-08-01
In surveillance applications, head and body orientation of people is of primary importance for assessing many behavioral traits. Unfortunately, in this context people are often encoded by a few, noisy pixels so that their characterization is difficult. We face this issue, proposing a computational framework which is based on an expressive descriptor, the covariance of features. Covariances have been employed for pedestrian detection purposes, actually a binary classification problem on Riemannian manifolds. In this paper, we show how to extend to the multiclassification case, presenting a novel descriptor, named weighted array of covariances, especially suited for dealing with tiny image representations. The extension requires a novel differential geometry approach in which covariances are projected on a unique tangent space where standard machine learning techniques can be applied. In particular, we adopt the Campbell-Baker-Hausdorff expansion as a means to approximate on the tangent space the genuine (geodesic) distances on the manifold in a very efficient way. We test our methodology on multiple benchmark datasets, and also propose new testing sets, getting convincing results in all the cases.
Yang, Dongmei; Pan, Shaoan; Ding, Yiting; Tyree, Melvin T
2017-03-01
This paper provides a mini-review of evidence for negative turgor pressure in leaf cells starting with experimental evidence in the late 1950s and ending with biomechanical models published in 2014. In the present study, biomechanical models were used to predict how negative turgor pressure might be manifested in dead tissue, and experiments were conducted to test the predictions. The main findings were as follows: (i) Tissues killed by heating to 60 or 80 °C or by freezing in liquid nitrogen all became equally leaky to cell sap solutes and all seemed to pass freely through the cell walls. (ii) Once cell sap solutes could freely pass the cell walls, the shape of pressure-volume curves was dramatically altered between living and dead cells. (iii) Pressure-volume curves of dead tissue seem to measure negative turgor defined as negative when inside minus outside pressure is negative. (iv) Robinia pseudoacacia leaves with small palisade cells had more negative turgor than Metasequoia glyptostroboides with large cells. (v) The absolute difference in negative turgor between R. pseudoacacia and M. glyptostroboides approached as much as 1.0 MPa in some cases. The differences in the manifestation of negative turgor in living versus dead tissue are discussed. © 2016 John Wiley & Sons Ltd.
Simulating triangulations. Graphs, manifolds and (quantum) spacetime
Energy Technology Data Exchange (ETDEWEB)
Krueger, Benedikt
2016-07-01
Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used
Holographic dimensional reduction: Center manifold theorem and E-infinity
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Department of Physics, University of Alexandria (Egypt); Department of Astrophysics, Cairo University (Egypt); Department of Physics, Mansura University (Egypt)
2006-08-15
Klein modular curve is shown to be the holographic boundary of E-infinity Cantorian spacetime. The conformal relation between the full dimensional and the reduced space is explored. We show that both spaces analyzed in the appropriate manner give the same results for certain aspects of high energy particle physics and quantum gravity. Similarity with the center manifold theorem of non-linear dynamics and the theory of bifurcating vector fields is discussed. In particular it was found that the transfinite version of the E{sub 8}-bar E{sub 8} theory corresponds to a fuzzy Kahler manifold with b{sub 2}{sup -}=19-{phi}{sup 6} and b{sub 2}{sup +}=5+{phi}{sup 3}, while the boundary theory of the {gamma}{sub c}(7) Klein modular space corresponds to another fuzzy Kahler manifold with b{sub 2}{sup -}=13-{phi}{sup 6} and b{sub 2}{sup +}=3-{phi}{sup 6}. Based on these results, we conclude that the {epsilon}{sup ({approx}}{sup )}-{gamma}{sub c}(7) theory represents a worked out example for the correctness of the holographic principle first proposed by G. 't Hooft. Hooft.
Triangulated manifold meshing method preserving molecular surface topology.
Chen, Minxin; Tu, Bin; Lu, Benzhuo
2012-09-01
Generation of manifold mesh is an urgent issue in mathematical simulations of biomolecule using boundary element methods (BEM) or finite element method (FEM). Defects, such as not closed mesh, intersection of elements and missing of small structures, exist in surface meshes generated by most of the current meshing method. Usually the molecular surface meshes produced by existing methods need to be revised carefully by third party software to ensure the surface represents a continuous manifold before being used in a BEM and FEM calculations. Based on the trace technique proposed in our previous work, in this paper, we present an improved meshing method to avoid intersections and preserve the topology of the molecular Gaussian surface. The new method divides the whole Gaussian surface into single valued pieces along each of x, y, z directions by tracing the extreme points along the fold curves on the surface. Numerical test results show that the surface meshes produced by the new method are manifolds and preserve surface topologies. The result surface mesh can also be directly used in surface conforming volume mesh generation for FEM type simulation. Copyright © 2012 Elsevier Inc. All rights reserved.
Integrability conditions on Engel-type manifolds
Calin, Ovidiu; Chang, Der-Chen; Hu, Jishan
2015-09-01
We introduce the concept of Engel manifold, as a manifold that resembles locally the Engel group, and find the integrability conditions of the associated sub-elliptic system , . These are given by , . Then an explicit construction of the solution involving an integral representation is provided, which corresponds to a Poincaré-type lemma for the Engel's distribution.
Target manifold formation using a quadratic SDF
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
Li, Tao
2011-01-01
We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We also construct toroidal such examples containing hyperbolic JSJ pieces.
An Explicit Nonlinear Mapping for Manifold Learning.
Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo
2013-02-01
Manifold learning is a hot research topic in the held of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there are no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the hrst time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of locally linear embedding and derive an explicit nonlinear manifold learning algorithm, which is named neighborhood preserving polynomial embedding. Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.
Gauged supergravities from Bianchi's group manifolds
Bergshoeff, E; Gran, U; Linares, R; Nielsen, M; Ortin, T; Roest, D
2004-01-01
We construct maximal D = 8 gauged supergravities by the reduction of D = I I supergravity over three-dimensional group manifolds. Such manifolds are classified into two classes, A and B, and eleven types. This Bianchi classification carries over to the gauged supergravities. The class A theories hav
Simplicial approach to derived differential manifolds
Borisov, Dennis
2011-01-01
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of homotopy rings (D.Spivak), thus preserving the classical cobordism ring. This reduction to the usual algebraic homotopy can potentially lead to virtual fundamental classes beyond obstruction theory.
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
YOE ITOKAWA; KATSUHIRO SHIOHAMA; BANKTESHWAR TIWARI
2016-10-01
The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, Jaap
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof.
Warped product submanifolds of Lorentzian paracosymplectic manifolds
Perkta\\cs, Selcen Yüksel; Kele\\cs, Sad\\ik
2011-01-01
In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\\times_{f}M_{\\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to $M$ is an usual Riemannian product manifold where totally geodesic and totally umbilical submanifolds of warped product are invariant and anti-invariant, respectively. We prove that the distributions involved in the definition of a warped product semi-invariant submanifold are always integrable. A necessary and sufficient condition for a semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be warped product semi-invariant submanifold is obtained. We also investigate the existence and nonexistence of warped product semi-slant and warped product anti-slant submanifolds in a Lorentzian paracosymplectic manifold.
Manifold-based learning and synthesis.
Huang, Dong; Yi, Zhang; Pu, Xiaorong
2009-06-01
This paper proposes a new approach to analyze high-dimensional data set using low-dimensional manifold. This manifold-based approach provides a unified formulation for both learning from and synthesis back to the input space. The manifold learning method desires to solve two problems in many existing algorithms. The first problem is the local manifold distortion caused by the cost averaging of the global cost optimization during the manifold learning. The second problem results from the unit variance constraint generally used in those spectral embedding methods where global metric information is lost. For the out-of-sample data points, the proposed approach gives simple solutions to transverse between the input space and the feature space. In addition, this method can be used to estimate the underlying dimension and is robust to the number of neighbors. Experiments on both low-dimensional data and real image data are performed to illustrate the theory.
Heterotic model building: 16 special manifolds
Energy Technology Data Exchange (ETDEWEB)
He, Yang-Hui [Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford OX14JD (United Kingdom); Lee, Seung-Joo [School of Physics, Korea Institute for Advanced Study,Seoul 130-722 (Korea, Republic of); Lukas, Andre; Sun, Chuang [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom)
2014-06-12
We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html.
Heisenberg symmetry and hypermultiplet manifolds
Antoniadis, Ignatios; Petropoulos, P Marios; Siampos, Konstantinos
2015-01-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\\"ahler and quaternionic spaces. This is motivated by the r\\^ole these spaces with this symmetry play in $\\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-K\\"ahler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-K\\"ahler spaces with Heisenberg algebra, which is reduced to $U(1)\\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\\text{Heisenberg} \\ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\\mathcal{N}=2$ conformal supergravity.
Moving Manifolds in Electromagnetic Fields
Directory of Open Access Journals (Sweden)
David V. Svintradze
2017-08-01
Full Text Available We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.
Heisenberg symmetry and hypermultiplet manifolds
Directory of Open Access Journals (Sweden)
Ignatios Antoniadis
2016-04-01
Full Text Available We study the emergence of Heisenberg (Bianchi II algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N=2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U(1×U(1 at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg⋉U(1. We finally discuss the realization of the latter by gauging appropriate Sp(2,4 generators in N=2 conformal supergravity.
Harmonic space and quaternionic manifolds
Galperin, A; Ogievetsky, O V
1994-01-01
We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local $Sp(1)$ group and an extra rigid $SU(2)$ group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to $N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic ...
Manifold Matching for High-Dimensional Pattern Recognition
HOTTA, Seiji
2008-01-01
In this chapter manifold matching for high-dimensional pattern classification was described. The topics described in this chapter were summarized as follows: The meaning and effectiveness of manifold matching The similarity between various classifiers from the point of view of manifold matching Accuracy improvement for manifold matching Learning rules for manifold matching Experimental results on handwritten digit datasets showed that manifold matching achieved lower error rates than other cl...
Oh, Hee
2010-01-01
We present recent results on counting and distribution of circles in a given circle packing invariant under a geometrically finite Kleinian group and discuss how the dynamics of flows on geometrically finite hyperbolic $3$ manifolds are related. Our results apply to Apollonian circle packings, Sierpinski curves, Schottky dances, etc.
Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds
Indian Academy of Sciences (India)
Bayram Sahin
2008-11-01
We study harmonic Riemannian maps on locally conformal Kaehler manifolds ($lcK$ manifolds). We show that if a Riemannian holomorphic map between $lcK$ manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the $lcK$ manifold is Kaehler. Then we find similar results for Riemannian maps between $lcK$ manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.
2013-09-26
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Space time manifolds and contact structures
Directory of Open Access Journals (Sweden)
K. L. Duggal
1990-01-01
Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.
Higher Order Hessian Structures on Manifolds
Indian Academy of Sciences (India)
R David Kumar
2005-08-01
In this paper we define th order Hessian structures on manifolds and study them. In particular, when =3, we make a detailed study and establish a one-to-one correspondence between third-order Hessian structures and a certain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also we define second-order geodesics of special second-order connection which gives a geometric characterization of symmetric third-order Hessian structures.
Loops in Reeb Graphs of 2-Manifolds
Energy Technology Data Exchange (ETDEWEB)
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
2004-12-16
Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.
Loops in Reeb Graphs of 2-Manifolds
Energy Technology Data Exchange (ETDEWEB)
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
2003-02-11
Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.
Calabi-Yau Manifolds Over Finite Fields, II
Candelas, Philip; Rodríguez-Villegas, F; Candelas, Philip; Ossa, Xenia de la; Rodriguez-Villegas, Fernando
2004-01-01
We study zeta-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The zeta-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to `see' these curves in the geometry of the quintic. Having these zeta-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the zeta-functions is suggested by an application of the Weil conjectures to Calabi-Yau threefolds: the zeta-functions are rational functions and the degrees of the numerators and denominators are exchanged between the zeta-functions for the manifold and its mirror. It is clear nevertheless that the zeta-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an inter...
Kelley; Dana A. , Farooque; Mohammad , Davis; Keith
2007-10-02
A fuel cell system with improved electrical isolation having a fuel cell stack with a positive potential end and a negative potential, a manifold for use in coupling gases to and from a face of the fuel cell stack, an electrical isolating assembly for electrically isolating the manifold from the stack, and a unit for adjusting an electrical potential of the manifold such as to impede the flow of electrolyte from the stack across the isolating assembly.
Black Strings, Black Rings and State-space Manifold
Bellucci, Stefano
2011-01-01
State-space geometry is considered, for diverse three and four parameter non-spherical horizon rotating black brane configurations, in string theory and $M$-theory. We have explicitly examined the case of unit Kaluza-Klein momentum $D_1D_5P$ black strings, circular strings, small black rings and black supertubes. An investigation of the state-space pair correlation functions shows that there exist two classes of brane statistical configurations, {\\it viz.}, the first category divulges a degenerate intrinsic equilibrium basis, while the second yields a non-degenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating $D_1D_5$ black strings and three charged rotating small black rings consort real degenerate state-space manifolds. Interestingly, arbitrary valued $M_5$-dipole charged rotating circular strings and Maldacena Strominger Witten black rings exhibit non-degenerate, positively curved, comprehensively regular state-space con...
The Grassmannian Manifold and Controllability of the Linear Time-Invariant Control Systems
Directory of Open Access Journals (Sweden)
Shirish M. Deshmukh
2010-07-01
Full Text Available The idea discussed here are mainly to develope some interesting relationship between the differential geometry of certain curves and the controllability of linear time-invariant (LTI control systems without considering any matrix riccati equation. The problem based on the basic concepts of controllability is considered here. The two point boundary value problem (TPBVP is described here as a flow in the Grassmannian manifold. Then a simple solution to determine a control function in the Grassmannian manifold is presented that transfer the system states from initial to final values and satisfies the conditions that are equivalent to the controllability of the systems.
The Hodge theory of projective manifolds
de Cataldo, Mark Andrea
2007-01-01
This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.
A Class of Homogeneous Einstein Manifolds
Institute of Scientific and Technical Information of China (English)
Yifang KANG; Ke LIANG
2006-01-01
A Riemannian manifold (M,g) is called Einstein manifold if its Ricci tensor satisfies r=c·g for some constant c. General existence results are hard to obtain,e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.
Branched standard spines of 3-manifolds
Benedetti, Riccardo
1997-01-01
This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.
CURVATURE COMPUTATIONS OF 2-MANIFOLDS IN IRk
Institute of Scientific and Technical Information of China (English)
Guo-liang Xu; Chandrajit L. Bajaj
2003-01-01
In this paper, we provide simple and explicit formulas for computing Riemannian cur-vatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk with k ≥ 3.
3-manifold groups are virtually residually p
Aschenbrenner, Matthias
2010-01-01
Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is well-known that finitely generated linear groups over fields of characteristic zero are virtually residually $p$ for all but finitely many $p$. In particular, fundamental groups of hyperbolic $3$-manifolds are virtually residually $p$. It is also well-known that fundamental groups of $3$-manifolds are residually finite. In this paper we prove a common generalization of these results: every $3$-manifold group is virtually residually $p$ for all but finitely many~$p$. This gives evidence for the conjecture (Thurston) that fundamental groups of $3$-manifolds are linear groups.
Hierarchical manifold learning for regional image analysis.
Bhatia, Kanwal K; Rao, Anil; Price, Anthony N; Wolz, Robin; Hajnal, Joseph V; Rueckert, Daniel
2014-02-01
We present a novel method of hierarchical manifold learning which aims to automatically discover regional properties of image datasets. While traditional manifold learning methods have become widely used for dimensionality reduction in medical imaging, they suffer from only being able to consider whole images as single data points. We extend conventional techniques by additionally examining local variations, in order to produce spatially-varying manifold embeddings that characterize a given dataset. This involves constructing manifolds in a hierarchy of image patches of increasing granularity, while ensuring consistency between hierarchy levels. We demonstrate the utility of our method in two very different settings: 1) to learn the regional correlations in motion within a sequence of time-resolved MR images of the thoracic cavity; 2) to find discriminative regions of 3-D brain MR images associated with neurodegenerative disease.
Regional manifold learning for disease classification.
Ye, Dong Hye; Desjardins, Benoit; Hamm, Jihun; Litt, Harold; Pohl, Kilian M
2014-06-01
While manifold learning from images itself has become widely used in medical image analysis, the accuracy of existing implementations suffers from viewing each image as a single data point. To address this issue, we parcellate images into regions and then separately learn the manifold for each region. We use the regional manifolds as low-dimensional descriptors of high-dimensional morphological image features, which are then fed into a classifier to identify regions affected by disease. We produce a single ensemble decision for each scan by the weighted combination of these regional classification results. Each weight is determined by the regional accuracy of detecting the disease. When applied to cardiac magnetic resonance imaging of 50 normal controls and 50 patients with reconstructive surgery of Tetralogy of Fallot, our method achieves significantly better classification accuracy than approaches learning a single manifold across the entire image domain.
Particle Filtering on the Audio Localization Manifold
Ettinger, Evan
2010-01-01
We present a novel particle filtering algorithm for tracking a moving sound source using a microphone array. If there are N microphones in the array, we track all $N \\choose 2$ delays with a single particle filter over time. Since it is known that tracking in high dimensions is rife with difficulties, we instead integrate into our particle filter a model of the low dimensional manifold that these delays lie on. Our manifold model is based off of work on modeling low dimensional manifolds via random projection trees [1]. In addition, we also introduce a new weighting scheme to our particle filtering algorithm based on recent advancements in online learning. We show that our novel TDOA tracking algorithm that integrates a manifold model can greatly outperform standard particle filters on this audio tracking task.
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Cohomogeneity Two Actions on Flat Riemannian Manifolds
Institute of Scientific and Technical Information of China (English)
R. MIRZAIE
2007-01-01
In this paper, we study fiat Riemannian manifolds which have codimension two orbits,under the action of a closed and connected Lie group G of isometries. We assume that G has fixedpoints, then characterize M and orbits of M.
Mathematical Background of Formalism of Operator Manifold
Ter-Kazarian, G T
1997-01-01
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The nature of operator manifold provides its elements with both quantum field and geometry aspects, a detailed study of which is a subject of present paper. It yields a quantization of geometry differing in principle from all earlier suggested schemes.
The convexity radius of a Riemannian manifold
Dibble, James
2014-01-01
The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.
Multiply manifolded molten carbonate fuel cells
Energy Technology Data Exchange (ETDEWEB)
Krumpelt, M.; Roche, M.F.; Geyer, H.K.; Johnson, S.A.
1994-08-01
This study consists of research and development activities related to the concept of a molten carbonate fuel cell (MCFC) with multiple manifolds. Objective is to develop an MCFC having a higher power density and a longer life than other MCFC designs. The higher power density will result from thinner gas flow channels; the extended life will result from reduced temperature gradients. Simplification of the gas flow channels and current collectors may also significantly reduce cost for the multiply manifolded MCFC.
Blowing up generalized Kahler 4-manifolds
Cavalcanti, Gil R
2011-01-01
We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.
On some applications of invariant manifolds
Institute of Scientific and Technical Information of China (English)
Xi-Yun Hou; Lin Liu; Yu-Hui Zhao
2011-01-01
Taking transfer orbits of a collinear libration point probe, a lunar probe and an interplanetary probe as examples, some applications of stable and unstable invariant manifolds of the restricted three-body problem are discussed. Research shows that transfer energy is not necessarily conserved when invariant manifolds are used. For the cases in which the transfer energy is conserved, the cost is a much longer transfer time.
Quaternionic-like manifolds and homogeneous twistor spaces.
Pantilie, Radu
2016-12-01
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the 'quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the ρ-quaternionic manifolds. Moreover, the notion of 'heaven space' finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a ρ-quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.
Robinson manifolds and Cauchy-Riemann spaces
Trautman, A
2002-01-01
A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...
Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds
Bento, G C; Oliveira, P R
2010-01-01
In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by the method is guaranteed. Under mild assumptions on the multicriteria function, we prove that each accumulation point (if they exist) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming quasi-convexity of the multicriteria function and non-negative curvature of the Riemannian manifold, we prove full convergence of the sequence to a Pareto critical.
The geometric median on Riemannian manifolds with application to robust atlas estimation.
Fletcher, P Thomas; Venkatasubramanian, Suresh; Joshi, Sarang
2009-03-01
One of the primary goals of computational anatomy is the statistical analysis of anatomical variability in large populations of images. The study of anatomical shape is inherently related to the construction of transformations of the underlying coordinate space, which map one anatomy to another. It is now well established that representing the geometry of shapes or images in Euclidian spaces undermines our ability to represent natural variability in populations. In our previous work we have extended classical statistical analysis techniques, such as averaging, principal components analysis, and regression, to Riemannian manifolds, which are more appropriate representations for describing anatomical variability. In this paper we extend the notion of robust estimation, a well established and powerful tool in traditional statistical analysis of Euclidian data, to manifold-valued representations of anatomical variability. In particular, we extend the geometric median, a classic robust estimator of centrality for data in Euclidean spaces. We formulate the geometric median of data on a Riemannian manifold as the minimizer of the sum of geodesic distances to the data points. We prove existence and uniqueness of the geometric median on manifolds with non-positive sectional curvature and give sufficient conditions for uniqueness on positively curved manifolds. Generalizing the Weiszfeld procedure for finding the geometric median of Euclidean data, we present an algorithm for computing the geometric median on an arbitrary manifold. We show that this algorithm converges to the unique solution when it exists. In this paper we exemplify the robustness of the estimation technique by applying the procedure to various manifolds commonly used in the analysis of medical images. Using this approach, we also present a robust brain atlas estimation technique based on the geometric median in the space of deformable images.
Topology and Closed Timelike Curves I: Dynamics
Monroe, H
2006-01-01
No closed timelike curve (CTC) on a Lorentzian manifold can be continuously deformed as a CTC to a point. Otherwise, any of the point's neighborhoods would contain a CTC, a contradiction as Lorentzian manifolds are locally causally well-behaved. Every CTC must pass through some topological feature, to be called a timelike wormhole, which prevents the it from being deformed to a point. Tipler showed that a closed timelike geodesic exists in a compact Lorentzian manifold if the covering space contains a compact Cauchy surface. A test particle free falling along this geodesic transits the timelike wormhole; in the test particle's frame of reference, the wormhole propagates toward the test particle, exhibiting photon-like behavior. In addition, a space-time that violates chronology at every point can experience topology change consistent with theorems of Geroch and Tipler.
Lattice QCD on Non-Orientable Manifolds
Mages, Simon; Borsanyi, Szabolcs; Fodor, Zoltan; Katz, Sandor; Szabo, Kalman K
2015-01-01
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge, when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the field configuration space becomes connected. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance completely. Here we propose to use a non-orientable manifold, and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is, that translational invariance is preserved up to exponentially small corrections. A Dirac-fermion on a non-orientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to...
