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.
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.
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.
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
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.
THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON STEIN MANIFOLDS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C(1) smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.
Homotopy formulas and ■-equation on local q- convex domains in Stein manifolds
Institute of Scientific and Technical Information of China (English)
钟同德
1997-01-01
The homotopy formulas of (r,s) differential forms and the solution of equation of type (r,s) on local q-convex domains in Stein manifolds are obtained.The homotopy formulas on local q-convex domains have important applications in uniform estimates of equation and holomorphic extension of CR-manifolds.
THE SOLUTION OF b的偏导-EQUATION OF （P,Q）-FORMS AND IT′ S Lp ＆ HOLDER ESTIMATES ON A STEIN MANIFOLD
Institute of Scientific and Technical Information of China (English)
WuXiaoqin
1994-01-01
By using the kernel of J. P. Demaily & Laurrent Thiebaut, the author constructs two opertors T and S which are compact and obtain the solution of b的偏导-equation of (p,q)forms and L & Holder estimates on a Stein Manifold.
On B-type open-closed Landau-Ginzburg theories defined on Calabi-Yau Stein manifolds
Babalic, Mirela; Lazaroiu, Calin Iuliu; Tavakol, Mehdi
2016-01-01
We consider the bulk algebra and topological D-brane category arising from the differential model of the open-closed B-type topological Landau-Ginzburg theory defined by a pair $(X,W)$, where $X$ is a non-compact Calabi-Yau manifold and $W$ has compact critical set. When $X$ is a Stein manifold (but not restricted to be a domain of holomorphy), we extract equivalent descriptions of the bulk algebra and of the category of topological D-branes which are constructed using only the analytic space associated to $X$. In particular, we show that the D-brane category is described by projective matrix factorizations defined over the ring of holomorphic functions of $X$. We also discuss simplifications of the analytic models which arise when $X$ is holomorphically parallelizable and illustrate these analytic models in a few classes of examples.
Stein manifolds and holomorphic mappings the homotopy principle in complex analysis
Forstnerič, Franc
2017-01-01
This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka t...
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.
Smooth embeddings with Stein surface images
Gompf, Robert E
2011-01-01
A simple characterization is given of open subsets of a complex surface that smoothly perturb to Stein open subsets. As applications, complex 2-space C^2 contains domains of holomorphy (Stein open subsets) that are exotic R^4's, and others homotopy equivalent to the 2-sphere but cut out by smooth, compact 3-manifolds. Pseudoconvex embeddings of Brieskorn spheres and other 3-manifolds into complex surfaces are constructed, as are pseudoconcave holomorphic fillings (with disagreeing contact and boundary orientations). Pseudoconcave complex structures on Milnor fibers are found. A byproduct of this construction is a simple polynomial expression for the signature of the (p,q,npq-1) Milnor fiber. Akbulut corks in complex surfaces can always be chosen to be pseudoconvex or pseudoconcave submanifods. The main theorem is expressed via Stein handlebodies (possibly infinite), which are defined holomorphically in all dimensions by extending Stein theory to manifolds with noncompact boundary.
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...
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.
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,...
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 $B$.
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.
Algebraic approximations of holomorphic maps from Stein domains to projective manifolds
Demailly, J P; Shiffman, B; Demailly, Jean-Pierre; Lempert, Laszlo; Shiffman, Bernard
1992-01-01
(Note: This paper is a revision of our manuscript of December 11, 1992. The present version contains many technical changes in the first three sections. More general results are obtained with a simpler proof.) --------- {\\bf Abstract.} It is shown that every holomorphic map $f$ from a Runge domain $\\Omega$ of an affine algebraic variety $S$ into a projective algebraic manifold $X$ is a uniform limit of Nash algebraic maps $f_\
Invariant measures and controllability of finite systems on compact manifolds
Jouan, Philippe
2010-01-01
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the Equivalence Theorem of \\cite{Jouan09} and of the existence of an invariant measure on certain compact homogeneous spaces.
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.
The Degree of Symmetry of Certain Compact Smooth Manifolds Ⅱ
Institute of Scientific and Technical Information of China (English)
Bin XU
2007-01-01
We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2 × V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.
Compactness of $\\Box_b$ in a CR manifold
Khanh, Tran Vu; Zampieri, Giuseppe
2011-01-01
This note is aimed at simplifying current literature about compactness estimates for the Kohn-Laplacian on CR manifolds. The approach consists in a tangential basic estimate in the formulation given by the first author in \\cite{Kh10} which refines former work by Nicoara \\cite{N06}. It has been proved by Raich \\cite{R10} that on a CR manifold of dimension $2n-1$ which is compact pseudoconvex of hypersurface type embedded in $\\C^n$ and orientable, the property named "$(CR-P_q)$" for $1\\leq q\\leq \\frac{n-1}2$, a generalization of the one introduced by Catlin in \\cite{C84}, implies compactness estimates for the Kohn-Laplacian $\\Box_b$ in degree $k$ for any $k$ satisfying $q\\leq k\\leq n-1-q$. The same result is stated by Straube in \\cite{S10} without the assumption of orientability. We regain these results by a simplified method and extend the conclusions in two directions. First, the CR manifold is no longer required to be embedded. Second, when $(CR-P_q)$ holds for $q=1$ (and, in case $n=1$, under the additional...
Random Lie group actions on compact manifolds: a perturbative analysis
Sadel, Christian
2008-01-01
A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the randomness. This effectiveness is expressed in terms of random Lie algebra elements and replaces the transience or Furstenberg's irreducibility hypothesis in related problems. The Birkhoff sum of any given smooth function then turns out to be equal to its integral w.r.t. a unique smooth measure on the manifold up to errors of the order of the coupling constant. Applications to the theory of products of random matrices and a model of a disordered quantum wire are presented.
Random Riesz energies on compact K\\"{a}hler manifolds
Feng, Renjie
2011-01-01
This article determines the asymptotics of the expected Riesz s-energy of the zero set of a Gaussian random systems of polynomials of degree N as the degree N tends to infinity in all dimensions and codimensions. The asymptotics are proved more generally for sections of any positive line bundle over any compact Kaehler manifold. In comparison with the results on energies of zero sets in one complex dimension due to Qi Zhong (arXiv:0705.2000) (see also [arXiv:0705.2000]), the zero sets have higher energies than randomly chosen points in dimensions > 2 due to clumping of zeros.
The $\\alpha'$ Expansion On A Compact Manifold Of Exceptional Holonomy
Becker, Katrin; Witten, Edward
2014-01-01
In the approximation corresponding to the classical Einstein equations, which is valid at large radius, string theory compactification on a compact manifold $M$ of $G_2$ or $\\mathrm{Spin}(7)$ holonomy gives a supersymmetric vacuum in three or two dimensions. Do $\\alpha'$ corrections to the Einstein equations disturb this statement? Explicitly analyzing the leading correction, we show that the metric of $M$ can be adjusted to maintain supersymmetry. Beyond leading order, a general argument based on low energy effective field theory in spacetime implies that this is true exactly (not just to all finite orders in $\\alpha'$). A more elaborate field theory argument that includes the massive Kaluza-Klein modes matches the structure found in explicit calculations. In M-theory compactification on a manifold $M$ of $G_2$ or Spin(7) holonomy, similar results hold to all orders in the inverse radius of $M$ -- but not exactly. The classical moduli space of $G_2$ metrics on a manifold $M$ is known to be locally a Lagrangi...
Fibrations and globalizations of compact homogeneous CR-manifolds
Gilligan, B.; Huckleberry, Alan T.
2009-06-01
Fibration methods which were previously used for complex homogeneous spaces and CR-homogeneous spaces of special types [1]-[4] are developed in a general framework. These include the \\mathfrak{g}-anticanonical fibration in the CR-setting, which reduces certain considerations to the compact projective algebraic case, where a Borel-Remmert type splitting theorem is proved. This leads to a reduction to spaces homogeneous under actions of compact Lie groups. General globalization theorems are proved which enable one to regard a homogeneous CR-manifold as an orbit of a real Lie group in a complex homogeneous space of a complex Lie group. In the special case of CR-codimension at most two, precise classification results are proved and are applied to show that in most cases there exists such a globalization.
Fibrations and globalizations of compact homogeneous CR-manifolds
Energy Technology Data Exchange (ETDEWEB)
Gilligan, B [University of Regina, Regina (Canada); Huckleberry, Alan T [Ruhr-Universitaet Bochum, Mathematischer Institut, Bochum (Germany)
2009-06-30
Fibration methods which were previously used for complex homogeneous spaces and CR-homogeneous spaces of special types [1]-[4] are developed in a general framework. These include the g-anticanonical fibration in the CR-setting, which reduces certain considerations to the compact projective algebraic case, where a Borel-Remmert type splitting theorem is proved. This leads to a reduction to spaces homogeneous under actions of compact Lie groups. General globalization theorems are proved which enable one to regard a homogeneous CR-manifold as an orbit of a real Lie group in a complex homogeneous space of a complex Lie group. In the special case of CR-codimension at most two, precise classification results are proved and are applied to show that in most cases there exists such a globalization.
$(k,s)$-positivity and vanishing theorems for compact Kahler manifolds
Yang, Qi-Lin
2010-01-01
We study the $(k,s)$-positivity for holomorphic vector bundles on compact complex manifolds. $(0,s)$-positivity is exactly the Demailly $s$-positivity and a $(k,1)$-positive line bundle is just a $k$-positive line bundle in the sense of Sommese. In this way we get a unified theory for all kinds of positivities used for semipositive vector bundles. Several new vanishing theorems for $(k,s)$-positive vector bundles are proved and the vanishing theorems for $k$-ample vector bundles on projective algebraic manifolds are generalized to $k$-positive vector bundles on compact K\\"ahler manifolds.
Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
2001-01-01
The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.
Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
Institute of Scientific and Technical Information of China (English)
LI Yuxiang
2005-01-01
Let (M, g) be a compact Riemannian manifold without boundary, and (N, g) a compact Riemannian manifold with boundary. We will prove in this paper that the ∫MudVg=o,sup∫M|(△↓)u|ndVg=1∫Meαn|u|n/n-1dVg,∫M(|(△↓)|n+|u|n)dVg=1∫Meαn|u|n/n-1dVg,and u|(e)N=0,∫Msup|(△↓)u|dVgN=1∫Neαn|u|n/n-1dVgn can be attained. Our proof uses the blow-up analysis.
Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
Assel, Benjamin; Murthy, Sameer; Yokoyama, Daisuke
2016-01-01
We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS$_3$. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supersymmetry in manifolds with a conformal boundary, including supersymmetric actions and boundary conditions.
Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results
Directory of Open Access Journals (Sweden)
Martin Schlichenmaier
2010-01-01
Full Text Available This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kähler manifolds. The basic objects, concepts, and results are given. This concerns the correct semiclassical limit behaviour of the operator quantization, the unique Berezin-Toeplitz deformation quantization (star product, covariant and contravariant Berezin symbols, and Berezin transform. Other related objects and constructions are also discussed.
Singularity links with exotic Stein fillings
Özbağcı, Burak; Akhmedov, Anar
2012-01-01
arXiv:1206.2468v3 [math.GT] 14 May 2014 SINGULARITY LINKS WITH EXOTIC STEIN FILLINGS ANAR AKHMEDOV AND BURAK OZBAGCI ABSTRACT. In [4], it was shown that there exist infinitely many contact Seifert fibered 3-manifolds each of which admits infinitely many exotic (homeomorphic but pairwise non-diffeomorphic) simply-connected Stein fillings. Here we extend this result to a larger set of contact Seifert fibered 3-manifolds with many singular fibers and observe that these 3- ma...
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.
A parametric design of compact exhaust manifold junction in heavy duty diesel engine using CFD
Directory of Open Access Journals (Sweden)
Naeimi Hessamedin
2011-01-01
Full Text Available Nowadays, computational fluid dynamics codes (CFD are prevalently used to simulate the gas dynamics in many fluid piping systems such as steam and gas turbines, inlet and exhaust in internal combustion engines. In this paper, a CFD software is used to obtain the total energy losses in adiabatic compressible flow at compact exhaust manifold junction. A steady state onedimensional adiabatic compressible flow with friction model has been applied to subtract the straight pipe friction losses from the total energy losses. The total pressure loss coefficient has been related to the extrapolated Mach number in the common branch and to the mass flow rate ratio between branches at different flow configurations, in both combining and dividing flows. The study indicate that the numerical results were generally in good agreement with those of experimental data from the literature and will be applied as a boundary condition in one-dimensional global simulation models of fluid systems in which these components are present.
A classification of taut, Stein surfaces with a proper $\\R$-action
Iannuzzi, Andrea
2010-01-01
We present a classification of 2-dimensional, taut, Stein manifolds with a proper $\\R$-action. For such manifolds the globalization with respect to the induced local $\\C$-action turns out to be Stein. As an application we determine all 2-dimensional taut, non-complete, Hartogs domains over a Riemann surface.
Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Trudinger, N. S., On embedding into Orlicz space and some applications, J. Math. Mech., 1967, 17: 473-484.[2]Moser, J., A sharp form of an Inequality by N.Trudinger, Ind. Univ. Math. J., 1971, 20: 1077-1091.[3]Adams, D. R., A sharp inequality of J. Moser for higher order derivatives, Anna. Math., 1988, 128: 385-398.[4]Fontana, L., Sharp borderline Sobolev inequalities on compact Riemannian manifolds. Comm. Math. Helv.,1993, 68: 415- 454.[5]Lin, K.C., Extremal functions for Moser's inequality, Trans. Amer.Math. Sco., 1996, 348: 2663-2671.[6]Carleson, L., Chang, S. Y. A., On the existence of an extremal function for an inequality of J.Moser, Bull. Sc.Math., 1986, 110: 113-127.[7]Flucher, M., Extremal functions for Trudinger-Moser inequality in 2 dimensions, Comment. Math. Helv., 1992,67: 471-497.[8]Adimurth, Struwe, M., Global compactness properties of semilinear elliptic equations with critical exponential growth, J. Funct. Anal., 2000, 175(1): 125-167.[9]Li,Y., Moser-Trudinger inequality on manifold of dimesion two, J. Partial Differential Equations, 2001, 14(2):163-192.[10]Kichenassamy, S., Veron, L., Singular solutions of the p-laplace equation, Math. Ann., 1986, 275: 599-615.[11]Ding, W. Y., Jost, J., Li, J. et al, The differential equation -△u = 8π - 8πheu on a compact Riemann Surface,Asia. J. Math., 1997, 1(2): 230-248.[12]Tolksdorf, P., Regularity for a more general class of qusilinear elliptic equations, J. D. E., 1984, 51:126-150.[13]Serrin, J., Local behavior of solutions of qusai-linear equations, Acta. Math., 1964, 111: 248-302.[14]Struwe, M., Positive solution of critical semilinear elliptic equations on non-contractible planar domain, J. Eur.Math. Soc., 2000, 2(4): 329-388.[15]Serrin, J., Isoled singularities of solutions of quasilinear equations, Acta. Math., 1965, 113: 219-240.[16]Struwe, M., Critical points of embedding of H01,n into Orlicz space, Ann. Inst. Henri., 1988, 5(5): 425-464.[17]Chen, W. X., Li, C., Classification of solutions of
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...
