Orientifolds of type IIA strings on Calabi-Yau manifolds
Indian Academy of Sciences (India)
The advent of D-branes has led to a better understanding of dualities involving strong coupling limits. In particular, Ж = 1 compactifications of the heterotic string (on Calabi-Yau manifolds) are no longer the only string theories of phe- nomenological interest. One such class is furnished by M-theory compactifications.
Holomorphic Yukawa couplings for complete intersection Calabi-Yau manifolds
Energy Technology Data Exchange (ETDEWEB)
Blesneag, Stefan [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom); Buchbinder, Evgeny I. [The University of Western Australia,35 Stirling Highway, Crawley WA 6009 (Australia); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)
2017-01-27
We develop methods to compute holomorphic Yukawa couplings for heterotic compactifications on complete intersection Calabi-Yau manifolds, generalising results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based on constructing the required bundle-valued forms explicitly and evaluating the relevant integrals over the projective ambient space. We also show how our approach relates to an earlier, algebraic one to calculate the holomorphic Yukawa couplings. A vanishing theorem, which we prove, implies that certain Yukawa couplings allowed by low-energy symmetries are zero due to topological reasons. To illustrate our methods, we calculate Yukawa couplings for SU(5)-based standard models on a co-dimension two complete intersection manifold.
Topological strings on Grassmannian Calabi-Yau manifolds
International Nuclear Information System (INIS)
Haghighat, Babak; Klemm, Albrecht
2009-01-01
We present solutions for the higher genus topological string amplitudes on Calabi-Yau-manifolds, which are realized as complete intersections in Grassmannians. We solve the B-model by direct integration of the holomorphic anomaly equations using a finite basis of modular invariant generators, the gap condition at the conifold and other local boundary conditions for the amplitudes. Regularity of the latter at certain points in the moduli space suggests a CFT description. The A-model amplitudes are evaluated using a mirror conjecture for Calabi-Yau complete intersections in Grassmannians by Batyrev, Ciocan-Fontanine, Kim and Van Straten. The integrality of the BPS states gives strong evidence for the conjecture.
Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry
Directory of Open Access Journals (Sweden)
Hyun Seok Yang
2017-01-01
Full Text Available We address the issue of why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6 requires us to consider the vector spaces of two forms and four forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles the variety of six-dimensional spin manifolds. We explore how the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the gauge theory formulation of six-dimensional Riemannian manifolds, we show that the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian Yang-Mills equations on the Calabi-Yau manifold. Therefore, the mirror symmetry of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory perspective.
Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds
Buchbinder, Evgeny; Lukas, Andre; Ovrut, Burt; Ruehle, Fabian
2017-10-01
We study Pfaffians that appear in non-perturbative superpotential terms arising from worldsheet instantons in heterotic theories. A result by Beasley and Witten shows that these instanton contributions cancel among curves within a given homology class for Calabi-Yau manifolds that can be described as hypersurfaces or complete intersections in projective or toric ambient spaces. We provide a prescription that identifies all ℙ1 curves in certain homology classes of complete intersection Calabi-Yau manifolds in products of projective spaces (CICYs) and cross-check our results by a comparison with the genus zero Gromov-Witten invariants. We then use this construction to study instanton superpotentials on those manifolds and their quotients. We identify a non-toric quotient of a non-favorable CICY with a single genus zero curve in a certain homology class, so that a cancellation à la Beasley-Witten is not possible. In another example, we study a non-toric quotient of a favorable CICY and check that the superpotential still vanishes. From this and related examples, we conjecture that the Beasley-Witten cancellation result can be extended to toric and non-toric quotients of CICYs, but can be avoided if the CICY is non-favorable.
Cyclic coverings, Calabi-Yau manifolds and complex multiplication
Rohde, Christian
2009-01-01
The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are a...
Iterated Mellin-Barnes integrals as period on the Calabi-Yau manifolds with several modules
International Nuclear Information System (INIS)
Passare, M.; Tsikh, A.K.; Cheshel', A.A.
1996-01-01
In superstring compactification theory the representation of periods on the Calabi-Yau manifolds with several modules is given by iterated Mellin-Barnes integrals. By using this representation and multidimensional residues a method of analytic continuation for fundamental period in terms of Gorn series is developed
Non-compact Calabi-Yau manifolds and localized gravity
International Nuclear Information System (INIS)
Antoniadis, Ignatios.; Minasian, Ruben.; Vanhove, Pierre.
2003-01-01
We study localization of gravity in flat space in superstring theory. We find that an induced Einstein-Hilbert term can be generated only in four dimensions, when the bulk is a non-compact Calabi-Yau threefold with non-vanishing Euler number. The origin of this term is traced to R 4 couplings in ten dimensions. Moreover, its size can be made much larger than the ten-dimensional gravitational Planck scale by tuning the string coupling to be very small or the Euler number to be very large. We also study the width of the localization and discuss the problems for constructing realistic string models with no compact extra dimensions
Results from an Algebraic Classification of Calabi-Yau Manifolds
Anselmo, F; Nanopoulos, Dimitri V; Volkov, G
2001-01-01
We present results from an inductive algebraic approach to the systematic construction and classification of the `lowest-level' CY3 spaces defined as zeroes of polynomial loci associated with reflexive polyhedra, derived from suitable vectors in complex projective spaces. These CY3 spaces may be sorted into `chains' obtained by combining lower-dimensional projective vectors classified previously. We analyze all the 4242 (259, 6, 1) two- (three-, four-, five-) vector chains, which have, respectively, K3 (elliptic, line-segment, trivial) fibres, yielding 174767 (an additional 6189, 1582, 199) distinct projective vectors that define reflexive polyhedra and thereby CY3 spaces, for a total of 182737. These CY3 spaces span 10827 (a total of 10882) distinct pairs of Hodge numbers h_11, h_12. Among these, we list explicitly a total of 212 projective vectors defining three-generation CY3 spaces with K3 fibrations, whose characteristics we provide.
One-dimensional super Calabi-Yau manifolds and their mirrors
Energy Technology Data Exchange (ETDEWEB)
Noja, S. [Dipartimento di Matematica, Università degli Studi di Milano,Via Saldini 50, I-20133 Milano (Italy); Cacciatori, S.L. [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy); Piazza, F. Dalla [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); Marrani, A. [Centro Studi e Ricerche ‘Enrico Fermi’,Via Panisperna 89A, I-00184 Roma (Italy); Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova,and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy); Re, R. [Dipartimento di Matematica e Informatica, Università degli Studi di Catania,Viale Andrea Doria 6, 95125 Catania (Italy)
2017-04-18
We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY’s having reduced manifold equal to ℙ{sup 1}, namely the projective super space ℙ{sup 1|2} and the weighted projective super space Wℙ{sub (2)}{sup 1|1}. Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces ℙ{sup n|m}. We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of ℙ{sup 1|2}, whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of ℙ{sup 1|m}, discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that ℙ{sup 1|2} is self-mirror, whereas Wℙ{sub (2)}{sup 1|1} has a zero dimensional mirror. Also, the mirror map for ℙ{sup 1|2} naturally endows it with a structure of N=2 super Riemann surface.
Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries
Braun, Volker; Cvetič, Mirjam; Donagi, Ron; Poretschkin, Maximilian
2017-07-01
We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z_2× Z_2 . Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the cfour-dimensional theory.
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.
Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications
Energy Technology Data Exchange (ETDEWEB)
Cicoli, Michele [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Mayrhofer, Christoph [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Kreuzer, Maximilian
2011-06-15
We analyse several explicit toric examples of compact K3-fibred Calabi-Yau three-folds which can be used for the study of string dualities and are crucial ingredients for the construction of LARGE Volume type IIB vacua with promising applications to cosmology and particle phenomenology. In order to build a phenomenologically viable model, on top of the two moduli corresponding to the base and the K3 fibre, we demand also the existence of two additional rigid divisors: the first supporting the non-perturbative effects needed to achieve moduli stabilisation, and the second allowing the presence of chiral matter on wrapped D-branes. We clarify the topology of these rigid divisors by discussing the interplay between a diagonal structure of the Calabi-Yau volume and D-terms. Del Pezzo divisors appearing in the volume form in a completely diagonal way are natural candidates for supporting non-perturbative effects and for quiver constructions, while 'non-diagonal' del Pezzo and rigid but not del Pezzo divisors are particularly interesting for model building in the geometric regime. Searching through the existing list of four dimensional reflexive lattice polytopes, we find 158 examples admitting a Calabi-Yau hypersurface which is a K3 fibration with four Kaehler moduli where at least one of them is a 'diagonal' del Pezzo. We work out explicitly the topological details of a few examples showing how, in the case of simplicial polytopes, all the del Pezzo divisors are 'diagonal', while 'non-diagonal' ones appear only in the case of non-simplicial polytopes. A companion paper will use these results in the study of moduli stabilisation for globally consistent explicit Calabi-Yau compactifications with the local presence of chirality. (orig.)
Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications
International Nuclear Information System (INIS)
Cicoli, Michele; Mayrhofer, Christoph; Kreuzer, Maximilian
2011-06-01
We analyse several explicit toric examples of compact K3-fibred Calabi-Yau three-folds which can be used for the study of string dualities and are crucial ingredients for the construction of LARGE Volume type IIB vacua with promising applications to cosmology and particle phenomenology. In order to build a phenomenologically viable model, on top of the two moduli corresponding to the base and the K3 fibre, we demand also the existence of two additional rigid divisors: the first supporting the non-perturbative effects needed to achieve moduli stabilisation, and the second allowing the presence of chiral matter on wrapped D-branes. We clarify the topology of these rigid divisors by discussing the interplay between a diagonal structure of the Calabi-Yau volume and D-terms. Del Pezzo divisors appearing in the volume form in a completely diagonal way are natural candidates for supporting non-perturbative effects and for quiver constructions, while 'non-diagonal' del Pezzo and rigid but not del Pezzo divisors are particularly interesting for model building in the geometric regime. Searching through the existing list of four dimensional reflexive lattice polytopes, we find 158 examples admitting a Calabi-Yau hypersurface which is a K3 fibration with four Kaehler moduli where at least one of them is a 'diagonal' del Pezzo. We work out explicitly the topological details of a few examples showing how, in the case of simplicial polytopes, all the del Pezzo divisors are 'diagonal', while 'non-diagonal' ones appear only in the case of non-simplicial polytopes. A companion paper will use these results in the study of moduli stabilisation for globally consistent explicit Calabi-Yau compactifications with the local presence of chirality. (orig.)
The web of D-branes at singularities in compact Calabi-Yau manifolds
Cicoli, Michele; Krippendorf, Sven; Mayrhofer, Christoph; Quevedo, Fernando; Valandro, Roberto
2013-05-01
We present novel continuous supersymmetric transitions which take place among different chiral configurations of D3/D7 branes at singularities in the context of type IIB Calabi-Yau compactifications. We find that distinct local models which admit a consistent global embedding can actually be connected to each other along flat directions by means of transitions of bulk-to-flavour branes. This has interesting interpretations in terms of brane recombination/splitting and brane/anti-brane creation/annihilation. These transitions give rise to a large web of quiver gauge theories parametrised by splitting/recombination modes of bulk branes which are not present in the non-compact case. We illustrate our results in concrete global embeddings of chiral models at a dP0 singularity.
On topological string theory with Calabi-Yau backgrounds
Energy Technology Data Exchange (ETDEWEB)
Haghighat, Babak
2010-06-15
String theory represents a unifying framework for quantum field theory as well as for general relativity combining them into a theory of quantum gravity. The topological string is a subsector of the full string theory capturing physical amplitudes which only depend on the topology of the compactification manifold. Starting with a review of the physical applications of topological string theory we go on to give a detailed description of its theoretical framework and mathematical principles. Having this way provided the grounding for concrete calculations we proceed to solve the theory on three major types of Calabi-Yau manifolds, namely Grassmannian Calabi-Yau manifolds, local Calabi-Yau manifolds, and K3 fibrations. Our method of solution is the integration of the holomorphic anomaly equations and fixing the holomorphic ambiguity by physical boundary conditions. We determine the correct parameterization of the ambiguity and new boundary conditions at various singularity loci in moduli space. Among the main results of this thesis are the tables of degeneracies of BPS states in the appendices and the veri cation of the correct microscopic entropy interpretation for five dimensional extremal black holes arising from compactifications on Grassmannian Calabi-Yau manifolds. (orig.)
On topological string theory with Calabi-Yau backgrounds
Energy Technology Data Exchange (ETDEWEB)
Haghighat, Babak
2009-10-29
String theory represents a unifying framework for quantum field theory as well as for general relativity combining them into a theory of quantum gravity. The topological string is a subsector of the full string theory capturing physical amplitudes which only depend on the topology of the compactification manifold. Starting with a review of the physical applications of topological string theory we go on to give a detailed description of its theoretical framework and mathematical principles. Having this way provided the grounding for concrete calculations we proceed to solve the theory on three major types of Calabi-Yau manifolds, namely Grassmannian Calabi-Yau manifolds, local Calabi-Yau manifolds, and K3 fibrations. Our method of solution is the integration of the holomorphic anomaly equations and fixing the holomorphic ambiguity by physical boundary conditions. We determine the correct parameterization of the ambiguity and new boundary conditions at various singularity loci in moduli space. Among the main results of this thesis are the tables of degeneracies of BPS states in the appendices and the verification of the correct microscopic entropy interpretation for five dimensional extremal black holes arising from compactifications on Grassmannian Calabi-Yau manifolds. (orig.)
Gauge Theory and Calibrated Geometry for Calabi-Yau 4-folds
Cao, Yalong
This thesis is devoted to the study of gauge theory and calibrated geometry for Calabi-Yau 4-folds. More specifically, our study is along the following five directions. 1. We develop Donaldson-Thomas type theory on Calabi-Yau 4-folds. Let X be a compact complex Calabi-Yau 4-fold. We define Donaldson-Thomas type deformation invariants (DT4 invariants) by studying moduli spaces of solutions to the Donaldson- Thomas equations on X. We also study sheaves counting problems on local Calabi-Yau 4-folds. We relate DT4 invariants of KY to the Donaldson-Thomas invariants of the associated Fano 3-fold Y. When the Calabi-Yau 4-fold is toric, we adapt the virtual localization formula to define the corresponding equivariant DT4 invariants. We also discuss the non-commutative version of DT4 invariants for quivers with relations. Finally, we compute DT4 invariants for certain Calabi-Yau 4-folds when moduli spaces are smooth and find a DT 4/GW correspondence for X. Examples of wall-crossing phenomenon in DT4 theory are also given. 2. Given a complex 4-fold X with an (Calabi-Yau 3-fold) anti-canonical divisor Y, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of Y. We also discuss gluing formulas which relate relative invariants and DT4 invariants for Calabi-Yau 4-folds. 3. We study orientability issues of moduli spaces from gauge theories on Calabi-Yau manifolds. Our results generalize and strengthen those for Donaldson-Thomas theory on Calabi-Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing formula in DT theory. 4. Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds. More precisely, we study calibrated geometry in the sense of Harvey-Lawson and Lagrangian
Mirror Symmetry, D-brane Superpotential and Ooguri-Vafa Invariants of Compact Calabi-Yau Manifolds
Zhang, Shan-Shan; Yang, Fu-Zhong
2015-01-01
The D-brane superpotential is very important in the low energy effective theory. As the generating function of all disk instantons from the worldsheet point of view, it plays a crucial role in deriving some important properties of the compact Calabi–Yau manifolds. By using the generalized GKZ hypergeometric system, we will calculate the D-brane superpotentials of two non-Fermat type compact Calabi–Yau hypersurfaces in toric varieties, respectively. Then according to the mirror symmetry, we ob...
New large volume Calabi-Yau threefolds
Altman, Ross; He, Yang-Hui; Jejjala, Vishnu; Nelson, Brent D.
2018-02-01
In previous work, we have commenced the task of unpacking the 473 800 776 reflexive polyhedra by Kreuzer and Skarke into a database of Calabi-Yau threefolds [R. Altman et al. J. High Energy Phys. 02 (2015) 158., 10.1007/JHEP02(2015)158] (see www.rossealtman.com). In this paper, following a pedagogical introduction, we present a new algorithm to isolate Swiss cheese solutions characterized by "holes," or small 4-cycles, descending from the toric divisors inherent to the original four dimensional reflexive polyhedra. Implementing these methods, we find 2268 explicit Swiss cheese manifolds, over half of which have h1 ,1=6 . Many of our solutions have multiple large cycles. Such Swiss cheese geometries facilitate moduli stabilization in string compactifications and provide flat directions for cosmological inflation.
Discrete gauge groups in F-theory models on genus-one fibered Calabi-Yau 4-folds without section
Kimura, Yusuke
2017-04-01
We determine the discrete gauge symmetries that arise in F-theory compactifications on examples of genus-one fibered Calabi-Yau 4-folds without a section. We construct genus-one fibered Calabi-Yau 4-folds using Fano manifolds, cyclic 3-fold covers of Fano 4-folds, and Segre embeddings of products of projective spaces. Discrete ℤ 5, ℤ 4, ℤ 3 and ℤ 2 symmetries arise in these constructions. We introduce a general method to obtain multisections for several constructions of genus-one fibered Calabi-Yau manifolds. The pullbacks of hyperplane classes under certain projections represent multisections to these genus-one fibrations. We determine the degrees of these multisections by computing the intersection numbers with fiber classes. As a result, we deduce the discrete gauge symmetries that arise in F-theory compactifications. This method applies to various Calabi-Yau genus-one fibrations.
TOPICAL REVIEW: The many symmetries of Calabi-Yau compactifications
Emam, Moataz H.
2010-08-01
We review the major mathematical concepts involved in the dimensional reduction of D = 11 {\\cal N}=1 supergravity theory over a Calabi-Yau manifold with non-trivial complex structure moduli resulting in ungauged D = 5 {\\cal N}=2 supergravity theory with hypermultiplets. The latter has a particularly rich structure with many underlying geometries. We reproduce the entire calculation and particularly emphasize its symplectic symmetry and how that arises from the topology of the underlying subspace. The review is intended to fill a specific gap in the literature with the hope that it will be useful to both the beginner and the expert alike.