New Spinor Fields on Lorentzian 7-Manifolds
Bonora, L
2016-01-01
This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. It extends to higher dimensions the so-called Lounesto spinor fields classification in Minkowski spacetime, which encompasses Dirac, Weyl, Majorana, and more generally flagpoles, flag-dipoles and dipole spinor fields. A generalized classification according to the bilinear covariants was previously studied on Euclidean 7-manifolds. It presents either just one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, by means of such spinors one can introduce a generalized current density which further serves...
Cork twisting exotic Stein 4-manifolds
Akbulut, Selman
2011-01-01
From any 4-dimensional oriented handlebody X without 3- and 4-handles and with $b_2\\geq 1$, we construct arbitrary many compact Stein 4-manifolds which are mutually homeomorphic but not diffeomorphic to each other, so that their topological invariants (their fundamental groups, homology groups, boundary homology groups, and intersection forms) coincide with those of X. We also discuss the induced contact structures on their boundaries. Furthermore, for any smooth 4-manifold pair (Z,Y) such that the complement $Z-\\textnormal{int}\\,Y$ is a handlebody without 3- and 4-handles and with $b_2\\geq 1$, we construct arbitrary many exotic embeddings of a compact 4-manifold Y' into Z, such that Y' has the same topological invariants as Y.
Unknotting tunnels in hyperbolic 3-manifolds
Adams, Colin
2012-01-01
An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions for it to be an unknotting tunnel. In particular, if the vertical geodesic corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover and has short enough length, it must be an unknotting tunnel. Furthermore, we consider a vertical geodesic that satisfies the elder sibling property, which means that in the universal cover, every horoball except the one centered at infinity is connected to a larger horoball by a lift of the vertical geodesic. Such a vertical geodesic with length less than ln(2) is then shown to be an unknotting tunnel.
Duality constructions from quantum state manifolds
Kriel, J N; Scholtz, F G
2015-01-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS_2/CFT_1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et. al. the corresponding state manifol...
Roughly isometric minimal immersions into Riemannian manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
A given metric (length-) space $X$ (whether compact or not) is roughly isometric to any one of its Kanai graphs $G$, which in turn can be {\\em{geometrized}} by considering each edge of $G$ as a 1-dimensional manifold with an associated metric $g$ giving the 'correct' length of the edge. In this t......A given metric (length-) space $X$ (whether compact or not) is roughly isometric to any one of its Kanai graphs $G$, which in turn can be {\\em{geometrized}} by considering each edge of $G$ as a 1-dimensional manifold with an associated metric $g$ giving the 'correct' length of the edge....... In this talk we will mainly be concerned with {\\em{minimal}} isometric immersions of such geometrized approximations $(G, g)$ of $X$ into Riemannian manifolds $N$ with bounded curvature. When such an immersion exists, we will call it an $X$-web in $N$. Such webs admit a natural 'geometric' extension...
Burning invariant manifolds in reactive front propagation
Mahoney, John; Mitchell, Kevin; Solomon, Tom
2011-01-01
We present theory and experiments on the dynamics of reaction fronts in a two-dimensional flow composed of a chain of alternating vortices. Inspired by the organization of passive transport by invariant manifolds, we introduce burning invariant manifolds (BIMs), which act as one-sided barriers to front propagation. The BIMs emerge from the theory when the advection-reaction- diffusion system is recast as an ODE for reaction front elements. Experimentally, we demonstrate how these BIMs can be measured and compare their behavior with simulation. Finally, a topological BIM formalism yields a maximum front propagation speed.
Radio Interferometric Calibration Using a Riemannian Manifold
Yatawatta, Sarod
2013-01-01
In order to cope with the increased data volumes generated by modern radio interferometers such as LOFAR (Low Frequency Array) or SKA (Square Kilometre Array), fast and efficient calibration algorithms are essential. Traditional radio interferometric calibration is performed using nonlinear optimization techniques such as the Levenberg-Marquardt algorithm in Euclidean space. In this paper, we reformulate radio interferometric calibration as a nonlinear optimization problem on a Riemannian manifold. The reformulated calibration problem is solved using the Riemannian trust-region method. We show that calibration on a Riemannian manifold has faster convergence with reduced computational cost compared to conventional calibration in Euclidean space.
The "Parity" Anomaly On An Unorientable Manifold
Witten, Edward
2016-01-01
The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. The "parity" anomaly has traditionally been studied on orientable manifolds only, but recent developments involving topological superconductors have made it clear that one can get more information by asking what happens on an unorientable manifold. In this paper, we analyze the "parity" anomaly for fermions coupled to gauge fields and gravity in $2+1$ dimensions. We consider applications to gapped boundary states of a topological superconductor and to M2-branes in string/M-theory.
Wilson Fermions on a Randomly Triangulated Manifold
Burda, Z; Krzywicki, A
1999-01-01
A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The construction is carried out explicitly in 2-d, on an arbitrary orientable manifold without boundary. It can be easily converted into a computer code. The equivalence, on a sphere, of Majorana fermions and Ising spins in 2-d is rederived. The method can, in principle, be extended to higher dimensions.
Unraveling flow patterns through nonlinear manifold learning.
Tauro, Flavia; Grimaldi, Salvatore; Porfiri, Maurizio
2014-01-01
From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap) to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.
Unraveling flow patterns through nonlinear manifold learning.
Directory of Open Access Journals (Sweden)
Flavia Tauro
Full Text Available From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.
Inertial manifold of the atmospheric equations
Institute of Scientific and Technical Information of China (English)
李建平; 丑纪范
1999-01-01
For a class of nonlinear evolution equations, their global attractors are studied and the existence of their inertial manifolds is discussed using the truncated method. Then, on the basis of the properties of operators of the atmospheric equations, it is proved that the operator equation of the atmospheric motion with dissipation and external forcing belongs to the class of nonlinear evolution equations. Therefore, it is known that there exists an inertial manifold of the atmospheric equations if the spectral gap condition for the dissipation operator is satisfied. These results furnish a basis for further studying the dynamical properties of global attractor of the atmospheric equations and for designing better numerical scheme.
Tangent bundles of Hantzsche-Wendt manifolds
Gaşior, A.; Szczepański, A.
2013-08-01
We formulate a condition for the existence of a SpinC-structure on an oriented flat manifold Mn with H2(Mn,R)=0. We prove that Mn has a SpinC-structure if and only if there exists a homomorphism ɛ:π1(Mn)→SpinC(n) such that λ∘ɛ=h, where h:π1(Mn)→SO(n) is a holonomy homomorphism and λ:SpinC(n)→SO(n) is a standard homomorphism defined. As an application we shall prove that all cyclic Hantzsche-Wendt manifolds do not have the SpinC-structure.
Generalized nonuniform dichotomies and local stable manifolds
Bento, António J G
2010-01-01
We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.
Sigma Models with Negative Curvature
Alonso, Rodrigo; Manohar, Aneesh V.
2016-01-01
We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold H^n, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n,1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values.
On Kähler–Norden Manifolds-Erratum
Indian Academy of Sciences (India)
M Iscan; A A Salimov
2009-02-01
This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler–Norden manifolds using the theory of Tachibana operators is presented.
$\\rm G_2$ holonomy manifolds are superconformal
Díaz, Lázaro O Rodríguez
2016-01-01
We study the chiral de Rham complex (CDR) over a manifold $M$ with holonomy $\\rm G_2$. We prove that the vertex algebra of global sections of the CDR associated to $M$ contains two commuting copies of the Shatashvili-Vafa $\\rm G_2$ superconformal algebra. Our proof is a tour de force, based on explicit computations.
Four-manifolds, geometries and knots
Hillman, Jonathan A
2007-01-01
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...
Einstein constraints on n dimensional compact manifolds
Choquet-Bruhat, Y
2004-01-01
We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions with unscaled sources.
Becker, Katrin; Robbins, Daniel
2015-01-01
In this talk we report on recent progress in describing compactifications of string theory and M-theory on G_2 and Spin(7) manifolds. We include the infinite set of alpha'-corrections and describe the entire tower of massless and massive Kaluza-Klein modes resulting from such compactifications.
Remarks on homogeneous manifolds satisfying Levi conditions
Huckleberry, Alan
2010-01-01
Homogeneous complex manifolds satisfying various types of Levi conditions are considered. Classical results which were of particular interest to Andreotti are recalled. Convexity and concavity properties of flag domains are discussed in some detail. A precise classification of pseudoconvex flag domains is given. It is shown that flag domains which are in a certain sense generic are pseudoconcave.
Exponential estimates of symplectic slow manifolds
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Wulff, C.
2016-01-01
is motivated by a paper of MacKay from 2004. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman...
Modelling of the Manifold Filling Dynamics
DEFF Research Database (Denmark)
Hendricks, Elbert; Chevalier, Alain Marie Roger; Jensen, Michael
1996-01-01
Mean Value Engine Models (MVEMs) are dynamic models which describe dynamic engine variable (or state) responses on time scales slightly longer than an engine event. This paper describes a new model of the intake manifold filling dynamics which is simple and easy to calibrate for use in engine con...
Duality constructions from quantum state manifolds
Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.
2015-11-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.
Heat Kernel Renormalization on Manifolds with Boundary
Albert, Benjamin I.
2016-01-01
In the monograph Renormalization and Effective Field Theory, Costello gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. In this paper, we extend Costello's renormalization procedure to a class of manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Geometrical description of denormalized thermodynamic manifold
Institute of Scientific and Technical Information of China (English)
Wu Li-Ping; Sun Hua-Fei; Cao Li-Mei
2009-01-01
In view of differential geometry,the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometrical metrics is obtained. Moreover an example is used to illustrate our conclusions.
On homological stability for configuration spaces on closed background manifolds
Cantero, Federico; Palmer, Martin
2014-01-01
We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the background manifold is closed, in which case the classical stabilisation map does not exist. We then establish conditions on the manifold and on the coefficients under which homological stability holds for configuration spaces on closed manifolds. These conditio...
Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds
Ivashkovich, S
2011-01-01
We prove the Royden's Lemma for complex Hilbert manifolds, i.e., that a holomorphic imbedding of the closure of a finite dimensional, strictly pseudoconvex domain into a complex Hilbert manifold extends to a biholomorphic mapping onto a product of this domain with the unit ball in Hilbert space. This reduces several problems concerning complex Hilbert manifolds to open subsets of a Hilbert space. As an illustration we prove some results on generalized loop spaces of complex manifolds.
Fluid manifold design for a solar energy storage tank
Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.
1975-01-01
A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.
On Self-Mapping Degrees of S3- Geometry Manifolds
Institute of Scientific and Technical Information of China (English)
Xiao Ming DU
2009-01-01
In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self-mapping degrees of all closed orientable 3-manifold in Thurston's picture.
Canonical connection on a class of Riemannian almost product manifolds
Mekerov, Dimitar
2009-01-01
The canonical connection on a Riemannian almost product manifolds is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with nonintegrable almost product structure.
NUMERICAL MANIFOLD METHOD AND ITS APPLICATION IN UNDERGROUND POENINGS
Institute of Scientific and Technical Information of China (English)
王芝银; 李云鹏
1998-01-01
A brief introduction is made for the Numerical Manifold Method and its analysingprocess in rock mechanics. Some aspects of the manifold method are improved in implementingprocess according to the practice of excavating underground openings. Corresponding formulasare given and a computer program of the Numerical Manifold Method has been completed in thispaper.
Wave equations on anti self dual (ASD) manifolds
Bashingwa, Jean-Juste; Kara, A. H.
2017-06-01
In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.
Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
Directory of Open Access Journals (Sweden)
Yvette Kosmann-Schwarzbach
2008-01-01
Full Text Available After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.
Local topology in deformation spaces of hyperbolic 3-manifolds
Brock, Jeffrey F; Canary, Richard D; Minsky, Yair N
2009-01-01
We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar results are obtained for deformation spaces of acylindrical 3-manifolds and Bers slices.
On the conformal geometry of transverse Riemann Lorentz manifolds
Aguirre, E.; Fernández, V.; Lafuente, J.
2007-06-01
Physical reasons suggested in [J.B. Hartle, S.W. Hawking, Wave function of the universe, Phys. Rev. D41 (1990) 1815-1834] for the Quantum Gravity Problem lead us to study type-changing metrics on a manifold. The most interesting cases are Transverse Riemann-Lorentz Manifolds. Here we study the conformal geometry of such manifolds.
Einstein Metrics, Four-Manifolds, and Differential Topology
2004-01-01
This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently encapsulates those aspects of Seiberg-Witten theory most relevant to the study of Riemannian variational problems on 4-manifolds.
Eikonal slant helices and eikonal Darboux helices in 3-dimensional pseudo-Riemannian manifolds
Önder, Mehmet; Ziplar, Evren
2013-01-01
In this study, we give definitions and characterizations of eikonal slant helices, eikonal Darboux helices and non-normed eikonal Darboux helices in 3-dimensional pseudo- Riemannian manifold M . We show that every eikonal slant helix is also an eikonal Darboux helix for timelike and spacelike curves. Furthermore, we obtain that if the non-null curve a is a non-normed eikonal Darboux helix, then a is an eikonal slant helix if and only if 2 2 e 3k +e1t = constant, where k and t are curvature an...
Eikonal Slant Helices and Eikonal Darboux Helices In 3-Dimensional Riemannian Manifolds
Önder, Mehmet; Ziplar, Evren; Kaya, Onur
2013-01-01
In this study, we give definitions and characterizations of eikonal slant helix curves, eikonal Darboux helices and non-normed eikonal Darboux helices in three dimensional Riemannian manifold 3 M . We show that every eikonal slant helix is also an eikonal Darboux helix. Furthermore, we obtain that if the curve a is a non-normed eikonal Darboux helix, then a is an eikonal slant helix if and only if k 2 +t 2 = constant, where k and t are curvature and torsion of a, respectively.
Knot Optimization for Biharmonic B-splines on Manifold Triangle Meshes.
Hou, Fei; He, Ying; Qin, Hong; Hao, Aimin
2017-09-01
Biharmonic B-splines, proposed by Feng and Warren, are an elegant generalization of univariate B-splines to planar and curved domains with fully irregular knot configuration. Despite the theoretic breakthrough, certain technical difficulties are imperative, including the necessity of Voronoi tessellation, the lack of analytical formulation of bases on general manifolds, expensive basis re-computation during knot refinement/removal, being applicable for simple domains only (e.g., such as euclidean planes, spherical and cylindrical domains, and tori). To ameliorate, this paper articulates a new biharmonic B-spline computing paradigm with a simple formulation. We prove that biharmonic B-splines have an equivalent representation, which is solely based on a linear combination of Green's functions of the bi-Laplacian operator. Consequently, without explicitly computing their bases, biharmonic B-splines can bypass the Voronoi partitioning and the discretization of bi-Laplacian, enable the computational utilities on any compact 2-manifold. The new representation also facilitates optimization-driven knot selection for constructing biharmonic B-splines on manifold triangle meshes. We develop algorithms for spline evaluation, data interpolation and hierarchical data decomposition. Our results demonstrate that biharmonic B-splines, as a new type of spline functions with theoretic and application appeal, afford progressive update of fully irregular knots, free of singularity, without the need of explicit parameterization, making it ideal for a host of graphics tasks on manifolds.
Yang, Dongmei; Li, Junhui; Ding, Yiting; Tyree, Melvin T
2017-03-01
The physiological advantages of negative turgor pressure, Pt , in leaf cells are water saving and homeostasis of reactants. This paper advances methods for detecting the occurrence of negative Pt in leaves. Biomechanical models of pressure-volume (PV) curves predict that negative Pt does not change the linearity of PV curve plots of inverse balance pressure, PB , versus relative water loss, but it does predict changes in either the y-intercept or the x-intercept of the plots depending on where cell collapse occurs in the PB domain because of negative Pt . PV curve analysis of Robinia leaves revealed a shift in the x-intercept (x-axis is relative water loss) of PV curves, caused by negative Pt of palisade cells. The low x-intercept of the PV curve was explained by the non-collapse of palisade cells in Robinia in the PB domain. Non-collapse means that Pt smoothly falls from positive to negative values with decreasing cell volume without a dramatic change in slope. The magnitude of negative turgor in non-collapsing living cells was as low as -1.3 MPa and the relative volume of the non-collapsing cell equaled 58% of the total leaf cell volume. This study adds to the growing evidence for negative Pt . © 2016 John Wiley & Sons Ltd.
Sparks, Rachel; Madabhushi, Anant
2012-03-01
Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because Gleason grading is done manually by a pathologist visually examining glass (or digital) slides, subtle morphologic and architectural differences of histological attributes may result in grading errors and hence cause high inter-observer variability. Recently some researchers have proposed computerized decision support systems to automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving nonlinear relationships between object instances. Classification can then be performed in the low dimensional space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain the low dimensional manifold to a specific range of possible manifold shapes, the range being determined via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1) identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM, and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a manifold constrained by the SSMM. We
Local Schrodinger flow into Kahler manifolds
Institute of Scientific and Technical Information of China (English)
DlNG; Weiyue(
2001-01-01
［1］Ding, W. Y. , Wang, Y. D. , Schrodinger flows of maps into symplectic manifolds, Science in China, Ser. A, 1998, 41(7): 746.［2］Landau, L. D., Lifshitz, E. M., On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys. Z.Sowj., 1935, 8: 153; reproduced in Collected Papers of L. D. Landau, New York: Pergaman Press, 1965, 101－114.［3］Faddeev, L., Takhtajan, L. A. , Hamiltonian Methods in the Theory of Solitons, Berlin-Heidelberg-New York: Springer-Verlag, 1987.［4］Nakamura, K., Sasada, T., Soliton and wave trains in ferromagnets, Phys. Lett. A, 1974, 48: 321.［5］Zhou, Y. , Guo, B. , Tan, S. , Existence and uniqueness of smooth solution for system of ferromagnetic chain, Science in China, Ser. A, 1991, 34(3): 257.［6］Pang, P. , Wang, H. , Wang, Y. D. , Schrodinger flow of maps into Kahler manifolds, Asian J. of Math. , in press.［7］Wang, H. , Wang, Y. D. , Global inhomogeneous Schrodinger flow, Int. J. Math., 2000, 11: 1079.［8］Pang, P., Wang, H., Wang, Y. D., Local existence for inhomogeneous Schrodinger flow of maps into Kahler manifolds,Acta Math. Sinica, English Series, 2000, 16: 487.［9］Temg, C. L., Uhlenbeck, K., Schrodinger flows on Grassmannians, in Integrable Systems, Geometry and Topology,Somervi11e, MA: International Press, in press.［10］Chang, N., Shatah, J., Uhlenbeck, K., Schrodinger maps, Commun. Pure Appl. Math., 2000, 53: 157.［11］Wang, Y. D., Ferromagnetic chain equation from a closed Riemannian manifold into S2, Int. J. Math., 1995, 6: 93.［12］Wang, Y. D., Heisenberg chain systems from compact manifolds into S2, J. Math. Phys., 1998, 39(1): 363.［13］Sulem, P., Sulem, C., Bardos, C., On the continuous limit for a system of classical spins, Commun. Math. Phys., 1986,107: 431.［14］Aubin, T., Nonlinear Analysis on Manifolds, Monge-Ampère Equations, Berlin-Heidelberg-New York: Springer-Verlag,1982.［15］Eells, J. , Lemaire, L. , Another report on harmonic maps, Bull. London
Lower bounds on volumes of hyperbolic Haken 3-manifolds
Agol, Ian; Storm, Peter A.; Thurston, William P.
2007-10-01
We prove a volume inequality for 3-manifolds having C^{0} metrics ``bent'' along a surface and satisfying certain curvature conditions. The result makes use of Perelman's work on the Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume of orientable hyperbolic 3-manifolds. An appendix compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.
THEORETICAL STUDY OF THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
LUO Shao-ming; ZHANG Xiang-wei; L(U) Wen-ge; JIANG Dong-ru
2005-01-01
The three-dimensional numerical manifold method(NMM) is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.
New Calabi-Yau Manifolds with Small Hodge Numbers
Candelas, Philip
2008-01-01
It is known that many Calabi-Yau manifolds form a connected web. The question of whether all Calabi-Yau manifolds form a single web depends on the degree of singularity that is permitted for the varieties that connect the distinct families of smooth manifolds. If only conifolds are allowed then, since shrinking two-spheres and three-spheres to points cannot affect the fundamental group, manifolds with different fundamental groups will form disconnected webs. We examine these webs for the tip of the distribution of Calabi-Yau manifolds where the Hodge numbers (h^{11}, h^{21}) are both small. In the tip of the distribution the quotient manifolds play an important role. We generate via conifold transitions from these quotients a number of new manifolds. These include a manifold with \\chi =-6 that is an analogue of the Tian-Yau manifold and manifolds with an attractive structure that may prove of interest for string phenomenology. We also examine the relation of some of these manifolds to the remarkable Gross-Pop...
Manifold learning-based subspace distance for machinery damage assessment
Sun, Chuang; Zhang, Zhousuo; He, Zhengjia; Shen, Zhongjie; Chen, Binqiang
2016-03-01
Damage assessment is very meaningful to keep safety and reliability of machinery components, and vibration analysis is an effective way to carry out the damage assessment. In this paper, a damage index is designed by performing manifold distance analysis on vibration signal. To calculate the index, vibration signal is collected firstly, and feature extraction is carried out to obtain statistical features that can capture signal characteristics comprehensively. Then, manifold learning algorithm is utilized to decompose feature matrix to be a subspace, that is, manifold subspace. The manifold learning algorithm seeks to keep local relationship of the feature matrix, which is more meaningful for damage assessment. Finally, Grassmann distance between manifold subspaces is defined as a damage index. The Grassmann distance reflecting manifold structure is a suitable metric to measure distance between subspaces in the manifold. The defined damage index is applied to damage assessment of a rotor and the bearing, and the result validates its effectiveness for damage assessment of machinery component.
Angles between Curves in Metric Measure Spaces
Directory of Open Access Journals (Sweden)
Han Bang-Xian
2017-08-01
Full Text Available The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.
Topological Field Theory and Rational Curves
Aspinwall, Paul S; Aspinwall, Paul S.; Morrison, David R.
1993-01-01
We analyze the superstring propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear sigma-model and the structure of rational curves on the Calabi-Yau manifold. We study in detail the case of the world-sheet of the string being mapped to a multiple cover of an isolated rational curve and we show that a natural compactification of the moduli space of such a multiple cover leads to a formula in agreement with a conjecture by Candelas, de la Ossa, Green and Parkes.
