Nearly pseudo-Kähler manifolds and related special holonomies
Schäfer, Lars
2017-01-01
Developing and providing an overview of recent results on nearly Kähler geometry on pseudo-Riemannian manifolds, this monograph emphasizes the differences with the classical Riemannian geometry setting. The focal objects of the text are related to special holonomy and Killing spinors and have applications in high energy physics, such as supergravity and string theory. Before starting into the field, a self-contained introduction to the subject is given, aimed at students with a solid background in differential geometry. The book will therefore be accessible to masters and Ph.D. students who are beginning work on nearly Kähler geometry in pseudo-Riemannian signature, and also to non-experts interested in gaining an overview of the subject. Moreover, a number of results and techniques are provided which will be helpful for differential geometers as well as for high energy physicists interested in the mathematical background of the geometric objects they need.
Supersymmetric backgrounds, the Killing superalgebra, and generalised special holonomy
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Coimbra, André [Institut des Hautes Études Scientifiques, Le Bois-Marie,35 route de Chartres, F-91440 Bures-sur-Yvette (France); Strickland-Constable, Charles [Institut des Hautes Études Scientifiques, Le Bois-Marie,35 route de Chartres, F-91440 Bures-sur-Yvette (France); Institut de physique théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers, F-91191 Gif-sur-Yvette (France)
2016-11-10
We prove that, for M theory or type II, generic Minkowski flux backgrounds preserving N supersymmetries in dimensions D≥4 correspond precisely to integrable generalised G{sub N} structures, where G{sub N} is the generalised structure group defined by the Killing spinors. In other words, they are the analogues of special holonomy manifolds in E{sub d(d)}×ℝ{sup +} generalised geometry. In establishing this result, we introduce the Kosmann-Dorfman bracket, a generalisation of Kosmann’s Lie derivative of spinors. This allows us to write down the internal sector of the Killing superalgebra, which takes a rather simple form and whose closure is the key step in proving the main result. In addition, we find that the eleven-dimensional Killing superalgebra of these backgrounds is necessarily the supertranslational part of the N-extended super-Poincaré algebra.
Properties of an affine transport equation and its generalized holonomy
Vines, Justin
2014-01-01
We investigate properties of a transport equation that was recently used to study the observer dependence of angular momentum in general relativity. The associated map between the tangent spaces at two points on a curve is affine, and for this reason, the operation was called "affine transport". The map consists of a homogeneous (linear) part given by the parallel transport map along the curve, plus an inhomogeneous part which is related to the development of a curve in a manifold into an affine tangent space (also described as the rolling of a manifold along a tangent space without slipping or twisting). For closed curves, the affine transport equation defines a "generalized holonomy". We use covariant bitensor calculus to compute the generalized holonomy around geodesic polygon loops, specifically for triangles and "parallelogramoids" with sides formed from geodesic segments. For small loops, we recover the well-known result for the leading-order holonomy of parallel transport ($\\sim$ Riemann $\\times$ area)...
Higher holonomies: comparing two constructions
DEFF Research Database (Denmark)
Schaetz, Florian; Arias Abad, Camilo
2015-01-01
We compare two different constructions of higher-dimensional parallel transport. On the one hand, there is the two-dimensional parallel transport associated with 2-connections on 2-bundles studied by Baez–Schreiber [2], Faria Martins–Picken [11] and Schreiber–Waldorf [12]. On the other hand......, there are the higher holonomies associated with flat superconnections as studied by Igusa [7], Block–Smith [3] and Arias Abad–Schätz [1]. We first explain how by truncating the latter construction one obtains examples of the former. Then we prove that the two-dimensional holonomies provided by the two approaches...
DEFF Research Database (Denmark)
Ravn, Ib
1988-01-01
This article attempts to clarify the meaning of "good" by linking it to a concept of wholeness derived from the process philosophy of David Bohm (1980a). Bohm draws a distinction between implicate order, which is a domain of reality characterized by flux and potentiality, and explicate order, whi...
Holonomy loops, spectral triples and quantum gravity
DEFF Research Database (Denmark)
Johannes, Aastrup; Grimstrup, Jesper Møller; Nest, Ryszard
2009-01-01
We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops...
The Influence of Equine Essentials on Teacher Holonomy
Snyder, Troy Ernest
2009-01-01
Analyzing the effects of the Equine Essentials discipline model by examining measurable differences in teacher holonomy at schools applying the model with varying degrees of intensity was the purpose of this study. The study decomposed the analysis into tests for the presence of each of the five dimensions of holonomy: efficacy, craftsmanship,…
Inflationary power spectra with quantum holonomy corrections
Mielczarek, Jakub
2013-01-01
In this paper we study slow-roll inflation with holonomy corrections from loop quantum cosmology. Both tensor and scalar power spectra of primordial perturbations are computed up to the first order in slow-roll parameters and $V/\\rho_{c}$, where $V$ is a potential of the scalar field and $\\rho_{c}$ is a critical energy density (expected to be of the order of the Planck energy density). Possible normalizations of modes at short scales are discussed. In case the normalization is performed with use of the Wronskian condition applied to adiabatic vacuum, the tensor and scalar spectral indices are not quantum corrected in the leading order. However, by choosing an alternative method of normalization one can obtain quantum corrections in the leading order. Furthermore, we show that the holonomy-corrected equation of motion for tensor modes can be derived from an effective background metric. This allows us to prove that the Wronskian normalization condition for the tensor modes preserves the classical form.
Nonlocal neurology: beyond localization to holonomy.
Globus, G G; O'Carroll, C P
2010-11-01
The concept of local pathology has long served neurology admirably. Relevant models include self-organizing nonlinear brain dynamics, global workspace and dynamic core theories. However such models are inconsistent with certain clinical phenomena found in Charles Bonnet syndrome, disjunctive agnosia and schizophrenia, where there is disunity of content within the unity of consciousness. This is contrasted with the split-brain case where there is disunity of content and disunity of consciousnesses. The development of quantum brain theory with it nonlocal mechanisms under the law of the whole ("holonomy") offers new possibilities for explaining disintegration within unity. Dissipative quantum brain dynamics and its approach to the binding problem, memory and consciousness are presented. A nonlocal neurology armed with a holonomic understanding might see more deeply into what clinical neurology has always aspired to: the patient as a whole. Copyright © 2010 Elsevier Ltd. All rights reserved.
An improved cosmic crystallography method to detect holonomies in flat spaces
Fujii, H.; Yoshii, Y.
2011-05-01
A new, improved version of a cosmic crystallography method for constraining cosmic topology is introduced. Like the circles-in-the-sky method using CMB data, we work in a thin, shell-like region containing plenty of objects. Two pairs of objects (quadruplet) linked by a holonomy show a specific distribution pattern, and three filters of separation, vectorial condition, and lifetime of objects extract these quadruplets. Each object Pi is assigned an integer si, which is the number of candidate quadruplets including Pi as their members. Then an additional device of si-histogram is used to extract topological ghosts, which tend to have high values of si. In this paper we consider flat spaces with Euclidean geometry, and the filters are designed to constrain their holonomies. As the second filter, we prepared five types that are specialized for constraining specific holonomies: one for translation, one for half-turn corkscrew motion and glide reflection, and three for nth turn corkscrew motion for n = 4,3, and 6. Every multiconnected space has holonomies that are detected by at least one of these five filters.Our method is applied to the catalogs of toy quasars in flat Λ-CDM universes whose typical sizes correspond to z ~ 5. With these simulations our method is found to work quite well. These are the situations in which type-II pair crystallography methods are insensitive because of the tiny number of ghosts. Moreover, in the flat cases, our method should be more sensitive than the type-I pair (or, in general, n-tuplet) methods because of its multifilter construction and its independence from n.
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Bishop, Richard L
2001-01-01
First published in 1964, this book served as a text on differential geometry to several generations of graduate students all over the world. The first half of the book (Chapters 1-6) presents basics of the theory of manifolds, vector bundles, differential forms, and Lie groups, with a special emphasis on the theory of linear and affine connections. The second half of the book (Chapters 7-11) is devoted to Riemannian geometry. Following the definition and main properties of Riemannian manifolds, the authors discuss the theory of geodesics, complete Riemannian manifolds, and curvature. Next, the
Sinha, Rajnikant
2014-01-01
This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book ...
Hempel, John
2004-01-01
A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. -Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The t
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
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.
Morrow, James
2006-01-01
This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965-66, is an excellent, well-written introduction to the study of abstract complex (analytic) manifolds-a subject that began in the late 1940's and early 1950's. It is largely self-contained, except for some standard results about elliptic partial differential equations, for which complete references are given. -D. C. Spencer, MathSciNet The book under review is the faithful reprint of the original edition of one of the most influential textbooks in modern complex analysis and geometry. The classic
Seven-Disk Manifold, alpha-attractors and B-modes
Ferrara, Sergio
2016-01-01
Cosmological alpha-attractor models in \\cN=1 supergravity are based on hyperbolic geometry of a Poincar\\'e disk with the radius square {\\cal R}^2=3\\alpha. The predictions for the B-modes, r\\approx 3\\alpha {4\\over N^2}, depend on moduli space geometry and are robust for a rather general class of potentials. Here we notice that starting with M-theory compactified on a 7-manifold with G_2 holonomy, with a special choice of Betti numbers, one can obtain d=4 \\cN=1 supergravity with rank 7 scalar coset \\Big[{SL(2)\\over SO(2)}\\Big]^7. In a model where these 7 unit size Poincar\\'e disks have identified moduli one finds that 3 alpha =7. Assuming that the moduli space geometry of the phenomenological models is inherited from this version of M-theory, one would predict r \\approx 10^{-2} for 53 e-foldings. We also describe the related maximal supergravity and M/string theory models leading to preferred values 3 alpha =1,2,3,4,5,6,7.
Introduction to differentiable manifolds
Auslander, Louis
2009-01-01
The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary diff
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
Universal Calabi-Yau Algebra Towards an Unification of Geometry with SU(n) Holonomy
Anselmo, F; Volkov, G
2002-01-01
We discuss some results in Calabi-Yau universal-gebra suitable for constructing and classifying the infinite series of the compact complex spaces with $SU(n)$ holonomy. This universal-gebraic approach includes natural extensions of reflexive weight vectors to higher dimensions. It includes a `dual' construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of Calabi-Yau spaces in arbitrary dimensions.
Nonlinear analysis on manifolds
Hebey, Emmanuel
2000-01-01
This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. "Several surprising phenomena appear when studying Sobolev spaces on manifolds," according to the author. "Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role." The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces fo
Wang, McKenzie
1999-01-01
This is the sixth volume in a series providing surveys of differential geometry. It addresses: Einstein manifolds with zero Ricci curvature; rigidity and compactness of Einstein metrics; general relativity; the stability of Minkowski space-time; and more.
Fintushel, R; Fintushel, Ronald; Stern, Ronald J.
1997-01-01
In this paper we introduce a technique, called rim surgery, which can change a smooth embedding of an orientable surface of positive genus and nonnegative self-intersection in a smooth 4-manifold while leaving the topological embedding unchanged.
Locally conformal symplectic manifolds
Directory of Open Access Journals (Sweden)
Izu Vaisman
1985-01-01
Full Text Available A locally conformal symplectic (l. c. s. manifold is a pair (M2n,Ω where M2n(n>1 is a connected differentiable manifold, and Ω a nondegenerate 2-form on M such that M=⋃αUα (Uα- open subsets. Ω/Uα=eσαΩα, σα:Uα→ℝ, dΩα=0. Equivalently, dΩ=ω∧Ω for some closed 1-form ω. L. c. s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetic canonical transformations. The paper discusses first Hamiltonian vector fields, and infinitesimal automorphisms (i. a. on l. c. s. manifolds. If (M,Ω has an i. a. X such that ω(X≠0, we say that M is of the first kind and Ω assumes the particular form Ω=dθ−ω∧θ. Such an M is a 2-contact manifold with the structure forms (ω,θ, and it has a vertical 2-dimensional foliation V. If V is regular, we can give a fibration theorem which shows that M is a T2-principal bundle over a symplectic manifold. Particularly, V is regular for some homogeneous l. c. s, manifolds, and this leads to a general construction of compact homogeneous l. c. s, manifolds. Various related geometric results, including reductivity theorems for Lie algebras of i. a. are also given. Most of the proofs are adaptations of corresponding proofs in symplectic and contact geometry. The paper ends with an Appendix which states an analogous fibration theorem in Riemannian geometry.
The spectral length of a map between Riemannian manifolds
Cornelissen, G.L.M.; de Jong, J.W.W.
2012-01-01
To a closed Riemannian manifold, we associate a set of (special values of) a family of Dirichlet series, indexed by functions on the manifold. We study the meaning of equality of two such families of spectral Dirichlet series under pullback along a map. This allows us to give a spectral
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.
Adams, Scot
2001-01-01
Within the general framework of the dynamics of "large" groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of the
Djordjevic, A.
1982-07-08
A tool guide that makes possible the insertion of cleaning and/or inspection tools into a manifold pipe that will dislocate and extract the accumulated sediment in such manifold pipes. The tool guide basically comprises a right angled tube (or other angled tube as required) which can be inserted in a large tube and locked into a radially extending cross pipe by adjustable spacer rods and a spring-loaded cone, whereby appropriate cleaning tools can be inserted into to cross pipe for cleaning, inspection, etc.
Maps between Grassmann manifolds
Indian Academy of Sciences (India)
Parameswaran Sankaran Institute of Mathematical Sciences Chennai, India sankaran@imsc.res.in Indian Academy of Sciences Platinum Jubilee Meeting Hyderabad
Maps between Grassmann manifolds. Parameswaran Sankaran. Institute of Mathematical Sciences. Chennai, India sankaran@imsc.res.in. Indian Academy of Sciences. Platinum Jubilee Meeting. Hyderabad. 2nd July, 2009. Parameswaran Sankaran Institute of Mathematical Sciences Chennai, India sankaran@imsc.res.in.
Cohen, R L
1982-05-01
This paper outlines a proof of the conjecture that every compact, differentiable, n-dimensional manifold immerses in Euclidean space of dimension 2n - alpha(n), where alpha(n) is the number of ones in the dyadic expansion of n.
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.
Two Categories of Dirac Manifolds
Milburn, Brett
2007-01-01
We define two categories of Dirac manifolds, i.e. manifolds with complex Dirac structures. The first notion of maps I call \\emph{Dirac maps}, and the category of Dirac manifolds is seen to contain the categories of Poisson and complex manifolds as full subcategories. The second notion, \\emph{dual-Dirac maps}, defines a \\emph{dual-Dirac category} which contains presymplectic and complex manifolds as full subcategories. The dual-Dirac maps are stable under B-transformations. In particular we ge...
Quantum computation in noiseless subsystems with fast non-Abelian holonomies
Zhang, J.; Kwek, L.-C.; Sjöqvist, Erik; Tong, D. M.; Zanardi, P.
2014-04-01
Quantum-information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control of the way quantum dynamics unfolds in the information-processing system. In this paper we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on nonadiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.
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
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.
Smooth maps of a foliated manifold in a symplectic manifold
Indian Academy of Sciences (India)
Let be a smooth manifold with a regular foliation F and a 2-form which induces closed forms on the leaves of F in the leaf topology. A smooth map f : ( M , F ) ⟶ ( 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 ...
Cobordism independence of Grassmann manifolds
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Introduction. This paper is a continuation of the ongoing study of cobordism of Grassmann manifolds. Let. F denote one of the division rings R of reals, C of complex numbers, or H of quaternions. Let t = dimRF. Then the Grassmannian manifold Gk(Fn+k) is defined to be the set of all k-dimensional (left) subspaces of Fn+k.
Manifold statistics for essential matrices
Dubbelman, G.; Dorst, L.; Pijls, H.
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
Diffeomorphisms of elliptic 3-manifolds
Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam
2012-01-01
This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...
Continuous Optimization on Constraint Manifolds
Dean, Edwin B.
1988-01-01
This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.
Fintushel, R; Fintushel, Ronald; Stern, Ronald J.
1996-01-01
In this paper we investigate the relationship between isotopy classes of knots and links in S^3 and the diffeomorphism types of homeomorphic smooth 4-manifolds. As a corollary of this initial investigation, we begin to uncover the surprisingly rich structure of diffeomorphism types of manifolds homeomorphic to the K3 surface.
Smooth maps of a foliated manifold in a symplectic manifold
Indian Academy of Sciences (India)
Abstract. Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f : (M, F) −→ (N,σ) in a symplectic manifold (N,σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the.
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...
On invariant submanifolds of (LCSn-manifolds
Directory of Open Access Journals (Sweden)
Absos Ali Shaikh
2016-04-01
Full Text Available The object of the present paper is to study the invariant submanifolds of (LCSn-manifolds. We study semiparallel and 2-semiparallel invariant submanifolds of (LCSn-manifolds. Among others we study 3-dimensional invariant submanifolds of (LCSn-manifolds. It is shown that every 3-dimensional invariant submanifold of a (LCSn-manifold is totally geodesic.
A versatile algorithm for computing invariant manifolds
Broer, H. W.; Hagen, A.; Vegter, G.; Gorban, AN; Kazantzis, NK; Kevrekidis, IG; Ottinger, HC; Theodoropoulos, C
2006-01-01
This paper deals with the numerical computation of invariant manifolds using a method of discretizing global manifolds. It provides a geometrically natural algorithm that converges regardless of the restricted dynamics. Common examples of such manifolds include limit sets, co-dimension 1 manifolds
Flow and Pressure Distribution in Fuel Cell Manifolds
DEFF Research Database (Denmark)
Lebæk, Jesper; Bang, Mads; Kær, Søren Knudsen
2010-01-01
differential pressure gauges, the flow distribution is mapped for several geometrical and operating conditions. Special attention is given to the inlet conditions of the manifold. Here, a diffuser design was constructed in order to replace the conventional circular inlet design. The diffuser design showed...
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
On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds
Ferrara, Sergio
2007-01-01
We study the ``flat'' directions of non-BPS extremal black hole attractors for N=2, d=4 supergravities whose vector multiplets' scalar manifold is endowed with homogeneous symmetric special Kahler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d=5 parent theory), whereas the moduli spaces of non-BPS attractors with vanishing central charge are certain Kahler homogeneous symmetric manifolds. The moduli spaces of the non-BPS attractors of the corresponding N=2, d=5 theories are also indicated, and shown to be rank-1 homogeneous symmetric manifolds.
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
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...
Hypersurfaces in nearly Kaehler manifold
Indian Academy of Sciences (India)
Biaogui Yang
2017-08-08
Aug 8, 2017 ... Nearly Kaehler manifold; contact hypersurface; contact metric structure; minimal hypersurface; shape operator; conformal vector field. 2010 Mathematics Subject Classification. 53C40; 53C15; 53C25; 53D15. 1. Introduction. It is known that the six-dimensional unit sphere S6 has a nearly Kaehler structure (J ...
Cobordism independence of Grassmann manifolds
Indian Academy of Sciences (India)
This note proves that, for F = R , C or 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 N d regarded as a Z 2 -vector space.
On complexifications of real manifolds.
Kulkarni, R S
1975-11-01
This paper studies the problem of obtaining complexifications of a differentiable manifold which have desirable analytic or algebraic properties and which are minimal in the sense described below. It is seen that there is a significant difference between analytic and algebraic complexifications.
De Rham cohomology and homotopy Frobenius manifolds
Dotsenko, V.; Shadrin, S.; Vallette, B.
2015-01-01
We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.
Riemannian geometry of contact and symplectic manifolds
Blair, David E
2002-01-01
This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter The text is carefully presented Topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds Principal circle bundles (Chapter 2) are then discussed as a prelude to the Boothby--Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds Chapter 4 focuses on the general setting of Riemannian metrics associated with both symplectic and contact structures, and Chapter 5 is devoted to integral submanifolds of the contact subbundle Topics treated in the subsequent chapters include Sasakian manifolds, the important study of the curvature of contact metric manifolds, submanifold theory in both the K"hler and Sasakian settings, tangent sphere bundles, curvature functionals, complex contact manifolds and 3-Sasakian manifolds The book serves both as a general reference for mathematicia...
Invariant manifolds near hyperbolic fixed points
Homburg, A.J.
2006-01-01
Abstract: In these notes, we discuss obstructions to the existence of local invariant manifolds of some smoothness class, near hyperbolic fixed points of diffeomorphisms. We present an elementary construction for continuously differentiable invariant manifolds that are not necessarily normally
Fluid delivery manifolds and microfluidic systems
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.
Numerical Approximation of Normally Hyperbolic Invariant Manifolds
Broer, Henk; Hagen, Aaron; Vegter, Gert
2003-01-01
This paper deals with the numerical continuation of invariant manifolds, regardless of the restricted dynamics. Typically, invariant manifolds make up the skeleton of the dynamics of phase space. Examples include limit sets, co-dimension 1 manifolds separating basins of attraction (separatrices),
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....
Minimal Webs in Riemannian Manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
For a given combinatorial graph $G$ a {\\it geometrization} $(G, g)$ of the graph is obtained by considering each edge of the graph as a $1-$dimensional manifold with an associated metric $g$. In this paper we are concerned with {\\it minimal isometric immersions} of geometrized graphs $(G, g......)$ 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...... 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...
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.
Effective forcing with Cantor manifolds
Kihara, Takayuki
2017-01-01
A set $A$ of integers is called total if there is an algorithm which, given an enumeration of $A$, enumerates the complement of $A$, and called cototal if there is an algorithm which, given an enumeration of the complement of $A$, enumerates $A$. Many variants of totality and cototality have been studied in computability theory. In this note, by an effective forcing construction with strongly infinite dimensional Cantor manifolds, which can be viewed as an effectivization of Zapletal's "half-...
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.
Differential geometry curves, surfaces, manifolds
Kühnel, Wolfgang
2015-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and-as a new feature-a good number of so
Perelman's collapsing theorem for 3-manifolds
Cao, Jianguo; Ge, Jian
2009-01-01
We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theo...
Minimal genera of open 4-manifolds
Gompf, Robert E.
2013-01-01
We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with much more control of these genus functions than the compact setting seems to allow. As an application, we expand the range of 4-manifolds known to have exotic smoothings (up to ...
On the manifold-mapping optimization technique
D. Echeverria (David); P.W. Hemker (Piet)
2006-01-01
textabstractIn 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
Harmonic manifolds with minimal horospheres are flat
Indian Academy of Sciences (India)
MS received 28 May 2013; revised 12 November 2013 ... The known examples of harmonic manifolds include flat ... periodic functions. Finally, using the characteristic property of an almost periodic function we prove that M is Ricci flat. In view of this, it is natural to ask: Can one affirm that harmonic manifolds with mini-.
Classical BV theories on manifolds with boundary
Cattaneo, A.S.; Mnev, P.; Reshetikhin, N.
2014-01-01
In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with
Classification of framed links in 3-manifolds
Indian Academy of Sciences (India)
manifolds, Preprint Series Univ. of Ljubljana 41 (2003) 906. [CRS2] Cencelj M, Repovš D and Skopenkov M, Classification of framed links in 3- manifolds, preprint, arXiv:math-gt/0705.4166v1. [Du] Dufraine E, Classes d'homotopie de champs de vecteurs Morse-Smale sans singular- ite sur les fibres de Seifert, Enseign.
Indian Academy of Sciences (India)
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. Author Affiliations. M Iscan1 A A Salimov1. Faculty of Arts and Science, Department of ...
Metric Ricci Curvature for PL Manifolds
Directory of Open Access Journals (Sweden)
David Xianfeng Gu
2013-01-01
Full Text Available We introduce a metric notion of Ricci curvature for PL manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers theorem, for surfaces as well as for a large class of higher dimensional manifolds.
Indian Academy of Sciences (India)
E-mail: miscan@atauni.edu.tr; asalimov@atauni.edu.tr. MS received 7 September 2007; revised 4 October 2007. Abstract. 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 ...
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.
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...
Static traversable wormholes in Lyra manifold
Jahromi, A. Sayahian; Moradpour, H.
At first, considering the Einstein framework, we introduce some new static traversable wormholes and study the effects of a dark energy-like source on them. Thereinafter, a brief review on Einstein field equations in Lyra manifold is presented, and we address some static traversable wormholes in the Lyra manifold which satisfy the energy conditions. It is also shown that solutions introduced in the Einstein framework may also meet the energy conditions in the Lyra manifold. Finally, we focus on vacuum Lyra manifold and find some traversable asymptotically flat wormholes. In summary, our study shows that it is theoretically possible to find a Lyra displacement vector field in a manner in which traversable wormholes satisfy the energy conditions in a Lyra manifold.
CERN Library
2014-01-01
Tuesday 25 March 2014 at 4 p.m. in the Library, bldg. 52-1-052 "Differential manifolds: a basic approach for experimental physicists" by Paul Baillon, World Scientific, 2013, ISBN 978-981-4449-56-4. Differential manifold is the framework of particle physics and astrophysics nowadays. It is important for all research physicists to be accustomed to it, and even experimental physicists should be able to manipulate equations and expressions in this framework. This book gives a comprehensive description of the basics of differential manifold with a full proof of elements. A large part of the book is devoted to the basic mathematical concepts, which are all necessary for the development of the differential manifold. This book is self-consistent; it starts from first principles. The mathematical framework is the set theory with its axioms and its formal logic. No special knowledge is needed. Coffee will be served from 3.30 p.m.
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.
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.
Neural Manifolds for the Control of Movement.
Gallego, Juan A; Perich, Matthew G; Miller, Lee E; Solla, Sara A
2017-06-07
The analysis of neural dynamics in several brain cortices has consistently uncovered low-dimensional manifolds that capture a significant fraction of neural variability. These neural manifolds are spanned by specific patterns of correlated neural activity, the "neural modes." We discuss a model for neural control of movement in which the time-dependent activation of these neural modes is the generator of motor behavior. This manifold-based view of motor cortex may lead to a better understanding of how the brain controls movement. Copyright © 2017 Elsevier Inc. 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.
Polynomial chaos representation of databases on manifolds
Soize, C.; Ghanem, R.
2017-04-01
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.
Averaging of Legendrian submanifolds of contact manifolds
Zambon, Marco
2004-01-01
We give a procedure to ``average'' canonically $C^1$-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves a Legendrian submanifold almost invariant, there is an invariant Legendrian submanifold nearby.
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.
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.
Hessian equations on closed Hermitian manifolds
Zhang, Dekai
2015-01-01
In this paper, using the technical tools in \\cite{TW5}, we solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the the K\\"ahler case results in \\cite{HMW} and \\cite{DK}.
megaman: Manifold Learning for Millions of Points
McQueen, James; Meila, Marina; VanderPlas, Jacob; Zhang, Zhongyue
2017-11-01
megaman is a scalable manifold learning package implemented in python. It has a front-end API designed to be familiar to scikit-learn but harnesses the C++ Fast Library for Approximate Nearest Neighbors (FLANN) and the Sparse Symmetric Positive Definite (SSPD) solver Locally Optimal Block Precodition Gradient (LOBPCG) method to scale manifold learning algorithms to large data sets. It is designed for researchers and as such caches intermediary steps and indices to allow for fast re-computation with new parameters.
Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry
Energy Technology Data Exchange (ETDEWEB)
Pan, Yiwen [C.N. Yang Institute for Theoretical Physics,Stony Brook, NY, 11790 (United States)
2014-05-12
In this note we generalize the methods of http://dx.doi.org/10.1007/JHEP08(2012)141, http://dx.doi.org/10.1007/JHEP01(2013)072 and http://dx.doi.org/10.1007/JHEP05(2013)017 to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity. The existence of 1 pair of solutions is related to almost contact metric structures. We also discuss special cases related to M=S{sup 1}×M{sub 4}, which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kähler. When there are 2 pairs of solutions, the closure of the isometry sub-algebra generated by the solutions requires M to be S{sup 3} or T{sup 3}-fibration over a Riemann surface. 4 pairs of solutions pin down the geometry of M to very few possibilities. Finally, we propose a new supersymmetric theory for N=1 vector multiplet on K-contact manifold admitting solutions to the Killing spinor equation.
Exponential estimates of symplectic slow manifolds
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Wulff, C.
2016-01-01
In this paper we prove the existence of an almost invariant symplectic slow manifold for analytic Hamiltonian slow-fast systems with finitely many slow degrees of freedom for which the error field is exponentially small. We allow for infinitely many fast degrees of freedom. The method we use...... 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...... on an invariant slow manifold to (finitely) many fast degrees of freedom....
Affine Flag Manifolds and Principal Bundles
Schmitt, Alexander HW
2010-01-01
Affine flag manifolds are infinite dimensional versions of familiar objects such as Gramann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel
Periodic orbits near a bifurcating slow manifold
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2015-01-01
(\\epsilon^{1/3})$-distance from the union of the normally elliptic slow manifolds that occur as a result of the bifurcation. Here $\\epsilon\\ll 1$ measures the time scale separation. These periodic orbits are predominantly unstable. The proof is based on averaging of two blowup systems, allowing one to estimate...... the effect of the singularity, combined with results on asymptotics of the second Painleve equation. The stable orbits of smallest amplitude that are {persistently} obtained by these methods remain slightly further away from the slow manifold being distant by an order $\\mathcal O(\\epsilon^{1/3}\\ln^{1/2}\\ln...
Projections and residues on manifolds with boundary
DEFF Research Database (Denmark)
Gaarde, Anders Borg
2008-01-01
It is a well-known result that the noncommutative residue of a pseudodifferential projection is zero on a compact manifold without boundary. Equivalently, the value of the zeta-function of P at zero, ¿¿(P, 0), is independent of ¿ for any elliptic operator P. Here ¿ denotes the angle of a ray where...... the resolvent of P has minimal growth. In this thesis, we consider the analogous questions on a compact manifold with boundary. We show that the noncommutative residue is zero for any projection in Boutet de Monvel’s calculus of pseudodifferential boundary problems. For an elliptic boundary problem {P+ + G, T...
Supersymmetry, Duality And Holonomy
Wen, W
2005-01-01
In this thesis, I study various aspects of solutions to eleven-dimensional supergravity and its descendents. The former is at one corner of the moduli space of M-theory. While it is not clear how to formulate M-theory; it is equally interesting to see how far we can proceed from this low energy window. First of all, various techniques are applied to construct supergravity solutions preserving partial supersymmetry. A seven-dimensional membrane solution in the gauged supergravity is constructed by lifting a self-dual string in six dimensions, and its supersymmetric property is explored in certain detail. Then fractional BPS solutions from Sn × Sn reduction of six and ten-dimensional supergravities are constructed via the method of G-structures. The form of the solutions is totally determined by Laplace equations with specified boundary conditions. Secondly, the concept of duality is realized in two aspects. A certain type of *-theory, obtained from time-like T-dualization of the usual string and M-t...
Foliations and the geometry of 3-manifolds
Calegari, Danny
2014-01-01
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
Study of Multi-Cylinder Engine Manifolds
1944-10-31
volumetria ef. ficiency. .4- PART 1. I.TI 1. !i.: s This part of the report has two purposes; the first purpose is to give a thorcuah discussion of... volumetria efficiencies to be obtained at high speeds. In order to study the effects of vibrations it was neo- essary to deain nany of the manifolds to give
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
... Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 126; Issue 4. Strictly convex functions on complete Finsler manifolds. YOE ITOKAWA KATSUHIRO SHIOHAMA BANKTESHWAR TIWARI. Research Article Volume 126 Issue 4 October 2016 pp 623-627 ...
Multiparametric tissue abnormality characterization using manifold regularization
Batmanghelich, Kayhan; Wu, Xiaoying; Zacharaki, Evangelia; Markowitz, Clyde E.; Davatzikos, Christos; Verma, Ragini
2008-03-01
Tissue abnormality characterization is a generalized segmentation problem which aims at determining a continuous score that can be assigned to the tissue which characterizes the extent of tissue deterioration, with completely healthy tissue being one end of the spectrum and fully abnormal tissue such as lesions, being on the other end. Our method is based on the assumptions that there is some tissue that is neither fully healthy or nor completely abnormal but lies in between the two in terms of abnormality; and that the voxel-wise score of tissue abnormality lies on a spatially and temporally smooth manifold of abnormality. Unlike in a pure classification problem which associates an independent label with each voxel without considering correlation with neighbors, or an absolute clustering problem which does not consider a priori knowledge of tissue type, we assume that diseased and healthy tissue lie on a manifold that encompasses the healthy tissue and diseased tissue, stretching from one to the other. We propose a semi-supervised method for determining such as abnormality manifold, using multi-parametric features incorporated into a support vector machine framework in combination with manifold regularization. We apply the framework towards the characterization of tissue abnormality to brains of multiple sclerosis patients.
Nonsmoothable involutions on spin 4-manifolds
Indian Academy of Sciences (India)
Nonsmoothable involutions on spin 4-manifolds. CHANGTAO XUE and XIMIN LIU. ∗. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, .... For our application, we also need their equivariant handle construction. Let B0 be a unit ball in C2, on which Z2 acts by multiplication of ±1. Take a Z2-.
Algorithms for computing normally hyperbolic invariant manifolds
Broer, H.W.; Osinga, H.M.; Vegter, G.
An effcient algorithm is developed for the numerical computation of normally hyperbolic invariant manifolds, based on the graph transform and Newton's method. It fits in the perturbation theory of discrete dynamical systems and therefore allows application to the setting of continuation. A
Compact integral manifolds of differential systems
Gorbuzov, V. N.
2010-01-01
The boundedness tests for the number of compact integral manifolds of autonomous ordinary differential systems, of autonomous total differential systems, of linear systems of partial differential equations, of Pfaff systems of equations, and of systems of exterior differential equations are proved.
Erratum On Kahler-Norden manifolds
Indian Academy of Sciences (India)
Erratum. (Proc. Indian Acad. Sci. (Math. Sci.), Vol. 119, No. 1, February 2009, pp. 71–80). On Kahler-Norden manifolds. M ISCAN and A A SALIMOV. Corollary 1 is not correct, we claim that the integrability of the structure ϕ is equivalent to the condition φϕg = 0 which is not true. This condition only implies integrability and.
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...
The structure of some classes of K-contact manifolds
Indian Academy of Sciences (India)
Abstract. We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi ...
Manifold Microchannel Heat Sink Design Using Optimization Under Uncertainty
Sarangi, S; Bodla, K. K.; Garimella, Suresh V; Murthy, J. Y.
2014-01-01
A three-dimensional numerical model is developed and validated to study the effect of geometric parameters such as microchannel depth and width, manifold depth, and manifold inlet and outlet lengths on the performance of a manifold microchannel (MMC) heat sink. The manifold arrangement used to distribute the flow through alternating inlet and outlet pairs greatly reduces the pressure drop incurred in conventional fluid supply arrangements due to its shorter flow paths, while simultaneously en...
Active contours on statistical manifolds and texture segmentaiton
Sang-Mook Lee; A. Lynn Abbott; Neil A. Clark; Philip A. Araman
2005-01-01
A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2- dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto-a set of probability density functions. In this novel framework, color or texture features are measured at each Image point and their statistical...