Duality Group for Calabi-Yau 2-Moduli Space
Ceresole, A.; D'Auria, R.; Regge, T.
1993-01-01
We present an efficient method for computing the duality group $\\Gamma$ of the moduli space \\cM for strings compactified on a Calabi-Yau manifold described by a two-moduli deformation of the quintic polynomial immersed in $\\CP(4)$, $\\cW={1\\over5}(\\iy_1^5+\\cdots+\\iy_5^5)-a\\,\\iy_4^3 \\iy_5^2 -b\\, \\iy_4^2 \\iy_5^3$. We show that $\\Gamma$ is given by a $3$--dimensional representation of a central extension of $B_5$, the braid group on five strands.
Heterotic Non-Kähler Geometries via Polystable Bundles on Calabi-Yau Threefolds
DEFF Research Database (Denmark)
Andreas, Bjorn; Garcia Fernandez, Mario
2012-01-01
In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi-Yau threefold X which satisfies c_2(X) = c_2(V ) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case...... compactifications via non-Kähler deformation of Calabi-Yau geometries with polystable bundles. As an application, we obtain examples of non- Kähler deformations of some three generation GUT models....
Instantons on Calabi-Yau cones
Sperling, Marcus
2015-12-01
The Hermitian Yang-Mills equations on certain vector bundles over Calabi-Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of Donaldson and Kronheimer used in the study of the original Nahm equations. Starting from certain equivariant connections, we show that the full set of instanton equations reduce, with a unique gauge transformation, to the holomorphicity condition alone.
Hermitian Yang-Mills instantons on Calabi-Yau cones
Paccetti Correia, Filipe
2009-12-01
We study and construct non-abelian hermitian Yang-Mills (HYM) instantons on Calabi-Yau cones. By means of a particular isometry preserving ansatz, the HYM equations are reduced to a novel Higgs-Yang-Mills flow on the Einstein-Kähler base. For any 2dBbb C-dimensional Calabi-Yau cone, we find explicit solutions of the flow equations that correspond to non-trivial SU(dBbb C) HYM instantons. These can be regarded as deformations of the spin connection of the Calabi-Yau cone.
Instantons on Calabi-Yau and hyper-Kähler cones
Geipel, Jakob C.; Sperling, Marcus
2017-10-01
The instanton equations on vector bundles over Calabi-Yau and hyper-Kähler cones can be reduced to matrix equations resembling Nahm's equations. We complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau cones, based on regular semi-simple elements, by a new set of (singular) boundary conditions which have a known instanton solution in one direction. This approach extends the classic results of Kronheimer by probing a relation between generalised Nahm's equations and nilpotent pairs/tuples. Moreover, we consider quaternionic instantons on hyper-Kähler cones over generic 3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up, using the fact that their analysis can be traced back to the intersection of three Hermitian Yang-Mills conditions.
Discrete Symmetries of Calabi-Yau Hypersurfaces in Toric Four-Folds
Braun, Andreas P.; Lukas, Andre; Sun, Chuang
2017-12-01
We analyze freely-acting discrete symmetries of Calabi-Yau three-folds defined as hypersurfaces in ambient toric four-folds. An algorithm that allows the systematic classification of such symmetries which are linearly realised on the toric ambient space is devised. This algorithm is applied to all Calabi-Yau manifolds with {h^{1,1}(X)≤ 3} obtained by triangulation from the Kreuzer-Skarke list, a list of some 350 manifolds. All previously known freely-acting symmetries on these manifolds are correctly reproduced and we find five manifolds with freely-acting symmetries. These include a single new example, a manifold with a {Z_2×Z_2} symmetry where only one of the {Z_2} factors was previously known. In addition, a new freely-acting {Z_2} symmetry is constructed for a manifold with {h^{1,1}(X)=6} . While our results show that there are more freely-acting symmetries within the Kreuzer-Skarke set than previously known, it appears that such symmetries are relatively rare.
The classification of 3-dimensional noetherian cubic Calabi-Yau algebras
Mori, Izuru; Ueyama, Kenta
2016-01-01
It is known that every 3-dimensional noetherian Calabi-Yau algebra generated in degree 1 is isomorphic to a Jacobian algebra of a superpotential. Recently, S. P. Smith and the first author classified all superpotentials whose Jacobian algebras are 3-dimensional noetherian quadratic Calabi-Yau algebras. The main result of this paper is to classify all superpotentials whose Jacobian algebras are 3-dimensional noetherian cubic Calabi-Yau algebras. As an application, we show that if $S$ is a 3-di...
Microscopic Calabi-Yau black holes in string theory
International Nuclear Information System (INIS)
Ansari, Saeid
2011-01-01
In this thesis we study microscopic aspects of Calabi-Yau black holes in string theory. We compute the absorption cross-section of the space-time massless scalars by the worldvolume of D2-branes, wrapped on the S 2 of an AdS 2 x S 2 x CY 3 geometry of a fourdimensional D4-D0 Calabi-Yau black hole. The D2-brane can also have a generic D0 probe-brane charge. However, we restrict ourselves to D2-branes with small D0-charge so that the perturbation theory is applicable. According to the proposed AdS 2 /QM correspondence the candidate for the dual theory is the quantum mechanics of a set of probe D0-branes in the AdS 2 geometry. For small but non-zero probe D0-charge we find the quantum mechanical absorption cross-section seen by an asymptotic anti-de Sitter observer. We repeat the calculations for vanishing probe D0-charge as well and discuss our result by comparing with the classical absorption cross-section. In other project, for a given fourdimensional Calabi-Yau black hole with generic D6-D4-D2-D0 charges we identify a set of supersymmetric branes, which are static or stationary in the global coordinates, of the corresponding eleven-dimensional near horizon geometry. The set of these BPS states, which include the branes partially or fully wrap the horizon, should play a role in understanding the partition function of black holes with D6-charge. (orig.)
Microscopic Calabi-Yau black holes in string theory
Energy Technology Data Exchange (ETDEWEB)
Ansari, Saeid
2011-07-22
In this thesis we study microscopic aspects of Calabi-Yau black holes in string theory. We compute the absorption cross-section of the space-time massless scalars by the worldvolume of D2-branes, wrapped on the S{sup 2} of an AdS{sub 2} x S{sup 2} x CY{sub 3} geometry of a fourdimensional D4-D0 Calabi-Yau black hole. The D2-brane can also have a generic D0 probe-brane charge. However, we restrict ourselves to D2-branes with small D0-charge so that the perturbation theory is applicable. According to the proposed AdS{sub 2}/QM correspondence the candidate for the dual theory is the quantum mechanics of a set of probe D0-branes in the AdS{sub 2} geometry. For small but non-zero probe D0-charge we find the quantum mechanical absorption cross-section seen by an asymptotic anti-de Sitter observer. We repeat the calculations for vanishing probe D0-charge as well and discuss our result by comparing with the classical absorption cross-section. In other project, for a given fourdimensional Calabi-Yau black hole with generic D6-D4-D2-D0 charges we identify a set of supersymmetric branes, which are static or stationary in the global coordinates, of the corresponding eleven-dimensional near horizon geometry. The set of these BPS states, which include the branes partially or fully wrap the horizon, should play a role in understanding the partition function of black holes with D6-charge. (orig.)
Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds
DEFF Research Database (Denmark)
Andreas, Björn; Garcia Fernandez, Mario
2012-01-01
We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(...
Orientifolds of type IIA strings on Calabi-Yau manifolds
Indian Academy of Sciences (India)
T. This plays the analogue of the S-matrix in Cardy's ansatz for the boundary states. The matrices Y k ij. И m smipmjpkm sm¼ plays a role analogous to the fusion matrix for boundary states. They satisfy the fusion algebra: YiYj = Nij. kYk with Y k јј = ∈k determining the KB projection. 4. An application: A = 2 minimal models.
Brane brick models, toric Calabi-Yau 4-folds and 2d (0,2) quivers
Energy Technology Data Exchange (ETDEWEB)
Franco, Sebastián [Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY 10031 (United States); The Graduate School and University Center, The City University of New York,365 Fifth Avenue, New York NY 10016 (United States); Lee, Sangmin [Center for Theoretical Physics, Seoul National University,Seoul 08826 (Korea, Republic of); Department of Physics and Astronomy, Seoul National University,Seoul 08826 (Korea, Republic of); College of Liberal Studies, Seoul National University,Seoul 08826 (Korea, Republic of); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Seong, Rak-Kyeong [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of)
2016-02-08
We introduce brane brick models, a novel type of Type IIA brane configurations consisting of D4-branes ending on an NS5-brane. Brane brick models are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d (generically) N=(0,2) gauge theories on the worldvolume of the D1-branes and streamline their connection to the probed geometries. For this purpose, we also introduce new combinatorial procedures for deriving the Calabi-Yau associated to a given gauge theory and vice versa.
Two two-dimensional supergravity theories from Calabi-Yau four-folds
Energy Technology Data Exchange (ETDEWEB)
Gates, S. James Jr. E-mail: gatess@wam.umd.edu; Gukov, Sergei E-mail: gukov@feynman.princeton.edu; Witten, Edward
2000-09-18
We consider two-dimensional supergravity theories with four supercharges constructed from compactification of Type II string theory on a generic Calabi-Yau four-fold. In type IIA and type IIB cases, respectively, new superspace formulations of N=(2,2) and N=(0,4) dilaton supergravities are found and their coupling to matter multiplets is discussed.
Hermitian Yang-Mills instantons on resolutions of Calabi-Yau cones
Paccetti Correia, Filipe
2011-02-01
We study the construction of Hermitian Yang-Mills instantons over resolutions of Calabi-Yau cones of arbitrary dimension. In particular, in d complex dimensions, we present an infinite family, parametrised by an integer k and a continuous modulus, of SU( d) instantons. A detailed study of their properties, including the computation of the instanton numbers is provided. We also explain how they can be used in the construction of heterotic non-Kähler compactifications.
Type IIA on a compact Calabi-Yau and D=11 supergravity uplift of its orientifold
International Nuclear Information System (INIS)
Misra, A.
2004-01-01
Using the prescription of K. Hori and C. Vafa for defining period integrals in the Landau-Ginsburg theory for compact Calabi-Yau's, we obtain the Picard-Fuchs equation and the Meijer basis of solutions for the compact Calabi-Yau CY 3 (3,243) expressed as a degree-24 Fermat hypersurface after resolution of the orbifold singularities. The importance of the method lies in the ease with which one can consider the large and small complex structure limits, as well as the ability to get the ''ln''-terms in the periods without having to parametrically differentiate infinite series. We consider in detail the evaluation of the monodromy matrix in the large and small complex structure limits. We also consider the action of the freely acting antiholomorphic involution on D=11 supergravity compactified on CY 3 (3,243) x S 1 and obtain the Kaehler potential for the same in the limit of large volume of the Calabi-Yau. As a by-product, we also give a conjecture for the action of the orientation-reversing antiholomorphic involution on the periods, given its action on the cohomology, using a canonical (co)homology basis. Finally, we also consider showing a null superpotential on the orientifold of type IIA on CY 3 (3,243), having taken care of the orbifold singularities. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Energy Technology Data Exchange (ETDEWEB)
Braun, Andreas P. [Rudolph Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford, OX1 3NP (United Kingdom); Mathematical Institute, University of Oxford, Woodstock Road,Oxford, OX2 6GG (United Kingdom); Rummel, Markus [Rudolph Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford, OX1 3NP (United Kingdom); Sumitomo, Yoske [High Energy Accelerator Research Organization, KEK,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Valandro, Roberto [Dipartimento di Fisica dell’Università di Trieste,Strada Costiera 11, 34151 Trieste (Italy); INFN - Sezione di Trieste,Via Valerio 2, 34127 Trieste (Italy); ICTP,Strada Costiera 11, 34151 Trieste (Italy)
2015-12-04
In http://dx.doi.org/10.1007/JHEP01(2015)015 a mechanism to fix the closed string moduli in a de Sitter minimum was proposed: a D-term potential generates a linear relation between the volumes of two rigid divisors which in turn produces at lower energies a race-track potential with de Sitter minima at exponentially large volume. In this paper, we systematically search for implementations of this mechanism among all toric Calabi-Yau hypersurfaces with h{sup 1,1}≤4 from the Kreuzer-Skarke list. For these, topological data can be computed explicitly allowing us to find the subset of three-folds which have two rigid toric divisors that do not intersect each other and that are orthogonal to h{sup 1,1}−2 independent four-cycles. These manifolds allow to find D7-brane configurations compatible with the de Sitter uplift mechanism and we find an abundance of consistent choices of D7-brane fluxes inducing D-terms leading to a de Sitter minimum. Finally, we work out a couple of models in detail, checking the global consistency conditions and computing the value of the potential at the minimum.
Periods for Calabi-Yau and Landau-Ginzburg vacua
Berglund, P; De la Ossa, X C; Font, A; Hübsch, T; Jancic, D; Quevedo, Fernando; Berglund, Per; Candelas, Philip; Ossa, Xenia de la; Font, Anamaria; Hubsch, Tristan; Jancic, Dubravka; Quevedo, Fernando
1994-01-01
The complete structure of the moduli space of \\cys\\ and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from (2,2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of \\cys. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.
On (orientifold of) type IIA on a compact Calabi-Yau
International Nuclear Information System (INIS)
Misra, A.
2004-01-01
We study the gauged sigma model and its mirror Landau-Ginsburg model corresponding to type IIA on the Fermat degree-24 hypersurface in WCP 4 [1,1,2,8,12] (whose blow-up gives the smooth CY 3 (3,243)) away from the orbifold singularities, and its orientifold by a freely-acting antiholomorphic involution. We derive the Picard-Fuchs equation obeyed a period integral of a parent N=2 type IIA theory. We obtain the Meijer's basis of solutions to the equation in the large and small complex structure limits (on the mirror Landau-Ginsburg side) of the abovementioned Calabi-Yau, and make some remarks about the monodromy properties associated at the same and another MATHEMATICAlly interesting point. Based on a recently shown N=1 four-dimensional triality between Heterotic on the self-mirror Calabi-Yau CY 3 (11,11), M theory on CY 3 (3,243) x S 1 /(Z 2 ) and F-theory on an elliptically fibered CY 4 with the base given by CP 1 x Enriques surface, we first give a heuristic argument that there can be no superpotential generated in the orientifold of of CY 3 (3,243), and then explicitly verify the same using a mirror symmetry formulation for the abovementioned hypersurface away from its orbifold singularities. We then discuss briefly the sigma model and the mirror Landau-Ginsburg model corresponding to the resolved Calabi-Yau as well. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
CFT's from Calabi-Yau four-folds
Energy Technology Data Exchange (ETDEWEB)
Gukov, Sergei E-mail: gukov@feynman.princeton.edu; Vafa, Cumrun; Witten, Edward
2000-09-18
We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau four-fold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes. We analyze the vacuum and soliton structure of these models, and show that near an isolated singularity, one often generates massless chiral superfields and a superpotential, and in many instances in two or three dimensions one obtains nontrivial superconformal field theories. In the case of two dimensions, we identify some of these theories with certain Kazama-Suzuki coset models, such as the N=2 minimal models.
Mirror Fermat Calabi-Yau Threefolds and Landau-Ginzburg Black Hole Attractors
Bellucci, S; Marrani, A; Yeranyan, A H
2006-01-01
We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY_{3}s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the moduli space of such 4-dimensional compactifications, we always find two species of extremal black hole attractors, depending on the choice of the Sp(4,Z) symplectic charge vector, one 1/2-BPS (which is always stable, according to general results of special Kahler geometry) and one non-BPS. The latter turns out to be stable (local minimum of the ``effective black hole potential'' V_{BH}) for non-vanishing central charge, whereas it is unstable (saddle point of V_{BH}) for the case of vanishing central charge. This is to be compared to the large volume limit of one-modulus CY_{3}-compactifications (of Type II A superstrings), in which the homogeneous symmetric special Kahler geometry based on cubic prepotential admits (beside the 1/2-BPS ones) only non-BPS extremal black hol...
Torrente-Lujan, E
2004-01-01
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge symmetries. In this work we continue to study the structure of graphs obtained from $CY_3$ reflexive polyhedra. We show how some particularly defined integral matrices can be assigned to these diagrams. This family of matrices and its associated graphs may be obtained by relaxing the restrictions on the individual entries of the generalized Cartan matrices associated with the Dynkin diagrams that characterize Cartan-Lie and affine Kac-Moody algebras. These graphs keep however the affine structure, as it was in Kac-Moody Dynkin diagrams. We presented a possible root structure for some simple cases. We conjecture that these generalized graphs and associated link matrices may characterize generalizations of these algebras.
Non-simply connected Calabi-Yau threefolds constructed as quotients of Schoen threefolds
Karayayla, Tolga
2017-07-01
The aim of this paper is to complete the classification of all Calabi-Yau threefolds which are constructed as the quotient of a smooth Schoen threefold X =B1×P1B2 (fiber product over P1 of two relatively minimal rational elliptic surfaces B1 and B2 with section) under a finite group action acting freely on the Schoen threefold X. The abelian group actions on smooth Schoen threefolds which induce cyclic group actions on the base curve P1 were studied by Bouchard and Donagi (2008), and all such actions were listed. We consider the actions on the Schoen threefold by finite groups G whose elements are given as a product τ1 ×τ2 of two automorphisms τ1 and τ2 of the rational elliptic surfaces B1 and B2 with section. In this paper, we use the classification of automorphism groups of rational elliptic surfaces with section given in Karayayla (2012) and Karayayla (2014) to generalize the results of Bouchard and Donagi to answer the question whether finite and freely acting group actions on Schoen threefolds which induce non-cyclic group actions on the base curve P1 exist or not. Despite the existence of group actions on rational elliptic surfaces which induce non-cyclic (even non-abelian) group actions on P1, it is shown in this paper that none of those actions can be lifted to free actions on a Schoen threefold. The main result is that there is no finite group action on a Schoen threefold X which acts freely on X and which induces a non-cyclic group action on the base curve P1. This result shows that the list given in Bouchard and Donagi (2008) is a complete list of non-simply connected Calabi-Yau threefolds constructed as the quotient of a smooth Schoen threefold by a finite group action.
Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs
Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo
2018-03-01
We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.
Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string
International Nuclear Information System (INIS)
Sun, Kaiwen; Wang, Xin; Huang, Min-xin
2017-01-01
We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mariño conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g, the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant ℏ and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and topological string, another quantization scheme was proposed by Grassi-Hatsuda-Mariño, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. The equivalence for mirror curves of genus one has been verified for some local del Pezzo surfaces. In this paper, we generalize the correspondence to higher genus, and analyze in detail the resolved ℂ"3/ℤ_5 orbifold and several SU(N) geometries. We also give a proof for some models at ℏ=2π/k.
Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string
Energy Technology Data Exchange (ETDEWEB)
Sun, Kaiwen [Department of Mathematics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China); Wang, Xin; Huang, Min-xin [Interdisciplinary Center for Theoretical Study,Department of Modern Physics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China)
2017-01-16
We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mariño conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g, the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant ℏ and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and topological string, another quantization scheme was proposed by Grassi-Hatsuda-Mariño, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. The equivalence for mirror curves of genus one has been verified for some local del Pezzo surfaces. In this paper, we generalize the correspondence to higher genus, and analyze in detail the resolved ℂ{sup 3}/ℤ{sub 5} orbifold and several SU(N) geometries. We also give a proof for some models at ℏ=2π/k.
The Classification of the Simply Laced Berger Graphs from Calabi-Yau $CY_3$ spaces
Ellis, Jonathan Richard; Volkov, G G
2004-01-01
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge symmetries. In this work we continue to study the structure of graphs obtained from $CY_3$ reflexive polyhedra. The objective is to describe the ``simply laced'' cases, those graphs obtained from three dimensional spaces with K3 fibers which lead to symmetric matrices. We study both the affine and, derived from them, non-affine cases. We present root and weight structurea for them. We study in particular those graphs leading to generalizations of the exceptional simply laced cases $E_{6,7,8}$ and $E_{6,7,8}^{(1)}$. We show how these integral matrices can be assigned: they may be obtained by relaxing the restrictions on the individual entries of the generalized Cartan matrices associated with the Dynkin diagrams that characterize Cartan-Lie and affine Kac-Moody algebras. These gr...
Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds
Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten
2018-01-01
We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.
Higher derivatives in Type II and M-theory on Calabi-Yau threefolds
Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias
2018-02-01
The four- and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten- and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kähler structure of the compact space and the form-field back-ground are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten- and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kähler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kähler modulus case is presented for both Type II theories and M-theory.
Calabi-Yau compactifications of non-supersymmetric heterotic string theory
International Nuclear Information System (INIS)
Blaszczyk, Michael; Groot Nibbelink, Stefan
2015-07-01
Phenomenological explorations of heterotic strings have conventionally focused primarily on the E 8 x E 8 theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric SO(16) x SO(16) theory and the related supersymmetric E 8 x E 8 and SO(32) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the nonsupersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion-couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five branes in the SO(16) x SO(16) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.
Towards mirror symmetry a la SYZ for generalized Calabi-Yau manifolds
Energy Technology Data Exchange (ETDEWEB)
Grange, P. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Schaefer-Nameki, S. [California Inst. of Tech., Pasadena, CA (United States)
2007-10-15
Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal sixmanifold M with static SU(2) structure and mirror M, it is argued that the product M x M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and M. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3) x SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry. (orig.)
Directory of Open Access Journals (Sweden)
Alexander Burinskii
2013-01-01
Full Text Available The 4D Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Newman. Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the structure of M-theory. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the critical N = 2 superstring.
Explicit Calabi-Yau metrics in D=6 possessing an isometry group with orbits of codimension one
Santillan, Osvaldo P.
2009-10-01
A method for constructing explicit Calabi-Yau metrics in six dimensions with an isometry group with orbits of codimension one is presented. The equations to solve are nonlinear, but become linear when certain geometrical objects defining the metric vary over a complex submanifold. It is shown that this method encode known examples such as the CY metrics of [G. Gibbons, H. Lu, C. Pope, K. Stelle, Nuclear Phys. B 623 (2002) 3] or the asymptotic form of the BKTY metrics of [S. Bando, R. Kobayashi, Math. Ann. 287 (1990) 175; Proc. 21st Int. Taniguchi Symp, Lecture Notes in Pure Math. 1339 (1988) 20] and [G. Gibbons, P. Rychenkova, J. Geom. Phys. 32 (2000) 311], but we construct new ones.
A generalized construction of mirror manifolds
International Nuclear Information System (INIS)
Berglund, P.; Huebsch, T.
1993-01-01
We generalize the known method for explicit construction of mirror pairs of (2,2)-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known. (orig.)
Stable Yang-Mills connections on special holonomy manifolds
Huang, Teng
2017-06-01
We prove that energy minimizing Yang-Mills connections on a compact G2-manifold has holonomy equal to G2 are G2-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing connections on a compact Calabi-Yau 3-fold that has holonomy equal to SU(3) subject to a similar condition are holomorphic.
Coset spaces as alternatives to Calabi-Yau spaces in the presence of Gaugino condensation
International Nuclear Information System (INIS)
Govindarajan, T.R.; Joshipura, A.S.; Rindani, S.D.; Sarkar, U.
1986-12-01
Compactification of the field-theory limit of the E 8 xE' 8 heterotic string on six-dimensional coset manifolds is discussed, with specific reference to maintaining four-dimensional supersymmetry. By choosing a torsion proportional to the background value of the three-index field H mnp occurring in the theory it is possible to satisfy the condition of SU(3) holonbmy necessary for supersymmetry. However, in all cases considered, it is found impossible to satisfy all the remaining conditions for supersymmetry. If gaugino condensation is assumed to occur, it is possible to preserve supersymmetry satisfying all the modified requirements of supersymmetry for the spaces SU(3)/U(1)xU(1), G 2 /SU(3) and SO(5)/SU(2)xU(1). The question of chiral fermions is examined in these cases using the Atiyah-Singer index theorem. Background gauge fields, which correspond to different numbers of generations of chiral fermions, are constructed explicitly. In all these cases the low-energy symmetry group is E 6 xE' 8 . (author)
SL(2;R)/U(1) supercoset and elliptic genera of Non-compact Calabi-Yau Manifolds
Eguchi, T
2004-01-01
We first discuss the relationship between the SL(2;)/U(1) supercoset and = 2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;)/U(1) theory correspond exactly to those massless representations of = 2 Liouville theory which are closed under modular transformations and studied in our previous work [18]. It is known that toroidal partition functions of SL(2;)/U(1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the space-time volume and is divergent in the infinite-volume limit while the part of discrete representations is volume-independent. In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2;)/U(1), we compute elliptic genera for various non-compact space-times such as the conifold, ...
Alekseevsky, D. V.; Cortes, V.
1997-01-01
The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K\\"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K\\"ahler manifolds correspond to certain (abstract) variations of Hodge structure which generalize the above example. We give the classification of homogeneous special pseudo K\\"ahler manifolds of semisimple groups with compact stabilizer.
Misra, Aalok
2008-01-01
We consider issues of moduli stabilization and "area codes" for type II flux compactifications, and the "Inverse Problem" and "Fake Superpotentials" for extremal (non)supersymmetric black holes in type II compactifications on (orientifold of) a compact two-parameter Calabi-Yau expressed as a degree-18 hypersurface in WCP^4[1,1,1,6,9] which has multiple singular loci in its moduli space. We argue the existence of extended "area codes" [1] wherein for the same set of large NS-NS and RR fluxes, one can stabilize all the complex structure moduli and the axion-dilaton modulus (to different sets of values) for points in the moduli space away as well as near the different singular conifold loci leading to the existence of domain walls. By including non-perturbative alpha' and instanton corrections in the Kaehler potential and superpotential [2], we show the possibility of getting a large-volume non-supersymmetric (A)dS minimum. Further, using techniques of [3] we explicitly show that given a set of moduli and choice...
Instantons on sine-cones over Sasakian manifolds
Bunk, Severin; Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.; Sperling, Marcus
2014-09-01
We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are Kähler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-Kähler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-Kähler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.
Compactifications of heterotic strings on non-Kaehler complex manifolds II
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Dasgupta, Keshav; Green, Paul S.; Sharpe, Eric
2004-01-01
We continue our study of heterotic compactifications on non-Kaehler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and possible supergravity description for a generic non-Kaehler complex manifold using the newly proposed superpotential. The manifolds studied in our earlier papers had zero Euler characteristics. We construct new examples of non-Kaehler complex manifolds with torsion in lower dimensions, that have nonzero Euler characteristics. Some of these examples are constructed from consistent backgrounds in F-theory and therefore are solutions to the string equations of motion. We discuss consistency conditions for compactifications of the heterotic string on smooth non-Kaehler manifolds and illustrate how some results well known for Calabi-Yau compactifications, including counting the number of generations, apply to the non-Kaehler case. We briefly address various issues regarding possible phenomenological applications
Sasaki-Einstein Manifolds and Volume Minimisation
Martelli, D; Yau, S T; Martelli, Dario; Sparks, James; Yau, Shing-Tung
2006-01-01
We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi-Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat-Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theo...
Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone
Schmude, Johannes
2015-01-01
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 5, T 1,1, Y 7,3, Y 2,1, Y 2,0, and Y 4,0. We find complete agreement with previous results obtained by Qiu and Zabzine using equivariant indices except for the orbifold limits Y p,0 with p > 1.
BIRS Workshop on Calabi-Yau Varieties and Mirror Symmetry
Yau, Shing-Tung; Lewis, James D; Mirror Symmetry V
2006-01-01
Since its discovery in the early 1990s, mirror symmetry, or more generally, string theory, has exploded onto the mathematical landscape. This topic touches upon many branches of mathematics and mathematical physics, and has revealed deep connections between subjects previously considered unrelated. The papers in this volume treat mirror symmetry from the perspectives of both mathematics and physics. The articles can be roughly grouped into four sub-categories within the topic of mirror symmetry: arithmetic aspects, geometric aspects, differential geometric and mathematical physics aspects, and geometric analytic aspects. In these works, the reader will find mathematics addressing, and in some cases solving, problems inspired and influenced by string theory. - See more at: http://bookstore.ams.org/amsip-38#sthash.imkmWYgJ.dpuf
K3-fibered Calabi-Yau threefolds II, singular fibers
Hunt, Bruce
1999-01-01
In part I of this paper we constructed certain fibered Calabi-Yaus by a quotient construction in the context of weighted hypersurfaces. In this paper look at the case of K3 fibrations more closely and study the singular fibers which occur. This differs from previous work since the fibrations we discuss have constant modulus, and the singular fibers have torsion monodromy.
Space-Time Transitions in String Theory
Witten, Edward
1993-01-01
Simple mean field methods can be used to describe transitions between different space-time models in string theory. These include transitions between different Calabi-Yau manifolds, and more exotic things such as the Calabi-Yau/Landau-Ginzberg correspondence.
Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
Martelli, D; Martelli, Dario; Sparks, James
2006-01-01
Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on S^2 x S^3 has been discovered, where p and q are two coprime positive integers, with q
manifolds are AdS/CFT dual to an infinite class of N=1 superconformal field theories arising as infra-red (IR) fixed points of toric quiver gauge theories with gauge group SU(N)^{2p}. As a non-trivial example, we show that Y^{2,1} is an explicit irregular Sasaki-Einstein metric on the horizon of the complex cone over the first del Pezz...
On topological approach to local theory of surfaces in Calabi-Yau threefolds
DEFF Research Database (Denmark)
Gukov, Sergei; Liu, Chiu-Chu Melissa; Sheshmani, Artan
2017-01-01
We study the web of dualities relating various enumerative invariants, notably Gromov-Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson-Thomas gauge theory and its reductions to D=4 and D=2 which are relevant to the local theory of surfaces...
Schütt, Matthias; Yui, Noriko
2015-01-01
This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.
de Sitter vacua in no-scale supergravities and Calabi-Yau string models
International Nuclear Information System (INIS)
Covi, L.; Gross, C.; Scrucca, C.A.
2008-04-01
We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N = 1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kaehler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the 'sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kaehler potential which break the no-scale property may allow to lift these masses. (orig.)
Higher-order blackhole solutions in N=2 supergravity and Calabi-Yau string backgrounds
Behrndt, K.; Cardoso, G.L.; de Wit, B.Q.P.J.; Lüst, D.; Mohaupt, T.; Sabra, W.A.
1998-01-01
Based on special geometry, we consider corrections to N=2 extremal black-hole solutions and their entropies originating from higher-order derivative terms in N=2 supergravity. These corrections are described by a holomorphic function, and the higher-order black-hole solutions can be expressed in
Directory of Open Access Journals (Sweden)
Masahiro Ibe
2016-07-01
Full Text Available We discuss an anthropic explanation of why there exist three generations of fermions. If one assumes that the right-handed neutrino sector is responsible for both the matter–antimatter asymmetry and the dark matter, then anthropic selection favors three or more families of fermions. For successful leptogenesis, at least two right-handed neutrinos are needed, while the third right-handed neutrino is invoked to play the role of dark matter. The number of the right-handed neutrinos is tied to the number of generations by the anomaly constraints of the U(1B−L gauge symmetry. Combining anthropic arguments with observational constraints, we obtain predictions for the X-ray observations, as well as for neutrinoless double-beta decay.
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
Kanazawa, Atsushi
2017-04-01
We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of X can be constructed by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds. The two crucial ideas in our proof are to obtain a complex structure by gluing the underlying affine manifolds and to construct the theta functions from the Landau-Ginzburg superpotentials.
International Nuclear Information System (INIS)
Aspinwall, P.S.; Luetken, C.A.
1991-01-01
We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kaehler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifolds are fixed, but the intersection numbes are highly ambiguous, presumably reflected a rich structure of multicritical points in the moduli space of the field theory. (orig.)
International Nuclear Information System (INIS)
Finkelstein, D.; Finkelstein, S.R.; Holm, C.
1986-01-01
Riemannian manifolds are but one of three ways to extrapolate from fourdimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors by N-ary hyperspinors with new ''internal'' components besides the usual two ''external'' ones, this leads to a second line, the hyperspin manifolds /sub n/ and their tangent spaces d/sub n/, different in structure and symmetry group from the Riemannian line, except that the binary spaces d 2 (Minkowski time space) and 2 (Minkowskian manifold) lie on both. d/sub n/ and /sub n/ have dimension n = N 2 . In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and the N-ary chronometric form is not quadratic, but N-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist
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
Geometrically induced metastability and holography
Energy Technology Data Exchange (ETDEWEB)
Aganagic, Mina; Aganagic, Mina; Beem, Christopher; Seo, Jihye; Vafa, Cumrun
2006-10-23
We construct metastable configurations of branes and anti-branes wrapping 2-spheres inside local Calabi-Yau manifolds and study their large N duals. These duals are Calabi-Yau manifolds in which the wrapped 2-spheres have been replaced by 3-spheres with flux through them, and supersymmetry is spontaneously broken. The geometry of the non-supersymmetric vacuum is exactly calculable to all orders of the't Hooft parameter, and to the leading order in 1/N. The computation utilizes the same matrix model techniques that were used in the supersymmetric context. This provides a novel mechanism for breaking supersymmetry in the context of flux compactifications.
Non-perturbative effects and the refined topological string
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematiques; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P{sup 1} x P{sup 1}, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.
Non-perturbative effects and the refined topological string
International Nuclear Information System (INIS)
Hatsuda, Yasuyuki; Tokyo Institute of Technology; Marino, Marcos; Moriyama, Sanefumi; Nagoya Univ.; Okuyama, Kazumi
2013-06-01
The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P 1 x P 1 , in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.
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
Topological Strings and Integrable Hierarchies
Aganagic, M; Klemm, A D; Marino, M; Vafa, C; Aganagic, Mina; Dijkgraaf, Robbert; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun
2006-01-01
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue that topological strings on Calabi-Yau geometries provide a unifying picture connecting non-critical (super)strings, integrable hierarchies, and various matrix models. In particular we show how the ordinary matrix model, the double scaling limit of matrix models, and Kontsevich-like matrix model are all related and arise from studying branes in specific local Calabi-Yau three-folds. We also show how A-model topological string on P^1 and local toric threefolds (and in particular the topological vertex) can be realized and solved as B-model topological string amplitudes on a Calabi-Yau manifold.
Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
Energy Technology Data Exchange (ETDEWEB)
Johnson, Samuel B.; Taylor, Washington [Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)
2016-08-15
We systematically analyze the local combinations of gauge groups and matter that can arise in 6D F-theory models over a fixed base. We compare the low-energy constraints of anomaly cancellation to explicit F-theory constructions using Weierstrass and Tate forms, and identify some new local structures in the ''swampland'' of 6D supergravity and SCFT models that appear consistent from low-energy considerations but do not have known F-theory realizations. In particular, we classify and carry out a local analysis of all enhancements of the irreducible gauge and matter contributions from ''non-Higgsable clusters,'' and on isolated curves and pairs of intersecting rational curves of arbitrary self-intersection. Such enhancements correspond physically to unHiggsings, and mathematically to tunings of the Weierstrass model of an elliptic CY threefold. We determine the shift in Hodge numbers of the elliptic threefold associated with each enhancement. We also consider local tunings on curves that have higher genus or intersect multiple other curves, codimension two tunings that give transitions in the F-theory matter content, tunings of abelian factors in the gauge group, and generalizations of the ''E{sub 8}'' rule to include tunings and curves of self-intersection zero. These tools can be combined into an algorithm that in principle enables a finite and systematic classification of all elliptic CY threefolds and corresponding 6D F-theory SUGRA models over a given compact base (modulo some technical caveats in various special circumstances), and are also relevant to the classification of 6D SCFT's. To illustrate the utility of these results, we identify some large example classes of known CY threefolds in the Kreuzer-Skarke database as Weierstrass models over complex surface bases with specific simple tunings, and we survey the range of tunings possible over one specific base. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Moduli Potentials in Type IIA Compactifications with RR and NS Flux
Energy Technology Data Exchange (ETDEWEB)
Kachru, S.