Constructing Dualities from Quantum State Manifolds
van Zyl, H J R
2015-01-01
The thesis develops a systematic procedure to construct semi-classical gravitational duals from quantum state manifolds. Though the systems investigated are simple quantum mechanical systems without gauge symmetry many familiar concepts from the conventional gauge/gravity duality come about in a very natural way. The investigation of the low-dimensional manifolds link existing results in the $AdS_2/CFT_1$ literature. We are able to extend these in various ways and provide an explicit dictionary. The higher dimensional investigation is also concluded with a simple dictionary, but this dictionary requires the inclusion of many bulk coordinates. Consequently further work is needed to relate these results to existing literature. Possible ways to achieve this are discussed.
Dynamical systems on 2- and 3-manifolds
Grines, Viacheslav Z; Pochinka, Olga V
2016-01-01
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are present...
New spinor fields on Lorentzian 7-manifolds
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA),Via Bonomea 265, 34136 Trieste (Italy); Rocha, Roldão da [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC,Avenida dos Estados, 5001, Santo André (Brazil)
2016-01-21
This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. The previously investigated Riemannian case is characterized by either one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general complex case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, these spinors can define a generalized current density which further defines a time Killing vector at the spatial infinity.
Manifold Learning by Preserving Distance Orders.
Ataer-Cansizoglu, Esra; Akcakaya, Murat; Orhan, Umut; Erdogmus, Deniz
2014-03-01
Nonlinear dimensionality reduction is essential for the analysis and the interpretation of high dimensional data sets. In this manuscript, we propose a distance order preserving manifold learning algorithm that extends the basic mean-squared error cost function used mainly in multidimensional scaling (MDS)-based methods. We develop a constrained optimization problem by assuming explicit constraints on the order of distances in the low-dimensional space. In this optimization problem, as a generalization of MDS, instead of forcing a linear relationship between the distances in the high-dimensional original and low-dimensional projection space, we learn a non-decreasing relation approximated by radial basis functions. We compare the proposed method with existing manifold learning algorithms using synthetic datasets based on the commonly used residual variance and proposed percentage of violated distance orders metrics. We also perform experiments on a retinal image dataset used in Retinopathy of Prematurity (ROP) diagnosis.
Adaptive graph construction for Isomap manifold learning
Tran, Loc; Zheng, Zezhong; Zhou, Guoqing; Li, Jiang
2015-03-01
Isomap is a classical manifold learning approach that preserves geodesic distance of nonlinear data sets. One of the main drawbacks of this method is that it is susceptible to leaking, where a shortcut appears between normally separated portions of a manifold. We propose an adaptive graph construction approach that is based upon the sparsity property of the l1 norm. The l1 enhanced graph construction method replaces k-nearest neighbors in the classical approach. The proposed algorithm is first tested on the data sets from the UCI data base repository which showed that the proposed approach performs better than the classical approach. Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.
Cosmic Topology of Double Action Manifolds
Aurich, Ralf
2012-01-01
The cosmic microwave background (CMB) anisotropies in spherical 3-spaces with a non-trivial topology are studied. This paper discusses the special class of the so-called double action manifolds, which are for the first time analysed with respect to their CMB anisotropies. The CMB anisotropies are computed for all double action manifolds generated by a dihedral and a cyclic group with a group order of up to 180 leading to 33 different topologies. Several spaces are found which show a suppression of the CMB anisotropies on large angular distances as it is found on the real CMB sky. It turns out that these spaces possess fundamental cells defined as Voronoi domains which are close to highly symmetric polyhedra like Platonic or Archimedean ones.
Geometry of manifolds with area metric
Schuller, F P
2005-01-01
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, showing that a general area metric is generated by a finite collection of metrics rather than by a single one. Employing curvature invariants for area metric manifolds we devise an entirely new class of gravity theories with inherently stringy character, and discuss gauge matter actions.
Transversality for Cyclic Negative Feedback Systems
2014-01-01
Transversality of stable and unstable manifolds of hyperbolic periodic trajectories is proved for monotone cyclic systems with negative feedback. Such systems in general are not in the category of monotone dynamical systems in the sense of Hirsch. Our main tool utilized in the proofs is the so-called cone of high rank. We further show that stable and unstable manifolds between a hyperbolic equilibrium and a hyperbolic periodic trajectory, or between two hyperbolic equilibria with different di...
BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS
Institute of Scientific and Technical Information of China (English)
钟同德; 钟春平
2003-01-01
Using non-linear connection of Finsler manifold M, the existence of localcoordinates which is normalized at a point x is proved, and the Laplace operator △ on1-form of M is defined by non-linear connection and its curvature tensor. After proving themaximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theoremof Killing vectors and harmonic 1-form are obtained.
Lightlike Submanifolds of Indefinite Sasakian Manifolds
Directory of Open Access Journals (Sweden)
K. L. Duggal
2007-01-01
submanifolds of indefinite Sasakian manifolds. Then, we introduce a general notion of contact Cauchy-Riemann (CR lightlike submanifolds and study the geometry of leaves of their distributions. We also study a class, namely, contact screen Cauchy-Riemann (SCR lightlike submanifolds which include invariant and screen real subcases. Finally, we prove characterization theorems on the existence of contact SCR, screen real, invariant, and contact CR minimal lightlike submanifolds.
Proper holomorphic mappings between hyperbolic product manifolds
Janardhanan, Jaikrishnan
2011-01-01
We generalize a result of Remmert and Stein, on proper holomorphic mappings between domains that are products of certain planar domains, to finite proper holomorphic mappings between complex manifolds that are products of hyper- bolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, our proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.
Symplectic Manifolds, Coherent States and Semiclassical Approximation
Rajeev, S G; Sen, S; Sen, Siddhartha
1994-01-01
We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using coherent state techniques. These path integrals can be evaluated exactly by semiclassical methods, thus providing examples of localisation formula. Along the way, we also give a local coordinate description for a class of Grassmannians.
Nonsmoothable Involutions on Spin 4-Manifolds
Indian Academy of Sciences (India)
Changtao Xue; Ximin Liu
2011-02-01
Let be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to $n(-E_8)\\oplus mH$, where is the hyperbolic form. In this paper, we prove that for such that $n≡ 2\\mathrm{mod} 4$, there exists a locally linear pseudofree $\\mathbb{Z}_2$-action on which is nonsmoothable with respect to any possible smooth structure on .
Manifold learning for image-based breathing gating with application to 4D ultrasound.
Wachinger, Christian; Yigitsoy, Mehmet; Navab, Nassir
2010-01-01
Breathing motion leads to a significant displacement and deformation of organs in the abdominal region. This makes the detection of the breathing phase for numerous applications necessary. We propose a new, purely image-based respiratory gating method for ultrasound. Further, we use this technique to provide a solution for breathing affected 4D ultrasound acquisitions with a wobbler probe. We achieve the gating with Laplacian eigenmaps, a manifold learning technique, to determine the low-dimensional manifold embedded in the high-dimensional image space. Since Laplacian eigenmaps assign each ultrasound frame a coordinate in low-dimensional space by respecting the neighborhood relationship, they are well suited for analyzing the breathing cycle. For the 4D application, we perform the manifold learning for each angle, and consecutively, align all the local curves and perform a curve fitting to achieve a globally consistent breathing signal. We performed the image-based gating on several 2D and 3D ultrasound datasets over time, and quantified its very good performance by comparing it to measurements from an external gating system.
Isometry group and geodesics of the Wagner lift of a riemannian metric on two-dimensional manifold
B., José Ricardo Arteaga
2010-01-01
In this paper we construct a functor from the category of two-dimensional Riemannian manifolds to the category of three-dimensional manifolds with generalized metric tensors. For each two-dimensional oriented Riemannian manifold $(M,g)$ we construct a metric tensor $\\hat g$ (in general, with singularities) on the total space $SO(M,g)$ of the principal bundle of the positively oriented orthonormal frames on $M$. We call the metric $\\hat g$ the Wagner lift of $g$. We study the relation between the isometry groups of $(M,g)$ and $(SO(M,g),\\hat g)$. We prove that the projections of the geodesics of $(SO(M,g),\\hat g)$ onto $M$ are the curves which satisfy the equation \\begin{equation*} \
Three-manifolds class field theory (Homology of coverings for a non-virtually Haken manifold)
Reznikov, A G
1996-01-01
This is a first in a series of papers, devoted to the relation betwwen three-manifolds and number fields. The present paper studies first homology of finite coverings of a three-manifold with primary interest in the Thurston $b_1$ conjecture.The main result reads: if $M$ does not yield the Thurston conjecture, then the pro-p completion of its fundamental group is a Poincaré duality pro-p group. Conceptually, it means that we have a ``p-adic'' three-manifold. We develop several algebraic techniques, including a new powerful specral seguence, to actually compute homology of coverings, assumong only information on homology of $M$, a thing never done before.A number of applications to the structure of finite group cohomology rings is also given.
A new approach to curved projective superspace
Butter, Daniel
2014-01-01
We present a new formulation of curved projective superspace. The 4D N=2 supermanifold M^{4|8} (four bosonic and eight Grassmann coordinates) is extended by an auxiliary SU(2) manifold, which involves introducing a vielbein and related connections on the full M^{7|8} = M^{4|8} x SU(2). Constraints are chosen so that it is always possible to return to the central gauge where the auxiliary SU(2) manifold largely decouples from the curved manifold M^{4|8} describing 4D N=2 conformal supergravity. We introduce the relevant projective superspace action principle in the analytic subspace of M^{7|8} and construct its component reduction in terms of a five-form J living on M^4 x C, with C a contour in SU(2). This approach is inspired by and generalizes the original approach taken in arXiv:0805.4683 and related works, which can be identified with a complexified version of the central gauge of the formulation presented here.
Integrable systems and symmetric products of curves
Vanhaecke, P
1994-01-01
show how there is associated to each non-constant polynomial F(x,y) a completely integrable system with polynomial invariants on \\Rd and on \\C{2d} for each d\\geq1; in fact the invariants are not only in involution for one Poisson bracket, but for a large class of polynomial Poisson brackets, indexed by the family of polynomials in two variables. We show that the complex invariant manifolds are isomorphic to affine parts of d-fold symmetric products of a deformation of the algebraic curve F(x,y)=0, and derive the structure of the real invariant manifolds from it. We also exhibit Lax equations for the hyperelliptic case (i.e., when F(x,y) is of the form y^2+f(x)) and we show that in this case the invariant manifolds are affine parts of distinguished (non-linear) subvarieties of the Jacobians of the curves. As an application the geometry of the H\\'enon-Heiles hierarchy --- a family of superimposable integrable polynomial potentials on the plane --- is revealed and Lax equations for the hierarchy are given.
Generalized Calabi-Yau manifolds and the mirror of a rigid manifold
Candelas, Philip; Parkes, L
1993-01-01
We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories with $c=9$ and so are perfectly good for compactifying the heterotic string to the four dimensions of space-time. As a check of mirror symmetry we compute the structure of the space of complex structures of the mirror and check that this reproduces the known results for the Yukawa couplings and metric appropriate to the Kahler class parameters on the Z orbifold together with their instanton corrections.
A Critical Centre-Stable Manifold for the Schroedinger Equation in Three Dimensions
Beceanu, Marius
2009-01-01
Consider the H^{1/2}-critical Schroedinger equation with a cubic nonlinearity in R^3, i \\partial_t \\psi + \\Delta \\psi + |\\psi|^2 \\psi = 0. It admits an eight-dimensional manifold of periodic solutions called solitons e^{i(\\Gamma + vx - t|v|^2 + \\alpha^2 t)} \\phi(x-2tv-D, \\alpha), where \\phi(x, \\alpha) is a positive ground state solution of the semilinear elliptic equation -\\Delta \\phi + \\alpha^2\\phi = \\phi^3. We prove that in the neighborhood of the soliton manifold there exists a H^{1/2} real analytic manifold N of asymptotically stable solutions of the Schroedinger equation, meaning they are the sum of a moving soliton and a dispersive term. Furthermore, a solution starting on N remains on N for all positive time and for some finite negative time and N can be identified as the centre-stable manifold for this equation. The proof is based on the method of modulation, introduced by Soffer and Weinstein and adapted by Schlag to the L^2-supercritical case. Novel elements include a different linearization and a S...
Does Negative Type Characterize the Round Sphere?
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2007-01-01
We discuss the measure theoretic metric invariants extent, mean distance and symmetry ratio and their relation to the concept of negative type of a metric space. A conjecture stating that a compact Riemannian manifold with symmetry ratio 1 must be a round sphere, was put forward in a previous paper....... We resolve this conjecture in the class of Riemannian symmetric spaces by showing, that a Riemannian manifold with symmetry ratio 1 must be of negative type and that the only compact Riemannian symmetric spaces of negative type are the round spheres....
The Ricci Curvature of Half-flat Manifolds
Ali, T; Ali, Tibra; Cleaver, Gerald B.
2007-01-01
We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of half-flat manifolds by exploiting the relationship between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our expressions are tested for Iwasawa and more general nilpotent manifolds. We also derive expressions, in the language of Calabi-Yau moduli spaces, for the torsion classes and the Ricci curvature of the \\emph{particular} half-flat manifolds that arise naturally via mirror symmetry in flux compactifications. Using these expressions we then derive a constraint on the K\\"ahler moduli space of type II string theory on these half-flat manifolds.
Complex synchronization manifold in coupled time-delayed systems
Energy Technology Data Exchange (ETDEWEB)
Hoang, Thang Manh, E-mail: hmt@mail.hut.edu.v [Signal and Information Processing Laboratory, Faculty of Electronics and Telecommunications, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi (Viet Nam)
2011-01-15
Research highlights: The complex synchronization manifold in coupled multiple time delay systems is demonstrated for the first time. The complex synchronization manifold is in the form of sum of multiple simple manifolds. The equation for driving signal is the sum of nonlinearly transformed components of delayed state variable. - Abstract: In the present paper, the complex synchronization manifold generated in coupled multiple time delay systems is demonstrated for the first time. There, the manifold is in the form of sum of multiple simple manifolds. The structure of master is identical to that of slave. The equation for driving signal is the sum of nonlinearly transformed components of delayed state variable. The specific examples will demonstrate and verify the effectiveness of the proposed model.
Regional manifold learning for deformable registration of brain MR images.
Ye, Dong Hye; Hamm, Jihun; Kwon, Dongjin; Davatzikos, Christos; Pohl, Kilian M
2012-01-01
We propose a method for deformable registration based on learning the manifolds of individual brain regions. Recent publications on registration of medical images advocate the use of manifold learning in order to confine the search space to anatomically plausible deformations. Existing methods construct manifolds based on a single metric over the entire image domain thus frequently miss regional brain variations. We address this issue by first learning manifolds for specific regions and then computing region-specific deformations from these manifolds. We then determine deformations for the entire image domain by learning the global manifold in such a way that it preserves the region-specific deformations. We evaluate the accuracy of our method by applying it to the LPBA40 dataset and measuring the overlap of the deformed segmentations. The result shows significant improvement in registration accuracy on cortex regions compared to other state of the art methods.
How to Find the Holonomy Algebra of a Lorentzian Manifold
Galaev, Anton S.
2015-02-01
Manifolds with exceptional holonomy play an important role in string theory, supergravity and M-theory. It is explained how one can find the holonomy algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de Rham and Wu decompositions, this problem is reduced to the case of locally indecomposable manifolds. In the case of locally indecomposable Riemannian manifolds, it is known that the holonomy algebra can be found from the analysis of special geometric structures on the manifold. If the holonomy algebra of a locally indecomposable Lorentzian manifold ( M, g) of dimension n is different from , then it is contained in the similitude algebra . There are four types of such holonomy algebras. Criterion to find the type of is given, and special geometric structures corresponding to each type are described. To each there is a canonically associated subalgebra . An algorithm to find is provided.
The Structure of some Classes of -Contact Manifolds
Indian Academy of Sciences (India)
Mukut Mani Tripathi; Mohit Kumar Dwivedi
2008-08-01
We study projective curvature tensor in -contact and Sasakian manifolds. We prove that (1) if a -contact manifold is quasi projectively flat then it is Einstein and (2) a -contact manifold is -projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a -contact manifold to be quasi projectively flat and -projectively flat are obtained. We also prove that for a (2+1)-dimensional Sasakian manifold the conditions of being quasi projectively flat, -projectively flat and locally isometric to the unit sphere $S^{2n+1}(1)$ are equivalent. Finally, we prove that a compact -projectively flat -contact manifold with regular contact vector field is a principal $S^1$-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4.
Two-phase Flow Distribution in Heat Exchanger Manifolds
Vist, Sivert
2004-01-01
The current study has investigated two-phase refrigerant flow distribution in heat exchange manifolds. Experimental data have been acquired in a heat exchanger test rig specially made for measurement of mass flow rate and gas and liquid distribution in the manifolds of compact heat exchangers. Twelve different manifold designs were used in the experiments, and CO2 and HFC-134a were used as refrigerants.
P-connection on Riemannian almost product manifolds
Mekerov, Dimitar
2009-01-01
In the present work, we introduce a linear connection (preserving the almost product structure and the Riemannian metric) on Riemannian almost product manifolds. This connection, called P-connection, is an analogue of the first canonical connection of Lichnerowicz in the Hermitian geometry and the B-connection in the geometry of the almost complex manifolds with Norden metric. Particularly, we consider the P-connection on a the class of manifolds with nonintegrable almost product structure.
Some hyperbolic three-manifolds that bound geometrically
KOLPAKOV, Alexander; Martelli, Bruno; Tschantz, Steven
2015-01-01
A closed connected hyperbolic $n$-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic $(n+1)$-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many manifolds that bound geometrically in every dimension. We construct here infinitely many explicit examples in dimension $n=3$ using right-angled dodecahedra and $120$-cells and a simple colouring technique introduced by M. Davis and T. Januszkiewicz. Namely, fo...
Notes on holonomy matrices of hyperbolic 3-manifolds with cusps
Fukui, Fumitaka
2013-01-01
In this paper, we give a method to construct holonomy matrices of hyperbolic 3-manifolds by extending the known method of hyperbolic 2-manifolds. It enables us to consider hyperbolic 3-manifolds with nontrivial holonomies. We apply our method to an ideal tetrahedron and succeed in making the holonomies nontrivial. We also derive the partition function of the ideal tetrahedron with nontrivial holonomies by using the duality proposed by Dimofte, Gaiotto and Gukov.
Logarithm Laws for Equilibrium States in Negative Curvature
Paulin, Frédéric; Pollicott, Mark
2016-08-01
Let M be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure m F associated with a potential F. We compute the Hausdorff dimension of the conditional measures of m F . We study the m F -almost sure asymptotic penetration behaviour of locally geodesic lines of M into small neighbourhoods of closed geodesics, and of other compact (locally) convex subsets of M. We prove Khintchine-type and logarithm law-type results for the spiraling of geodesic lines around these objects. As an arithmetic consequence, we give almost sure Diophantine approximation results of real numbers by quadratic irrationals with respect to general Hölder quasi-invariant measures.
Frobenius manifolds, quantum cohomology, and moduli spaces
Manin, Yuri I
1999-01-01
This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the con
Becker, Katrin; Becker, Melanie; Robbins, Daniel
2015-11-01
In this talk we report on recent progress in describing compactifications of string theory and M-theory on G2 and Spin(7) manifolds. We include the infinite set of α’-corrections and describe the entire tower of massless and massive Kaluza-Klein modes resulting from such compactifications. Contribution to the ‘Focus Issue on Gravity, Supergravity and Fundamental Physics: the Richard Arnowitt Symposium’, to be published in Physica Scripta. Based on a talk delivered by Becker at the workshop ‘Superstring Perturbation Theory’ at the Perimeter Institute, 22-24 April 2015.
Semiclassical Asymptotics on Manifolds with Boundary
Koldan, Nilufer; Shubin, Mikhail
2008-01-01
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.
Lefschetz Fibrations on Compact Stein Manifolds
Akbulut, Selman
2010-01-01
Here we prove that a compact Stein manifold W of dimension 2n+2>4 admits a Lefschetz fibration over the 2-disk with Stein fibers, such that the monodromy of the fibration is a symplectomorphism induced by compositions of "generalized Dehn twists" along imbedded n-spheres on the generic fiber. Also, the open book on the boundary of W, which is determined by the fibration, is compatible with the contact structure induced by the Stein structure. This generalizes the Stein surface case of n=1, previously proven by Loi-Piergallini and Akbulut-Ozbagci.
Manifold parameter space and its applications
Sato, Atsushi
2004-11-01
We review the several features of the new parameter space which we presented in the previous paper, and show the differentiable manifold properties of this parameter space coordinate. Using this parameter coordinate we calculate three Feynman amplitudes of the vacuum polarization with a gluon loop, a quark loop and a ghost loop in QCD and show that the results are perfectly equal to those of the usual calculations by the Feynman parametrization technique in the scheme of the dimensional regularization. Then we try to calculate the anomalous magnetic moment of an on-shell quark in QCD by using the dimensional regularization, our new parametrization and integral method.
Laplacian embedded regression for scalable manifold regularization.
Chen, Lin; Tsang, Ivor W; Xu, Dong
2012-06-01
Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real
Optical manifold for light-emitting diodes
Chaves, Julio C.; Falicoff, Waqidi; Minano, Juan C.; Benitez, Pablo; Parkyn, Jr., William A.; Alvarez, Roberto; Dross, Oliver
2008-06-03
An optical manifold for efficiently combining a plurality of blue LED outputs to illuminate a phosphor for a single, substantially homogeneous output, in a small, cost-effective package. Embodiments are disclosed that use a single or multiple LEDs and a remote phosphor, and an intermediate wavelength-selective filter arranged so that backscattered photoluminescence is recycled to boost the luminance and flux of the output aperture. A further aperture mask is used to boost phosphor luminance with only modest loss of luminosity. Alternative non-recycling embodiments provide blue and yellow light in collimated beams, either separately or combined into white.
Multimodal manifold-regularized transfer learning for MCI conversion prediction.
Cheng, Bo; Liu, Mingxia; Suk, Heung-Il; Shen, Dinggang; Zhang, Daoqiang
2015-12-01
As the early stage of Alzheimer's disease (AD), mild cognitive impairment (MCI) has high chance to convert to AD. Effective prediction of such conversion from MCI to AD is of great importance for early diagnosis of AD and also for evaluating AD risk pre-symptomatically. Unlike most previous methods that used only the samples from a target domain to train a classifier, in this paper, we propose a novel multimodal manifold-regularized transfer learning (M2TL) method that jointly utilizes samples from another domain (e.g., AD vs. normal controls (NC)) as well as unlabeled samples to boost the performance of the MCI conversion prediction. Specifically, the proposed M2TL method includes two key components. The first one is a kernel-based maximum mean discrepancy criterion, which helps eliminate the potential negative effect induced by the distributional difference between the auxiliary domain (i.e., AD and NC) and the target domain (i.e., MCI converters (MCI-C) and MCI non-converters (MCI-NC)). The second one is a semi-supervised multimodal manifold-regularized least squares classification method, where the target-domain samples, the auxiliary-domain samples, and the unlabeled samples can be jointly used for training our classifier. Furthermore, with the integration of a group sparsity constraint into our objective function, the proposed M2TL has a capability of selecting the informative samples to build a robust classifier. Experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database validate the effectiveness of the proposed method by significantly improving the classification accuracy of 80.1 % for MCI conversion prediction, and also outperforming the state-of-the-art methods.