Active contours on statistical manifolds and texture segmentation
Sang-Mook Lee; A. Lynn Abbott; Neil A. Clark; Philip A. Araman
2005-01-01
A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2- dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto a set of probability density functions. In this novel framework, color or texture features are measured at each image point and their statistical...
Wave equations on anti self dual (ASD) manifolds
Bashingwa, Jean-Juste; Kara, A. H.
2017-11-01
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.
Examples and counter-examples of log-symplectic manifolds
Cavalcanti, Gil R.
We study topological properties of log-symplectic structures and produce examples of compact manifolds with such structures. Notably, we show that several symplectic manifolds do not admit bona fide log-symplectic structures and several bona fide log-symplectic manifolds do not admit symplectic
Gauge theory of gravity and supergravity on a group manifold
Energy Technology Data Exchange (ETDEWEB)
Ne' eman, Y.; Regge, T.
1977-12-01
The natural arena for the physics of gravity, supergravity and their enlargements appears to be the group manifold of the Poincare group P, the graded Poincare group GP of supersymmetry, and the corresponding enlargements. The dynamics of these theories correspond to geometrical algorithms in P and GP. Differential geometry on Lie groups is reviewed and results applied to P and GP. Curvature, gauge transformations and factorization are introduced. Also reviewed is the general coordinate transformation group and a hybrid gauge transformation, the anholonomized G.C.T. gauge. A study is made of the construction of an action, including the introduction of a set of special 2 forms, the ''pseudo curvatures.'' The possibilities of factorization in supersymmetry are analyzed. The version of supergravity is present which has now become a completely geometrical theory.
Balanced metrics for vector bundles and polarised manifolds
DEFF Research Database (Denmark)
Garcia Fernandez, Mario; Ross, Julius
2012-01-01
We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter α, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of α, we prove that the limit of a convergent sequence of balanced metrics...... leads to a Hermitian-Einstein metric on E and a constant scalar curvature Kähler metric in c_1(L). For special values of α, limits of balanced metrics are solutions of a system of coupled equations relating a Hermitian-Einstein metric on E and a Kähler metric in c1(L). For this, we compute the top two...
Moves for standard skeleta of 3-manifolds with marked boundary
Amendola, Gennaro
2008-01-01
We prove that the classical set of moves for standard spines of 3-manifolds (i.e. the MP-move and the V-move) does not suffice to relate to each other any two standard skeleta of a 3-manifold with marked boundary. We also describe a condition on the 3-manifold with marked boundary that tells whether the generalised set of moves, made up of the MP-move and the L-move, suffices to relate to each other any two standard skeleta of the 3-manifold with marked boundary. For the 3-manifolds with mark...
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.
Lattes-type mappings on compact manifolds
Astola, Laura; Kangaslampi, Riikka; Peltonen, Kirsi
A uniformly quasiregular mapping acting on a compact Riemannian manifold distorts the metric by a bounded amount, independently of the number of iterates. Such maps are rational with respect to some measurable conformal structure and there is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We study a rich subclass of uniformly quasiregular mappings that can be produced using an analogy of classical Lattes' construction of chaotic rational functions acting on the extended plane bar{C} . We show that there is a plenitude of compact manifolds that support these mappings. Moreover, we find that in some cases there are alternative ways to construct this type of mapping with different Julia sets.
Saliency detection based on manifold learning
Yang, Zhi; Li, DeHua; Wang, Jie; Li, Xuan
2013-10-01
Visual saliency has recently attracted lots of research interest in the computer vision community. In this paper, we propose a novel computational model for bottom-up saliency detection based on manifold learning. A typical graphbased manifold learning algorithm, namely the diffusion map, is adopted for establishing our saliency model. In the proposed method, firstly, a graph is constructed using low-level image features. Then, the diffusion map algorithm is performed to learn the diffusion distances, which are utilized to derive the saliency measure. Compared to existing saliency models, our method has the advantage of being able to capture the intrinsic nonlinear structures in the original feature space. Moreover, due to the inherent characteristics of the diffusion map algorithm, our method can deal with the multi-scale issue effectively, which is crucial to any saliency model. Experimental results on publicly available data demonstrate that our method outperforms the state-of-the-art saliency models, both qualitatively and quantitatively.
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.
Positively invariant manifolds: concept and applications
Sazhin, Sergei S.; Shchepakina, Elena; Sobolev, Vladimir
2017-02-01
In many applications of the system order reduction models, including those focused on spray ignition and combustion processes, it is assumed that all functions in corresponding differential equations are Lipschitzian. This assumption has not been checked in most cases and the cases when these functions were non-Lipschitzian have sometimes been overlooked. This allows us to question the results of application of the conventional theory of integral manifolds to some such systems. The aim of this paper is to demonstrate that even in the case of singular perturbed systems with non-Lipschitzian nonlinearities the order reduction can be performed, using a new concept of positively invariant manifolds. This is illustrated by several examples including the problem of heating, evaporation, ignition and combustion of Diesel fuel sprays.
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...
Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels.
Jayasumana, Sadeep; Hartley, Richard; Salzmann, Mathieu; Li, Hongdong; Harandi, Mehrtash
2015-12-01
In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, usual Euclidean computer vision and machine learning algorithms yield inferior results on such data. In this paper, we define Gaussian radial basis function (RBF)-based positive definite kernels on manifolds that permit us to embed a given manifold with a corresponding metric in a high dimensional reproducing kernel Hilbert space. These kernels make it possible to utilize algorithms developed for linear spaces on nonlinear manifold-valued data. Since the Gaussian RBF defined with any given metric is not always positive definite, we present a unified framework for analyzing the positive definiteness of the Gaussian RBF on a generic metric space. We then use the proposed framework to identify positive definite kernels on two specific manifolds commonly encountered in computer vision: the Riemannian manifold of symmetric positive definite matrices and the Grassmann manifold, i.e., the Riemannian manifold of linear subspaces of a Euclidean space. We show that many popular algorithms designed for Euclidean spaces, such as support vector machines, discriminant analysis and principal component analysis can be generalized to Riemannian manifolds with the help of such positive definite Gaussian kernels.
Fuel Manifold Resists Embrittlement by Hydrogen
Adams, T.
1986-01-01
Completely-cast hydrogen-compatible alloy preferable to protective plating. Complexity of plating, welding, and brazing unnecessary if hydrogen-compatible alloy used for entire casting instead of protective overlay. Parts exposed to high-pressure hydrogen made immune to hydrogen embrittlement if fabricated from new alloy, Incoly 903 (or equivalent). Material strong and compatible with hydrogen at all temperatures and adapted for outlet manifold of Space Shuttle main combustion chamber.
Manifold learning in machine vision and robotics
Bernstein, Alexander
2017-02-01
Smart algorithms are used in Machine vision and Robotics to organize or extract high-level information from the available data. Nowadays, Machine learning is an essential and ubiquitous tool to automate extraction patterns or regularities from data (images in Machine vision; camera, laser, and sonar sensors data in Robotics) in order to solve various subject-oriented tasks such as understanding and classification of images content, navigation of mobile autonomous robot in uncertain environments, robot manipulation in medical robotics and computer-assisted surgery, and other. Usually such data have high dimensionality, however, due to various dependencies between their components and constraints caused by physical reasons, all "feasible and usable data" occupy only a very small part in high dimensional "observation space" with smaller intrinsic dimensionality. Generally accepted model of such data is manifold model in accordance with which the data lie on or near an unknown manifold (surface) of lower dimensionality embedded in an ambient high dimensional observation space; real-world high-dimensional data obtained from "natural" sources meet, as a rule, this model. The use of Manifold learning technique in Machine vision and Robotics, which discovers a low-dimensional structure of high dimensional data and results in effective algorithms for solving of a large number of various subject-oriented tasks, is the content of the conference plenary speech some topics of which are in the paper.
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.
Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent.
Guan, Naiyang; Tao, Dacheng; Luo, Zhigang; Yuan, Bo
2011-07-01
Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole. For practical classification tasks, however, NMF ignores both the local geometry of data and the discriminative information of different classes. In addition, existing research results show that the learned basis is unnecessarily parts-based because there is neither explicit nor implicit constraint to ensure the representation parts-based. In this paper, we introduce the manifold regularization and the margin maximization to NMF and obtain the manifold regularized discriminative NMF (MD-NMF) to overcome the aforementioned problems. The multiplicative update rule (MUR) can be applied to optimizing MD-NMF, but it converges slowly. In this paper, we propose a fast gradient descent (FGD) to optimize MD-NMF. FGD contains a Newton method that searches the optimal step length, and thus, FGD converges much faster than MUR. In addition, FGD includes MUR as a special case and can be applied to optimizing NMF and its variants. For a problem with 165 samples in R(1600), FGD converges in 28 s, while MUR requires 282 s. We also apply FGD in a variant of MD-NMF and experimental results confirm its efficiency. Experimental results on several face image datasets suggest the effectiveness of MD-NMF.
Soft Manifold Dynamics behind Negative Thermal Expansion
Schlesinger, Z.; Rosen, J. A.; Hancock, J. N.; Ramirez, A. P.
2008-07-01
Minimal models are developed to examine the origin of large negative thermal expansion in underconstrained systems. The dynamics of these models reveals how underconstraint can organize a thermodynamically extensive manifold of low-energy modes which not only drives negative thermal expansion but extends across the Brillioun zone. Mixing of twist and translation in the eigenvectors of these modes, for which in ZrW2O8 there is evidence from infrared and neutron scattering measurements, emerges naturally in our model as a signature of the dynamics of underconstraint.
Path Integrals on Manifolds with Boundary
Ludewig, Matthias
2017-09-01
We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimensional path spaces of piecewise geodesics subordinated to increasingly fine partitions of the time interval. We consider a subclass of mixed boundary conditions which includes standard Dirichlet and Neumann boundary conditions.
Roughly isometric minimal immersions into Riemannian manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
. 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...... of the intrinsic combinatorial discrete Laplacian, and we will show that they share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in $N$. The intrinsic properties thus obtained may hence serve as roughly invariant descriptors for the original metric space $X$....
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
Dean, Edwin B.
1990-01-01
Design-to-cost is a popular technique for controlling costs. Although qualitative techniques exist for implementing design to cost, quantitative methods are sparse. In the launch vehicle and spacecraft engineering process, the question whether to minimize mass is usually an issue. The lack of quantification in this issue leads to arguments on both sides. This paper presents a mathematical technique which both quantifies the design-to-cost process and the mass/complexity issue. Parametric cost analysis generates and applies mathematical formulas called cost estimating relationships. In their most common forms, they are continuous and differentiable. This property permits the application of the mathematics of differentiable manifolds. Although the terminology sounds formidable, the application of the techniques requires only a knowledge of linear algebra and ordinary differential equations, common subjects in undergraduate scientific and engineering curricula. When the cost c is expressed as a differentiable function of n system metrics, setting the cost c to be a constant generates an n-1 dimensional subspace of the space of system metrics such that any set of metric values in that space satisfies the constant design-to-cost criterion. This space is a differentiable manifold upon which all mathematical properties of a differentiable manifold may be applied. One important property is that an easily implemented system of ordinary differential equations exists which permits optimization of any function of the system metrics, mass for example, over the design-to-cost manifold. A dual set of equations defines the directions of maximum and minimum cost change. A simplified approximation of the PRICE H(TM) production-production cost is used to generate this set of differential equations over [mass, complexity] space. The equations are solved in closed form to obtain the one dimensional design-to-cost trade and design-for-cost spaces. Preliminary results indicate that cost
Fixed point indices and manifolds with collars
Directory of Open Access Journals (Sweden)
Daniel Henry Gottlieb
2006-05-01
Full Text Available This paper concerns a formula which relates the Lefschetz number L(f for a map f:MÃ¢Â†Â’MÃ¢Â€Â² to the fixed point index I(f summed with the fixed point index of a derived map on part of the boundary of Ã¢ÂˆÂ‚M. Here M is a compact manifold and MÃ¢Â€Â² is M with a collar attached.
Semi-invariant submanifolds of (g, F-manifolds
Directory of Open Access Journals (Sweden)
Novac-Claudiu Chiriac
2010-09-01
Full Text Available We introduce (g,F-manifolds and initiate a study of their semi-invariant submanifolds. These submanifolds are generalizations of CR-submanifolds of Kaehler manifolds. We obtain necessary and sufficient conditions for the integrability of distributions on a semi-invariant submanifold and study the geometry of foliations defined by these distributions. In particular, for a large class of (g,F-manifolds we prove the existence of a natural foliation on their semi-invariant submanifolds.
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 ...
The "parity" anomaly on an unorientable manifold
Witten, Edward
2016-11-01
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. This 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 give a full description of the "parity" anomaly for fermions coupled to gauge fields and gravity in 2 +1 dimensions on a possibly unorientable spacetime. We consider an application to topological superconductors and another application to M theory. The application to topological superconductors involves using knowledge of the "parity" anomaly as an ingredient in constructing gapped boundary states of these systems and in particular in gapping the boundary of a ν =16 system in a topologically trivial fashion. The application to M theory involves showing the consistency of the path integral of an M theory membrane on a possibly unorientable worldvolume. In the past, this has been done only in the orientable case.
Fuel rod assembly to manifold attachment
Donck, Harry A.; Veca, Anthony R.; Snyder, Jr., Harold J.
1980-01-01
A fuel element is formed with a plurality of fuel rod assemblies detachably connected to an overhead support with each of the fuel rod assemblies having a gas tight seal with the support to allow internal fission gaseous products to flow without leakage from the fuel rod assemblies into a vent manifold passageway system on the support. The upper ends of the fuel rod assemblies are located at vertically extending openings in the support and upper threaded members are threaded to the fuel rod assemblies to connect the latter to the support. The preferred threaded members are cap nuts having a dome wall encircling an upper threaded end on the fuel rod assembly and having an upper sealing surface for sealing contact with the support. Another and lower seal is achieved by abutting a sealing surface on each fuel rod assembly with the support. A deformable portion on the cap nut locks the latter against inadvertent turning off the fuel rod assembly. Orienting means on the fuel rod and support primarily locates the fuel rods azimuthally for reception of a deforming tool for the cap nut. A cross port in the fuel rod end plug discharges into a sealed annulus within the support, which serves as a circumferential chamber, connecting the manifold gas passageways in the support.
Multiple Manifold Clustering Using Curvature Constrained Path.
Babaeian, Amir; Bayestehtashk, Alireza; Bandarabadi, Mojtaba
2015-01-01
The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface near by the intersection and result in incorrect clustering. The Isomap algorithm uses shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighborhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as a input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering.
Multiple Manifold Clustering Using Curvature Constrained Path.
Directory of Open Access Journals (Sweden)
Amir Babaeian
Full Text Available The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface near by the intersection and result in incorrect clustering. The Isomap algorithm uses shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighborhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as a input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering.
Smooth manifold structure for extreme channels
Iten, Raban; Colbeck, Roger
2018-01-01
A quantum channel from a system A of dimension dA to a system B of dimension dB is a completely positive trace-preserving map from complex dA × dA to dB × dB matrices, and the set of all such maps with Kraus rank r has the structure of a smooth manifold. We describe this set in two ways. First, as a quotient space of (a subset of) the rdB × dA dimensional Stiefel manifold. Second, as the set of all Choi-states of a fixed rank r. These two descriptions are topologically equivalent. This allows us to show that the set of all Choi-states corresponding to extreme channels from system A to system B of a fixed Kraus rank r is a smooth submanifold of dimension 2 r dAdB-dA2-r2 of the set of all Choi-states of rank r. As an application, we derive a lower bound on the number of parameters required for a quantum circuit topology to be able to approximate all extreme channels from A to B arbitrarily well.
Lagrangian descriptors of driven chemical reaction manifolds
Craven, Galen T.; Junginger, Andrej; Hernandez, Rigoberto
2017-08-01
The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015), 10.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.
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...
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
Manifold mapping: a two-level optimization technique
D. Echeverria (David); P.W. Hemker (Piet)
2008-01-01
textabstractIn 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
Growth of fundamental group for Finsler manifolds with integral Ricci ...
Indian Academy of Sciences (India)
Keywords. Finsler manifold; fundamental group; integral Ricci curvature; uniformity constant; reversibility. Abstract. In this paper, an upper bound on the growth of fundamental group for a class of Finsler manifolds with integral Ricci curvature bound is given. This generalizes the corresponding results with pointwise Ricci ...
Erratum to the paper: Compact hyperkaehler manifolds: basic results
Huybrechts, Daniel
2001-01-01
This is an Erratum to the paper: Compact hyperkaehler manifolds: basic results. (alg-geom/9705025, Inv. math. 135). We give a correct proof of the projectivity criterion for hyperkaehler manifolds. We use a recent result of Demailly and Paun math.AG/0105176.
Slant Riemannian maps from almost hermitian manifolds | Sahin ...
African Journals Online (AJOL)
As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples, obtain the existence conditions of slant Riemannian maps and investigate harmonicity of such maps.
Harmonic Riemannian maps on locally conformal Kaehler manifolds
Indian Academy of Sciences (India)
Abstract. We study harmonic Riemannian maps on locally conformal Kaehler mani- folds (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, ...
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....
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...
Double field theory on group manifolds
Blumenhagen, Ralph; Hassler, Falk; Lüst, Dieter
2015-02-01
A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order. The action and gauge transformations are derived for fluctuations around the generalized group manifold background up to cubic order, revealing the appearance of a generalized Lie derivative and a corresponding C-bracket upon invoking a new version of the strong constraint. In all these quantities a background dependent covariant derivative appears reducing to the partial derivative for a toroidal background. This approach sheds some new light on the conceptual status of DFT, its background (in-)dependence and the up-lift of non-geometric Scherk-Schwarz reductions.
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...
Model Transport: Towards Scalable Transfer Learning on Manifolds
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Black, Michael J.
2014-01-01
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......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...... “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...
Extrinsic local regression on manifold-valued data
Lin, Lizhen; St Thomas, Brian; Zhu, Hongtu; Dunson, David B.
2017-01-01
We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach. PMID:29225385
On the geometry of some special projective varieties
Russo, Francesco
2016-01-01
Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classi...
Stochastic development regression on non-linear manifolds
DEFF Research Database (Denmark)
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded......We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...
Scientific data interpolation with low dimensional manifold model
Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley
2018-01-01
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Stochastic development regression on non-linear manifolds
DEFF Research Database (Denmark)
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion proce...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....
Killing superalgebras for Lorentzian four-manifolds
Energy Technology Data Exchange (ETDEWEB)
Medeiros, Paul de [Department of Mathematics and Natural Sciences, University of Stavanger,4036 Stavanger (Norway); Figueroa-O’Farrill, José; Santi, Andrea [Maxwell Institute and School of Mathematics, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland (United Kingdom)
2016-06-20
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of 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.
On the Scalar Manifold of Exceptional Supergravity
Cacciatori, Sergio L; Marrani, Alessio
2012-01-01
We construct two parametrizations of the non compact exceptional Lie group G=E7(-25), based on a fibration which has the maximal compact subgroup K=(E6 x U(1))/Z_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 E6 invariant d-tensor, and hence exhibits the maximal possible manifest [(E6 x U(1))/Z_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" Freu...
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...
Spatial context driven manifold learning for hyperspectral image classification
CSIR Research Space (South Africa)
Zhang, Y
2014-06-01
Full Text Available learning methods. Empirically, the study reveals that use of spatial contextual information has a bearing on the structure of the graph Laplacian that in turn links image pixel observations to their manifold spaces. Further experimental results demonstrate...
Monopole classes and Perelman's invariant of four-manifolds
Kotschick, D.
2006-01-01
We calculate Perelman's invariant for compact complex surfaces and a few other smooth four-manifolds. We also prove some results concerning the dependence of Perelman's invariant on the smooth structure.
A survey on the Convergence of Manifolds with Boundary
Perales, Raquel
2013-01-01
This survey reviews precompactness theorems for classes of Riemannian manifolds with boundary. We begin with the works of Kodani, Anderson-Katsuda-Kurylev-Lassas-Taylor and Wong. We then present new results of Knox and the author with Sormani.
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.
Some functional inequalities on non-reversible Finsler manifolds
Indian Academy of Sciences (India)
SHIN-ICHI OHTA
2017-11-13
Riemannian Finsler manifold of weighted Ricci curvature bounded below satisfies the curvature-dimension condition (in the naturally extended form to asymmetric distances), but the Rieman- nian curvature-dimension condition never ...
q-oscillators, (non-)Kaehler manifolds and constrained dynamics
Shabanov, Sergey V.
1994-01-01
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class constraints.
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.
A simple proof of Perelman's collapsing theorem for 3-manifolds
Cao, Jianguo; Ge, Jian
2010-01-01
We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the class...
Humanoid posture generation on non-Euclidean manifolds
Brossette, Stanislas; Escande, Adrien; Duchemin, Grégoire; Chrétien, Benjamin; Kheddar, Abderrahmane
2015-01-01
International audience; We present a reformulation of the posture generation problem that encompasses non-Euclidean manifolds. Such a formulation allows a more elegant mathematical description of the constraints, which we exemplify through some scenarios in the simulation results section. In our previous work, the posture generation problem is formulated as a non-linear optimization program with constraints expressed only through Euclidean manifolds; we solve the latter problem using on-the-s...
Visual tracking with L1-Grassmann manifold modeling
Chachlakis, Dimitris G.; Markopoulos, Panos P.; Muchhala, Raj J.; Savakis, Andreas
2017-05-01
We present a novel method for robust tracking in video frame sequences via L1-Grassmann manifolds. The proposed method represents adaptively the target as a point on the Grassmann manifold, calculated by means of L1-norm Principal-Component Analysis (L1-PCA). For this purpose, an efficient algorithm for adaptive L1-PCA is presented. Our experimental studies illustrate that the presented tracking method, leveraging the outlier resistance of L1-PCA, demonstrates robustness against target occlusions and illumination variations.
Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation
Weigang Wen; Gao, Robert X.; Weidong Cheng
2016-01-01
The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by w...
Dimensionality reduction of collective motion by principal manifolds
Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.
2015-01-01
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.
Chekroun, Mickaël D; Wang, Shouhong
2015-01-01
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
LIFE CYCLE DESIGN OF AIR INTAKE MANIFOLDS; PHASE I: 2.0 L FORD CONTOUR AIR INTAKE MANIFOLD
The project team applied the life cycle design methodology to the design analysis of three alternative air intake manifolds: a sand cast aluminum, brazed aluminum tubular, and nylon composite. The design analysis included a life cycle inventory analysis, environmental regulatory...
Holst, Michael; Meier, Caleb; Tsogtgerel, G.
2017-11-01
In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (Class Quantum Gravity 30:205011, 2013), and Holst et al. (Phys Rev Lett 100(16):161101, 2008, Commun Math Phys 288(2):547-613, 2009), and also on the work of Maxwell (J Hyperbolic Differ Eqs 2(2):521-546, 2005a, Commun Math Phys 253(3):561-583, 2005b, Math Res Lett 16(4):627-645, 2009) and Dain (Class Quantum Gravity 21(2):555-573, 2004), under reasonable assumptions on the data we prove existence of both near- and far-from-constant mean curvature (CMC) solutions for a class of Robin boundary conditions commonly used in the literature for modeling black holes, with a third existence result for CMC appearing as a special case. Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the CMC setting, with interior boundary conditions representing excised interior black hole regions. Holst and Tsogtgerel compiled the interior boundary results covered by Dain and Maxwell, and then developed general interior conditions to model the apparent horizon boundary conditions of Dainand Maxwell for compact manifolds with boundary, and subsequently proved existence of solutions to the Lichnerowicz equation on compact manifolds with such boundary conditions. This paper picks up where Holst and Tsogtgerel left off, addressing the general non-CMC case for compact manifolds with boundary. As in our previous articles, our focus here is again on low regularity data and on the interaction between different types of boundary conditions. While our work here serves primarily to extend the solution theory for the compact with boundary case, we also develop several technical tools that have
Quasi-Newton Exploration of Implicitly Constrained Manifolds
Tang, Chengcheng
2011-08-01
A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.
Smooth Approximation of Lipschitz Functions on Finsler Manifolds
Directory of Open Access Journals (Sweden)
M. I. Garrido
2013-01-01
Full Text Available We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f:M→ℝ defined on a connected, second countable Finsler manifold M, for each positive continuous function ε:M→(0,∞ and each r>0, there exists a C1-smooth Lipschitz function g:M→ℝ such that |f(x-g(x|≤ε(x, for every x∈M, and Lip(g≤Lip(f+r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebra Cb1(M of all C1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T:Cb1(N→Cb1(M as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.
Hyperbolic normal forms and invariant manifolds: Astronomical applications
Directory of Open Access Journals (Sweden)
Efthymiopoulos C.
2012-01-01
Full Text Available In recent years, the study of the dynamics induced by the invariant manifolds of unstable periodic orbits in nonlinear Hamiltonian dynamical systems has led to a number of applications in celestial mechanics and dynamical astronomy. Two applications of main current interest are i space manifold dynamics, i.e. the use of the manifolds in space mission design, and, in a quite different context, ii the study of spiral structure in galaxies. At present, most approaches to the computation of orbits associated with manifold dynamics (i.e. periodic or asymptotic orbits rely either on the use of the so-called Poincaré - Lindstedt method, or on purely numerical methods. In the present article we briefly review an analytic method of computation of invariant manifolds, first introduced by Moser (1958, and developed in the canonical framework by Giorgilli (2001. We use a simple example to demonstrate how hyperbolic normal form computations can be performed, and we refer to the analytic continuation method of Ozorio de Almeida and co-workers, by which we can considerably extend the initial domain of convergence of Moser’s normal form.
Compactifications of IIA supergravity on SU(2)-structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Spanjaard, B.
2008-07-15
In this thesis, we study compactifications of type IIA supergravity on six-dimensional manifolds with an SU(2)-structure. A general study of six-dimensional manifolds with SU(2)-structure shows that IIA supergravity compactified on such a manifold should yield a four-dimensional gauged N=4 supergravity. We explicitly derive the bosonic spectrum, gauge transformations and action for IIA supergravity compactified on two different manifolds with SU(2)-structure, one of which also has an H{sup (3)}{sub 10}-flux, and confirm that the resulting four-dimensional theories are indeed N=4 gauged supergravities. In the second chapter, we study an explicit construction of a set of SU(2)-structure manifolds. This construction involves a Scherk-Schwarz duality twist reduction of the half-maximal six-dimensional supergravity obtained by compactifying IIA supergravity on a K3. This reduction results in a gauged N=4 four-dimensional supergravity, where the gaugings can be divided into three classes of parameters. We relate two of the classes to parameters we found before, and argue that the third class of parameters could be interpreted as a mirror flux. (orig.)
Trajectory design using periapse maps and invariant manifolds
Haapala, Amanda F.
The invariant manifolds associated with periodic orbits in the vicinity of the collinear libration points in the planar CR3BP have been previously demonstrated as mechanisms for transport. Trajectories that pass between adjoining regions within the zero-velocity curves pass through the invariant manifold tubes. In particular, the invariant manifolds associated with the unstable L1 and L2 periodic libration point orbits may be exploited to construct transit orbits between the interior and exterior regions associated with the zero-velocity curves. In this investigation, periapse Poincare maps are used to display the manifolds and to distinguish regions of escape and, conversely, regions of long-term capture. Manifold periapse structures are employed as a design tool to construct planar trajectories with predetermined characteristics. The strategies that are developed are demonstrated by producing planar trajectories with predetermined behaviors, namely, long-term capture orbits and transit trajectories, as well as heteroclinic and homoclinic connections. Additionally, path approximations are generated for four Jupiter family comets that experience temporary satellite capture. Periapse Poincare maps are also employed to design three-dimensional transit trajectories in the spatial circular restricted three-body problem.
Light transport on path-space manifolds
Jakob, Wenzel Alban
-stepping limitations of the theory, they often suffer from unusably slow convergence; improvements to this situation have been hampered by the lack of a thorough theoretical understanding. We address these problems by developing a new theory of path-space light transport which, for the first time, cleanly incorporates specular scattering into the standard framework. Most of the results obtained in the analysis of the ideally smooth case can also be generalized to rendering of glossy materials and volumetric scattering so that this dissertation also provides a powerful new set of tools for dealing with them. The basis of our approach is that each specular material interaction locally collapses the dimension of the space of light paths so that all relevant paths lie on a submanifold of path space. We analyze the high-dimensional differential geometry of this submanifold and use the resulting information to construct an algorithm that is able to "walk" around on it using a simple and efficient equation-solving iteration. This manifold walking algorithm then constitutes the key operation of a new type of Markov Chain Monte Carlo (MCMC) rendering method that computes lighting through very general families of paths that can involve arbitrary combinations of specular, near-specular, glossy, and diffuse surface interactions as well as isotropic or highly anisotropic volume scattering. We demonstrate our implementation on a range of challenging scenes and evaluate it against previous methods.
Multiscale singular value manifold for rotating machinery fault diagnosis
Energy Technology Data Exchange (ETDEWEB)
Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)
2017-01-15
Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.
Schoen manifold with line bundles as resolved magnetized orbifolds
Energy Technology Data Exchange (ETDEWEB)
Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
We give an alternative description of the Schoen manifold as the blow-up of a Z{sub 2} x Z{sub 2} orbifold in which one Z{sub 2} factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.
Weyl-Euler-Lagrange Equations of Motion on Flat Manifold
Directory of Open Access Journals (Sweden)
Zeki Kasap
2015-01-01
Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
Total Variation Regularization for Functions with Values in a Manifold
Lellmann, Jan
2013-12-01
While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.
Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation
Directory of Open Access Journals (Sweden)
Weigang Wen
2016-01-01
Full Text Available The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by wavelet enveloping. The envelope energy is adopted as an indicator to select meshing frequency band. Manifold learning is utilized to reduce the effect of noise within meshing frequency band. The fault characteristic frequency of the planetary gear is shown by spectrogram. The planetary gearbox model and test rig are established and experiments with planet gear faults are conducted for verification. All results of experiment analysis demonstrate its effectiveness and reliability.
Extended Hamiltonian learning on Riemannian manifolds: numerical aspects.
Fiori, Simone
2012-01-01
This paper is the second part of a study initiated with the paper S. Fiori, "Extended Hamiltonian learning on Riemannian manifolds: Theoretical aspects," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 687-700, May 2011, which aimed at introducing a general framework to develop a theory of learning on differentiable manifolds by extended Hamiltonian stationary-action principle. This paper discusses the numerical implementation of the extended Hamiltonian learning paradigm by making use of notions from geometric numerical integration to numerically solve differential equations on manifolds. The general-purpose integration schemes and the discussion of several cases of interest show that the implementation of the dynamical learning equations exhibits a rich structure. The behavior of the discussed learning paradigm is illustrated via several numerical examples and discussions of case studies. The numerical examples confirm the theoretical developments presented in this paper as well as in its first part.
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
Fiori, Simone
2017-06-01
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning
DEFF Research Database (Denmark)
Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan
2017-01-01
We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approxi......We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space...... that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric...
Manifold boundaries give "gray-box" approximations of complex models
Transtrum, Mark K
2016-01-01
We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric approximation problem. It operates iteratively, removing one parameter at a time, by approximating a high-dimension, but thin manifold by its boundary. Although the method makes no explicit assumption about the functional form of the model, it does require that the model manifold exhibit a hierarchy of boundaries, i.e., faces, edges, corners, hyper-corners, etc. We empirically show that a variety of model classes have this curious feature, making them amenable to MBAM. These model classes include models composed of elementary functions (e.g., rational functions, exponentials, and partition functions), a variety of dynamical system (e.g., chemical and biochemical kinetics, Linear Time Invariant (LTI) systems, and compartment models), network models (e.g., Bayesian networks, Marko...
Postoperative 3D spine reconstruction by navigating partitioning manifolds
Energy Technology Data Exchange (ETDEWEB)
Kadoury, Samuel, E-mail: samuel.kadoury@polymtl.ca [Department of Computer and Software Engineering, Ecole Polytechnique Montreal, Montréal, Québec H3C 3A7 (Canada); Labelle, Hubert, E-mail: hubert.labelle@recherche-ste-justine.qc.ca; Parent, Stefan, E-mail: stefan.parent@umontreal.ca [CHU Sainte-Justine Hospital Research Center, Montréal, Québec H3T 1C5 (Canada)
2016-03-15
Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities.
Scars of Invariant Manifolds in Interacting Few-Body Systems
Papenbrock, T; Weidenmüller, H A
1997-01-01
We present a novel extension of the concept of scars for the wave functions of classically chaotic few--body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space which are invariant under the action of a common subgroup of these two symmetries. Such manifolds are associated with highly symmetric configurations and, if sufficiently stable, support quantum resonances. Although not directly associated to individual periodic orbits, the resonances nevertheless cause scars which signify collective motion on the quantum level and which should be experimentally observable.
The Persistence of a Slow Manifold with Bifurcation
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P.; Robert, M.
2012-01-01
his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated...... by tethered satellites. It is shown that an almost full measure subset of a neighborhood of the slow manifold's normally elliptic branches persists in an adiabatic sense. We prove this using averaging and a blow-up near the bifurcation....
Great sphere foliations and manifolds with curvature bounded above
Rovenskii, V Y; Rovenskii, Vladimir Y.; Toponogov, Victor A.
1996-01-01
The survey is devoted to Toponogov's conjecture, that {\\it if a complete simply connected Riemannian manifold with sectional curvature $\\le 4$ and injectivity radius $\\ge \\pi/2$ has extremal diameter $\\pi/2$, then it is isometric to CROSS}. In Section 1 the relations of problem with geodesic foliations of a round sphere are considered, but the proof of conjecture on this way is not complete. In Section 2 the proof based on recent results and methods for topology and volume of Blaschke manifolds is given.
Lectures on the geometry of Manifolds
Nicolaescu, Liviu I
1996-01-01
The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. In writing it we had in mind the beginning graduate student willing to specialize in this very challenging field of mathematics. The necessary prerequisite is a good knowledge of the calculus with several variables, linear algebra and some elementary point-set topology.We tried to address several issues. 1. The Language; 2. The Problems; 3. The Methods; 4. The Answers.Historically, the problems came first, then came the methods and the language while the answers came last. The
Integral Manifolds of the Charged Three-Body Problem
Zaman, Mohammad
2017-01-01
This thesis is dedicated to the study of the In- tegral Manifolds of the Charged Three-Body Problem. My aim is to give a mathematical analysis of the physical mechanical system that consists of three charged particles moving in space and interacting via a Coulomb potential. The system is
Curvature Properties of Lorentzian Manifolds with Large Isometry Groups
Energy Technology Data Exchange (ETDEWEB)
Batat, Wafaa [Ecole Normale Superieure de L' Enseignement Technique d' Oran, Departement de Mathematiques et Informatique (Algeria)], E-mail: wafa.batat@enset-oran.dz; Calvaruso, Giovanni, E-mail: giovanni.calvaruso@unile.it; Leo, Barbara De [University of Salento, Dipartimento di Matematica ' E. De Giorgi' (Italy)], E-mail: barbara.deleo@unile.it
2009-08-15
The curvature of Lorentzian manifolds (M{sup n},g), admitting a group of isometries of dimension at least 1/2n(n - 1) + 1, is completely described. Interesting behaviours are found, in particular as concerns local symmetry, local homogeneity and conformal flatness.