2004-12-01
We describe a simple class of type IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the Kaehler moduli. This class of models corresponds to gauged {Nu} = 2 supergravities, and the potential is completely determined by a choice of gauging and by data of the {Nu} = 2 Calabi-Yau model--the prepotential for vector multiplets and the quaternionic metric on the hypermultiplet moduli space. Using mirror symmetry, one can determine many (though not all) of the quantum corrections which are relevant in these models.
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
On the AKSZ formulation of the Rozansky-Witten theory and beyond
International Nuclear Information System (INIS)
Qiu Jian; Zabzine, Maxim
2009-01-01
Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the Rozansky-Witten model, which can be defined for any complex manifold with a closed (2,0)-form. We also construct the holomorphic version of Rozansky-Witten theory defined over Calabi-Yau 3-fold.
International Nuclear Information System (INIS)
Latorre, J.I.; Luetken, C.A.
1988-11-01
We construct a large new class of two dimensional sigma models with Kaehler target spaces which are algebraic manifolds realized as complete interactions in weighted CP n spaces. They are N=2 superconformally symmetric and particular choices of constraints give Calabi-Yau target spaces which are nontrivial string vacua. (orig.)
GUTs on Compact Type IIB Orientifolds
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph; /Munich, Max Planck Inst.; Braun, Volker; /Dublin Inst.; Grimm, Thomas W.; /Bonn U.; Weigand, Timo; /SLAC
2008-12-01
We systematically analyze globally consistent SU(5) GUT models on intersecting D7-branes in genuine Calabi-Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realization of SU(5) GUTs with gauge symmetry breaking via U(1)Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P{sub 1,1,1,6,9}[18] and of the Quintic P{sub 1,1,1,1,1}[5], respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of these geometries and present five globally consistent string GUT models in detail, including a 3-generation SU(5) model with no exotics whatsoever. We also realize other phenomenological features such as the 10 10 5{sub H} Yukawa coupling and comment on the possibility of moduli stabilization, where we find an entire new set of so-called swiss-cheese type Calabi-Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi-Yau fourfolds.
The Euler characteristic correction to the Kähler potential — revisited
Energy Technology Data Exchange (ETDEWEB)
Bonetti, Federico [C.N. Yang Institute for Theoretical Physics, SUNY Stony Brook,Stony Brook, New York 11794 (United States); Weissenbacher, Matthias [Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa-no-ha 5-1-5, 277-8583 (Japan)
2017-01-02
We confirm the leading α{sup ′3} correction to the 4d, N=1 Kähler potential of type IIB orientifold compactifications, proportional to the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We present the explicit solution for the α{sup ′3}-modified internal background metric in terms of the non-harmonic part of the third Chern form of the leading order Calabi-Yau manifold. The corrected internal manifold is almost Calabi-Yau and admits an SU(3) structure with non-vanishing torsion. We also find that the full ten-dimensional Einstein frame background metric is multiplied by a non-trivial Weyl factor. Performing a Kaluza-Klein reduction on the modified background we derive the α{sup ′3}-corrected kinetic terms for the dilaton and the Kähler deformations of the internal Calabi-Yau threefold for arbitrary h{sup 1,1}. We analyze these kinetic terms in the 4d, N=2 un-orientifolded theory, confirming the expected correction to the Kähler moduli space prepotential, as well as in the 4d, N=1 orientifolded theory, thus determining the corrections to the Kähler potential and Kähler coordinates.
Three Generations of Distance Education Pedagogy
Anderson, Terry; Dron, Jon
2011-01-01
This paper defines and examines three generations of distance education pedagogy. Unlike earlier classifications of distance education based on the technology used, this analysis focuses on the pedagogy that defines the learning experiences encapsulated in the learning design. The three generations of cognitive-behaviourist, social constructivist,…
Mirror symmetry in the presence of branes
Energy Technology Data Exchange (ETDEWEB)
Mertens, Adrian
2011-10-11
This work deals with mirror symmetry for N=1 compactifications on compact Calabi-Yau threefolds with branes. The mayor tool is a combined deformation space for the Calabi-Yau and a hypersurface within it. Periods of this deformation space contain information about B-type branes within the hypersurface in addition to the usual closed string data. To study these periods we generalize techniques used in closed string mirror symmetry. We derive the Picard-Fuchs system and encode the information in extended toric polytopes. Solutions of the Picard-Fuchs equations give superpotentials for certain brane configurations. This is an efficient way to calculate superpotentials. The deformations we consider are massive for all branes with non trivial superpotential. Depending on a choice of a family of hypersurfaces, the superpotential of the effective low energy theory depends on different massive fields. A priori there is no reason for these fields to be lighter then other fields that are not included. We find however examples where the superpotential is nearly at. In these examples we use the Gauss-Manin connection on the combined deformation space to define an open string mirror map. We find instanton generated superpotentials of A-type branes. This gives predictions for Ooguri-Vafa invariants counting holomorphic disks that end on a Lagrangian brane on the Quintic. A second class of examples does not have preferred nearly massless deformations and different families of hypersurfaces can be used to calculate the same on-shell superpotential. We calculate examples of superpotentials for branes in Calabi-Yau manifolds with several moduli. The on-shell superpotentials are mapped to the mirror A-model to study the instanton expansion and to obtain predictions for disk invariants. The combined deformation spaces are equivalent to the quantum corrected Kaehler deformation spaces of certain non compact Calabi-Yau fourfolds. These fourfolds are fibrations of Calabi-Yau threefolds
Mirror symmetry in the presence of branes
International Nuclear Information System (INIS)
Mertens, Adrian
2011-01-01
This work deals with mirror symmetry for N=1 compactifications on compact Calabi-Yau threefolds with branes. The mayor tool is a combined deformation space for the Calabi-Yau and a hypersurface within it. Periods of this deformation space contain information about B-type branes within the hypersurface in addition to the usual closed string data. To study these periods we generalize techniques used in closed string mirror symmetry. We derive the Picard-Fuchs system and encode the information in extended toric polytopes. Solutions of the Picard-Fuchs equations give superpotentials for certain brane configurations. This is an efficient way to calculate superpotentials. The deformations we consider are massive for all branes with non trivial superpotential. Depending on a choice of a family of hypersurfaces, the superpotential of the effective low energy theory depends on different massive fields. A priori there is no reason for these fields to be lighter then other fields that are not included. We find however examples where the superpotential is nearly at. In these examples we use the Gauss-Manin connection on the combined deformation space to define an open string mirror map. We find instanton generated superpotentials of A-type branes. This gives predictions for Ooguri-Vafa invariants counting holomorphic disks that end on a Lagrangian brane on the Quintic. A second class of examples does not have preferred nearly massless deformations and different families of hypersurfaces can be used to calculate the same on-shell superpotential. We calculate examples of superpotentials for branes in Calabi-Yau manifolds with several moduli. The on-shell superpotentials are mapped to the mirror A-model to study the instanton expansion and to obtain predictions for disk invariants. The combined deformation spaces are equivalent to the quantum corrected Kaehler deformation spaces of certain non compact Calabi-Yau fourfolds. These fourfolds are fibrations of Calabi-Yau threefolds
Pilca, Mihaela
2016-09-01
Vaisman manifolds are strongly related to Kähler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if a complete Vaisman manifold is toric, then the associated Sasaki manifold is also toric. Conversely, a toric complete Sasaki manifold, whose Kähler cone is equipped with an appropriate compatible action, gives rise to a toric Vaisman manifold. In the special case of a strongly regular compact Vaisman manifold, we show that it is toric if and only if the corresponding Kähler quotient is toric.
Renteln, Paul
2013-11-01
Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.
Vertex algebras and mirror symmetry
International Nuclear Information System (INIS)
Borisov, L.A.
2001-01-01
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)
Three Generations of Distance Education Pedagogy
Directory of Open Access Journals (Sweden)
Terry Anderson
2011-03-01
Full Text Available This paper defines and examines three generations of distance education pedagogy. Unlike earlier classifications of distance education based on the technology used, this analysis focuses on the pedagogy that defines the learning experiences encapsulated in the learning design. The three generations of cognitive-behaviourist, social constructivist, and connectivist pedagogy are examined, using the familiar community of inquiry model (Garrison, Anderson, & Archer, 2000 with its focus on social, cognitive, and teaching presences. Although this typology of pedagogies could also be usefully applied to campus-based education, the need for and practice of openness and explicitness in distance education content and process makes the work especially relevant to distance education designers, teachers, and developers. The article concludes that high-quality distance education exploits all three generations as determined by the learning content, context, and learning expectations.
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
Mathematical Sciences Research Institute Workshop
Mirror Symmetry I
1998-01-01
This volume is an updated edition of ""Essays on Mirror Manifolds"", the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here. Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hubsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and $N=2$ supergravity. Rocek proposed possible mirrors for Calabi-Yau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics.
Generalized N=1 orientifold compactifications and the Hitchin functionals
Energy Technology Data Exchange (ETDEWEB)
Benmachiche, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Grimm, T.W. [Wisconsin Univ., Madison, WI (United States). Dept. of Physics
2006-02-15
The four-dimensional N=1 supergravity theories arising in compactifications of type IIA and type IIB on generalized orientifold backgrounds with background fluxes are discussed. The Kaehler potentials are derived for reductions on SU(3) structure orientifolds and shown to consist of the logarithm of the two Hitchin functionals. These are functions of even and odd forms parameterizing the geometry of the internal manifold, the B-field and the dilaton. The superpotentials induced by background fluxes and the non-Calabi-Yau geometry are determined by a reduction of the type IIA and type IIB fermionic actions on SU(3) and generalized SU(3) x SU(3) manifolds. Mirror spaces of Calabi-Yau orientifolds with electric and part of the magnetic NS-NS fluxes are conjectured to be certain SU(3) x SU(3) structure manifolds. Evidence for this identification is provided by comparing the generalized type IIA and type IIB superpotentials. (orig.)
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
2009-07-02
Jul 2, 2009 ... Regarding self-maps of (complex) Grassmann manifolds the following results are well-known: Parameswaran Sankaran Institute of Mathematical Sciences Chennai, India sankaran@imsc.res.in. Indian Academy of Sciences Platinum Jubilee Meeting Hyderabad. Maps between Grassmann manifolds ...
Manifold Partition Discriminant Analysis.
Yang Zhou; Shiliang Sun
2017-04-01
We propose a novel algorithm for supervised dimensionality reduction named manifold partition discriminant analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is consistent with the local variation of the data manifold, while nearby data belonging to different classes are well separated. By partitioning the data manifold into a number of linear subspaces and utilizing the first-order Taylor expansion, MPDA explicitly parameterizes the connections of tangent spaces and represents the data manifold in a piecewise manner. While graph Laplacian methods capture only the pairwise interaction between data points, our method captures both pairwise and higher order interactions (using regional consistency) between data points. This manifold representation can help to improve the measure of within-class similarity, which further leads to improved performance of dimensionality reduction. Experimental results on multiple real-world data sets demonstrate the effectiveness of the proposed method.
Voisin-Borcea manifolds and heterotic orbifold models
Energy Technology Data Exchange (ETDEWEB)
Buchmuller, W.; Schmidt, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Louis, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Valandro, R. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2012-08-15
We study the relation between a heterotic T{sup 6}/Z{sub 6} orbifold model and a compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with non-trivial line bundles. This orbifold can be seen as a Z{sub 2} quotient of T{sup 4}/Z{sub 3} x T{sup 2}. We consider a two-step resolution, whose intermediate step is (K3 x T{sup 2})/Z{sub 2}. This allows us to identify the massless twisted states which correspond to the geometric Kaehler and complex structure moduli. We work out the match of the two models when non-zero expectation values are given to all twisted geometric moduli. We find that even though the orbifold gauge group contains an SO(10) factor, a possible GUT group, the subgroup after Higgsing does not even include the standard model gauge group. Moreover, after Higgsing, the massless spectrum is non-chiral under the surviving gauge group.
Ensemble manifold regularization.
Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng
2012-06-01
We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.
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
Understanding fine structure constants and three generations
International Nuclear Information System (INIS)
Bennett, D.L.; Nielsen, H.B.
1988-02-01
We put forward a model inspired by random dynamics that relates the smallness of the gauge coupling constants to the number of generations being 'large'. The new element in the present version of our model is the appearance of a free parameter χ that is a measure of the (presumably relatively minor) importance of a term in the plaquette action proportional to the trace in the (1/6, 2, 3) representation of the Standard Model. Calling N gen the number of generations, the sets of allowed (N gen , χN gen )-pairs obtained by imposing the three measured coupling constant values of the Standard Model form three lines. In addition to finding that these lines cross at a single point (as needed for a consistent fit), the intersection occurs with surprising accuracy at the integer N gen = 3 (thereby predicting exactly three generations). It is also encouraging that the parameter χ turns out to be small and positive as expected. (orig.)
ADE string chains and mirror symmetry
Haghighat, Babak; Yan, Wenbin; Yau, Shing-Tung
2018-01-01
6d superconformal field theories (SCFTs) are the SCFTs in the highest possible dimension. They can be geometrically engineered in F-theory by compactifying on non-compact elliptic Calabi-Yau manifolds. In this paper we focus on the class of SCFTs whose base geometry is determined by -2 curves intersecting according to ADE Dynkin diagrams and derive the corresponding mirror Calabi-Yau manifold. The mirror geometry is uniquely determined in terms of the mirror curve which has also an interpretation in terms of the Seiberg-Witten curve of the four-dimensional theory arising from torus compactification. Adding the affine node of the ADE quiver to the base geometry, we connect to recent results on SYZ mirror symmetry for the A case and provide a physical interpretation in terms of little string theory. Our results, however, go beyond this case as our construction naturally covers the D and E cases as well.
Mirror symmetry for two-parameter models. Pt. 2
International Nuclear Information System (INIS)
Candelas, Philip; Font, Anamaria; Katz, Sheldon; Morrison, David R.
1994-01-01
We describe in detail the space of the two Kaehler parameters of the Calabi-Yau manifold P 4 (1,1,1,6,9) [D. R. Morrison, 1993] by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large radius limit, is found by studying the monodromy of the periods about the discriminant locus, the boundary of the moduli space corresponding to singular Calabi-Yau manifolds. A symplectic basis of periods is found and the action of the Sp(6, Z) generators of the modular group is determined. From the mirror map we compute the instanton expansion of the Yukawa couplings and the generalized N=2 index, arriving at the numbers of instantons of genus zero and genus one of each bidegree. We find that these numbers can be negative, even in genus zero. We also investigate an SL(2, Z) symmetry that acts on a boundary of the moduli space. ((orig.))
Topological string on elliptic CY 3-folds and the ring of Jacobi forms
Energy Technology Data Exchange (ETDEWEB)
Huang, Min-xin [Interdisciplinary Center for Theoretical Study,University of Science and Technology of China, Hefei, Anhui 230026 (China); Katz, Sheldon [Department of Mathematics, University of Illinois at Urbana-Champaign,1409 W. Green St., Urbana, IL 6180 (United States); Klemm, Albrecht [Bethe Center for Theoretical Physics (BCTP),Physikalisches Institut, Universität Bonn, 53115 Bonn (Germany)
2015-10-20
We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi-Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows quadratically with the base degree. The denominators of these forms have a simple universal form with the property that the poles of the meromorphic form lie only at torsion points. The modular parameter corresponds to the fibre class while the rôle of the string coupling is played by the elliptic parameter. As a consequence the topological string amplitudes are modular and quasi periodic in the string coupling. This leads to very strong all genus results on these geometries, which are checked against results from curve counting. The structure can be viewed as an indication that an N=2 analog of the reciprocal of the Igusa cusp form exists that might govern the topological string theory on these Calabi-Yau manifolds completely.
Intergenerational Relationship Quality Across Three Generations
Tighe, Lauren A.; Fingerman, Karen L.; Zarit, Steven H.
2012-01-01
Objectives. Studies of intergenerational relationship quality often include one or two generations. This study examined within-family differences and similarities or transmission of positive and negative relationship quality across three generations. Method. Participants included 633 middle-aged individuals (G2; 52% women, ages 40–60 years), 592 of their offspring (G3; 53% daughters; ages 18–41 years), and 337 of their parents (i.e., grandparents; G1; 69% women; ages 59–96 years). Results. Multilevel models revealed differences and similarities in relationship quality across generations. The oldest generation (G1) reported greater positive and less negative quality relationships than the middle (G2) and the younger (G3) generations. There was limited evidence of transmission. Middle-aged respondents who reported more positive and less negative ties with their parents (G1) reported more positive and less negative ties with their own children (G3). Grandmother (G1) reports of more positive relationship quality were associated with G3 reports of more positive relationship quality with G2. Discussion. Findings are consistent with the intergenerational stake hypothesis and only partially consistent with the theory of intergenerational transmission. Overall, this study suggests that there is greater within-family variability than similarities in how family members feel about one another. PMID:22628478
Hodge numbers for all CICY quotients
Energy Technology Data Exchange (ETDEWEB)
Constantin, Andrei [Department of Physics and Astronomy, Uppsala University, SE-751 20, Uppsala (Sweden); Gray, James [Physics Department, Robeson Hall, Virginia Tech,Blacksburg, VA 24061 (United States); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)
2017-01-02
We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.