3-manifolds with(out) metrics of nonpositive curvature
Leeb, B
1994-01-01
In the context of Thurstons geometrisation program we address the question which compact aspherical 3-manifolds admit Riemannian metrics of nonpositive curvature. We show that non-geometric Haken manifolds generically, but not always, admit such metrics. More precisely, we prove that a Haken manifold with, possibly empty, boundary of zero Euler characteristic admits metrics of nonpositive curvature if the boundary is non-empty or if at least one atoroidal component occurs in its canonical topological decomposition. Our arguments are based on Thurstons Hyperbolisation Theorem. We give examples of closed graph-manifolds with linear gluing graph and arbitrarily many Seifert components which do not admit metrics of nonpositive curvature.
Blow-up of generalized complex 4-manifolds
Cavalcanti, Gil R
2009-01-01
We introduce blow-up and blow-down operations for generalized complex 4-manifolds. Combining these with a surgery analogous to the logarithmic transform, we then construct generalized complex structures on nCP2 # m \\bar{CP2} for n odd, a family of 4-manifolds which admit neither complex nor symplectic structures unless n=1. We also extend the notion of a symplectic elliptic Lefschetz fibration, so that it expresses a generalized complex 4-manifold as a fibration over a two-dimensional manifold with boundary.
Backfire prediction in a manifold injection hydrogen internal combustion engine
Energy Technology Data Exchange (ETDEWEB)
Liu, Xing-hua; Liu, Fu-shui; Zhou, Lei; Sun, Bai-gang [School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing 100081 (China); Schock, Harold J. [Engine Research Laboratory, Michigan State University, East Lansing, MI (United States)
2008-07-15
Hydrogen internal combustion engine (H2ICE) easily occur inlet manifold backfire and other abnormal combustion phenomena because of the low ignition energy, wide flammability range and rapid combustion speed of hydrogen. In this paper, the effect of injection timing on mixture formation in a manifold injection H2ICE was studied in various engine speed and equivalence ratio by CFD simulation. It was concluded that H2ICE of manifold injection have an limited injection end timing in order to prevent backfire in the inlet manifold. Finally, the limit of injection end timing of the H2ICE was proposed and validated by engine experiment. (author)
Noncommutative Deformations of Locally Symmetric K\\"ahler manifolds
Hara, Kentaro
2016-01-01
We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of K\\"ahler manifolds, which is introduced by Karabegov. From the recurrence relations, concrete expressions of star products for one-dimensional local symmetric K\\"ahler manifolds and ${\\mathbb C}P^N$ are constructed. The recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied too.
LCD OF AIR INTAKE MANIFOLDS PHASE 2: FORD F250 AIR INTAKE MANIFOLD
The life cycle design methodology was applied to the design analysis of three alternatives for the lower plehum of the air intake manifold for us with a 5.4L F-250 truck engine: a sand cast aluminum, a lost core molded nylon composite, and a vibration welded nylon composite. The ...
On the trace-manifold generated by the deformations of a body-manifold
Directory of Open Access Journals (Sweden)
Boja Nicolae
2003-01-01
Full Text Available In this paper, concerned to the study of continuous deformations of material media using some tools of modem differential geometry, a moving frame of Frenet type along the orbits of an one-parameter group acting on a so-called "trace-manifold", M, associated to the deformations, is constructed. The manifold M is defined as an infinite union of non-disjoint compact manifolds, generated by the consecutive positions in the Euclidean affine 3-space of a body-manifold under deformations in a closed time interval. We put in evidence a skew-symmetric band tensor of second order, ω, which describes the deformation in a small neighborhood of any point along the orbits. The non-null components ωi,i+i, (i =1,2, of ω are assimilated as like curvatures at each point of an orbit in the planes generated by the pairs of vectors (ĕi,ĕi+i of a moving frame in M associated to the orbit in a similar way as the Frenet's frame is. Also a formula for the energy of the orbits is given and its relationship with some stiffness matrices is established.
Rational-slice Knots via Strongly Negative-amphicheiral Knots
Institute of Scientific and Technical Information of China (English)
KAWAUCHI AKIO
2009-01-01
We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the 0-surgery man-ifold of a certain strongly negative amphicheiral knot such as the figure-eight knot bounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-sphere such that a second homology class of the 4-manifold is represented by a smoothly embedded 2-sphere if and only if the modulo two reduction of it is zero.
Willmore Spheres in Compact Riemannian Manifolds
Mondino, Andrea
2012-01-01
The paper is devoted to the variational analysis of the Willmore, and other L^2 curvature functionals, among immersions of 2-dimensional surfaces into a compact riemannian m-manifold (M^m,h) with m>2. The goal of the paper is twofold, on one hand, we give the right setting for doing the calculus of variations (including min max methods) of such functionals for immersions into manifolds and, on the other hand, we prove existence results for possibly branched Willmore spheres under various constraints (prescribed homotopy class, prescribed area) or under curvature assumptions for M^m. To this aim, using the integrability by compensation, we develop first the regularity theory for the critical points of such functionals. We then prove a rigidity theorem concerning the relation between CMC and Willmore spheres. Then we prove that, for every non null 2-homotopy class, there exists a representative given by a Lipschitz map from the 2-sphere into M^m realizing a connected family of conformal smooth (possibly branche...
Real group orbits on flag manifolds
Akhiezer, Dmitri
2011-01-01
In this survey, we gather together various results on the action of a real form of a complex semisimple Lie group on its flag manifolds. We start with the finiteness theorem of J.Wolf implying that at least one of the orbits is open. We give a new proof of the converse statement for real forms of inner type, essentially due to F.M.Malyshev. Namely, if a real semisimple Lie group of inner type has an open orbit on an algebraic homogeneous space of the complexified group then the homogeneous space is a flag manifold. To prove this, we recall, partly with proofs, some results of A.L.Onishchik on the factorizations of reductive groups. Finally, we discuss the cycle spaces of open orbits and define the crown of a symmetric space of non-compact type. With some exceptions, the cycle space agrees with the crown. We sketch a complex analytic proof of this result, due to G.Fels, A.Huckleberry and J.Wolf.
Energy Technology Data Exchange (ETDEWEB)
Kocia, Lucas, E-mail: lkocia@fas.harvard.edu; Heller, Eric J. [Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138 (United States)
2014-11-14
A simplification of the Heller-Herman-Kluk-Kay (HK) propagator is presented that does not suffer from the need for an increasing number of trajectories with dimensions of the system under study. This is accomplished by replacing HK’s uniformizing integral over all of phase space by a one-dimensional curve that is appropriately selected to lie along the fastest growing manifold of a defining trajectory. It is shown that this modification leads to eigenspectra of quantum states in weakly anharmonic systems that can outperform the comparatively computationally cheap thawed Gaussian approximation method and frequently approach the accuracy of spectra obtained with the full HK propagator.
Kocia, Lucas; Heller, Eric J.
2014-11-01
A simplification of the Heller-Herman-Kluk-Kay (HK) propagator is presented that does not suffer from the need for an increasing number of trajectories with dimensions of the system under study. This is accomplished by replacing HK's uniformizing integral over all of phase space by a one-dimensional curve that is appropriately selected to lie along the fastest growing manifold of a defining trajectory. It is shown that this modification leads to eigenspectra of quantum states in weakly anharmonic systems that can outperform the comparatively computationally cheap thawed Gaussian approximation method and frequently approach the accuracy of spectra obtained with the full HK propagator.
Elliptically fibered Calabi–Yau manifolds and the ring of Jacobi forms
Energy Technology Data Exchange (ETDEWEB)
Huang, Min-xin, E-mail: minxin@ustc.edu.cn [Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026 (China); Katz, Sheldon, E-mail: katz@math.uiuc.edu [Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green St., Urbana, IL 61801 (United States); Klemm, Albrecht, E-mail: aklemm@th.physik.uni-bonn.de [Bethe Center for Theoretical Physics (BCTP), Physikalisches Institut, Universität Bonn, 53115 Bonn (Germany)
2015-09-15
We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi–Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows quadratically with the base degree. The denominators of these forms have a simple universal form with the property that the poles of the meromorphic form lie only at torsion points. The modular parameter corresponds to the fibre class while the role of the string coupling is played by the elliptic parameter. This leads to very strong all genus results on these geometries, which are checked against results from curve counting.
THE GEOMETRY OF HYPERSURFACES IN A KAEHLER MANIFOLD
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Abstract The geometry of hypersurfaces of a Kaehler manifold are studied. Some wellknown formulas and theorems in theory of surfaces of Euclidean 3-space are generalized to the hypersurfaces in a Kaehler manifold, such as Gauss's formulae, second fundamental form, the equation of Gauss and Codazzi and so forth.
HAMILTONIAN MECHANICS ON K(A)HLER MANIFOLDS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.
The quantum equivariant cohomology of toric manifolds through mirror symmetry
Baptista, J.M.
2009-01-01
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.
Modeling the Uniformity of Manifold with Various Configurations
Directory of Open Access Journals (Sweden)
Jafar M. Hassan
2014-01-01
Full Text Available The flow distribution in manifolds is highly dependent on inlet pressure, configuration, and total inlet flow to the manifold. The flow from a manifold has many applications and in various fields of engineering such as civil, mechanical, and chemical engineering. In this study, physical and numerical models were employed to study the uniformity of the flow distribution from manifold with various configurations. The physical model consists of main manifold with uniform longitudinal section having diameter of 10.16 cm (4 in, five laterals with diameter of 5.08 cm (2 in, and spacing of 22 cm. Different inlet flows were tested and the values of these flows are 500, 750, and 1000 L/min. A manifold with tapered longitudinal section having inlet diameters of 10.16 cm (4 in and dead end diameter of 5.08 cm (2 in with the same above later specifications and flow rates was tested for its uniformity too. The percentage of absolute mean deviation for manifold with uniform diameter was found to be 34% while its value for the manifold with nonuniform diameter was found to be 14%. This result confirms the efficiency of the nonuniform distribution of fluids.
Manifold mapping: a two-level optimization technique
Echeverria, D.; Hemker, P.W.
2008-01-01
In this paper, we analyze in some detail the manifold-mapping optimization technique introduced recently [Echeverría and Hemker in space mapping and defect correction. Comput Methods Appl Math 5(2): 107-–136, 2005]. Manifold mapping aims at accelerating optimal design procedures that otherwise requi
Deformations of log-Lagrangian submanifolds of Poisson manifolds
2013-01-01
We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lagrangian-like property.
Approximate Inertial Manifolds for Chemotaxis-Growth System
Institute of Scientific and Technical Information of China (English)
Hong LUO; Zhilin PU
2012-01-01
The long-time behaviour of solution to chemotaxis-growth system with Neumann condition is considered in this paper.The approximate inertial manifolds of such equations are constructed based on the contraction principle,and the orders of approximations of the manifolds to the global attractor are derived.
Embedding universal covers of graph manifolds in products of trees
Hume, David
2011-01-01
We prove that the universal cover of any graph manifold quasi-isometrically embeds into a product of three trees. In particular we show that the Assouad-Nagata dimension of the universal cover of any closed graph manifold is 3, proving a conjecture of Smirnov.
Existence and bifurcation of integral manifolds with applications
Institute of Scientific and Technical Information of China (English)
HAN; Mao'an; CHEN; Xianfeng
2005-01-01
In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.
Variable volume combustor with nested fuel manifold system
Energy Technology Data Exchange (ETDEWEB)
McConnaughhay, Johnie Franklin; Keener, Christopher Paul; Johnson, Thomas Edward; Ostebee, Heath Michael
2016-09-13
The present application provides a combustor for use with a gas turbine engine. The combustor may include a number of micro-mixer fuel nozzles, a fuel manifold system in communication with the micro-mixer fuel nozzles to deliver a flow of fuel thereto, and a linear actuator to maneuver the micro-mixer fuel nozzles and the fuel manifold system.
Characterizing pathological deviations from normality using constrained manifold-learning.
Duchateau, Nicolas; De Craene, Mathieu; Piella, Gemma; Frangi, Alejandro F
2011-01-01
We propose a technique to represent a pathological pattern as a deviation from normality along a manifold structure. Each subject is represented by a map of local motion abnormalities, obtained from a statistical atlas of motion built from a healthy population. The algorithm learns a manifold from a set of patients with varying degrees of the same pathology. The approach extends recent manifold-learning techniques by constraining the manifold to pass by a physiologically meaningful origin representing a normal motion pattern. Individuals are compared to the manifold population through a distance that combines a mapping to the manifold and the path along the manifold to reach its origin. The method is applied in the context of cardiac resynchronization therapy (CRT), focusing on a specific motion pattern of intra-ventricular dyssynchrony called septal flash (SF). We estimate the manifold from 50 CRT candidates with SF and test it on 38 CRT candidates and 21 healthy volunteers. Experiments highlight the need of nonlinear techniques to learn the studied data, and the relevance of the computed distance for comparing individuals to a specific pathological pattern.
Hetero-manifold Regularisation for Cross-modal Hashing.
Zheng, Feng; Tang, Yi; Shao, Ling
2016-12-28
Recently, cross-modal search has attracted considerable attention but remains a very challenging task because of the integration complexity and heterogeneity of the multi-modal data. To address both challenges, in this paper, we propose a novel method termed hetero-manifold regularisation (HMR) to supervise the learning of hash functions for efficient cross-modal search. A hetero-manifold integrates multiple sub-manifolds defined by homogeneous data with the help of cross-modal supervision information. Taking advantages of the hetero-manifold, the similarity between each pair of heterogeneous data could be naturally measured by three order random walks on this hetero-manifold. Furthermore, a novel cumulative distance inequality defined on the hetero-manifold is introduced to avoid the computational difficulty induced by the discreteness of hash codes. By using the inequality, cross-modal hashing is transformed into a problem of hetero-manifold regularised support vector learning. Therefore, the performance of cross-modal search can be significantly improved by seamlessly combining the integrated information of the hetero-manifold and the strong generalisation of the support vector machine. Comprehensive experiments show that the proposed HMR achieve advantageous results over the state-of-the-art methods in several challenging cross-modal tasks.
Manifold mapping: a two-level optimization technique
Echeverría, D.; Hemker, P.W.
2008-01-01
In this paper, we analyze in some detail the manifold-mapping optimization technique introduced recently [Echeverría and Hemker in space mapping and defect correction. Comput Methods Appl Math 5(2): 107--136, 2005]. Manifold mapping aims at accelerating optimal design procedures that otherwise requi
4-manifolds and intersection forms with local coefficients
DEFF Research Database (Denmark)
Frøyshov, Kim Anders
2012-01-01
We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.......We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds....
Hilbert manifold structure for asymptotically hyperbolic relativistic initial data
Fougeirol, Jérémie
2016-01-01
We provide a Hilbert manifold structure {\\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.
Dynamical systems on a Riemannian manifold that admit normal shift
Energy Technology Data Exchange (ETDEWEB)
Boldin, A.Yu.; Dmitrieva, V.V.; Safin, S.S.; Sharipov, R.A. [Bashkir State Univ. (Russian Federation)
1995-11-01
Newtonian dynamical systems that admit normal shift on an arbitrary Riemannian manifold are considered. The determining equations for these systems, which constitute the condition of weak normality, are derived. The extension of the algebra of tensor fields to manifolds is considered.
Sun, Jiaqi; Xie, Yuchen; Ye, Wenxing; Ho, Jeffrey; Entezari, Alireza; Blackband, Stephen J; Vemuri, Baba C
2013-01-01
In this paper, we present a novel dictionary learning framework for data lying on the manifold of square root densities and apply it to the reconstruction of diffusion propagator (DP) fields given a multi-shell diffusion MRI data set. Unlike most of the existing dictionary learning algorithms which rely on the assumption that the data points are vectors in some Euclidean space, our dictionary learning algorithm is designed to incorporate the intrinsic geometric structure of manifolds and performs better than traditional dictionary learning approaches when applied to data lying on the manifold of square root densities. Non-negativity as well as smoothness across the whole field of the reconstructed DPs is guaranteed in our approach. We demonstrate the advantage of our approach by comparing it with an existing dictionary based reconstruction method on synthetic and real multi-shell MRI data.
Baykur, R Inanc
2010-01-01
In this article, we produce infinite families of 4-manifolds with positive first betti numbers and meeting certain conditions on their homotopy and smooth types so as to conclude the non-vanishing of the stable cohomotopy Seiberg-Witten invariants of their connected sums. Elementary building blocks used in the earlier work of Ishida and Sasahira are shown to be included in our general construction scheme as well. We then use these families to construct the first examples of families of closed smooth 4-manifolds for which Gromov's simplicial volume is nontrivial, Perelman's lambda-bar invariant is negative, and the relevant Gromov-Hitchin-Thorpe type inequality is satisfied, yet no non-singular solution to the normalized Ricci flow for any initial metric can be obtained. Fang, Zhang and Zhang conjectured that the existence of any non-singular solution to the normalized Ricci flow on smooth 4-manifolds with non-trivial Gromov's simplicial volume and negative Perelman's lambda-bar invariant implies the Gromov-Hi...
Manifold learning based feature extraction for classification of hyper-spectral data
CSIR Research Space (South Africa)
Lunga, D
2013-08-01
Full Text Available often lie on sparse, nonlinear manifolds whose geometric and topological structures can be exploited via manifold learning techniques. In this article, we focused on demonstrating the opportunities provided by manifold learning for classification...
Investigating performance of microchannel evaporators with different manifold structures
Energy Technology Data Exchange (ETDEWEB)
Shi, Junye; Qu, Xiaohua; Qi, Zhaogang; Chen, Jiangping [Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, No. 800, Dongchuan Rd, Shanghai 200240 (China)
2011-01-15
In this paper, the performances of microchannel evaporators with different manifold structures are experimentally investigated. Eight evaporator samples with 7 different designs of the I/O manifold and 5 different designs of the return manifold are made for this study. The performances of the evaporator samples are tested on a psychometric calorimeter test bench with the refrigerant 134A at a real automotive AC condition. The results on the variations of the cooling capacity and air temperature distribution of the evaporator due to the deflector designs in the I/O manifold and flow hole arrangements in the return manifold are presented and analyzed. By studying the KPI's for the performance of an evaporator, the design trade-off for an evaporator designer is summarized and discussed. (author)
Natural connections on conformal Riemannian P-manifolds
Gribacheva, Dobrinka
2011-01-01
The class of conformal Riemannian P-manifolds is the largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric. This class is an analogue of the class of conformal Kaehler manifolds in almost Hermitian geometry. In the present work we study on a conformal Riemannian P-manifold (M, P, g) the natural linear connections, i.e. the linear connections preserving the almost product structure P and the Riemannian metric g. We find necessary and sufficient conditions the curvature tensor of such a connection to have similar properties like the ones of the Kaehler tensor in Hermitian geometry. We determine the type of the manifolds admitting a natural connection with a parallel torsion.
MOCVD manifold switching effects on growth and characterization
Clark, Ivan O.; Fripp, Archibald L.; Jesser, William A.
1991-01-01
A combined modeling and experimental approach is used to quantify the effects of various manifold components on the switching speed in metalorganic chemical vapor deposition (MOCVD). In particular, two alternative vent-run high-speed switching manifold designs suitable for either continuous or interrupted growth have been investigated. Both designs are incorporated in a common manifold, instrumented with a mass spectrometer. The experiments have been performed using nitrogen as the transport gas and argon as the simulated source gas. The advantages and limitations of two designs are discussed. It is found that while constant flow manifold switching systems may have fluid dynamic advantages, care must be taken to minimize sections of the supply manifold with low flow rates if rapid changes in alloy composition are required.
Some conformally flat spin manifolds, Dirac operators and automorphic forms
Krau[Ss]Har, R. S.; Ryan, John
2007-01-01
In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/[Gamma] where U is a subdomain of either Sn or Rn and [Gamma] is a Kleinian group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S1xSn-1. Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of [Gamma] are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Plemelj projection operators for Lp spaces of hypersurfaces lying in these manifolds.
Local Linear Regression on Manifolds and its Geometric Interpretation
Cheng, Ming-Yen
2012-01-01
We study nonparametric regression with high-dimensional data, when the predictors lie on an unknown, lower-dimensional manifold. In this context, recently \\cite{aswani_bickel:2011} suggested performing the conventional local linear regression (LLR) in the ambient space and regularizing the estimation problem using information obtained from learning the manifold locally. By contrast, our approach is to reduce the dimensionality first and then construct the LLR directly on a tangent plane approximation to the manifold. Under mild conditions, asymptotic expressions for the conditional mean squared error of the proposed estimator are derived for both the interior and the boundary cases. One implication of these results is that the optimal convergence rate depends only on the intrinsic dimension $d$ of the manifold, but not on the ambient space dimension $p$. Another implication is that the estimator is design adaptive and automatically adapts to the boundary of the unknown manifold. The bias and variance expressi...
Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds
Directory of Open Access Journals (Sweden)
Satya Prakash Yadav
2014-01-01
Full Text Available The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with (f,g,u,v,λ-structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with (f,g,u,v,λ-structure have been calculated provided f is parallel. In addition, the eigenvalues of f have been found and proved that a noninvariant hypersurface with (f,g,u,v,λ-structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with (f,g,u,v,λ-structure of a nearly trans-Sasakian manifold.
Model Transport: Towards Scalable Transfer Learning on Manifolds
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Black, Michael J.
2014-01-01
“commutes” with learning. Consequently, our compact framework, applicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image......We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use...... ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer...
Evolutionary global optimization, manifolds and applications
Aguiar e Oliveira Junior, Hime
2016-01-01
This book presents powerful techniques for solving global optimization problems on manifolds by means of evolutionary algorithms, and shows in practice how these techniques can be applied to solve real-world problems. It describes recent findings and well-known key facts in general and differential topology, revisiting them all in the context of application to current optimization problems. Special emphasis is put on game theory problems. Here, these problems are reformulated as constrained global optimization tasks and solved with the help of Fuzzy ASA. In addition, more abstract examples, including minimizations of well-known functions, are also included. Although the Fuzzy ASA approach has been chosen as the main optimizing paradigm, the book suggests that other metaheuristic methods could be used as well. Some of them are introduced, together with their advantages and disadvantages. Readers should possess some knowledge of linear algebra, and of basic concepts of numerical analysis and probability theory....