Attraction properties of the Ginzburg-Landau manifold
Eckhaus, W.; Shepeleva, A.
1994-01-01
We consider solutions of weakly unstable PDE on an unbounded spatial domain. It has been shown earlier by the first author that the set of modulated solutions (called "Ginzburg-Landau manifold") is attracting. We seek to understand "how big" is the domain of attraction. Starting with general initial
Valve and Manifold considerations for Efficient Digital Hydraulic Machines
DEFF Research Database (Denmark)
Roemer, Daniel Beck; Nørgård, Christian; Bech, Michael Møller
2016-01-01
This paper seeks to shed light on the topic of design and sizing of switching valves and connecting manifolds found in large digital hydraulic motors, also known commercially as Digital Displacement Motors. These motors promise very high operation efficiencies with broad operation ranges, which set...
Two new variants of the manifold-mapping technique
D. Echeverria (David)
2006-01-01
htmlabstractManifold-mapping is an efficient surrogate-based optimization technique aimed at the acceleration of very time-consuming design problems. In this paper we present two new variants of the original algorithm that make it applicable to a broader range of optimization scenarios. The first
AdS 3-manifolds and Higgs bundles
DEFF Research Database (Denmark)
Alessandrini, Daniele; Li, Qiongling
2017-01-01
In this paper we investigate the relationships between closed AdS $3$-manifolds and Higgs bundles. We have a new way to construct AdS structures that allows us to see many of their properties explicitly, for example we can recover the very recent formula by Tholozan for their volume. We give natu...
Global Identification from the equilibrium Manifold under Incomplete markets
Carvajal, Andreas; Riascos, Alvaro
2004-01-01
We show that, even under incomplete markets, the equilibrium manifold identifies individual demands everywhere in their domains. For this, we assume conditions of smoothness, interiority and regularity, and avoid observational requirements at the individual level. It is crucial that there be date-zero consumption. As a by-product, we develop some duality theory under incomplete markets.
Coisotropic Displacement and Small Subsets of a Symplectic Manifold
Ziltener, Fabian; Swoboda, J.
2012-01-01
We prove a coisotropic intersection result and deduce the following: Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. A stable non-squeezing result for neighborhoods of products of unit spheres. Existence of a
On conformal minimal 2-spheres in complex Grassmann manifold G ...
Indian Academy of Sciences (India)
For a harmonic map from a Riemann surface into a complex Grassmann manifold, Chern and Wolfson [4] constructed new harmonic maps and ¯ f through the fundamental collineations and ¯ respectively. In this paper ... Some examples are given to show that the hypotheses in our theorems are reasonable.
Convexity of spheres in a manifold without conjugate points
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. For a non-compact, complete and simply connected manifold M without conjugate points, we prove that if the determinant of the second fundamental form of the geodesic spheres in M is a radial function, then the geodesic spheres are convex. We also show that if M is two or three dimensional and without ...
An algorithmic approach to construct crystallizations of 3-manifolds ...
Indian Academy of Sciences (India)
Abstract. We have defined the weight of the pair (〈S | R〉, R) for a given presen- tation 〈S | R〉 of a group, where the number of generators is equal to the number of relations. We present an algorithm to construct crystallizations of 3-manifolds whose fundamental group has a presentation with two generators and two relations ...
Airfoil optimization by using the Manifold Mapping method
M. van der Jagt (Martin)
2007-01-01
textabstractIn this report it is investigated if the Manifold Mapping method can be used in airfoil optimization. Before the method can be implemented, a suitable airfoil parametrization must be chosen. Furthermore a coarse and fine model must be assigned. These models are the key to success for the
Energy identity for harmonic maps into standard stationary Lorentzian manifolds
Han, Xiaoli; Zhao, Liang; Zhu, Miaomiao
2017-04-01
For a harmonic map from a closed Riemann surface into a standard stationary Lorentzian manifold, we prove that its Hopf differential is holomorphic. Moreover, we prove that for a sequence of such maps with their energy uniformly bounded, the Lorentzian energy identity holds during the blow-up process.
Gauge theory and the topology of four-manifolds
Friedman, Robert Marc
1998-01-01
The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying SU(2)-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the SU(2)-moduli spaces may one day be important for purposes beyond the algebraic invariants that ...
Cost-effective and detailed modelling of compressor manifold vibrations
Eijk, A.; Egas, G.; Smeulers, J.P.M.
1996-01-01
In systems with large reciprocating compressors, so-called compressor manifold vibrations can contribute to fatigue failure of the pipe system. These vibrations are excited by pulsation-induced forces and by forces generated by the compressor. This paper describes an advanced and accurate method for
Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations
Bakri, Taoufik; Meijer, Hil Gaétan Ellart; Verhulst, Ferdinand
2009-01-01
Persistence and bifurcations of Lyapunov manifolds can be studied by a combination of averaging-normalization and numerical bifurcation methods. This can be extended to infinite-dimensional cases when using suitable averaging theorems. The theory is applied to the case of a parametrically excited
Growth of fundamental group for Finsler manifolds with integral Ricci ...
Indian Academy of Sciences (India)
In this paper, an upper bound on the growth of fundamental group for a class of Finsler manifolds with integral Ricci curvature bound is given. The result generalizes the corresponding results with pointwise Ricci curvature in the literature. The maximal and minimal volume forms (see §2 for the definition) are used throughout ...
Manifold learning based feature extraction for classification of hyper-spectral data
CSIR Research Space (South Africa)
Lunga, D
2013-08-01
Full Text Available of remotely sensed data. Challenges and opportunities remain for future research in manifold learning, including joint exploitation of advantages of global and local structures in dynamic, multi-temporal environments, multiscale manifolds, and integration...
Formation of a Chern-Simons cylindrical wormhole during evolution of manifolds
Sepehri, Alireza; Ghaffary, Tooraj; Naimi, Yaghoob; Ghaforyan, Hossein; Ebrahimzadeh, Majid
In this paper, the formation of cylindrical wormhole during evolution of manifolds is studied. It is shown that this type of wormholes may be produced at two stages and then disappeared very fast at the third stage. First, one N-dimensional is formed by joining point-like manifolds. Then, this manifold is torn and two child manifolds plus one Chern-Simons manifold appeared. Our universe is born on one of the child manifolds and connected to the other one by Chern-Simons manifold. At the third stage, this Chern-Simons manifold-which plays the role of cylindrical wormhole, dissolves into universes and gives its energy to them and causes inflation. Thus, the Chern-Simons cylindrical wormhole is unstable and dissolves in our four-dimensional universes and another universe very fast.
Person-Independent Head Pose Estimation Using Biased Manifold Embedding
Directory of Open Access Journals (Sweden)
Sethuraman Panchanathan
2008-02-01
Full Text Available Head pose estimation has been an integral problem in the study of face recognition systems and human-computer interfaces, as part of biometric applications. A fine estimate of the head pose angle is necessary and useful for several face analysis applications. To determine the head pose, face images with varying pose angles can be considered to be lying on a smooth low-dimensional manifold in high-dimensional image feature space. However, when there are face images of multiple individuals with varying pose angles, manifold learning techniques often do not give accurate results. In this work, we propose a framework for a supervised form of manifold learning called Biased Manifold Embedding to obtain improved performance in head pose angle estimation. This framework goes beyond pose estimation, and can be applied to all regression applications. This framework, although formulated for a regression scenario, unifies other supervised approaches to manifold learning that have been proposed so far. Detailed studies of the proposed method are carried out on the FacePix database, which contains 181 face images each of 30 individuals with pose angle variations at a granularity of 1Ã¢ÂˆÂ˜. Since biometric applications in the real world may not contain this level of granularity in training data, an analysis of the methodology is performed on sparsely sampled data to validate its effectiveness. We obtained up to 2Ã¢ÂˆÂ˜ average pose angle estimation error in the results from our experiments, which matched the best results obtained for head pose estimation using related approaches.
Chern-Simons and twisted supersymmetry in various dimensions
Energy Technology Data Exchange (ETDEWEB)
Baulieu, L. [Paris-6 Univ., 75 (France). Lab. de Physique Theorique et Hautes Energies; Losev, A. [Paris-6 Univ., 75 (France). Lab. de Physique Theorique et Hautes Energies]|[Institute of Theoretical and Experimental Physics, 117259, Moscow (Russian Federation)]|[Department of Physics, Yale University, Box 208120, New Haven, CT 06520 (United States); Nekrasov, N. [Paris-6 Univ., 75 (France). Lab. de Physique Theorique et Hautes Energies]|[Institute of Theoretical and Experimental Physics, 117259, Moscow (Russian Federation)]|[Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138 (United States)
1998-06-29
We introduce special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight-folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles and/or solutions to the analogues of instanton equations in higher dimensions. The theories may occur on the world-volumes of D-branes wrapping manifolds of a special holonomy. We also discuss the theories with matter. (orig.) 44 refs.
21 CFR 870.4290 - Cardiopulmonary bypass adaptor, stopcock, manifold, or fitting.
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Cardiopulmonary bypass adaptor, stopcock, manifold... Devices § 870.4290 Cardiopulmonary bypass adaptor, stopcock, manifold, or fitting. (a) Identification. A cardiopulmonary bypass adaptor, stopcock, manifold, or fitting is a device used in cardiovascular diagnostic...
Pontani, Mauro; Giancotti, Marco; Teofilatto, Paolo
2014-12-01
Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth-Moon system and in alternative multibody environments. With regard to lunar missions, exterior and interior transfers, based on the transit through the regions where the collinear libration points L1 and L2 are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is focused on the definition and use of a special isomorphic mapping for low-energy mission analysis. A convenient set of cylindrical coordinates is employed to describe the spacecraft dynamics (i.e. position and velocity), in the context of the circular restricted three-body problem, used to model the spacecraft motion in the Earth-Moon system. This isomorphic mapping of trajectories allows the identification and intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Heteroclinic connections, i.e. the trajectories that belong to both the stable and the unstable manifolds of two distinct periodic orbits, can be easily detected by means of this representation. This paper illustrates the use of isomorphic mapping for finding (a) periodic orbits, (b) heteroclinic connections between trajectories emanating from two Lyapunov orbits, the first at L1, and the second at L2, and (c) heteroclinic connections between trajectories emanating from the Lyapunov orbit at L1 and from a particular unstable lunar orbit. Heteroclinic trajectories are asymptotic trajectories that travels at zero-propellant cost. In practical situations, a modest delta-v budget is required to perform transfers along the manifolds. This circumstance implies the possibility of performing complex missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible
Classification and equivariant cohomology of circle actions on 3d manifolds
He, Chen
2017-10-01
The classification of Seifert manifolds was given in terms of numeric data by Seifert (1933), and then generalized by Raymond (1968) and Orlik and Raymond (1968) to circle actions on closed 3d manifolds. In this paper, we further generalize the classification to circle actions on 3d manifolds with boundaries by adding a numeric parameter and a graph of cycles. Then, we describe the rational equivariant cohomology of 3d manifolds with circle actions in terms of ring, module and vector-space structures. We also compute equivariant Betti numbers and Poincaré series for these manifolds and discuss the equivariant formality.
Laplacian manifold regularization method for fluorescence molecular tomography
He, Xuelei; Wang, Xiaodong; Yi, Huangjian; Chen, Yanrong; Zhang, Xu; Yu, Jingjing; He, Xiaowei
2017-04-01
Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ℓ1-regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ℓ1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai-Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ℓ1 minimization method in both spatial aggregation and location accuracy.
Determination of a Riemannian manifold from the distance difference functions
Lassas, Matti; Saksala, Teemu
2015-01-01
Let $(N,g)$ be a Riemannian manifold with the distance function $d(x,y)$ and an open subset $M\\subset N$. For $x\\in M$ we denote by $D_x$ the distance difference function $D_x:F\\times F\\to \\mathbb R$, given by $D_x(z_1,z_2)=d(x,z_1)-d(x,z_2)$, $z_1,z_2\\in F=N\\setminus M$. We consider the inverse problem of determining the topological and the differentiable structure of the manifold $M$ and the metric $g|_M$ on it when we are given the distance difference data, that is, the set $F$, the metric...
A supermembrane with central charges on a G2 manifold
Energy Technology Data Exchange (ETDEWEB)
Belhaj, A; Segui, A [Departamento de Fisica Teorica, Universidad de Zaragoza, 12, Pedro Cerbuna, 50009 Zaragoza (Spain); Moral, M P Garcia del [Dipartimento di Fisica Teorica, Universita di Torino and INFN-Sezione di Torino, Via P Giuria 1, I-10125 Torino (Italy); Restuccia, A [Max-Planck-Institut fuer Gravitationphysik, Albert-Einstein-Institut, Muelenberg 1, D-14476 Potsdam (Germany); Veiro, J P [Departamento de Matematicas Puras y Aplicadas, Universidad Simon BolIvar, Apartado 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of)], E-mail: belhaj@unizar.es, E-mail: garcia@to.infn.it, E-mail: restucci@aei.mpg.de, E-mail: arestu@usb.ve, E-mail: segui@unizar.es, E-mail: pierre@ma.usb.ve
2009-08-14
We construct an 11D supermembrane with topological central charges induced through an irreducible winding on a G2 manifold realized from the T{sup 7}/Z{sup 3}{sub 2} orbifold construction. The Hamiltonian H of the theory on a T{sup 7} target has a discrete spectrum. Within the discrete symmetries of H associated with large diffeomorphisms, the Z{sub 2} x Z{sub 2} x Z{sub 2} group of automorphisms of the quaternionic subspaces preserving the octonionic structure is relevant. By performing the corresponding identification on the target space, the supermembrane may be formulated on a G2 manifold, preserving the discreteness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N = 1 supersymmetry.
A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds
Turki, Yahya
2015-04-01
On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points project onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least defines an integrable distribution-a class of bivector fields generalizing twisted Poisson structures that we study in detail.
An algorithmic approach to construct crystallizations of 3-manifolds ...
Indian Academy of Sciences (India)
As an application, we have constructed some new crystallizations of 3-manifolds. We have generalized our algorithm for presentations with three generators and a certain class of relations. For m ≥ 3 and m ≥ n ≥ k ≥ 2 , our generalized algorithm gives a 2 ( 2 m + 2 n + 2 k − 6 + δ n 2 + δ k 2 ) -vertex crystallization of the ...
Amplifying vibrational circular dichroism by manipulation of the electronic manifold.
Domingos, Sérgio R; Panman, Matthijs R; Bakker, Bert H; Hartl, Frantisek; Buma, Wybren J; Woutersen, Sander
2012-01-11
Vibrational circular dichroism is a powerful technique to study the stereochemistry of chiral molecules, but often suffers from small signal intensities. Electrochemical modulation of the energies of the electronically excited state manifold is now demonstrated to lead to an order of magnitude enhancement of the differential absorption. Quantum-chemical calculations show that increased mixing between ground and excited states is at the origin of this amplification. This journal is © The Royal Society of Chemistry 2012
Evaluation of human dynamic balance in Grassmann manifold
Michalczuk, Agnieszka; Wereszczyński, Kamil; Mucha, Romualda; Świtoński, Adam; Josiński, Henryk; Wojciechowski, Konrad
2017-07-01
The authors present an application of Grassmann manifold to the evaluation of human dynamic balance based on the time series representing movements of hip, knee and ankle joints in the sagittal, frontal and transverse planes. Time series were extracted from gait sequences which were recorded in the Human Motion Laboratory (HML) of the Polish-Japanese Academy of Information Technology in Bytom, Poland using the Vicon system.
Integral foliated simplicial volume of hyperbolic 3-manifolds
Löh, Clara; Pagliantini, Cristina
2016-01-01
Integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coewefficients with the flexibility of measure spaces. In this article, using the language of measure equivalence of groups we prove a proportionality principle for integral foliated simplicial volume for aspherical manifolds and give refined upper bounds of integral foliated simplicial volume in terms of stable integral simplicial volume. This allows us to compute the integral foliated si...
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....
Groups and manifolds lectures for physicists with examples in Mathematica
Fré, Pietro Giuseppe
2018-01-01
Groups and Manifolds is an introduction to the mathematics of symmetry with a variety of examples for physicists. It covers both classical symmetry as seen in crystallography as well as the mathematical concepts used in super-symmetric field theories. After a basic introduction of group theory, Lie algebras and a basic notion of differential geometry are discussed. Group-theoretical constructions are done using Mathematica.
Optimal reconfigurations of two-craft Coulomb formations along manifolds
Jones, Drew R.; Schaub, Hanspeter
2013-02-01
Coulomb formations refer to swarms of closely flying spacecraft, in which the net electric charge of each vehicle is controlled. Active charge control is central to this concept and enables a propulsion system with highly desirable characteristics, albeit with limited controllability. Numerous Coulomb formation equilibria have been derived, but to maintain and maneuver these configurations, some inertial thrust is required to supplement the nearly propellant-less charge control. In this work, invariant manifold theory is applied to two-craft Coulomb equilibria, which are admitted in a linearized two-body gravity model. The manifolds associated with these systems are analyzed for the first time, and are then utilized as part of a general procedure for formulating optimal reconfigurations. Specifically, uncontrolled flows along the manifolds are sought which provide near continuous transfers from one equilibrium to another. Control is then introduced to match continuity, while minimizing inertial thrusting. This methodology aims to exploit uncontrolled motions and charge control to realize the shape-changing ability of these formations, without large inertial control efforts. Some variations in formulating and parameterizing the optimal transfers are discussed, and analytical expressions are derived to aid in establishing control parameter limits, under certain assumptions. Numerical results are provided, as demonstrative examples of the optimization procedure, using relatively simple control approximations. Finally, Particle Swarm Optimization, a novel stochastic method, is used with considerable success to solve the numerically difficult parameter optimization problems.
Hyperspherical Manifold for EEG Signals of Epileptic Seizures
Directory of Open Access Journals (Sweden)
Tahir Ahmad
2012-01-01
Full Text Available The mathematical modelling of EEG signals of epileptic seizures presents a challenge as seizure data is erratic, often with no visible trend. Limitations in existing models indicate a need for a generalized model that can be used to analyze seizures without the need for apriori information, whilst minimizing the loss of signal data due to smoothing. This paper utilizes measure theory to design a discrete probability measure that reformats EEG data without altering its geometric structure. An analysis of EEG data from three patients experiencing epileptic seizures is made using the developed measure, resulting in successful identification of increased potential difference in portions of the brain that correspond to physical symptoms demonstrated by the patients. A mapping then is devised to transport the measure data onto the surface of a high-dimensional manifold, enabling the analysis of seizures using directional statistics and manifold theory. The subset of seizure signals on the manifold is shown to be a topological space, verifying Ahmad's approach to use topological modelling.
Computing unstable manifolds of periodic orbits in delay differential equations
Krauskopf, B
2003-01-01
We present the first algorithm for computing unstable manifolds of saddle-type periodic orbits with one unstable Floquet multiplier in systems of autonomous delay differential equations (DDEs) with one fixed delay. Specifically, we grow the one-dimensional unstable manifold W sup u (q) of an associated saddle fixed point q of a Poincare map defined by a suitable Poincare section SIGMA. Starting close to q along the linear approximation to W sup u (q) given by the associated eigenfunction, our algorithm grows the manifold as a sequence of points, where the distance between points is governed by the curvature of the one-dimensional intersection curve W sup u (q intersection SIGMA of W sup u (q) with SIGMA. Our algorithm makes it possible to study global bifurcations in DDEs. We illustrate this with the break-up of an invariant torus and a subsequent crisis bifurcation to chaos in a DDE model of a semiconductor laser with phase-conjugate feedback.
Geometric Hamilton-Jacobi theory on Nambu-Poisson manifolds
de León, M.; Sardón, C.
2017-03-01
The Hamilton-Jacobi theory is a formulation of classical mechanics equivalent to other formulations as Newtonian, Lagrangian, or Hamiltonian mechanics. The primordial observation of a geometric Hamilton-Jacobi theory is that if a Hamiltonian vector field XH can be projected into the configuration manifold by means of a 1-form dW, then the integral curves of the projected vector field XHd Wcan be transformed into integral curves of XH provided that W is a solution of the Hamilton-Jacobi equation. Our aim is to derive a geometric Hamilton-Jacobi theory for physical systems that are compatible with a Nambu-Poisson structure. For it, we study Lagrangian submanifolds of a Nambu-Poisson manifold and obtain explicitly an expression for a Hamilton-Jacobi equation on such a manifold. We apply our results to two interesting examples in the physics literature: the third-order Kummer-Schwarz equations and a system of n copies of a first-order differential Riccati equation. From the first example, we retrieve the original Nambu bracket in three dimensions and from the second example, we retrieve Takhtajan's generalization of the Nambu bracket to n dimensions.
Canonical Correlation Analysis on Riemannian Manifolds and Its Applications.
Kim, Hyunwoo J; Adluru, Nagesh; Bendlin, Barbara B; Johnson, Sterling C; Vemuri, Baba C; Singh, Vikas
2014-01-01
Canonical correlation analysis (CCA) is a widely used statistical technique to capture correlations between two sets of multi-variate random variables and has found a multitude of applications in computer vision, medical imaging and machine learning. The classical formulation assumes that the data live in a pair of vector spaces which makes its use in certain important scientific domains problematic. For instance, the set of symmetric positive definite matrices (SPD), rotations and probability distributions, all belong to certain curved Riemannian manifolds where vector-space operations are in general not applicable. Analyzing the space of such data via the classical versions of inference models is rather sub-optimal. But perhaps more importantly, since the algorithms do not respect the underlying geometry of the data space, it is hard to provide statistical guarantees (if any) on the results. Using the space of SPD matrices as a concrete example, this paper gives a principled generalization of the well known CCA to the Riemannian setting. Our CCA algorithm operates on the product Riemannian manifold representing SPD matrix-valued fields to identify meaningful statistical relationships on the product Riemannian manifold. As a proof of principle, we present results on an Alzheimer's disease (AD) study where the analysis task involves identifying correlations across diffusion tensor images (DTI) and Cauchy deformation tensor fields derived from T1-weighted magnetic resonance (MR) images.
Directory of Open Access Journals (Sweden)
Massimiliano Ferrara
2013-01-01
Full Text Available Matsumoto and Szidarovszky (2011 examined a delayed continuous-time growth model with a special mound-shaped production function and showed a Hopf bifurcation that occurs when time delay passes through a critical value. In this paper, by applying the center manifold theorem and the normal form theory, we obtain formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Moreover, Lindstedt’s perturbation method is used to calculate the bifurcated periodic solution, the direction of the bifurcation, and the stability of the periodic motion resulting from the bifurcation.
Energy Technology Data Exchange (ETDEWEB)
Ike, M.; Akiyama, K. (Nissan Motor Co. Ltd., Tokyo (Japan)); Otsuka, K.; Ito, K. (Hitachi Metals, Ltd., Tokyo (Japan))
1991-07-01
Any exhaust manifold is exposed to the severer thermal cycle condition by exhasut gas of the maximum temperature reaching near 1273K and therefore the thermal resistance reliability should be improved. A new cast heat resistant steel for the exhaust manifold which had better thermal fatigue resistance and oxidation resistance than conventional Ni-resist cast iron was developed this time. The developed material was based on the 18Cr ferritic heat resistant steel of low coefficent of thermal expansion and the oxidation resistance was improved, and further the thermal fatigue life was improved by aiming at the structural stability through elevating the transformation point to the upper limit of service temperature or more. These requirements were achieved by grasping the above mentioned characteristics of the part material and by studying the effect of main composing elements, C, N, Cr, Nb, Mo, on these characteristics. The cheaper exhaust manifold of higher thermal resistant reliability than conventional one could be put into practical use by using a newly developed casting process in addition to the use of this developed material. 7 refs., 11 figs., 5 tabs.
Dictionary Pair Learning on Grassmann Manifolds for Image Denoising.
Zeng, Xianhua; Bian, Wei; Liu, Wei; Shen, Jialie; Tao, Dacheng
2015-11-01
Image denoising is a fundamental problem in computer vision and image processing that holds considerable practical importance for real-world applications. The traditional patch-based and sparse coding-driven image denoising methods convert 2D image patches into 1D vectors for further processing. Thus, these methods inevitably break down the inherent 2D geometric structure of natural images. To overcome this limitation pertaining to the previous image denoising methods, we propose a 2D image denoising model, namely, the dictionary pair learning (DPL) model, and we design a corresponding algorithm called the DPL on the Grassmann-manifold (DPLG) algorithm. The DPLG algorithm first learns an initial dictionary pair (i.e., the left and right dictionaries) by employing a subspace partition technique on the Grassmann manifold, wherein the refined dictionary pair is obtained through a sub-dictionary pair merging. The DPLG obtains a sparse representation by encoding each image patch only with the selected sub-dictionary pair. The non-zero elements of the sparse representation are further smoothed by the graph Laplacian operator to remove the noise. Consequently, the DPLG algorithm not only preserves the inherent 2D geometric structure of natural images but also performs manifold smoothing in the 2D sparse coding space. We demonstrate that the DPLG algorithm also improves the structural SIMilarity values of the perceptual visual quality for denoised images using the experimental evaluations on the benchmark images and Berkeley segmentation data sets. Moreover, the DPLG also produces the competitive peak signal-to-noise ratio values from popular image denoising algorithms.
Towards Optimal Manifold Hashing via Discrete Locally Linear Embedding.
Ji, Rongrong; Liu, Hong; Cao, Liujuan; Liu, Di; Wu, Yongjian; Huang, Feiyue
2017-08-02
Binary code learning, a.k.a. hashing, has received increasing attention in large-scale visual search. By transforming high-dimensional features to binary codes, the original Euclidean distance is approximated via Hamming distance. More recently, it is advocated that it is the manifold distance, rather than the Euclidean distance, that should be preserved in the Hamming space. However, it retains as an open problem to directly preserve the manifold structure by hashing. In particular, it needs first to build the local linear embedding in the original feature space, and then quantize such embedding to binary codes. Such a twostep coding is problematic and less optimized. Besides, the offline learning is extremely time and memory consuming, which needs to calculate the similarity matrix of the original data. In this paper, we propose a novel hashing algorithm, termed Discrete Locality Linear Embedding Hashing (DLLH), which well addresses the above challenges. DLLH directly reconstructs the manifold structure in the Hamming space, which learns optimal hash codes to maintain the local linear relationship of data points. To learn Discrete Locally Linear Embedding (DLLE) codes, we further propose a discrete optimization algorithm with an iterative parameters updating scheme. Moreover, an anchor-based acceleration scheme, termed Anchor-DLLH (ADLLH), is further introduced, which approximates the large similarity matrix by the product of two low rank matrices. Experimental results on three widely used benchmark datasets, i.e. CIFAR10, NUS-WIDE, and Youtube Face, have shown superior performance of the proposed DLLH over the state-of-the-art approaches.
Manifolds in random media: beyond the variational approximation
Goldschmidt, Yadin Y.
1994-01-01
In this paper we give a closed form expression for the 1/d corrections to the selfenergy characterizing the correlation function of a manifold in random media. This amounts to the first confection beyond the variational approximation. At this time we were able to evaluate these corrections in the high temperature "phase" of the notorious toy-model describing a classical particle subject to the influence of both a harmonic potential and a random potential. Although in this phase the correct solution is replica symmetric the calculation is non-trivial. The outcome is compared with previous analytical and numerical results. The corrections diverge at the "transition" temperature.
Bures metric over thermal state manifolds and quantum criticality
Zanardi, Paolo; Campos Venuti, Lorenzo; Giorda, Paolo
2007-12-01
We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows one to complement the understanding of the phase diagram including crossover regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.
Manifolds, tensors and, forms an introduction for mathematicians and physicists
Renteln, Paul
2014-01-01
Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, and degree theory. It also features over 250 detailed exercises, and a variety of applications revealing fundamental connections to classical mechanics, electromagnetism (including circuit theory), general relativity and gauge theory. Solutions to the problems are available for instructors at www.cambridge.org/9781107042193.
New hyper-K{umlt a}hler manifolds by fixing monopoles
Energy Technology Data Exchange (ETDEWEB)
Houghton, C.J. [DAMTP, Silver Street, Cambridge, CB3 9EW (United Kingdom)
1997-07-01
The construction of new hyper-K{umlt a}hler manifolds by taking the infinite monopole mass limit of certain Bogomol{close_quote}nyi-Prasad-Sommerfield monopole moduli spaces is considered. The one-parameter family of hyper-K{umlt a}hler manifolds due to Dancer is shown to be an example of such manifolds. A new family of fixed monopole spaces is constructed. They are the moduli spaces of four SU{sub 4} monopoles, in the infinite mass limit of two of the monopoles. These manifolds are shown to be nonsingular when the fixed monopole positions are distinct. {copyright} {ital 1997} {ital The American Physical Society}
Heat shield manifold system for a midframe case of a gas turbine engine
Energy Technology Data Exchange (ETDEWEB)
Mayer, Clinton A.; Eng, Jesse; Schopf, Cheryl A.
2017-07-25
A heat shield manifold system for an inner casing between a compressor and turbine assembly is disclosed. The heat shield manifold system protects the outer case from high temperature compressor discharge air, thereby enabling the outer case extending between a compressor and a turbine assembly to be formed from less expensive materials than otherwise would be required. In addition, the heat shield manifold system may be configured such that compressor bleed air is passed from the compressor into the heat shield manifold system without passing through a conventional flange to flange joint that is susceptible to leakage.
The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold
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J. A. Helayël-Neto
2017-01-01
Full Text Available It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.
Geometrical interpretation of electromagnetism in a 5-dimensional manifold
Kim, TaeHun; Kim, Hyunbyuk
2017-08-01
In this paper, Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ratio has a physical meaning of the ratio between the movement along the direction of the 5th axis and the movement in the 4D space-time. In order to have a 5D matter which is consistent with the construction of the 5D manifold, a notion of particle-thread is suggested. Examinations on the compatibility of reference frames reveal a covariance breaking of the 5th dimension. The field equations which extend Einstein’s field equations give the total energy-momentum tensor as a sum of that of matter, electromagnetic field, and the interaction between electric current and electromagnetic potential. Finally, the experimental implications are calculated for the weak potential case.
Data assimilation on the exponentially accurate slow manifold.
Cotter, Colin
2013-05-28
I describe an approach to data assimilation making use of an explicit map that defines a coordinate system on the slow manifold in the semi-geostrophic scaling in Lagrangian coordinates, and apply the approach to a simple toy system that has previously been proposed as a low-dimensional model for the semi-geostrophic scaling. The method can be extended to Lagrangian particle methods such as Hamiltonian particle-mesh and smooth-particle hydrodynamics applied to the rotating shallow-water equations, and many of the properties will remain for more general Eulerian methods. Making use of Hamiltonian normal-form theory, it has previously been shown that, if initial conditions for the system are chosen as image points of the map, then the fast components of the system have exponentially small magnitude for exponentially long times as ε→0, and this property is preserved if one uses a symplectic integrator for the numerical time stepping. The map may then be used to parametrize initial conditions near the slow manifold, allowing data assimilation to be performed without introducing any fast degrees of motion (more generally, the precise amount of fast motion can be selected).
Attracting manifolds for attitude estimation in flatland and otherlands
Akella, Maruthi R.; Seo, Dongeun; Zanetti, Renato
2006-12-01
Non-convex and non-affine parameterizations of uncertainty are intrinsic within every attitude estimation problem given the fact that minimal and/or nonsingular representations of the attitude matrix are invariably nonlinear functions of the unknown attitude variables. Of course, this fact remains true for rotation matrices both in the 2-D plane (flatland) and in higher dimensional spaces (otherlands). Therefore, estimation problems involving minimal nonsingular representations of unknown attitude matrices bring significant challenges to the adaptive estimation community. This paper develops a novel algorithm for attitude estimation. The proposed algorithm relies upon the design of an adaptive update law for the attitude estimate while preserving its inherent orthogonal structure. The underlying approach borrows from the classical Poisson differential equation in rigid-body rotational kinematics and endows certain manifold attractivity features within the adaptive estimation algorithm. Consequently, we are not only able to efficiently handle the non-affine and non-convex nature of the parameter uncertainty, but are also ensured of estimation algorithm stability and robustness under bounded measurement noise. In addition to a rigorous discussion on the overall methodology, the paper provides example simulations that help demonstrate the effectiveness of the attracting manifolds design.
Manifold regularized multitask feature learning for multimodality disease classification.
Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang
2015-02-01
Multimodality based methods have shown great advantages in classification of Alzheimer's disease (AD) and its prodromal stage, that is, mild cognitive impairment (MCI). Recently, multitask feature selection methods are typically used for joint selection of common features across multiple modalities. However, one disadvantage of existing multimodality based methods is that they ignore the useful data distribution information in each modality, which is essential for subsequent classification. Accordingly, in this paper we propose a manifold regularized multitask feature learning method to preserve both the intrinsic relatedness among multiple modalities of data and the data distribution information in each modality. Specifically, we denote the feature learning on each modality as a single task, and use group-sparsity regularizer to capture the intrinsic relatedness among multiple tasks (i.e., modalities) and jointly select the common features from multiple tasks. Furthermore, we introduce a new manifold-based Laplacian regularizer to preserve the data distribution information from each task. Finally, we use the multikernel support vector machine method to fuse multimodality data for eventual classification. Conversely, we also extend our method to the semisupervised setting, where only partial data are labeled. We evaluate our method using the baseline magnetic resonance imaging (MRI), fluorodeoxyglucose positron emission tomography (FDG-PET), and cerebrospinal fluid (CSF) data of subjects from AD neuroimaging initiative database. The experimental results demonstrate that our proposed method can not only achieve improved classification performance, but also help to discover the disease-related brain regions useful for disease diagnosis. © 2014 Wiley Periodicals, Inc.
Black-Box Optimization Using Geodesics in Statistical Manifolds
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Jérémy Bensadon
2015-01-01
Full Text Available Information geometric optimization (IGO is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function on a Riemannian manifold, defining a parametrization-invariant first order differential equation and, thus, yielding an approximately parametrization-invariant algorithm (up to second order in the step size. We define the geodesic IGO update, a fully parametrization-invariant algorithm using the Riemannian structure, and we compute it for the manifold of Gaussians, thanks to Noether’s theorem. However, in similar algorithms, such as CMA-ES (Covariance Matrix Adaptation - Evolution Strategy and xNES (exponential Natural Evolution Strategy, the time steps for the mean and the covariance are decoupled. We suggest two ways of doing so: twisted geodesic IGO (GIGO and blockwise GIGO. Finally, we show that while the xNES algorithm is not GIGO, it is an instance of blockwise GIGO applied to the mean and covariance matrix separately. Therefore, xNES has an almost parametrization-invariant description.