Integrable mappings via rational elliptic surfaces
International Nuclear Information System (INIS)
Tsuda, Teruhisa
2004-01-01
We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi-Yau manifolds, is also presented
A note on ODEs from mirror symmetry
Klemm, A D; Roan, S S; Yau, S T
1994-01-01
We give close formulas for the counting functions of rational curves on complete intersection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the instanton corrected Yukawa coupling.
Hodge numbers for all CICY quotients
International Nuclear Information System (INIS)
Constantin, Andrei; Gray, James; Lukas, Andre
2017-01-01
We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.
A note on flux induced superpotentials in string theory
International Nuclear Information System (INIS)
Becker, Melanie; Constantin, Dragos
2003-01-01
Non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory. Gukov has conjectured the explicit form of this superpotential. We check this conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well as for warped M-theory compactifications on Spin(7) holonomy manifolds, by performing a Kaluza-Klein reduction. (author)
F-theory and the landscape of intersecting D7-branes
Energy Technology Data Exchange (ETDEWEB)
Braun, Andreas
2010-02-05
In this work, the moduli of D7-branes in type IIB orientifold compactifications and their stabilization by fluxes is studied from the perspective of F-theory. In F-theory, the moduli of the D7-branes and the moduli of the orientifold are unified in the moduli space of an elliptic Calabi-Yau manifold. This makes it possible to study flux the stabilization of D7-branes in an elegant manner. To answer phenomenological questions, one has to translate the deformations of the elliptic Calabi-Yau manifold of F-theory back to the positions and the shape of the D7-branes. We address this problem by constructing the homology cycles that are relevant for the deformations of the elliptic Calabi-Yau manifold.We show the viability of our approach for the case of elliptic two- and three-folds. Furthermore, we discuss a consistency conditions related to the intersections between D7-branes and orientifold planes which is automatically fulfilled in F-theory. Finally, we use our results to study the flux stabilization of D7-branes on the orientifold K3 x T{sup 2}/Z{sub 2} using F-theory on K3 x K3. In this context, we derive conditions on the fluxes to stabilize a given configuration of D7-branes. (orig.)
F-theory and the landscape of intersecting D7-branes
International Nuclear Information System (INIS)
Braun, Andreas
2010-01-01
In this work, the moduli of D7-branes in type IIB orientifold compactifications and their stabilization by fluxes is studied from the perspective of F-theory. In F-theory, the moduli of the D7-branes and the moduli of the orientifold are unified in the moduli space of an elliptic Calabi-Yau manifold. This makes it possible to study flux the stabilization of D7-branes in an elegant manner. To answer phenomenological questions, one has to translate the deformations of the elliptic Calabi-Yau manifold of F-theory back to the positions and the shape of the D7-branes. We address this problem by constructing the homology cycles that are relevant for the deformations of the elliptic Calabi-Yau manifold.We show the viability of our approach for the case of elliptic two- and three-folds. Furthermore, we discuss a consistency conditions related to the intersections between D7-branes and orientifold planes which is automatically fulfilled in F-theory. Finally, we use our results to study the flux stabilization of D7-branes on the orientifold K3 x T 2 /Z 2 using F-theory on K3 x K3. In this context, we derive conditions on the fluxes to stabilize a given configuration of D7-branes. (orig.)
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.
Manifold Regularized Reinforcement Learning.
Li, Hongliang; Liu, Derong; Wang, Ding
2018-04-01
This paper introduces a novel manifold regularized reinforcement learning scheme for continuous Markov decision processes. Smooth feature representations for value function approximation can be automatically learned using the unsupervised manifold regularization method. The learned features are data-driven, and can be adapted to the geometry of the state space. Furthermore, the scheme provides a direct basis representation extension for novel samples during policy learning and control. The performance of the proposed scheme is evaluated on two benchmark control tasks, i.e., the inverted pendulum and the energy storage problem. Simulation results illustrate the concepts of the proposed scheme and show that it can obtain excellent performance.
International Nuclear Information System (INIS)
Lisboa, P.; Michael, C.
1982-01-01
We address the question of designing optimum discrete sets of points to represent numerically a continuous group manifold. We consider subsets which are extensions of the regular discrete subgroups. Applications to Monte Carlo simulation of SU(2) and SU(3) gauge theory are discussed. (orig.)
Analytic manifolds in uniform algebras
International Nuclear Information System (INIS)
Tonev, T.V.
1988-12-01
Here we extend Bear-Hile's result concerning the version of famous Bishop's theorem for one-dimensional analytic structures in two directions: for n-dimensional complex analytic manifolds, n>1, and for generalized analytic manifolds. 14 refs
Black Hole Attractors and Pure Spinors
Energy Technology Data Exchange (ETDEWEB)
Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro
2006-02-21
We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to {Sigma}f{sub k} = Im(C{Phi}), where {Phi} is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, {Phi} = {Omega} and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.
Black Hole Attractors and Pure Spinors
International Nuclear Information System (INIS)
Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro
2006-01-01
We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to Σf k = Im(CΦ), where Φ is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, Φ = (Omega) and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation
Lectures on Warped Compactifications and Stringy Brane Constructions
Energy Technology Data Exchange (ETDEWEB)
Kachru, Shamit
2001-07-26
In these lectures, two different aspects of brane world scenarios in 5d gravity or string theory are discussed. In the first two lectures, work on how warped compactifications of 5d gravity theories can change the guise of the hierarchy problem and the cosmological constant problem is reviewed, and a discussion of several issues which remain unclear in this context is provided. In the next two lectures, microscopic constructions in string theory which involve D-branes wrapped on cycles of Calabi-Yau manifolds are described. The focus is on computing the superpotential in the brane worldvolume field theory. Such calculations may be a necessary step towards understanding e.g. supersymmetry breaking and moduli stabilization in stringy realizations of such scenarios, and are of intrinsic interest as probes of the quantum geometry of the Calabi-Yau space.
Voisin, Claire
1999-01-01
This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...
Eigenvalue pinching on spinc manifolds
Roos, Saskia
2017-02-01
We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.
Explicit de Sitter flux vacua for global string models with chiral matter
Cicoli, Michele; Klevers, Denis; Krippendorf, Sven; Mayrhofer, Christoph; Quevedo, Fernando; Valandro, Roberto
2014-05-01
We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kähler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content or some close extensions. In order to control complex structure moduli stabilisation we consider Calabi-Yau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kähler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative α ' corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP3 singularity.
Explicit de Sitter flux vacua for global string models with chiral matter
Energy Technology Data Exchange (ETDEWEB)
Cicoli, Michele [Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna (Italy); INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna (Italy); ICTP, Strada Costiera 11, 34014 Trieste (Italy); Klevers, Denis [Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6396 (United States); Krippendorf, Sven [Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn, Nussallee 12, 53115 Bonn (Germany); Mayrhofer, Christoph [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120 Heidelberg (Germany); Quevedo, Fernando [ICTP, Strada Costiera 11, 34014 Trieste (Italy); DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Valandro, Roberto [ICTP, Strada Costiera 11, 34014 Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy)
2014-05-05
We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kähler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content or some close extensions. In order to control complex structure moduli stabilisation we consider Calabi-Yau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kähler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative α{sup ′} corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP{sub 6} singularity which can be higgsed to the phenomenologically interesting class of models at the dP{sub 3} singularity.
Heterotic String/F-theory Duality from Mirror Symmetry
Berglund, Per
1998-01-01
We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds $X_{n+1}$ to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of these data as valid classical solutions of the heterotic string compactified on Z_n proves F-theory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n+1-fold $X_{n+1}$ a toric n fold Z_n together with a specific family of sheafs on it. This allows for a systematic construction of phenomenologically interesting d=4 N=1 heterotic vacua, e.g. on deformations of the tangent bundle, with grand unified and SU(3)\\times SU(2) gauge groups. As another application we find non-perturbative gauge enhancements of the heterotic string on singular Calabi-Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds.
On discrete symmetries and torsion homology in F-theory
Energy Technology Data Exchange (ETDEWEB)
Mayrhofer, Christoph [Arnold-Sommerfeld-Center, Ludwig-Maximilians-Universität München,München (Germany); Palti, Eran; Till, Oskar; Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg,Heidelberg (Germany)
2015-06-04
We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a ℤ{sub 2} symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a ℤ{sub 2} gauge symmetry. We show that the resulting five-dimensional theories do not have a ℤ{sub 2} symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit torsion in homology. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a ℤ{sub 2} symmetry in five dimensions and, accordingly, we find explicitly an associated torsion cycle. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.
Topological sigma B model in 4-dimensions
International Nuclear Information System (INIS)
Jun, Hyun-Keun; Park, Jae-Suk
2008-01-01
We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensional topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.
Hidden Symmetries of Euclideanised Kerr-NUT-(AdS Metrics in Certain Scaling Limits
Directory of Open Access Journals (Sweden)
Mihai Visinescu
2012-08-01
Full Text Available The hidden symmetries of higher dimensional Kerr-NUT-(AdS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. Finally the Killing forms on mixed 3-Sasaki manifolds are briefly described.
Bragman, Felix J S; McClelland, Jamie R; Jacob, Joseph; Hurst, John R; Hawkes, David J
2017-09-01
Analysis of CT scans for studying Chronic Obstructive Pulmonary Disease (COPD) is generally limited to mean scores of disease extent. However, the evolution of local pulmonary damage may vary between patients with discordant effects on lung physiology. This limits the explanatory power of mean values in clinical studies. We present local disease and deformation distributions to address this limitation. The disease distribution aims to quantify two aspects of parenchymal damage: locally diffuse/dense disease and global homogeneity/heterogeneity. The deformation distribution links parenchymal damage to local volume change. These distributions are exploited to quantify inter-patient differences. We used manifold learning to model variations of these distributions in 743 patients from the COPDGene study. We applied manifold fusion to combine distinct aspects of COPD into a single model. We demonstrated the utility of the distributions by comparing associations between learned embeddings and measures of severity. We also illustrated the potential to identify trajectories of disease progression in a manifold space of COPD.
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.
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.
Manifold Regularized Correlation Object Tracking
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2017-01-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped fr...
Extended no-scale structure and {alpha}'{sup 2} corrections to the type IIB action
Energy Technology Data Exchange (ETDEWEB)
Pedro, F.G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Rummel, M. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Hong Kong Univ. of Science and Technology (China). Inst. for Advanced Study; Westphal, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kavali Institute for Theoretical Physics, Santa Barbara, CA (United States)
2013-06-15
We analyse a new N=1 string tree level correction at O({alpha}'{sup 2}) to the Kaehler potential of the volume moduli of type IIB Calabi-Yau flux compactification found recently by T. W. Grimm, R. Savelli and M. Weissenbacher (arXiv:1303.3317 [hep-th]) and its impact on the moduli potential. We find that it imposes a strong lower bound the Calabi-Yau volume in the Large Volume Scenario of moduli stabilisation. For KKLT-like scenarios we find that consistency of the action imposes an upper bound on the flux superpotential vertical stroke W{sub 0} vertical stroke
Exploring the web of heterotic string theories using anomalies
Energy Technology Data Exchange (ETDEWEB)
Ruehle, Fabian
2013-07-15
We investigate how anomalies can be used to infer relations among different descriptions of heterotic string theory. Starting from the observation that the construction mechanism of heterotic orbifold compactifications considered up to now prevents them from being resolved into fully smooth Calabi-Yau compactification manifolds, we use a new mechanism to obtain an orbifold which does not suffer from the aforementioned limitations. We explain in general how to resolve orbifolds into smooth Calabi-Yau using toric geometry and gauged linear sigma models. The latter allow for studying the theory in various other regions of the string moduli space as well, which unveils interesting intermediate geometries. By following anomalies through the different regimes, we can match the orbifold theories to their smooth Calabi-Yau counterparts. In the process, we investigate discrete R and non-R orbifold symmetries and propose a mechanism for studying their fate in other regions of the moduli space. Finally, we introduce a novel anomaly cancelation mechanism in gauged linear sigma models, which manifests itself in target space as a description of compactification geometries with torsion and Neveu-Schwarz five branes.
Picard-Fuchs uniformization and modularity of the mirror map
International Nuclear Information System (INIS)
Doran, C.F.
2000-01-01
Arithmetic properties of mirror symmetry (type IIA-IIB string duality) are studied. We give criteria for the mirror map q-series of certain families of Calabi-Yau manifolds to be automorphic functions. For families of elliptic curves and lattice polarized K3 surfaces with surjective period mappings, global Torelli theorems allow one to present these criteria in terms of the ramification behavior of natural algebraic invariants - the functional and generalized functional invariants respectively. In particular, when applied to one parameter families of rank 19 lattice polarized K3 surfaces, our criterion demystifies the mirror-Moonshine phenomenon of Lian and Yau and highlights its non-monstrous nature. The lack of global Torelli theorems and presence of instanton corrections makes Calabi-Yau threefold families more complicated. Via the constraints of special geometry, the Picard-Fuchs equations for one parameter families of Calabi-Yau threefolds imply a differential equation criterion for automorphicity of the mirror map in terms of the Yukawa coupling. In the absence of instanton corrections, the projective periods map to a twisted cubic space curve. A hierarchy of ''algebraic'' instanton corrections correlated with the differential Galois group of the Picard-Fuchs equation is proposed. (orig.)
Exploring the web of heterotic string theories using anomalies
International Nuclear Information System (INIS)
Ruehle, Fabian
2013-07-01
We investigate how anomalies can be used to infer relations among different descriptions of heterotic string theory. Starting from the observation that the construction mechanism of heterotic orbifold compactifications considered up to now prevents them from being resolved into fully smooth Calabi-Yau compactification manifolds, we use a new mechanism to obtain an orbifold which does not suffer from the aforementioned limitations. We explain in general how to resolve orbifolds into smooth Calabi-Yau using toric geometry and gauged linear sigma models. The latter allow for studying the theory in various other regions of the string moduli space as well, which unveils interesting intermediate geometries. By following anomalies through the different regimes, we can match the orbifold theories to their smooth Calabi-Yau counterparts. In the process, we investigate discrete R and non-R orbifold symmetries and propose a mechanism for studying their fate in other regions of the moduli space. Finally, we introduce a novel anomaly cancelation mechanism in gauged linear sigma models, which manifests itself in target space as a description of compactification geometries with torsion and Neveu-Schwarz five branes.
Morse theory on banach manifolds
International Nuclear Information System (INIS)
Wang, T.
1986-01-01
The Morse Theory of critical points was extended by Palais and Smale to a certain class of functions on Hilbert manifolds. However, there are many variational problems in a nonlinear setting which for technical reasons are posed not on Hilbert but on Banach manifolds of mappings. This paper introduces a concept of a multivalued gradient vector field for a function defined on a Banach manifold. Using this concept, the Morse theory is generalized to some kind of Banach manifolds. The first chapter gives a definition of nondegeneracy of critical points for a real valued function defined on a reflexive Banach manifold, and then a handle-body decomposition theorem and Morse inequalities for this manifold are obtained. The second chapter proves the existence of solutions for a differential inclusion for a so-called accretive multi-valued mapping on a Finsler manifold. The third chapter introduces a definition of nondegeneracy of critical points for a real valued function defined on a general Banach manifold and, furthermore, generalizes the Morse handle-body decomposition theorem and the Morse inequalities to the Banach manifold
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.
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...
Supersymmetric gauge theories from string theory
International Nuclear Information System (INIS)
Metzger, St.
2005-12-01
This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G 2 -manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G 2 -manifold is known. Here we construct families of metrics on compact weak G 2 -manifolds, which contain two conical singularities. Weak G 2 -manifolds have properties that are similar to the ones of proper G 2 -manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E 8 x E 8 -heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the classical action. (author)
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.
Manifold Regularized Correlation Object Tracking.
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2018-05-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions. Thus, the final classifier in our method is trained with positive, negative, and unlabeled base samples, which is a semisupervised learning framework. A block optimization strategy is further introduced to learn a manifold regularization-based correlation filter for efficient online tracking. Experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state-of-the-art tracking approaches.
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...
Moduli space of torsional manifolds
International Nuclear Information System (INIS)
Becker, Melanie; Tseng, L.-S.; Yau, S.-T.
2007-01-01
We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be Hermitian Yang-Mills, and also the anomaly cancellation be satisfied. We perform the linearized variation of these constraints to derive the defining equations for the local moduli. We explicitly determine the metric deformations of the smooth flux solution corresponding to a torus bundle over K3
Indian Academy of Sciences (India)
manifolds. Some properties of Riemannian curvature tensors and curvature scalars of. Kähler–Norden manifolds using the theory of Tachibana operators is presented. Keywords. Kähler–Norden manifold; Norden metric; twin metric; pure tensor; holo- morphic tensor. 1. Introduction. Let M2n be a Riemannian manifold with a ...
N=1 domain wall solutions of massive type II supergravity as generalized geometries
International Nuclear Information System (INIS)
Louis, J.
2006-05-01
We study N=1 domain wall solutions of type IIB supergravity compactified on a Calabi-Yau manifold in the presence of RR and NS electric and magnetic fluxes. We show that the dynamics of the scalar fields along the direction transverse to the domain wall is described by gradient flow equations controlled by a superpotential W. We then provide a geometrical interpretation of the gradient flow equations in terms of the mirror symmetric compactification of type IIA. They correspond to a set of generalized Hitchin flow equations of a manifold with SU(3) x SU(3)structure which is fibered over the direction transverse to the domain wall. (Orig.)
Three Generations of Greek Americans: A Study in Ethnicity.
Scourby, Alice
1980-01-01
Measures ethnic identity among three generations of Greek Americans living in the New York Metropolitan area. Shows that, though there is a generational variation, the majority of Greeks still have relatively strong attachment to their ethnic culture, despite their identification with American society. (Author/GC)
Initially Approximated Quasi Equilibrium Manifold
International Nuclear Information System (INIS)
Shahzad, M.; Arif, H.; Gulistan, M.; Sajid, M.