The Operator Manifold Formalism; 2, Physical Applications
Ter-Kazarian, G T
1998-01-01
Within the operator manifold approach (part I, hep-th/9812181) we derive the Gell-Mann-Nishijima relation and flavour group, whereas the leptons are particles with integer electric and leptonic charges and free of confinement, while quarks carry fractional electric and baryonic charges and imply the confinement. We consider the unified electroweak interactions with small number of free parameters, exploit the background of the local expanded symmetry $SU(2)\\otimes U(1)$ and P-violation. The Weinberg mixing angle is shown to have fixed value at $30^{o}$. The Higgs bosons arise on an analogy of the Cooper pairs in superconductivity. Within the present microscopic approach we predict the Kobayashi-Maskawa quark flavour mixing; the appearance of the CP-violation phase; derive the mass-spectrum of leptons and quarks, as well as other emerging particles, and also some useful relations between their masses.
Killing superalgebras for Lorentzian four-manifolds
de Medeiros, Paul; Santi, Andrea
2016-01-01
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of $\\mathbb{Z}$-graded subalgebras with maximum odd dimension of the $N{=}1$ Poincar\\'e superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the $N{=}1$ Poincar\\'e superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of ma...
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
Cusp geometry of fibered 3-manifolds
Futer, David
2011-01-01
Let F be a surface and suppose that \\phi: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_\\phi\\ is hyperbolic and contains a maximal cusp C about the puncture p. We show that the area and height of the cusp torus bounding C are equal, up to explicit multiplicative error, to the stable translation distance of \\phi\\ acting on the arc complex A(F,p). Our proofs rely on elementary facts about the hyperbolic geometry of pleated surfaces. In particular, we do not use any deep results in Teichmueller theory, Kleinian group theory, or the coarse geometry of A(F,p). A similar result holds for quasi-Fuchsian manifolds N = (F x R). In that setting, we prove a combinatorial estimate on the area and height of the cusp annulus in the convex core of N and give explicit multiplicative and additive errors.
Biomedical data analysis by supervised manifold learning.
Alvarez-Meza, A M; Daza-Santacoloma, G; Castellanos-Dominguez, G
2012-01-01
Biomedical data analysis is usually carried out by assuming that the information structure embedded into the biomedical recordings is linear, but that statement actually does not corresponds to the real behavior of the extracted features. In order to improve the accuracy of an automatic system to diagnostic support, and to reduce the computational complexity of the employed classifiers, we propose a nonlinear dimensionality reduction methodology based on manifold learning with multiple kernel representations, which learns the underlying data structure of biomedical information. Moreover, our approach can be used as a tool that allows the specialist to do a visual analysis and interpretation about the studied variables describing the health condition. Obtained results show how our approach maps the original high dimensional features into an embedding space where simple and straightforward classification strategies achieve a suitable system performance.
Stochastic gradient descent on Riemannian manifolds
Bonnabel, Silvere
2011-01-01
Stochastic gradient descent is a simple appproach to find the local minima of a function whose evaluations are corrupted by noise. In this paper, mostly motivated by machine learning applications, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Euclidian case, the descent algorithm converges to a critical point of the cost function. The algorithm has numerous potential applications, and we show several well-known algorithms can be cast in our versatile geometric framework. We also address the gain tuning issue in connection with the tools of the recent theory of symmetry-preserving observers.
Classification of Framed Links in 3-Manifolds
Indian Academy of Sciences (India)
Matija Cencelj; Dušan Repovš; Mikhail B Skopenkov
2007-08-01
We present a short and complete proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in detail. Let be a connected oriented closed smooth 3-manifold, $L_1(M)$ be the set of framed links in up to a framed cobordism, and $\\deg: L_1(M)→ H_1(M;\\mathbb{Z})$ be the map taking a framed link to its homology class. Then for each $\\in H_1(M;\\mathbb{Z})$ there is a one-to-one correspondence between the set $\\deg^{-1}$ and the group $\\mathbb{Z}_{2d()}$, where () is the divisibility of the projection of to the free part of $H_1(M;\\mathbb{Z})$.
Degeneracy of holomorphic curves in surfaces
Institute of Scientific and Technical Information of China (English)
LIU Yuancheng; RU Min
2005-01-01
Let X be a complex projective algebraic manifold of dimension 2 and let D1,..., Du be distinct irreducible divisors on X such that no three of them share a common point. Let f: C → X\\(U1≤i≤uDi) be a holomorphic map. Assume that u ≥ 4 and that there exist positive integers n1,...,nu, c such that ninj(Di.Dj) = c for all pairs i, j. Then f is algebraically degenerate, i.e. its image is contained in an algebraic curve on X.
Diffusion Harmonics and Dual Geometry on Carnot Manifolds
Constantin, Sarah
The "curse of dimensionality" motivates the importance of techniques for computing low-dimensional approximations of high-dimensional data. It is often necessary to use nonlinear techniques to recover a low-dimensional manifold embedded via a nonlinear map in a high-dimensional space; this family of techniques is referred to as "manifold learning." The accuracy of manifold-learning-based approximations is founded on asymptotic results that assume the data is drawn from a low-dimensional Riemannian manifold. However, in natural datasets, this assumption is often overly restrictive. In the first part of this thesis we examine a more general class of manifolds known as Carnot manifolds, a type of sub-Riemannian manifold that governs natural phenomena such as chemical kinetics and configuration spaces of jointed objects. We find that diffusion maps can be generalized to Carnot manifolds and that the projection onto diffusion harmonics gives an almost isometric embedding; as a side effect, the diffusion distance is a computationally fast estimate for the shortest distance between two points on a Carnot manifold. We apply this theory to biochemical network data and observe that the chemical kinetics of the EGFR network are governed by a Carnot, but not Riemannian, manifold. In the second part of this thesis we examine the Heisenberg group, a classical example of a Carnot manifold. We obtain a representation-theoretic proof that the eigenfunctions of the sub-Laplacian on SU(2) approach the eigenfunctions of the sub-Laplacian on the Heisenberg group, in the limit as the radius of the sphere becomes large, in analogy with the limiting relationship between the Fourier series on the circle and the Fourier transform on the line. This result also illustrates how projecting onto the sub-Laplacian eigenfunctions of a non-compact Carnot manifold can be locally approximated by projecting onto the sub-Laplacian eigenfunctions of a tangent compact Carnot manifold. In the third part
Piping structural design for the ITER thermal shield manifold
Energy Technology Data Exchange (ETDEWEB)
Noh, Chang Hyun, E-mail: chnoh@nfri.re.kr [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Chung, Wooho, E-mail: whchung@nfri.re.kr [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Nam, Kwanwoo; Kang, Kyoung-O. [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Bae, Jing Do; Cha, Jong Kook [Korea Marine Equipment Research Institute, Busan 606-806 (Korea, Republic of); Kim, Kyoung-Kyu [Mecha T& S, Jinju-si 660-843 (Korea, Republic of); Hamlyn-Harris, Craig; Hicks, Robby; Her, Namil; Jun, Chang-Hoon [ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France)
2015-10-15
Highlights: • We finalized piping design of ITER thermal shield manifold for procurement. • Support span is determined by stress and deflection limitation. • SQP, which is design optimization method, is used for the pipe design. • Benchmark analysis is performed to verify the analysis software. • Pipe design is verified by structural analyses. - Abstract: The thermal shield (TS) provides the thermal barrier in the ITER tokamak to minimize heat load transferred by thermal radiation from the hot components to the superconducting magnets operating at 4.2 K. The TS is actively cooled by 80 K pressurized helium gas which flows from the cold valve box to the cooling tubes on the TS panels via manifold piping. This paper describes the manifold piping design and analysis for the ITER thermal shield. First, maximum allowable span for the manifold support is calculated based on the simple beam theory. In order to accommodate the thermal contraction in the manifold feeder, a contraction loop is designed and applied. Sequential Quadratic Programming (SQP) method is used to determine the optimized dimensions of the contraction loop to ensure adequate flexibility of manifold pipe. Global structural behavior of the manifold is investigated when the thermal movement of the redundant (un-cooled) pipe is large.
A matrix model for the topological string II: The spectral curve and mirror geometry
Eynard, Bertrand; Marchal, Olivier
2010-01-01
In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing certain minimality assumptions on the spectral curve, the large volume limit of the BKMP "remodeling the B-model" conjecture, the claim that Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the spectral invariants of its mirror curve.
Cohomological rigidity of manifolds defined by 3-dimensional polytopes
Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.
2017-04-01
A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, J
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the uniformity of all estimates throughout the proof. The $C^{k,\\alpha}$-smoothness result is optimal with respect to the spectral gap condition involved. The core of the persistence proof is based on the Perron method. In the process we derive new results on noncompact submanifolds in bounded geometry: a uniform tubular neighborhood theorem and uniform smooth approximation of a submanifold. The submanifolds considered are assumed to be uniformly $C^k$ bounded in an appropriate sense.
4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings
Davis, M; Lafont, J -F
2010-01-01
We construct examples of smooth 4-dimensional manifolds M supporting a locally CAT(0)-metric, whose universal cover X satisfy Hruska's isolated flats condition, and contain 2-dimensional flats F with the property that the boundary at infinity of F defines a nontrivial knot in the boundary at infinity of X. As a consequence, we obtain that the fundamental group of M cannot be isomorphic to the fundamental group of any Riemannian manifold of nonpositive sectional curvature. In particular, M is a locally CAT(0)-manifold which does not support any Riemannian metric of nonpositive sectional curvature.
A global Torelli theorem for hyperkaehler manifolds (after Verbitsky)
Huybrechts, Daniel
2011-01-01
Compact hyperkaehler manifolds are higher-dimensional generalizations of K3 surfaces. The classical Global Torelli theorem for K3 surfaces, however, does not hold in higher dimensions. More precisely, a compact hyperkaehler manifold is in general not determined by its natural weight-two Hodge structure. The text gives an account of a recent theorem of M. Verbitsky, which can be regarded as a weaker version of the Global Torelli theorem phrased in terms of the injectivity of the period map on the connected components of the moduli space of marked manifolds.
Solving Einstein's Equation Numerically on Manifolds with Arbitrary Topologie
Lindblom, Lee
2017-01-01
This talk will summarize some of the numerical methods we have developed for solving Einstein's equation numerically on manifolds with arbitrary spatial topologies. These methods include the use of multi-cube representations of arbitrary manifolds, a convenient new way to specify the differential structure on multi-cube representations, and a new fully covariant first-order symmetric hyperbolic representation of Einstein's equation. Progress on the problem of constructing the ``reference metrics'' (which are an essential element of our numerical method) for arbitrary manifolds will be described, and numerical results will be presented for some example simulations.
Understanding 3-manifolds in the context of permutations
Null, Karoline P
2011-01-01
We demonstrate how a 3-manifold, a Heegaard diagram, and a group presentation can each be interpreted as a pair of signed permutations in the symmetric group $S_d.$ We demonstrate the power of permutation data in programming and discuss an algorithm we have developed that takes the permutation data as input and determines whether the data represents a closed 3-manifold. We therefore have an invariant of groups, that is given any group presentation, we can determine if that presentation presents a closed 3-manifold.
Operators from mirror curves and the quantum dilogarithm
Kashaev, Rinat
2015-01-01
Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo Calabi-Yau threefolds, these operators are of trace class. In some simple geometries, like local P2, we calculate the integral kernel of the corresponding operators in terms of Faddeev's quantum dilogarithm. Their spectral traces are expressed in terms of multi-dimensional integrals, similar to the state-integrals appearing in three-manifold topology, and we show that they can be evaluated explicitly in some cases. Our results provide further verifications of a recent conjecture which gives an explicit expression for the Fredholm determinant of these operators, in terms of enumerative invariants of the underlying Calabi-Yau threefolds.
Operators from Mirror Curves and the Quantum Dilogarithm
Kashaev, Rinat; Mariño, Marcos
2016-09-01
Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo Calabi-Yau threefolds, these operators are of trace class. In some simple geometries, like local {{P}^2}, we calculate the integral kernel of the corresponding operators in terms of Faddeev's quantum dilogarithm. Their spectral traces are expressed in terms of multi-dimensional integrals, similar to the state-integrals appearing in three-manifold topology, and we show that they can be evaluated explicitly in some cases. Our results provide further verifications of a recent conjecture which gives an explicit expression for the Fredholm determinant of these operators, in terms of enumerative invariants of the underlying Calabi-Yau threefolds.
Altering symplectic manifolds by homologous recombination
Abouzaid, Mohammed
2010-01-01
We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a method, which we call homologous recombination, for constructing a Lefschetz fibration whose total space is smoothly equivalent to the original variety, but for which symplectic cohomology with coefficients in the given set of primes vanishes (there is also a simpler version that kills symplectic cohomology completely). Rather than relying on a geometric analysis of periodic orbits of a flow, the computation of symplectic cohomology depends on describing the Fukaya category associated to the new fibration. As a consequence we use a result of McLean to prove, for example, that an affine variety of real dimension greater than or equal to 4 supports infinitely many different (Wein)stein structures of finite type, and, assuming a mild cohomological condition, uncountably many d...
An underlying geometrical manifold for Hamiltonian mechanics
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Double Field Theory on Group Manifolds (Thesis)
Hassler, Falk
2015-01-01
This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. It renders T-duality on a torus manifest by adding $D$ winding coordinates in addition to the $D$ space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for field configurations which depend on half of the coordinates of the arising doubled space. I derive DFT${}_\\mathrm{WZW}$, a generalization of the current formalism. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constrai...
Eignets for function approximation on manifolds
Mhaskar, H N
2009-01-01
Let $\\XX$ be a compact, smooth, connected, Riemannian manifold without boundary, $G:\\XX\\times\\XX\\to \\RR$ be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form $\\sum_{j=1}^M a_jG(\\circ,y_j)$, where $a_j\\in\\RR$, $y_j\\in\\XX$, $1\\le j\\le M$. We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in $L^p(\\mu;\\XX)$ for a general class of measures $\\mu$ and kernels $G$. Our algorithm yields linear operators. Using the minimal separation amongst the centers $y_j$ as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every \\emph{individual function}. We also give estimates on the coefficients $a_j$ in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in ter...
More on Cotton Flow on Three Manifolds
Kilicarslan, Ercan; Tekin, Bayram
2015-01-01
Cotton flow tends to evolve a given initial metric on a three manifold to a conformally flat one. Here we expound upon the earlier work on Cotton flow and study the linearized version of it around a generic initial metric by employing a modified form of the DeTurck trick. We show that the flow around the flat space, as a critical point, reduces to an anisotropic generalization of linearized KdV equation with complex dispersion relations one of which is an unstable mode, rendering the the flat space unstable under small perturbations. We also show that Einstein spaces and some conformally flat non-Einstein spaces are linearly unstable. We refine the gradient flow formalism and compute the second variation of the entropy and show that generic critical points are extended Cotton solitons. We study some properties of these solutions and find a Topologically Massive soliton that is built from Cotton and Ricci solitons. In the Lorentzian signature, we also show that the pp-wave metrics are both Cotton and Ricci sol...
On the scalar manifold of exceptional supergravity
Energy Technology Data Exchange (ETDEWEB)
Cacciatori, S.L. [Dipartimento di Scienze ed Alta Tecnologia, Universita dell' Insubria, Via Valleggio, 11, 22100 Como (Italy); INFN, Sezione di Milano, Via Celoria, 16, 20133 Milano (Italy); Cerchiai, B.L. [INFN, Sezione di Milano, Via Celoria, 16, 20133 Milano (Italy); Dipartimento di Matematica, Universita degli Studi di Milano, Via Saldini, 50, 20133 Milano (Italy); Marrani, A. [Physics Department, Theory Unit, CERN, 1211, Geneva 23 (Switzerland)
2012-07-15
We construct two parametrizations of the non compact exceptional Lie group G = E{sub 7(-25)}, based on a fibration which has the maximal compact subgroup [(E{sub 6} x U(1))/Z{sub 3}] as a fiber. It is well known that G plays an important role in the N = 2 d = 4 magic exceptional supergravity, where it describes the U-duality of the theory and where the symmetric space M=G/K gives the vector multiplets' scalar manifold. First, by making use of the exponential map, we compute a realization of G/K, that is based on the E{sub 6} invariant d-tensor, and hence exhibits the maximal possible manifest [(E{sub 6} x U(1))/Z{sub 3}]-covariance. This provides a basis for the corresponding supergravity theory, which is the analogue of the Calabi-Vesentini coordinates. Then we study the Iwasawa decomposition. Its main feature is that it is SO(8)-covariant and therefore it highlights the role of triality. Along the way we analyze the relevant chain of maximal embeddings which leads to SO(8). It is worth noticing that being based on the properties of a ''mixed'' Freudenthal-Tits magic square, the whole procedure can be generalized to a broader class of groups of type E{sub 7}. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Learning the manifold of quality ultrasound acquisition.
El-Zehiry, Noha; Yan, Michelle; Good, Sara; Fang, Tong; Zhou, S Kevin; Grady, Leo
2013-01-01
Ultrasound acquisition is a challenging task that requires simultaneous adjustment of several acquisition parameters (the depth, the focus, the frequency and its operation mode). If the acquisition parameters are not properly chosen, the resulting image will have a poor quality and will degrade the patient diagnosis and treatment workflow. Several hardware-based systems for autotuning the acquisition parameters have been previously proposed, but these solutions were largely abandoned because they failed to properly account for tissue inhomogeneity and other patient-specific characteristics. Consequently, in routine practice the clinician either uses population-based parameter presets or manually adjusts the acquisition parameters for each patient during the scan. In this paper, we revisit the problem of autotuning the acquisition parameters by taking a completely novel approach and producing a solution based on image analytics. Our solution is inspired by the autofocus capability of conventional digital cameras, but is significantly more challenging because the number of acquisition parameters is large and the determination of "good quality" images is more difficult to assess. Surprisingly, we show that the set of acquisition parameters which produce images that are favored by clinicians comprise a 1D manifold, allowing for a real-time optimization to maximize image quality. We demonstrate our method for acquisition parameter autotuning on several live patients, showing that our system can start with a poor initial set of parameters and automatically optimize the parameters to produce high quality images.
Manifold Regularized Experimental Design for Active Learning.
Zhang, Lining; Shum, Hubert P H; Shao, Ling
2016-12-02
Various machine learning and data mining tasks in classification require abundant data samples to be labeled for training. Conventional active learning methods aim at labeling the most informative samples for alleviating the labor of the user. Many previous studies in active learning select one sample after another in a greedy manner. However, this is not very effective because the classification models has to be retrained for each newly labeled sample. Moreover, many popular active learning approaches utilize the most uncertain samples by leveraging the classification hyperplane of the classifier, which is not appropriate since the classification hyperplane is inaccurate when the training data are small-sized. The problem of insufficient training data in real-world systems limits the potential applications of these approaches. This paper presents a novel method of active learning called manifold regularized experimental design (MRED), which can label multiple informative samples at one time for training. In addition, MRED gives an explicit geometric explanation for the selected samples to be labeled by the user. Different from existing active learning methods, our method avoids the intrinsic problems caused by insufficiently labeled samples in real-world applications. Various experiments on synthetic datasets, the Yale face database and the Corel image database have been carried out to show how MRED outperforms existing methods.
Killing superalgebras for Lorentzian four-manifolds
de Medeiros, Paul; Figueroa-O'Farrill, José; Santi, Andrea
2016-06-01
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of mathbb{Z} -graded subalgebras with maximum odd dimension of the N = 1 Poincaré superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the N = 1 Poincaré superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of maximally supersymmetric backgrounds whose associated Killing superalgebras are precisely the filtered deformations we classify in this paper.
Lectures on four-manifolds and topological gauge theories
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. [Amsterdam Univ. (Netherlands). Dept. of Math.
1996-02-01
I give an elementary introduction to the theory of four-manifold invariants and its relation with topological field theory. I review the recent developments in the theory of Donaldson and Seiberg-Witten invariants. (orig.).
Lectures on four-manifolds and topological gauge theories
Dijkgraaf, Robbert
1996-02-01
I give an elementary introduction to the theory of four-manifold invariants and its relation with topological field theory. I review the recent developments in the theory of Donaldson and Seiberg-Witten invariants.
The Banach-Tarski paradox for flag manifolds
Komori, Yohei
2011-01-01
The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.
Geometry of almost-product Lorentzian manifolds and relativistic observer
Borowiec, Andrzej
2013-01-01
The notion of relativistic observer is confronted with Naveira's classification of (pseudo-)Riemannian almost-product structures on space-time manifolds. Some physical properties and their geometrical counterparts are shortly discussed.
Poincare duality angles for Riemannian manifolds with boundary
Shonkwiler, Clayton
2009-01-01
On a compact Riemannian manifold with boundary, the absolute and relative cohomology groups appear as certain subspaces of harmonic forms. DeTurck and Gluck showed that these concrete realizations of the cohomology groups decompose into orthogonal subspaces corresponding to cohomology coming from the interior and boundary of the manifold. The principal angles between these interior subspaces are all acute and are called Poincare duality angles. This paper determines the Poincare duality angles of a collection of interesting manifolds with boundary derived from complex projective spaces and from Grassmannians, providing evidence that the Poincare duality angles measure, in some sense, how "close" a manifold is to being closed. This paper also elucidates a connection between the Poincare duality angles and the Dirichlet-to-Neumann operator for differential forms, which generalizes the classical Dirichlet-to-Neumann map arising in the problem of Electrical Impedance Tomography. Specifically, the Poincare duality...
Kink manifolds in (1+1)-dimensional scalar field theory
Energy Technology Data Exchange (ETDEWEB)
Alonso Izquierdo, A.; Gonzalez Leon, M.A. [Departamento de Estadistica y Matematica Aplicadas, Facultad de Ciencias, Universidad de Salamanca, Salamanca (Spain); Mateos Guilarte, J. [Departamento de Fisica, Facultad de Ciencias, Universidad de Salamanca, Salamanca (Spain)
1998-01-09
The general structure of kink manifolds in (1+1)-dimensional complex scalar field theory is described by analysing three special models. New solitary waves are reported. Kink energy sum rules arise between different types of solitary waves. (author)
Manifold learning based feature extraction for classification of hyperspectral data
CSIR Research Space (South Africa)
Lunga, D
2014-01-01
Full Text Available Interest in manifold learning for representing the topology of large, high dimensional nonlinear data sets in lower, but still meaningful dimensions for visualization and classification has grown rapidly over the past decade, and particularly...
Twisted Fock representations of noncommutative Kähler manifolds
Sako, Akifumi; Umetsu, Hiroshi
2016-09-01
We introduce twisted Fock representations of noncommutative Kähler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by applying creation operators to a vacuum state. "Twisted" means that creation operators are not Hermitian conjugate of annihilation operators in this representation. In deformation quantization of Kähler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the Kähler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative Kähler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative Kähler manifolds concretely.