The constraint equations for the Einstein-scalar field system on compact manifolds
Choquet-Bruhat, Y; Pollack, D; Choquet-Bruhat, Yvonne; Isenberg, James; Pollack, Daniel
2006-01-01
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed sca...
The constraint equations for the Einstein-scalar field system on compact manifolds
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne [University of Paris VI, 4 place jussieu, 75005, Paris (France); Isenberg, James [Department of Mathematics, University of Oregon, Eugene, Oregon 97403-5203 (United States); Pollack, Daniel [Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350 (United States)
2007-02-21
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.
Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum
Zhitnitsky, Ariel R
2015-01-01
We study novel type of contributions to the partition function of the Maxwell system defined on a small compact manifold ${\\mathbb{M}}$ such as torus. These new terms can not be described in terms of the physical propagating photons with two transverse polarizations. Rather, these novel contributions emerge as a result of tunnelling events when transitions occur between topologically different but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that if the same system is considered in the background of a small external time-dependent magnetic field, than there will be emission of photons from the vacuum, similar to the Dynamical Casimir Effect (DCE) when real particles are radiated from the vacuum due to the time-dependent boundary conditions. The difference with conventional DCE is that the dynamics of the vacuum in our system is not related to the fluctuations of the conventional degrees of freedom, the virtual phot...
Ritt's theorem and the Heins map in hyperbolic complex manifolds
Institute of Scientific and Technical Information of China (English)
Marco; Abate; Filippo; Bracci
2005-01-01
Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic self-map f: X →X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.
MOSER-TR DINGER INEQUALITY ON COMPACT RIEMANNIAN MANIFOLDS OF DIMENSION TWO
Institute of Scientific and Technical Information of China (English)
Li Yuxiang
2001-01-01
In this paper, we prove Moser-Triidinger inequality in any two dimen- sional manifolds. Let (M,gM) be a two dimensional manifold without boundary and (g, gN) with boundary, we shall prove the following three inequalities: Moreover, we shall show that there exist of extremal functions which attain the above three inequalities.
Pitman, Jim
2012-01-01
We discuss a characterization of the centered Gaussian distribution which can be read from results of Archimedes and Maxwell, and relate it to Charles Stein's well-known characterization of the same distribution. These characterizations fit into a more general framework involving the beta-gamma algebra, which explains some other characterizations appearing in the Stein's method literature.
Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds
Danielsson, Ulf H.; Olsson, Martin E.; Vonk, Marcel
2004-11-01
We study the relation between c = 1 matrix models at self-dual radii and topological strings on non-compact Calabi-Yau manifolds. Particularly the special case of the deformed matrix model is investigated in detail. Using recent results on the equivalence of the partition function of topological strings and that of four dimensional BPS black holes, we are able to calculate the entropy of the black holes, using matrix models. In particular, we show how to deal with the divergences that arise as a result of the non-compactness of the Calabi-Yau. The main result is that the entropy of the black hole at zero temperature coincides with the canonical free energy of the matrix model, up to a proportionality constant given by the self-dual temperature of the matrix model.
Certain Ergodic Properties of a Differential System on a Compact Differentiable Manifold
Institute of Scientific and Technical Information of China (English)
LIAO Shan-tao
2006-01-01
Let Mn be an n-dimensional compact C∞-differentiable manifold,n≥2,and let S be a C1 -differential system on Mn.The system induces a one-parameter C1 transformation group φt(-∞＜t＜∞) over Mn and,thus,naturally induces a one-parameter transformation group of the tangent bundle of Mn.The aim of this paper,in essence,is to study certain ergodic properties of this latter transformation group.Among various results established in the paper,we mention here only the following,which might describe quite well the nature of our study.(A) Let M be the set of regular points in Mn of the differential system S.With respect to a given C∞ Riemannian metric of Mn,we consider the bundle (ζ)# of all (n-2) spheres Qxn-2,x∈M,where Qxn-2 for each x consists of all unit tangent vectors of Mn orthogonal to the trajectory through x.Then,the differential system S gives rise naturally to a one-parameter transformation group Ψt#(-∞＜t＜∞) of (ζ)#.For an l-frame α=(u1,u2,…,ul) of Mn at a point x in M,1 ≥l≥n-1,each ui being in (ζ)#,we shall denote the volume of the parallelotope in the tangent space of Mn at x with edges u1,u2,…,ut by v(α),and let η*α(t)=v(Ψ#t (u1),Ψ#t(u2),…,Ψ#t (ul)).This is a continuous real function of t.Let I*+(α)=-limT→∞1/T∫T0η*α(t)dt,I*-(α)=-limT→-∞1/T∫T0η*α(t)dt.α is said to be positively linearly independent of the mean if I+*(α)＞0.Similarly,α is said to be negatively linearly independent of the mean if I_ *(a)＞0.A point x of M is said to possess positive generic index κ=κ+*(x) if,at x,there is a κ-frame α= (u1,u2,…,Uκ),ui ∈(ζ)#,of Mn having the property of being positively linearly independent in the mean,but at x,every l-frame β=(v1,v2,…,vl),vi ∈(ζ)#,of Mn with l＞κ does not have the same property.Similarly,we define the negative generic index κ_*(x) of x.For a nonempty closed subset F of Mn consisting of regular points of S,invariant under φt(-∞＜t＜∞),let the (positive and
Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature
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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.
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne [Universite Paris 6, 4 Place Jussieu, 75005 Paris (France)
2004-02-07
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{sub 2} when n = 3) and solutions with unscaled sources.
2015-02-27
cubesats. The CINEMA (Cubesat for Ions Neutrals Electrons and Magnetic 1 Approved for public release; distribution is unlimited. fields) was the primary...intended host for STEIN. Additionally some calibration efforts were performed with the CINEMA spacecraft as an element of the readout. This resulted...designed to accept a clock from its host spacecraft (as was the design case for CINEMA ) of 8.38MHz (specifically 2^23 Hz). As well as a spacecraft
Discrete Stein characterizations and discrete information distances
Ley, Christophe
2012-01-01
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
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.
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.
SL(2;R)/U(1) supercoset and elliptic genera of Non-compact Calabi-Yau Manifolds
Eguchi, T
2004-01-01
We first discuss the relationship between the SL(2;)/U(1) supercoset and = 2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;)/U(1) theory correspond exactly to those massless representations of = 2 Liouville theory which are closed under modular transformations and studied in our previous work [18]. It is known that toroidal partition functions of SL(2;)/U(1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the space-time volume and is divergent in the infinite-volume limit while the part of discrete representations is volume-independent. In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2;)/U(1), we compute elliptic genera for various non-compact space-times such as the conifold, ...
What Edith Stein Can Teach Adult Educators
Culkin, David T.
2016-01-01
Many think of Edith Stein as a phenomenological philosopher who experienced a dramatic religious conversion, but contemporary adult educators may also look to her as a model for the application of social activism based in theory. This article explores Stein's continued relevance for adult educators who research and then try to apply key concepts…
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.
Recursive Estimation of the Stein Center of SPD Matrices & its Applications.
Salehian, Hesamoddin; Cheng, Guang; Vemuri, Baba C; Ho, Jeffrey
2013-12-01
Symmetric positive-definite (SPD) matrices are ubiquitous in Computer Vision, Machine Learning and Medical Image Analysis. Finding the center/average of a population of such matrices is a common theme in many algorithms such as clustering, segmentation, principal geodesic analysis, etc. The center of a population of such matrices can be defined using a variety of distance/divergence measures as the minimizer of the sum of squared distances/divergences from the unknown center to the members of the population. It is well known that the computation of the Karcher mean for the space of SPD matrices which is a negatively-curved Riemannian manifold is computationally expensive. Recently, the LogDet divergence-based center was shown to be a computationally attractive alternative. However, the LogDet-based mean of more than two matrices can not be computed in closed form, which makes it computationally less attractive for large populations. In this paper we present a novel recursive estimator for center based on the Stein distance - which is the square root of the LogDet divergence - that is significantly faster than the batch mode computation of this center. The key theoretical contribution is a closed-form solution for the weighted Stein center of two SPD matrices, which is used in the recursive computation of the Stein center for a population of SPD matrices. Additionally, we show experimental evidence of the convergence of our recursive Stein center estimator to the batch mode Stein center. We present applications of our recursive estimator to K-means clustering and image indexing depicting significant time gains over corresponding algorithms that use the batch mode computations. For the latter application, we develop novel hashing functions using the Stein distance and apply it to publicly available data sets, and experimental results have shown favorable comparisons to other competing methods.
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.
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.
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.
L’ANTROPOLOGIA FENOMENOLOGICA DI EDITH STEIN
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ANGELA ALES BELLO
2011-11-01
Full Text Available The complexity of the work of Edith Stein is made by the concatenation of the early Husserlian ideas with themes of ethics, psychology, politics, that are significantly in the present days. In this paper Idwell on the centrality of human being in Steinian phenomenologicalanthropology, which is emphasized as communion with the others byactivating the value of empathy. The problem of inter-subjectivity is very important for the entire philosophy of Stein to understanding the human being within the dynamism of the life-world, in the process of self-thinking and, no less, of thinking the other humans.
Ruptures of vulnerability: Linda Stein's Knight Series.
Bible, Ann Vollmann
2010-01-01
Drawing on the work of Monique Wittig, this article understands Linda Stein's Knight Series as a lacunary writing communicating both her challenges to come to representation and her creative registration of subjectivity. The argument is grounded in an exploration of the rich interplay of power and vulnerability across the series as against the discourse of escapist fashion. Specifically, Stein's critical contradictions of inside and outside, conflated temporality, disjunctions between decoration and abstraction, and fluidity of sex and gender are examined. The discussion is elaborated through consideration of the work of Julia Kristeva, Elizabeth Grosz, and Hayao Miyazaki.
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
On a connection between Stein characterizations and Fisher information
Ley, Christophe
2011-01-01
We generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator in terms of a generalized (standardized) score function. We use this result to connect Stein characterizations with information distances such as the generalized (standardized) Fisher information.
Composing Mystics: Gertrude Stein between Zen and Zeit
DEFF Research Database (Denmark)
Elias, Camelia
2012-01-01
Critics claim that there's no connection between Gertrude Stein and mysticism, but the passages they quote to support this claim show exactly the opposite. While it may be that Stein was no Zen master, her writing discloses something about the psychology of creativity. For Stein, the creation of ...
Lanzani-Stein inequalities in Heisenberg groups
Directory of Open Access Journals (Sweden)
Annalisa Baldi
2013-12-01
Full Text Available Lanzani & Stein consider a class of div-curl inequalities in de Rham's complex. In this note we examine the natural counterpart of that kind of inequalities for dierential forms in Heisenberg groups H1 and H2.
Stein’s Phenomenon and Nanoparticle Characterization
2013-01-01
statistical inference and modern data analysis. We offer a few highlights here for convenience. Stein (1956) showed that, if one wished to estimate...Whale M.D. (1997). A fluctuational electrodynamics analysis of microscale radiative heat transfer and the design of microscale thermophotovoltaic
Perspektiven der Edith-Stein-Forschung
Wulf, Mariéle; Gerl-Falkovitz, Hanna-Barbara; Lebech, Mette
2017-01-01
Die Edith-Stein-Forschung findet in den letzten Jahren immer größere internationale Beach-tung. Neben der globalen läßt sich auch eine inhaltliche Expansion feststellen, die zu stimulie-ren sich dieser Forschungsausblick anschickt. Dabei wird eine Forschung ad intra von einer ad extra unterschieden.
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.
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.
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.
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.
Stein and Leventhal: 80 years on.
Azziz, Ricardo; Adashi, Eli Y
2016-02-01
Eighty years ago a publication in the Journal proved to be seminal and transformative. The report by Irving Freiler Stein and Michael Leventhal titled, "Amenorrhea associated with polycystic ovaries," has proven to be a remarkably lasting and influential publication. The growth in related literature has been increasing exponentially: the 50 years between 1950 and 2000 saw a little more than 8000 publications on the topic, whereas the 15 year period between 2001 and 2015 (so far) has seen more than 20,000 related publications, a greater than 8-fold increase in the publication rate after 2000. As we commemorate the 80th anniversary year of the publication of the report by Stein and Leventhal, it is important to ask ourselves, "Was this publication truly as seminal as it is generally assumed to be? And why did it gain such a strong foothold on the medical psyche?" To the first question, a review of the antecedent medical literature makes it clear that the report of Drs Stein and Leventhal in 1935, although not flawless, was both seminal and transformative. In fact, it was the first report to describe a series of patients, rather than isolated cases, who demonstrated the triad of polycystic ovaries, hirsutism, and oligo/amenorrhea, connecting what had previously been disparate features of polycystic ovaries and menorrhagia, and hirsutism and oligo/amenorrhea. Second, the facts that Dr Stein and his collaborators were relatively prolific writers, consistent and clear in their message and descriptions; that a possible therapy (bilateral ovarian wedge resection) had been conveniently included in the report; and that the disorder was (is) relatively prevalent, permitted what would eventually be called the Stein-Leventhal syndrome to gain a strong foothold in contemporary medical practice. Overall, we in the field of medicine have much to celebrate, as we commemorate the 80th anniversary of the publication of the report by Stein and Leventhal in 1935, for a new disorder was
[Contribution of Stein's Anthropology to Personalistic Bioethics].
Robles Morejón, Jeannette Beatriz
2016-01-01
Dr. Juan Manuel Burgos proposes ″a challenge″ to whom aims to consolidate the dignity of the human person as the center of a thought structure. Burgos presents a well-founded trilogy, citing Wojtyla, Sgreccia and he himself, as a perfect combination to support personalist bioethics. However, the possibility of giving a solid anthropological support to this bioethics remains open provided that a substantial list of personalistic authors is revised. This research seeks to collate Stein's anthropological proposal to personalist bioethics needs expressed by Burgos. The study aims to prove how Stein's anthropology can be assembled to the characteristics of personalism, and thus infer that more specific levels of the personalist bioethics can be based on this anthropology.