2015-01-01
Most commonly, kinetics model reduction techniques are based on exploiting time scale separation into fast and slow reaction processes. Then, a researcher approximates the system dynamically with dimension reduction for slow ones eliminating the fast modes. The main idea behind the construction of the lower dimension manifold is based on finding its initial approximation using Quasi Equilibrium Manifold (QEM). Here, we provide an efficient numerical method, which allow us to calculate low dimensional manifolds of chemical reaction systems. This computation technique is not restricted to our specific complex problem, but it can also be applied to other reacting flows or dynamic systems provided with the condition that a large number of extra (decaying) components can be eliminated from the system. Through computational approach, we approximate low dimensional manifold for a mechanism of six chemical species to simplify complex chemical kinetics. A reduced descriptive form of slow invariant manifold is obtained from dissipative system. This method is applicable for higher dimensions and is applied over an oxidation of CO/Pt. (author)
Slow manifolds in chemical kinetics
International Nuclear Information System (INIS)
Shahzad, M.; Haq, I. U.; Sultan, F.; Wahab, A.; Faizullah, F.; Rahman, G. U.
2016-01-01
Modelling the chemical system, especially for complex and higher dimensional problems, gives an easy way to handle the ongoing reaction process with respect to time. Here, we will consider some of the newly developed computational methods commonly used for model reductions in a chemical reaction. An effective (simple) method is planned to measure the low dimensional manifold, which reduces the higher dimensional system in such a way that it may not affect the precision of the whole mechanism. The phase flow of the solution trajectories near the equilibrium point is observed while the initial approximation is measured with the spectral quasi equilibrium manifold, which starts from the equilibrium point. To make it an invariant curve, the approximated curve is first refined a certain number of times using the method of invariant grids. The other way of getting the reduced data in the low dimensional manifold is possible through the intrinsic low dimensional manifold. Then, we compare these two invariant curves given by both the methods. Finally, the idea is extended to the higher dimensional manifold, where more number of progress variables will be added. (author)
Transmission of attachment across three generations: Continuity and reversal.
Hautamäki, Airi; Hautamäki, Laura; Neuvonen, Leena; Maliniemi-Piispanen, Sinikka
2010-07-01
We followed a normative Finnish sample of primiparous mothers, fathers, and maternal grandmothers from pregnancy until the child was 3 years old (N = 32 families). The Adult Attachment Interview (AAI) was used to assess attachment in mothers, fathers and grandmothers during the last trimester of the mother's pregnancy. The Preschool Assessment of Attachment (PAA) was used to assess attachment in children at 3 years. Forty-seven percent of the 32 grandmother-mother-infant triads had the corresponding attachment classifications. Using EXACON for the analysis of single cells of 3 x 3 contingency tables with type-antitype classifications, and frequency tabulation of the major three-generation combinations, both triads indicating continuity across three generations (B/B/B 22% and A/A/A 19%) and reversal reactions (A/C/A and C/A/C 22%) were found. The results indicated continuity across three generations for Type B and for Type A and alternations from A to C and vice versa for insecure attachment. We discuss the implications of these findings for theory development and clinical work.
Fivebranes and 3-manifold homology
Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun
2017-07-01
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[ M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.
Generalized graph manifolds and their effective recognition
International Nuclear Information System (INIS)
Matveev, S V
1998-01-01
A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only...... in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimize a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend...
Blowup for flat slow manifolds
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2017-01-01
In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a......) the regularization of piecewise smooth systems by tanh, (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b)....
Blowup for flat slow manifolds
Kristiansen, K. U.
2017-05-01
In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a) the regularization of piecewise smooth systems by \\tanh , (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b).
Matrix regularization of 4-manifolds
Trzetrzelewski, M.
2012-01-01
We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...
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
Dilaton stabilization in three-generation heterotic string model
Energy Technology Data Exchange (ETDEWEB)
Beye, Florian, E-mail: fbeye@eken.phys.nagoya-u.ac.jp [Kawasaki (Japan); Kobayashi, Tatsuo, E-mail: kobayashi@particle.sci.hokudai.ac.jp [Department of Physics, Hokkaido University, Sapporo 060-0810 (Japan); Kuwakino, Shogo, E-mail: kuwakino@cc.kyoto-su.ac.jp [Maskawa Institute for Science and Culture, Kyoto Sangyo University, Kamigamo-Motoyama, Kita-ku, Kyoto 603-8555 (Japan)
2016-09-10
We study dilaton stabilization in heterotic string models. By utilizing the asymmetric orbifold construction, we construct an explicit three-generation model whose matter content in the visible sector is the supersymmetric standard model with additional vectorlike matter. This model does not contain any geometric moduli fields except the dilaton field. Model building at a symmetry enhancement point in moduli space enlarges the rank of the hidden gauge group. By analyzing multiple hidden gauge sectors, the dilaton field is stabilized by the racetrack mechanism. We also discuss a supersymmetry breaking scenario and F-term uplifting.
Collective coordinates on symplectic manifolds
International Nuclear Information System (INIS)
Razumov, A.V.; Taranov, A.Yu.
1981-01-01
For an arbitrary Lie group of canonical transformations on a symplectic manifold collective coordinates are introduced. They describe a motion of the dynamical system as a whole under the group transformations. Some properties of Lie group of canonical transformations are considered [ru
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 $(G, g)$ int...
Cayley transform on Stiefel manifolds
Macías-Virgós, Enrique; Pereira-Sáez, María José; Tanré, Daniel
2018-01-01
The Cayley transform for orthogonal groups is a well known construction with applications in real and complex analysis, linear algebra and computer science. In this work, we construct Cayley transforms on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimization problems are presented.
An imbedding of Lorentzian manifolds
International Nuclear Information System (INIS)
Kim, Do-Hyung
2009-01-01
A new method for imbedding a Lorentzian manifold with a non-compact Cauchy surface is presented. As an application, it is shown that any two-dimensional globally hyperbolic spacetime with a non-compact Cauchy surface can be causally isomorphically imbedded into two-dimensional Minkowski spacetime.
Minimal surfaces in Riemannian manifolds
International Nuclear Information System (INIS)
Ji Min; Wang Guangyin
1990-10-01
A multiple solution to the Plateau problem in a Riemannian manifold is established. In S n , the existence of two solutions to this problem is obtained. The Morse-Tompkins-Shiffman theorem is extended to the case when the ambient space admits no minimal sphere. (author). 20 refs
Obstruction theory on 8-manifolds
Czech Academy of Sciences Publication Activity Database
Čadek, M.; Crabb, M.; Vanžura, Jiří
2008-01-01
Roč. 127, č. 2 (2008), s. 167-186 ISSN 0025-2611 R&D Projects: GA ČR GA201/05/2117 Institutional research plan: CEZ:AV0Z10190503 Keywords : 8-manifolds * obstruction theory Subject RIV: BA - General Mathematics Impact factor: 0.509, year: 2008
The dynamics of slow manifolds
Verhulst, F.; Bakri, T.
2006-01-01
Invited lecture at Konferensi Nasional Matematika XIII, Semarang, 24-27 juli, 2006; to be publ. in J. Indones. Math. Soc. (2007) After reviewing a number of results from geometric singular perturbation theory, we discuss several approaches to obtain periodic solutions in a slow manifold.
Indian Academy of Sciences (India)
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 Tachibana operators is presented.
Quotient of manifolds by discrete groups
International Nuclear Information System (INIS)
Ardalan, F.; Arfaei, H.
1985-09-01
Quotient of manifolds by discrete subgroups of their isometry group are considered. In particular, symmetry breaking due to the quotient structure, topological properties and harmonic analysis of the resultant manifolds are discussed and illustrated by two dimensional examples. (author)
A viewpoint on nearly conformally symmetric manifold
International Nuclear Information System (INIS)
Rahman, M.S.
1990-06-01
Some observations, with definition, on Nearly Conformally Symmetric (NCS) manifold are made. A number of theorems concerning conformal change of metric and parallel tensors on NCS manifolds are presented. It is illustrated that a manifold M = R n-1 x R + 1 , endowed with a special metric, is NCS but not of harmonic curvature. (author). 8 refs
An integrality theorem for spinc manifolds
International Nuclear Information System (INIS)
Seade, J.A.
1990-04-01
A spin c manifold M n is an oriented, Riemannian manifold with an associated hermitian live bundle det(M), together with a lifting to B(spin n c ) of the classifying map of the bundle TMxU(1). We prove here an integrality theorem for spin c manifolds. 11 refs
Natural Connections on Riemannian Product Manifolds
Gribacheva, Dobrinka
2011-01-01
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
Persistent Educational Advantage Across Three Generations: Empirical Evidence for Germany
Directory of Open Access Journals (Sweden)
Andrea Ziefle
2016-12-01
Full Text Available This article uses survey data from the German Socio-Economic Panel (GSOEP to analyze the persistence of educational attainment across three generations in Germany. I obtain evidence of a robust effect of grandparents' education on respondents' own educational attainment in West Germany, net of parental class, education, occupational status, family income, parents' relationship history, and family size. I also test whether the grandparent effect results from resource compensation or cumulative advantage and find empirical support for both mechanisms. In comparison, the intergenerational association between grandparents' and respondents' education is considerably weaker in East Germany and is also mediated completely by parental education. There are hardly any gender differences in the role of grandparents for respondents’ educational attainment, except for the fact that resource compensation is found to be exclusively relevant for women’s attainment in both West Germany and in East Germany after German reunification and the associated transition to an open educational system.
Supersymmetry breaking effects using the pure spinor formalism of the superstring
Berkovits, Nathan; Witten, Edward
2014-06-01
The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously break supersymmetry at one-loop order even when it is unbroken at tree-level. It is known that calculating the supersymmetry-breaking effects in this model gives a relatively accessible test case of the subtleties of superstring perturbation theory in the RNS formalism. In the present paper, we calculate the relevant amplitudes in the pure spinor approach to superstring perturbation theory, and show that the regulator used in computing loop amplitudes in the pure spinor formalism leads to subtleties somewhat analogous to the more familiar subtleties of the RNS approach.
Supersymmetry breaking effects using the pure spinor formalism of the superstring
Energy Technology Data Exchange (ETDEWEB)
Berkovits, Nathan [ICTP South American Institute for Fundamental Research,Instituto de Física Teórica, UNESP - Univ. Estadual Paulista,Rua Dr. Bento T. Ferraz 271, 01140-070, São Paulo, SP (Brazil); Witten, Edward [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 (United States)
2014-06-23
The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously break supersymmetry at one-loop order even when it is unbroken at tree-level. It is known that calculating the supersymmetry-breaking effects in this model gives a relatively accessible test case of the subtleties of superstring perturbation theory in the RNS formalism. In the present paper, we calculate the relevant amplitudes in the pure spinor approach to superstring perturbation theory, and show that the regulator used in computing loop amplitudes in the pure spinor formalism leads to subtleties somewhat analogous to the more familiar subtleties of the RNS approach.
Towards a K-theory description of quantum hair
Energy Technology Data Exchange (ETDEWEB)
Garcia-Compean, H.; Loaiza-Brito, O. [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del I.P.N., P.O. Box 14-740, 07000, Mexico D.F (Mexico); Departamento de Fisica, Universidad de Guanajuato, C.P. 37150, Leon, Guanajuato (Mexico)
2012-08-24
The first steps towards a proposal for a description of the quantum hair in 4D supersymmetric black holes in string Calabi-Yau (CY) compactifications are given. The quantum hair consisting of electric and magnetic fractional charges in black holes are derived from periods of the CY's torsion cycles. In the process a K-theory interpretation of the quantum hair in terms of the Atiyah-Hirzebruch spectral sequence is carried out. Finally, the same procedure is considered for torsion cycles of certain generalized CY's threefolds such as half-flat manifolds.
Non-perturbative scalar potential inspired by type IIA strings on rigid CY
Energy Technology Data Exchange (ETDEWEB)
Alexandrov, Sergei [Laboratoire Charles Coulomb (L2C), UMR 5221, CNRS-Université de Montpellier,F-34095, Montpellier (France); Ketov, Sergei V. [Department of Physics, Tokyo Metropolitan University,1-1 Minami-ohsawa, Hachioji-shi, Tokyo 192-0397 (Japan); Kavli Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo,Chiba 277-8568 (Japan); Institute of Physics and Technology, Tomsk Polytechnic University,30 Lenin Ave., Tomsk 634050 (Russian Federation); Wakimoto, Yuki [Department of Physics, Tokyo Metropolitan University,1-1 Minami-ohsawa, Hachioji-shi, Tokyo 192-0397 (Japan)
2016-11-10
Motivated by a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we derive a non-perturbative potential of all scalar fields from the exact D-instanton corrected metric on the hypermultiplet moduli space. Applying this potential to moduli stabilization, we find a discrete set of exact vacua for axions. At these critical points, the stability problem is decoupled into two subspaces spanned by the axions and the other fields (dilaton and Kähler moduli), respectively. Whereas the stability of the axions is easily achieved, numerical analysis shows instabilities in the second subspace.
Renormalization Method and Mirror Symmetry
Directory of Open Access Journals (Sweden)
Si Li
2012-12-01
Full Text Available This is a brief summary of our works [arXiv:1112.4063, arXiv:1201.4501] on constructing higher genus B-model from perturbative quantization of BCOV theory. We analyze Givental's symplectic loop space formalism in the context of B-model geometry on Calabi-Yau manifolds, and explain the Fock space construction via the renormalization techniques of gauge theory. We also give a physics interpretation of the Virasoro constraints as the symmetry of the classical BCOV action functional, and discuss the Virasoro constraints in the quantum theory.
Anomaly cancellation and smooth non-Kahler solutions in heterotic string theory
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Fu Jixiang; Tseng, L.-S.; Yau, S.-T.
2006-01-01
We show that six-dimensional backgrounds that are T 2 bundle over a Calabi-Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can only be satisfied if the base is K3 while a T 4 base is excluded. The conditions imposed by anomaly cancellation for the T 2 bundle structure, the dilaton field, and the holomorphic stable bundles are analyzed and the solutions determined. Applying duality, we check the consistency of the anomaly cancellation constraints with those for flux backgrounds of M-theory on eight-manifolds
Exact quantization conditions for the relativistic Toda lattice
International Nuclear Information System (INIS)
Hatsuda, Yasuyuki; Mariño, Marcos
2016-01-01
Inspired by recent connections between spectral theory and topological string theory, we propose exact quantization conditions for the relativistic Toda lattice of N particles. These conditions involve the Nekrasov-Shatashvili free energy, which resums the perturbative WKB expansion, but they require in addition a non-perturbative contribution, which is related to the perturbative result by an S-duality transformation of the Planck constant. We test the quantization conditions against explicit calculations of the spectrum for N=3. Our proposal can be generalized to arbitrary toric Calabi-Yau manifolds and might solve the corresponding quantum integrable system of Goncharov and Kenyon.
Higgs bundles and four manifolds
International Nuclear Information System (INIS)
Park, Jae-Suk.
2002-01-01
It is known that the Seiberg-Witten invariants, derived from supersymmetric Yang-Mill theories in four dimensions, do not distinguish smooth structure of certain non-simply-connected four manifolds. We propose generalizations of Donaldson-Witten and Vafa-Witten theories on a Kaehler manifold based on Higgs bundles. We showed, in particular, that the partition function of our generalized Vafa-Witten theory can be written as the sum of contributions our generalized Donaldson-Witten invariants and generalized Seiberg-Witten invariants. The resulting generalized Seiberg-Witten invariants might have, conjecturally, information on smooth structure beyond the original Seiberg-Witten invariants for non-simply-connected case
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.
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.
Torsions of 3-dimensional manifolds
Wurzbacher, T
2002-01-01
From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews
Hierarchy of graph matchbox manifolds
Lukina, Olga
2011-01-01
We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity which we call its level. We develop the fusion construction, which allows us to associate to every two graph foliated spaces a third one which contains the former two in its closure. Although the underlying idea of the fusion is simple, it gives us a powerful tool to study graph foliated spaces. Using fusi...
Invariant Bayesian estimation on manifolds
Jermyn, Ian H.
2005-01-01
A frequent and well-founded criticism of the maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter \\gamma taking values in a differentiable manifold \\Gamma is that they are not invariant to arbitrary ``reparameterizations'' of \\Gamma. This paper clarifies the issues surrounding this problem, by pointing out the difference between coordinate invariance, which is a sine qua non for a mathematically well-defined problem, and diffeomorphism invarianc...
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-...
A stringy origin of M2 brane Chern-Simons theories
International Nuclear Information System (INIS)
Aganagic, Mina
2010-01-01
We show that string duality relates M-theory on a local Calabi-Yau fourfold singularity X 4 to type IIA string theory on a Calabi-Yau threefold X 3 fibered over a real line, with RR 2-form fluxes turned on. The RR flux encodes how the M-theory circle is fibered over the IIA geometry. The theories on N D2 branes probing X 3 are the well-known quiver theories with N=2 supersymmetry in three dimensions. We show that turning on fluxes, and fibering the X 3 over a direction transverse to the branes, corresponds to turning on N=2 Chern-Simons couplings. String duality implies that, in the strong coupling limit, the N D2 branes on X 3 in this background become N M2 branes on X 4 . This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi-Yau fourfolds in terms of N=2 quiver Chern-Simons theories. We also provide a new N=2 Chern-Simons theory dual to AdS 4 xQ 1,1,1 . Type IIA/M-theory duality also relates IIA string theory on X 3 with only the RR fluxes turned on, to M-theory on a G 2 holonomy manifold. We show that this implies that the N M2 branes probing the G 2 manifold are described by the quiver Chern-Simons theory originating from the D2 branes probing X 3 , except that now Chern-Simons terms preserve only N=1 supersymmetry in three dimensions.