Linear approximation of the first eigenvalue on compact manifolds
Institute of Scientific and Technical Information of China (English)
CHEN; Mufa(陈木法); E.; Scacciatelli; YAO; Liang(姚亮)
2002-01-01
For compact, connected Riemannian manifolds with Ricci curvature bounded below by a constant, what is the linear approximation of the first eigenvalue of Laplacian? The answer is presented with computer assisted proof and the result is optimal in certain sense.
Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction
Zhou, Tianyi; Wu, Xindong
2010-01-01
It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \\cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local...
Flat coordinates for Saito Frobenius manifolds and string theory
Belavin, A. A.; Gepner, D.; Kononov, Ya. A.
2016-12-01
We investigate the connection between the models of topological conformal theory and noncritical string theory with Saito Frobenius manifolds. For this, we propose a new direct way to calculate the flat coordinates using the integral representation for solutions of the Gauss-Manin system connected with a given Saito Frobenius manifold. We present explicit calculations in the case of a singularity of type A n . We also discuss a possible generalization of our proposed approach to SU( N) k /( SU( N) k+1 × U(1)) Kazama-Suzuki theories. We prove a theorem that the potential connected with these models is an isolated singularity, which is a condition for the Frobenius manifold structure to emerge on its deformation manifold. This fact allows using the Dijkgraaf-Verlinde-Verlinde approach to solve similar Kazama-Suzuki models.
Salient object detection: manifold-based similarity adaptation approach
Zhou, Jingbo; Ren, Yongfeng; Yan, Yunyang; Gao, Shangbing
2014-11-01
A saliency detection algorithm based on manifold-based similarity adaptation is proposed. The proposed algorithm is divided into three steps. First, we segment an input image into superpixels, which are represented as the nodes in a graph. Second, a new similarity measurement is used in the proposed algorithm. The weight matrix of the graph, which indicates the similarities between the nodes, uses a similarity-based method. It also captures the manifold structure of the image patches, in which the graph edges are determined in a data adaptive manner in terms of both similarity and manifold structure. Then, we use local reconstruction method as a diffusion method to obtain the saliency maps. The objective function in the proposed method is based on local reconstruction, with which estimated weights capture the manifold structure. Experiments on four bench-mark databases demonstrate the accuracy and robustness of the proposed method.
Supervised learning for neural manifold using spatiotemporal brain activity
Kuo, Po-Chih; Chen, Yong-Sheng; Chen, Li-Fen
2015-12-01
Objective. Determining the means by which perceived stimuli are compactly represented in the human brain is a difficult task. This study aimed to develop techniques for the construction of the neural manifold as a representation of visual stimuli. Approach. We propose a supervised locally linear embedding method to construct the embedded manifold from brain activity, taking into account similarities between corresponding stimuli. In our experiments, photographic portraits were used as visual stimuli and brain activity was calculated from magnetoencephalographic data using a source localization method. Main results. The results of 10 × 10-fold cross-validation revealed a strong correlation between manifolds of brain activity and the orientation of faces in the presented images, suggesting that high-level information related to image content can be revealed in the brain responses represented in the manifold. Significance. Our experiments demonstrate that the proposed method is applicable to investigation into the inherent patterns of brain activity.
Manifold learning based registration algorithms applied to multimodal images.
Azampour, Mohammad Farid; Ghaffari, Aboozar; Hamidinekoo, Azam; Fatemizadeh, Emad
2014-01-01
Manifold learning algorithms are proposed to be used in image processing based on their ability in preserving data structures while reducing the dimension and the exposure of data structure in lower dimension. Multi-modal images have the same structure and can be registered together as monomodal images if only structural information is shown. As a result, manifold learning is able to transform multi-modal images to mono-modal ones and subsequently do the registration using mono-modal methods. Based on this application, in this paper novel similarity measures are proposed for multi-modal images in which Laplacian eigenmaps are employed as manifold learning algorithm and are tested against rigid registration of PET/MR images. Results show the feasibility of using manifold learning as a way of calculating the similarity between multimodal images.
A new embedding quality assessment method for manifold learning
Zhang, Peng; Zhang, Bo
2011-01-01
Manifold learning is a hot research topic in the field of computer science. A crucial issue with current manifold learning methods is that they lack a natural quantitative measure to assess the quality of learned embeddings, which greatly limits their applications to real-world problems. In this paper, a new embedding quality assessment method for manifold learning, named as Normalization Independent Embedding Quality Assessment (NIEQA), is proposed. Compared with current assessment methods which are limited to isometric embeddings, the NIEQA method has a much larger application range due to two features. First, it is based on a new measure which can effectively evaluate how well local neighborhood geometry is preserved under normalization, hence it can be applied to both isometric and normalized embeddings. Second, it can provide both local and global evaluations to output an overall assessment. Therefore, NIEQA can serve as a natural tool in model selection and evaluation tasks for manifold learning. Experi...
GrassmannOptim: An R Package for Grassmann Manifold Optimization
Directory of Open Access Journals (Sweden)
Ko Placid Adragni
2012-07-01
Full Text Available The optimization of a real-valued objective function f(U, where U is a p X d,p > d, semi-orthogonal matrix such that UTU=Id, and f is invariant under right orthogonal transformation of U, is often referred to as a Grassmann manifold optimization. Manifold optimization appears in a wide variety of computational problems in the applied sciences. In this article, we present GrassmannOptim, an R package for Grassmann manifold optimization. The implementation uses gradient-based algorithms and embeds a stochastic gradient method for global search. We describe the algorithms, provide some illustrative examples on the relevance of manifold optimization and finally, show some practical usages of the package.
A family quantization formula for symplectic manifolds with boundary
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
his paper generalizes the family quantization formula of Zh angto the case of manifolds with boundary. As an application, Tian-Zhang's ana lytic version of the Guillemin-Kalkman-Martin residue formula is generalized to the family case.
Kauffman polynomials of some links and invariants of 3-manifolds
Institute of Scientific and Technical Information of China (English)
李起升
2002-01-01
Kauffman bracket polynomials of the so-called generalized tree-like links are studied. An algorithm of Witten type invariants, which was defined by Blanchet and Habegger et al. of more general 3-manifolds is given.
Spatial context driven manifold learning for hyperspectral image classification
CSIR Research Space (South Africa)
Zhang, Y
2014-06-01
Full Text Available Manifold learning techniques have demonstrated various levels of success in their ability to represent spectral signature characteristics in hyperspectral imagery. Such images consists of spectral features with very subtle differences and at times...
Twisted Fock Representations of Noncommutative K\\"ahler Manifolds
Sako, Akifumi
2016-01-01
We introduce twisted Fock representations of noncommutative K\\"ahler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by acting creation operators on a vacuum state. "Twisted" means that creation operators are not hermitian conjugate of annihilation operators in this representation. In deformation quantization of K\\"ahler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the K\\"ahler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative K\\"ahler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative K\\"ahler manifolds concretely.
MADMM: a generic algorithm for non-smooth optimization on manifolds
Kovnatsky, Artiom; Glashoff, Klaus; Bronstein, Michael M.
2015-01-01
Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for manifold-constrained non-smooth optimization problems and show its application to several challenging problems in dimensionality reduction, data analysis, and manifold learning.
On the de Rham-Wu decomposition for Riemannian and Lorentzian manifolds
Galaev, Anton S
2016-01-01
It is explained how to find the de~Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold.
Almost complex connections on almost complex manifolds with Norden metric
Teofilova, Marta
2011-01-01
A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A two-parametric family of complex connections is studied on a conformal K\\"{a}hler manifold with Norden metric. The curvature tensors of these connections are proved to coincide.
THE VARIATIONAL PRINCIPLE AND APPLICATION OF NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
骆少明; 张湘伟; 蔡永昌
2001-01-01
The physical-cover-oriented variational principle of numerical manifold method (NMM) for the analysis of linear elastic static problems was put forward according to the displacement model and the characters of numerical manifold method. The theoretical calculating formulations and the controlling equation of NMM were derived. As an example,the plate with a hole in the center is calculated and the results show that the solution precision and efficiency of NMM are agreeable.
A plug with infinite order and some exotic 4-manifolds
Tange, Motoo
2012-01-01
Every exotic pair in 4-dimension is obtained each other by twisting a {\\it cork} or {\\it plug} which are codimension 0 submanifolds embedded in the 4-manifolds. The twist was an involution on the boundary of the submanifold. We define cork (or plug) with order $p\\in {\\Bbb N}\\cup \\{\\infty\\}$ and show there exists a plug with infinite order. Furthermore we show twisting $(P,\\varphi^2)$ gives to enlargements of $P$ compact exotic manifolds with boundary.
Webs of Lagrangian Tori in Projective Symplectic Manifolds
Hwang, Jun-Muk
2012-01-01
For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.
The Identification of Convex Function on Riemannian Manifold
Directory of Open Access Journals (Sweden)
Li Zou
2014-01-01
Full Text Available The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.
Characteristic varieties of quasi-projective manifolds and orbifolds
Bartolo, Enrique Artal; Matei, Daniel
2010-01-01
We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called \\emph{translated} components of the characteristic varieties, and shows that the zero-dimensional components are indeed torsion. The main result is used to derive further obstructions for a group to be the fundamental group of a quasi-projective manifold.
Quasi-rigidity of hyperbolic 3-manifolds and scattering theory
Borthwick, D; Taylor, E; Borthwick, David; Rae, Alan Mc; Taylor, Edward
1996-01-01
Take two isomorphic convex co-compact co-infinite volume Kleinian groups, whose regular sets are diffeomorphic. The quotient of hyperbolic 3-space by these groups gives two hyperbolic 3-manifolds whose scattering operators may be compared. We prove that the operator norm of the difference between the scattering operators is small, then the groups are related by a coorespondingly small quasi-conformal deformation. This in turn implies that the two hyperbolic 3-manifolds are quasi-isometric.
Finite Time and Exact Time Controllability on Compact Manifolds
Jouan, Philippe
2010-01-01
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to give a new and elementary proof of the equivalence between controllability for essentially bounded inputs and for piecewise constant ones. Two sufficient conditions for controllability at exact time on a compact manifold are then stated. Some applications,...
A Note on Heegaard Splittings of Amalgamated 3-Manifolds
Institute of Scientific and Technical Information of China (English)
Kun DU; Xutao GAO
2011-01-01
Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi ∪Hi Wi with d(H1) + d(H2) ≥ 2(g(M1) + g(M2) -g(F)) + 1, then g(M) = g(M1) + g(M2) - g(F).
Solid state optical refrigeration using stark manifold resonances in crystals
Energy Technology Data Exchange (ETDEWEB)
Seletskiy, Denis V.; Epstein, Richard; Hehlen, Markus P.; Sheik-Bahae, Mansoor
2017-02-21
A method and device for cooling electronics is disclosed. The device includes a doped crystal configured to resonate at a Stark manifold resonance capable of cooling the crystal to a temperature of from about 110K to about 170K. The crystal host resonates in response to input from an excitation laser tuned to exploit the Stark manifold resonance corresponding to the cooling of the crystal.
Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation
Weigang Wen; Gao, Robert X.; Weidong Cheng
2016-01-01
The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by w...
Some properties of Fr\\'echet medians in Riemannian manifolds
Yang, Le
2011-01-01
The consistency of Fr\\'echet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fr\\'echet medians are estimated. It is also shown that, in compact Riemannian manifolds, the Fr\\'echet sample medians of generic data points are always unique.
Automorphisms and examples of compact non K\\"ahler manifolds
Magnússon, Gunnar Þór
2012-01-01
Let $X$ be a compact K\\"ahler manifold with zero first Chern class and finite fundamental group. Folklore says that if an automorphism $f$ of $X$ fixes a K\\"ahler class, then its order is finite. We apply this result to construct a compact non K\\"ahler manifold $F$ as a fibration $X \\to F \\to B$ over a complex torus $B$.
Holonomy reductions of Cartan geometries and curved orbit decompositions
Cap, Andreas; Gover, A. Rod; Hammerl, Matthias
2011-01-01
We develop a holonomy reduction procedure for general Cartan geometries. We show that, given a reduction of holonomy, the underlying manifold naturally decomposes into a disjoint union of initial submanifolds. Each such submanifold corresponds to an orbit of the holonomy group on the modeling homogeneous space and carries a canonical induced Cartan geometry. The result can therefore be understood as a “curved orbit decomposition.” The theory is then applied to the study of several invariant o...
An introduction to supersymmetric field theories in curved space
Dumitrescu, Thomas T
2016-01-01
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background fields. We present the general principles, which broadly apply to theories with different amounts of supersymmetry in diverse dimensions, as well as specific applications to N=1 theories in four dimensions and their three-dimensional cousins with N=2 supersymmetry.
From integral manifolds and metrics to potential maps
Directory of Open Access Journals (Sweden)
Udriste, C
2004-01-01
Full Text Available Our paper contains two main results: (1 the integral manifolds of a distribution together with two Riemann metrics produce potential maps which are in fact least squares approximations of the starting integral manifolds; (2 the least squares energy admits extremals satisfying periodic boundary conditions. Section 1 contains historical and bibliographical notes. Section 2 analyses some elements of the geometry produced on the jet bundle of order one by a semi-Riemann Sasaki-like metric. Section 3 describes the maximal integral manifolds of a distribution as solutions of a PDEs system of order one. Section 4 studies Poisson-like second-order prolongations of first order PDE systems and formulates the Lorentz-Udriste World-Force Law on a suitable semi-Riemann-Lagrange manifold (the base manifold of the jet bundle of order one. Section 5 exploits the idea of least squares Lagrangians, to include the integral manifolds of a distribution into a class of extremals. Section 6 gives conditions for the existence of extremals in conditions of multi-periodicity. Section 7 refers to the canonical forms of the vertical metric d-tensor produced by a density of energy on jet bundle of order one.
Generalized Einstein Tensor for a Weyl Manifold and Its Applications
Institute of Scientific and Technical Information of China (English)
Abdülkadir （O）ZDE（G）ER
2013-01-01
It is well known that the Einstein tensor G for a Piemannian manifold defined by Gβα =Rβα-1/2Rδα,Rβα =gβγRγα where Rγα and R are respectively the Ricci tensor and the scalar curvature of the manifold,plays an important part in Einstein's theory of gravitation as well as in proving some theorems in Riemannian geometry.In this work,we first obtain the generalized Einstein tensor for a Weyl manifold.Then,after studying some properties of generalized Einstein tensor,we prove that the conformed invariance of the generalized Einstein tensor implies the conformed invariance of the curvature tensor of the Weyl manifold and conversely.Moreover,we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogoned trajectories of which are geodesics.Finally,a necessary and sufficient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points.
Manifold learning of brain MRIs by deep learning.
Brosch, Tom; Tam, Roger
2013-01-01
Manifold learning of medical images plays a potentially important role for modeling anatomical variability within a population with pplications that include segmentation, registration, and prediction of clinical parameters. This paper describes a novel method for learning the manifold of 3D brain images that, unlike most existing manifold learning methods, does not require the manifold space to be locally linear, and does not require a predefined similarity measure or a prebuilt proximity graph. Our manifold learning method is based on deep learning, a machine learning approach that uses layered networks (called deep belief networks, or DBNs) and has received much attention recently in the computer vision field due to their success in object recognition tasks. DBNs have traditionally been too computationally expensive for application to 3D images due to the large number of trainable parameters. Our primary contributions are (1) a much more computationally efficient training method for DBNs that makes training on 3D medical images with a resolution of up to 128 x 128 x 128 practical, and (2) the demonstration that DBNs can learn a low-dimensional manifold of brain volumes that detects modes of variations that correlate to demographic and disease parameters.
Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.
Sun, Shiliang; Xie, Xijiong
2016-09-01
Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.
LIFE CYCLE DESIGN OF AIR INTAKE MANIFOLDS; PHASE I: 2.0 L FORD CONTOUR AIR INTAKE MANIFOLD
The project team applied the life cycle design methodology to the design analysis of three alternative air intake manifolds: a sand cast aluminum, brazed aluminum tubular, and nylon composite. The design analysis included a life cycle inventory analysis, environmental regulatory...
Institute of Scientific and Technical Information of China (English)
张振跃; 查宏远
2004-01-01
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
[A new algorithm for NIR modeling based on manifold learning].
Hong, Ming-Jian; Wen, Zhi-Yu; Zhang, Xiao-Hong; Wen, Quan
2009-07-01
Manifold learning is a new kind of algorithm originating from the field of machine learning to find the intrinsic dimensionality of numerous and complex data and to extract most important information from the raw data to develop a regression or classification model. The basic assumption of the manifold learning is that the high-dimensional data measured from the same object using some devices must reside on a manifold with much lower dimensions determined by a few properties of the object. While NIR spectra are characterized by their high dimensions and complicated band assignment, the authors may assume that the NIR spectra of the same kind of substances with different chemical concentrations should reside on a manifold with much lower dimensions determined by the concentrations, according to the above assumption. As one of the best known algorithms of manifold learning, locally linear embedding (LLE) further assumes that the underlying manifold is locally linear. So, every data point in the manifold should be a linear combination of its neighbors. Based on the above assumptions, the present paper proposes a new algorithm named least square locally weighted regression (LS-LWR), which is a kind of LWR with weights determined by the least squares instead of a predefined function. Then, the NIR spectra of glucose solutions with various concentrations are measured using a NIR spectrometer and LS-LWR is verified by predicting the concentrations of glucose solutions quantitatively. Compared with the existing algorithms such as principal component regression (PCR) and partial least squares regression (PLSR), the LS-LWR has better predictability measured by the standard error of prediction (SEP) and generates an elegant model with good stability and efficiency.
Optimization on shape curves with application to specular stereo
Balzer, Jonathan
2010-01-01
We state that a one-dimensional manifold of shapes in 3-space can be modeled by a level set function. Finding a minimizer of an independent functional among all points on such a shape curve has interesting applications in computer vision. It is shown how to replace the commonly encountered practice of gradient projection by a projection onto the curve itself. The outcome is an algorithm for constrained optimization, which, as we demonstrate theoretically and numerically, provides some important benefits in stereo reconstruction of specular surfaces. © 2010 Springer-Verlag.
Target detection performed on manifold approximations recovered from hyperspectral data
Ziemann, Amanda K.; Messinger, David W.; Albano, James A.
2013-05-01
In high dimensional data, manifold learning seeks to identify the embedded lower-dimensional, non-linear mani- fold upon which the data lie. This is particularly useful in hyperspectral imagery where inherently m-dimensional data is often sparsely distributed throughout the d-dimensional spectral space, with m << d. By recovering the manifold, inherent structures and relationships within the data - which are not typically apparent otherwise - may be identified and exploited. The sparsity of data within the spectral space can prove challenging for many types of analysis, and in particular with target detection. In this paper, we propose using manifold recovery as a preprocessing step for spectral target detection algorithms. A graph structure is first built upon the data and the transformation into the manifold space is based upon that graph structure. Then, the Adaptive Co- sine/Coherence Estimator (ACE) algorithm is applied. We present an analysis of target detection performance in the manifold space using scene-derived target spectra from two different hyperspectral images.
Compactifications of IIA supergravity on SU(2)-structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Spanjaard, B.
2008-07-15
In this thesis, we study compactifications of type IIA supergravity on six-dimensional manifolds with an SU(2)-structure. A general study of six-dimensional manifolds with SU(2)-structure shows that IIA supergravity compactified on such a manifold should yield a four-dimensional gauged N=4 supergravity. We explicitly derive the bosonic spectrum, gauge transformations and action for IIA supergravity compactified on two different manifolds with SU(2)-structure, one of which also has an H{sup (3)}{sub 10}-flux, and confirm that the resulting four-dimensional theories are indeed N=4 gauged supergravities. In the second chapter, we study an explicit construction of a set of SU(2)-structure manifolds. This construction involves a Scherk-Schwarz duality twist reduction of the half-maximal six-dimensional supergravity obtained by compactifying IIA supergravity on a K3. This reduction results in a gauged N=4 four-dimensional supergravity, where the gaugings can be divided into three classes of parameters. We relate two of the classes to parameters we found before, and argue that the third class of parameters could be interpreted as a mirror flux. (orig.)
Physics on the adiabatically changed Finslerian manifold and cosmology
Lipovka, Anton A
2016-01-01
In present paper we confirm our previous result [4] that Planck constant is adiabatic invariant of electromagnetic field propagating on the adiabatically changed Finslerian manifold. Direct calculation from cosmological parameters gives value h=6x10(-27) (erg s). We also confirm that Planck constant (and hence other fundamental constants which depend on h) is varied on time due to changing of geometry. As an example the variation of the fine structure constant is calculated. Its relative variation ((da/dt)/a) consist 1.0x10(-18) (1/s). We show that on the Finsler manifold characterized by adiabatically changed geometry, classical free electromagnetic field is quantized geometrically, from the properties of the manifold in such manner that adiabatic invariant of field is ET=6x10(-27)=h. Electrodynamic equations on the Finslerian manifold are suggested. It is stressed that quantization naturally appears from these equations and is provoked by adiabatically changed geometry of manifold. We consider in details tw...
Hierarchical discriminant manifold learning for dimensionality reduction and image classification
Chen, Weihai; Zhao, Changchen; Ding, Kai; Wu, Xingming; Chen, Peter C. Y.
2015-09-01
In the field of image classification, it has been a trend that in order to deliver a reliable classification performance, the feature extraction model becomes increasingly more complicated, leading to a high dimensionality of image representations. This, in turn, demands greater computation resources for image classification. Thus, it is desirable to apply dimensionality reduction (DR) methods for image classification. It is necessary to apply DR methods to relieve the computational burden as well as to improve the classification accuracy. However, traditional DR methods are not compatible with modern feature extraction methods. A framework that combines manifold learning based DR and feature extraction in a deeper way for image classification is proposed. A multiscale cell representation is extracted from the spatial pyramid to satisfy the locality constraints for a manifold learning method. A spectral weighted mean filtering is proposed to eliminate noise in the feature space. A hierarchical discriminant manifold learning is proposed which incorporates both category label and image scale information to guide the DR process. Finally, the image representation is generated by concatenating dimensionality reduced cell representations from the same image. Extensive experiments are conducted to test the proposed algorithm on both scene and object recognition datasets in comparison with several well-established and state-of-the-art methods with respect to classification precision and computational time. The results verify the effectiveness of incorporating manifold learning in the feature extraction procedure and imply that the multiscale cell representations may be distributed on a manifold.
Enhanced manifold regularization for semi-supervised classification.
Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong
2016-06-01
Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.