On nondegenerate umbilical affine hypersurfaces in recurrent affine manifolds
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Zbigniew Olszak
2004-05-01
Full Text Available Let $widetilde{M}$ be a differentiable manifold of dimension $geqslant 5$, which is endowed with a (torsion-free affine connection $widetildeabla$ of recurrent curvature. Let $M$ be a nondegenerate umbilical affine hypersurface in $widetilde{M}$, whose shape operator does not vanish at every point of $M$. Denote by $abla$ and $h$, respectively, the affine connection and the affine metric induced on $M$ from the ambient manifold. Under the additional assumption that the induced connection $abla$ is related to the Levi-Civita connection $abla^{ast}$ of $h$ by the formula [ abla_XY = abla_X^{ast}Y + varphi(XY + varphi(YX + h(X,YE, ] $varphi$ being a $1$-form and $E$ a vector field on $M$, it is proved that the affine metric $h$ is conformally flat. Relations to totally umbilical pseudo-Riemannian hypersurfaces are also discussed. In this paper, certain ideas from my unpublished report [14] (cf. also [15] are generalized.
Geography of Spin Symplectic Four-Manifolds With Abelian Fundamental Group
Torres, Rafael
2011-01-01
We study the geography and botany of symplectic spin four-manifolds with abelian fundamental group. By building on the constructions of J. Park and of B. D. Park and Szabó, we can give alternative proofs and extend several results on the geography of simply connected four-manifolds to the nonsimply connected realm.
Black Strings, Black Rings and State-space Manifold
Bellucci, Stefano
2011-01-01
State-space geometry is considered, for diverse three and four parameter non-spherical horizon rotating black brane configurations, in string theory and $M$-theory. We have explicitly examined the case of unit Kaluza-Klein momentum $D_1D_5P$ black strings, circular strings, small black rings and black supertubes. An investigation of the state-space pair correlation functions shows that there exist two classes of brane statistical configurations, {\\it viz.}, the first category divulges a degenerate intrinsic equilibrium basis, while the second yields a non-degenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating $D_1D_5$ black strings and three charged rotating small black rings consort real degenerate state-space manifolds. Interestingly, arbitrary valued $M_5$-dipole charged rotating circular strings and Maldacena Strominger Witten black rings exhibit non-degenerate, positively curved, comprehensively regular state-space con...
Numerical Manifold Method with Endochronic Theory for Elastoplasticity Analysis
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Wei Zeng
2014-01-01
Full Text Available Numerical manifold method (NMM was originally developed based on linear elastic constitutive model. For many problems it is difficult to obtain accurate results without elastoplasticity analysis, and an elastoplasticity version of NMM is needed. In this paper, the incremental endochronic theory is extended into NMM analysis and an endochronic NMM algorithm is proposed for elastoplasticity analysis. It is well known that endochronic theory is one of the widely used elastoplasticity theories which can deal with elastoplasticity problems without a yield surface and loading or unloading judgments. Numerical tests show that the proposed algorithm of endochronic NMM possesses a good accuracy. The proposed algorithm is also applied to analyze a crack problem and a soft clay foundation under traffic loading problem. Results demonstrate the convenience of the endochronic NMM in analyzing elastoplasticity discontinuous problems.
RELATIVE CAMERA POSE ESTIMATION METHOD USING OPTIMIZATION ON THE MANIFOLD
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C. Cheng
2017-05-01
Full Text Available To solve the problem of relative camera pose estimation, a method using optimization with respect to the manifold is proposed. Firstly from maximum-a-posteriori (MAP model to nonlinear least squares (NLS model, the general state estimation model using optimization is derived. Then the camera pose estimation model is applied to the general state estimation model, while the parameterization of rigid body transformation is represented by Lie group/algebra. The jacobian of point-pose model with respect to Lie group/algebra is derived in detail and thus the optimization model of rigid body transformation is established. Experimental results show that compared with the original algorithms, the approaches with optimization can obtain higher accuracy both in rotation and translation, while avoiding the singularity of Euler angle parameterization of rotation. Thus the proposed method can estimate relative camera pose with high accuracy and robustness.
[Anomaly Detection of Multivariate Time Series Based on Riemannian Manifolds].
Xu, Yonghong; Hou, Xiaoying; Li Shuting; Cui, Jie
2015-06-01
Multivariate time series problems widely exist in production and life in the society. Anomaly detection has provided people with a lot of valuable information in financial, hydrological, meteorological fields, and the research areas of earthquake, video surveillance, medicine and others. In order to quickly and efficiently find exceptions in time sequence so that it can be presented in front of people in an intuitive way, we in this study combined the Riemannian manifold with statistical process control charts, based on sliding window, with a description of the covariance matrix as the time sequence, to achieve the multivariate time series of anomaly detection and its visualization. We made MA analog data flow and abnormal electrocardiogram data from MIT-BIH as experimental objects, and verified the anomaly detection method. The results showed that the method was reasonable and effective.
System theory on group manifolds and coset spaces.
Brockett, R. W.
1972-01-01
The purpose of this paper is to study questions regarding controllability, observability, and realization theory for a particular class of systems for which the state space is a differentiable manifold which is simultaneously a group or, more generally, a coset space. We show that it is possible to give rather explicit expressions for the reachable set and the set of indistinguishable states in the case of autonomous systems. We also establish a type of state space isomorphism theorem. Our objective is to reduce all questions about the system to questions about Lie algebras generated from the coefficient matrices entering in the description of the system and in that way arrive at conditions which are easily visualized and tested.
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.
Spectral Quasi-Equilibrium Manifold for Chemical Kinetics.
Kooshkbaghi, Mahdi; Frouzakis, Christos E; Boulouchos, Konstantinos; Karlin, Iliya V
2016-05-26
The Spectral Quasi-Equilibrium Manifold (SQEM) method is a model reduction technique for chemical kinetics based on entropy maximization under constraints built by the slowest eigenvectors at equilibrium. The method is revisited here and discussed and validated through the Michaelis-Menten kinetic scheme, and the quality of the reduction is related to the temporal evolution and the gap between eigenvalues. SQEM is then applied to detailed reaction mechanisms for the homogeneous combustion of hydrogen, syngas, and methane mixtures with air in adiabatic constant pressure reactors. The system states computed using SQEM are compared with those obtained by direct integration of the detailed mechanism, and good agreement between the reduced and the detailed descriptions is demonstrated. The SQEM reduced model of hydrogen/air combustion is also compared with another similar technique, the Rate-Controlled Constrained-Equilibrium (RCCE). For the same number of representative variables, SQEM is found to provide a more accurate description.
Face recognition based on LDA in manifold subspace
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Hung Phuoc Truong
2016-05-01
Full Text Available Although LDA has many successes in dimensionality reduction and data separation, it also has disadvantages, especially the small sample size problem in training data because the "within-class scatter" matrix may not be accurately estimated. Moreover, this algorithm can only operate correctly with labeled data in supervised learning. In practice, data collection is very huge and labeling data requires high-cost, thus the combination of a part of labeled data and unlabeled data for this algorithm in Manifold subspace is a novelty research. This paper reports a study that propose a semi-supervised method called DSLM, which aims at overcoming all these limitations. The proposed method ensures that the discriminative information of labeled data and the intrinsic geometric structure of data are mapped to new optimal subspace. Results are obtained from the experiments and compared to several related methods showing the effectiveness of our proposed method.
Space Manifold Dynamics Novel Spaceways for Science and Exploration
Perozzi, Ettore
2010-01-01
This book presents an overview of the outcomes resulting from applying the dynamical systems approach to space mission design, a topic referred to as "Space Manifold Dynamics" (SMD). It is a natural follow-on to the international workshop "Novel Spaceways for Scientific and Exploration Missions," which was held in October 2007 at the Telespazio Fucino Space Centre (Italy) under the auspices of the Space OPS Academy. The benefits and drawbacks of using the Lagrangian points and the associated trajectories for present and future space missions are discussed. The related methods and algorithms are also described in detail. Each topic is presented in articles that were written as far as possible to be self consistent; the use of introductory sections and of extended explanations is included in order to address the different communities potentially interested in SMD: space science, the aerospace industry, manned and unmanned exploration, celestial mechanics, and flight dynamics.
Wind Turbine Gearbox Fault Diagnosis Method Based on Riemannian Manifold
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Shoubin Wang
2014-01-01
Full Text Available As multivariate time series problems widely exist in social production and life, fault diagnosis method has provided people with a lot of valuable information in the finance, hydrology, meteorology, earthquake, video surveillance, medical science, and other fields. In order to find faults in time sequence quickly and efficiently, this paper presents a multivariate time series processing method based on Riemannian manifold. This method is based on the sliding window and uses the covariance matrix as a descriptor of the time sequence. Riemannian distance is used as the similarity measure and the statistical process control diagram is applied to detect the abnormity of multivariate time series. And the visualization of the covariance matrix distribution is used to detect the abnormity of mechanical equipment, leading to realize the fault diagnosis. With wind turbine gearbox faults as the experiment object, the fault diagnosis method is verified and the results show that the method is reasonable and effective.
Notions of the ergodic hierarchy for curved statistical manifolds
Gomez, Ignacio S.
2017-10-01
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and families of probability distributions belonging to the canonical ensemble, which for the case of the quadratic Hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law. From this, we obtain an information geometric method for studying Hamiltonian dynamics in the canonical ensemble. We illustrate the results with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2 × 2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.
Whale, Ben E; 10.1016/j.geomphys.2010.12.013
2011-01-01
We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the `edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on this `edge'. The ability to talk about the same objects, e.g., singularities, via different structures provides alternative routes for investigation which can be invaluable in the pursuit of physically motivated problems where certain types of information are unavailable or difficult to use.
Flow bench testing of prototype intake manifolds for ultralight aircraft engine
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Swiatek Piotr
2017-01-01
Full Text Available The article describes the research on the intake manifold for ultralight aircraft engine Vaxell 100i. It presents the actual and new redesigned manifold construction and points out the design requirements. The results of previously made numerical simulation of air flow inside the manifold are discussed. Computer analysis confirmed the appropriateness of internal guide vanes usage to improve the uniform air distribution between cylinders. For verification, a flow bench test stand was made for multicylinder intake manifold testing. A prototype manifold was built with the possibility of guide vane adjustment. The best variant had almost 5 times better uniformity of air distribution comparing to variant without the guide vane. Flow bench results confirmed the conclusions from numerical simulations.
Computation of Lickorish's Three Manifold Invariant Using Chern-Simons Theory
Ramadevi, P.; Naik, Swatee
It is well known that any three-manifold can be obtained by surgery on a framed link in S3. Lickorish gave an elementary proof for the existence of the three-manifold invariant of Witten using a framed link description of the manifold and the formalisation of the bracket polynomial as the Temperley-Lieb Algebra. Kaul determined a three-manifold invariant from link polynomials in SU(2) Chern-Simons theory. Lickorish's formula for the invariant involves computation of bracket polynomials of several cables of the link. We describe an easier way of obtaining the bracket polynomial of a cable using representation theory of composite braiding in SU(2) Chern-Simons theory. We prove that the cabling corresponds to taking tensor products of fundamental representations of SU(2). This enables us to verify that the two apparently distinct three-manifold invariants are equivalent for a specific relation of the polynomial variables.
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Haroun A.K. Shahad
2017-05-01
Full Text Available Hydrogen is a clean fuel for internal combustion engines as it produces only water vapor and nitrogen oxides when it burns. In this research, hydrogen is used as a blending fuel with diesel to reduce pollutants emission and to improve performance. It is inducted in the inlet manifold, (continuous manifold induction, which is of a single cylinder, four stroke, direct injection, variable compression ratio water cold diesel engine, type (Kirloskar. This technique of hydrogen blending is selected because of its simplicity and low cost. Hydrogen blending is built on the basis of energy replacement. A special electronic unit is designed and fabricated to control hydrogen blending ratio. The maximum achieved ratio is 30% of input energy and beyond that the engine operation becomes unsatisfactory. Tests are done with 17.5 compression ratio and 1500 rpm. The brake specific fuel consumption is reduced by 29% and the engine thermal efficiency increased by 16% at these operating conditions. The pollutant emissions of carbon oxides, UHC, and smoke opacity are dramatically decreased by 19.5%, 13%,and 45% respectively while NOx emission increased by 10%.
T4 fibrations over Calabi–Yau two-folds and non-Kähler manifolds in string theory
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Hai Lin
2016-08-01
Full Text Available We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial T4 fibrations over Calabi–Yau two-folds. These give rise to eight-dimensional non-Kähler Hermitian manifolds with SU(4 structure. The eight-manifold is also a circle fibration over a seven-dimensional G2 manifold with skew torsion. The eight-manifolds of this type appear as internal manifolds with SU(4 structure in type IIB string theory with F3 and F7 fluxes. These manifolds have generalized calibrated cycles in the presence of fluxes.
DEFF Research Database (Denmark)
Swann, Andrew Francis; Madsen, Thomas Bruun
2012-01-01
We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second...... and third Lie algebra Betti numbers are zero. We show that these form a special class of solvable Lie groups and provide a structural characterisation. We provide many examples of multi-moment maps for different geometries and use them to describe manifolds with holonomy contained in G(2) preserved by a two...
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Hossein Zare
Full Text Available Transcriptional networks consist of multiple regulatory layers corresponding to the activity of global regulators, specialized repressors and activators as well as proteins and enzymes shaping the DNA template. Such intrinsic complexity makes uncovering connections difficult and it calls for corresponding methodologies, which are adapted to the available data. Here we present a new computational method that predicts interactions between transcription factors and target genes using compendia of microarray gene expression data and documented interactions between genes and transcription factors. The proposed method, called Kernel Embedding of Regulatory Networks (KEREN, is based on the concept of gene-regulon association, and captures hidden geometric patterns of the network via manifold embedding. We applied KEREN to reconstruct transcription regulatory interactions on a genome-wide scale in the model bacteria Escherichia coli (E. coli. Application of the method not only yielded accurate predictions of verifiable interactions, which outperformed on certain metrics comparable methodologies, but also demonstrated the utility of a geometric approach in the analysis of high-dimensional biological data. We also described possible applications of kernel embedding techniques to other function and network discovery algorithms.
Zare, Hossein; Kaveh, Mostafa; Khodursky, Arkady
2011-01-01
Transcriptional networks consist of multiple regulatory layers corresponding to the activity of global regulators, specialized repressors and activators as well as proteins and enzymes shaping the DNA template. Such intrinsic complexity makes uncovering connections difficult and it calls for corresponding methodologies, which are adapted to the available data. Here we present a new computational method that predicts interactions between transcription factors and target genes using compendia of microarray gene expression data and documented interactions between genes and transcription factors. The proposed method, called Kernel Embedding of Regulatory Networks (KEREN), is based on the concept of gene-regulon association, and captures hidden geometric patterns of the network via manifold embedding. We applied KEREN to reconstruct transcription regulatory interactions on a genome-wide scale in the model bacteria Escherichia coli (E. coli). Application of the method not only yielded accurate predictions of verifiable interactions, which outperformed on certain metrics comparable methodologies, but also demonstrated the utility of a geometric approach in the analysis of high-dimensional biological data. We also described possible applications of kernel embedding techniques to other function and network discovery algorithms.
King, Nathan D.; Ruuth, Steven J.
2017-05-01
Maps from a source manifold M to a target manifold N appear in liquid crystals, color image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance color images.
Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds
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M. D. Siddiqi
2017-12-01
Full Text Available In the present paper, we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\
The parameterization method for invariant manifolds from rigorous results to effective computations
Haro, Àlex; Figueras, Jordi-Lluis; Luque, Alejandro; Mondelo, Josep Maria
2016-01-01
This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.
From Stein to Weinstein and back symplectic geometry of affine complex manifolds
Cieliebak, Kai
2013-01-01
A beautiful and comprehensive introduction to this important field. -Dusa McDuff, Barnard College, Columbia University This excellent book gives a detailed, clear, and wonderfully written treatment of the interplay between the world of Stein manifolds and the more topological and flexible world of Weinstein manifolds. Devoted to this subject with a long history, the book serves as a superb introduction to this area and also contains the authors' new results. -Tomasz Mrowka, MIT This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine co
de Hoop, Maarten V.; Ilmavirta, Joonas
2017-12-01
We study ray transforms on spherically symmetric manifolds with a piecewise C1, 1 metric. Assuming the Herglotz condition, the x-ray transform is injective on the space of L 2 functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a C1, 1 metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.
Applications of lagrangian coherent structures to expression of invariant manifolds in astrodynamics
Qi, Rui; Xu, Shi Jie
2014-05-01
This paper investigates the relationship between invariant manifold and Lagrangian coherent structure (LCS) in dynamical systems. LCS is defined as the ridge of finite-time Lyapunov exponent (FTLE) field, and is proving to be excellent platform for studies of stable and unstable manifold in flows with arbitrary time dependence. In this study, the LCS tool is applied to autonomous systems, simple pendulum and planar circular restricted three-body problem (PCR3BP), and also non-autonomous ones, double-gyre flow and bicircular problem (BCP). A comparison between LCS and invariant manifold is presented.
Yin, Aijun; Gou, Yanli; Ran, Hongbin; Li, Jiang
2017-08-01
Eddy current pulsed thermography (ECPT) has been extensively used for detection and evaluation of conductive material defect, in that spatial-transient-stage thermography implies crucial information about material properties. This paper presents a material state evaluation method using multidimensional manifold space projection and similarity measurement of principal curves to characterize and track the variation of material properties. The mathematical theories about manifold space projection and principal curves extraction have been introduced and the corresponding physical models are established. The simulations and real experiments are conducted to validate the proposed method. The combination of manifold learning method with ECPT has shown promising potential in characterizing and tracking material properties.
Covariant Schrödinger semigroups on Riemannian manifolds
Güneysu, Batu
2017-01-01
This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also inc...
Noise reduction in intracranial pressure signal using causal shape manifolds.
Rajagopal, Abhejit; Hamilton, Robert B; Scalzo, Fabien
2016-07-01
We present the Iterative/Causal Subspace Tracking framework (I/CST) for reducing noise in continuously monitored quasi-periodic biosignals. Signal reconstruction of the basic segments of the noisy signal (e.g. beats) is achieved by projection to a reduced space on which probabilistic tracking is performed. The attractiveness of the presented method lies in the fact that the subspace, or manifold, is learned by incorporating temporal, morphological, and signal elevation constraints, so that segment samples with similar shapes, and that are close in time and elevation, are also close in the subspace representation. Evaluation of the algorithm's effectiveness on the intracranial pressure (ICP) signal serves as a practical illustration of how it can operate in clinical conditions on routinely acquired biosignals. The reconstruction accuracy of the system is evaluated on an idealized 20-min ICP recording established from the average ICP of patients monitored for various ICP related conditions. The reconstruction accuracy of the ground truth signal is tested in presence of varying levels of additive white Gaussian noise (AWGN) and Poisson noise processes, and measures significant increases of 758% and 396% in the average signal-to-noise ratio (SNR).
Multimodal Medical Image Fusion by Adaptive Manifold Filter
Directory of Open Access Journals (Sweden)
Peng Geng
2015-01-01
Full Text Available Medical image fusion plays an important role in diagnosis and treatment of diseases such as image-guided radiotherapy and surgery. The modified local contrast information is proposed to fuse multimodal medical images. Firstly, the adaptive manifold filter is introduced into filtering source images as the low-frequency part in the modified local contrast. Secondly, the modified spatial frequency of the source images is adopted as the high-frequency part in the modified local contrast. Finally, the pixel with larger modified local contrast is selected into the fused image. The presented scheme outperforms the guided filter method in spatial domain, the dual-tree complex wavelet transform-based method, nonsubsampled contourlet transform-based method, and four classic fusion methods in terms of visual quality. Furthermore, the mutual information values by the presented method are averagely 55%, 41%, and 62% higher than the three methods and those values of edge based similarity measure by the presented method are averagely 13%, 33%, and 14% higher than the three methods for the six pairs of source images.
Inertial Manifold and Large Deviations Approach to Reduced PDE Dynamics
Cardin, Franco; Favretti, Marco; Lovison, Alberto
2017-09-01
In this paper a certain type of reaction-diffusion equation—similar to the Allen-Cahn equation—is the starting point for setting up a genuine thermodynamic reduction i.e. involving a finite number of parameters or collective variables of the initial system. We firstly operate a finite Lyapunov-Schmidt reduction of the cited reaction-diffusion equation when reformulated as a variational problem. In this way we gain a finite-dimensional ODE description of the initial system which preserves the gradient structure of the original one and that is exact for the static case and only approximate for the dynamic case. Our main concern is how to deal with this approximate reduced description of the initial PDE. To start with, we note that our approximate reduced ODE is similar to the approximate inertial manifold introduced by Temam and coworkers for Navier-Stokes equations. As a second approach, we take into account the uncertainty (loss of information) introduced with the above mentioned approximate reduction by considering the stochastic version of the ODE. We study this reduced stochastic system using classical tools from large deviations, viscosity solutions and weak KAM Hamilton-Jacobi theory. In the last part we suggest a possible use of a result of our approach in the comprehensive treatment non equilibrium thermodynamics given by Macroscopic Fluctuation Theory.
Topological field theories on manifolds with Wu structures
Monnier, Samuel
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4ℓ + 3 endowed with a Wu structure of degree 2ℓ + 2. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf-Witten theories. We take a general point of view where the Chern-Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern-Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the ℓ = 1 case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with (2, 0) supersymmetry, as will be discussed elsewhere.
Indoor localization using unsupervised manifold alignment with geometry perturbation
Majeed, Khaqan
2014-04-01
The main limitation of deploying/updating Received Signal Strength (RSS) based indoor localization is the construction of fingerprinted radio map, which is quite a hectic and time-consuming process especially when the indoor area is enormous and/or dynamic. Different approaches have been undertaken to reduce such deployment/update efforts, but the performance degrades when the fingerprinting load is reduced below a certain level. In this paper, we propose an indoor localization scheme that requires as low as 1% fingerprinting load. This scheme employs unsupervised manifold alignment that takes crowd sourced RSS readings and localization requests as source data set and the environment\\'s plan coordinates as destination data set. The 1% fingerprinting load is only used to perturb the local geometries in the destination data set. Our proposed algorithm was shown to achieve less than 5 m mean localization error with 1% fingerprinting load and a limited number of crowd sourced readings, when other learning based localization schemes pass the 10 m mean error with the same information.
Descriptor Learning via Supervised Manifold Regularization for Multioutput Regression.
Zhen, Xiantong; Yu, Mengyang; Islam, Ali; Bhaduri, Mousumi; Chan, Ian; Li, Shuo
2017-09-01
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.
Type IIA orientifolds on SU(2)-structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Danckaert, Thomas
2010-11-15
We investigate the possible supersymmetry-preserving orientifold projections of type IIA string theory on a six-dimensional background with SU(2)-structure. We find two categories of projections which preserve half of the low-energy supersymmetry, reducing the effective theory from an N=4 supergravity theory, to an N=2 supergravity. For these two cases, we impose the projection on the low-energy spectrum and reduce the effective N=4 supergravity action accordingly. We can identify the resulting gauged N=2 supergravity theory and bring the action into canonical form. We compute the scalar moduli spaces and characterize the gauged symmetries in terms of the geometry of these moduli spaces. Due to their origin in N=4 supergravity, which is a highly constrained theory, the moduli spaces are of a very simple form. We find that, for suitable background manifolds, isometries in all scalar sectors can become gauged. The obtained gaugings share many features with those of N=2 supergravities obtained previously from other G-structure compactifications. (orig.)
Hyperspectral image filtering with adaptive manifold for classification
Xie, Weiying; Li, Yunsong; Zhou, Weiping
2017-05-01
Hyperspectral image (HSI) is a three-dimensional data cube containing two spatial information dimensions and one spectral information dimension. The spectral vectors of different classes may have similar tendency and value that may bring about negative influences on classification. It is, therefore, important to introduce signal preprocessing techniques in the spatial domain to improve classification accuracy of HSIs. Assuming that local pixels in HSI have some correlations with each other, this paper proposes a spatial filtering model based on adaptive manifold (AM) for HSI. The AM for spatial filtering emphasizes the similar neighboring pixels and is robust to resist the noisy points with fast speed. The rich information in the filtered data is effective for improving the performance of the subsequent classification. The filtered data are classified by an extreme learning machine (ELM). The experimental results indicate that the framework built based on AM and ELM provides competitive performance. Specifically, by classifying the filtered data, the average accuracy of ELM can be improved as high as 30.54%, while performing tens to hundreds times faster than those state-of-the-art classifiers.
Pseudo-Reimannian manifolds endowed with an almost para f-structure
Directory of Open Access Journals (Sweden)
Vladislav V. Goldberg
1985-01-01
Full Text Available Let M˜(U,Ω˜,η˜,ξ,g˜ be a pseudo-Riemannian manifold of signature (n+1,n. One defines on M˜ an almost cosymplectic para f-structure and proves that a manifold M˜ endowed with such a structure is ξ-Ricci flat and is foliated by minimal hypersurfaces normal to ξ, which are of Otsuki's type. Further one considers on M˜ a 2(n−1-dimensional involutive distribution P⊥ and a recurrent vector field V˜. It is proved that the maximal integral manifold M⊥ of P⊥ has V as the mean curvature vector (up to 1/2(n−1. If the complimentary orthogonal distribution P of P⊥ is also involutive, then the whole manifold M˜ is foliate. Different other properties regarding the vector field V˜ are discussed.
Deep Manifold Learning Combined With Convolutional Neural Networks for Action Recognition.
Chen, Xin; Weng, Jian; Lu, Wei; Xu, Jiaming; Weng, Jiasi
2017-09-15
Learning deep representations have been applied in action recognition widely. However, there have been a few investigations on how to utilize the structural manifold information among different action videos to enhance the recognition accuracy and efficiency. In this paper, we propose to incorporate the manifold of training samples into deep learning, which is defined as deep manifold learning (DML). The proposed DML framework can be adapted to most existing deep networks to learn more discriminative features for action recognition. When applied to a convolutional neural network, DML embeds the previous convolutional layer's manifold into the next convolutional layer; thus, the discriminative capacity of the next layer can be promoted. We also apply the DML on a restricted Boltzmann machine, which can alleviate the overfitting problem. Experimental results on four standard action databases (i.e., UCF101, HMDB51, KTH, and UCF sports) show that the proposed method outperforms the state-of-the-art methods.
Directory of Open Access Journals (Sweden)
Feng Qi
2014-10-01
Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.
Towards representation of a perceptual color manifold using associative memory for color constancy.
Seow, Ming-Jung; Asari, Vijayan K
2009-01-01
In this paper, we propose the concept of a manifold of color perception through empirical observation that the center-surround properties of images in a perceptually similar environment define a manifold in the high dimensional space. Such a manifold representation can be learned using a novel recurrent neural network based learning algorithm. Unlike the conventional recurrent neural network model in which the memory is stored in an attractive fixed point at discrete locations in the state space, the dynamics of the proposed learning algorithm represent memory as a nonlinear line of attraction. The region of convergence around the nonlinear line is defined by the statistical characteristics of the training data. This learned manifold can then be used as a basis for color correction of the images having different color perception to the learned color perception. Experimental results show that the proposed recurrent neural network learning algorithm is capable of color balance the lighting variations in images captured in different environments successfully.
Proximal subgradient and a characterization of Lipschitz function on Riemannian manifolds
Ferreira, Orizon P.
2006-01-01
A characterization of Lipschitz behavior of functions defined on Riemannian manifolds is given in this paper. First, it is extended the concept of proximal subgradient and some results of proximal analysis from Hilbert space to Riemannian manifold setting. A technique introduced by Clarke, Stern and Wolenski [F.H. Clarke, R.J. Stern, P.R. Wolenski, Subgradient criteria for monotonicity, the Lipschitz condition, and convexity, Canad. J. Math. 45 (1993) 1167-1183], for generating proximal subgradients of functions defined on a Hilbert spaces, is also extended to Riemannian manifolds in order to provide that characterization. A number of examples of Lipschitz functions are presented so as to show that the Lipschitz behavior of functions defined on Riemannian manifolds depends on the Riemannian metric.
30 CFR 250.444 - What are the choke manifold requirements?
2010-07-01
... OIL AND GAS AND SULPHUR OPERATIONS IN THE OUTER CONTINENTAL SHELF Oil and Gas Drilling Operations... abrasiveness of drilling fluids and well fluids that you may encounter. (b) Choke manifold components must have...
High-order parameterization of (un)stable manifolds for hybrid maps: Implementation and applications
Naudot, Vincent; Mireles James, J. D.; Lu, Qiuying
2017-12-01
In this work we study, from a numerical point of view, the (un)stable manifolds of a certain class of dynamical systems called hybrid maps. The dynamics of these systems are generated by a two stage procedure: the first stage is continuous time advection under a given vector field, the second stage is discrete time advection under a given diffeomorphism. Such hybrid systems model physical processes where a differential equation is occasionally kicked by a strong disturbance. We propose a numerical method for computing local (un)stable manifolds, which leads to high order polynomial parameterization of the embedding. The parameterization of the invariant manifold is not the graph of a function and can follow folds in the embedding. Moreover we obtain a representation of the dynamics on the manifold in terms of a simple conjugacy relation. We illustrate the utility of the method by studying a planar example system.
Compactifications of heterotic theory on non-Kaehler complex manifolds, I
Becker, K; Das-Gupta, K; Green, P S
2003-01-01
We study new compactifications of the SO(32) heterotic string theory on compact complex non-Kaehler manifolds. These manifolds have many interesting features like fewer moduli, torsional constraints, vanishing Euler character and vanishing first Chern class, which make the four-dimensional theory phenomenologically attractive. We take a particular compact example studied earlier and determine various geometrical properties of it. In particular we calculate the warp factor and study the sigma model description of strings propagating on these backgrounds. The anomaly cancellation condition and enhanced gauge symmetry are shown to arise naturally in this framework, if one considers the effect of singularities carefully. We then give a detailed mathematical analysis of these manifolds and construct a large class of them. The existence of a holomorphic (3,0) form is important for the construction. We clarify some of the topological properties of these manifolds and evaluate the Betti numbers. We also determine the...
Gain Scheduling Control of Nonlinear Shock Motion Based on Equilibrium Manifold Linearization Model
National Research Council Canada - National Science Library
Cui Tao Yu Daren Bao Wen Yang Yongbin
2007-01-01
The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model...
The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds
Dunajski, Maciej
1998-01-01
The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a potential that generalises Plebanski's second heavenly equation for hyper-Kahler 4-manifolds. A class of examples of hyper-Hermitian metrics which depend on two arbitrary functions of two complex variables is given. The twistor theory of four-dimensional hyper-Hermitian manifolds is formulated as a combination of the Nonlinear Graviton Construction with the Ward transform for anti-self-dual Maxwell f...
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.
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.
On the geometry of Riemannian manifolds with a Lie structure at infinity
Directory of Open Access Journals (Sweden)
Bernd Ammann
2004-01-01
Full Text Available We study a generalization of the geodesic spray and give conditions for noncomapct manifolds with a Lie structure at infinity to have positive injectivity radius. We also prove that the geometric operators are generated by the given Lie algebra of vector fields. This is the first one in a series of papers devoted to the study of the analysis of geometric differential operators on manifolds with Lie structure at infinity.
Some cosmological implications and restrictions from geometry and topology of 3 and 4 manifolds
Asselmeyer-Maluga, Torsten; Król, Jerzy
2013-02-01
We show that the requirement of contractability and smoothness of certain 4-manifolds representing the cosmic evolution restricts the possible spatial models. In particular certain models like the Poincare sphere are excluded. Turning to the case of a fake S3×R it is argued that the inflation can be explained by the exotic smooth structure of this 4-manifold. Finally, we discuss the exotic R4 to which we assign a gravitational instanton.
Platonic polyhedra tune the three-sphere: II. Harmonic analysis on cubic spherical three-manifolds
Energy Technology Data Exchange (ETDEWEB)
Kramer, Peter [Institut fuer Theoretische Physik, University Tuebingen (Germany)], E-mail: peter.kramer@uni-tuebingen.de
2009-08-15
From the homotopy groups of two distinct cubic spherical three-manifolds, we construct the isomorphic groups of deck transformations acting on the three-sphere. These groups become the cyclic group of order eight and the quaternion group, respectively. By reduction of representations from the orthogonal group to the identity representation of these subgroups we provide two subgroup-periodic bases for the harmonic analysis on the three-manifolds, which have applications to cosmic topology.
Kharlamov, Mikhail P.; Savushkin, Alexander Y.
2008-01-01
In the phase space of the integrable Hamiltonian system with three degrees of freedom used to describe the motion of a Kowalevski-type top in a double constant force field, we point out the four-dimensional invariant manifold. It is shown that this manifold consists of critical motions generating a smooth sheet of the bifurcation diagram, and the induced dynamic system is Hamiltonian with certain subset of points of degeneration of the symplectic structure. We find the transformation separati...
Stability of The Synchronization Manifold in An All-To-All Time LAG- Diffusively Coupled Oscillators
Directory of Open Access Journals (Sweden)
Adu A.M. Wasike
2009-06-01
Full Text Available we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting.
Sacchelli, Ludovic; Sigalotti, Mario
2017-01-01
In this article we study the validity of the Whitney $C^1$ extension property for horizontal curves in sub-Riemannian manifolds endowed with 1-jets that satisfy a first-order Taylor expansion compatibility condition. We first consider the equiregular case, where we show that the extension property holds true whenever a suitable non-singularity property holds for the input-output maps on the Carnot groups obtained by nilpotent approximation. We then discuss the case of sub-Riemannian manifolds...
Definability and stability of multiscale decompositions for manifold-valued data
Grohs, Philipp
2012-06-01
We discuss multiscale representations of discrete manifold-valued data. As it turns out that we cannot expect general manifold analogs of biorthogonal wavelets to possess perfect reconstruction, we focus our attention on those constructions which are based on upscaling operators which are either interpolating or midpoint-interpolating. For definable multiscale decompositions we obtain a stability result. © 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Soft-group-manifold structure of supergravity, and the proof of unitarity
Energy Technology Data Exchange (ETDEWEB)
Thierry-Mieg, J.; Ne' eman, Y.
1979-01-01
The Soft Group Manifold (SGM) method of gauging a non-internal group is reviewed. Applications to three different versions of Extended Supergravity are presented. Then the geometric identification of the ghost fields and BRS equations, another aspect of the Group Manifold method, is summarized. The results are applied to Supergravity, and a completion of the proof of Unitarity of Sterman, Townsend, and Van Nieuwenhuizen is provided. 3 figures.
Estimating Turaev-Viro three-manifold invariants is universal for quantum computation
Alagic, Gorjan; Jordan, Stephen P.; König, Robert; Reichardt, Ben W.
2010-01-01
The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-dimensional topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem ef...
Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation
Alagic, Gorjan; Jordan, Stephen P.; Koenig, Robert; Reichardt, Ben W.
2010-01-01
The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-D topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently ...
Wang, Wen; Wang, Ruiping; Huang, Zhiwu; Shan, Shiguang; Chen, Xilin
To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more
Invariant Manifolds and the Transport and Capture of Comet Shoemaker-Levy 9
Swenson, Travis; Lo, Martin W.