An assessment of organisational justice perceptions across three generational cohorts
Directory of Open Access Journals (Sweden)
Ophillia Ledimo
2015-09-01
Full Text Available Despite several reviews of generational differences across cohorts regarding their career stages in organisations, relatively few empirical investigations have been conducted to understand these cohorts’s behaviour and perceptions. Hence there is paucity of studies that explored the generational differences on the construct organisational justice across generational cohorts. The objective of this study was to assess the differences across three generational cohorts (Millennials, Generation X, and Baby Boomers on dimensions of the organisational justice construct using the Organisational Justice Measurement Instrument (OJMI. Data was collected through the administration of OJMI to a random sample size of organisational employees (n=289. Descriptive statistics and analysis of variance were conducted to interpret the data. These findings provide evidence that differences do exist across cohorts on dimensions of organisational justice, and some differences may be a result of respondents’ different perception of their organisation’s practices and processes. In terms of contributions and practical implications, insight gained from the findings may be used in proposing organisational development interventions to manage multigenerational employees as well as to conduct future research.
Three generation production biotechnology of biomass into bio-fuel
Zheng, Chaocheng
2017-08-01
The great change of climate change, depletion of natural resources, and scarcity of fossil fuel in the whole world nowadays have witnessed a sense of urgency home and abroad among scales of researchers, development practitioners, and industrialists to search for completely brand new sustainable solutions in the area of biomass transforming into bio-fuels attributing to our duty-that is, it is our responsibility to take up this challenge to secure our energy in the near future with the help of sustainable approaches and technological advancements to produce greener fuel from nature organic sources or biomass which comes generally from organic natural matters such as trees, woods, manure, sewage sludge, grass cuttings, and timber waste with a source of huge green energy called bio-fuel. Biomass includes most of the biological materials, livings or dead bodies. This energy source is ripely used industrially, or domestically for rather many years, but the recent trend is on the production of green fuel with different advance processing systems in a greener. More sustainable method. Biomass is becoming a booming industry currently on account of its cheaper cost and abundant resources all around, making it fairly more effective for the sustainable use of the bio-energy. In the past few years, the world has witnessed a remarkable development in the bio-fuel production technology, and three generations of bio-fuel have already existed in our society. The combination of membrane technology with the existing process line can play a vital role for the production of green fuel in a sustainable manner. In this paper, the science and technology for sustainable bio-fuel production will be introduced in detail for a cleaner world.
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
Similarity Learning of Manifold Data.
Chen, Si-Bao; Ding, Chris H Q; Luo, Bin
2015-09-01
Without constructing adjacency graph for neighborhood, we propose a method to learn similarity among sample points of manifold in Laplacian embedding (LE) based on adding constraints of linear reconstruction and least absolute shrinkage and selection operator type minimization. Two algorithms and corresponding analyses are presented to learn similarity for mix-signed and nonnegative data respectively. The similarity learning method is further extended to kernel spaces. The experiments on both synthetic and real world benchmark data sets demonstrate that the proposed LE with new similarity has better visualization and achieves higher accuracy in classification.
Cobordism independence of Grassmann manifolds
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
ν(m) divides m. Given a positive integer d, let G(d) denote the set of bordism classes of all non-bounding. Grassmannian manifolds Gk(Fn+k) having real dimension d such that k < n. The restric- tion k
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 ...
Holomorphic bundles over elliptic manifolds
International Nuclear Information System (INIS)
Morgan, J.W.
2000-01-01
In this lecture we shall examine holomorphic bundles over compact elliptically fibered manifolds. We shall examine constructions of such bundles as well as (duality) relations between such bundles and other geometric objects, namely K3-surfaces and del Pezzo surfaces. We shall be dealing throughout with holomorphic principal bundles with structure group GC where G is a compact, simple (usually simply connected) Lie group and GC is the associated complex simple algebraic group. Of course, in the special case G = SU(n) and hence GC = SLn(C), we are considering holomorphic vector bundles with trivial determinant. In the other cases of classical groups, G SO(n) or G = Sympl(2n) we are considering holomorphic vector bundles with trivial determinant equipped with a non-degenerate symmetric, or skew symmetric pairing. In addition to these classical cases there are the finite number of exceptional groups. Amazingly enough, motivated by questions in physics, much interest centres around the group E8 and its subgroups. For these applications it does not suffice to consider only the classical groups. Thus, while often first doing the case of SU(n) or more generally of the classical groups, we shall extend our discussions to the general semi-simple group. Also, we shall spend a good deal of time considering elliptically fibered manifolds of the simplest type, namely, elliptic curves
On natural inflation and moduli stabilisation in string theory
Energy Technology Data Exchange (ETDEWEB)
Palti, Eran [Institut für Theoretische Physik, Ruprecht-Karls-Universität, Philosophenweg 19, Heidelberg, 69120 (Germany)
2015-10-28
Natural inflation relies on the existence of an axion decay constant which is super-Planckian. In string theory only sub-Planckian axion decay constants have been found in any controlled regime. However in field theory it is possible to generate an enhanced super-Planckian decay constant by an appropriate aligned mixing between axions with individual sub-Planckian decay constants. We study the possibility of such a mechanism in string theory. In particular we construct a new realisation of an alignment scenario in type IIA string theory compactifications on a Calabi-Yau where the alignment is induced through fluxes. Within field theory the original decay constants are taken to be independent of the parameters which induce the alignment. In string theory however they are moduli dependent quantities and so interact gravitationally with the physics responsible for the mixing. We show that this gravitational effect of the fluxes on the moduli can precisely cancel any enhancement of the effective decay constant. This censorship of an effective super-Planckian decay constant depends on detailed properties of Calabi-Yau moduli spaces and occurs for all the examples and classes that we study. We expand these results to a general superpotential assuming only that the axion superpartners are fixed supersymmetrically and are able to show for a large class of Calabi-Yau manifolds, but not all, that the cancellation effect occurs and is independent of the superpotential. We also study simple models where the moduli are fixed non-supersymmetrically and find that similar cancellation behaviour can emerge. Finally we make some comments on a possible generalisation to axion monodromy inflation models.
Target manifold formation using a quadratic SDF
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
Numerical continuation of normally hyperbolic invariant manifolds
Broer, H. W.; Hagen, A.; Vegter, G.
2007-06-01
This paper deals with the numerical continuation of invariant manifolds regardless of the restricted dynamics. Common examples of such manifolds include limit sets, codimension 1 manifolds separating basins of attraction (separatrices), stable/unstable/centre manifolds, nested hierarchies of attracting manifolds in dissipative systems and manifolds appearing in bifurcations. The approach is based on the general principle of normal hyperbolicity, where the graph transform leads to the numerical algorithms. This gives a highly multiple purpose method. The graph transform and linear graph transform compute the perturbed manifold with its hyperbolic splitting. To globally discretize manifolds, a discrete tubular neighbourhood is used, induced by a transverse bundle composed of discrete stable and unstable bundles. This approach allows the development of the discrete graph transform/linear graph transform analogous to the usual smooth case. Convergence results are given. The discrete vector bundle construction and associated local k-plane interpolation may be of independent interest. A practical numerical implementation for solving the global equations underlying the graph transform is proposed. Relevant numerical techniques are discussed and computational tests included. An additional application is the computation of the 'slow-transient' surface of an enzyme reaction.
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
minimum set of a super Busemann function contains a soul of M. Clearly, a complete simply connected Riemannian manifold H of non-positive sec- tional curvature, called Hadamard manifold, has the property that the distance function to an arbitrary fixed point is strongly convex exhaustion. Also, the exponential map expp :.
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss ... map expp at some point p ∈ M (and hence at every point on M) is defined on the whole tangent space Mp to M at ... The influence of the existence of convex functions on the metric and topology of under- lying manifolds has ...
Integrability conditions on Engel-type manifolds
Calin, Ovidiu; Chang, Der-Chen; Hu, Jishan
2015-09-01
We introduce the concept of Engel manifold, as a manifold that resembles locally the Engel group, and find the integrability conditions of the associated sub-elliptic system , . These are given by , . Then an explicit construction of the solution involving an integral representation is provided, which corresponds to a Poincaré-type lemma for the Engel's distribution.
Holomorphic curves in exploded manifolds: Kuranishi structure
Parker, Brett
2013-01-01
This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside a moduli stack of curves. The construction also works for the moduli stack of holomorphic curves in any compact symplectic manifold.
Harmonic manifolds with minimal horospheres are flat
Indian Academy of Sciences (India)
Abstract. In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting ...
Harmonic Manifolds with Minimal Horospheres are Flat
Indian Academy of Sciences (India)
In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem.
Some comparison theorems for Kahler manifolds
Tam, Luen-Fai; Yu, Chengjie
2010-01-01
In this work, we will verify some comparison results on Kahler manifolds. They are complex Hessian comparison for the distance function from a closed complex submanifold of a Kahler manifold with holomorphic bisectional curvature bounded below by a constant, eigenvalue comparison and volume comparison in terms of scalar curvature. This work is motivated by comparison results of Li and Wang .
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)
spaces and locally rank one symmetric spaces. ... any simply connected harmonic manifold is either flat or a rank one symmetric space. .... constant functions on manifolds. The derivatives ∇. (k) σp···σp ωp can be expressed in terms of the curvature tensor and its covariant derivatives. For example, we have for v ∈ SpM,.
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
Differential geometry of quasi-Sasakian manifolds
International Nuclear Information System (INIS)
Kirichenko, V F; Rustanov, A R
2002-01-01
The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of CR 1 quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the B-transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind
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.
Harmonic space and quaternionic manifolds
International Nuclear Information System (INIS)
Galperin, A.; Ogievetsky, O.; Ivanov, E.
1992-10-01
A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs
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...
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.
International Nuclear Information System (INIS)
Chiang, Yuan-Jen.
1989-01-01
Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S
Topological strings from quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-12-15
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P{sup 2}, local P{sup 1} x P{sup 1} and local F{sub 1}. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
Klevers, Denis; Oehlmann, Paul-Konstantin; Piragua, Hernan; Reuter, Jonas
2015-01-01
We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in P^2, P^1x P^1 and the recently studied ...
Energy Technology Data Exchange (ETDEWEB)
Anderson, Lara B.; Gao, Xin; Gray, James; Lee, Seung-Joo [Physics Department, Virginia Tech,Robeson Hall, Blacksburg, VA 24061 (United States)
2016-11-02
We provide a set of tools for analyzing the geometry of elliptically fibered Calabi-Yau manifolds, starting with a description of the total space rather than with a Weierstrass model or a specified type of fiber/base. Such an approach to the subject of F-theory compactification makes certain geometric properties, which are usually hidden, manifest. Specifically, we review how to isolate genus-one fibrations in such geometries and then describe how to find their sections explicitly. This includes a full parameterization of the Mordell-Weil group where non-trivial. We then describe how to analyze the associated Weierstrass models, Jacobians and resolved geometries. We illustrate our discussion with concrete examples which are complete intersections in products of projective spaces (CICYs). The examples presented include cases exhibiting non-abelian symmetries and higher rank Mordell-Weil group. We also make some comments on non-flat fibrations in this context. In a companion paper http://arxiv.org/abs/1608.07555 to this one, these results will be used to analyze the consequences for string dualities of the ubiquity of multiple fibrations in known constructions of Calabi-Yau manifolds.
Black branes in flux compactifications
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Torroba, Gonzalo; Wang, Huajia
2013-10-01
We construct charged black branes in type IIA flux compactifications that are dual to (2 + 1)-dimensional field theories at finite density. The internal space is a general Calabi-Yau manifold with fluxes, with internal dimensions much smaller than the AdS radius. Gauge fields descend from the 3-form RR potential evaluated on harmonic forms of the Calabi-Yau, and Kaluza-Klein modes decouple. Black branes are described by a four-dimensional effective field theory that includes only a few light fields and is valid over a parametrically large range of scales. This effective theory determines the low energy dynamics, stability and thermodynamic properties. Tools from flux compactifications are also used to construct holographic CFTs with no relevant scalar operators, that can lead to symmetric phases of condensed matter systems stable to very low temperatures. The general formalism is illustrated with simple examples such as toroidal compactifications and manifolds with a single size modulus. We initiate the classification of holographic phases of matter described by flux compactifications, which include generalized Reissner-Nordstrom branes, nonsupersymmetric AdS_{2}×R^{2} and hyperscaling violating solutions.
Topological strings from quantum mechanics
International Nuclear Information System (INIS)
Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki
2014-12-01
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
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.
Reduction of locally conformal symplectic manifolds with examples of non-Kähler manifolds
Noda, Tomonori
2004-01-01
Let $(M, \\Omega)$ be a locally conformal symplectic manifold. $\\Omega$ is a non-degenerate 2-form on $M$ such that there is a closed 1-form $\\omega$, called the Lee form, satisfing $ d\\Omega=\\omega\\wedge\\Omega$. In this paper we consider Marsden-Weinstein reduction theorem which induces Jacobi-Liouville theorem as a special case. For locally conformal Kähler manifolds, this reduction theorem gives a construction of non-Kähler manifolds in general dimension.
Final design of ITER thermal shield manifold
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Kim, Kyung-Kyu [Mecha T& S, Jinju-si 52811 (Korea, Republic of); Noh, Chang Hyun, E-mail: chnoh@nfri.re.kr [National Fusion Research Institute, Daejeon 34133 (Korea, Republic of); Kim, Yun-Kyu; Park, Sungwoo [Mecha T& S, Jinju-si 52811 (Korea, Republic of); Nam, Kwanwoo [National Fusion Research Institute, Daejeon 34133 (Korea, Republic of); Chung, Wooho [Mecha T& S, Jinju-si 52811 (Korea, Republic of); Kang, Dongkwon; Kang, Kyung-O. [National Fusion Research Institute, Daejeon 34133 (Korea, Republic of); Park, Sungmun [SFA Engineering Corporation, Hwaseong-si 10060 (Korea, Republic of); Bae, Jing Do [Korea Marine Equipment Research Institute, Busan 49111 (Korea, Republic of)
2016-11-01
Highlights: • Engineering design of thermal shield manifold is finalized. • Pipe routing, support design and flow balance are verified by analysis. • Mock-ups are fabricated to verify the design. - Abstract: The ITER thermal shield is actively cooled by 80 K pressurized helium gas. The helium coolant flows from the cold valve box to the cooling tubes on the TS panels via manifold piping. This paper describes the final design of thermal shield manifold. Pipe design to accommodate the thermal contraction considering interface with adjacent components and detailed design of support structure are presented. R&D for the pipe branch connection is carried out to find a feasible manufacturing method. Global structural behavior and structural integrity of the manifold including pipe supports are investigated by a finite element analysis based on ASME B31.3 code. Flow analyses are performed to check the flow distribution.
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.
The Hodge theory of projective manifolds
de Cataldo, Mark Andrea
2007-01-01
This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.
Stable harmonic maps from complete manifolds
International Nuclear Information System (INIS)
Xin, Y.L.
1986-01-01
By choosing distinguished cross-sections in the second variational formula for harmonic maps from manifolds with not too fast volume growth into certain submanifolds in the Euclidean space some Liouville type theorems have been proved in this article. (author)
Polynomial chaos representation of databases on manifolds
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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.
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
The Hypermultiplet with Heisenberg Isometry in N=2 Global and Local Supersymmetry
Ambrosetti, Nicola; Derendinger, Jean-Pierre; Tziveloglou, Panteleimon
2011-01-01
The string coupling of N=2 supersymmetric compactifications of type II string theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hypermultiplet, that has four real scalars living on a quaternion-Kaehler manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of perturbative isometries, reduces the possible manifolds to a one-parameter family that describes the tree-level effective action deformed by the only possible perturbative correction arising at one-loop level. A similar argument can be made at the level of global supersymmetry where the scalar manifold is hyper-Kaehler. In this work, the connection between global and local supersymmetry is explicitly constructed, providing a non-trivial gravity decoupled limit of type II strings already in perturbation theory.
A Generalization of the Goldberg-Sachs theorem and its consequences
Batista, Carlos
2013-07-01
The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds endowed with torsion-free connection compatible with the metric, the treatment includes all signatures as well as complex manifolds. It is shown that when the Weyl tensor is algebraically special severe geometric restrictions are imposed. In particular it is demonstrated that the simple self-dual eigenbivectors of the Weyl tensor generate integrable isotropic planes. Another result obtained here is that if the self-dual part of the Weyl tensor vanishes in a Ricci-flat manifold of (2,2) signature the manifold must be Calabi-Yau or symplectic and admits a solution for the source-free Einstein-Maxwell equations.
Higher-dimensional analogues of Donaldson-Witten theory
International Nuclear Information System (INIS)
Acharya, B.S.; Spence, B.
1997-01-01
We present a Donaldson-Witten-type field theory in eight dimensions on manifolds with Spin(7) holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi-Yau threefolds and manifolds of G 2 holonomy, respectively. We point out that these theories arise by considering supersymmetric Yang-Mills theory defined on such manifolds. The theories are invariant under metric variations preserving the holonomy structure without the need for twisting. This statement is a higher-dimensional analogue of the fact that Donaldson-Witten field theory on hyper-Kaehler 4-manifolds is topological without twisting. Higher-dimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory. (orig.)
The "Parity" Anomaly On An Unorientable Manifold
Witten, Edward
2016-01-01
The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. 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 descript...
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.
Minimal contact triangulations of 3-manifolds
Datta, Basudeb; Kulkarni, Dheeraj
2016-01-01
In this paper, we explore minimal contact triangulations on contact 3-manifolds. We give many explicit examples of contact triangulations that are close to minimal ones. The main results of this article say that on any closed oriented 3-manifold the number of vertices for minimal contact triangulations for overtwisted contact structures grows at most linearly with respect to the relative $d^3$ invariant. We conjecture that this bound is optimal. We also discuss, in great details, contact tria...
Layered-triangulations of 3-manifolds
Jaco, William; Rubinstein, J. Hyam
2006-01-01
A family of one-vertex triangulations of 3-manifolds, layered-triangulations, is defined. Layered-triangulations are first described for handlebodies and then extended to all 3-manifolds via Heegaard splittings. A complete and detailed analysis of layered-triangulations is given in the cases of the solid torus and lens spaces, including the classification of all normal and almost normal surfaces in these triangulations. Minimal layered-triangulations of lens spaces provide a common setting fo...