Manifold Learning for Biomarker Discovery in MR Imaging
Wolz, Robin; Aljabar, Paul; Hajnal, Joseph V.; Rueckert, Daniel
We propose a framework for the extraction of biomarkers from low-dimensional manifolds representing inter- and intra-subject brain variation in MR image data. The coordinates of each image in such a low-dimensional space captures information about structural shape and appearance and, when a phenotype exists, about the subject's clinical state. A key contribution is that we propose a method for incorporating longitudinal image information in the learned manifold. In particular, we compare simultaneously embedding baseline and follow-up scans into a single manifold with the combination of separate manifold representations for inter-subject and intra-subject variation. We apply the proposed methods to 362 subjects enrolled in the Alzheimer's Disease Neuroimaging Initiative (ADNI) and classify healthy controls, subjects with Alzheimer's disease (AD) and subjects with mild cognitive impairment (MCI). Learning manifolds based on both the appearance and temporal change of the hippocampus, leads to correct classification rates comparable with those provided by state-of-the-art automatic segmentation estimates of hippocampal volume and atrophy. The biomarkers identified with the proposed method are data-driven and represent a potential alternative to a-priori defined biomarkers derived from manual or automated segmentations.
Analysis on singular spaces: Lie manifolds and operator algebras
Nistor, Victor
2016-07-01
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called "Lie manifolds" -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.
Hyperbolic normal forms and invariant manifolds: Astronomical applications
Directory of Open Access Journals (Sweden)
Efthymiopoulos C.
2012-01-01
Full Text Available In recent years, the study of the dynamics induced by the invariant manifolds of unstable periodic orbits in nonlinear Hamiltonian dynamical systems has led to a number of applications in celestial mechanics and dynamical astronomy. Two applications of main current interest are i space manifold dynamics, i.e. the use of the manifolds in space mission design, and, in a quite different context, ii the study of spiral structure in galaxies. At present, most approaches to the computation of orbits associated with manifold dynamics (i.e. periodic or asymptotic orbits rely either on the use of the so-called Poincaré - Lindstedt method, or on purely numerical methods. In the present article we briefly review an analytic method of computation of invariant manifolds, first introduced by Moser (1958, and developed in the canonical framework by Giorgilli (2001. We use a simple example to demonstrate how hyperbolic normal form computations can be performed, and we refer to the analytic continuation method of Ozorio de Almeida and co-workers, by which we can considerably extend the initial domain of convergence of Moser’s normal form.
Quasi-Newton Exploration of Implicitly Constrained Manifolds
Tang, Chengcheng
2011-08-01
A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.
Shock detachment from curved wedges
Mölder, S.
2017-03-01
Curved shock theory is used to show that the flow behind attached shocks on doubly curved wedges can have either positive or negative post-shock pressure gradients depending on the freestream Mach number, the wedge angle and the two wedge curvatures. Given enough wedge length, the flow near the leading edge can choke to force the shock to detach from the wedge. This local choking can preempt both the maximum deflection and the sonic criteria for shock detachment. Analytical predictions for detachment by local choking are supported by CFD results.
Shock detachment from curved wedges
Mölder, S.
2017-09-01
Curved shock theory is used to show that the flow behind attached shocks on doubly curved wedges can have either positive or negative post-shock pressure gradients depending on the freestream Mach number, the wedge angle and the two wedge curvatures. Given enough wedge length, the flow near the leading edge can choke to force the shock to detach from the wedge. This local choking can preempt both the maximum deflection and the sonic criteria for shock detachment. Analytical predictions for detachment by local choking are supported by CFD results.
Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems
Borot, Gaetan
2015-01-01
We consider the Gopakumar-Ooguri-Vafa correspondence, relating U(N) Chern-Simons theory at large N to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $S^\\Gamma=S^3/\\Gamma$ of the three-sphere by the free action of a finite isometry group. Guided by string theory dualities, we propose a large N dual description in terms of both A- and B-twisted topological strings on (in general non-toric) local Calabi-Yau threefolds. The target space of the B-model theory is obtained from the spectral curve of Toda-type integrable systems constructed on the double Bruhat cells of the simply-laced group identified by the ADE label of $\\Gamma$. Its mirror A-model theory is realized as the local Gromov-Witten theory of suitable ALE fibrations on $CP^1$ generalizing the results known for lens spaces. We propose an explicit construction of the family of target manifolds relevant for the correspondence, which we verify through a large N analysis of the matrix model that expresses the contri...
Multiphasic growth curve analysis.
Koops, W.J.
1986-01-01
Application of a multiphasic growth curve is demonstrated with 4 data sets, adopted from literature. The growth curve used is a summation of n logistic growth functions. Human height growth curves of this type are known as "double logistic" (n = 2) and "triple logistic" (n = 3) growth curves (Bock
A twistor sphere of generalized Kahler potentials on hyperkahler manifolds
Dyckmanns, Malte
2011-01-01
We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose description in projective superspace is fully understood. We use this relation to determine an S^2-family of generalized Kahler potentials for Euclidean space and for the Eguchi-Hanson geometry. Cotangent bundles of Hermitian symmetric spaces constitute a class of hyperkahler manifolds where our method can be applied immediately since the necessary results from projective superspace are already available. As a non-trivial higher-dimensional example, we determine the generalized potential for T*CP^n, which generalizes the Eguchi-Hanson result.
Weyl-Euler-Lagrange Equations of Motion on Flat Manifold
Directory of Open Access Journals (Sweden)
Zeki Kasap
2015-01-01
Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
Rigidity of complete noncompact bach-flat n-manifolds
Chu, Yawei; Feng, Pinghua
2012-11-01
Let (Mn,g) be a complete noncompact Bach-flat n-manifold with the positive Yamabe constant and constant scalar curvature. Assume that the L2-norm of the trace-free Riemannian curvature tensor R∘m is finite. In this paper, we prove that (Mn,g) is a constant curvature space if the L-norm of R∘m is sufficiently small. Moreover, we get a gap theorem for (Mn,g) with positive scalar curvature. This can be viewed as a generalization of our earlier results of 4-dimensional Bach-flat manifolds with constant scalar curvature R≥0 [Y.W. Chu, A rigidity theorem for complete noncompact Bach-flat manifolds, J. Geom. Phys. 61 (2011) 516-521]. Furthermore, when n>9, we derive a rigidity result for R<0.
Manifold boundaries give "gray-box" approximations of complex models
Transtrum, Mark K
2016-01-01
We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric approximation problem. It operates iteratively, removing one parameter at a time, by approximating a high-dimension, but thin manifold by its boundary. Although the method makes no explicit assumption about the functional form of the model, it does require that the model manifold exhibit a hierarchy of boundaries, i.e., faces, edges, corners, hyper-corners, etc. We empirically show that a variety of model classes have this curious feature, making them amenable to MBAM. These model classes include models composed of elementary functions (e.g., rational functions, exponentials, and partition functions), a variety of dynamical system (e.g., chemical and biochemical kinetics, Linear Time Invariant (LTI) systems, and compartment models), network models (e.g., Bayesian networks, Marko...
Gradient Algorithm on Stiefel Manifold and Application in Feature Extraction
Directory of Open Access Journals (Sweden)
Zhang Jian-jun
2013-09-01
Full Text Available To improve the computational efficiency of system feature extraction, reduce the occupied memory space, and simplify the program design, a modified gradient descent method on Stiefel manifold is proposed based on the optimization algorithm of geometry frame on the Riemann manifold. Different geodesic calculation formulas are used for different scenarios. A polynomial is also used to lie close to the geodesic equations. JiuZhaoQin-Horner polynomial algorithm and the strategies of line-searching technique and change of the step size of iteration are also adopted. The gradient descent algorithm on Stiefel manifold applied in Principal Component Analysis (PCA is discussed in detail as an example of system feature extraction. Theoretical analysis and simulation experiments show that the new method can achieve superior performance in both the convergence rate and calculation efficiency while ensuring the unitary column orthogonality. In addition, it is easier to implement by software or hardware.
Flow and Pressure Distribution in Fuel Cell Manifolds
DEFF Research Database (Denmark)
Lebæk, Jesper; Bang, Mads; Kær, Søren Knudsen
2010-01-01
The manifold is an essential part of the fuel cell stack. Evidently, evenly distributed reactants are a prerequisite for an efficient fuel cell stack. In this study, the cathode manifold ability to distribute air to the cells of a 70 cell stack is investigated experimentally. By means of 20...... differential pressure gauges, the flow distribution is mapped for several geometrical and operating conditions. Special attention is given to the inlet conditions of the manifold. Here, a diffuser design was constructed in order to replace the conventional circular inlet design. The diffuser design showed...... significant improvements to the flow distribution in comparison to the circular design. Moreover, the best flow distribution was found using a U-shaped configuration....
Multiscale singular value manifold for rotating machinery fault diagnosis
Energy Technology Data Exchange (ETDEWEB)
Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)
2017-01-15
Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.
Schoen manifold with line bundles as resolved magnetized orbifolds
Energy Technology Data Exchange (ETDEWEB)
Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
We give an alternative description of the Schoen manifold as the blow-up of a Z{sub 2} x Z{sub 2} orbifold in which one Z{sub 2} factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.
Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation
Directory of Open Access Journals (Sweden)
Weigang Wen
2016-01-01
Full Text Available The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by wavelet enveloping. The envelope energy is adopted as an indicator to select meshing frequency band. Manifold learning is utilized to reduce the effect of noise within meshing frequency band. The fault characteristic frequency of the planetary gear is shown by spectrogram. The planetary gearbox model and test rig are established and experiments with planet gear faults are conducted for verification. All results of experiment analysis demonstrate its effectiveness and reliability.
Quantum Chaos on Hyperbolic Manifolds A New Approach to Cosmology
Tomaschitz, R
1992-01-01
We consider classical and quantum motion on multiply connected hyperbolic spaces, which appear as space-like slices in Robertson-Walker cosmologies. The topological structure of these manifolds creates on the one hand bounded chaotic trajectories, and on the other hand quantal bound states whose wave functions can be reconstructed from the chaotic geodesics. We obtain an exact relation between a probabilistic quantum mechanical wave field and the corresponding classical system, which is likewise probabilistic because of the instabilities of the trajectories with respect to the initial conditions. The central part in this reconstruction is played by the fractal limit set of the covering group of the manifold. This limit set determines the bounded chaotic trajectories on the manifold. Its Hausdorff measure and dimension determine the wave function of the quantum mechanical bound state for geodesic motion. We investigate relativistic scalar wave fields in de Sitter cosmologies, coupled to the curvature scalar of...
Why Deep Learning Works: A Manifold Disentanglement Perspective.
Brahma, Pratik Prabhanjan; Wu, Dapeng; She, Yiyuan
2016-10-01
Deep hierarchical representations of the data have been found out to provide better informative features for several machine learning applications. In addition, multilayer neural networks surprisingly tend to achieve better performance when they are subject to an unsupervised pretraining. The booming of deep learning motivates researchers to identify the factors that contribute to its success. One possible reason identified is the flattening of manifold-shaped data in higher layers of neural networks. However, it is not clear how to measure the flattening of such manifold-shaped data and what amount of flattening a deep neural network can achieve. For the first time, this paper provides quantitative evidence to validate the flattening hypothesis. To achieve this, we propose a few quantities for measuring manifold entanglement under certain assumptions and conduct experiments with both synthetic and real-world data. Our experimental results validate the proposition and lead to new insights on deep learning.
Adaptive sampling for nonlinear dimensionality reduction based on manifold learning
DEFF Research Database (Denmark)
Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan
2017-01-01
We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space...... that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric...... to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime....
Behavior of Graph Laplacians on Manifolds with Boundary
Zhou, Xueyuan
2011-01-01
In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from sampled data to certain continuous operators has become an active research topic recently. Most of the existing work has been done under the assumption that the data is sampled from a manifold without boundary or that the functions of interests are evaluated at a point away from the boundary. However, the question of boundary behavior is of considerable practical and theoretical interest. In this paper we provide an analysis of the behavior of graph Laplacians at a point near or on the boundary, discuss their convergence rates and their implications and provide some numerical results. It turns out that while points near the boundary occupy only a small part of the total volume of a manifold, the behavior of graph Laplacian there has different scaling properties from its beh...
Valve and Manifold considerations for Efficient Digital Hydraulic Machines
DEFF Research Database (Denmark)
Roemer, Daniel Beck; Nørgård, Christian; Bech, Michael Møller
2016-01-01
This paper seeks to shed light on the topic of design and sizing of switching valves and connecting manifolds found in large digital hydraulic motors, also known commercially as Digital Displacement Motors. These motors promise very high operation efficiencies with broad operation ranges, which set...... strict requirements to the switching valves and the overall manifold design. To investigate this topic, the largest known digital motor (3.5 megawatt) is studied using models and optimization. Based on the limited information available about this motor, a detailed reconstruction of the motor architecture...... valves when considering also the manifold flow losses. A global optimization is conducted by use of the generalized differential evolution 3 algorithm, where the valve diameters, valve stroke lengths, actuator force capabilities and actuator timing signals are used as design variables. The results...
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
Fiori, Simone
2017-06-01
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
Pseudo-differential operators on manifolds with singularities
Schulze, B-W
1991-01-01
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
Total Variation Regularization for Functions with Values in a Manifold
Lellmann, Jan
2013-12-01
While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.
Postoperative 3D spine reconstruction by navigating partitioning manifolds
Energy Technology Data Exchange (ETDEWEB)
Kadoury, Samuel, E-mail: samuel.kadoury@polymtl.ca [Department of Computer and Software Engineering, Ecole Polytechnique Montreal, Montréal, Québec H3C 3A7 (Canada); Labelle, Hubert, E-mail: hubert.labelle@recherche-ste-justine.qc.ca; Parent, Stefan, E-mail: stefan.parent@umontreal.ca [CHU Sainte-Justine Hospital Research Center, Montréal, Québec H3T 1C5 (Canada)
2016-03-15
Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities.
Detecting Lo cal Manifold Structure for Unsup ervised Feature Selection
Institute of Scientific and Technical Information of China (English)
FENG Ding-Cheng; CHEN Feng; XU Wen-Li
2014-01-01
Unsupervised feature selection is fundamental in statistical pattern recognition, and has drawn persistent attention in the past several decades. Recently, much work has shown that feature selection can be formulated as nonlinear dimensionality reduction with discrete constraints. This line of research emphasizes utilizing the manifold learning techniques, where feature selection and learning can be studied based on the manifold assumption in data distribution. Many existing feature selection methods such as Laplacian score, SPEC (spectrum decomposition of graph Laplacian), TR (trace ratio) criterion, MSFS (multi-cluster feature selection) and EVSC (eigenvalue sensitive criterion) apply the basic properties of graph Laplacian, and select the optimal feature subsets which best preserve the manifold structure defined on the graph Laplacian. In this paper, we propose a new feature selection perspective from locally linear embedding (LLE), which is another popular manifold learning method. The main difficulty of using LLE for feature selection is that its optimization involves quadratic programming and eigenvalue decomposition, both of which are continuous procedures and different from discrete feature selection. We prove that the LLE objective can be decomposed with respect to data dimensionalities in the subset selection problem, which also facilitates constructing better coordinates from data using the principal component analysis (PCA) technique. Based on these results, we propose a novel unsupervised feature selection algorithm, called locally linear selection (LLS), to select a feature subset representing the underlying data manifold. The local relationship among samples is computed from the LLE formulation, which is then used to estimate the contribution of each individual feature to the underlying manifold structure. These contributions, represented as LLS scores, are ranked and selected as the candidate solution to feature selection. We further develop a
Manifold invariants affect dynamics in ADS gravity
Liko, Tomas
2013-01-01
The first-order Holst action with negative cosmological constant is rendered finite by requiring functional differentiability on the configuration space of tetrads and connections. The surface terms that arise in the action for ADS gravity are equivalent to the Euler and Pontryagin densities with fixed weight factors; these terms modify the Noether charges that arise from diffeomorphism invariance of the action.
Manifold learning techniques and model reduction applied to dissipative PDEs
Sonday, Benjamin E; Gear, C William; Kevrekidis, Ioannis G
2010-01-01
We link nonlinear manifold learning techniques for data analysis/compression with model reduction techniques for evolution equations with time scale separation. In particular, we demonstrate a `"nonlinear extension" of the POD-Galerkin approach to obtaining reduced dynamic models of dissipative evolution equations. The approach is illustrated through a reaction-diffusion PDE, and the performance of different simulators on the full and the reduced models is compared. We also discuss the relation of this nonlinear extension with the so-called "nonlinear Galerkin" methods developed in the context of Approximate Inertial Manifolds.
Geometry and physics of pseudodifferential operators on manifolds
Esposito, Giampiero; Napolitano, George M.
2016-09-01
A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: existence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic calculus; the two kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian manifold; the concept of symbol as an equivalence class. Physical motivations and applications are then outlined, with emphasis on Green functions of quantum field theory and Parker's evaluation of Hawking radiation.
Frobenius manifolds, Integrable Hierarchies and Minimal Liouville Gravity
Belavin, A A
2014-01-01
We use the connection between the Frobrenius manifold and the Douglas string equation to further investigate Minimal Liouville gravity. We search a solution of the Douglas string equation and simultaneously a proper transformation from the KdV to the Liouville frame which ensure the fulfilment of the conformal and fusion selection rules. We find that the desired solution of the string equation has explicit and simple form in the flat coordinates on the Frobenious manifold in the general case of (p,q) Minimal Liouville gravity.
Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds
Bachman, David
2012-01-01
Let M_1 and M_2 be compact, orientable 3-manifolds with incompressible boundary, and M the manifold obtained by gluing with a homeomorphism $\\phi:\\bdy M_1 \\to \\bdy M_2$. We analyze the relationship between the sets of low genus Heegaard splittings of M_1, M_2, and M, assuming the map \\phi is "sufficiently complicated." This analysis yields counter-examples to the Stabilization Conjecture, a resolution of the higher genus analogue of a conjecture of Gordon, and a result about the uniqueness of expressions of Heegaard splittings as amalgamations.
A New Infinite Class of Sasaki-Einstein Manifolds
Gauntlett, J P; Sparks, J F; Waldram, D; Gauntlett, Jerome P.; Martelli, Dario; Sparks, James F.; Waldram, Daniel
2004-01-01
We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we obtain new supersymmetric AdS_4 x X_7 solutions of D=11 supergravity. Both are expected to provide new supergravity duals of superconformal field theories.
Valve and Manifold considerations for Efficient Digital Hydraulic Machines
DEFF Research Database (Denmark)
Roemer, Daniel Beck; Nørgård, Christian; Bech, Michael Møller;
2016-01-01
This paper seeks to shed light on the topic of design and sizing of switching valves and connecting manifolds found in large digital hydraulic motors, also known commercially as Digital Displacement Motors. These motors promise very high operation efficiencies with broad operation ranges, which set...... valves when considering also the manifold flow losses. A global optimization is conducted by use of the generalized differential evolution 3 algorithm, where the valve diameters, valve stroke lengths, actuator force capabilities and actuator timing signals are used as design variables. The results...
Latent common manifold learning with alternating diffusion: analysis and applications
Talmon, Ronen
2016-01-01
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We introduce a latent common manifold model underlying multiple sensor observations for the purpose of multimodal data fusion. A method based on alternating diffusion is presented and analyzed; we provide theoretical analysis of the method under the latent common manifold model. To exemplify the power of the proposed framework, experimental results in several applications are reported.
Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvature
Mangoubi, Oren; Smith, Aaron
2016-01-01
We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\\mathcal{M}$, which we call the $\\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional curvature $C_{x}(u,v)$ bounded both above and below by $0 < \\mathfrak{m}_{2} \\leq C_{x}(u,v) \\leq \\mathfrak{M}_2 < \\infty$ is $\\mathcal{O}^*\\left(\\frac{\\mathfrak{M}_2}{\\mathfrak{m}_2}\\right)$. In particular, this bound on the mixing time does not depend expli...
Scars of Invariant Manifolds in Interacting Few-Body Systems
Papenbrock, T; Weidenmüller, H A
1997-01-01
We present a novel extension of the concept of scars for the wave functions of classically chaotic few--body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space which are invariant under the action of a common subgroup of these two symmetries. Such manifolds are associated with highly symmetric configurations and, if sufficiently stable, support quantum resonances. Although not directly associated to individual periodic orbits, the resonances nevertheless cause scars which signify collective motion on the quantum level and which should be experimentally observable.
Distributed mean curvature on a discrete manifold for Regge calculus
Conboye, Rory; Ray, Shannon
2015-01-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as a fractional rate of change of the normal vector.
String Corrected Spacetimes and SU(N)-Structure Manifolds
Becker, Katrin; Robbins, Daniel
2015-01-01
Using an effective field theory approach and the language of SU(N)-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that the internal geometry remains flat and uncorrected. For n=4, 6, Kahler manifolds with SU(N)-holonomy can become corrected to SU(N)-structure, while preserving supersymmetry, once corrections are included.
String corrected spacetimes and SU(N-structure manifolds
Directory of Open Access Journals (Sweden)
Katrin Becker
2015-09-01
Full Text Available Using an effective field theory approach and the language of SU(N-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that internal geometry remains flat and uncorrected. For n=4,6, Kähler manifolds with SU(N-holonomy can become corrected to SU(N-structure, while preserving supersymmetry, once corrections are included.
Szpak, Nikodem
2014-01-01
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple manipulations of the optical setup. Examples presented here contain two-dimensional spaces of positive and negative curvature as well as homogeneous cosmological models and metric waves. Most of them are extendable to three spatial dimensions. We mention some interesting phenomena of quantum field theory in curved spacetimes which might be simulated in such optical lattices loaded with bosonic or fermionic ultra-cold atoms. We also argue that methods of differential geometry can be used, as an alternative mathematical approach, for dealing with realistic inhomogeneous optical lattices.
Unstable manifold computations for the two-dimensional plane Poiseuille flow
Energy Technology Data Exchange (ETDEWEB)
Casas, Pablo S. [Universidad Politecnica de Cataluna, Departamento de Matematica Aplicada I, Barcelona (Spain); Jorba, Angel [Universidad de Barcelona, Departamento de Matematica Aplicada y Analisis, Barcelona (Spain)
2004-11-01
We follow the unstable manifold of periodic and quasi-periodic solutions in time for the Poiseuille problem, using two formulations: holding a constant flux or mean pressure gradient. By means of a numerical integrator of the Navier-Stokes equations, we let the fluid evolve from an initially perturbed unstable solution until the fluid reaches an attracting state. Thus, we detect several connections among different configurations of the flow such as laminar, periodic, quasi-periodic with two or three basic frequencies, and more complex sets that we have not been able to classify. These connections make possible the location of new families of solutions, usually hard to find by means of numerical continuation of curves, and show the richness of the dynamics of the Poiseuille flow. (orig.)