Stein's method in high dimensions with applications
Röllin, Adrian
2011-01-01
Let $h$ be a three times partially differentiable function on $R^n$, let $X=(X_1,\\dots,X_n)$ be a collection of real-valued random variables and let $Z=(Z_1,\\dots,Z_n)$ be a multivariate Gaussian vector. In this article, we develop Stein's method to give error bounds on the difference $E h(X) - E h(Z)$ in cases where the coordinates of $X$ are not necessarily independent, focusing on the high dimensional case $n\\to\\infty$. In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy, local dependence, Curie-Weiss model etc. We will also give applications to the Sherrington-Kirkpatrick model and last passage percolation on thin rectangles.
Moral experience in Edith Stein's philosophy
Directory of Open Access Journals (Sweden)
Piotr Janik
2017-01-01
Full Text Available The expression “moral experience”, along with the concomitant notion of experience itself, seems to have been understood in divergent ways. Taking as a background three views currently operative in our culture - emotivism, the ethics of duty, and the notion of an ethics “beyond good and evil” - a conception of ethical experience will be presented based on the findings of Edith Stein as elaborated in her work "Philosophy of Psychology and the Humanities".
The Cratering History of Asteroid (2867) Steins
Marchi, S; Kueppers, M; Marzari, F; Davidsson, B; Keller, H U; Besse, S; Lamy, P; Mottola, S; Massironi, M; Cremonese, G
2010-01-01
The cratering history of main belt asteroid (2867) Steins has been investigated using OSIRIS imagery acquired during the Rosetta flyby that took place on the 5th of September 2008. For this purpose, we applied current models describing the formation and evolution of main belt asteroids, that provide the rate and velocity distributions of impactors. These models coupled with appropriate crater scaling laws, allow the cratering history to be estimated. Hence, we derive Steins' cratering retention age, namely the time lapsed since its formation or global surface reset. We also investigate the influence of various factors -like bulk structure and crater erasing- on the estimated age, which spans from a few hundred Myrs to more than 1Gyr, depending on the adopted scaling law and asteroid physical parameters. Moreover, a marked lack of craters smaller than about 0.6km has been found and interpreted as a result of a peculiar evolution of Steins cratering record, possibly related either to the formation of the 2.1km ...
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.
Ejes transversales del pensamiento de Edith Stein
2010-01-01
el pensamiento de un autor puede reducirse a pocas palabras cuando se ha comprendido su tema principal. Una visión de conjunto del pensamiento de Edith Stein detecta dos grandes etapas y un concepto clave que es transversal y sistemático en dicho pensamiento: el concepto de espíritu. A partir de él pueden iluminarse otros ejes temáticos que están presentes a lo largo de su obra, algunos de los cuales se señalan en este artículo. Finalmente, la clave del pensamiento steiniano ofrece valiosas s...
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.
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 $\\C\\P^1\\times\\C\\P^1$.
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.
Directory of Open Access Journals (Sweden)
Fan Yang
2015-07-01
Full Text Available Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC. Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR sensor of the Jet Propulsion Laboratory (JPL and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR sensor of the Technical University of Denmark (DTU. Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.
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.
Ejes transversales del pensamiento de Edith Stein
Directory of Open Access Journals (Sweden)
José Luis Caballero Bono
2010-01-01
Full Text Available el pensamiento de un autor puede reducirse a pocas palabras cuando se ha comprendido su tema principal. Una visión de conjunto del pensamiento de Edith Stein detecta dos grandes etapas y un concepto clave que es transversal y sistemático en dicho pensamiento: el concepto de espíritu. A partir de él pueden iluminarse otros ejes temáticos que están presentes a lo largo de su obra, algunos de los cuales se señalan en este artículo. Finalmente, la clave del pensamiento steiniano ofrece valiosas sugerencias en orden a una comprensión de la espiritualidad desde el espíritu.An author's thoughts can be summarized in few words once his/her key point has been understood. An overview of Edith Stein's thought legacy detects two main stages and a key concept that is transversal and systematic in said thinking: the concept of the spirit. Based on this, other thematic axes that are present throughout her work can be highlighted, some of which are shown in this paper. Finally, the key of Steinian thinking offers valuable suggestions in order to comprehend spirituality from the Spirit.
Advances in analysis the legacy of Elias M. Stein
Fefferman, Charles; Phong, DH; Wainger, Stephen
2014-01-01
Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze-Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collabora
Topology of multiple log transforms of 4-manifolds
Akbulut, Selman
2012-01-01
Given a 4-manifold X and an imbedding T^2 x B^2 into X, we describe an algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained from X by (p,q)-logarithmic transforms along the parallel tori. By using this algorithm, we obtain a simple handle picture of the Dolgachev surface E(1)_{p,q}, and from that deduce that the exotic copy E(1)_{p,q} # 5(-CP^2) of E(1) # 5(-CP^2) differs from the original one by a codimension zero simply connected Stein submanifold M_{p,q}. This gives examples of infinitely many small Stein manifolds M_{p,q} which are exotic copies of each other (rel boundaries). Also by using the description of S^2 x S^2 as a union of two cusps glued along their boundaries, and by using this algorithm, we show that the multiple log transforms along the tori in these cusps do not change smooth structure of S^2 x S^2.
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.
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...
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.
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.
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...
MYSTICAL ASPECT OF EDITH STEIN'S ANTHROPOLOGY: FROM PHENOMENOLOGY TO THOMISM
Directory of Open Access Journals (Sweden)
J. A. Shabanova
2016-12-01
Full Text Available The aim of the study is to find mystical elements in Edith Stein's anthropology as a connecting principle between phenomenology and Thomism. Relying on methodological definition of philosophical mystic, as a matching of theological and philosophical doctrines, based upon reflection on experience of ecstatic unity with the Absolute, it was shown that phenomenology is implicitly directed towards research of real structure of immediate experience which in all its limits approaches to mystical experience. Not the mind and not the faith, but will (that directs knowledge to mystical unity of immanent subject and transcendental object in finding the truth is defining for the mystical character of Stein's creative method. Stein, being a bright representative of phenomenology, gradually disagrees with Husserl at some points: 1. Stein considers the world as an immediate contemplation on the entity that transcends the identity of being and thinking; 2. In her opinion, phenomenology neglects the ontological Absolute. As a result, there is misplace of the Absolute by structural-cognitive aims, that, in its turn, was a reason for amalgamation of onthology and epistemology, according to Stein's views. 3. Stein strives to overcome epistemological rationality and achieve a sphere of philosophical mystic where ontological object and epistemological subject are identical in the act of mystical contemplation. 4. Lack of metaphysical elements in phenomenology leads Stein to Thomism in which she potentially seeks a way out of metaphysical limits and the way which leads to the level of transpersonal states of mind. 5. Stein reproaches transcendentalism in loss of the world and she ignores the changes in Husserl's world outlook, his transcendental turn and genealogy of the trustworthy acquaintance with the world. An empathy, as a model of extrapolation of the principle (of to be get used to the experience of the Other onto mystical act of overcoming of subject
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.
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.
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.
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.
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...
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.
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
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.
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.
Univariate and multivariate Chen-Stein characterizations -- a parametric approach
Ley, Christophe
2011-01-01
We provide a general framework for characterizing families of (univariate, multivariate, discrete and continuous) distributions in terms of a parameter of interest. We show how this allows for recovering known Chen-Stein characterizations, and for constructing many more. Several examples are worked out in full, and different potential applications are discussed.
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.
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...
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.
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.
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).
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.
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,
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...
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.
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...
Aspectos fundamentales del método de Edith Stein
Directory of Open Access Journals (Sweden)
Mariano Crespo
2010-01-01
Full Text Available este trabajo aborda tres aspectos fundamentales del método filosófico de Edith Stein. En primer lugar, se alude a las cosas mismas como el punto de partida del filosofar de esta autora. En segundo lugar, se considera el aspecto que constituye uno de los aportes fundamentales del método fenomenológico y que es claramente reconocible en nuestra autora, a saber, el haber puesto de manifiesto la imposibilidad de hacer filosofía primera sin tomar en cuenta la vida consciente ante la que todas las cosas se abren. En tercer lugar, se remite a la individualidad de la persona como un aspecto de la antropología de Stein especialmente relevante. Al final del análisis de cada uno de estos tres aspectos metodológicos se intenta mostrar en qué sentido éstos pueden ser de relevancia para emprender el camino hacia la pregunta por la mujer.This paper addresses three fundamental aspects of Edith Stein's philosophical method. Firstly, it looks at issues such as the author's starting point of philosophizing. Secondly, it considers the aspect, which constitutes one of the fundamental contributions of the phenomenological method and is clearly recognizable in our author, such as having highlighted that it is impossible to carry out first philosophy without taking into account conscious life, before which all things are opened. Thirdly it looks at the individuality of the person as an especially relevant aspect of Stein's anthropology After analyzing each of these methodological aspects, this paper attempts to show how they may be relevant in laying out the path towards the question of the woman.
Implications of Stein's Paradox for Environmental Standard Compliance Assessment.
Qian, Song S; Stow, Craig A; Cha, YoonKyung
2015-05-19
The implications of Stein's paradox stirred considerable debate in statistical circles when the concept was first introduced in the 1950s. The paradox arises when we are interested in estimating the means of several variables simultaneously. In this situation, the best estimator for an individual mean, the sample average, is no longer the best. Rather, a shrinkage estimator, which shrinks individual sample averages toward the overall average is shown to have improved overall accuracy. Although controversial at the time, the concept of shrinking toward overall average is now widely accepted as a good practice for improving statistical stability and reducing error, not only in simple estimation problems, but also in complicated modeling problems. However, the utility of Stein's insights are not widely recognized in the environmental management community, where mean pollutant concentrations of multiple waters are routinely estimated for management decision-making. In this essay, we introduce Stein's paradox and its modern generalization, the Bayesian hierarchical model, in the context of environmental standard compliance assessment. Using simulated data and nutrient monitoring data from wadeable streams around the Great Lakes, we show that a Bayesian hierarchical model can improve overall estimation accuracy, thereby improving our confidence in the assessment results, especially for standard compliance assessment of waters with small sample sizes.
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.
On stable compact minimal submanifolds
Torralbo, Francisco
2010-01-01
Stable compact minimal submanifolds of the product of a sphere and any Riemannian manifold are classified whenever the dimension of the sphere is at least three. The complete classification of the stable compact minimal submanifolds of the product of two spheres is obtained. Also, it is proved that the only stable compact minimal surfaces of the product of a 2-sphere and any Riemann surface are the complex ones.
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.
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.
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.
Target-local Gromov compactness
Fish, Joel W
2009-01-01
We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in families of degenerating target manifolds which have unbounded geometry (e.g. no uniform energy threshold). Core elements of the proof regard curves as submanifolds (rather than maps) and then adapt methods from the theory of minimal surfaces.
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.
General formula for lower bound of the first eigenvalue on Riemannian manifolds
Institute of Scientific and Technical Information of China (English)
陈木法; 王凤雨
1997-01-01
A general formula for the lower bound of the first eigenvalue on compact Riemannian manifolds is presented. The formula improves the main known sharp estimates including Lichnerowicz’s estimate and Zhong-Yang’s estimate. Moreover, the results are extended to the noncompact manifolds. The study is based on the probabilistic approach (i.e. the coupling method).
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).
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
Supersymmetric Proof of the Hirzebruch-Riemann-Roch Theorem for Non-Kähler Manifolds
Directory of Open Access Journals (Sweden)
Andrei V. Smilga
2012-01-01
Full Text Available We present the proof of the HRR theorem for a generic complex compact manifold by evaluating the functional integral for the Witten index of the appropriate supersymmetric quantum mechanical system.
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...
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.
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.
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.
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.)
Composing Mystics: Gertrude Stein between Zen and Zeit
DEFF Research Database (Denmark)
Elias, Camelia
2012-01-01
of an 'other' world through writing has not only a symbolic significance but also a metaphysical one – an idea also explored by her professor at Radcliffe, William James, in his work, 'The Varieties of Religious Experience.' Stein's compositions can be said to resemble old shamanic and mystical practices...... of creating out of ritualistic words and visions an 'other' physical reality. My claim is that by enlarging the horizon of the word, one turns writing not only into a tool for higher expression, but also into a gate that opens towards a higher form of consciousness....
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.
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.
The Imprint of Williams James on Gertrude Stein in Three Lives
Institute of Scientific and Technical Information of China (English)
刘莹
2013-01-01
Gertrude Stein is regarded as one of the most remarkable writers of the twentieth century. This paper tries to analyze her early work Three Lives under the influence of Williams James from the aspect of Jamesian psychology analysis and the famous prolonged present to conclude that Gertrude Stein is undeniably unorthodox.
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}.
Photometric Analysis of Asteroid (2867) Steins from Rosetta OSIRIS Images
La Forgia, F.; Magrin, S.; Bertini, I.; Lazzarin, M.; Pajola, M.; Barbieri, C.
We present a method for analyzing the reflectance properties of atmosphereless bodies as asteroids and comet nuclei. The method is self-consistent, independent of the shape model of the object and can be easily applied for any space mission target. We used it for the E-type Main Belt asteroid (2867) Steins, observed from the OSIRIS-WAC camera onboard Rosetta spacecraft during a close approach on September 5, 2008. We investigate the reflectance dependence on phase angle which is interpreted in terms of the Hapke's theory of bidirectional reflectance. A deeper analysis allows to obtain an estimate of the typical size of the regolith grains. Steins regolith layer seems to be made of large, highly scattering iron-poor opaque silicate particles. The macroscopic roughness, probably influenced by the global irregular shape, appears fairly high, comparable with radar measurements of other E-type asteroids. Assuming an enstatite composition, we estimated a grain size of about 30-130 mu m and we noticed a correlation between grain size and wavelength, suggesting the existence of a grain size distribution, as expected from real surfaces. The comparison with more accurate calculations (Spjuth \\textit{et al.}, 2009) shows that our simplified method is robust and reliable for a preliminary and shape-independent analysis of the reflectance properties of atmosphereless bodies.
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.
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 ...
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
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.
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.
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
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.
Gabriele Stein. Developing Your English Vocabulary: A Systematic New Approach
Directory of Open Access Journals (Sweden)
Michaël Abecassis
2011-10-01
Full Text Available Gabriele Stein is professor of English linguistics at the University of Heidelberg in Germany and has published widely on lexicography and lexicology. The objective of this book is twofold: to compile a lexical core and to maximise the skills of language students by developing ways of expanding this core. It is intended to function as a teaching aid for teachers of English as well as a self-study book for learners of English as a second language. Lexical knowledge is a crucial part of language acquisition and depends on different external factors such as the age and profession of the learner, his/her goals, expectations and needs in learning a language. Beck et al. (2002 have demonstrated the small extent of the emphasis on the acquisition vocabulary in school curricula.