2017-06-01
Poincaré stated that “periodic orbits” are the only means by which we can understand the dynamics of differential equations. The objects he really meant are the “invariant manifolds of periodic orbits” which he discovered. It was the intersection of invariant manifolds that led to his discovery of homoclinic orbits and deterministic chaos in his celebrated work on the 3 body problem. Koon, Lo, Marsden, Ross 2000 explained the theory of how invariant manifolds of periodic orbits around the L1 and L2 Lagrange points control the transport of small bodies between the 2:3 resonance outside of Jupiter’s orbit to the 3:2 resonance inside of Jupiter’s orbit. This resonance transition is exhibited by many members of the Jupiter Family of comets as shown by Howell, Marchand, and Lo 2001 computed in the JPL ephemeris model. These comets include Gehrels 3, Helin-Roman-Crockett, Oterma, and others. We present some recent work on the role of invariant manifolds for the capture and impact of comet Shoemaker-Levy9 (SL9). The comet underwent resonance transition in the Sun-Saturn three-body problem until it was captured by invariant manifolds of the Sun-Jupiter three-body problem. We show how these manifolds guided SL9 towards Jupiter and through the periodic orbits which act as gateways to Jupiter and the inner solar system. We demonstrate that invariant manifolds controlled the dynamics of capture, ultimately leading to the impact of SL9 in 1994.
Marlet, Renaud
2013-01-01
This book presents the principles and techniques of program specialization - a general method to make programs faster (and possibly smaller) when some inputs can be known in advance. As an illustration, it describes the architecture of Tempo, an offline program specializer for C that can also specialize code at runtime, and provides figures for concrete applications in various domains. Technical details address issues related to program analysis precision, value reification, incomplete program specialization, strategies to exploit specialized program, incremental specialization, and data speci
Some functional inequalities on non-reversible Finsler manifolds
Indian Academy of Sciences (India)
Proceedings – Mathematical Sciences. Current Issue : Vol. 127, Issue 5 · Current Issue Volume 127 | Issue 5. November 2017. Home · Volumes & Issues · Special Issues · Forthcoming Articles · Search · Editorial Board · Information for Authors · Subscription ...
A new proof of the theorem: Harmonic manifolds with minimal ...
Indian Academy of Sciences (India)
Proceedings – Mathematical Sciences. Current Issue : Vol. 127, Issue 5 · Current Issue Volume 127 | Issue 5. November 2017. Home · Volumes & Issues · Special Issues · Forthcoming Articles · Search · Editorial Board · Information for Authors · Subscription ...
Khan, Zulfiqar Hasan; Gu, Irene Yu-Hua
2013-12-01
This paper proposes a novel Bayesian online learning and tracking scheme for video objects on Grassmann manifolds. Although manifold visual object tracking is promising, large and fast nonplanar (or out-of-plane) pose changes and long-term partial occlusions of deformable objects in video remain a challenge that limits the tracking performance. The proposed method tackles these problems with the main novelties on: 1) online estimation of object appearances on Grassmann manifolds; 2) optimal criterion-based occlusion handling for online updating of object appearances; 3) a nonlinear dynamic model for both the appearance basis matrix and its velocity; and 4) Bayesian formulations, separately for the tracking process and the online learning process, that are realized by employing two particle filters: one is on the manifold for generating appearance particles and another on the linear space for generating affine box particles. Tracking and online updating are performed in an alternating fashion to mitigate the tracking drift. Experiments using the proposed tracker on videos captured by a single dynamic/static camera have shown robust tracking performance, particularly for scenarios when target objects contain significant nonplanar pose changes and long-term partial occlusions. Comparisons with eight existing state-of-the-art/most relevant manifold/nonmanifold trackers with evaluations have provided further support to the proposed scheme.
Multilayer Joint Gait-Pose Manifolds for Human Gait Motion Modeling.
Ding, Meng; Fan, Guolian
2015-11-01
We present new multilayer joint gait-pose manifolds (multilayer JGPMs) for complex human gait motion modeling, where three latent variables are defined jointly in a low-dimensional manifold to represent a variety of body configurations. Specifically, the pose variable (along the pose manifold) denotes a specific stage in a walking cycle; the gait variable (along the gait manifold) represents different walking styles; and the linear scale variable characterizes the maximum stride in a walking cycle. We discuss two kinds of topological priors for coupling the pose and gait manifolds, i.e., cylindrical and toroidal, to examine their effectiveness and suitability for motion modeling. We resort to a topologically-constrained Gaussian process (GP) latent variable model to learn the multilayer JGPMs where two new techniques are introduced to facilitate model learning under limited training data. First is training data diversification that creates a set of simulated motion data with different strides. Second is the topology-aware local learning to speed up model learning by taking advantage of the local topological structure. The experimental results on the Carnegie Mellon University motion capture data demonstrate the advantages of our proposed multilayer models over several existing GP-based motion models in terms of the overall performance of human gait motion modeling.
Parts-based stereoscopic image assessment by learning binocular manifold color visual properties
Xu, Haiyong; Yu, Mei; Luo, Ting; Zhang, Yun; Jiang, Gangyi
2016-11-01
Existing stereoscopic image quality assessment (SIQA) methods are mostly based on the luminance information, in which color information is not sufficiently considered. Actually, color is part of the important factors that affect human visual perception, and nonnegative matrix factorization (NMF) and manifold learning are in line with human visual perception. We propose an SIQA method based on learning binocular manifold color visual properties. To be more specific, in the training phase, a feature detector is created based on NMF with manifold regularization by considering color information, which not only allows parts-based manifold representation of an image, but also manifests localized color visual properties. In the quality estimation phase, visually important regions are selected by considering different human visual attention, and feature vectors are extracted by using the feature detector. Then the feature similarity index is calculated and the parts-based manifold color feature energy (PMCFE) for each view is defined based on the color feature vectors. The final quality score is obtained by considering a binocular combination based on PMCFE. The experimental results on LIVE I and LIVE Π 3-D IQA databases demonstrate that the proposed method can achieve much higher consistency with subjective evaluations than the state-of-the-art SIQA methods.
Improving head and body pose estimation through semi-supervised manifold alignment
Heili, Alexandre
2014-10-27
In this paper, we explore the use of a semi-supervised manifold alignment method for domain adaptation in the context of human body and head pose estimation in videos. We build upon an existing state-of-the-art system that leverages on external labelled datasets for the body and head features, and on the unlabelled test data with weak velocity labels to do a coupled estimation of the body and head pose. While this previous approach showed promising results, the learning of the underlying manifold structure of the features in the train and target data and the need to align them were not explored despite the fact that the pose features between two datasets may vary according to the scene, e.g. due to different camera point of view or perspective. In this paper, we propose to use a semi-supervised manifold alignment method to bring the train and target samples closer within the resulting embedded space. To this end, we consider an adaptation set from the target data and rely on (weak) labels, given for example by the velocity direction whenever they are reliable. These labels, along with the training labels are used to bias the manifold distance within each manifold and to establish correspondences for alignment.
Latash, Mark L
2017-12-23
The main goal of this paper is to introduce the concept of iso-perceptual manifold for perception of body configuration and related variables (kinesthetic perception) and to discuss its relation to the equilibrium-point hypothesis and the concepts of reference coordinate and uncontrolled manifold. Hierarchical control of action is postulated with abundant transformations between sets of spatial reference coordinates for salient effectors at different levels. Iso-perceptual manifold is defined in the combined space of afferent and efferent variables as the subspace corresponding to a stable percept. Examples of motion along an iso-perceptual manifold (perceptually equivalent motion) are considered during various natural actions. Some combinations of afferent and efferent signals, in particular those implying a violation of body's integrity, give rise to variable percepts by artificial projection onto iso-perceptual manifolds. This framework is used to interpret unusual features of vibration-induced kinesthetic illusions and to predict new illusions not yet reported in the literature. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.
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.
Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau
Aleshkin, Konstantin; Belavin, Alexander
2018-01-01
We clarify the recently proposed method for computing a special Kähler metric on a Calabi-Yau complex structure moduli space using the fact that the moduli space is a subspace of a particular Frobenius manifold. We use this method to compute a previously unknown special Kähler metric in a two-moduli non-Fermat model.
Conformal Killing Vectors Of Plane Symmetric Four Dimensional Lorentzian Manifolds
Khan, Suhail; Bokhari, Ashfaque H; Khan, Gulzar Ali; Mathematics, Department of; Peshawar, University of; Pakhtoonkhwa, Peshawar Khyber; Pakistan.,; Petroleum, King Fahd University of; Minerals,; 31261, Dhahran; Arabia, Saudi
2015-01-01
In this paper, we investigate conformal Killing's vectors (CKVs) admitted by some plane symmetric spacetimes. Ten conformal Killing's equations and their general forms of CKVs are derived along with their conformal factor. The existence of conformal Killing's symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. Considering the cases of time-like and inheriting CKVs, we obtain spacetimes admitting plane conformal symmetry. Integrability conditions are solved completely for some known non-conformally flat and conformally flat classes of plane symmetric spacetimes. A special vacuum plane symmetric spacetime is obtained, and it is shown that for such a metric CKVs are just the homothetic vectors (HVs). Among all the examples considered, there exists only one case with a six dimensional algebra of special CKVs admitting one proper CKV. In all other examples of non-conformally flat metrics, no proper ...
On Mesh Editing, Manifold Learning, and Diffusion Wavelets
Rustamov, R. M.
We spell out a formal equivalence between the naive Laplacian editing and semi-supervised learning by bi-Laplacian Regularized Least Squares. This allows us to write the solution to Laplacian mesh editing in a ‘closed’ form, based on which we introduce the Generalized Linear Editing (GLE). GLE has both naive Laplacian editing and gradient based editing as special cases. GLE allows using diffusion wavelets for mesh editing. We present preliminary experiments, and shortly discuss connections to segmentation.
Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points
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Bielawski Roger
2017-02-01
Full Text Available We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of GL(n, ℂ is isomorphic to the deformation of the D2-singularity if n = 2, the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if n = 3, and to the Atiyah-Hitchin manifold itself if n = 4. For higher n, such slices to the sum of two orbits, each having only two distinct eigenvalues, are either empty or biholomorphic to open subsets of the Hilbert scheme of points on one of the above surfaces. In particular, these open subsets of Hilbert schemes of points carry complete hyperkähler metrics. In the case of the double cover of the Atiyah-Hitchin manifold this metric turns out to be the natural L2-metric on a hyperkähler submanifold of the monopole moduli space.
Coherent Quantum Dynamics in Steady-State Manifolds of Strongly Dissipative Systems
Zanardi, Paolo; Campos Venuti, Lorenzo
2014-12-01
Recently, it has been realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit, we consider strongly dissipative quantum systems admitting a nontrivial manifold of steady states. We show how one can enact adiabatic coherent unitary manipulations, e.g., quantum logical gates, inside this steady-state manifold by adding a weak, time-rescaled, Hamiltonian term into the system's Liouvillian. The effective long-time dynamics is governed by a projected Hamiltonian which results from the interplay between the weak unitary control and the fast relaxation process. The leakage outside the steady-state manifold entailed by the Hamiltonian term is suppressed by an environment-induced symmetrization of the dynamics. We present applications to quantum-computation in decoherence-free subspaces and noiseless subsystems and numerical analysis of nonadiabatic errors.
Mielke, Alexander
1991-01-01
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists,...
A Set of Axioms for the Degree of a Tangent Vector Field on Differentiable Manifolds
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Furi Massimo
2010-01-01
Full Text Available Given a tangent vector field on a finite-dimensional real smooth manifold, its degree (also known as characteristic or rotation is, in some sense, an algebraic count of its zeros and gives useful information for its associated ordinary differential equation. When, in particular, the ambient manifold is an open subset of , a tangent vector field on can be identified with a map , and its degree, when defined, coincides with the Brouwer degree with respect to zero of the corresponding map . As is well known, the Brouwer degree in is uniquely determined by three axioms called Normalization, Additivity, and Homotopy Invariance. Here we shall provide a simple proof that in the context of differentiable manifolds the degree of a tangent vector field is uniquely determined by suitably adapted versions of the above three axioms.
A Set of Axioms for the Degree of a Tangent Vector Field on Differentiable Manifolds
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Marco Spadini
2010-01-01
Full Text Available Given a tangent vector field on a finite-dimensional real smooth manifold, its degree (also known as characteristic or rotation is, in some sense, an algebraic count of its zeros and gives useful information for its associated ordinary differential equation. When, in particular, the ambient manifold is an open subset U of ℝm, a tangent vector field v on U can be identified with a map v→:U→ℝm, and its degree, when defined, coincides with the Brouwer degree with respect to zero of the corresponding map v→. As is well known, the Brouwer degree in ℝm is uniquely determined by three axioms called Normalization, Additivity, and Homotopy Invariance. Here we shall provide a simple proof that in the context of differentiable manifolds the degree of a tangent vector field is uniquely determined by suitably adapted versions of the above three axioms.
The twisted photon associated to hyper-Hermitian four-manifolds
Dunajski, Maciej
1999-06-01
The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a pair of potentials that generalises Plebanski's second heavenly equation for hyper-Kähler four-manifolds. A class of examples of hyper-Hermitian metrics which depend on two arbitrary functions of two complex variables is given. The twistor theory of four-dimensional hyper-Hermitian manifolds is formulated as a combination of the Nonlinear Graviton Construction with the Ward transform for anti-self-dual Maxwell fields.
Upper bound theorem for odd-dimensional flag triangulations of manifolds
DEFF Research Database (Denmark)
Adamaszek, Michal Jan; Hladký, Jan
2016-01-01
We prove that among all flag triangulations of manifolds of odd dimension 2r-1, with a sufficient number of vertices, the unique maximizer of the entries of the f-, h-, g- and γ-vector is the balanced join of cycles. Our proof uses methods from extremal graph theory.......We prove that among all flag triangulations of manifolds of odd dimension 2r-1, with a sufficient number of vertices, the unique maximizer of the entries of the f-, h-, g- and γ-vector is the balanced join of cycles. Our proof uses methods from extremal graph theory....
Renormalization and 3-manifolds which fiber over the circle (AM-142)
McMullen, Curtis T
2014-01-01
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitativ
Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
DEFF Research Database (Denmark)
Spotti, Cristiano; Sun, Song
2017-01-01
We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds in all complex dimensions bigger than two (Fano K-moduli spaces). We also discuss potential applications to explicit study of moduli spaces of K-stable Fano...... manifolds with large anti-canonical volume. Our arguments are based on recent progress about the geometry of metric tangent cones and on related ideas about the algebro-geometric study of singularities of K-stable Fano varieties....
Whether Lyra's Manifold Itself is aHidden Source of Dark Energy
Singh, Kangujam Priyokumar; Singh, Koijam Manihar; Mollah, Mahbubur Rahman
2017-08-01
In the course of investigation of some interesting cosmic string universes in the five dimensional Lyra manifold it is excitingly found that the geometry itself of Lyra manifold behaves as a new source of dark energy and this energy takes a form similar to that of quintessence in most of the cases, though in one case the dark energy comes out to be that of the cosmological constant type. The behaviour of the universes and their contribution to the process of evolution are examined. Further study of such type of universes will be very helpful in explaining the present accelerated expansion behaviour of the universe.
Pompano subsea development: Template/manifold, tree and ROV intervention systems
Energy Technology Data Exchange (ETDEWEB)
Beckmann, M.M.; Byrd, M.L.; Holt, J.; Riley, J.W.; Snell, C.K.; Tyer, C.; Brewster, D.
1996-12-31
BP Exploration`s Pompano Subsea Development, in 1,865 ft of water in the Gulf of Mexico, uses a subsea production system to produce oil to a host platform 4{1/2} miles away. The 10-slot subsea template/manifold supports Through FlowLine (TFL) wells, which are controlled by means of an electrohydraulic control system. All process components of the system are retrievable with ROV intervention. This paper describes the template/manifold system, TFL tree system and ROV intervention systems.
Complexes and manifolds the mathematical works of J. H. C. Whitehead
James, I M
1962-01-01
The Mathematical Works of J. H. C. Whitehead, Volume 2: Complexes and Manifolds contains papers that are related in some way to the classification problem for manifolds, especially the Poincare conjecture, but towards the end one sees the gradual transition in the direction of algebraic topology. This volume includes all Whitehead's published work up to the year 1941, as well as a few later papers. The book begins with a list of Whitehead's works, in chronological order of writing. This is followed by separate chapters on topics such as analytical complexes; duality and intersection chains in
Geometry of hypersurfaces of a quarter symmetric non metric connection in a quasi-Sasakian manifold
Directory of Open Access Journals (Sweden)
Sh. Rahman
2016-01-01
Full Text Available The purpose of the paper is to study the notion of CR-submanifold and the existence of some structures on a hypersurface of a quarter symmetric non metric connection in a quasi-Sasakian manifold. We study the existence of a Kahler structure on $M$ and the existence of a globally metric frame $f$-structure in sence of Goldberg S.I., Yano K. We discuss the integrability of distributions on $M$ and geometry of their leaves. We have tries to relate this result with those before obtained by Goldberg V., Rosca R. devoted to Sasakian manifold and conformal connections.
Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
DEFF Research Database (Denmark)
Spotti, Cristiano; Sun, Song
We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds in all complex dimensions bigger than two (Fano K-moduli spaces). We also discuss potential applications to explicit study of moduli spaces of K-stable Fano...... manifolds with large anti-canonical volume. Our arguments are based on recent progress about the geometry of metric tangent cones and on related ideas about the algebro-geometric study of singularities of K-stable Fano varieties....
Generation of large-area microscale manifolds using excimer laser ablation
Zhou, Simon; Kilgo, Marvin M., III; Williams, Charles N.
1999-08-01
Excimer laser ablation of polymeric materials is a widely used technology for the generation of nozzles and through- holes. Ablation is also a viable process to create more complex fluidic structures such as channels and manifolds. This paper presents recent results of experiments demonstrating the creation of manifolds in 25 micrometers polyimide films. These structures include cross-over points, and channels of various widths. The results presented include photomicrographs and SEMS, and characterization of channel wall taper and width control as well as an assessment of ablation depth uniformity over large fields. The characteristics of projection ablation systems are reviewed, and the experimental system is described in detail.
Variational principles and symmetries on fibered multisymplectic manifolds
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Gaset Jordi
2016-12-01
Full Text Available The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (premulti-symplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws, symmetries, Cartan (Noether symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous mechanics.
Special vortex in relativistic hydrodynamics
Chupakhin, A. P.; Yanchenko, A. A.
2017-10-01
An exact solution of the Euler equations governing the flow of a compressible fluid in relativistic hydrodynamics is found and studied. It is a relativistic analogue of the Ovsyannikov vortex (special vortex) investigated earlier for classical gas dynamics. Solutions are partially invariant of Defect 1 and Rank 2 with respect to the rotation group. A theorem on the representation of the factor-system in the form of a union of a non-invariant subsystem for the function determining the deviation of the velocity vector from the meridian, and invariant subsystem for determination of thermodynamic parameters, the Lorentz factor and the radial velocity component is proved. Compatibility conditions for the overdetermined non-invariant subsystem are obtained. A stationary solution of this type is studied in detail. It is proved that its invariant subsystem reduces to an implicit differential equation. For this equation, the manifold of branching of solutions is investigated, and a set of singular points is found.
Diffusion in the special theory of relativity.
Herrmann, Joachim
2009-11-01
The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.
Srivastava, Vineet K.; Kumar, Jai; Kushvah, Badam Singh
2018-01-01
In this paper, we study the invariant manifold and its application in transfer trajectory problem from a low Earth parking orbit to the Sun-Earth L1 and L2-halo orbits with the inclusion of radiation pressure and oblateness. Invariant manifold of the halo orbit provides a natural entrance to travel the spacecraft in the solar system along some specific paths due to its strong hyperbolic character. In this regard, the halo orbits near both collinear Lagrangian points are computed first. The manifold's approximation near the nominal halo orbit is computed using the eigenvectors of the monodromy matrix. The obtained local approximation provides globalization of the manifold by applying backward time propagation to the governing equations of motion. The desired transfer trajectory well suited for the transfer is explored by looking at a possible intersection between the Earth's parking orbit of the spacecraft and the manifold.
Adaptive manifold-mapping using multiquadric interpolation applied to linear actuator design
D.J.P. Lahaye (Domenico); A. Canova; G. Gruosso; M. Repetto
2006-01-01
htmlabstractIn this work a multilevel optimization strategy based on manifold-mapping combined with multiquadric interpolation for the coarse model construction is presented. In the proposed approach the coarse model is obtained by interpolating the fine model using multiquadrics in a small
Random Wandering Around Homoclinic-like Manifolds in Symplectic Map Chain
Goto, Shin-itiro; Nozaki, Kazuhiro; Yamada, Hiroyasu
2001-01-01
We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour. It is found that the modulational instability in the reduced map triggers random wandering of orbits around some homoclinic-like manifolds, which is understood as the Bernoulli shifts.
Random Wandering around Homoclinic-Like Manifolds in a Symplectic Map Chain
Shin-itiro, GOTO; Kazuhiro, NOZAKI; Hiroyasu, YAMADA; Department of Physics, Nagoya University
2002-01-01
We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behavior. It is found that the modulational instability in the reduced map triggers random wandering of orbits around some homoclinic-like manifolds. This behavior is understood as Bernoulli shifts.
Pressure Losses in Multiple-Elbow Paths and in V-Bends of Hydraulic Manifolds
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Barbara Zardin
2017-06-01
Full Text Available Hydraulic manifolds are used to realize compact circuit layouts, but may introduce high pressure losses in the system because their design is usually oriented to achieving minimum size and weight more than reducing the pressure losses. The purpose of this work is to obtain the pressure losses when the internal connections within the manifold are creating complex paths for the fluid and the total loss cannot be calculated simply as the sum of the single losses. To perform the analysis both Computational Fluid Dynamic (CFD analysis and experimental tests have been executed. After the comparison between numerical and experimental results, it was possible to assess that the numerical analysis developed in this work is able to depict the correct trends of the pressure losses also when complex fluid path are realized in the manifold. Successively, the numerical analysis was used to calculate the pressure loss for inclined connections of channels (or V-bends, a solution that is sometimes adopted in manifolds to meet the design requirements aimed towards the minimum room-minimum weight objective.
Directory of Open Access Journals (Sweden)
Meiting Yu
2018-02-01
Full Text Available The extraction of a valuable set of features and the design of a discriminative classifier are crucial for target recognition in SAR image. Although various features and classifiers have been proposed over the years, target recognition under extended operating conditions (EOCs is still a challenging problem, e.g., target with configuration variation, different capture orientations, and articulation. To address these problems, this paper presents a new strategy for target recognition. We first propose a low-dimensional representation model via incorporating multi-manifold regularization term into the low-rank matrix factorization framework. Two rules, pairwise similarity and local linearity, are employed for constructing multiple manifold regularization. By alternately optimizing the matrix factorization and manifold selection, the feature representation model can not only acquire the optimal low-rank approximation of original samples, but also capture the intrinsic manifold structure information. Then, to take full advantage of the local structure property of features and further improve the discriminative ability, local sparse representation is proposed for classification. Finally, extensive experiments on moving and stationary target acquisition and recognition (MSTAR database demonstrate the effectiveness of the proposed strategy, including target recognition under EOCs, as well as the capability of small training size.
Normal Anti-Invariant Submanifolds of Paraquaternionic Kähler Manifolds
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Novac-Claudiu Chiriac
2006-12-01
Full Text Available We introduce normal anti-invariant submanifolds of paraquaternionic Kähler manifolds and study the geometric structures induced on them. We obtain necessary and sufficient conditions for the integrability of the distributions defined on a normal anti-invariant submanifold. Also, we present characterizations of local (global anti-invariant products.
Impulse/response functions of individual components of flow-injection manifolds
van Nugteren-Osinga, I.C.; Bos, M.; van der Linden, W.E.
1988-01-01
The dispersion behaviour of the various individual parts making up a flow-injection manifold is often difficult to establish because it is virtually impossible to obtainthe required very small injection and detection volumes. It is shown that it is possible, under suitable experimental conditions,
Norizan, A.; Rahman, M. T. A.; Amin, N. A. M.; Basha, M. H.; Ismail, M. H. N.; Hamid, A. F. A.
2017-10-01
This paper describes the design differences between the intake manifold and restrictor used in racing cars that participate in the Formula Student (FSAE) competition. To fulfil the criteria of rules and regulation of the race, each race car must have a restriction device that has a maximum diameter of 20 mm installed between the throttle body and intake manifold. To overcome these problems, a restrictor has been designed and analysed using the steady state analysis, to reduce the loss of pressure in the restrictor. Design of the restrictor has a fixed parameter of the maximum diameter of 20mm. There are some differences that have been taken to make the comparison between the design of the restrictor, the diameter of the inlet and outlet, the curvature of the surface, convergence and divergence angle and length of the restrictor. Intake manifold was designed based on the design of the chassis, which shall not exceed the envelope defined by the FSAE competition. A good intake manifold design will affect the performance of the engine. Each design have made an analysis designed to ensure that each cylinder engine gets its air evenly. To verify the design, steady state analysis was made for a total mass flow rate and the velocity of air leaving a runner in each engine. Data such as the engine MAP reading was recorded by using Haltech ECU Management Software as reference purposes.
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...
A novel multi-manifold classification model via path-based clustering for image retrieval
Zhu, Rong; Yuan, Zhijun; Xuan, Junying
2011-12-01
Nowadays, with digital cameras and mass storage devices becoming increasingly affordable, each day thousands of pictures are taken and images on the Internet are emerged at an astonishing rate. Image retrieval is a process of searching valuable information that user demanded from huge images. However, it is hard to find satisfied results due to the well known "semantic gap". Image classification plays an essential role in retrieval process. But traditional methods will encounter problems when dealing with high-dimensional and large-scale image sets in applications. Here, we propose a novel multi-manifold classification model for image retrieval. Firstly, we simplify the classification of images from high-dimensional space into the one on low-dimensional manifolds, largely reducing the complexity of classification process. Secondly, considering that traditional distance measures often fail to find correct visual semantics of manifolds, especially when dealing with the images having complex data distribution, we also define two new distance measures based on path-based clustering, and further applied to the construction of a multi-class image manifold. One experiment was conducted on 2890 Web images. The comparison results between three methods show that the proposed method achieves the highest classification accuracy.
Dumping topological charges on neighbors: ice manifolds for colloids and vortices
Nisoli, Cristiano
2014-11-01
We investigate the recently reported analogies between pinned vortices in nano-structured superconductors or colloids in optical traps, and spin ice materials. It has been found experimentally and numerically that both colloids and vortices exhibit ice or quasi-ice manifolds. However, the frustration of colloids and vortices differs essentially from spin ice at the vertex level. We show that the effective vertex energetics of the colloidal/vortex systems is made identical to that of spin ice materials by the contribution of an emergent field associated to the topological charge of the vertex. The similarity extends to the local low-energy dynamics of the ice manifold, where the effect of geometric hard constraints can be subsumed into the spatial modulation of the emergent field, which mediates an entropic interaction between topological charges. There, as in spin ice materials, genuine ice manifolds enter a Coulomb phase, whereas quasi-ice manifolds posses a well defined screening length, provided by a plasma of embedded topological charges. We also show that such similarities break down in lattices of mixed coordination because of topological charge transfer between sub-latices. This opens interesting perspective for extensions beyond physics, to social and economical networks.
Tensor calculus with open-source software: the SageManifolds project
Gourgoulhon, Eric; Mancini, Marco
2014-01-01
The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. As Sage itself, it is free, open-source and is based on the Python programming language. We discuss here some details of the implementation, which relies on Sage's category pattern, and present a concrete example of use.
Gauging isometries on hyperKahler cones and quaternion Kahler manifolds
Wit, Bernard de; Rocek, M.; Vandoren, S.
2001-01-01
We extend our previous results on the relation between quaternion-Kähler manifolds and hyperk¨ahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kähler space. As an example of the general construction, we discuss the gauging and
Particle Image Velocimetry and Computational Fluid Dynamics Analysis of Fuel Cell Manifold
DEFF Research Database (Denmark)
Lebæk, Jesper; Blazniak Andreasen, Marcin; Andresen, Henrik Assenholm
2010-01-01
The inlet effect on the manifold flow in a fuel cell stack was investigated by means of numerical methods (computational fluid dynamics) and experimental methods (particle image velocimetry). At a simulated high current density situation the flow field was mapped on a 70 cell simulated cathode...
Nehari manifold for non-local elliptic operator with concave–convex ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 125; Issue 4. Nehari manifold for non-local elliptic operator with concave–convex nonlinearities and sign-changing weight functions. Sarika Goyal K Sreenadh. Volume 125 Issue 4 November 2015 pp 545-558 ...
Granados, Albert
2017-08-01
Energy harvesting systems based on oscillators aim to capture energy from mechanical oscillations and convert it into electrical energy. Widely extended are those based on piezoelectric materials, whose dynamics are Hamiltonian submitted to different sources of dissipation: damping and coupling. These dissipations bring the system to low energy regimes, which is not desired in long term as it diminishes the absorbed energy. To avoid or to minimize such situations, we propose that the coupling of two oscillators could benefit from theory of Arnold diffusion. Such phenomenon studies O(1) energy variations in Hamiltonian systems and hence could be very useful in energy harvesting applications. This article is a first step towards this goal. We consider two piezoelectric beams submitted to a small forcing and coupled through an electric circuit. By considering the coupling, damping and forcing as perturbations, we prove that the unperturbed system possesses a 4-dimensional Normally Hyperbolic Invariant Manifold with 5 and 4-dimensional stable and unstable manifolds, respectively. These are locally unique after the perturbation. By means of the parameterization method, we numerically compute parameterizations of the perturbed manifold, its stable and unstable manifolds and study its inner dynamics. We show evidence of homoclinic connections when the perturbation is switched on.
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren
2010-01-01
and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...
Methodology for CFD Design Analysis of National Launch System Nozzle Manifold
Haire, Scot L.
1993-01-01
The current design environment dictates that high technology CFD (Computational Fluid Dynamics) analysis produce quality results in a timely manner if it is to be integrated into the design process. The design methodology outlined describes the CFD analysis of an NLS (National Launch System) nozzle film cooling manifold. The objective of the analysis was to obtain a qualitative estimate for the flow distribution within the manifold. A complex, 3D, multiple zone, structured grid was generated from a 3D CAD file of the geometry. A Euler solution was computed with a fully implicit compressible flow solver. Post processing consisted of full 3D color graphics and mass averaged performance. The result was a qualitative CFD solution that provided the design team with relevant information concerning the flow distribution in and performance characteristics of the film cooling manifold within an effective time frame. Also, this design methodology was the foundation for a quick turnaround CFD analysis of the next iteration in the manifold design.
Modelling the inner disc of the Milky Way with manifolds - I. A first step
Romero-Gomez, M.; Athanassoula, E.; Antoja Castelltort, Teresa; Figueras, F.
2011-01-01
We study the bar-driven dynamics in the inner part of the Milky Way by using invariant manifolds. This theory has been successfully applied to describe the morphology and kinematics of rings and spirals in external galaxies, and now, for the first time, we apply it to the Milky Way. In particular,
Generic Submanifolds of Nearly Kaehler Manifolds with Certain Parallel Canonical Structure
Zhu, Qingqing; Yang, Biaogui
2014-01-01
The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds, and CR-submanifolds. In this paper we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamental results in this paper will be obtained. PMID:27355057
Automorphisms of $\\mathbb C^k$ and associated compact complex manifolds
Renaud, Julie
2005-01-01
In this paper, we first construct $k$-dimensional compact complex manifolds from automorphisms of $\\mathbb{C}^k$ which admit a fixed attracting point at infinity. Then, we charactize the fundamental group as well as the universal covering of the attracting basin of this fixed point thanks to a generalization of the method described by T. Bousch in his thesis.
Side branch absorber for exhaust manifold of two-stroke internal combustion engine
Harris, Ralph E [San Antonio, TX; Broerman, III, Eugene L.; Bourn, Gary D [Laramie, WY
2011-01-11
A method of improving scavenging operation of a two-stroke internal combustion engine. The exhaust pressure of the engine is analyzed to determine if there is a pulsation frequency. Acoustic modeling is used to design an absorber. An appropriately designed side branch absorber may be attached to the exhaust manifold.
Constraints on spacetime manifold in Euclidean supergravity in terms of Dirac eigenvalues
Ciuhu, C.; Vancea, I. V.
1998-01-01
We generalize previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the spacetime manifold under which spacetime admits Dirac eigenvalues as observables, are derived.
A geometrical take on invariants of low-dimensional manifolds found by integration
Wintraecken, M.H.M.J.; Vegter, G.
2013-01-01
An elementary geometrical proof of the fact that the Euler characteristic is the only topological invariant of a surface that can be found by integration (using Gauss-Bonnet) is given. A similar method is also applied to three-dimensional manifolds. (C) 2013 Elsevier B.V. All rights reserved.
Durning, Joseph G., III; Westover, Shayne C.; Cone, Darren M.
2011-01-01
In June 2010, an 870 lbf Space Shuttle Orbiter Reaction Control System Primary Thruster experienced an unintended shutdown during a test being performed at the NASA White Sands Test Facility. Subsequent removal and inspection of the thruster revealed permanent deformation and misalignment of the thruster valve mounting plate. Destructive evaluation determined that after three nominal firing sequences, the thruster had experienced an energetic event within the fuel (monomethylhydrazine) manifold at the start of the fourth firing sequence. The current understanding of the phenomenon of intra-manifold explosions in hypergolic bipropellant thrusters is documented in literature where it is colloquially referred to as a ZOT. The typical ZOT scenario involves operation of a thruster in a gravitational field with environmental pressures above the triple point pressure of the propellants. Post-firing, when the thruster valves are commanded closed, there remains a residual quantity of propellant in both the fuel and oxidizer (nitrogen tetroxide) injector manifolds known as the "dribble volume". In an ambient ground test configuration, these propellant volumes will drain from the injector manifolds but are impeded by the local atmospheric pressure. The evacuation of propellants from the thruster injector manifolds relies on the fluids vapor pressure to expel the liquid. The higher vapor pressure oxidizer will evacuate from the manifold before the lower vapor pressure fuel. The localized cooling resulting from the oxidizer boiling during manifold draining can result in fuel vapor migration and condensation in the oxidizer passage. The liquid fuel will then react with the oxidizer that enters the manifold during the next firing and may produce a localized high pressure reaction or explosion within the confines of the oxidizer injector manifold. The typical ZOT scenario was considered during this failure investigation, but was ultimately ruled out as a cause of the explosion
Enhanced low-rank representation via sparse manifold adaption for semi-supervised learning.