2D-Manifold Boundary Surfaces Extraction from Heterogeneous Object on GPU
Institute of Scientific and Technical Information of China (English)
Ming Wang; Jie-Qing Feng
2012-01-01
The conventional isosurface techniques are not competent for meshing a heterogeneous object because they assume that the object is homogeneous.Thus the visualization method taking the heterogeneity into account is desired.In this paper,we propose a novel algorithm to extract the boundary surfaces from a heterogeneous object in one pass,whose remarkable advantage is free of the number of materials contained.The heterogeneous object is first classified into a series of homogeneous material components.Then each component is enclosed with a 2D-manifold boundary surface extracted via our algorithm.The information important to the heterogeneous object is also provided,such as the interface between two materials,the intersection curve where three materials meet and the intersection point where four materials meet.To improve the performance,the algorithm is also designed and implemented on GPU.Experimental results demonstrate the effectiveness and efficiency of the proposed algorithm.
Manifold adaptation for constant false alarm rate ship detection in South African oceans
CSIR Research Space (South Africa)
Schwegmann, CP
2015-04-01
Full Text Available into a threshold manifold. The manifold is adjusted using a Simulated Annealing algorithm to optimally fit to information provided by the ship distribution map which is generated from transponder data. By carefully selecting the input solution...
Besov continuity for pseudo-differential operators on compact homogeneous manifolds
Cardona, Duván
2016-01-01
In this paper we study the Besov continuity of pseudo-differential operators on compact homogeneous manifolds $M=G/K.$ We use the global quantization of these operators in terms of the representation theory of compact homogeneous manifolds.
Conjugate Points on a Type of K(a)hler Manifolds
Institute of Scientific and Technical Information of China (English)
Wei Ming LIU; Fu Sheng DENG
2013-01-01
We study conjugate points on a type of K(a)hler manifolds,which are submanifolds of Grassmannian manifolds.And then we give the applications to the study of the index of geodesics and homotopy groups.
Quantum general relativity and the classification of smooth manifolds
Pfeiffer, H
2004-01-01
The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth manifolds. This is an opportunity to review results on the classification of smooth, piecewise-linear and topological manifolds. It turns out that differential topology distinguishes the space-time dimension d=3+1 from any other lower or higher dimension and relates the sought-after path integral quantization of general relativity in d=3+1 with an open problem in topology, namely to construct non-trivial invariants of smooth manifolds using their piecewise-linear structure. In any dimension d<=5+1, the classification results provide us with triangulations of space-time which are not merely approximations nor introduce any physical cut-off, but which rather capture the full information about smooth manifolds up to diffeomorphism. Conditions on refinements of these triangulations...
Invariants of 3-Manifolds derived from finite dimensional hopf algebras
Kauffman, L H; Louis H Kauffman; David E Radford
1994-01-01
Abstract: This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.
The Persistence of a Slow Manifold with Bifurcation
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P.; Robert, M.
2012-01-01
his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated...
Curvature Properties of Lorentzian Manifolds with Large Isometry Groups
Energy Technology Data Exchange (ETDEWEB)
Batat, Wafaa [Ecole Normale Superieure de L' Enseignement Technique d' Oran, Departement de Mathematiques et Informatique (Algeria)], E-mail: wafa.batat@enset-oran.dz; Calvaruso, Giovanni, E-mail: giovanni.calvaruso@unile.it; Leo, Barbara De [University of Salento, Dipartimento di Matematica ' E. De Giorgi' (Italy)], E-mail: barbara.deleo@unile.it
2009-08-15
The curvature of Lorentzian manifolds (M{sup n},g), admitting a group of isometries of dimension at least 1/2n(n - 1) + 1, is completely described. Interesting behaviours are found, in particular as concerns local symmetry, local homogeneity and conformal flatness.
The Koppelman-Leray formula on complex Finsler manifolds
Institute of Scientific and Technical Information of China (English)
QIU Chunhui; ZHONG Tongde
2005-01-01
By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.
Coordination of a heterogeneous coastal hydrodynamics application in manifold
C.L. Blom (Kees); F. Arbab (Farhad); S. Hummel; I.J.P. Elshoff
1998-01-01
textabstractIn this paper we show how the coordination language Manifold can be used to control the interactions of multiple heterogeneous application programs. We use a concrete example from Delft Hydaulics, a consulting and research company which develops models of natural hydraulic systems (e.g.,
AdS 3-manifolds and Higgs bundles
DEFF Research Database (Denmark)
Alessandrini, Daniele; Li, Qiongling
2015-01-01
In this paper we investigate the relationships between closed AdS 3-manifolds and Higgs bundles. We have a new way to construct AdS structures that allows us to see many of their properties explicitly, for example we can recover the very recent formula by Tholozan for the volumes. We also find...
Quadrature rules and distribution of points on manifolds
Brandolini, Luca; Colzani, Leonardo; Gigante, Giacomo; Seri, Raffaello; Travaglini, Giancarlo
2010-01-01
We study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.
Orientifolds of type IIA strings on Calabi-Yau manifolds
Govindarajan, S; Govindarajan, Suresh; Majumder, Jaydeep
2004-01-01
We identify type IIA orientifolds that are dual to M-theory compactifications on manifolds with G_2-holonomy. We then discuss the construction of crosscap states in Gepner models. (Based on a talk presented by S.G. at PASCOS 2003 held at the Tata Institute of Fundamental Research, Mumbai during Jan. 3-8, 2003.)
Beckner Inequality on Finite- and Infinite-Dimensional Manifolds
Institute of Scientific and Technical Information of China (English)
Pingji DENG; Fengyu WANG
2006-01-01
By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery's argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems.In particular, some results in [1, 2] are generalized.
Noise reduction method based on weighted manifold decomposition
Institute of Scientific and Technical Information of China (English)
Gan Jian-Chao; Xiao Xian-Ci
2004-01-01
A noise reduction method based on weighted manifold decomposition is proposed in this paper, which does not need knowledge of the chaotic dynamics and choosing number of eigenvalues. The simulation indicates that the performance of this method can increase the signal-to-noise ratio of noisy chaotic time series.
Data-driven facial animation based on manifold Bayesian regression
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Driving facial animation based on tens of tracked markers is a challenging task due to the complex topology and to the non-rigid nature of human faces. We propose a solution named manifold Bayesian regression. First a novel distance metric, the geodesic manifold distance, is introduced to replace the Euclidean distance. The problem of facial animation can be formulated as a sparse warping kernels regression problem, in which the geodesic manifold distance is used for modelling the topology and discontinuities of the face models. The geodesic manifold distance can be adopted in traditional regression methods, e.g. radial basis functions without much tuning. We put facial animation into the framework of Bayesian regression. Bayesian approaches provide an elegant way of dealing with noise and uncertainty. After the covariance matrix is properly modulated, Hybrid Monte Carlo is used to approximate the integration of probabilities and get deformation results. The experimental results showed that our algorithm can robustly produce facial animation with large motions and complex face models.
Almost conformal transformation in a class of Riemannian manifolds
Dzhelepov, Georgi; Dokuzova, Iva
2010-01-01
We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we construct an infinite series of circulant metrics which are successively almost conformaly related. In this case we get some properties.
Cost-effective and detailed modelling of compressor manifold vibrations
Eijk, A.; Egas, G.; Smeulers, J.P.M.
1996-01-01
In systems with large reciprocating compressors, so-called compressor manifold vibrations can contribute to fatigue failure of the pipe system. These vibrations are excited by pulsation-induced forces and by forces generated by the compressor. This paper describes an advanced and accurate method for
Two new variants of the manifold-mapping technique
Echeverria, D.
2006-01-01
Manifold-mapping is an efficient surrogate-based optimization technique aimed at the acceleration of very time-consuming design problems. In this paper we present two new variants of the original algorithm that make it applicable to a broader range of optimization scenarios. The first variant is use
Manifold learning on brain functional networks in aging.
Qiu, Anqi; Lee, Annie; Tan, Mingzhen; Chung, Moo K
2015-02-01
We propose a new analysis framework to utilize the full information of brain functional networks for computing the mean of a set of brain functional networks and embedding brain functional networks into a low-dimensional space in which traditional regression and classification analyses can be easily employed. For this, we first represent the brain functional network by a symmetric positive matrix computed using sparse inverse covariance estimation. We then impose a Log-Euclidean Riemannian manifold structure on brain functional networks whose norm gives a convenient and practical way to define a mean. Finally, based on the fact that the computation of linear operations can be done in the tangent space of this Riemannian manifold, we adopt Locally Linear Embedding (LLE) to the Log-Euclidean Riemannian manifold space in order to embed the brain functional networks into a low-dimensional space. We show that the integration of the Log-Euclidean manifold with LLE provides more efficient and succinct representation of the functional network and facilitates regression analysis, such as ridge regression, on the brain functional network to more accurately predict age when compared to that of the Euclidean space of functional networks with LLE. Interestingly, using the Log-Euclidean analysis framework, we demonstrate the integration and segregation of cortical-subcortical networks as well as among the salience, executive, and emotional networks across lifespan.
Manifold learning for object tracking with multiple nonlinear models.
Nascimento, Jacinto C; Silva, Jorge G; Marques, Jorge S; Lemos, Joao M
2014-04-01
This paper presents a novel manifold learning algorithm for high-dimensional data sets. The scope of the application focuses on the problem of motion tracking in video sequences. The framework presented is twofold. First, it is assumed that the samples are time ordered, providing valuable information that is not presented in the current methodologies. Second, the manifold topology comprises multiple charts, which contrasts to the most current methods that assume one single chart, being overly restrictive. The proposed algorithm, Gaussian process multiple local models (GP-MLM), can deal with arbitrary manifold topology by decomposing the manifold into multiple local models that are probabilistic combined using Gaussian process regression. In addition, the paper presents a multiple filter architecture where standard filtering techniques are integrated within the GP-MLM. The proposed approach exhibits comparable performance of state-of-the-art trackers, namely multiple model data association and deep belief networks, and compares favorably with Gaussian process latent variable models. Extensive experiments are presented using real video data, including a publicly available database of lip sequences and left ventricle ultrasound images, in which the GP-MLM achieves state of the art results.
Sampling from Determinantal Point Processes for Scalable Manifold Learning.
Wachinger, Christian; Golland, Polina
2015-01-01
High computational costs of manifold learning prohibit its application for large datasets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire dataset with the Nyström method. The two main challenges that arise are: (i) the landmarks selected in non-Euclidean geometries must result in a low reconstruction error, (ii) the graph constructed from sparsely sampled landmarks must approximate the manifold well. We propose to sample the landmarks from determinantal distributions on non-Euclidean spaces. Since current determinantal sampling algorithms have the same complexity as those for manifold learning, we present an efficient approximation with linear complexity. Further, we recover the local geometry after the sparsification by assigning each landmark a local covariance matrix, estimated from the original point set. The resulting neighborhood selection .based on the Bhattacharyya distance improves the embedding of sparsely sampled manifolds. Our experiments show a significant performance improvement compared to state-of-the-art landmark selection techniques on synthetic and medical data.
An index formula for perturbed Dirac operators on Lie manifolds
Carvalho, Catarina
2011-01-01
We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := D+ V, where D is a Dirac operators and V is an unbounded potential at infinity on a possibly non-compact manifold M_0. We assume that M_0 is a Lie manifold with compactification denoted M. Examples of Lie manifolds are provided by asymptotically Euclidean or asymptotically hyperbolic spaces. The potential V is required to be invertible outside a compact set K and V^{-1} extends to a smooth function on M\\K that vanishes on all faces of M in a controlled way. Using tools from analysis on non-compact Riemannian manifolds, we show that the computation of the index of P reduces to the computation of the index of an elliptic pseudodifferential operator of order zero on M_0 that is a multiplication operator at infinity. The index formula for P can then be obtained from earlier results. The proof also yields similar index formulas for Callias-type pseudodifferential operators ...
Stability and Spectrum of Compactifications on Product Manifolds
Brown, Adam R
2013-01-01
We study the spectrum and perturbative stability of Freund-Rubin compactifications on $M_p \\times M_{Nq}$, where $M_{Nq}$ is itself a product of $N$ $q$-dimensional Einstein manifolds. The higher-dimensional action has a cosmological term $\\Lambda$ and a $q$-form flux, which individually wraps each element of the product; the extended dimensions $M_p$ can be anti-de Sitter, Minkowski, or de Sitter. We find the masses of every excitation around this background, as well as the conditions under which these solutions are stable. This generalizes previous work on Freund-Rubin vacua, which focused on the $N=1$ case, in which a $q$-form flux wraps a single $q$-dimensional Einstein manifold. The $N=1$ case can have a classical instability when the $q$-dimensional internal manifold is a product---one of the members of the product wants to shrink while the rest of the manifold expands. Here, we will see that individually wrapping each element of the product with a lower-form flux cures this cycle-collapse instability. ...
Eigenvalues of the Dirac operator on manifolds with boundary
Energy Technology Data Exchange (ETDEWEB)
Hijazi, O. [Inst. Elie Cartan, Univ. Henri Poincare, Nancy (France); Montiel, S. [Dept. de Geometria y Topologia, Universidad de Granada (Spain); Zhang, X. [Inst. of Mathematics, Academy of Mathematics and Systems Sciences, Beijing (China)
2001-07-01
Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. For the local boundary conditions, limiting cases are characterized by the existence of real Killing spinors and the minimality of the boundary. (orig.)
The Anosov theorem for flat generalized Hantzsche-Wendt manifolds
Dekimpe, K.; De Rock, B.; Malfait, W.
2004-10-01
In this paper we prove that N( f)=| L( f)| for any continuous map f on a given orientable flat generalized Hantzsche-Wendt manifold. This is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We also show that the theorem always fails in the non-orientable case.
Attraction properties of the Ginzburg-Landau manifold
Eckhaus, W.; Shepeleva, A.
2001-01-01
We consider solutions of weakly unstable PDE on an unbounded spatial domain. It has been shown earlier by the first author that the set of modulated solutions (called "Ginzburg-Landau manifold") is attracting. We seek to understand "how big" is the domain of attraction. Starting with general initial
VECTOR-FIELDS AS DERIVATIONS ON NUCLEAR MANIFOLDS
THOMAS, EGF
1995-01-01
If M is a manifold modelled over a nuclear Frechet space, the smooth vector fields, as in the finite dimensional case, may be identified with continuous derivations in the space E(M) of real C-infinity functions on M. This applies for instance to the loop groups and the group of diffeomorphisms of
The Batalin-Vilkovisky formalism on fermionic Kahler manifolds
Aoyama, S.; Vandoren, S.
2007-01-01
We show that the K¨ahler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic K¨ahler manifold. By introducing an isometry we explicitly construct the fermionic irreducible hermitian symmetric space. We then give some so
K-homology and index theory on contact manifolds
Baum, Paul F
2011-01-01
Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index problem for this class of operators. The solution is achieved by combining Van Erp's earlier partial result with the Baum-Douglas isomorphism of analytic and geometric K-homology.
Levchenko, E. A.; Shapovalov, A. V.; Trifonov, A. Yu
2016-07-01
In this paper we construct asymptotic solutions for the nonlocal multidimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation in the class of functions concentrated on a one-dimensional manifold (curve) using a semiclassical approximation technique. We show that the construction of these solutions can be reduced to solving a similar problem for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov in the class of functions concentrated at a point (zero-dimensional manifold) together with an additional operator condition. The general approach is exemplified by constructing a two-dimensional two-parametric solution, which describes quasi-steady-state patterns on a circumference.
Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points
Institute of Scientific and Technical Information of China (English)
Fei LIU; Fang WANG
2016-01-01
In this article, we consider the entropy-expansiveness of geodesic flows on closed Rieman-nian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.
Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases
Sobolev, Vladimir
2016-06-01
We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by several examples.
There are four natural curves in the spinal column. The cervical, thoracic, lumbar, and sacral curvature. The curves, along with the intervertebral disks, help to absorb and distribute stresses that occur from everyday activities such as walking or from ...
Directory of Open Access Journals (Sweden)
Janusz Charatonik
1991-11-01
Full Text Available Results concerning contractibility of curves (equivalently: of dendroids are collected and discussed in the paper. Interrelations tetween various conditions which are either sufficient or necessary for a curve to be contractible are studied.
Parametrizing Algebraic Curves
Lemmermeyer, Franz
2011-01-01
We present the technique of parametrization of plane algebraic curves from a number theorist's point of view and present Kapferer's simple and beautiful (but little known) proof that nonsingular curves of degree > 2 cannot be parametrized by rational functions.
Mitigating noise in global manifold coordinates for hyperspectral image classification
Jin, Can; Bachmann, Charles M.
2016-09-01
Over the past decade, manifold and graph representations of hyperspectral imagery (HSI) have been explored widely in HSI applications. Among many data-driven approaches to deriving manifold coordinate representations including Isometric Mapping (ISOMAP), Local Linear Embedding (LLE), Laplacian Eigenmaps (LE), and Diffusion Kernels (DK), ISOMAP is the only global method that well represents the large scale nonlinear geometric structure of the data. In recent years, methods such as ENH-ISOMAP as well as its parallel computing accelerations makes ISOMAP practical for hyperspectral image dimensionality reduction. However, the noise problem in these methods has not been well addressed, which is critical to classification accuracy based on the manifold coordinates derived from these methods. While standard linear techniques to reduce the effects of noise can be applied as a preliminary step, these are based on global statistics and are applied globally across the entire data set, resulting in the risk of losing subtle nonlinear features before classification. To solve this problem, in this paper, we explore several approaches to modeling and mitigating noise in HSI in a local sense to improve the performance of the ENH-ISOMAP algorithm, aiming to reduce the noise effect on the manifold representations of the HSI. A new method to split data into local spectral subsets is introduced. Based on the local spectral subsets obtained with this method, a local noise model guided landmark selection scheme is proposed. In addition, a new robust adaptive neighborhood method using intrinsic dimensionality information to construct the k-Nearest Neighbor graph is introduced to increase the fidelity of the graph, based on the same framework of local spectral subsetting. The improved algorithm produces manifold coordinates with less noise, and shows a better classification accuracy using k-Nearest Neighbor classifier.
Person-Independent Head Pose Estimation Using Biased Manifold Embedding
Directory of Open Access Journals (Sweden)
Sethuraman Panchanathan
2008-02-01
Full Text Available Head pose estimation has been an integral problem in the study of face recognition systems and human-computer interfaces, as part of biometric applications. A fine estimate of the head pose angle is necessary and useful for several face analysis applications. To determine the head pose, face images with varying pose angles can be considered to be lying on a smooth low-dimensional manifold in high-dimensional image feature space. However, when there are face images of multiple individuals with varying pose angles, manifold learning techniques often do not give accurate results. In this work, we propose a framework for a supervised form of manifold learning called Biased Manifold Embedding to obtain improved performance in head pose angle estimation. This framework goes beyond pose estimation, and can be applied to all regression applications. This framework, although formulated for a regression scenario, unifies other supervised approaches to manifold learning that have been proposed so far. Detailed studies of the proposed method are carried out on the FacePix database, which contains 181 face images each of 30 individuals with pose angle variations at a granularity of 1Ã¢ÂˆÂ˜. Since biometric applications in the real world may not contain this level of granularity in training data, an analysis of the methodology is performed on sparsely sampled data to validate its effectiveness. We obtained up to 2Ã¢ÂˆÂ˜ average pose angle estimation error in the results from our experiments, which matched the best results obtained for head pose estimation using related approaches.
DEFF Research Database (Denmark)
Bernstein, Daniel J.; Birkner, Peter; Lange, Tanja;
2013-01-01
This paper introduces EECM-MPFQ, a fast implementation of the elliptic-curve method of factoring integers. EECM-MPFQ uses fewer modular multiplications than the well-known GMP-ECM software, takes less time than GMP-ECM, and finds more primes than GMP-ECM. The main improvements above the modular......-arithmetic level are as follows: (1) use Edwards curves instead of Montgomery curves; (2) use extended Edwards coordinates; (3) use signed-sliding-window addition-subtraction chains; (4) batch primes to increase the window size; (5) choose curves with small parameters and base points; (6) choose curves with large...
Negative Point Mass Singularities in General Relativity
Robbins, Nicholas
2010-01-01
First we review the definition of a negative point mass singularity. Then we examine the gravitational lensing effects of these singularities in isolation and with shear and convergence from continuous matter. We review the Inverse Mean Curvature Flow and use this flow to prove some new results about the mass of a singularity, the ADM mass of the manifold, and the capacity of the singularity. We describe some particular examples of these singularities that exhibit additional symmetries.
Johnson, L. E.; Kim, J.; Cifelli, R.; Chandra, C. V.
2016-12-01
Potential water retention, S, is one of parameters commonly used in hydrologic modeling for soil moisture accounting. Physically, S indicates total amount of water which can be stored in soil and is expressed in units of depth. S can be represented as a change of soil moisture content and in this context is commonly used to estimate direct runoff, especially in the Soil Conservation Service (SCS) curve number (CN) method. Generally, the lumped and the distributed hydrologic models can easily use the SCS-CN method to estimate direct runoff. Changes in potential water retention have been used in previous SCS-CN studies; however, these studies have focused on long-term hydrologic simulations where S is allowed to vary at the daily time scale. While useful for hydrologic events that span multiple days, the resolution is too coarse for short-term applications such as flash flood events where S may not recover its full potential. In this study, a new method for estimating a time-variable potential water retention at hourly time-scales is presented. The methodology is applied for the Napa River basin, California. The streamflow gage at St Helena, located in the upper reaches of the basin, is used as the control gage site to evaluate the model performance as it is has minimal influences by reservoirs and diversions. Rainfall events from 2011 to 2012 are used for estimating the event-based SCS CN to transfer to S. As a result, we have derived the potential water retention curve and it is classified into three sections depending on the relative change in S. The first is a negative slope section arising from the difference in the rate of moving water through the soil column, the second is a zero change section representing the initial recovery the potential water retention, and the third is a positive change section representing the full recovery of the potential water retention. Also, we found that the soil water moving has traffic jam within 24 hours after finished first
Negative Energy Density in Calabi-Yau Compactifications
Hertog, Thomas; Horowitz, Gary T.; Maeda, Kengo
2003-01-01
We show that a large class of supersymmetric compactifications, including all simply connected Calabi-Yau and G_2 manifolds, have classical configurations with negative energy density as seen from four dimensions. In fact, the energy density can be arbitrarily negative -- it is unbounded from below. Nevertheless, positive energy theorems show that the total ADM energy remains positive. Physical consequences of the negative energy density include new thermal instabilities, and possible violati...
A Numerical Scheme for Computing Stable and Unstable Manifolds in Nonautonomous Flows
Balasuriya, Sanjeeva
2016-12-01
There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.