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
Millennial fandom: Television audiences in the transmedia age, by Louisa Ellen Stein [book review
Directory of Open Access Journals (Sweden)
Helena Louise Dare-Edwards
2016-09-01
Full Text Available Review of Louisa Ellen Stein, Millennial fandom: Television audiences in the transmedia age. Iowa City: University of Iowa Press, 2015, paperback, $24 (224p ISBN 978-1609383558; e-book, $24, ISBN 978-1609383565.
Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors
DEFF Research Database (Denmark)
Hillebrand, Eric Tobias; Lee, Tae-Hwy
We examine the Stein-rule shrinkage estimator for possible improvements in estimation and forecasting when there are many predictors in a linear time series model. We consider the Stein-rule estimator of Hill and Judge (1987) that shrinks the unrestricted unbiased OLS estimator towards a restricted...... biased principal component (PC) estimator. Since the Stein-rule estimator combines the OLS and PC estimators, it is a model-averaging estimator and produces a combined forecast. The conditions under which the improvement can be achieved depend on several unknown parameters that determine the degree......-to-noise ratio is low, the PC estimator is superior. If the signal-to-noise ratio is high, the OLS estimator is superior. In out-of-sample forecasting with AR(1) predictors, the Stein-rule shrinkage estimator can dominate both OLS and PC estimators when the predictors exhibit low persistence....
A Hermeneutical Journey throughout the Phenomenology of Edith Stein and Hedwig Conrad-Martius
Directory of Open Access Journals (Sweden)
Carmen Cozma
2011-05-01
Full Text Available Book review to: Angela Ales Bello, Francesco Alfieri, Mobeen Shahid (eds.. Edith Stein. Hedwig Conrad-Martius. Fenomenologia Metafisica Scienze. Bari: Edizioni Giuseppe Laterza di Giuseppe Laterza, 2010. Pp.500
Overarching: Duns Scotus and Edith Stein on Individuality and Individuation Problem
Directory of Open Access Journals (Sweden)
Carmen Cozma
2012-05-01
Full Text Available Book review to: Francesco Alfieri, OFM. La presenza di Duns Scoto nel pensiero di Edith Stein. La questione dell’individualità. Roma: Pontificia Universitas Lateranensis, 2011. Pp. 331.
E-type asteroid (2867) Steins as imaged by OSIRIS on board Rosetta.
Keller, H U; Barbieri, C; Koschny, D; Lamy, P; Rickman, H; Rodrigo, R; Sierks, H; A'Hearn, M F; Angrilli, F; Barucci, M A; Bertaux, J-L; Cremonese, G; Da Deppo, V; Davidsson, B; De Cecco, M; Debei, S; Fornasier, S; Fulle, M; Groussin, O; Gutierrez, P J; Hviid, S F; Ip, W-H; Jorda, L; Knollenberg, J; Kramm, J R; Kührt, E; Küppers, M; Lara, L-M; Lazzarin, M; Lopez Moreno, J; Marzari, F; Michalik, H; Naletto, G; Sabau, L; Thomas, N; Wenzel, K-P; Bertini, I; Besse, S; Ferri, F; Kaasalainen, M; Lowry, S; Marchi, S; Mottola, S; Sabolo, W; Schröder, S E; Spjuth, S; Vernazza, P
2010-01-08
The European Space Agency's Rosetta mission encountered the main-belt asteroid (2867) Steins while on its way to rendezvous with comet 67P/Churyumov-Gerasimenko. Images taken with the OSIRIS (optical, spectroscopic, and infrared remote( )imaging system) cameras on board Rosetta show that Steins is an oblate body with an effective spherical diameter of 5.3 kilometers. Its surface does not show color variations. The morphology of Steins is dominated by linear faults and a large 2.1-kilometer-diameter crater near its south pole. Crater counts reveal a distinct lack of small craters. Steins is not solid rock but a rubble pile and has a conical appearance that is probably the result of reshaping due to Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) spin-up. The OSIRIS images constitute direct evidence for the YORP effect on a main-belt asteroid.
An Integral Representation of Functions on Stein Manifold%Stein流形上的一个积分表示
Institute of Scientific and Technical Information of China (English)
钟春平; 姚宗元
2000-01-01
利用文献[1]在Cn空间中建立抽象积分表示的思想及Henkin和Leiterer在文献[2]中构造的Stein流形上积分核的方法,将Stein流形上已有的一些积分表示进行拓广.得到Stein流形上具逐块光滑边界的相对紧开集D上f连续且f也连续的一个抽象积分表示,这个积分表示的特点是含有m个可供选择的Leray截面和m个可供选择的实参数,当适当选取其中的Leray截面和实参数时,不但可得到Stein流形上已有的B-M公式、Leray-Stokes公式、Cauchy-Fantappi公式,而且还可得到这些公式相应的拓广式.
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...
The Hantzsche-Wendt manifold in cosmic topology
Aurich, R.; Lustig, S.
2014-08-01
The Hantzsche-Wendt space is one of the 17 multiply connected spaces of the three-dimensional Euclidean space {{{E}}^{3}}. It is a compact and orientable manifold which can serve as a model for a spatial finite universe. Since it possesses much fewer matched back-to-back circle pairs on the cosmic microwave background (CMB) sky than the other compact flat spaces, it can escape the detection by a search for matched circle pairs. The suppression of temperature correlations C(\\vartheta ) on large angular scales on the CMB sky is studied. It is shown that the large-scale correlations are of the same order as for the three-torus topology but express a much larger variability. The Hantzsche-Wendt manifold provides a topological possibility with reduced large-angle correlations that can hide from searches for matched back-to-back circle pairs.
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.
The topology of certain 3-Sasakian 7-manifolds
DEFF Research Database (Denmark)
A. Hepworth, Richard
2007-01-01
We calculate the integer cohomology ring and stable tangent bundle of a family of compact, 3-Sasakian 7-manifolds constructed by Boyer, Galicki, Mann, and Rees. Previously only the rational cohomology ring was known. The most important part of the cohomology ring is a torsion group that we describe...... explicitly and whose order we compute. There is a surprising connection with the combinatorics of trees....
Learning Discriminative Stein Kernel for SPD Matrices and Its Applications.
Zhang, Jianjia; Wang, Lei; Zhou, Luping; Li, Wanqing
2016-05-01
Stein kernel (SK) has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue that directly using the original eigenvalues may be problematic because: 1) eigenvalue estimation becomes biased when the number of samples is inadequate, which may lead to unreliable kernel evaluation, and 2) more importantly, eigenvalues reflect only the property of an individual SPD matrix. They are not necessarily optimal for computing SK when the goal is to discriminate different classes of SPD matrices. To address the two issues, we propose a discriminative SK (DSK), in which an extra parameter vector is defined to adjust the eigenvalues of input SPD matrices. The optimal parameter values are sought by optimizing a proxy of classification performance. To show the generality of the proposed method, three kernel learning criteria that are commonly used in the literature are employed as a proxy. A comprehensive experimental study is conducted on a variety of image classification tasks to compare the proposed DSK with the original SK and other methods for evaluating the similarity between SPD matrices. The results demonstrate that the DSK can attain greater discrimination and better align with classification tasks by altering the eigenvalues. This makes it produce higher classification performance than the original SK and other commonly used methods.
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.
A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
Directory of Open Access Journals (Sweden)
Abimbola Abolarinwa
2014-08-01
Full Text Available In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.
Global Regularity for the ∂-b-Equation on CR Manifolds of Arbitrary Codimension
Directory of Open Access Journals (Sweden)
Shaban Khidr
2014-01-01
Full Text Available Let M be a C∞ compact CR manifold of CR-codimension l≥1 and CR-dimension n-l in a complex manifold X of complex dimension n≥3. In this paper, assuming that M satisfies condition Y(s for some s with 1≤s≤n-l-1, we prove an L2-existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for (0,s-forms on M.
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.
Behzadan, A
2015-01-01
In this article we consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we establish existence of coupled non-CMC weak solutions for AF manifolds. As is the case for the analogous existence results for non-CMC solutions on closed manifolds and compact manifolds with boundary, our results here avoid the near-CMC assumption by assuming that the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small. The non-CMC rough solutions results here for AF manifolds may be viewed as extending to AF manifolds the 2009 and 2014 results on rough far-from-CMC positive Yamabe solutions for closed and compact manifolds with boundary. Similarly, our results may be viewed as extending the recent 2014 results for AF m...
On the string topology category of compact Lie groups
2013-01-01
This paper examines the string topology category of a manifold, defined by Blumberg, Cohen and Teleman. Since the string topology category is a subcategory of a compactly generated triangulated category, the machinery of stratification, constructed by Benson, Krause and Iyengar, can be applied in order to gain an understanding of the string topology category. It is shown that an appropriate stratification holds when the manifold in question is a simply connected compact Lie group. This last r...
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.
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...
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.
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)
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.
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...
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.
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...
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.
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)
Periodic Solutions of Lagrangian Systems on a Compact Manifold.
1983-09-01
purposes, by virtue of Theorem 3.1 it is enough to study the topology of AN. We have the following results of Vigue- Poirrier and Sullivan: Theorem 3.2...352. [VPS] Vigue- Poirrier , M. end Sullivan, D., The homology theory of the closed geodesic problem, 3. Differential Geometry 11, 633-644 (1979). VB/ed
ASYMPTOTIC LINKING INVARIANTS FOR RKACTIONS IN COMPACT RIEMANNIAN MANIFOLDS
JOSE LUIS LIZARBE CHIRA
2005-01-01
Arnold no seu trabalho The asymptotic Hopf Invariant and its applications de 1986, considerou sobre um domínio (ômega maiúsculo) compacto de R3 com bordo suave e homología trivial campos X e Y de divergência nula e tangentes ao bordo de (ômega maiúsculo) e definiu o índice de enlaçamento assintótico lk(X; Y ) e o invariante de Hopf associados a X e Y pela integral I(X; Y ) = (integral em ômega maiúsculo de alfa produto d- beta), onde (d-alfa) = iX-vol e (d-b...
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.
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.
$\\mathcal{N}=2$ 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.
Elliptic Equations in Weighted Besov Spaces on Asymptotically Flat Riemannian Manifolds
Brauer, Uwe
2012-01-01
This paper deals with the applications of weighted Besov spaces to elliptic equations on asymptotically flat Riemannian manifolds, and in particular to the solutions of Einstein's constraints equations. We establish existence theorems for the Hamiltonian an momentum constraints with constant mean curvature and with a background metric which satisfies very low regularity assumptions. These results extend the regularity results of Holst, Nagy and Tsogtgerel about the constraint equations on compact manifolds in the Besov space $B_{p,p}^s$, to asymptotically flat manifolds. We also consider the Brill--Cantor criterion in the weighted Besov spaces. Our results improve the regularity assumptions on asymptotically flat manifolds Choquet--Bruhat, Isenberg and Pollack, and Maxwell, as well as they enable us to construct the initial data for the Einstein--Euler system.
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.
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
Possible applications of RIA of LH and FSH in diagnosis of Stein-Leventhal syndrome
Energy Technology Data Exchange (ETDEWEB)
Zenisek, L.; Talas, M.; Stehlikova, J.; Fingerova, H.; Duskova, M.
1981-01-01
LH determination in the serum significantly assists in diagnosing polycystic ovaries. Values exceeding 22 mIU/ml serum are indicative of a typical picture of polycystic ovaries similar to those found in the Stein-Leventhal syndrome. Lower levels indicate an atypical picture of polycystic ovaries or low-cyst ovary degeneration. FSH level cannot be used for this diagnosis.
Bithoracochaeta Stein: descriptions and first records from Colombia (Diptera, Muscidae, Coenosiinae
Directory of Open Access Journals (Sweden)
Marcia S. Couri
2005-01-01
Full Text Available Bithoracochaeta Stein is a Neotropical genus of Muscidae, Coenosiinae, known from ten species recorded from Argentina, Brazil, Costa Rica, Cuba, Ecuador, Guyana, Jamaica, Mexico, Panama, Paraguay, Peru, Puerto Rico, Surinam, Uruguay and Venezuela. The genus is recorded for the first time from Colombia, with the occurrence of the following species: B. annulata Stein, 1911; B. calopus (Bigot, 1885; B. flavicoxa Malloch, 1934; B. leucoprocta (Wiedemann, 1830; B. maricaensis Couri & Motta, 1995 and B. varicornis (Coquilett, 1900. B. nigricoxa, spec. nov. is described from Mexico and Brazil. A brief diagnosis of the known species and a complete description of the new species are given.Bithoracochaeta Stein é um gênero Neotropical de Muscidae, Coenosiinae, com 10 espécies descritas da Argentina, Brasil, Costa Rica, Cuba, Equador, Guiana, Jamaica, México, Panamá, Paraguai, Peru, Porto Rico, Suriname, Uruguai e Venezuela. O gênero é registrado pela primeira vez na Colômbia, com a ocorrência das seguintes espécies: B. annulata Stein, 1911; B. calopus (Bigot, 1885; B. flavicoxa Malloch, 1934; B. leucoprocta (Wiedemann, 1830; B. maricaensis Couri & Motta, 1995 e B. varicornis (Coquilett, 1900. B. nigricoxa spec. nov. é descrita do México e do Brasil. Uma breve diagnose das espécies conhecidas e a descrição completa da nova espécie são apresentadas.
IS THE LARGE CRATER ON THE ASTEROID (2867) STEINS REALLY AN IMPACT CRATER?
Energy Technology Data Exchange (ETDEWEB)
Morris, A. J. W.; Price, M. C.; Burchell, M. J., E-mail: m.j.burchell@kent.ac.uk [Centre for Astrophysics and Planetary Science, School of Physical Science, University of Kent, Canterbury, Kent CT2 7NH (United Kingdom)
2013-09-01
The large crater on the asteroid (2867) Steins attracted much attention when it was first observed by the Rosetta spacecraft in 2008. Initially, it was widely thought to be unusually large compared to the size of the asteroid. It was quickly realized that this was not the case and there are other examples of similar (or larger) craters on small bodies in the same size range; however, it is still widely accepted that it is a crater arising from an impact onto the body which occurred after its formation. The asteroid (2867) Steins also has an equatorial bulge, usually considered to have arisen from redistribution of mass due to spin-up of the body caused by the YORP effect. Conversely, it is shown here that, based on catastrophic disruption experiments in laboratory impact studies, a similarly shaped body to the asteroid Steins can arise from the break-up of a parent in a catastrophic disruption event; this includes the presence of a large crater-like feature and equatorial bulge. This suggests that the large crater-like feature on Steins may not be a crater from a subsequent impact, but may have arisen directly from the fragmentation process of a larger, catastrophically disrupted parent.