Peng, Yong; Lu, Bao-Liang; Wang, Suhang
2015-05-01
Constructing an informative and discriminative graph plays an important role in various pattern recognition tasks such as clustering and classification. Among the existing graph-based learning models, low-rank representation (LRR) is a very competitive one, which has been extensively employed in spectral clustering and semi-supervised learning (SSL). In SSL, the graph is composed of both labeled and unlabeled samples, where the edge weights are calculated based on the LRR coefficients. However, most of existing LRR related approaches fail to consider the geometrical structure of data, which has been shown beneficial for discriminative tasks. In this paper, we propose an enhanced LRR via sparse manifold adaption, termed manifold low-rank representation (MLRR), to learn low-rank data representation. MLRR can explicitly take the data local manifold structure into consideration, which can be identified by the geometric sparsity idea; specifically, the local tangent space of each data point was sought by solving a sparse representation objective. Therefore, the graph to depict the relationship of data points can be built once the manifold information is obtained. We incorporate a regularizer into LRR to make the learned coefficients preserve the geometric constraints revealed in the data space. As a result, MLRR combines both the global information emphasized by low-rank property and the local information emphasized by the identified manifold structure. Extensive experimental results on semi-supervised classification tasks demonstrate that MLRR is an excellent method in comparison with several state-of-the-art graph construction approaches. Copyright © 2015 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Tauzia, Xavier; Maiboom, Alain; Shah, Samiur Rahman [Laboratoire de Mecanique des Fluides, UMR CNRS 6598, Internal Combustion Engine Team, Ecole Centrale de Nantes, BP 92101, 44321 Nantes Cedex 3 (France)
2010-09-15
This paper describes an experimental study conducted on a modern high speed common-rail automotive Diesel engine in order to evaluate the effects on combustion and pollutant emissions of water injected as a fine mist in the inlet manifold. First, a literature survey describing the several ways to introduce water in an internal combustion engine and reporting the main results from previous studies is presented. It is followed by a short description of the engine and experimental set-up. After that, various results are presented. A special focus is made on water injection (WI) cooling effect. Then, the influence of WI on ignition delay, rate of heat release, nitrogen oxides (NOx) and particulate matter (PM) emissions and engine efficiency is analysed, for various engine operating conditions (speed and load) and various amount of water (up to 4 times the amount of fuel injected). A comparison is made with exhaust gas recirculation to evaluate the potential of inlet WI as an in-cylinder emissions reduction device for automotive application. (author)
Rapid evolution of manifold CRISPR systems for plant genome editing
Directory of Open Access Journals (Sweden)
Yiping Qi
2016-11-01
Full Text Available Advanced CRISPR-Cas9 based technologies first validated in mammalian cell systems are quickly being adapted for use in plants. These new technologies increase CRISPR-Cas9’s utility and effectiveness by diversifying cellular capabilities through expression construct system evolution and enzyme orthogonality, as well as enhanced efficiency through delivery and expression mechanisms. Here, we review the current state of advanced CRISPR-Cas9 and Cpf1 capabilities in plants and cover the rapid evolution of these tools from first generation inducers of double strand breaks for basic genetic manipulations to second and third generation multiplexed systems with myriad functionalities, capabilities and specialized applications. We offer perspective on how to utilize these tools for currently untested research endeavors and analyze strengths and weaknesses of novel CRISPR systems in plants. Advanced CRISPR functionalities and delivery options demonstrated in plants are primarily reviewed but new technologies just coming to the forefront of CRISPR development, or those on the horizon, are briefly discussed. Topics covered are focused on the expansion of expression and delivery capabilities for CRISPR-Cas9 components and broadening targeting range through orthogonal Cas9 and Cpf1 proteins.
Jin, Dakai; Lu, Jia; Zhang, Xiaoliu; Chen, Cheng; Bai, ErWei; Saha, Punam K.
2017-03-01
Osteoporosis is associated with increased fracture risk. Recent advancement in the area of in vivo imaging allows segmentation of trabecular bone (TB) microstructures, which is a known key determinant of bone strength and fracture risk. An accurate biomechanical modelling of TB micro-architecture provides a comprehensive summary measure of bone strength and fracture risk. In this paper, a new direct TB biomechanical modelling method using nonlinear manifold-based volumetric reconstruction of trabecular network is presented. It is accomplished in two sequential modules. The first module reconstructs a nonlinear manifold-based volumetric representation of TB networks from three-dimensional digital images. Specifically, it starts with the fuzzy digital segmentation of a TB network, and computes its surface and curve skeletons. An individual trabecula is identified as a topological segment in the curve skeleton. Using geometric analysis, smoothing and optimization techniques, the algorithm generates smooth, curved, and continuous representations of individual trabeculae glued at their junctions. Also, the method generates a geometrically consistent TB volume at junctions. In the second module, a direct computational biomechanical stress-strain analysis is applied on the reconstructed TB volume to predict mechanical measures. The accuracy of the method was examined using micro-CT imaging of cadaveric distal tibia specimens (N = 12). A high linear correlation (r = 0.95) between TB volume computed using the new manifold-modelling algorithm and that directly derived from the voxel-based micro-CT images was observed. Young's modulus (YM) was computed using direct mechanical analysis on the TB manifold-model over a cubical volume of interest (VOI), and its correlation with the YM, computed using micro-CT based conventional finite-element analysis over the same VOI, was examined. A moderate linear correlation (r = 0.77) was observed between the two YM measures. This
Federal Laboratory Consortium — Supporting Navy special weapons, the division provides an array of engineering services, technical publication support services, logistics support services, safety...
Hadamard States for the Klein-Gordon Equation on Lorentzian Manifolds of Bounded Geometry
Gérard, Christian; Oulghazi, Omar; Wrochna, Michał
2017-06-01
We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime and the maximal globally hyperbolic extension of the Kerr outer region. In this setup, we give an approximate diagonalization and a microlocal decomposition of the Cauchy evolution using a time-dependent version of the pseudodifferential calculus on Riemannian manifolds of bounded geometry. We apply this result to construct all pure regular Hadamard states (and associated Feynman inverses), where regular refers to the state's two-point function having Cauchy data given by pseudodifferential operators. This allows us to conclude that there is a one-parameter family of elliptic pseudodifferential operators that encodes both the choice of (pure, regular) Hadamard state and the underlying spacetime metric.
Wilson loops on three-manifolds and their M2-brane duals
Energy Technology Data Exchange (ETDEWEB)
Farquet, Daniel; Sparks, James [Mathematical Institute, University of Oxford,Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG (United Kingdom)
2014-12-30
We compute the large N limit of Wilson loop expectation values for a broad class of N=2 supersymmetric gauge theories defined on a general class of background three-manifolds M{sub 3}, diffeomorphic to S{sup 3}. We find a simple closed formula which depends on the background geometry only through a certain supersymmetric Killing vector field. The supergravity dual of such a Wilson loop is an M2-brane wrapping the M-theory circle, together with a complex curve Σ{sub 2} in a self-dual Einstein manifold M{sub 4}, whose conformal boundary is M{sub 3}. We show that the regularized action of this M2-brane also depends only on the supersymmetric Killing vector, precisely reproducing the large N field theory computation.
Towards an Algebraic Classification of Calabi-Yau Manifolds; 1, Study of K3 Spaces
Anselmo, F; Nanopoulos, Dimitri V; Volkov, G
2001-01-01
We present an inductive algebraic approach to the systematic construction andclassification of generalized Calabi-Yau (CY) manifolds in different numbers ofcomplex dimensions, based on Batyrev's formulation of CY manifolds as toricvarieties in weighted complex projective spaces associated with reflexivepolyhedra. We show how the allowed weight vectors in lower dimensions may beextended to higher dimensions, emphasizing the roles of projection andintersection in their dual description, and the natural appearance ofCartan-Lie algebra structures. The 50 allowed extended four-dimensional vectorsmay be combined in pairs (triples) to form 22 (4) chains containing 90 (91) K3spaces, of which 94 are distinct, and one further K3 space is found usingduality. In the case of CY_3 spaces, pairs (triples) of the 10~270 allowedextended vectors yield 4242 (259) chains with K3 (elliptic) fibers containing730 additional K3 polyhedra. A more complete study of CY_3 spaces is left forlater work.
Directory of Open Access Journals (Sweden)
Morteza Pourmehdi
2016-04-01
Full Text Available In this manuscript, for the first time, a fractional-order manifold in a synergetic approach using a fractional order controller is introduced. Furtheremore, in the synergetic theory a macro variable is expended into a linear combination of state variables. An aim is to increase the convergence rate as well as time response of the whole closed loop system. Quality of the proposed controller is investigated to control and synchronize a nonlinear chaotic Coullet system in comparison with an integer order manifold synergetic controller. The stability of the proposed controller is proven using the Lyapunov method. In this regard stabilizing control effort is yielded. Simulation result confirm convergence of states towards zero. This is achieved through a control effort with fewer oscillations and lower amplitude of signls which confirm feasibility of the control effort in practice.KEYWORDS: synergetic control theory; fractional order system; synchronization; nonlinear chaotic Coullet system; chaos control
Material and technique of S i-Mo heatresistant vermicular iron exhaust manifold
Directory of Open Access Journals (Sweden)
Jin Yong-xi
2006-08-01
Full Text Available Si-Mo vermicular iron is an ideal material for exhaust manifold that works in high temperature and therm alcycle conditions because its properties oftherm alfatigue resistance and thermal distortion resistance are significantly better than that of gray cast iron and nodular iron. This paper explains that the verm icularity of Si-Mo verm icular iron is better to be controlled approxim ately to 50% for the applications of exhaust manifold castings, and generalizes the successful experience ofverm icularizing technique thatuses sandwich(pouroverprocess combining with cored-wire injection in trough process together,and uses rare earths-magnesium-silicon as verm icularizing alloy in Disa high speed molding line and autom atic plug rod airpressure pouring furnace. In addition, this paper also describes the method to solve the shrinkage hole and porosity defects in the exhaustm anifold production.
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.
Robust Optimization of Thermal Aspects of Friction Stir Welding Using Manifold Mapping Techniques
DEFF Research Database (Denmark)
Larsen, Anders Astrup; Lahaye, Domenico; Schmidt, Henrik Nikolaj Blicher
2008-01-01
The aim of this paper is to optimize a friction stir welding process taking robustness into account. The optimization problems are formulated with the goal of obtaining desired mean responses while reducing the variance of the response. We restrict ourselves to a thermal model of the process...... and use the manifold mapping technique to solve the optimization problems using a fast analytical coarse and an expensive accurate fine model. The statistics of the response are calculated using Taylor expansions and are compared to Monte Carlo simulations. The results show that the use of manifold...... mapping reduces the number of fine model evaluations required and that the Taylor expansion approach gives good results when compared to Monte Carlo simulations....
Air/fuel ratio for an internal combustion engine controlled by gas sensor in intake manifold
Energy Technology Data Exchange (ETDEWEB)
Barnard, D.D.
1978-08-22
In a closed loop fuel management system for an internal combustion engine, a gas sensor is positioned in the intake manifold and is responsive to a characteristic of the fuel mixture for generating an electrical control signal for controlling the metering of the fuel to the mixture. In the preferred embodiment, the air and fuel are mixed together and the resultant mixture passes by an oxygen gas sensor prior to being distributed to the cylinders through the intake manifold system. The output signal of the sensor is used for controlling the metering of the fuel. Fuel delivery correction delays due to transport lag in conventional closed loop fuel management systems using oxygen gas sensors are eliminated.
Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold
Grafke, Tobias; Vanden-Eijnden, Eric
2017-09-01
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within the realm of large deviation theory. It is shown that these non-equilibrium transitions make use of a reaction channel created by the bifurcation structure of the slow manifold, leading to vastly increased transition rates. Several examples are used to illustrate these findings, including an insect outbreak model, a system modeling phase separation in the presence of evaporation, and a system modeling transitions in active matter self-assembly. The last example involves a spatially extended system modeled by a stochastic partial differential equation.
Partition functions for equivariantly twisted N=2 gauge theories on toric Kähler manifolds
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Gomez, Diego; Schmude, Johannes [Department of Physics, Universidad de Oviedo,Avda. Calvo Sotelo 18, 33007, Oviedo (Spain)
2015-05-21
We consider N=2 supersymmetric pure gauge theories on toric Kähler manifolds, with particular emphasis on ℂℙ{sup 2}. By choosing a vector generating a U(1) action inside the torus of the manifold, we construct equivariantly twisted theories. Then, using localization, we compute their supersymmetric partition functions. As expected, these receive contributions from a classical, a one-loop, and an instanton term. It turns out that the one-loop term is trivial and that the instanton contributions are localized at the fixed points of the U(1). In fact the full partition function can be re-written in a factorized form with contributions from each of the fixed points. The full significance of this is yet to be understood.
Lightweight Exhaust Manifold and Exhaust Pipe Ducting for Internal Combustion Engines
Northam, G. Burton (Inventor); Ransone, Philip O. (Inventor); Rivers, H. Kevin (Inventor)
1999-01-01
An improved exhaust system for an internal combustion gasoline-and/or diesel-fueled engine includes an engine exhaust manifold which has been fabricated from carbon- carbon composite materials in operative association with an exhaust pipe ducting which has been fabricated from carbon-carbon composite materials. When compared to conventional steel. cast iron. or ceramic-lined iron paris. the use of carbon-carbon composite exhaust-gas manifolds and exhaust pipe ducting reduces the overall weight of the engine. which allows for improved acceleration and fuel efficiency: permits operation at higher temperatures without a loss of strength: reduces the "through-the wall" heat loss, which increases engine cycle and turbocharger efficiency and ensures faster "light-off" of catalytic converters: and, with an optional thermal reactor, reduces emission of major pollutants, i.e. hydrocarbons and carbon monoxide.
Objects in Manifold Times: Deleuze adn teh Speculative Philosophy of Objects as Processes
Directory of Open Access Journals (Sweden)
James Williams
2011-06-01
Full Text Available This essay shows how real objects must be processes for Gilles Deleuze. These processes are determined by his account of time as a nine-fold manifold of processes deduced from Deleuze’s account of three interconnected syntheses of time in his Difference and Repetition (Différence et repetition, henceforth DR. It will also be argued that Deleuze’s philosophy of time is speculative in a broad sense and that Deleuze’s account of the real is opposed to forms of abstraction which associate objects with conceptual, perceptual or transcendental identity. In order to demonstrate the radical and systematic nature of Deleuze’s account of process, there is a discussion of a basic process underlying his manifold of time. This process is opposed to Markov chains, in order to set up an opposition to interpretations of Deleuze’s philosophy that deny its metaphysical and speculative approach in favour of scientific realism.
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
Heterotic and type II orientifold compactifications on SU(3) structure manifolds
Energy Technology Data Exchange (ETDEWEB)
Benmachiche, I.
2006-07-15
We study the four-dimensional N=1 effective theories of generic SU(3) structure compactifications in the presence of background fluxes. For heterotic and type IIA/B orientifold theories, the N=1 characteristic data are determined by a Kaluza-Klein reduction of the fermionic actions. The Kaehler potentials, superpotentials and the D-terms are entirely encoded by geometrical data of the internal manifold. The background flux and the intrinsic torsion of the SU(3) structure manifold, gives rise to contributions to the four-dimensional F-terms. The corresponding superpotentials generalize the Gukov-Vafa-Witten superpotential. For the heterotic compactification, the four-dimensional fermionic supersymmetry variations, as well as the conditions on supersymmetric vacua, are determined. The Yukawa couplings of the theory turn out to be similar to their Calabi-Yau counterparts. (Orig.)
Casadevall, Arturo; Fang, Ferric C
2014-04-01
As the body of scientific knowledge in a discipline increases, there is pressure for specialization. Fields spawn subfields that then become entities in themselves that promote further specialization. The process by which scientists join specialized groups has remarkable similarities to the guild system of the middle ages. The advantages of specialization of science include efficiency, the establishment of normative standards, and the potential for greater rigor in experimental research. However, specialization also carries risks of monopoly, monotony, and isolation. The current tendency to judge scientific work by the impact factor of the journal in which it is published may have roots in overspecialization, as scientists are less able to critically evaluate work outside their field than before. Scientists in particular define themselves through group identity and adopt practices that conform to the expectations and dynamics of such groups. As part of our continuing analysis of issues confronting contemporary science, we analyze the emergence and consequences of specialization in science, with a particular emphasis on microbiology, a field highly vulnerable to balkanization along microbial phylogenetic boundaries, and suggest that specialization carries significant costs. We propose measures to mitigate the detrimental effects of scientific specialism.
DEFF Research Database (Denmark)
Mousten, Birthe; Laursen, Anne Lise
2016-01-01
Across different fields of research, one feature is often overlooked: the use of language for specialized purposes (LSP) as a cross-discipline. Mastering cross-disciplinarity is the precondition for communicating detailed results within any field. Researchers in specialized languages work cross......-disciplinarily, because they work with both derivative and contributory approaches. Derivative, because specialized language retrieves its philosophy of science as well as methods from both the natural sciences, social sciences and humanistic sciences. Contributory because language results support the communication...... science fields communicate their findings. With this article, we want to create awareness of the work in this special area of language studies and of the inherent cross-disciplinarity that makes LSP special compared to common-core language. An acknowledgement of the importance of this field both in terms...
The Manifold Catchment model a link between linear systems and Kinematic overland flow
Pegram, G. G. S.
2003-04-01
Those working in Hydrology are indebted to Dooge (1973) for "cleaning up" the ragged notation of the unit Hydrograph and founding it properly in Linear System Theory. The concepts are primarily based on linear storage elements, for which a strong field of mathematical results is available. These linear models lend themselves to manipulation by transform techniques and state-space formulations, leading naturally to the Kalman Filter. On the physical modelling side, Dooge (1973), and Eagleson (1970) both present the treatment by Henderson and Wooding of overland flow, Eagleson extending the ideas further. The Kinematic overland flow solution has thus become a classic, as identified by these two authors. This presentation will revisit an article by Pegram and Diskin (1987), who suggested the Manifold model, an alternative catchment model to those of the cascade type (suggested by Nash &Dooge). This is a semi-distributed model comprising as many pairs of linear storage elements in parallel to each other as there are sub-catchments, the distance of the sub-catchment (or cell) from the catchment outlet being one of the parameters of the model. They showed that in the limit, as the elements merge into a continuous model, the impulse response function (IRF) of the Manifold model converges to a function closely resembling the Kinematic flow IRF, unlike the IRF of the Nash cascade which converges to a rectangular pulse. Interesting as that might be, on a more practical note, the Manifold model is easily described by an ARMA-type linear difference equation (recently extended to three storage elements for each cell by Sinclair), based on the state-space representation’s parameters, which makes it a useful modelling concept in on-line flood forecasting work, where computational efficiency is an advantage. The presentation will highlight the advantages of the Manifold model.
An analogue of Weyl’s law for quantized irreducible generalized flag manifolds
Energy Technology Data Exchange (ETDEWEB)
Matassa, Marco, E-mail: marco.matassa@gmail.com, E-mail: mmatassa@math.uio.no [Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo (Norway)
2015-09-15
We prove an analogue of Weyl’s law for quantized irreducible generalized flag manifolds. This is formulated in terms of a zeta function which, similarly to the classical setting, satisfies the following two properties: as a functional on the quantized algebra it is proportional to the Haar state and its first singularity coincides with the classical dimension. The relevant formulas are given for the more general case of compact quantum groups.
Modified pressure loss model for T-junctions of engine exhaust manifold
Wang, Wenhui; Lu, Xiaolu; Cui, Yi; Deng, Kangyao
2014-11-01
The T-junction model of engine exhaust manifolds significantly influences the simulation precision of the pressure wave and mass flow rate in the intake and exhaust manifolds of diesel engines. Current studies have focused on constant pressure models, constant static pressure models and pressure loss models. However, low model precision is a common disadvantage when simulating engine exhaust manifolds, particularly for turbocharged systems. To study the performance of junction flow, a cold wind tunnel experiment with high velocities at the junction of a diesel exhaust manifold is performed, and the variation in the pressure loss in the T-junction under different flow conditions is obtained. Despite the trend of the calculated total pressure loss coefficient, which is obtained by using the original pressure loss model and is the same as that obtained from the experimental results, large differences exist between the calculated and experimental values. Furthermore, the deviation becomes larger as the flow velocity increases. By improving the Vazsonyi formula considering the flow velocity and introducing the distribution function, a modified pressure loss model is established, which is suitable for a higher velocity range. Then, the new model is adopted to solve one-dimensional, unsteady flow in a D6114 turbocharged diesel engine. The calculated values are compared with the measured data, and the result shows that the simulation accuracy of the pressure wave before the turbine is improved by 4.3% with the modified pressure loss model because gas compressibility is considered when the flow velocities are high. The research results provide valuable information for further junction flow research, particularly the correction of the boundary condition in one-dimensional simulation models.
Holomorphic two-spheres in the complex Grassmann manifold G(k, n)
Indian Academy of Sciences (India)
Abstract. In this paper, we study the non-degenerate holomorphic S2 in the complex. Grassmann manifold G(k, n), 2k ≤ n, by the method of moving frame. For a non- degenerate holomorphic one, there exists globally defined positive functions λ1,...,λk on S2. We first show that the holomorphic S2 in G(k, 2k) is totally ...
G2-manifolds from K3 surfaces with non-symplectic automorphisms
Pumperla, Max; Reidegeld, Frank
2012-11-01
We show that K3 surfaces with non-symplectic automorphisms of prime order can be used to construct new compact irreducible G2-manifolds. This technique was carried out in detail by Kovalev and Lee for non-symplectic involutions. We use the Chen-Ruan orbifold cohomology to determine the Hodge diamonds of certain complex threefolds, which are the building blocks for this approach.
Motor synergies research in physical therapy: advantages of the uncontrolled manifold approach
Vaz,Daniela Virgínia
2017-01-01
ABSTRACT Movement is central to physical therapy identity and practice. Advances in the science of movement control, motor learning and development are thus inextricably tied to professional development and clinical activity. This paper aims to describe a prominent approach to motor control with potential to greatly advance the understanding of movement dysfunction: the uncontrolled manifold (UCM). An argument is formulated for incorporating this method of data analysis in rehabilitation rese...
Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature
Directory of Open Access Journals (Sweden)
Arnaldo S. Nascimento
2010-05-01
Full Text Available We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N-dimensional Riemannian manifolds without boundary and non-negative Ricci curvature. Conversely, for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative, we prove the existence of nonconstant local minimizers for the same class of functionals.
The bifurcation set and topology of integral manifolds in the heavy body problem
Artigue, Michele; Gautheron, Veronique; Isambert, Emmanuel
The topology of integral manifolds of the motion of a massive, rigid body in motion around a fixed point is investigated analytically. Cerf diagrams (1968) are generated in terms of a bifurcation set of functions in phase space. The discussion focuses on situations where the center of gravity of the body is situated on or near the planes of inertia passing the fixed point. The techniques developed permit identifying the number and positions of stationary rotations of the body in question.
On the uniqueness of the fixed point index on differentiable manifolds
Directory of Open Access Journals (Sweden)
Marco Spadini
2004-12-01
Full Text Available It is well known that some of the properties enjoyed by the fixed point index can be chosen as axioms, the choice depending on the class of maps and spaces considered. In the context of finite-dimensional real differentiable manifolds, we will provide a simple proof that the fixed point index is uniquely determined by the properties of normalization, additivity, and homotopy invariance.
On the uniqueness of the fixed point index on differentiable manifolds
Directory of Open Access Journals (Sweden)
Furi Massimo
2004-01-01
Full Text Available It is well known that some of the properties enjoyed by the fixed point index can be chosen as axioms, the choice depending on the class of maps and spaces considered. In the context of finite-dimensional real differentiable manifolds, we will provide a simple proof that the fixed point index is uniquely determined by the properties of normalization, additivity, and homotopy invariance.
Algorithms on Flag Manifolds for Knowledge Discovery in N-way Arrays
2015-11-20
support vector machines [7]. We address the identification of optimal biomarkers for the rapid diagnosis of neonatal sepsis . We employ both distances on...from infants with suspected sepsis from Yale-New Haven Hospital’s Neonatal Intensive Care Unit (NICU). Grassmann manifold distances are shown to be...biomarkers. These results suggest an enhanced sepsis scoring system for neonatal sepsis that includes these five biomarkers. 16DISTRIBUTION A
Page 1 The geometry and spectra of hyperbolic manifolds 753 The ...
Indian Academy of Sciences (India)
The geometry and spectra of hyperbolic manifolds 753. The remainder terms E, are compact. This follows from the estimates mentioned above and the boundedness of lis(L.) L(logxi) n(x,x) on 3%,(A) for n with compact support in x, and x * 1, the proof of which is technical. As for the first term in (2.77) we use the compactness ...
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.
The effective action of the heterotic string compactified on manifolds with SU(3) structure
Benmachiche, Iman; Louis, Jan; Martínez-Pedrera, Danny
2008-07-01
We derive the N = 1 effective action of the heterotic string compactified on manifolds with SU(3) structure in the presence of background fluxes. We use a Kaluza Klein reduction and compute the moduli dependence of the Kähler potential, the gauge kinetic function and the superpotential entirely from fermionic terms of the reduced action. Work supported by: DFG—The German Science Foundation, European RTN Program MRTN-CT-2004-503369 and the DAAD—the German Academic Exchange Service.
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.
Indoor Localization Using Semi-Supervised Manifold Alignment with Dimension Expansion
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Qiao Zhang
2016-11-01
Full Text Available Location estimation plays a crucial role in Location-Based Services (LBSs with satisfactory user experience. The Wireless Local Area Network (WLAN localization approach is preferred as a cost-efficient solution to indoor localization on account of the widely-deployed WLAN infrastructures. In this paper, we propose a new WLAN Received Signal Strength (RSS-based indoor localization approach using the semi-supervised manifold alignment with dimension expansion. In concrete terms, we first construct an innovative objective function based on the augmented physical coordinates and the corresponding WLAN RSS measurements. Second, the closed-form solution to the objective function is derived out according to the Lagrange multiplier equation, which results in the manifold in physical coordinate space. Third, the target location is estimated by matching the transformed newly-collected RSS against the manifold. The localization performance with noise perturbation is analyzed upon the constructed objective function, and meanwhile, the closed-form solution to the objective function with respect to multiple types of measurements is also derived out for the sake of leveraging all of the potential measurements for indoor localization. The extensive testing results show that the proposed approach performs well in localization accuracy even at low calibration load, and its performance can be further improved by using multiple types of measurements for localization.
Tu, Enmei; Zhang, Yaqian; Zhu, Lin; Yang, Jie; Kasabov, Nikola
2016-01-01
$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-based $k$NN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propos...
Flockerzi, Dietrich; Heineken, Wolfram
2006-12-01
It is claimed by Rhodes, Morari, and Wiggins [Chaos 9, 108-123 (1999)] that the projection algorithm of Maas and Pope [Combust. Flame 88, 239-264 (1992)] identifies the slow invariant manifold of a system of ordinary differential equations with time-scale separation. A transformation to Fenichel normal form serves as a tool to prove this statement. Furthermore, Rhodes, Morari, and Wiggins [Chaos 9, 108-123 (1999)] conjectured that away from a slow manifold, the criterion of Maas and Pope will never be fulfilled. We present two examples that refute the assertions of Rhodes, Morari, and Wiggins. In the first example, the algorithm of Maas and Pope leads to a manifold that is not invariant but close to a slow invariant manifold. The claim of Rhodes, Morari, and Wiggins that the Maas and Pope projection algorithm is invariant under a coordinate transformation to Fenichel normal form is shown to be not correct in this case. In the second example, the projection algorithm of Maas and Pope leads to a manifold that lies in a region where no slow manifold exists at all. This rejects the conjecture of Rhodes, Morari, and Wiggins mentioned above.
Parallel translation in warped product spaces: application to the Reissner-Nordstroem spacetime
Energy Technology Data Exchange (ETDEWEB)
Raposo, A P; Del Riego, L [Facultad de Ciencias, Universidad Autonoma de San Luis PotosI, Av Salvador Nava s/n, Zona Universitaria, 78290 San Luis PotosI, SLP (Mexico)
2005-07-21
A formal treatment of the parallel translation transformations in warped product manifolds is presented and related to those parallel translation transformations in each of the factor manifolds. A straightforward application to the Schwarzschild and Reissner-Nordstroem geometries, considered here as particular examples, explains some apparently surprising properties of the holonomy in these manifolds.
DEFF Research Database (Denmark)
Schultz, Ulrik Pagh; Lawall, Julia Laetitia; Consel, Charles
2000-01-01
Design patterns offer many advantages for software development, but can introduce inefficiency into the final program. Program specialization can eliminate such overheads, but is most effective when targeted by the user to specific bottlenecks. Consequently, we propose that these concepts...
DEFF Research Database (Denmark)
Mousten, Birthe; Laursen, Anne Lise
2016-01-01
Across different fields of research, one feature is often overlooked: the use of language for specialized purposes (LSP) as a cross-discipline. Mastering cross-disciplinarity is the precondition for communicating detailed results within any field. Researchers in specialized languages work cross-d...... of more empirical studies and in terms of a greater application of the results would give language specialists in trade and industry a solid and updated basis for communication and language use....... science fields communicate their findings. With this article, we want to create awareness of the work in this special area of language studies and of the inherent cross-disciplinarity that makes LSP special compared to common-core language. An acknowledgement of the importance of this field both in terms......Across different fields of research, one feature is often overlooked: the use of language for specialized purposes (LSP) as a cross-discipline. Mastering cross-disciplinarity is the precondition for communicating detailed results within any field. Researchers in specialized languages work cross...
Directory of Open Access Journals (Sweden)
Jun Zhang
2013-12-01
Full Text Available Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability density functions over a measure space, (Χ,μ. Classical information geometry prescribes, on Μθ: (i a Riemannian metric given by the Fisher information; (ii a pair of dual connections (giving rise to the family of α-connections that preserve the metric under parallel transport by their joint actions; and (iii a family of divergence functions ( α-divergence defined on Μθ x Μθ, which induce the metric and the dual connections. Here, we construct an extension of this differential geometric structure from Μθ (that of parametric probability density functions to the manifold, Μ, of non-parametric functions on X, removing the positivity and normalization constraints. The generalized Fisher information and α-connections on M are induced by an α-parameterized family of divergence functions, reflecting the fundamental convex inequality associated with any smooth and strictly convex function. The infinite-dimensional manifold, M, has zero curvature for all these α-connections; hence, the generally non-zero curvature of M can be interpreted as arising from an embedding of Μθ into Μ. Furthermore, when a parametric model (after a monotonic scaling forms an affine submanifold, its natural and expectation parameters form biorthogonal coordinates, and such a submanifold is dually flat for α = ± 1, generalizing the results of Amari’s α-embedding. The present analysis illuminates two different types of duality in information geometry, one concerning the referential status of a point (measurable function expressed in the divergence function (“referential duality” and the other concerning its representation under an arbitrary monotone scaling (“representational duality”.
Arabadjis, Dimitris; Rousopoulos, Panayiotis; Papaodysseus, Constantin; Exarhos, Michalis; Panagopoulos, Michail; Papazoglou-Manioudaki, Lena
2011-11-01
In this paper, a general methodology is introduced for the determination of potential prototype curves used for the drawing of prehistoric wall paintings. The approach includes 1) preprocessing of the wall-paintings contours to properly partition them, according to their curvature, 2) choice of prototype curves families, 3) analysis and optimization in 4-manifold for a first estimation of the form of these prototypes, 4) clustering of the contour parts and the prototypes to determine a minimal number of potential guides, and 5) further optimization in 4-manifold, applied to each cluster separately, in order to determine the exact functional form of the potential guides, together with the corresponding drawn contour parts. The methodology introduced simultaneously deals with two problems: 1) the arbitrariness in data-points orientation and 2) the determination of one proper form for a prototype curve that optimally fits the corresponding contour data. Arbitrariness in orientation has been dealt with a novel curvature based error, while the proper forms of curve prototypes have been exhaustively determined by embedding curvature deformations of the prototypes into 4-manifolds. Application of this methodology to celebrated wall paintings excavated at Tyrins, Greece, and the Greek island of Thera manifests that it is highly probable that these wall paintings were drawn by means of geometric guides that correspond to linear spirals and hyperbolae. These geometric forms fit the drawings’ lines with an exceptionally low average error, less than 0.39 mm. Hence, the approach suggests the existence of accurate realizations of complicated geometric entities more than 1,000 years before their axiomatic formulation in the Classical Ages.
You, Zhu-Hong; Lei, Ying-Ke; Gui, Jie; Huang, De-Shuang; Zhou, Xiaobo
2010-11-01
High-throughput protein interaction data, with ever-increasing volume, are becoming the foundation of many biological discoveries, and thus high-quality protein-protein interaction (PPI) maps are critical for a deeper understanding of cellular processes. However, the unreliability and paucity of current available PPI data are key obstacles to the subsequent quantitative studies. It is therefore highly desirable to develop an approach to deal with these issues from the computational perspective. Most previous works for assessing and predicting protein interactions either need supporting evidences from multiple information resources or are severely impacted by the sparseness of PPI networks. We developed a robust manifold embedding technique for assessing the reliability of interactions and predicting new interactions, which purely utilizes the topological information of PPI networks and can work on a sparse input protein interactome without requiring additional information types. After transforming a given PPI network into a low-dimensional metric space using manifold embedding based on isometric feature mapping (ISOMAP), the problem of assessing and predicting protein interactions is recasted into the form of measuring similarity between points of its metric space. Then a reliability index, a likelihood indicating the interaction of two proteins, is assigned to each protein pair in the PPI networks based on the similarity between the points in the embedded space. Validation of the proposed method is performed with extensive experiments on densely connected and sparse PPI network of yeast, respectively. Results demonstrate that the interactions ranked top by our method have high-functional homogeneity and localization coherence, especially our method is very efficient for large sparse PPI network with which the traditional algorithms fail. Therefore, the proposed algorithm is a much more promising method to detect both false positive and false negative interactions
Using space manifold dynamics to deploy a small satellite constellation around the Moon
Marson, Riccardo; Pontani, Mauro; Perozzi, Ettore; Teofilatto, Paolo
2010-02-01
The possibility of communicating with the far side of the Moon is essential for keeping a continuous radio link with lunar orbiting spacecraft, as well as with manned or unmanned surface facilities in locations characterized by poor coverage from Earth. If the exploration and the exploitation of the Moon must be sustainable in the medium/long term, we need to develop the capability to realize and service such facilities at an affordable cost. Minimizing the spacecraft mass and the number of launches is a driving parameter to this end. The aim of this study is to show how Space Manifold Dynamics can be profitably applied in order to launch three small spacecraft onboard the same launch vehicle and send them to different orbits around the Moon with no significant difference in the Delta-V budgets. Internal manifold transfers are considered to minimize also the transfer time. The approach used is the following: we used the linearized solution of the equations of motion in the Circular Restricted Three Body Problem to determine a first-guess state vector associated with the Weak Stability Boundary regions, either around the collinear Lagrangian point L1 or around the Moon. The resulting vector is then used as initial state in a numerical backward-integration sequence that outputs a trajectory on a manifold. The dynamical model used in the numerical integration is four-body and non-circular, i.e. the perturbations of the Sun and the lunar orbital eccentricity are accounted for. The trajectory found in this way is used as the principal segment of the lunar transfer. After separation, with minor maneuvers each satellite is injected into different orbits that lead to ballistic capture around the Moon. Finally, one or more circularization maneuvers are needed in order to achieve the final circular orbits. The whole mission profile, from launch to insertion into the final lunar orbits, is modeled numerically with the commercial software STK.