Wulf, Mariéle; Gerl-Falkovitz, Hanna-Barbara; Lebach, Mette
2017-01-01
Stein entwickelt in ihrer Anthropologie ein eigenständiges Modell der Freiheit: Sie ist individuell – weil in der Person und ihrer Individualität begründet; sie ist relational – weil wesenhaft bezogen auf anderes und andere; sie ist existentiell – weil sie, in ein Werte- und Sinnsystem einbezogen,
Frei in Beziehung - in Würde frei : Zur originellen existentiellen Anthropologie Edith Steins
Wulf, Mariéle
2016-01-01
Freiheit kann in der oder gegen die Würde gelebt werden. Freiheit ist individuell, absolut und doch auch gebunden. Stein unterscheidet eine dynamische und statische Freiheit. Freiheit entfaltet sich in Grundbeziehung und angesichts von Grundwerten; sie ist existentielle und muss in Verantwortung
Branson, T P; Vasilevich, D V
1998-01-01
Let M be a compact Riemannian manifold with smooth boundary. We study the vacuum expectation value of an operator Q by studying Tr Qe^{-tD}, where D is an operator of Laplace type on M, and where Q is a second order operator with scalar leading symbol; we impose Dirichlet or modified Neumann boundary conditions.
On the Residual Finiteness of Out(π1(M))of Certain Seifert Manifolds
Institute of Scientific and Technical Information of China (English)
R.B.J.T. Allenby; Goansu Kim; C.Y. Tang
2003-01-01
In [2], Grossman proved that the outer automorphism group of a compact orientable surface is residually finite, whence the mapping class groups of surface groups are residually finite. In this paper, we prove a similar result for Seifert manifolds with non-trivial boundary.
Shadowing effects in Newton’s law from compact extra dimensions
Kleidis, K.; Oikonomou, V. K.
2016-10-01
One problem that appears in theories with compact extra dimensions is the shadowing phenomenon, which makes it difficult to identify the topology and the geometry of the extra-dimensional manifold, if it exists. In this paper, we address this problem from the perspective of Newton’s law modifications caused by compact extra dimensions. After providing the modifications cause by some of the most phenomenologically interesting compact manifolds, we qualitatively study and compare the modifications that these manifolds cause to Newton’s law. As we demonstrate, the shadowing phenomenon persists in this approach too, and it seems that the shadowing phenomenon is grouped in “shadowing zones”. At these points, it is impossible to distinguish which compact space causes the modification of Newton’s law. However, away from the shadowing zones, the effects of the different compact manifolds are distinguishable. It is possible that these effects can be observed in the next generation of Newton’s law experiments.
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.
Convexity of Spheres in a Manifold without Conjugate Points
Indian Academy of Sciences (India)
Akhil Ranjan; Hemangi Shah
2002-11-01
For a non-compact, complete and simply connected manifold without conjugate points, we prove that if the determinant of the second fundamental form of the geodesic spheres in is a radial function, then the geodesic spheres are convex. We also show that if is two or three dimensional and without conjugate points, then, at every point there exists a ray with no focal points on it relative to the initial point of the ray. The proofs use a result from the theory of vector bundles combined with the index lemma.
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...
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.
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.
Callisto III e la Cometa di Halley: la ricerca di Johan Stein SJ tra leggenda e storia
Sigismondi, Costantino
The Dutch Jesuit astronomer Johan Stein published in 1909 a text about the legend on a papal bull of Pope Callixtus III against the comet of 1456. This comet happened to be the Halley's one. The original documents, either chronicles and observations, and coeval testimonies are deeply investigated by Stein and the falsity of that legend is clearly demonstrated. In the occasion of the 200 years of the restoration of the Societas Jesu made in 1814 by Pope Pius VII an Italian edition of the full text of Johan Stein is here presented.
Callisto III e la Cometa di Halley: la ricerca di Johan Stein SJ tra leggenda e storia
Sigismondi, Costantino
2014-01-01
The Dutch Jesuit astronomer Johan Stein published in 1909 a text about the legend on a papal bull of Pope Callixtus III against the comet of 1456. This comet happened to be the Halley's one. The original documents, either chronicles and observations, and coeval testimonies are deeply investigated by Stein and the falsity of that legend is clearly demonstrated. In the occasion of the 200 years of the restoration of the Societas Jesu made in 1814 by Pope Pius VII an Italian edition of the full text of Johan Stein is here presented.
Solidaridad de intereses: la transformación del derecho social como dominación en Lorenz von Stein
Directory of Open Access Journals (Sweden)
Jinú Carvajalino Guerrero
2013-08-01
Full Text Available Lorenz von Stein is a German philosopher and jurist who has traditionally been proposed as one of the forerunners of the Social State. However, there are few studies of him in Spanish or English. The purpose of this paper is to demonstrate how, based on Social Movements and Monarchy, von Stein describes a new dimension of social rights in the Republic of mutual interest that Gurvitch disregarded. With the ideas of solidarity and mutual interests, von Stein builds a new dimension of social rights, which are transformed by the movement of the society and class interests.
Sirrine, Nicole K.; McCarthy, Shauna K.
2008-05-01
Gertrude Stein (1874 1946) is well known as an early twentieth century writer, but less well known is her involvement in automatic writing research. Critics of Stein’s literary works suggest that her research had a significant influence on her poetry and fiction, though Stein denied any influence. A partial replication of Stein’s 1896 study was conducted with the goal of addressing three historical questions: (1) What contributed to Stein’s involvement in automatic writing research?; (2) To what extent did Stein believe that she experienced automatic writing?; and (3) To what extent did her automatic writing research influence her later literary works?
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.
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.
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
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...
Constructing reference metrics on multicube representations of arbitrary manifolds
Lindblom, Lee; Taylor, Nicholas W.; Rinne, Oliver
2016-05-01
Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics automatically on multicube representations of manifolds with arbitrary topologies. The method is tested here by constructing reference metrics for compact, orientable two-dimensional manifolds with genera between zero and five. These metrics are shown to satisfy the Gauss-Bonnet identity numerically to the level of truncation error (which converges toward zero as the numerical resolution is increased). These reference metrics can be made smoother and more uniform by evolving them with Ricci flow. This smoothing procedure is tested on the two-dimensional reference metrics constructed here. These smoothing evolutions (using volume-normalized Ricci flow with DeTurck gauge fixing) are all shown to produce reference metrics with constant scalar curvatures (at the level of numerical truncation error).
Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
de la Ossa, Xenia; Svanes, Eirik Eik
2016-01-01
We describe the infinitesimal moduli space of pairs $(Y, V)$ where $Y$ is a manifold with $G_2$ holonomy, and $V$ is a vector bundle on $Y$ with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical $G_2$ cohomology $H^*_{{\\check{\\rm d}}_E}(Y,E)$ developed by Reyes-Carri\\'on and Fern\\'andez and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli $H^1_{{\\check{\\rm d}}_A}(Y,{\\rm End}(V))$ plus the moduli of the $G_2$ structure preserving the instanton condition. The latter piece is contained in $H^1_{{\\check{\\rm d}}_\
Määttä, Sylvia M
2006-01-01
This paper emanates from the concept of empathy as understood by the German philosopher Edith Stein. It begins by highlighting different interpretations of empathy. According to the German philosopher Martin Buber, empathy cannot be achieved as an act of will. In contrast, the psychologist Carl Rogers believes that empathy is identical with dialogue and is the outcome of a cognitive act of active listening. The empathy concept of Edith Stein, philosopher and follower of Edmund Husserl's phenomenology, goes beyond these conflicting views and offers a more complex interpretation, with relevance for both healthcare and nursing education. When studying Stein's three-level model of empathy, a field of tension between perspectives of closeness and distance becomes apparent. The paper concludes by suggesting Stein's model of empathy as a strategy to overcome the tension and meet the demands of empathy.
THE GREAT MASTERS OF PUBLIC ADMINISTRATION: JUSTI, STEIN, BONNIN AND GONZÁLEZ
Directory of Open Access Journals (Sweden)
Omar Guerrero Orozco
2015-06-01
Full Text Available Pubic administration, like other disciplines, has great thinkers whose contributions are the foundation of its scientific development. They are the leaders and masters of the field of study. During the 18th century, Johann Heinrich von Justi studied the “police”, preceding the first studies in public administration that would be pioneered by Lorenz von Stein (Germany and Charles-Jean Bonnin (France one century later. Stein developed an administrative version of the rule of law in the 19th century. On the other hand, inspired by the French Revolution and Napoleon’s Empire, Bonnin created the modern concept of public administration. During the same period, Florentino González, a notable Colombian intellectual, wrote the first book on public administration in a Republic. This article studies the contributions of these great masters of public administration.
Ficción en la idea de empatía de Edith Stein
Directory of Open Access Journals (Sweden)
Fernando Infante del Rosal
2013-01-01
Full Text Available En su primera investigación, Edith Stein se propuso definir la esencia de la Einfühlung (empatía como experiencia de la conciencia ajena; pretendía así fundamentar que, como había indicado Husserl, ese acto abría la posibilidad de una intersubjetividad trascendental como solución al solipsismo de la conciencia. Stein halló la clave de esa esencia en la idea de originariedad, pero intentó evitar el problema de la empatía estética, sirviéndose de Los ídolos del autoconocimiento de Scheler.
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.
Sarah Abrevaya Stein, Saharan Jews and the fate of French Algeria
Everett, Sami
2015-01-01
The local is the global; the personal is the political. This simple maxim crudely encapsulates the intellectual approach taken over a prolific decade of writing about Mediterranean Jewries by the Professor of History and Maurice Amado Chair in sephardic studies, at the University of California, Sarah Abrevaya Stein. Her project renders transnational and local nuance to Jewish diasporic lives and puts that polyphony into conversation with the processes of classifying, segregating, and differen...
General upper and lower tail estimates using Malliavin calculus and Stein's equations
Eden, Richard; Viens, Frederi
2010-01-01
Following a strategy recently developed by Ivan Nourdin and Giovanni Peccati, we provide a general technique to compare the tail of a given random variable to that of a reference distribution. This enables us to give concrete conditions to ensure upper and/or lower bounds on the random variable's tail of various power or exponential types. The Nourdin-Peccati strategy analyzes the relation between Stein's method and the Malliavin calculus, and is adapted to dealing with comparisons to the Gau...
An isometric study of the Lindeberg-Feller CLT via Stein's method
Berckmoes, Ben; Van Casteren, Jan
2011-01-01
We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a rowwise independent triangular array of random variables which is asymptotically negligible in the sense of Feller. A natural example shows that the upper bound is of optimal order. The lower bound improves a result by Andrew Barbour and Peter Hall.
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.
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.
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.
Wilce, A
2004-01-01
We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove that any compact regular TOA is atomistic, and has a compact center. We prove also that any compact TOA with isolated 0 is of finite height. We then focus on stably ordered TOAs: those in which the upper-set generated by an open set is open. These include both topological orthomodular lattices and interval orthoalgebras -- in particular, projection lattices. We show that the topology of a compact stably-ordered TOA with isolated 0 is determined by that of of its space of atoms.
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.
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.
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...
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...
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.
Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds
Energy Technology Data Exchange (ETDEWEB)
Parkhomenko, S.E., E-mail: spark@itp.ac.ru [Landau Institute for Theoretical Physics, 142432 Chernogolovka, Moscow region (Russian Federation); Moscow Institute of Physics and Technology, 141707 Dolgoprudny, Moscow region (Russian Federation)
2014-04-15
In this note we calculate elliptic genus in various examples of twisted chiral de Rham complex on two-dimensional toric compact manifolds and Calabi–Yau hypersurfaces in toric manifolds. At first the elliptic genus is calculated for the line bundle twisted chiral de Rham complex on a compact smooth toric manifold and K3 hypersurface in P{sup 3}. Then we twist chiral de Rham complex by sheaves localized on positive codimension submanifolds in P{sup 2} and calculate in each case the elliptic genus. In the last example the elliptic genus of chiral de Rham complex on P{sup 2} twisted by SL(N) vector bundle with instanton number k is calculated. In all the cases considered we find the infinite tower of open string oscillator contributions and identify directly the open string boundary conditions of the corresponding bound state of D-branes.
Butail, Sachit; Bollt, Erik M; Porfiri, Maurizio
2013-11-07
In this paper, we build a framework for the analysis and classification of collective behavior using methods from generative modeling and nonlinear manifold learning. We represent an animal group with a set of finite-sized particles and vary known features of the group structure and motion via a class of generative models to position each particle on a two-dimensional plane. Particle positions are then mapped onto training images that are processed to emphasize the features of interest and match attainable far-field videos of real animal groups. The training images serve as templates of recognizable patterns of collective behavior and are compactly represented in a low-dimensional space called embedding manifold. Two mappings from the manifold are derived: the manifold-to-image mapping serves to reconstruct new and unseen images of the group and the manifold-to-feature mapping allows frame-by-frame classification of raw video. We validate the combined framework on datasets of growing level of complexity. Specifically, we classify artificial images from the generative model, interacting self-propelled particle model, and raw overhead videos of schooling fish obtained from the literature. © 2013 Elsevier Ltd. All rights reserved.
The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension
Lee, Yng-Ing
2010-01-01
Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are critical points of the volume functional under Hamiltonian deformations. They can be considered as a generalization of special Lagrangians or Lagrangian and minimal submanifolds. Joyce, Schoen and the author show that given any compact rigid Hamiltonian stationary Lagrangian in $\\C^n$, one can always find a family of Hamiltonian stationary Lagrangians of the same type in any compact symplectic manifolds with a compatible metric. The advantage of this result is that it holds in very general classes. But the disadvantage is that we do not know where these examples locate and examples in this family might be far apart. In this paper, we derive a local condition on Kahler manifolds which ensures the existence of one family of Hamiltonian stationary Lagrangian tori near a point with given frame satisfying the criterion. Butscher and Corvino ever proposed a condition in n=2. But our condition appears to be different from theirs. The condition d...
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.
An, Lihua; Fung, Karen Y; Krewski, Daniel
2010-09-01
Spontaneous adverse event reporting systems are widely used to identify adverse reactions to drugs following their introduction into the marketplace. In this article, a James-Stein type shrinkage estimation strategy was developed in a Bayesian logistic regression model to analyze pharmacovigilance data. This method is effective in detecting signals as it combines information and borrows strength across medically related adverse events. Computer simulation demonstrated that the shrinkage estimator is uniformly better than the maximum likelihood estimator in terms of mean squared error. This method was used to investigate the possible association of a series of diabetic drugs and the risk of cardiovascular events using data from the Canada Vigilance Online Database.
On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations
Directory of Open Access Journals (Sweden)
Abdeslem Hafid Bentbib
2017-03-01
Full Text Available In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B − X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration and others. The proposed methods are based on projection onto the extended block Krylov subspace with a Galerkin approach (GA or with the minimization of the norm of the residual. We give some results on the residual and error norms and report some numerical experiments.
Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps
Pfaff, Jonathan
2012-01-01
For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of SL_2(C) to the corresponding Reidemeister torsion. Our proof rests on an expression of the analytic torsion in terms of special values of Ruelle zeta functions as well as on recent work of Pere Menal-Ferrer and Joan Porti.
On the uniform perfectness of equivariant diffeomorphism groups for principal G manifolds
Directory of Open Access Journals (Sweden)
Kazuhiko Fukui
2017-01-01
Full Text Available We proved in [K. Abe, K. Fukui, On commutators of equivariant diffeomorphisms, Proc. Japan Acad. 54 (1978, 52-54] that the identity component \\(\\text{Diff}\\,^r_{G,c}(M_0\\ of the group of equivariant \\(C^r\\-diffeomorphisms of a principal \\(G\\ bundle \\(M\\ over a manifold \\(B\\ is perfect for a compact connected Lie group \\(G\\ and \\(1 \\leq r \\leq \\infty\\ (\\(r \
NMS Flows on Three-Dimensional Manifolds with One Saddle Periodic Orbit
Institute of Scientific and Technical Information of China (English)
B. CAMPOS; A. CORDERO; J. Mart(i)nez ALFARO; P. VINDEL
2004-01-01
The simplest NMS flow is a polar flow formed by an attractive periodic orbit and a repulsive periodic orbit as limit sets. In this paper we show that the only orientable, simple, compact,3-dimensional manifolds without boundary that admit an NMS flow with none or one saddle periodic orbit are lens spaces.We also see that when a fattened round handle is a connected sum of tori, the corresponding flow is also a trivial connected sum of flows.
Gicquaud, Romain
2014-01-01
We construct solutions to the constraint equations in general relativity using the limit equation criterion introduced by Dahl, Humbert and the first author. We focus on solutions over compact 3-manifolds admitting a $\\bS^1$-symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results.
"Lizzie do you mind": Gertrude Stein's laws of genre in blood on the dining-room floor.
Robbins, Amy Moorman
2013-01-01
Against previous critics' readings of Stein's Blood on the Dining-Room Floor as a failed attempt at the hard-boiled genre, this article argues for the many ways in which the novel re-writes the gothic/domestic detective story in a brilliant tour de force that frames all that is un-natural about heteronormative Victorian family life while offering a lesbian alternative. In Stein's subversive and serious play with the forms and conventions of popular fiction, her positive invocations of Lizzie Borden as textual witness, her wide-reaching references to lesbian relationships in other of her works, and, finally, her virtuosic use of silence, Stein writes a profound critique of the patriarchal family through a radical unmaking of a thoroughly domestic literary form.
Edith Stein – “Great Daughter of Israel and Carmel”, Searching for the Truth Every Day
Directory of Open Access Journals (Sweden)
Andrzej Pryba
2016-04-01
Full Text Available Edith Stein was born in a traditional religious Jewish family. In her youth, she stopped praying and lost her faith in God. She was, however, very faithful in searching for the truth, which had become her life’s passion. First, the article presents various definitions of truth. Then it deals with phenomenological methods of discovering the truth about man, which were characteristic of Edith Stein. Finally, it shows her discovery of the God of Love, who pulled her towards mystical union in the spirituality of Carmel. St. Teresa Benedicta of the Cross (Edith Stein died in the concentration camp at Auschwitz experiencing the mystery of the Cross of Christ and sacrificing herself for her nation.
Crystal Melting and Toric Calabi-Yau Manifolds
Ooguri, Hirosi
2008-01-01
We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.
Analysis III analytic and differential functions, manifolds and Riemann surfaces
Godement, Roger
2015-01-01
Volume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a "canonical'' language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques. Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular fun...
Symplectic manifolds with no Kähler structure
Tralle, Aleksy
1997-01-01
This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.
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.
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.
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.
Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
de la Ossa, Xenia; Larfors, Magdalena; Svanes, Eirik E.
2016-11-01
We describe the infinitesimal moduli space of pairs ( Y, V) where Y is a manifold with G 2 holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G 2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli {H}_{{overset{ěe }{d}}_A}^1(Y,End(V)) plus the moduli of the G 2 structure preserving the instanton condition. The latter piece is contained in {H}_{overset{ěe }{d}θ}^1(Y,TY) , and is given by the kernel of a map overset{ěe }{F} which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map overset{ěe }{F} is given in terms of the curvature of the bundle and maps {H}_{overset{ěe }{d}θ}^1(Y,TY) into {H}_{{overset{ěe }{d}}_A}^2(Y,End(V)) , and moreover can be used to define a cohomology on an extension bundle of TY by End( V). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on ( Y, V) when α' = 0.
First albedo determination of 2867 Steins, target of the Rosetta mission
Fornasier, S; Fulchignoni, M; Barucci, M A; Barbieri, C
2006-01-01
We present the first albedo determination of 2867 Steins, the asteroid target o f the Rosetta space mission together with 21 Lutetia. The data were obtained in polarimetric mode at the ESO-VLT telescope with the FORS1 instrument in the V and R filters. Observations were carried out from Jun e to August 2005 covering the phase angle range from 10.3 deg. to 28.3 deg., allowing the determination of the asteroid albedo by the well known experimenta l relationship between the albedo and the slope of the polarimetric curve at th e inversion angle. The measured polarization values of Steins are small, confirming an E-type cla ssification for this asteroid, as already suggested from its spectral propertie s. The inversion angle of the polarization curve in the V and R filters is resp ectively of 17.3 +/-1.5deg. and 18.4+/-1.0 deg., and the corresponding sl ope parameter is of 0.037+/-0.003 %/deg and 0.032+/-0.003 %/deg. On the basis of its polarimetric slope value, we have derived an albedo of 0.45 +/-0.1, that gives...
Dose-response modeling in mental health using stein-like estimators with instrumental variables.
Ginestet, Cedric E; Emsley, Richard; Landau, Sabine
2017-02-21
A mental health trial is analyzed using a dose-response model, in which the number of sessions attended by the patients is deemed indicative of the dose of psychotherapeutic treatment. Here, the parameter of interest is the difference in causal treatment effects between the subpopulations that take part in different numbers of therapy sessions. For this data set, interactions between random treatment allocation and prognostic baseline variables provide the requisite instrumental variables. While the corresponding two-stage least squares (TSLS) estimator tends to have smaller bias than the ordinary least squares (OLS) estimator; the TSLS suffers from larger variance. It is therefore appealing to combine the desirable properties of the OLS and TSLS estimators. Such a trade-off is achieved through an affine combination of these two estimators, using mean squared error as a criterion. This produces the semi-parametric Stein-like (SPSL) estimator as introduced by Judge and Mittelhammer (2004). The SPSL estimator is used in conjunction with multiple imputation with chained equations, to provide an estimator that can exploit all available information. Simulated data are also generated to illustrate the superiority of the SPSL estimator over its OLS and TSLS counterparts. A package entitled SteinIV implementing these methods has been made available through the R platform. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
Die Familie im Leben und in den Schriften der Heiligen Theresia Benedikta vom Kreuz (Edith Stein
Directory of Open Access Journals (Sweden)
Wojciech Zyzak
2017-04-01
Full Text Available In modern times as never before, marriage and family are in danger. The contemporary problems were already present in many aspects in the times of Edith Stein. The author of the article studies the life and the works of the Saint with regard to marriage and family. For Edith Stein, marriage is an inseparable union of a man and woman, which, thanks to the sacramental grace, is filled with special strength to maintain reciprocal love and fidelity and also to cooperate with God in giving life and educating children. In Edith Stein’s opinion, both the husband and the wife in the family have rights and duties connected with being God’s image, bearing and bringing up children and transforming the world by their work. Edith, however, noted the difference between sexes and the way in which the tasks were realised according to the nature and the different callings. The Saint saw the necessity of complementarity of sexes and generations in a harmonious family. Such a vision of marriage and family is still applicable in our times.
Villa Stein-De by le Corbusier (1926-1928): Conservation Strategies Between Research and Education
Balletti, C.; Di Resta, S.; Faccio, P.; Guerra, F.; Pandolfo, M.
2017-05-01
The paper focuses on the educational experience produced during the International Workshop, organized by the IUAV University of Venice and dedicated to both the understanding and conservation of the maison Stein-de-Monzie "Les Terrasses", an emblematic work of Le Corbusier's early career period. The villa, located in Garches (Vaucresson), was designed and built between 1926 and 1928, the exact same years when Le Corbusier was elaborating the "Five Points of Architecture" (1927): the building is the first complete application of these principles, while it represents an evolution of the maison Dom-Ino's structural scheme. Nowadays, both the interior spaces and the external surfaces of the maison Stein-de-Monzie show profound changes caused by problematic events leading to the present-day appearance of the building, in many cases misrepresenting the original design goals. The building's integrated instrumental survey (laser scanning, photogrammetry, topography) allowed to document and understand the history of the villa beyond the mere and well known project phase, contributing to the definition of the actual construction characteristics and to ascertain both the material consistency and the state of conservation. The knowledge acquisition process - supported by survey data - constitutes a prerequisite to outline the design of new solutions, which could effectively express the cultural choices connected to the conservation of the Twentieth-Century built heritage.
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...
On the Picard group of a compact flat projective variety
Michelacakis, NJ
1996-01-01
In this note, we describe the Picard group of the class of compact, smooth, flat, projective varieties. In view of Charlap's work and Johnson's characterization, we construct line bundles over such manifolds as the holonomy-invariant elements of the Neron-Severi group of a projective flat torus cove
Directory of Open Access Journals (Sweden)
Jose Luis Caballero Bono
2012-09-01
Full Text Available Edith Stein leyó la obra de Martin Heidegger Ser y tiempo en 1927, el mismo año de su publicación. Este artículo trata de reconstruir la «hermenéutica blanca» de esa lectura, es decir, las reacciones que pudo suscitar y que no fueron puestas por escrito en ese momento. Se toman como guía tres comentarios azarosos de la autora en relación tanto a Ser y tiempo como a la filosofía de Heidegger en general.Edith Stein read Martin Heidegger’s Being and Time in 1927, the year of its publication. This article explores a «white hermeneutics» of her reading, tracing some possible reactions to this work that Stein did not record at the time. Three incidental comments on Being and Time and Heidegger’s philosophy in general made by Stein guide our research.
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Marita Kampshoff
2009-03-01
Full Text Available Für das besprochene Buch haben einige ehemalige Student/-innen der Herausgeberin, der Professorin für Allgemeine Psychologie und Sozialpsychologie Gisela Steins, ihre Abschlussarbeit zusammengefasst. Die meisten Beiträge befassen sich mit kleineren empirischen Studien zum Thema Schule und Geschlecht. Gisela Steins selbst hat eine längere Einführung und knappe Überleitungen zwischen den Aufsätzen verfasst. Die Artikel der Student/-innen sind teilweise interessant, aber es stellt sich die Frage, für welche Leserschaft dieses Buch gedacht ist.This book introduces a selection of examinations written for the First State Board Examination for prospective teachers. Former students of the editor, Dr. Gisela Steins, a professor for general psychology and social psychology, each summarized their final papers in essays. Most of the essays contain smaller empirical studies on the topic of school and gender. The two final contributions deal with the themes of body disaffection and the sensitization of school children toward processes of stigmatization using the example of obesity. Gisela Steins herself composed an introduction as well as short transitions between the articles. The students’ articles are for the most part interesting, although the question remains at to the book’s intended audience.
Viewpoint Manifolds for Action Recognition
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Souvenir Richard
2009-01-01
Full Text Available Abstract Action recognition from video is a problem that has many important applications to human motion analysis. In real-world settings, the viewpoint of the camera cannot always be fixed relative to the subject, so view-invariant action recognition methods are needed. Previous view-invariant methods use multiple cameras in both the training and testing phases of action recognition or require storing many examples of a single action from multiple viewpoints. In this paper, we present a framework for learning a compact representation of primitive actions (e.g., walk, punch, kick, sit that can be used for video obtained from a single camera for simultaneous action recognition and viewpoint estimation. Using our method, which models the low-dimensional structure of these actions relative to viewpoint, we show recognition rates on a publicly available dataset previously only achieved using multiple simultaneous views.
Viewpoint Manifolds for Action Recognition
Directory of Open Access Journals (Sweden)
Richard Souvenir
2009-01-01
Full Text Available Action recognition from video is a problem that has many important applications to human motion analysis. In real-world settings, the viewpoint of the camera cannot always be fixed relative to the subject, so view-invariant action recognition methods are needed. Previous view-invariant methods use multiple cameras in both the training and testing phases of action recognition or require storing many examples of a single action from multiple viewpoints. In this paper, we present a framework for learning a compact representation of primitive actions (e.g., walk, punch, kick, sit that can be used for video obtained from a single camera for simultaneous action recognition and viewpoint estimation. Using our method, which models the low-dimensional structure of these actions relative to viewpoint, we show recognition rates on a publicly available dataset previously only achieved using multiple simultaneous views.
Energy Technology Data Exchange (ETDEWEB)
Bluemich, Bernhard; Haber-Pohlmeier, Sabina; Zia, Wasif [RWTH Aachen Univ. (Germany). Inst. fuer Technische und Makromolekulare Chemie (ITMC)
2014-06-01
Nuclear Magnetic Resonance (NMR) spectroscopy is the most popular method for chemists to analyze molecular structures, while Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool for medical doctors that provides high-contrast images of biological tissue. In both applications, the sample (or patient) is positioned inside a large, superconducting magnet to magnetize the atomic nuclei. Interrogating radio-frequency pulses result in frequency spectra that provide the chemist with molecular information, the medical doctor with anatomic images, and materials scientist with NMR relaxation parameters. Recent advances in magnet technology have led to a variety of small permanent magnets to allow compact and low-cost instruments. The goal of this book is to provide an introduction to the practical use of compact NMR at a level nearly as basic as the operation of a smart phone.
Bazeia, D; Marques, M A; Menezes, R; Zafalan, I
2016-01-01
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane.
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Losano, L.; Marques, M.A.; Zafalan, I. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2017-02-15
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane. (orig.)
Descriptor Learning via Supervised Manifold Regularization for Multioutput Regression.
Zhen, Xiantong; Yu, Mengyang; Islam, Ali; Bhaduri, Mousumi; Chan, Ian; Li, Shuo
2016-06-08
Multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis. However, due to the huge image variability and ambiguity, it is fundamentally challenging to handle the highly complex input-target relationship of multioutput regression, especially with indiscriminate high-dimensional representations. In this paper, we propose a novel supervised descriptor learning (SDL) algorithm for multioutput regression, which can establish discriminative and compact feature representations to improve the multivariate estimation performance. The SDL is formulated as generalized low-rank approximations of matrices with a supervised manifold regularization. The SDL is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low-dimensional space aligned to targets. The achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression, which enables more accurate and efficient multivariate estimation. We conduct extensive evaluation of the proposed SDL on both synthetic data and real-world multioutput regression tasks for both computer vision and medical image analysis. Experimental results have shown that the proposed SDL can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts. Our method establishes a novel SDL framework for multioutput regression, which can be widely used to boost the performance in different applications.