Quasi-quantum groups, knots, three-manifolds, and topological field theory
Altschüler, D R; Altschuler, Daniel; Coste, Antoine
1992-01-01
We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group $G$, and a 3-cocycle $\\om$, which was first studied by Dijkgraaf, Pasquier and Roche. We treat this example in more detail, and argue that in this case the invariants agree with the partition function of the topological field theory of Dijkgraaf and Witten depending on the same data $G, \\,\\om$.
On stable integral manifolds for impulsive Kolmogorov systems of fractional order
Stamov, Gani; Stamova, Ivanka
2017-05-01
In this paper, an impulsive Kolmogorov-type system using the Caputo fractional-order derivative is developed. The fractional-order system displays many interesting dynamic behaviors and fractional integrals can be used to describe the fractal media. The existence and stability of integral manifolds for the impulsive fractional model are considered. The main results are proved by means of piecewise continuous Lyapunov functions and the new fractional comparison principle. The impulses are realized at variable impulsive moments of time and can be considered as a control. Finally, an example is given to illustrate our results.
Decoding Complex Cognitive States Online by Manifold Regularization in Real-Time fMRI
DEFF Research Database (Denmark)
Hansen, Toke Jansen; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
2011-01-01
Human decision making is complex and influenced by many factors on multiple time scales, reflected in the numerous brain networks and connectivity patterns involved as revealed by fMRI. We address mislabeling issues in paradigms involving complex cognition, by considering a manifold regularizing...... prior for modeling a sequence of neural events leading to a decision. The method is directly applicable for online learning in the context of real-time fMRI, and our experimental results show that the method can efficiently avoid model degeneracy caused by mislabeling....
Worldline approach to quantum field theories on flat manifolds with boundaries
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G.
2006-01-01
We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on R_+ x R^{D-1} which leads us to study the associated heat kernel through a one dimensional (worldline) path integral. To calculate the latter we map it onto an auxiliary path integral on the full R^D using an image charge. The main technical difficulty lies in the fact that a smooth potential on R_+ x R^{D-1} extends to a potential which gen...
P-Cell Gauge Theories, Manifold Space, and Multi-Dimensional Integrability
Larsson, T. A.
We construct lattice gauge theories where the gauge potentials live on p-cells, using ideas from the theory of multi-dimensional lattice integrability. The classical limit of these models can naturally be considered as chiral models in the space ΩPM of p-dimensional manifolds on M, or alternatively as gauge theories in ΩP-1M. The continuum models have an infinite set of functionally conserved currents in ΩPM, which are classical analogs of the simplex equations of lattice integrable systems.
A manifold learning approach to data-driven computational materials and processes
Ibañez, Ruben; Abisset-Chavanne, Emmanuelle; Aguado, Jose Vicente; Gonzalez, David; Cueto, Elias; Duval, Jean Louis; Chinesta, Francisco
2017-10-01
Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, …), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ universal laws while minimizing the need of explicit, often phenomenological, models. They are based on manifold learning methodologies.
Moment Maps, Scalar Curvature and Quantization of Kähler Manifolds
Arezzo, Claudio; Loi, Andrea
Building on Donaldson's work on constant scalar curvature metrics, we study the space of regular Kähler metrics Eω, i.e. those for which deformation quantization has been defined by Cahen, Gutt and Rawnsley. After giving, in Sects. 2 and 3 a review of Donaldson's moment map approach, we study the ``essential'' uniqueness of balanced basis (i.e. of coherent states) in a more general setting (Theorem 2.5). We then study the space Eω in Sect.4 and we show in Sect.5 how all the tools needed can be defined also in the case of non-compact manifolds.
Boundary control and tomography of Riemannian manifolds (the BC-method)
Belishev, M. I.
2017-08-01
The BC-method provides one of the approaches to inverse problems of mathematical physics. A characteristic feature of this method is the great variety of interdisciplinary relations involved: in addition to partial differential equations as a source of problems, use is made of control theory and systems theory, asymptotic methods, functional analysis, operator theory, Banach algebras, and so on. The purpose of this paper is to present the principal ideas and tools of the BC-method and to give a survey of some results. One of the main achievements of the method is chosen for presentation: the reconstruction of Riemannian manifolds from dynamical and spectral boundary data. Bibliography: 108 titles.
Bhattacharya, Abhishek; Dunson, David B
2012-08-01
This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels.
African Journals Online (AJOL)
Sarra
Introduction. Nephrology is a relatively recent speciality which was. Introduced in tunisia during the nineteenYsixties by. Professor Hassouna Ben Ayed. He introduced peritoneal dialysis, the artificial Nidney and renal biopsy in the department of medicine of Charles Nicole hospital in tunis. Prof. H. Ben Ayed received his ...
Directory of Open Access Journals (Sweden)
Lin Liang
2015-01-01
Full Text Available A new method for extracting the low-dimensional feature automatically with self-organization mapping manifold is proposed for the detection of rotating mechanical nonlinear faults (such as rubbing, pedestal looseness. Under the phase space reconstructed by single vibration signal, the self-organization mapping (SOM with expectation maximization iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention. After that, the local tangent space alignment algorithm is adopted to compress the high-dimensional phase space into low-dimensional feature space. The proposed method takes advantages of the manifold learning in low-dimensional feature extraction and adaptive neighborhood construction of SOM and can extract intrinsic fault features of interest in two dimensional projection space. To evaluate the performance of the proposed method, the Lorenz system was simulated and rotation machinery with nonlinear faults was obtained for test purposes. Compared with the holospectrum approaches, the results reveal that the proposed method is superior in identifying faults and effective for rotating machinery condition monitoring.
Manifold optimization-based analysis dictionary learning with an ℓ1∕2-norm regularizer.
Li, Zhenni; Ding, Shuxue; Li, Yujie; Yang, Zuyuan; Xie, Shengli; Chen, Wuhui
2018-02-01
Recently there has been increasing attention towards analysis dictionary learning. In analysis dictionary learning, it is an open problem to obtain the strong sparsity-promoting solutions efficiently while simultaneously avoiding the trivial solutions of the dictionary. In this paper, to obtain the strong sparsity-promoting solutions, we employ the ℓ 1∕2 norm as a regularizer. The very recent study on ℓ 1∕2 norm regularization theory in compressive sensing shows that its solutions can give sparser results than using the ℓ 1 norm. We transform a complex nonconvex optimization into a number of one-dimensional minimization problems. Then the closed-form solutions can be obtained efficiently. To avoid trivial solutions, we apply manifold optimization to update the dictionary directly on the manifold satisfying the orthonormality constraint, so that the dictionary can avoid the trivial solutions well while simultaneously capturing the intrinsic properties of the dictionary. The experiments with synthetic and real-world data verify that the proposed algorithm for analysis dictionary learning can not only obtain strong sparsity-promoting solutions efficiently, but also learn more accurate dictionary in terms of dictionary recovery and image processing than the state-of-the-art algorithms. Copyright © 2017 Elsevier Ltd. All rights reserved.
Pan, Han; Jing, Zhongliang; Qiao, Lingfeng; Li, Minzhe
2017-09-25
Image restoration is a difficult and challenging problem in various imaging applications. However, despite of the benefits of a single overcomplete dictionary, there are still several challenges for capturing the geometric structure of image of interest. To more accurately represent the local structures of the underlying signals, we propose a new problem formulation for sparse representation with block-orthogonal constraint. There are three contributions. First, a framework for discriminative structured dictionary learning is proposed, which leads to a smooth manifold structure and quotient search spaces. Second, an alternating minimization scheme is proposed after taking both the cost function and the constraints into account. This is achieved by iteratively alternating between updating the block structure of the dictionary defined on Grassmann manifold and sparsifying the dictionary atoms automatically. Third, Riemannian conjugate gradient is considered to track local subspaces efficiently with a convergence guarantee. Extensive experiments on various datasets demonstrate that the proposed method outperforms the state-of-the-art methods on the removal of mixed Gaussian-impulse noise.
Examples of integrable and non-integrable systems on singular symplectic manifolds
Delshams, Amadeu; Kiesenhofer, Anna; Miranda, Eva
2017-05-01
We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with singularities which are mainly of two types: bm-symplectic and m-folded symplectic structures. These examples comprise the three body problem as non-integrable exponent and some integrable reincarnations such as the two fixed-center problem. Given that the geometrical and dynamical properties of bm-symplectic manifolds and folded symplectic manifolds are well-understood [10-12,9,15,13,14,24,20,22,25,28], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.
Sanroman-Junquera, Margarita; Mora-Jimenez, Inmaculada; Garcia-Alberola, Arcadi; Caamano, Antonio J; Trenor, Beatriz; Rojo-Alvarez, Jose Luis
2017-06-15
Spatial and temporal processing of intracardiac electrograms provides relevant information to support the arrhythmia ablation during electrophysiological studies. Current Cardiac Navigation Systems (CNS) and Electrocardiographic Imaging (ECGI) build detailed three-dimensional electroanatomical maps (EAM), which represent the spatial anatomical distribution of bioelectrical features, such as activation time or voltage. We present a principled methodology for spectral analysis of both EAM geometry and bioelectrical feature in CNS or ECGI, including their spectral representation, cut-off frequency, or spatial sampling rate (SSR). Existing manifold harmonic techniques for spectral mesh analysis are adapted to account for a fourth dimension, corresponding to the EAM bioelectrical feature. Appropriate scaling is required to address different magnitudes and units. With our approach, simulated and real EAM showed strong SSR dependence on both the arrhythmia mechanism and the cardiac anatomical shape. For instance, high frequencies increased significantly the SSR because of the ``early-meets-late'' in flutter EAM, compared with the sinus rhythm. Besides, higher frequency components were obtained for the left atrium (more complex anatomy) than for the right atrium in sinus rhythm. The proposed manifold harmonics methodology opens the field towards new signal processing tools for principled EAM spatio-feature analysis in CNS and ECGI, and to an improved knowledge on arrhythmia mechanisms.
Feature selection and multi-kernel learning for sparse representation on a manifold
Wang, Jim Jing-Yan
2014-03-01
Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao etal. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. © 2013 Elsevier Ltd.
3-D Human Action Recognition by Shape Analysis of Motion Trajectories on Riemannian Manifold.
Devanne, Maxime; Wannous, Hazem; Berretti, Stefano; Pala, Pietro; Daoudi, Mohamed; Del Bimbo, Alberto
2015-07-01
Recognizing human actions in 3-D video sequences is an important open problem that is currently at the heart of many research domains including surveillance, natural interfaces and rehabilitation. However, the design and development of models for action recognition that are both accurate and efficient is a challenging task due to the variability of the human pose, clothing and appearance. In this paper, we propose a new framework to extract a compact representation of a human action captured through a depth sensor, and enable accurate action recognition. The proposed solution develops on fitting a human skeleton model to acquired data so as to represent the 3-D coordinates of the joints and their change over time as a trajectory in a suitable action space. Thanks to such a 3-D joint-based framework, the proposed solution is capable to capture both the shape and the dynamics of the human body, simultaneously. The action recognition problem is then formulated as the problem of computing the similarity between the shape of trajectories in a Riemannian manifold. Classification using k-nearest neighbors is finally performed on this manifold taking advantage of Riemannian geometry in the open curve shape space. Experiments are carried out on four representative benchmarks to demonstrate the potential of the proposed solution in terms of accuracy/latency for a low-latency action recognition. Comparative results with state-of-the-art methods are reported.
The mesh-LBP: a framework for extracting local binary patterns from discrete manifolds.
Werghi, Naoufel; Berretti, Stefano; del Bimbo, Alberto
2015-01-01
In this paper, we present a novel and original framework, which we dubbed mesh-local binary pattern (LBP), for computing local binary-like-patterns on a triangular-mesh manifold. This framework can be adapted to all the LBP variants employed in 2D image analysis. As such, it allows extending the related techniques to mesh surfaces. After describing the foundations, the construction and the main features of the mesh-LBP, we derive its possible variants and show how they can extend most of the 2D-LBP variants to the mesh manifold. In the experiments, we give evidence of the presence of the uniformity aspect in the mesh-LBP, similar to the one noticed in the 2D-LBP. We also report repeatability experiments that confirm, in particular, the rotation-invariance of mesh-LBP descriptors. Furthermore, we analyze the potential of mesh-LBP for the task of 3D texture classification of triangular-mesh surfaces collected from public data sets. Comparison with state-of-the-art surface descriptors, as well as with 2D-LBP counterparts applied on depth images, also evidences the effectiveness of the proposed framework. Finally, we illustrate the robustness of the mesh-LBP with respect to the class of mesh irregularity typical to 3D surface-digitizer scans.
Manifold absolute pressure estimation using neural network with hybrid training algorithm.
Muslim, Mohd Taufiq; Selamat, Hazlina; Alimin, Ahmad Jais; Haniff, Mohamad Fadzli
2017-01-01
In a modern small gasoline engine fuel injection system, the load of the engine is estimated based on the measurement of the manifold absolute pressure (MAP) sensor, which took place in the intake manifold. This paper present a more economical approach on estimating the MAP by using only the measurements of the throttle position and engine speed, resulting in lower implementation cost. The estimation was done via two-stage multilayer feed-forward neural network by combining Levenberg-Marquardt (LM) algorithm, Bayesian Regularization (BR) algorithm and Particle Swarm Optimization (PSO) algorithm. Based on the results found in 20 runs, the second variant of the hybrid algorithm yields a better network performance than the first variant of hybrid algorithm, LM, LM with BR and PSO by estimating the MAP closely to the simulated MAP values. By using a valid experimental training data, the estimator network that trained with the second variant of the hybrid algorithm showed the best performance among other algorithms when used in an actual retrofit fuel injection system (RFIS). The performance of the estimator was also validated in steady-state and transient condition by showing a closer MAP estimation to the actual value.
Manifold absolute pressure estimation using neural network with hybrid training algorithm.
Directory of Open Access Journals (Sweden)
Mohd Taufiq Muslim
Full Text Available In a modern small gasoline engine fuel injection system, the load of the engine is estimated based on the measurement of the manifold absolute pressure (MAP sensor, which took place in the intake manifold. This paper present a more economical approach on estimating the MAP by using only the measurements of the throttle position and engine speed, resulting in lower implementation cost. The estimation was done via two-stage multilayer feed-forward neural network by combining Levenberg-Marquardt (LM algorithm, Bayesian Regularization (BR algorithm and Particle Swarm Optimization (PSO algorithm. Based on the results found in 20 runs, the second variant of the hybrid algorithm yields a better network performance than the first variant of hybrid algorithm, LM, LM with BR and PSO by estimating the MAP closely to the simulated MAP values. By using a valid experimental training data, the estimator network that trained with the second variant of the hybrid algorithm showed the best performance among other algorithms when used in an actual retrofit fuel injection system (RFIS. The performance of the estimator was also validated in steady-state and transient condition by showing a closer MAP estimation to the actual value.
Implications of Non-Differentiable Entropy on a Space-Time Manifold
Directory of Open Access Journals (Sweden)
Maricel Agop
2015-04-01
Full Text Available Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-time manifold in the hydrodynamic version and its correspondence with motion variables (energy, momentum, etc. are established. Moreover, for the same non-differentiability type, through a scale resolution dependence of a fundamental length and wave function independence with respect to the proper time, a non-differentiable Klein–Gordon-type equation in the wave function version is obtained. For a phase-amplitude functional dependence on the wave function, the non-differentiable spontaneous symmetry breaking mechanism implies pattern generation in the form of Cooper non-differentiable-type pairs, while its non-differentiable topology implies some fractal logic elements (fractal bit, fractal gates, etc..
A Study of System Pressure Transients Generated by Isolation Valve Open/Closure in Orifice Manifold
Energy Technology Data Exchange (ETDEWEB)
Kim, M. [KEPCO, Daejeon (Korea, Republic of); Bae, S. W.; Kim, J. I.; Park, S. J. [KHNP, Abu Dhabi (United Arab Emirates)
2016-05-15
In this study, we explore the effects of pressure transients on peak and minimal pressures caused by the actuation of isolation valve and control valve reacting to the combined orifice operation of orifice manifold with motor-operated valve installed in the rear of the orifice. We then use the collected data to direct our effort towards cause analysis and propose improvements to efficiency and safety of operation. This formation is used to by domestic and foreign nuclear power plants as a mean to control flow rate, producing required flow rate jointly together by combination of the orifices. No significant impacts on the internals of manifold orifice due to peak pressure has been observed, although chance of cavitation at the outlet of control valve is significant. Considering the peak pressure, as well as minimum pressure occurs in low flow rate conditions, the pressure transient is more so affected by the characteristics (modified equal percentage) of control valve. Isolation valve of the orifice and control valve operate organically, therefore stroke time for valves need to be applied in order for both valves to cooperatively formulate an optimized operation.
Object Manifold Alignment for Multi-Temporal High Resolution Remote Sensing Images Classification
Gao, G.; Zhang, M.; Gu, Y.
2017-05-01
Multi-temporal remote sensing images classification is very useful for monitoring the land cover changes. Traditional approaches in this field mainly face to limited labelled samples and spectral drift of image information. With spatial resolution improvement, "pepper and salt" appears and classification results will be effected when the pixelwise classification algorithms are applied to high-resolution satellite images, in which the spatial relationship among the pixels is ignored. For classifying the multi-temporal high resolution images with limited labelled samples, spectral drift and "pepper and salt" problem, an object-based manifold alignment method is proposed. Firstly, multi-temporal multispectral images are cut to superpixels by simple linear iterative clustering (SLIC) respectively. Secondly, some features obtained from superpixels are formed as vector. Thirdly, a majority voting manifold alignment method aiming at solving high resolution problem is proposed and mapping the vector data to alignment space. At last, all the data in the alignment space are classified by using KNN method. Multi-temporal images from different areas or the same area are both considered in this paper. In the experiments, 2 groups of multi-temporal HR images collected by China GF1 and GF2 satellites are used for performance evaluation. Experimental results indicate that the proposed method not only has significantly outperforms than traditional domain adaptation methods in classification accuracy, but also effectively overcome the problem of "pepper and salt".
Liu, Zhong-bao; Gao, Yan-yun; Wang, Jian-zhen
2015-01-01
Support vector machine (SVM) with good leaning ability and generalization is widely used in the star spectra data classification. But when the scale of data becomes larger, the shortages of SVM appear: the calculation amount is quite large and the classification speed is too slow. In order to solve the above problems, twin support vector machine (TWSVM) was proposed by Jayadeva. The advantage of TSVM is that the time cost is reduced to 1/4 of that of SVM. While all the methods mentioned above only focus on the global characteristics and neglect the local characteristics. In view of this, an automatic classification method of star spectra data based on manifold fuzzy twin support vector machine (MF-TSVM) is proposed in this paper. In MF-TSVM, manifold-based discriminant analysis (MDA) is used to obtain the global and local characteristics of the input data and the fuzzy membership is introduced to reduce the influences of noise and singular data on the classification results. Comparative experiments with current classification methods, such as C-SVM and KNN, on the SDSS star spectra datasets verify the effectiveness of the proposed method.
Learning Dual Multi-Scale Manifold Ranking for Semantic Segmentation of High-Resolution Images
Directory of Open Access Journals (Sweden)
Mi Zhang
2017-05-01
Full Text Available Semantic image segmentation has recently witnessed considerable progress by training deep convolutional neural networks (CNNs. The core issue of this technique is the limited capacity of CNNs to depict visual objects. Existing approaches tend to utilize approximate inference in a discrete domain or additional aides and do not have a global optimum guarantee. We propose the use of the multi-label manifold ranking (MR method in solving the linear objective energy function in a continuous domain to delineate visual objects and solve these problems. We present a novel embedded single stream optimization method based on the MR model to avoid approximations without sacrificing expressive power. In addition, we propose a novel network, which we refer to as dual multi-scale manifold ranking (DMSMR network, that combines the dilated, multi-scale strategies with the single stream MR optimization method in the deep learning architecture to further improve the performance. Experiments on high resolution images, including close-range and remote sensing datasets, demonstrate that the proposed approach can achieve competitive accuracy without additional aides in an end-to-end manner.
Phases of Supersymmetric D-branes on Kaehler Manifolds and the McKay correspondence
Mayr, Peter
2001-01-01
We study the topological zero mode sector of type II strings on a K\\"ahler manifold $X$ in the presence of boundaries. We construct two finite bases, in a sense bosonic and fermionic, that generate the the topological sector of the Hilbert space with boundaries. The fermionic basis localizes on compact submanifolds in $X$. A variation of the FI terms interpolates between the description of these ground states in terms of the ring of chiral fields at the boundary at small volume and helices of exceptional bundles at large volume, respectively. The identification of the bosonic/fermionic basis with the dual bases for the non-compact/compact K-theory group on $X$ gives a natural explanation of the McKay correspondence in terms of a linear sigma model and suggests a simple generalization of McKay to singular resolutions. The construction provides also a very effective way to describe D-brane states on generic, compact Calabi--Yau manifolds and allows to recover detailed information on the moduli space, such as mo...
DAMPING OF THE MILKY WAY BAR BY MANIFOLD-DRIVEN SPIRALS
Energy Technology Data Exchange (ETDEWEB)
Łokas, Ewa L. [Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw (Poland)
2016-10-10
We describe a new phenomenon of “bar damping” that may have played an important role in shaping the Milky Way bar and bulge as well as its spiral structure. We use a collisionless N -body simulation of a Milky Way–like galaxy initially composed of a dark matter halo and an exponential disk with a Toomre parameter slightly above unity. In this configuration, dominated by the disk in the center, a bar forms relatively quickly, after 1 Gyr of evolution. This is immediately followed by the formation of two manifold-driven spiral arms and the outflow of stars that modifies the potential in the vicinity of the bar, apparently shifting the position of the L {sub 1}/ L {sub 2} Lagrange points. This modification leads to the shortening of the bar and the creation of a next generation of manifold-driven spiral arms at a smaller radius. The process repeats itself a few times over the next 0.5 Gyr resulting in further substantial weakening and shortening of the bar. The time when the damping comes to an end coincides with the first buckling episode in the bar that rebuilds the orbital structure so that no more new spiral arms are formed. The morphology of the bar and the spiral structure at this time show remarkable similarity to the present properties of the Milky Way. Later on, the bar starts to grow rather steadily again, weakened only by subsequent buckling episodes occurring at more distant parts of the disk.
DEFF Research Database (Denmark)
Kleindienst, Ingo; Geisler Asmussen, Christian; Hutzschenreuter, Thomas
2012-01-01
little about performance implications, if we do not know, and do not ask, how the firm has diversified. Therefore, building on the two broad arguments of operating flexibility and location-specific commitment, we develop a theoretical framework that focuses on the extent to which a firm's international...... arbitrage strategy is characterized by specialization versus replication and argue that these different strategies may have differential impact on profitability and risk reduction. Developing a sophisticated measure of international specialization and using a unique panel data set of 92 German MNEs to test......Whether and how international diversification and cross-border arbitrage affects firm performance remains one of the major unresolved research questions in the strategy and international business literatures. We propose that knowing how much a firm has internationally diversified tells us very...
Sun, Jiaqi; Xie, Yuchen; Ye, Wenxing; Ho, Jeffrey; Entezari, Alireza; Blackband, Stephen J.
2013-01-01
In this paper, we present a novel dictionary learning framework for data lying on the manifold of square root densities and apply it to the reconstruction of diffusion propagator (DP) fields given a multi-shell diffusion MRI data set. Unlike most of the existing dictionary learning algorithms which rely on the assumption that the data points are vectors in some Euclidean space, our dictionary learning algorithm is designed to incorporate the intrinsic geometric structure of manifolds and performs better than traditional dictionary learning approaches when applied to data lying on the manifold of square root densities. Non-negativity as well as smoothness across the whole field of the reconstructed DPs is guaranteed in our approach. We demonstrate the advantage of our approach by comparing it with an existing dictionary based reconstruction method on synthetic and real multi-shell MRI data. PMID:24684004
Giberti, Claudio; Vernia, Cecilia
1994-12-01
We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable.
Staff Association
2011-01-01
SPECIAL OFFER FOR OUR MEMBERS Tarif unique Adulte/Enfant Entrée Zone terrestre 19 euros instead of 23 euros Entrée “Zone terrestre + aquatique” 24 euros instead of 31 euros Free for children under 3, with limited access to the attractions. Walibi Rhône-Alpes is open daily from 22 June to 31 August, and every week end from 3 September until 31 October. Closing of the “zone aquatique” 11 September.
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2010-01-01
Special offer for members of the Staff Association and their families 10% reduction on all products in the SEPHORA shop (sells perfume, beauty products etc.) in Val Thoiry ALL YEAR ROUND. Plus 20% reduction during their “vente privée”* three or four times a year. Simply present your Staff Association membership card when you make your purchase. * next “vente privée” from 24th to 29th May 2010
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Lorenzeti, Jorge Fernando Canato; Silva, Haroldo Benedito da [Petroleo Brasileiro S.A. (PETROBRAS), Rio de Janeiro, RJ (Brazil)
2012-07-01
This work presents the main challenges and the solutions found in the development of the Mexilhao Gas Field, located in the Santos Basin, about 145 kilometers off the Brazilian coast. Many technological innovations were devised for the subsea system, such as the use of subsea control valves in the manifold (for monoethylene glycol, MEG, injection), the use of HIPPS (High Integrity Pipeline Protection System) and the thermal insulation of the Wet Christmas Tree (WCT). It is also presented the sequence of the interlocking protection logic and the results observed during production. The cooling down of the WCT block after a stop production is showed. This is very important feature in this project for mitigating hydrate formation and allowing a higher operational flexibility during the restarting of production. The good simulation results by OLGA are also presented and they are compared to the real thermal-hydraulic profile data observed during the restart. The correct timing of this operation is essential to ensure not only that the overpressure protection logic is not triggered during the restart, but to prevent very low temperatures downstream of the choke (Joule-Thompson effect). (author)
The Seiberg-Witten equations and applications to the topology of smooth four-manifolds (MN-44)
Morgan, John W
2014-01-01
The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next com
Staff Association
2011-01-01
OFFRE SPECIALE POUR NOS MEMBRES Les vendredis 29 juillet, 5 et 12 août, Aquaparc fermera ses portes exceptionnellement à 22h00. Pour ces évènements, des tarifs défiant toute concurrence vous sont proposés. Au programme : Clown spécialiste de la sculpture de ballons de 16h00 à 21h00 Ambiance Salsa avec danseurs professionnel : Démonstration et Cours de Salsa. Les tarifs : Pour une entrée à partir de 15h00 : Enfant : CHF 22.- Adulte : CHF 26.-
Staff Association
2011-01-01
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2011-01-01
Are you a member of the Staff Association? Did you know that as a member you can benefit from the following special offers: BCGE (Banque Cantonale de Genève): personalized banking solutions with preferential conditions. TPG: reduced rates on annual transport passes for active and retired staff. Aquaparc: reduced ticket prices for children and adults at this Swiss waterpark in Le Bouveret. Walibi: reduced prices for children and adults at this French attraction park in Les Avenières. FNAC: 5% reduction on FNAC vouchers. For more information about all these offers, please consult our web site: http://association.web.cern.ch/association/en/OtherActivities/Offers.html
Energy Technology Data Exchange (ETDEWEB)
Banks, E.M.; Wikoff, W.O.; Shaffer, L.L. [NUCON International, Inc., Columbus, OH (United States)
1997-08-01
At the current level of maturity and experience in the nuclear industry, regarding testing of air treatment systems, it is now possible to design and qualify injection and sample manifolds for most applications. While the qualification of sample manifolds is still in its infancy, injection manifolds have reached a mature stage that helps to eliminate the {open_quotes}hit or miss{close_quotes} type of design. During the design phase, manifolds can be adjusted to compensate for poor airflow distribution, laminar flow conditions, and to take advantage of any system attributes. Experience has shown that knowing the system attributes before the design phase begins is an essential element to a successful manifold design. The use of a spreadsheet type program commonly found on most personal computers can afford a greater flexibility and a reduction in time spent in the design phase. The experience gained from several generations of manifold design has culminated in a set of general design guidelines. Use of these guidelines, along with a good understanding of the type of testing (theoretical and practical), can result in a good manifold design requiring little or no field modification. The requirements for manifolds came about because of the use of multiple banks of components and unconventional housing inlet configurations. Multiple banks of adsorbers and pre and post HEPA`s required that each bank be tested to insure that each one does not exceed a specific allowable leakage criterion. 5 refs., 5 figs., 1 tab.
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.
Fast 2D DOA Estimation Algorithm by an Array Manifold Matching Method with Parallel Linear Arrays.
Yang, Lisheng; Liu, Sheng; Li, Dong; Jiang, Qingping; Cao, Hailin
2016-02-23
In this paper, the problem of two-dimensional (2D) direction-of-arrival (DOA) estimation with parallel linear arrays is addressed. Two array manifold matching (AMM) approaches, in this work, are developed for the incoherent and coherent signals, respectively. The proposed AMM methods estimate the azimuth angle only with the assumption that the elevation angles are known or estimated. The proposed methods are time efficient since they do not require eigenvalue decomposition (EVD) or peak searching. In addition, the complexity analysis shows the proposed AMM approaches have lower computational complexity than many current state-of-the-art algorithms. The estimated azimuth angles produced by the AMM approaches are automatically paired with the elevation angles. More importantly, for estimating the azimuth angles of coherent signals, the aperture loss issue is avoided since a decorrelation procedure is not required for the proposed AMM method. Numerical studies demonstrate the effectiveness of the proposed approaches.
Directory of Open Access Journals (Sweden)
Eloísa Lamilla Guerrero
2011-07-01
Full Text Available Through an ethnographic analysis of Central Cemetery in the city of Neiva (Huila, this text proposes to exemplify how cemeteries are privileged settings for the embodiment, organization and resignification of the manifold memories Neivan society collectively build and imagine in order to represent themselves in a dispute for identities and remembrance. They mirror what they are, have been, and aim at being. Those memories may be traced through the battle of signs, the persistence of hegemonies, the nation’s narrative, the bipartisan imprint, tenacity and the horror of the armed conflict, popular claims, the desire for a miracle, the vindication of affection, resistance, regional identity, the ephemeral, the transcendent and oblivion.
Fundamentals of tensor calculus for engineers with a primer on smooth manifolds
Mühlich, Uwe
2017-01-01
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth...
A new strategy for protein interface identification using manifold learning method.
Wang, Bing; Huang, De-Shuang; Jiang, Changjun
2014-06-01
Protein interactions play vital roles in biological processes. The study for protein interface will allow people to elucidate the mechanism of protein interaction. However, a large portion of protein interface data is incorrectly collected in current studies. In this paper, a novel strategy of dataset reconstruction using manifold learning method has been proposed for dealing with the noises in the interaction interface data whose definition is based on the residue distances among the different chains within protein complexes. Three support vector machine-based predictors are constructed using different protein features to identify the functional sites involved in the formation of protein interface. The experimental results achieved in this work demonstrate that our strategy can remove noises, and therefore improve the ability for identification of protein interfaces with 77.8% accuracy.
M Theory on the Stiefel manifold and 3d Conformal Field Theories
Ceresole, Anna; D'Auria, R.; Ferrara, S.
2000-01-01
We compute the mass and multiplet spectrum of M theory compactified on the product of AdS(4) spacetime by the Stiefel manifold V(5,2)=SO(5)/SO(3), and we use this information to deduce via the AdS/CFT map the primary operator content of the boundary N=2 conformal field theory. We make an attempt for a candidate supersymmetric gauge theory that, at strong coupling, should be related to parallel M2-branes on the singular point of the non-compact Calabi-Yau four-fold $\\sum_{a=1}^5 z_a^2 = 0$, describing the cone on V(5,2).
Time-dependent variational principle in matrix-product state manifolds: Pitfalls and potential
Kloss, Benedikt; Lev, Yevgeny Bar; Reichman, David
2018-01-01
We study the applicability of the time-dependent variational principle in matrix-product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time dynamics are known we demonstrate that convergence of long time observables is subtle and needs to be examined carefully. Remarkably, for the disordered nonintegrable system we consider the long time dynamics are in good agreement with the rigorously obtained short time behavior and with previous obtained numerically exact results, suggesting that at least in this case, the apparent convergence of this approach is reliable. Our study indicates that, while great care must be exercised in establishing the convergence of the method, it may still be asymptotically accurate for a class of disordered nonintegrable quantum systems.
Ye, Qing; Pan, Hao; Liu, Changhua
2015-01-01
A novel semisupervised extreme learning machine (ELM) with clustering discrimination manifold regularization (CDMR) framework named CDMR-ELM is proposed for semisupervised classification. By using unsupervised fuzzy clustering method, CDMR framework integrates clustering discrimination of both labeled and unlabeled data with twinning constraints regularization. Aiming at further improving the classification accuracy and efficiency, a new multiobjective fruit fly optimization algorithm (MOFOA) is developed to optimize crucial parameters of CDME-ELM. The proposed MOFOA is implemented with two objectives: simultaneously minimizing the number of hidden nodes and mean square error (MSE). The results of experiments on actual datasets show that the proposed semisupervised classifier can obtain better accuracy and efficiency with relatively few hidden nodes compared with other state-of-the-art classifiers.
Directory of Open Access Journals (Sweden)
Qing Ye
2015-01-01
Full Text Available A novel semisupervised extreme learning machine (ELM with clustering discrimination manifold regularization (CDMR framework named CDMR-ELM is proposed for semisupervised classification. By using unsupervised fuzzy clustering method, CDMR framework integrates clustering discrimination of both labeled and unlabeled data with twinning constraints regularization. Aiming at further improving the classification accuracy and efficiency, a new multiobjective fruit fly optimization algorithm (MOFOA is developed to optimize crucial parameters of CDME-ELM. The proposed MOFOA is implemented with two objectives: simultaneously minimizing the number of hidden nodes and mean square error (MSE. The results of experiments on actual datasets show that the proposed semisupervised classifier can obtain better accuracy and efficiency with relatively few hidden nodes compared with other state-of-the-art classifiers.
Non-Abelian localization for supersymmetric Yang-Mills-Chern-Simons theories on a Seifert manifold
Ohta, Kazutoshi; Yoshida, Yutaka
2012-11-01
We derive non-Abelian localization formulas for supersymmetric Yang-Mills-Chern-Simons theory with matters on a Seifert manifold M, which is the three-dimensional space of a circle bundle over a two-dimensional Riemann surface Σ, by using the cohomological approach introduced by Källén. We find that the partition function and the vacuum expectation value of the supersymmetric Wilson loop reduces to a finite dimensional integral and summation over classical flux configurations labeled by discrete integers. We also find that the partition function reduces further to just a discrete sum over integers in some cases, and evaluate the supersymmetric index (Witten index) exactly on S1×Σ. The index completely agrees with the previous prediction from field theory and branes. We discuss a vacuum structure of the Aharony-Bergman-Jafferis-Maldacena theory deduced from the localization.
Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
Directory of Open Access Journals (Sweden)
Sheng-lan Chen
2014-01-01
Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.