Flux formulation of DFT on group manifolds and generalized Scherk-Schwarz compactifications
Energy Technology Data Exchange (ETDEWEB)
Bosque, Pascal du [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Fakultät für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Hassler, Falk [University of North Carolina, Department of Physics and Astronomy,Phillips Hall, CB #3255, 120 E. Cameron Ave., Chapel Hill, NC 27599-3255 (United States); City University of New York, The Graduate Center,365 Fifth Avenue, New York, NY 10016 (United States); Columbia University, Department of Physics,Pupin Hall, 550 West 120th St., New York, NY 10027 (United States); Lüst, Dieter [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Fakultät für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany)
2016-02-04
A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a 2D-dimensional, pseudo Riemannian manifold, which is isomorphic to a Lie group embedded into O(D,D). All fields and parameters of generalized diffeomorphisms are supported on this manifold, whose metric is spanned by the background vielbein E{sub A}{sup I}∈ GL(2D). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, E{sub A}{sup I} is identified with the left invariant Maurer-Cartan form on the group manifold, in the same way as it is done in geometric Scherk-Schwarz reductions. We show in detail how the Maurer-Cartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3,3), we calculate E{sub A}{sup I}.
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.
Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
Jaramillo, J A; Sanchez-Gonzalez, L
2011-01-01
In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete $C^k$ Finsler manifold $M$ is determined by the normed algebra $C_b^k(M)$ of all real-valued, bounded and $C^k$ smooth functions with bounded derivative defined on $M$. As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete $C^k$ Finsler manifold $M$ is determined by the algebra $C_b^k(M)$; (ii) the weak Finsler structure of a separable and complete $C^k$ Finsler manifold $M$ modeled on a Banach space with a Lipschitz and $C^k$ smooth bump function is determined by the algebra $C^k_b(M)$; (iii) the weak Finsler structure of a $C^k$ uniformly bumpable and complete $C^k$ Finsler manifold $M$ modeled on a Weakly Compactly Generated (WCG) Banach space with an (equivalent) $C^k$ smooth norm is determined by the algebra $C^k_b(M)$; and (iii) the isometric structure of a WCG Banach space $X$ with an $C^1$ smooth bump function is determined by the algebra $C_b^1(X)$.
Husserl and Stein on the Phenomenology of Empathy: Perception and Explication
DEFF Research Database (Denmark)
Jardine, James Alexander
2015-01-01
Within the phenomenological tradition, one frequently finds the bold claim that interpersonal understanding is rooted in a sui generis form of intentional experience, most commonly labeled empathy (Einfühlung). The following paper explores this claim, emphasizing its distinctive character......, and examining the phenomenological considerations offered in its defense by two of its main proponents, Edmund Husserl and Edith Stein. After offering in section 2 some preliminary indications of how empathy should be understood, I then turn to some characterizations of its distinctive structure, considering......, in section 3, the Husserlian claim that certain forms of empathy are perceptual in nature, and in section 4, Stein’s insistence that empathetic experience frequently involves explicating the other’s own intentional experiences. Section 5 will conclude by assessing the extent to which their analyses lead...
The implications of culture shock for health educators: Reflections with Barer-Stein
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M. L. Arthur
1996-05-01
Full Text Available Culture shock is an intensely personal universal human experience that may emerge in any cross cultural social encounter. Therefore, it may be deduced that culture shock is an experience that may occur in all spheres of life in which individuals are confronted by world views and life styles that differ from their own whether in terms of health, education or occupation amongst others. It is a situation that calls for adaptation or adjustment on the part of the individual. TTtis article explores the relationship between culture shock and culture adaptation as an aspect of learning which has been developed by Thelma Barer-Stein. Stress is laid on the role of the individual, as health educator, and the choices must make if he/she is to gain an understanding of the community in which he/she serves and to attribute new meanings to the situation by which he/she is confronted
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...
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...
The Framework, Causal and Co-compact Structure of Space-time
Kovár, Martin
2013-01-01
We introduce a canonical, compact topology, which we call weakly causal, naturally generated by the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by certain problems of quantum gravity. We show that for every four-dimensional globally hyperbolic Lorentzian manifold there exists an associated causal site, whose weakly causal topology is co-compact with respect to the manifold topology and vice versa. Thus, the causal site has the full information about the topology of space-time, represented by the Lorentzian manifold. In addition, we show that there exist also non-Lorentzian causal sites (whose causal relation is not a continuous poset) and so the weakly causal topology and its de Groot dual extends the usual manifold topology of space-time beyond topologies generated by the traditional, smooth model. As a source of inspiration in topologizing the studied causal structures, we use some methods and constructions of general topology and formal concept analysis.
La empatía según Edith Stein y sus aplicaciones en enfermería en el contexto familiar
Nogales Espert, Amparo
2008-01-01
A través de un análisis de textos sobre la biografía y la obra de Edith Stein, se pretenden extraer aquellos aspectos de su personalidad coincidentes con los valores de la enfermería. Through a text analysis of Edith Stein's biography and work, we tried to draw those aspects of her personality that coincide with nursing values. A través de uma análise de textos sobre a biografia e a obra de Edith Stein, pretendese extrair aqueles aspectos de sua personalidade coincidentes...
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.
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.
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.
Determining the first order perturbation of a polyharmonic operator on admissible manifolds
Assylbekov, Yernat M.; Yang, Yang
2017-01-01
We consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator L g , X , q, with X being a W 1 , ∞ vector field and q being an L∞ function on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. We show that the knowledge of the Dirichlet-to-Neumann map determines X and q uniquely. The method is based on the construction of complex geometrical optics solutions using the Carleman estimate for the Laplace-Beltrami operator due to Dos Santos Ferreira, Kenig, Salo and Uhlmann. Notice that the corresponding uniqueness result does not hold for the first order perturbation of the Laplace-Beltrami operator.
Near-equality of the Penrose Inequality for rotationally symmetric Riemannian manifolds
Lee, Dan A
2011-01-01
This article is the sequel to our previous paper [LS] dealing with the near-equality case of the Positive Mass Theorem. We study the near-equality case of the Penrose Inequality for the class of complete asymptotically flat rotationally symmetric Riemannian manifolds with nonnegative scalar curvature whose boundaries are outermost minimal hypersurfaces. Specifically, we prove that if the Penrose Inequality is sufficiently close to being an equality on one of these manifolds, then it must be close to a Schwarzschild space with an appended cylinder, in the sense of Lipschitz Distance. Since the Lipschitz Distance bounds the Intrinsic Flat Distance on compact sets, we also obtain a result for Intrinsic Flat Distance, which is a more appropriate distance for more general near-equality results, as discussed in [LS
A Lower Bound of the Genus of a Self-amalgamated 3-manifolds
Institute of Scientific and Technical Information of China (English)
LI XU; LEI FENG-CHUN
2011-01-01
Let M be a compact connected oriented 3-manifold with boundary,Q1, Q2 (C)(э)M be two disjoint homeomorphic subsurfaces of (э)M, and h: Q1 → Q2 be an orientation-reversing homeomorphism. Denote by Mh or MQ1＝Q2 the 3-manifold obtained from M by gluing Q1 and Q2 together via h. Mh is called a self-amalgamation of M along Q1 and Q2. Suppose Q1 and Q2 lie on the same component F′ of (э)M′, and F′ - Q1 ∪ Q2 is connected. We give a lower bound to the Heegaard genus of M when M′ has a Heegaard splitting with sufficiently high distance.
A sufficient condition for the genus of an amalgamated 3-manifold not to go down
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Let M i be a connected, compact, orientable 3-manifold, F i a boundary component of M i with g(F i ) 2, i = 1, 2, and F 1 ≌ F 2 . Let : F 1 → F 2 be a homeomorphism, and M = M 1 ∪ M 2 , F = F 2 = (F 1 ). Then it is known that g(M ) g(M 1 ) + g(M 2 ) - g(F ). In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (Q i1 , Q i ) in (M i1 , F i ) satisfying χ(Q i ) > 3 - 2g(M i ), i = 1, 2. Then g(M ) = g(M 1 ) + g(M 2 ) - g(F ).
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...
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.
Jose Luis Caballero Bono
2012-01-01
Edith Stein leyó la obra de Martin Heidegger Ser y tiempo en 1927, el mismo año de su publicación. Este artículo trata de reconstruir la «hermenéutica blanca» de esa lectura, es decir, las reacciones que pudo suscitar y que no fueron puestas por escrito en ese momento. Se toman como guía tres comentarios azarosos de la autora en relación tanto a Ser y tiempo como a la filosofía de Heidegger en general.Edith Stein read Martin Heidegger’s Being and Time in 1927, the year of its publicatio...
ATLANTA - United States Attorney Bill Nettles stated late yesterday that Nancy Marie Stein, age 62, of Anderson, South Carolina , was sentenced by Senior United States District Judge Henry M. Herlong in federal court in Greenville, to a total of 73
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.
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.
Holst, Michael
2014-01-01
In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary S. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on S, similar to those analyzed previously by Dain (2004), by Maxwell (2004, 2005), and by Holst and Tsogtgerel (2013) as a model of black holes in various CMC settings, and by Holst, Meier, and Tsogtgerel (2013) in the setting of far-from-CMC solutions on compact manifolds with boundary. These "marginally trapped surface" Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region S are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assumi...
L’‘Orestea’ di Eschilo secondo Peter Stein: storia di una messa in scena (1974-1994
Directory of Open Access Journals (Sweden)
Lorenzo Galletti
2014-12-01
Full Text Available The massive, pragmatic and intellectual work by Peter Stein on the Oresteia of Aeschylus perfectly summarizes the German director’s conception of ‘classic’. This essay reviews the twenty-years period which started with the first experimental approach to ancient tragedy by the Schaubühne to the staging of the trilogy in Moscow in 1994. In his work, Stein investigates the origins of western theatre, compares the role of gestures and words at the dawn of theatre with that of the contemporary age, and then moves, in line with the evolution of the Aeschylus trilogy plot, to the study of the purely political connotation of the text. Precisely the post-soviet Russia represented the ideal setting where to reproduce the rite of dismissal of high hierarchies, whether of divine nature or not, and the affirmation of the new democratic system.L’imponente lavoro pratico e intellettuale di Peter Stein sull’Orestea di Eschilo riassume in maniera esemplare il pensiero del regista tedesco riguardo all’idea di ‘classico’. Nel saggio si traccia il percorso lungo i vent’anni che vanno dal primo sperimentale approccio alla tragedia antica da parte del gruppo della Schaubühne fino alla messinscena moscovita della trilogia del 1994. Nel suo lavoro Stein riflette sulle origini del teatro in Occidente, sul ruolo del gesto e della parola agli albori del teatro e in epoca contemporanea, spostando poco a poco lo sguardo, in linea con l’evoluzione dell’intreccio della trilogia eschilea, sul significato prettamente politico del testo. Proprio la Russia postcomunista si qualifica allora luogo ideale in cui ripetere il rito di destituzione di ogni ordine superiore (ove il termine sia da intendere nel senso più lato, non solo divino e affermazione del nuovo sistema democratico.
Kolokolova, Ludmilla; La Forgia, Fiorangela; Lazzarin, Monica; Magrin, Sara
2014-11-01
Rosetta OSIRIS optical system is equipped with a total of 25 medium and narrow-band filters which allow studying spectral dependence of photometric data obtained by this instrument. In this study we analyze the OSIRIS data for asteroids Steins and Lutetia at small phase angles to see how characteristics of their opposition effect depend on the wavelength and what mechanism can explain this dependence. For asteroid Steins, the data are available for the phase angles ranging from 0.36° up to 136° acquired with 9 filters that cover the wavelength range 295.9 - 631.6 nanometers; the images of asteroid Lutetia cover phase angles from 0.15° up to 156° in 16 filters in the range of wavelengths 269.3 - 989.3 nanometers. The data for Lutetia have a good coverage for phase angels smaller than 5° for three filters, whereas in the case of Steins only for the WAC filter 631.6 nm the angles smaller than 5° are covered. For other filters, a special interpolation procedure was performed; it is described in detail in La Forgia et al. (Mem. S.A.It. Suppl. Vol. 20, 15, 2012).Both asteroids demonstrate significant brightness surge at small phase angles, however, its dependence on the wavelength is opposite: the sharpness of the surge increases with wavelength for asteroid Steins and decreases for asteroid Lutetia. The wavelength behavior of Steins’ opposition effect is consistent with the coherent backscattering as the main mechanism that produces the opposition surge. However, the wavelength behavior of Lutetia’s opposition surge cannot be explained either by coherent backscattering or by shadow hiding. We explore other opportunities to explain the specifics of the opposition effect for asteroid Lutetia. Particularly, we consider if the properties of individual particles can be responsible for the wavelength dependence of Lutetia’s opposition effect.
Logos y poesía como acontecimientos del mundo y de la carne: Edith Stein y Christophe Lebreton
Directory of Open Access Journals (Sweden)
Cecilia Avenatti de Palumbo
2016-01-01
Full Text Available The scope of the present article is to evidence the confluence of two different kind of speech: the rational and the poetic one, moving from the Works of Edith Stein and Christophe Lebreton. Both types of speech, usually presented as opposed, belong to the realm of the human spirit - incarnated in time. Therefore, they do not exclude each other but they meet themselves at the event of flesh.
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
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.
The cohomology of the affine Deligne-Lusztig varieties in the affine flag manifold of $GL_2$
Ivanov, Alexander
2009-01-01
This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of GL_2. At first we determine all such varieties up to isomorphy. After this we investigate the representations of the sigma-stabilizer of an element b of the group on the etale cohomology of the affine Deligne-Lusztig variety X_w(b). We describe such representations as inductions from compact subgroups and in terms of noncuspidal representations.
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.
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...
Compace Hypersurfaces of a Sasakian Manifold%Sasaki流形的紧致超曲面
Institute of Scientific and Technical Information of China (English)
罗崇善
2001-01-01
In this paper some compact orientable gypersurfaces of a Sasakianmanifold and Sasskian space form are investigated. Some integral formulas for these gypersurfaces are deduced. From them , some geometrical properties of hypersurfaces, ambient Sasakian manifold and its structure vector are obtained.%要积分公式作为工具,研究了Sasaki流形和Sasaki空间形式的几种紧致可定向超曲面,得出了涉及超曲面、外围流形及其结构向量的一些几何性质。
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.
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.
Limit theorems in the imitative monomer-dimer mean-field model via Stein's method
Chen, Wei-Kuo
2016-08-01
We consider the imitative monomer-dimer model on the complete graph introduced in the work of Alberici et al. [J. Math. Phys. 55, 063301-1-063301-27 (2014)]. It was shown that this model is described by the monomer density and has a phase transition along certain coexistence curve, where the monomer and dimer phases coexist. More recently, it was understood [D. Alberici et al., Commun. Math. Phys. (published online, 2016)] that the monomer density exhibits the central limit theorem away from the coexistence curve and enjoys a non-normal limit theorem at criticality with normalized exponent 3/4. By reverting the model to a weighted Curie-Weiss model with hard core interaction, we establish the complete description of the fluctuation properties of the monomer density on the full parameter space via Stein's method of exchangeable pairs. Our approach recovers what were established in the work of Alberici et al. [Commun. Math. Phys. (published online, 2016)] and furthermore allows to obtain the conditional central limit theorems along the coexistence curve. In all these results, the Berry-Esseen inequalities for the Kolmogorov-Smirnov distance are given.
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.
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 .
Moduli Spaces of Abelian Vortices on Kahler Manifolds
Baptista, J M
2012-01-01
We consider the self-dual vortex equations on a positive line bundle L --> M over a compact Kaehler manifold of arbitrary dimension. When M is simply connected, the moduli space of vortex solutions is a projective space. When M is an abelian variety, the moduli space is the projectivization of the Fourier-Mukai transform of L. We extend this description of the moduli space to general abelian GLSM, i.e. to vortex equations with a torus gauge group acting linearly on a complex vector space. In this case the vortex moduli space becomes a toric orbifold and a toric fibration over a cartesian product of Pic^0(M)'s, respectively. In all these examples we compute the Kaehler class of the natural L^2-metric on the moduli space. In the simplest examples we compute the volume and total scalar curvature of the muduli space. Finally, in the case of abelian GLSM, we note that the vortex moduli space is a compactification of the space of holomorphic maps from M to toric targets, just as in the usual case of M being a Riema...
Foliated eight-manifolds for M-theory compactification
Babalic, Elena Mirela
2014-01-01
We characterize compact eight-manifolds M which arise as internal spaces in N=1 flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part of the supersymmetry generator is everywhere non-chiral. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation of M which carries a leafwise G2 structure, such that the O'Neill-Gray tensors, non-adapted part of the normal connection and torsion classes of the G2 structure are given in terms of the supergravity four-form field strength by explicit formulas which we derive. We discuss the topology of such foliations, showing that the C star algebra of the foliation is a noncommutative torus of dimension given by the irrationality rank of a certain cohomology class constructed from the four-form field strength, which must satisfy the Latour obstruction. We also give a criterion in terms of this class for when such foliations are fibrations over the circle. When t...
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.
Lorentzian Cobordisms, Compact Horizons and the Generic Condition
Larsson, Eric
2014-01-01
We consider the problem of determining which conditions are necessary for cobordisms to admit Lorentzian metrics with certain properties. In particular, we prove a result originally due to Tipler without a smoothness hypothesis necessary in the original proof. In doing this, we prove that compact horizons in a smooth spacetime satisfying the null energy condition are smooth. We also prove that the "generic condition" is indeed generic in the set of Lorentzian metrics on a given manifold.
Energy Technology Data Exchange (ETDEWEB)
Caballero, Magdalena; Rubio, Rafael M [Departamento de Matematicas, Campus de Rabanales, Universidad de Cordoba, 14071 Cordoba (Spain); Romero, Alfonso, E-mail: magdalena.caballero@uco.es, E-mail: aromero@ugr.es, E-mail: rmrubio@uco.es [Departamento de Geometria y Topologia, Universidad de Granada, 18071 Granada (Spain)
2011-07-21
A new technique to study spacelike hypersurfaces of constant mean curvature in a spacetime which admits a timelike gradient conformal vector field is introduced. As an application, the leaves of the natural spacelike foliation of such spacetimes are characterized in some relevant cases. The global structure of this class of spacetimes is analyzed and the relation with its well-known subfamily of generalized Robertson-Walker spacetimes is exposed in detail. Moreover, some known uniqueness results for compact spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes are widely extended. Finally, and as a consequence, several Calabi-Bernstein problems are solved obtaining all the entire solutions on a compact Riemannian manifold to the constant mean curvature spacelike hypersurface equation, under natural geometric assumptions.
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.
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.
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.
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.
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.
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.
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 ...
Compaction Behavior of Isomalt after Roll Compaction
2012-01-01
The suitability of the new isomalt grade galenIQ™ 801 for dry granulation and following tableting is evaluated in this study. Isomalt alone, as well as a blend of equal parts with dibasic calcium phosphate, is roll compacted and tableted. Particle size distribution and flowability of the granules and friability and disintegration time of the tablets are determined. Tensile strength of tablets is related to the specific compaction force during roll compaction and the tableting force....
Shapiro, Johanna
2016-09-01
This article explores how medical anthropologist Howard Stein's poetry and his unique practice of sharing this poetry with the patients, physicians, and administrators who inspired it create ways of knowing that are at once revelatory and emancipatory. Stein's writing shows readers that poetry can be considered as a form of data and as a method of investigation into the processes of the human soul. Furthermore, it represents a kind of intervention that invites health professional readers toward connection, bridge building, and solidarity with their patients and with one another. (PsycINFO Database Record
Directory of Open Access Journals (Sweden)
Marita Kampshoff
2009-03-01
Full Text Available Für das besprochene Buch haben einige ehemalige Student/-innen der Herausgeberin, der Professorin für Allgemeine Psychologie und Sozialpsychologie Gisela Steins, ihre Abschlussarbeit zusammengefasst. Die meisten Beiträge befassen sich mit kleineren empirischen Studien zum Thema Schule und Geschlecht. Gisela Steins selbst hat eine längere Einführung und knappe Überleitungen zwischen den Aufsätzen verfasst. Die Artikel der Student/-innen sind teilweise interessant, aber es stellt sich die Frage, für welche Leserschaft dieses Buch gedacht ist.
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.
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...
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.
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...
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...
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.
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....
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.
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...
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.
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 $H_1(M;\\mathbb{Z})$.
Institute of Scientific and Technical Information of China (English)
Muhammet Turkoglu
2016-01-01
This study focused on daily variations and harmful algal bloom features of toxic dinoflagellate Prorocentrum lima (Ehrenberg) F. Stein (P. lima), 1878 in middle summer period (9th July–6th August 2013) in the Dardanelles. Harmful algal bloom of P. lima was recorded for the first time in the Turkish Straits System. Density of P. lima reached to 2.40 × 106 cells/L and exhibited four excessive blooms over 1.0 × 106 cells/L during the study. The contribution of P. lima to both Prorocentrum spp. and dinoflagellates reached to 100%, particularly at the moment of the harmful algal bloom attested by regresion (R≥0.70) and correlation findings (R≥0.80). Nutrient concentrations were lower than previous levels due to excessive blooms. Concentrations of NO-2+NO-3, PO-34 and SiO4 varied between 0.20 and 0.78 µmol/L [(0.44 ± 0.17) µmol/L], 0.08 and 0.18 µmol/L [(0.12 ± 0.03) µmol/L] and 0.25 and 0.65 µmol/L [(0.41 ± 0.09) µmol/L] respectively. During the bloom, nutrient ratios were more different than redfield ratios due to eutrophication (NO-2+NO-3/PO-34=4.04 ± 1.74;SiO4/PO-34=3.79 ± 1.24;SiO4/NO-2+NO-3=1.04 ± 0.36). Chlorophyll a concentration reached to 8.52 µg/L (average:4.82 ± 2.29 mg/L) in the bloom period. Temperature [(24.70 ± 0.44) °C], salinity [(22.9 ± 0.49) ppt], pH (8.23 ± 0.15) and dissolved oxygen levels (7.35 ± 0.60 mg/L) were approximately constant. The compact bloom of P. lima, similar to excessive blooms of other dinoflagellates and diatoms, was associated not only with eutrophication, but also with ocean warming interactions. Results revealed that it will be possible to reach to millions of cell number of P. lima (2.40 × 106 cells/L) in eutrophied waters characterized by high chlorophyll a biomass (8.52 µg/L).
Continuité et nouveauté dans la vie spirituelle: Quand Edith Stein interprète Thérèse d'Avila
Betschart, Christof OCD
2013-01-01
Les écrits thérésiens appellent une relecture pour les actualiser. Edith Stein propose une interprétation de la découverte thérésienne de la présence d'immensité au moment de l'oraison d'union.
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.
Institute of Scientific and Technical Information of China (English)
Ping WANG; Jiong Sheng LI
2005-01-01
Let G be a finite simple graph with adjacency matrix A, and let P(A) be the convex closure of the set of all permutation matrices commuting with A. G is said to be compact if every doubly stochastic matrix which commutes with A is in P(A). In this paper, we characterize 3-regular compact graphs and prove that if G is a connected regular compact graph, G - v is also compact, and give a family of almost regular compact connected graphs.
Directory of Open Access Journals (Sweden)
Nakasho Kazuhisa
2016-09-01
Full Text Available In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness, sequential compactness, and totally boundedness with completeness in metric spaces.
Skomorowski, Wojciech; Pawłowski, Filip; Koch, Christiane P; Moszynski, Robert
2012-05-21
State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A(1)Σ(u)(+), c(3)Π(u), and a(3)Σ(u)(+) manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X(1)Σ(g)(+) to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0(u)(+) state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Knöckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A(1)Σ(u)(+)←X(1)Σ(g (+) transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the (1)S(0) + (3)P(1) dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.
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.
GUTs on Compact Type IIB Orientifolds
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph; /Munich, Max Planck Inst.; Braun, Volker; /Dublin Inst.; Grimm, Thomas W.; /Bonn U.; Weigand, Timo; /SLAC
2008-12-01
We systematically analyze globally consistent SU(5) GUT models on intersecting D7-branes in genuine Calabi-Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realization of SU(5) GUTs with gauge symmetry breaking via U(1)Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P{sub 1,1,1,6,9}[18] and of the Quintic P{sub 1,1,1,1,1}[5], respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of these geometries and present five globally consistent string GUT models in detail, including a 3-generation SU(5) model with no exotics whatsoever. We also realize other phenomenological features such as the 10 10 5{sub H} Yukawa coupling and comment on the possibility of moduli stabilization, where we find an entire new set of so-called swiss-cheese type Calabi-Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi-Yau fourfolds.
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.
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.
Convergence of random zeros on complex manifolds
Institute of Scientific and Technical Information of China (English)
Bernard SHIFFMAN
2008-01-01
We show that the zeros of random sequences of Gaussian systems of polynomials of in-creasing degree almost surely converge to the expected limit distribution under very general hypotheses.In particular,the normalized distribution of zeros of systems of m polynomials of degree N,orthonor-malized on a regular compact set K(∪)Cm,almost surely converge to the equilibrium measure on K as N →∞.
Convergence of random zeros on complex manifolds
Institute of Scientific and Technical Information of China (English)
Bernard; SHIFFMAN
2008-01-01
We show that the zeros of random sequences of Gaussian systems of polynomials of in- creasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular,the normalized distribution of zeros of systems of m polynomials of degree N,orthonor- malized on a regular compact set K(?)C~m,almost surely converge to the equilibrium measure on K as N→∞.
Entropy production of stationary diffusions on non-compact Riemannian manifolds
Institute of Scientific and Technical Information of China (English)
龚光鲁; 钱敏平
1997-01-01
The closed form of the entropy production of stationary diffusion processes with bounded Nelson’s current velocity is given.The limit of the entropy productions of a sequence of reflecting diffusions is also discussed.
Calabi-Yau metrics on compact Kaihler manifolds with some divisors deleted
Institute of Scientific and Technical Information of China (English)
Chengjie YU
2008-01-01
In this article, we provide a systematic method to construct examples of complete Ricci flat metrics on CP2, with three lines in the general position deleted by Hsieh [Proc. AMS, 1995, 123: 1873-1877] and generalize them to higher dimensions. In addition, we further show that the examples of Hsieh are indeed all flat.
The construction of periodic unfolding operators on some compact Riemannian manifolds
DEFF Research Database (Denmark)
Dobberschütz, Sören; Böhm, Michael
2014-01-01
The notion of periodic unfolding has become a standard tool in the theory of periodic homogenization. However, all the results obtained so far are only applicable to the "flat" Euclidean space R n. In this paper, we present a generalization of the method of periodic unfolding applicable to struct...
La Forgia, F.; Magrin, S.; Bertini, I.; Lazzarin, M.; Pajola, M.; Barbieri, C.
2013-09-01
We present a photometric method for the interpretation of the reflectance properties of atmosphereless bodies such as asteroids and comets nuclei. The method is self-consistent, easily reusable for any space mission target and independent of the shape model of the object. We investigated the reflectance dependence on the phase angle, interpreted in terms of the Hapke theory of bidirectional reflectance. We then present a method for the estimate of the grain size of the regolith on the surfaces of the asteroids. We applied the method to the two Main Belt asteroids 2867-Steins and 21- Lutetia observed from the OSIRIS camera onboard Rosetta spacecraft on 5 September 2008 and on 10 July 2010 respectively.
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.
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...
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.
The Green's Functions of the Boundaries at Infinity of the Hyperbolic 3-Manifolds
Heydarpour, Majid
2009-01-01
The work is motivated by a result of Manin, which relates the Arakelov Green function on a compact Riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with Schottky uniformization, having the Riemann surface as conformal boundary at infinity. A natural question is to what extent the result of Manin can be generalized to cases where, instead of dealing with a single Riemann surface, one has several Riemann surfaces whose union is the boundary of a hyperbolic 3-manifold, uniformized no longer by a Schottky group, but by a Fuchsian, quasi-Fuchsian, or more general Kleinian group. We have considered this question in this work and obtained several partial results that contribute towards constructing an analog of Manin's result in this more general context.
The Green’s functions of the boundaries at infinity of the hyperbolic 3-manifolds
Heydarpour, Majid
2012-04-01
The work is motivated by a result of Manin in [1], which relates the Arakelov Green's function on a compact Riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with Schottky uniformization, having the Riemann surface as a conformal boundary at infinity. A natural question is to what extent the result of Manin can be generalized to cases where, instead of dealing with a single Riemann surface, one has several Riemann surfaces whose union is the boundary of a hyperbolic 3-manifold, uniformized no longer by a Schottky group, but by a Fuchsian, quasi-Fuchsian, or more general Kleinian group. We have considered this question in this work and obtained several partial results that contribute towards constructing an analog of Manin's result in this more general context.
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.
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.
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.
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.
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.
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.