Vincke, Cécile; Gutiérrez, Carlos; Wernery, Ulrich; Devoogdt, Nick; Hassanzadeh-Ghassabeh, Gholamreza; Muyldermans, Serge
2012-01-01
Immunizing a camelid (camels and llamas) with soluble, properly folded proteins raises an affinity-matured immune response in the unique camelid heavy-chain only antibodies (HCAbs). The peripheral blood lymphocytes of the immunized animal are used to clone the antigen-binding antibody fragment from the HCAbs in a phage display vector. A representative aliquot of the library of these antigen-binding fragments is used to retrieve single domain antigen-specific binders by successive rounds of panning. These single domain antibody fragments are cloned in tandem to generate manifold constructs (bivalent, biparatopic or bispecific constructs) to increase their functional affinity, to increase specificity, or to connect two independent antigen molecules.
Perancangan Ulang Sistem Hidrolik Pada Mesin FFAF Dengan Menggunakan Manifold Sebagai Pengganti Pipa
Directory of Open Access Journals (Sweden)
Ngarifin Ngarifin
2014-10-01
Full Text Available Mesin FFAF merupakan mesin yang digunakan untuk membuat filter FFAF (Full Fabrics Air Filter yaitu filter yang terbuat dari kertas woven. Pada mesin FFAF bekerja 3 proses utama secara berurutan yaitu forming (pembentukan, cooling (pendinginan, dan trimming (pemotongan. Mesin FFAF menggunakan sumber tenaga berupa sitem hidrolik untuk ketiga proses tersebut. Pada awalnya sistem hidrolik pada mesin ini menggunakan pipa sebagai media transmisi fluida. Penggunaan pipa tersebut memiliki kelemahan antara lain memerlukan tempat yang luas untuk penempatan pipa-pipa, kesulitan dalam perawatan dan perbaikan, dan pengurangan tekanan (head lose karena panjang dan belokan pipa serta rentan terhadap kebocoran. Dari kelemahan tersebut penulis melakukan perancangan ulang sistem hidrolik dengan mengganti pipa menjadi manifold yang merupakan penyederhanaan dari sistem pipa yang rumit dan berantakan.
Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone
Energy Technology Data Exchange (ETDEWEB)
Schmude, Johannes [Department of Physics, Universidad de Oviedo, Avda. Calvo Sotelo 18, 33007, Oviedo (Spain)
2015-01-22
We study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting holomorphic functions on the associated Calabi-Yau cone. This observation allows us to use standard techniques developed in the context of quiver gauge theories to obtain explicit results for a number of examples; namely S{sup 5}, T{sup 1,1}, Y{sup 7,3}, Y{sup 2,1}, Y{sup 2,0}, and Y{sup 4,0}. We find complete agreement with previous results obtained by Qiu and Zabzine using equivariant indices except for the orbifold limits Y{sup p,0} with p>1.
On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction.
Molnar, T G; Dombovari, Z; Insperger, T; Stepan, G
2017-11-01
The single-degree-of-freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double Hopf bifurcation point. Centre manifold reduction and normal form calculations are performed to investigate the long-term dynamics of the cutting process. The normal form of the four-dimensional centre subsystem is derived analytically, and the possible topologies in the infinite-dimensional phase space of the system are revealed. It is shown that bistable parameter regions exist where unstable periodic and, in certain cases, unstable quasi-periodic motions coexist with the equilibrium. Taking into account the non-smoothness caused by loss of contact between the tool and the workpiece, the boundary of the bistable region is also derived analytically. The results are verified by numerical continuation. The possibility of (transient) chaotic motions in the global non-smooth dynamics is shown.
A vacuum system for the thermal insulation of the SciFi distribution lines and manifolds
Joram, Christian
2017-01-01
This note describes some calculations and estimates for the layout, technology choice and performance of a vacuum system which shall ensure thermal insulation of the distribution lines and manifolds of the SiPM cooling system of the LHCb SciFi detector. We estimate the heat losses in concentric corrugated stainless steel pipes which leads to the conclusion that the pipes need to be evacuated to a pressure of about 1·10$^{-4}$ mbar. We then estimate the pumping conductance of the pipes and find that it will dominate over the effective pumping speed of any pump. We therefore conclude that a turbo molecular pump of small nominal pumping speed, which can easily achieve end pressures below 10$^{-5}$ mbar is adequate for this purpose. A preliminary layout of the vacuum system is being discussed at the end of the document.
Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof
2017-10-01
We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.
Acoustic space learning for sound-source separation and localization on binaural manifolds.
Deleforge, Antoine; Forbes, Florence; Horaud, Radu
2015-02-01
In this paper, we address the problems of modeling the acoustic space generated by a full-spectrum sound source and using the learned model for the localization and separation of multiple sources that simultaneously emit sparse-spectrum sounds. We lay theoretical and methodological grounds in order to introduce the binaural manifold paradigm. We perform an in-depth study of the latent low-dimensional structure of the high-dimensional interaural spectral data, based on a corpus recorded with a human-like audiomotor robot head. A nonlinear dimensionality reduction technique is used to show that these data lie on a two-dimensional (2D) smooth manifold parameterized by the motor states of the listener, or equivalently, the sound-source directions. We propose a probabilistic piecewise affine mapping model (PPAM) specifically designed to deal with high-dimensional data exhibiting an intrinsic piecewise linear structure. We derive a closed-form expectation-maximization (EM) procedure for estimating the model parameters, followed by Bayes inversion for obtaining the full posterior density function of a sound-source direction. We extend this solution to deal with missing data and redundancy in real-world spectrograms, and hence for 2D localization of natural sound sources such as speech. We further generalize the model to the challenging case of multiple sound sources and we propose a variational EM framework. The associated algorithm, referred to as variational EM for source separation and localization (VESSL) yields a Bayesian estimation of the 2D locations and time-frequency masks of all the sources. Comparisons of the proposed approach with several existing methods reveal that the combination of acoustic-space learning with Bayesian inference enables our method to outperform state-of-the-art methods.
Energy Technology Data Exchange (ETDEWEB)
Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.u, E-mail: rsuarez@ucu.edu.u [Universidad Catolica del Uruguay, Montevideo (Uruguay). Fac. de Ingenieria y Tecnologias. Dept. de Matematica; Ministerio de Industria, Energia y Mineria, Montevideo (Uruguay). Direccion General de Secretaria
2011-07-01
One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)
TU-F-BRF-06: 3D Pancreas MRI Segmentation Using Dictionary Learning and Manifold Clustering
Energy Technology Data Exchange (ETDEWEB)
Gou, S; Rapacchi, S; Hu, P; Sheng, K [UCLA School of Medicine, Los Angeles, CA (United States)
2014-06-15
Purpose: The recent advent of MRI guided radiotherapy machines has lent an exciting platform for soft tissue target localization during treatment. However, tools to efficiently utilize MRI images for such purpose have not been developed. Specifically, to efficiently quantify the organ motion, we develop an automated segmentation method using dictionary learning and manifold clustering (DLMC). Methods: Fast 3D HASTE and VIBE MR images of 2 healthy volunteers and 3 patients were acquired. A bounding box was defined to include pancreas and surrounding normal organs including the liver, duodenum and stomach. The first slice of the MRI was used for dictionary learning based on mean-shift clustering and K-SVD sparse representation. Subsequent images were iteratively reconstructed until the error is less than a preset threshold. The preliminarily segmentation was subject to the constraints of manifold clustering. The segmentation results were compared with the mean shift merging (MSM), level set (LS) and manual segmentation methods. Results: DLMC resulted in consistently higher accuracy and robustness than comparing methods. Using manual contours as the ground truth, the mean Dices indices for all subjects are 0.54, 0.56 and 0.67 for MSM, LS and DLMC, respectively based on the HASTE image. The mean Dices indices are 0.70, 0.77 and 0.79 for the three methods based on VIBE images. DLMC is clearly more robust on the patients with the diseased pancreas while LS and MSM tend to over-segment the pancreas. DLMC also achieved higher sensitivity (0.80) and specificity (0.99) combining both imaging techniques. LS achieved equivalent sensitivity on VIBE images but was more computationally inefficient. Conclusion: We showed that pancreas and surrounding normal organs can be reliably segmented based on fast MRI using DLMC. This method will facilitate both planning volume definition and imaging guidance during treatment.
Mqcd, ("barely") G2 Manifolds and (orientifold Of) a Compact Calabi-Yau
Misra, Aalok
We begin with a discussion on two apparently disconnected topics — one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G2-manifold evaluated by the path-integral inside a path-integral approach of Ref. 1, and the other centered around the compact Calabi-Yau CY3(3, 243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP4[1, 1, 2, 8, 12]. For the former, we compare the results with the ones of Witten on heterotic worldsheet instantons.2 The subtopics covered in the latter include an =1 triality between Heterotic, M- and F-theories, evaluation of RP2-instanton superpotential, Picard-Fuchs equation for the mirror Landau-Ginzburg model corresponding to CY3(3, 243), D = 11 supergravity corresponding to M-theory compactified on a "barely" G2 manifold involving CY3(3, 243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then shown an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD.3 As an aside, we show that in the limit of vanishing "ζ", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD, the infinite series of Ref. 4 used to represent a suitable embedding of a supersymmetric 3-cycle in a G2-mannifold, can be summed.
Haapala, A. F.; Howell, K. C.
2013-07-01
Temporary satellite capture (TSC) of Jupiter-family comets has been a focus of investigation within the astronomy community for decades. More recently, TSC has been approached from the perspective of dynamical systems theory, within the context of the circular restricted three-body problem (CR3BP). Thus, this problem serves as a testbed for exploring techniques that support trajectory design in similar dynamical regimes. In particular, an association between the invariant manifolds of libration point orbits and the paths of comets that experience TSC has been explored. In this investigation, TSC is further examined from the perspective of transit, that is, transition through the gateways associated with the collinear libration points, in the three-body problem. Periapsis Poincaré maps, previously employed for trajectory design in several investigations, are used to deliver insight into the nature of transit trajectories for energy levels near those associated with several Jupiter-family comets. The evolution of transit trajectories with increasing energy is explored, and the existence of solutions with similar characteristics to the paths of comets P/1996 R2, 82P/Gehrels 3, and 147P/Kushida-Muramatsu is demonstrated within the context of the planar CR3BP using planar periapsis maps. During TSC, the path of comet 111P/Helin-Roman-Crockett is highly inclined with respect to Jupiter; the motion of this comet is examined relative to invariant manifolds in the spatial CR3BP. A method to display the information contained in higher-dimensional Poincaré maps is also demonstrated, and is employed to locate a trajectory possessing the same qualitative characteristics as the path of 111P/Helin-Roman-Crockett.
DEFF Research Database (Denmark)
Larsen, Anders Astrup; Bendsøe, Martin P.; Hattel, Jesper Henri
2009-01-01
The aim of this paper is to optimize a thermal model of a friction stir welding process by finding optimal welding parameters. The optimization is performed using space mapping and manifold mapping techniques in which a coarse model is used along with the fine model to be optimized. Different...
Ebert, Johannes
2016-01-01
We formulate and prove a generalization of the Atiyah-Singer family index theorem in the context of the theory of spaces of manifolds \\`a la Madsen, Tillmann, Weiss, Galatius and Randal-Williams. Our results are for Dirac-type operators linear over arbitrary $C^*$-algebras.
Zagaris, Antonios; Vandekerckhove, Christophe; Gear, C. William; Kaper, Tasso J.; Kevrekidis, Ioannis G.
In [C. W. Gear, T. J. Kaper, I. G. Kevrekidis and A. Zagaris, Projecting to a slow manifold: Singularly perturbed systems and legacy codes, SIAM J. Appl. Dyn. Syst. 4 (2005), 711--732], we developed the family of constrained runs algorithms to find points on low-dimensional, attracting, slow
1981-01-01
The Sunmaster DEC 8A Large Manifold solar collector using simulated conditions was evaluated. The collector provided 17.17 square feet of gross collector area. Test conditions, test requirements, an analysis of results, and tables of test data are reported.
DEFF Research Database (Denmark)
Zimmermann, Ralf
2017-01-01
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm...
Faraoni, Valerio
2013-01-01
This book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski spacetime. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its covariant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates. Every chapter...
Association du personnel
2011-01-01
Are you a member of the Staff Association? Did you know that as a member you can benefit from the following special offers: BCGE (Banque Cantonale de Genève): personalized banking solutions with preferential conditions. TPG: reduced rates on annual transport passes for active and retired staff. Aquaparc: reduced ticket prices for children and adults at this Swiss waterpark in Le Bouveret. Walibi: reduced prices for children and adults at this French attraction park in Les Avenières. FNAC: 5% reduction on FNAC vouchers. For more information about all these offers, please consult our web site: http://association.web.cern.ch/association/en/OtherActivities/Offers.html
Staff Association
2011-01-01
Are you a member of the Staff Association? Did you know that as a member you can benefit from the following special offers: BCGE (Banque Cantonale de Genève): personalized banking solutions with preferential conditions. TPG: reduced rates on annual transport passes for all active and retired staff. Aquaparc: reduced ticket prices for children and adults at this Swiss waterpark in Le Bouveret. Walibi: reduced prices for children and adults at this French attraction park in Les Avenières. FNAC: 5% reduction on FNAC vouchers. For more information about all these offers, please consult our web site: http://association.web.cern.ch/association/en/OtherActivities/Offers.html
2007-01-01
A special wide-load convoy will affect traffic between Hall 180 (Meyrin site) and Point 1 (ATLAS) on Tuesday 29 May. The following measures will be in place: Partial closure of Route Arago and Route Einstein between 9.00 a.m. and 12 midday, depending on the rate at which the convoy advances. Closure of Route Einstein between 12 and 2.00 p.m. between Building 104 and Route Veksler (see diagram). Closure of Entrance B in both directions between 12 and 2.30 p.m. Please use Entrance A. For safety reasons, cyclists and pedestrians will not be allowed to ride or walk alongside the convoy. Please comply with the instructions given by the convoy officers. TS-IC Group (tel : 160319 - 163012)
Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model
Sinou, J.-J.; Thouverez, F.; Jezequel, L.
2003-08-01
This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.
Association du personnel
2012-01-01
Special discount to the members of the Staff Association Aquaparc Discounted prices on admission of whole day. Children from 5 to 15 years: 26.– CHF instead of 35.– CHF; Adults from 16 years: 32.– CHF instead of 43.– CHF.Tickets on sale to the Staff Association Secretariat. BCGE Account management on salary account and annual subscription to credit cards free of charge. Other benefits on mortgage loan and financial planning. Comédie de Genève 20% off on full price tickets (also available for partner): from 24 to 32 CHF a ticket instead of 30 to 40 CHF depending on the shows. Ezee Suisse 15% off on the range of electric bikes upon presentation of your Staff Association membership card before payment. FNAC 5% discount on gifts card available in four Swiss shops without any restriction. Gifts card on sale to the Staff Association Secretariat. FutureKids 15% off for the Staff Association members who enrol their children of 5 to 16 years old in ...
Uncontrolled manifold reference feedback control of multi-joint robot arms
Directory of Open Access Journals (Sweden)
Shunta Togo
2016-07-01
Full Text Available The brain must coordinate with redundant bodies to perform motion tasks. The aim of the present study is to propose a novel control model that predicts the characteristics of human joint coordination at a behavioral level. To evaluate the joint coordination, an uncontrolled manifold (UCM analysis that focuses on the trial-to-trial variance of joints has been proposed. The UCM is a nonlinear manifold associated with redundant kinematics. In this study, we directly applied the notion of the UCM to our proposed control model called the UCM reference feedback control. To simplify the problem, the present study considered how the redundant joints were controlled to regulate a given target hand position. We considered a conventional method that pre-determined a unique target joint trajectory by inverse kinematics or any other optimization method. In contrast, our proposed control method generates a UCM as a control target at each time step. The target UCM is a subspace of joint angles whose variability does not affect the hand position. The joint combination in the target UCM is then selected so as to minimize the cost function, which consisted of the joint torque and torque change. To examine whether the proposed method could reproduce human-like joint coordination, we conducted simulation and measurement experiments. In the simulation experiments, a three-link arm with a shoulder, elbow, and wrist regulates a one-dimensional target of a hand through proposed method. In the measurement experiments, subjects performed a one-dimensional target-tracking task. The kinematics, dynamics, and joint coordination were quantitatively compared with the simulation data of the proposed method. As a result, the UCM reference feedback control could quantitatively reproduce the difference of the mean value for the end hand position between the initial postures, the peaks of the bell-shape tangential hand velocity, the sum of the squared torque, the mean value for
Design and fabrication of intake manifold for formula SAE (Society of Automotive Engineers) race car
Dore, Sylvie; Lavallee, Patrice
1997-01-01
Every year, a group of students from Ecole de technologie superieure (ETS) in Montreal design and build a formula-type race car and compete in the Formula SAE competition. In this paper, we examine the design and fabrication of the ir intake system, A number of constraints challenge the designers. For example, to ensure the security of amateur drivers, motors are restrained to 600 cc and a circular restriction of 20 mm in diameter is placed at the entry of the system. Under these conditions, it is important to optimize the quality of the air/fuel mixture which depends mostly on the air intake system. A theoretical analysis reduced the field of possible runner length. However, the influence of runner configuration, plenum shape and size can only be determined experimentally. Polyacrylic functional prototypes were produced and tested on a dynamometric bench. A stereolithography model representing the inner passageways of the optimal intake manifold was built and used as a positive for a polyurethane mold. A composite lamination process was used to laminate the pre-production prototype over a molded wax plug. The major advantage of this approach over craftsmanship or even machining is the time saved to make the mold and the unlimited complexity of the shape permitted by the rapid prototyping systems.
Joint infrared target recognition and segmentation using a shape manifold-aware level set.
Yu, Liangjiang; Fan, Guoliang; Gong, Jiulu; Havlicek, Joseph P
2015-04-29
We propose new techniques for joint recognition, segmentation and pose estimation of infrared (IR) targets. The problem is formulated in a probabilistic level set framework where a shape constrained generative model is used to provide a multi-class and multi-view shape prior and where the shape model involves a couplet of view and identity manifolds (CVIM). A level set energy function is then iteratively optimized under the shape constraints provided by the CVIM. Since both the view and identity variables are expressed explicitly in the objective function, this approach naturally accomplishes recognition, segmentation and pose estimation as joint products of the optimization process. For realistic target chips, we solve the resulting multi-modal optimization problem by adopting a particle swarm optimization (PSO) algorithm and then improve the computational efficiency by implementing a gradient-boosted PSO (GB-PSO). Evaluation was performed using the Military Sensing Information Analysis Center (SENSIAC) ATR database, and experimental results show that both of the PSO algorithms reduce the cost of shape matching during CVIM-based shape inference. Particularly, GB-PSO outperforms other recent ATR algorithms, which require intensive shape matching, either explicitly (with pre-segmentation) or implicitly (without pre-segmentation).
Vibration sensor data denoising using a time-frequency manifold for machinery fault diagnosis.
He, Qingbo; Wang, Xiangxiang; Zhou, Qiang
2013-12-27
Vibration sensor data from a mechanical system are often associated with important measurement information useful for machinery fault diagnosis. However, in practice the existence of background noise makes it difficult to identify the fault signature from the sensing data. This paper introduces the time-frequency manifold (TFM) concept into sensor data denoising and proposes a novel denoising method for reliable machinery fault diagnosis. The TFM signature reflects the intrinsic time-frequency structure of a non-stationary signal. The proposed method intends to realize data denoising by synthesizing the TFM using time-frequency synthesis and phase space reconstruction (PSR) synthesis. Due to the merits of the TFM in noise suppression and resolution enhancement, the denoised signal would have satisfactory denoising effects, as well as inherent time-frequency structure keeping. Moreover, this paper presents a clustering-based statistical parameter to evaluate the proposed method, and also presents a new diagnostic approach, called frequency probability time series (FPTS) spectral analysis, to show its effectiveness in fault diagnosis. The proposed TFM-based data denoising method has been employed to deal with a set of vibration sensor data from defective bearings, and the results verify that for machinery fault diagnosis the method is superior to two traditional denoising methods.
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-11-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
Simulation of two-phase flow in horizontal fracture networks with numerical manifold method
Ma, G. W.; Wang, H. D.; Fan, L. F.; Wang, B.
2017-10-01
The paper presents simulation of two-phase flow in discrete fracture networks with numerical manifold method (NMM). Each phase of fluids is considered to be confined within the assumed discrete interfaces in the present method. The homogeneous model is modified to approach the mixed fluids. A new mathematical cover formation for fracture intersection is proposed to satisfy the mass conservation. NMM simulations of two-phase flow in a single fracture, intersection, and fracture network are illustrated graphically and validated by the analytical method or the finite element method. Results show that the motion status of discrete interface significantly depends on the ratio of mobility of two fluids rather than the value of the mobility. The variation of fluid velocity in each fracture segment and the driven fluid content are also influenced by the ratio of mobility. The advantages of NMM in the simulation of two-phase flow in a fracture network are demonstrated in the present study, which can be further developed for practical engineering applications.
Directory of Open Access Journals (Sweden)
HongZhong Tang
2016-01-01
Full Text Available Optimizing the mutual coherence of a learned dictionary plays an important role in sparse representation and compressed sensing. In this paper, a efficient framework is developed to learn an incoherent dictionary for sparse representation. In particular, the coherence of a previous dictionary (or Gram matrix is reduced sequentially by finding a new dictionary (or Gram matrix, which is closest to the reference unit norm tight frame of the previous dictionary (or Gram matrix. The optimization problem can be solved by restricting the tightness and coherence alternately at each iteration of the algorithm. The significant and different aspect of our proposed framework is that the learned dictionary can approximate an equiangular tight frame. Furthermore, manifold optimization is used to avoid the degeneracy of sparse representation while only reducing the coherence of the learned dictionary. This can be performed after the dictionary update process rather than during the dictionary update process. Experiments on synthetic and real audio data show that our proposed methods give notable improvements in lower coherence, have faster running times, and are extremely robust compared to several existing methods.
Wei, Chao; Luo, Senlin; Ma, Xincheng; Ren, Hao; Zhang, Ji; Pan, Limin
2016-01-01
Topic models and neural networks can discover meaningful low-dimensional latent representations of text corpora; as such, they have become a key technology of document representation. However, such models presume all documents are non-discriminatory, resulting in latent representation dependent upon all other documents and an inability to provide discriminative document representation. To address this problem, we propose a semi-supervised manifold-inspired autoencoder to extract meaningful latent representations of documents, taking the local perspective that the latent representation of nearby documents should be correlative. We first determine the discriminative neighbors set with Euclidean distance in observation spaces. Then, the autoencoder is trained by joint minimization of the Bernoulli cross-entropy error between input and output and the sum of the square error between neighbors of input and output. The results of two widely used corpora show that our method yields at least a 15% improvement in document clustering and a nearly 7% improvement in classification tasks compared to comparative methods. The evidence demonstrates that our method can readily capture more discriminative latent representation of new documents. Moreover, some meaningful combinations of words can be efficiently discovered by activating features that promote the comprehensibility of latent representation.
Analysis and algebra on differentiable manifolds a workbook for students and teachers
Gadea, P M
2001-01-01
A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Henc...
Manifold decrease of sialic acid synthase in fetal Down syndrome brain.
Gulesserian, T; Engidawork, E; Fountoulakis, M; Lubec, G
2007-01-01
Down syndrome (DS, trisomy 21) is the most common genetic cause of mental retardation. A large series of biochemical defects have been observed in fetal and adult DS brain that help in unraveling the molecular mechanisms underlying mental retardation. As sialylation of glycoconjugates plays an important role in brain development, this study aimed to look at the sialic acid metabolism by measuring sialic acid synthase (SAS; N-acetylneuraminate synthase) in early second trimester fetal control and DS brain. In this regard, protein profiling was performed by two-dimensional gel electrophoresis coupled to matrix-assisted laser desorption/ionization mass-spectrometry followed by database search and subsequent quantification of spot using specific software. SAS, the enzyme catalyzing synthesis of N-acetyl-neuraminic acid (syn: sialic acid) was represented as a single spot and found to be significantly and manifold reduced (P sialic acid metabolism, required for brain development and, more specifically, for sialylation of key brain proteins, including neuronal cell adhesion molecule and myelin associated glycoprotein.
EEG-based emotion recognition with manifold regularized extreme learning machine.
Peng, Yong; Zhu, Jia-Yi; Zheng, Wei-Long; Lu, Bao-Liang
2014-01-01
EEG signals, which can record the electrical activity along the scalp, provide researchers a reliable channel for investigating human emotional states. In this paper, a new algorithm, manifold regularized extreme learning machine (MRELM), is proposed for recognizing human emotional states (positive, neutral and negative) from EEG data, which were previously evoked by watching different types of movie clips. The MRELM can simultaneously consider the geometrical structure and discriminative information in EEG data. Using differential entropy features across whole five frequency bands, the average accuracy of MRELM is 81.01%, which is better than those obtained by GELM (80.25%) and SVM (76.62%). The accuracies obtained from high frequency band features (β, γ) are obviously superior to those of low frequency band features, which shows β and γ bands are more relevant to emotional states transition. Moreover, experiments are conducted to further evaluate the efficacy of MRELM, where the training and test sets are from different sessions. The results demonstrate that the proposed MRELM is a competitive model for EEG-based emotion recognition.
Toy Models of Universe with an Effective Varying Λ-Term in Lyra Manifold
Directory of Open Access Journals (Sweden)
Martiros Khurshudyan
2015-01-01
Full Text Available Research on the accelerated expansion of our Universe captures a lot of attention. The dark energy (DE is a way to explain it. In this paper we will consider scalar field quintessence DE with ωDE>-1 EoS, where the dynamics of the DE models related to the dynamics of the scalar field. We are interested in the study of the behavior of the Universe in the presence of interacting quintessence DE models in Lyra manifold with a varying Λt. In a considered framework we also would like to propose a new form for Λt. We found that the models correspond to the transit Universe, which will enter the accelerated expansion phase and will remain there with a constant deceleration parameter q. We found also that the Λt is a decreasing function which takes a small positive value with Ωm≠0 and ΩQ→const dominating Ωm in the old Universe. Observational constraints are applied and causality issue via CS2 is discussed as a possible way to either reject or accept the models.
Zhu, Rong; Liu, Jin-Xing; Zhang, Yuan-Ke; Guo, Ying
2017-12-02
Detecting genomes with similar expression patterns using clustering techniques plays an important role in gene expression data analysis. Non-negative matrix factorization (NMF) is an effective method for clustering the analysis of gene expression data. However, the NMF-based method is performed within the Euclidean space, and it is usually inappropriate for revealing the intrinsic geometric structure of data space. In order to overcome this shortcoming, Cai et al. proposed a novel algorithm, called graph regularized non-negative matrices factorization (GNMF). Motivated by the topological structure of the GNMF-based method, we propose improved graph regularized non-negative matrix factorization (GNMF) to facilitate the display of geometric structure of data space. Robust manifold non-negative matrix factorization (RM-GNMF) is designed for cancer gene clustering, leading to an enhancement of the GNMF-based algorithm in terms of robustness. We combine the l 2 , 1 -norm NMF with spectral clustering to conduct the wide-ranging experiments on the three known datasets. Clustering results indicate that the proposed method outperforms the previous methods, which displays the latest application of the RM-GNMF-based method in cancer gene clustering.
Arruga, H.; Scholl, F.; Kettner, M.; Amad, O. I.; Klaissle, M.; Giménez, B.
2017-10-01
Design and development of gas CHP (combined heat and power) engines are strongly influenced by the progressively more severe European NOx emissions normative. Water injection represents a promising approach to reduce these emissions while attaining high engine efficiency. In this work, the effect of intake manifold water injection on combustion parameters and performance of a single-cylinder naturally aspirated natural gas spark ignition engine is presented. First, the most appropriate injector was selected, using a spray test bed. Subsequently, engine experiments at constant indicated mean effective pressure (IMEP) and engine speed were conducted with water-fuel ratios of 0.1 to 0.3. IMEP was kept constant at about 6.3 bar by adjusting both air-fuel ratio and spark timing. A NOx reduction of 0.2 g/kWhi (15 %) for a constant ISFC of about 204 g/kWhi was achieved. In the low NOx regime, water injection allows for an improvement of the NOx-ISFC trade-off, while leading to poor fuel consumption at same NOx in the high efficiency regime. Furthermore, water injection implies a reduction of intake mixture temperature, lengthened burning delay and combustion duration and a moderate increase of combustion instability.
Discriminant analysis of resting-state functional connectivity patterns on the Grassmann manifold
Fan, Yong; Liu, Yong; Jiang, Tianzi; Liu, Zhening; Hao, Yihui; Liu, Haihong
2010-03-01
The functional networks, extracted from fMRI images using independent component analysis, have been demonstrated informative for distinguishing brain states of cognitive functions and neurological diseases. In this paper, we propose a novel algorithm for discriminant analysis of functional networks encoded by spatial independent components. The functional networks of each individual are used as bases for a linear subspace, referred to as a functional connectivity pattern, which facilitates a comprehensive characterization of temporal signals of fMRI data. The functional connectivity patterns of different individuals are analyzed on the Grassmann manifold by adopting a principal angle based subspace distance. In conjunction with a support vector machine classifier, a forward component selection technique is proposed to select independent components for constructing the most discriminative functional connectivity pattern. The discriminant analysis method has been applied to an fMRI based schizophrenia study with 31 schizophrenia patients and 31 healthy individuals. The experimental results demonstrate that the proposed method not only achieves a promising classification performance for distinguishing schizophrenia patients from healthy controls, but also identifies discriminative functional networks that are informative for schizophrenia diagnosis.
Inferring imagined speech using EEG signals: a new approach using Riemannian manifold features
Nguyen, Chuong H.; Karavas, George K.; Artemiadis, Panagiotis
2018-02-01
Objective. In this paper, we investigate the suitability of imagined speech for brain–computer interface (BCI) applications. Approach. A novel method based on covariance matrix descriptors, which lie in Riemannian manifold, and the relevance vector machines classifier is proposed. The method is applied on electroencephalographic (EEG) signals and tested in multiple subjects. Main results. The method is shown to outperform other approaches in the field with respect to accuracy and robustness. The algorithm is validated on various categories of speech, such as imagined pronunciation of vowels, short words and long words. The classification accuracy of our methodology is in all cases significantly above chance level, reaching a maximum of 70% for cases where we classify three words and 95% for cases of two words. Significance. The results reveal certain aspects that may affect the success of speech imagery classification from EEG signals, such as sound, meaning and word complexity. This can potentially extend the capability of utilizing speech imagery in future BCI applications. The dataset of speech imagery collected from total 15 subjects is also published.
Wu, Jiayi; Ma, Yong-Bei; Congdon, Charles; Brett, Bevin; Chen, Shuobing; Xu, Yaofang; Ouyang, Qi; Mao, Youdong
2017-01-01
Structural heterogeneity in single-particle cryo-electron microscopy (cryo-EM) data represents a major challenge for high-resolution structure determination. Unsupervised classification may serve as the first step in the assessment of structural heterogeneity. However, traditional algorithms for unsupervised classification, such as K-means clustering and maximum likelihood optimization, may classify images into wrong classes with decreasing signal-to-noise-ratio (SNR) in the image data, yet demand increased computational costs. Overcoming these limitations requires further development of clustering algorithms for high-performance cryo-EM data processing. Here we introduce an unsupervised single-particle clustering algorithm derived from a statistical manifold learning framework called generative topographic mapping (GTM). We show that unsupervised GTM clustering improves classification accuracy by about 40% in the absence of input references for data with lower SNRs. Applications to several experimental datasets suggest that our algorithm can detect subtle structural differences among classes via a hierarchical clustering strategy. After code optimization over a high-performance computing (HPC) environment, our software implementation was able to generate thousands of reference-free class averages within hours in a massively parallel fashion, which allows a significant improvement on ab initio 3D reconstruction and assists in the computational purification of homogeneous datasets for high-resolution visualization.
Modeling of EGR Mixing in an Engine Intake Manifold Using LES
Directory of Open Access Journals (Sweden)
Sakowitz A.
2013-10-01
Full Text Available We investigate the mixing process of exhaust gases with fresh air in Internal Combustion Engines (ICE. For this purpose, the flow in an inlet manifold of a six-cylinder heavy-duty Diesel engine is computed using compressible Large Eddy Simulations (LES. The Exhaust Gas Recirculation (EGR concentration is modeled as a passive scalar. The results are validated by on-engine measurements of the EGR concentration using COZ probes. The boundary conditions for the highly pulsating flow are taken partly from one-dimensional simulations, partly from pressure measurements on the engine. In order to assess the sensitivity to the boundary conditions, changes are applied to the base-line case. The mixing quality is evaluated in terms of cylinder-to-cylinder distribution and the spatial RMS over the outlet cross- sections. Different averaging techniques are applied. It was found that the temporal and spatial EGR distribution is different among the cylinders. The EGR distribution within the cylinder inlet is non-uniform. These factors imply that one should not use a time-averaged EGR value as indicator for the EGR content. Furthermore, it was found that the flow pulsations at the EGR inlet have a large influence on the EGR distribution. By comparing the LES results with measurements, it was shown that LES gives a better and deeper insight into the mixing in such turbulent, pulsating flow situations.
Reissner-Nordstrøm-de Sitter manifold: photon sphere and maximal analytic extension
Mokdad, Mokdad
2017-09-01
This paper is devoted to the study of Reissner-Nordstrøm-de Sitter black holes and their maximal analytic extensions. Here, we find the necessary and sufficient conditions on the parameters of the Reissner-Nordstrøm-de Sitter metric—namely, the mass, the charge, and the cosmological constant—to have three horizons. Under these conditions, we prove that there is only one photon sphere and we locate it. We then give a detailed construction of the maximal analytic extension of the Reissner-Nordstrøm-de Sitter manifold in the case of three horizons. Studying these properties lays the groundwork for obtaining (in separate papers) decay results (Mokdad 2017 Decay of Maxwell fields on Reissner-Nordstrøm-de Sitter black holes (arXiv:1704.06441)) and constructing conformal scattering theories for test fields on such spacetimes (Mokdad 2017 Conformal scattering of Maxwell fields on Reissner-Nordstrøm-de Sitter black hole spacetimes (arXiv:1706.06993)).
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-07-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
Inferring imagined speech using EEG signals: a new approach using Riemannian Manifold features.
Nguyen, Chuong H; Karavas, Georgios; Artemiadis, Panagiotis
2017-07-26
In this paper, we investigate the suitability of imagined speech for Brain-Computer Interface applications (BCI). A novel method based on covariance matrix descriptors, which lie in Riemannian manifold, and the Relevance Vector Machines classifier is proposed. The method is applied on ElectroEncephaloGraphic (EEG) signals and tested in multiple subjects. The method is shown to outperform other approaches in the field with respect to accuracy and robustness. The algorithm is validated on various categories of speech, such as imagined pronunciation of vowels, short words and long words. The classification accuracy of our methodology is in all cases significantly above chance level, reaching a maximum of 70% for cases where we classify three words and 95% for cases of two words. The results reveal certain aspects that may affect the success of speech imagery classification from EEG signals, such as sound, meaning and word complexity. This can potentially extend the capability of utilizing speech imagery in future BCI applications. The dataset of speech imagery collected from total 15 subjects is also published. © 2017 IOP Publishing Ltd.