Computer calculation of Witten's 3-manifold invariant
International Nuclear Information System (INIS)
Freed, D.S.; Gompf, R.E.
1991-01-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
Online Manifold Regularization by Dual Ascending Procedure
Sun, Boliang; Li, Guohui; Jia, Li; Zhang, Hui
2013-01-01
We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approache...
The manifold model for space-time
International Nuclear Information System (INIS)
Heller, M.
1981-01-01
Physical processes happen on a space-time arena. It turns out that all contemporary macroscopic physical theories presuppose a common mathematical model for this arena, the so-called manifold model of space-time. The first part of study is an heuristic introduction to the concept of a smooth manifold, starting with the intuitively more clear concepts of a curve and a surface in the Euclidean space. In the second part the definitions of the Csub(infinity) manifold and of certain structures, which arise in a natural way from the manifold concept, are given. The role of the enveloping Euclidean space (i.e. of the Euclidean space appearing in the manifold definition) in these definitions is stressed. The Euclidean character of the enveloping space induces to the manifold local Euclidean (topological and differential) properties. A suggestion is made that replacing the enveloping Euclidean space by a discrete non-Euclidean space would be a correct way towards the quantization of space-time. (author)
Right-angled polyhedra and hyperbolic 3-manifolds
Vesnin, A. Yu.
2017-04-01
Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. Bibliography: 89 titles.
On Riemannian manifolds (Mn, g) of quasi-constant curvature
International Nuclear Information System (INIS)
Rahman, M.S.
1995-07-01
A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs
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Metzger, St
2005-12-15
This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G{sub 2}-manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G{sub 2}-manifold is known. Here we construct families of metrics on compact weak G{sub 2}-manifolds, which contain two conical singularities. Weak G{sub 2}-manifolds have properties that are similar to the ones of proper G{sub 2}-manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E{sub 8} x E{sub 8}-heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the
New complete noncompact Spin(7) manifolds
International Nuclear Information System (INIS)
Cvetic, M.; Gibbons, G.W.; Lue, H.; Pope, C.N.
2002-01-01
We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by (A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S 4 . Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S 4 , our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L 2 -normalisable harmonic 4-form for the (A)) 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L 2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 - similar to B 8
Moduli stabilization in type IIB orientifolds
International Nuclear Information System (INIS)
Schulgin, W.
2007-01-01
This thesis deals with the stabilization of the moduli fields in the compactifications of the type IIB string theory on orientifolds. A concrete procedure for the construction of solutions, in which all moduli fields are fixed, yields the KKLT scenario. We study, on which models the scenario can be applied, if approximations of the original KKLT work are abandoned. We find that in a series of models, namely such without complex-structure moduli the construction of the consistent solutions in the framework of the KKLT scenario is not possible. The nonperturbative effects, like D3 instantons and gaugino condensates are a further component of the KKLT scenario. They lead to the stabilization of the Kaehler moduli. We present criteria for the generation of the superpotential due to the D3 instantons at a Calaby-Yau manifold in presence of fluxes. Furthermore we show that although the presence of the nonperturbative superpotential in the equations of motions is correlated with the switching on of all ISD and IASD fluxes, the deciding criterium for the generation of the nonperturbative superpotential depends only on the fluxes of the type (2,1). Thereafter we discuss two models, in which we stabilize all moduli fields. Thereby it deals with Calabi-Yau orientifolds which have been obtained by a blow-up procedure from the Z 6-II and Z 2 x Z 4 orientifolds
Higher-Derivative Supergravity and Moduli Stabilization
Energy Technology Data Exchange (ETDEWEB)
Ciupke, David; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Louis, Jan [Hamburg Univ. (Germany). Fachberich Physik; Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik
2015-05-15
We review the ghost-free four-derivative terms for chiral superfields in N=1 supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar potential. We discuss the different solutions and argue that only one of them is consistent with the principles of effective field theory. Special attention is paid to the corrections along flat directions which can be stabilized or destabilized by the higher-derivative terms. We then compute these higher-derivative terms explicitly for the type IIB string compactified on a Calabi-Yau orientifold with fluxes via Kaluza-Klein reducing the (α'){sup 3}R{sup 4} corrections in ten dimensions for the respective N=1 Kaehler moduli sector. We prove that together with flux and the known (α'){sup 3}-corrections the higher-derivative term stabilizes all Calabi-Yau manifolds with positive Euler number, provided the sign of the new correction is negative.
Brane brick models in the mirror
Energy Technology Data Exchange (ETDEWEB)
Franco, Sebastián [Physics Department, The City College of the CUNY,160 Convent Avenue, New York, NY 10031 (United States); The Graduate School and University Center, The City University of New York,365 Fifth Avenue, New York NY 10016 (United States); Lee, Sangmin [Center for Theoretical Physics, Seoul National University,Seoul 08826 (Korea, Republic of); Department of Physics and Astronomy, Seoul National University,Seoul 08826 (Korea, Republic of); College of Liberal Studies, Seoul National University,Seoul 08826 (Korea, Republic of); Seong, Rak-Kyeong [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of); Vafa, Cumrun [Jefferson Physical Laboratory, Harvard University,Cambridge, MA 02138 (United States)
2017-02-21
Brane brick models are Type IIA brane configurations that encode the 2dN=(0,2) gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect. We also explain how 2d(0,2) triality is realized in terms of geometric transitions in the mirror geometry. Mirror symmetry leads to a geometric unification of dualities in different dimensions, where the order of duality is n−1 for a Calabi-Yau n-fold. This makes us conjecture the existence of a quadrality symmetry in 0d. Finally, we comment on how the M-theory lift of brane brick models connects to the classification of 2d(0,2) theories in terms of 4-manifolds.
Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
Cvetic, Mirjam; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-01-01
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required ...
Online Manifold Regularization by Dual Ascending Procedure
Directory of Open Access Journals (Sweden)
Boliang Sun
2013-01-01
Full Text Available We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approaches. An important conclusion is that our online MR algorithms can handle the settings where the target hypothesis is not fixed but drifts with the sequence of examples. We also recap and draw connections to earlier works. This paper paves a way to the design and analysis of online manifold regularization algorithms.
Harmonic maps of finite energy for Finsler manifolds
Li, Jintang; Wang, Yiling
2018-03-01
In this paper, we study some properties of harmonic maps for Finsler manifolds. Some Liouville theorems on harmonic maps for Finsler manifolds are given. Let M be a complete simply connected Riemannian manifold with non-negative Ricci curvature and M bar be a complete Berwald manifold with non-positive flag curvature. The main purpose of this paper is to prove that there exists no non-degenerate harmonic map ϕ from M to M bar with ∫SM e(ϕ) dVSM < ∞, which generalizes the result of Schoen and Yau (1976) from Riemannian manifolds to Berwald manifolds.
7D supersymmetric Yang-Mills on curved manifolds
Polydorou, Konstantina; Rocén, Andreas; Zabzine, Maxim
2017-12-01
We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms of a cohomological complex. In principle this cohomological complex makes sense for any K-contact manifold. For the case of toric Sasaki-Einstein manifolds we derive explicitly the perturbative part of the partition function and speculate about the non-perturbative part. We also briefly discuss the case of 3-Sasaki manifolds and suggest a plausible form for the full non-perturbative answer.
Approaching Moons from Resonance via Invariant Manifolds
Anderson, Rodney L.
2012-01-01
In this work, the approach phase from the final resonance of the endgame scenario in a tour design is examined within the context of invariant manifolds. Previous analyses have typically solved this problem either by using numerical techniques or by computing a catalog of suitable trajectories. The invariant manifolds of a selected set of libration orbits and unstable resonant orbits are computed here to serve as guides for desirable approach trajectories. The analysis focuses on designing an approach phase that may be tied into the final resonance in the endgame sequence while also targeting desired conditions at the moon.
Unraveling flow patterns through nonlinear manifold learning.
Tauro, Flavia; Grimaldi, Salvatore; Porfiri, Maurizio
2014-01-01
From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap) to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.
Effective Field Theory on Manifolds with Boundary
Albert, Benjamin I.
In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Matrix regularization of embedded 4-manifolds
International Nuclear Information System (INIS)
Trzetrzelewski, Maciej
2012-01-01
We consider products of two 2-manifolds such as S 2 ×S 2 , embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N 2 ×N 2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S 3 also possible).
String theory flux vacua on twisted tori and generalized complex geometry
International Nuclear Information System (INIS)
Andriot, David
2010-01-01
This thesis is devoted to the study of flux vacua of string theory, with the ten-dimensional space-time split into a four-dimensional maximally symmetric space-time, and a six-dimensional internal manifold M, taken to be a solv-manifold (twisted torus). Such vacua are of particular interest when trying to relate string theory to supersymmetric (SUSY) extensions of the standard model of particles, or to cosmological models. For SUSY solutions of type II supergravities, allowing for fluxes on M helps to solve the moduli problem. Then, a broader class of manifolds than just the Calabi-Yau can be considered for M, and a general characterization is given in terms of Generalized Complex Geometry: M has to be a Generalized Calabi-Yau (GCY). A subclass of solv-manifolds have been proven to be GCY, so we look for solutions with such M. To do so, we use an algorithmic resolution method. Then we focus on specific new solutions: those admitting an intermediate SU(2) structure. A transformation named the twist is then discussed. It relates solutions on torus to solutions on solv-manifolds. Working out constraints on the twist to generate solutions, we can relate known solutions, and find a new one. We also use the twist to relate flux vacua of heterotic string. Finally we consider ten-dimensional de Sitter solutions. Looking for such solutions is difficult, because of several problems among which the breaking of SUSY. We propose an Ansatz for SUSY breaking sources which helps to overcome these difficulties. We give an explicit solution on a solv-manifold, and discuss partially its four-dimensional stability. (author)
Language loss and language processing : three generations of Dutch migrants in New Zealand
Hulsen, Madeleine Elisabeth Helena
2000-01-01
This dissertation investigates the relationship between language shift, language loss, and language processing. Three generations of Dutch immigrants to New Zealand were tested to investigate intra- and intergenerational patterns of language use, social networks, perceived ethnolinguistic vitality,
Sevinc, Yesim
2016-01-01
Drawing on questionnaire and interview data, this study explores the process of language maintenance and shift across three generations of Turkish immigrants in the Netherlands. It compares three generations of Turkish-Dutch bilinguals by examining age and place of language learning, self-rated language proficiency, and language choices in six domains (home, school, work, friends, media and leisure time activities, and cognitive activities). Furthermore, it investigates bilinguals’ experience...
Toric geometry of G2-manifolds
DEFF Research Database (Denmark)
Madsen, Thomas Bruun; Swann, Andrew Francis
We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz...
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.
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 ...
Cohomology theories on locally conformal symplectic manifolds
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van; Vanžura, Jiří
2015-01-01
Roč. 19, č. 1 (2015), s. 45-82 ISSN 1093-6106 Institutional support: RVO:67985840 Keywords : locally conformal symplectic manifold * Lichnerowicz-Novikov cohomology * primitive cohomology Subject RIV: BA - General Mathematics Impact factor: 0.722, year: 2015 http://www.intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0019/0001/a003/
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 Koch curve as a smooth manifold
International Nuclear Information System (INIS)
Epstein, Marcelo; Sniatycki, Jedrzej
2008-01-01
We show that there exists a homeomorphism between the closed interval [0,1] is contained in R and the Koch curve endowed with the subset topology of R 2 . We use this homeomorphism to endow the Koch curve with the structure of a smooth manifold with boundary
Indian Academy of Sciences (India)
M ISCAN and A A SALIMOV. Faculty of Arts and Science, Department of Mathematics, Ataturk University, ... This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of ..... function f , then we shall call f a holomorphic (analytic) function and g its associated function [17]. If such a function ...
Classification of framed links in 3-manifolds
Indian Academy of Sciences (India)
Classification of framed links in 3-manifolds. MATIJA CENCELJ, DUŠAN REPOVŠ and. MIKHAIL B SKOPENKOV. ∗. Institute for Mathematics, Physics and Mechanics and Faculty of Education, University of Ljubljana, P.O. Box 2964, 1001 Ljubljana, Slovenia. ∗Department of Differential Geometry, Faculty of Mechanics and ...
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Robbins, Daniel
2015-01-01
In this talk we report on recent progress in describing compactifications of string theory and M-theory on G 2 and Spin(7) manifolds. We include the infinite set of α’-corrections and describe the entire tower of massless and massive Kaluza–Klein modes resulting from such compactifications. (invited comment)
Nonsmoothable involutions on spin 4-manifolds
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 121, No. 1, February 2011, pp. 37–44. c Indian Academy of Sciences. Nonsmoothable involutions on spin 4-manifolds. CHANGTAO XUE and ... A group action is said to be pseudofree if each nontrivial group element has a discrete ... For our application, we also need their equivariant handle construction.
Higher order Hessian structures on manifolds
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
the bundle of bases for the tangent spaces. When we take a connection ∇XY to be given by Koszul's definition, we see that Hessian structures and symmetric connections can be directly related to each other. Before proceeding further, we state certain results relating to higher order derivatives on manifolds. For m ∈ M, let F.
Conservative systems with ports on contact manifolds
Eberard, D.; Maschke, B.M.; van der Schaft, Arjan; Piztek, P.
In this paper we propose an extension of port Hamiltonian systems, called conservative systems with ports, which encompass systems arising from the Irreversible Thermodynamics. Firstly we lift a port Hamiltonian system from its state space manifold to the thermodynamic phase space to a contact
Some functional inequalities on non-reversible Finsler manifolds
Indian Academy of Sciences (India)
SHIN-ICHI OHTA
2017-11-13
0043, Japan ... The aim of this article is to put forward geometric analysis on possibly non-reversible. Finsler manifolds (in the sense of F(−v) ..... weighted Riemannian manifolds and has many geometric and analytic applications.
International Nuclear Information System (INIS)
Hecht, Michael
2011-01-01
This thesis addresses two different topics within the field of string theory. In the first part it is shown how Hodge-theoretic methods in conjunction with open string mirror symmetry can be used to compute non-perturbative effective superpotential couplings for type II/F-theory compactifications with D-branes and fluxes on compact Calabi-Yau manifolds. This is achieved by studying the at structure of operators which derives from the open/closed Β-model geometry. We analyze the variation of mixed Hodge structure of the relative cohomology induced by a family of divisors, which is wrapped by a D7-brane. This leads to a Picard-Fuchs system of differential operators, which can be used to compute the moduli dependence of the superpotential couplings as well as the mirror maps at various points in the open/closed deformation space. These techniques are used to obtain predictions for genuine A-model Ooguri-Vafa invariants of special Lagrangian submanifolds in compact Calabi-Yau geometries and real enumerative invariants of on-shell domain wall tensions. By an open/closed duality the system of differential equations can also be obtained from a gauged linear σ-model, which describes a non-compact Calabi-Yau four-fold compactification without branes. This is used in the examples of multi-parameter models to study the various phases of the combined open/closed deformation space. It is furthermore shown how the brane geometry can be related to a F-theory compactification on a compact Calabi-Yau four-fold, where the Hodge-theoretic techniques can be used to compute the G-flux induced Gukov-Vafa-Witten potential. The dual F-theory picture also allows to conjecture the form of the Kaehler potential on the full open/closed deformation space. In the second part we analyze the background dependence of theories which derive from multiple wrapped M5-branes. Using the Kontsevich-Soibelman wall-crossing formula and the theory of mock modular forms we derive a holomorphic anomaly
Energy Technology Data Exchange (ETDEWEB)
Hecht, Michael
2011-10-20
This thesis addresses two different topics within the field of string theory. In the first part it is shown how Hodge-theoretic methods in conjunction with open string mirror symmetry can be used to compute non-perturbative effective superpotential couplings for type II/F-theory compactifications with D-branes and fluxes on compact Calabi-Yau manifolds. This is achieved by studying the at structure of operators which derives from the open/closed {beta}-model geometry. We analyze the variation of mixed Hodge structure of the relative cohomology induced by a family of divisors, which is wrapped by a D7-brane. This leads to a Picard-Fuchs system of differential operators, which can be used to compute the moduli dependence of the superpotential couplings as well as the mirror maps at various points in the open/closed deformation space. These techniques are used to obtain predictions for genuine A-model Ooguri-Vafa invariants of special Lagrangian submanifolds in compact Calabi-Yau geometries and real enumerative invariants of on-shell domain wall tensions. By an open/closed duality the system of differential equations can also be obtained from a gauged linear {sigma}-model, which describes a non-compact Calabi-Yau four-fold compactification without branes. This is used in the examples of multi-parameter models to study the various phases of the combined open/closed deformation space. It is furthermore shown how the brane geometry can be related to a F-theory compactification on a compact Calabi-Yau four-fold, where the Hodge-theoretic techniques can be used to compute the G-flux induced Gukov-Vafa-Witten potential. The dual F-theory picture also allows to conjecture the form of the Kaehler potential on the full open/closed deformation space. In the second part we analyze the background dependence of theories which derive from multiple wrapped M5-branes. Using the Kontsevich-Soibelman wall-crossing formula and the theory of mock modular forms we derive a holomorphic
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 ...
Some theorems on a class of harmonic manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Chen Weihuan.
1993-08-01
A class of harmonic n-manifold, denoted by HM n , is, in fact, focussed on a Riemannian manifold with harmonic curvature. A variety of results, with properties, on HM n is presented in a fair order. Harmonic manifolds are then touched upon manifolds with recurrent Ricci curvature, biRicci-recurrent curvature and recurrent conformal curvature, and, in consequence, a sequence of theorems are deduced. (author). 21 refs
Fluid manifold design for a solar energy storage tank
Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.
1975-01-01
A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.
Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds
Martínez-Torres, David; Miranda, Eva
2018-01-01
We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.
Hyperbolic manifolds as vacuum solutions in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Volovich, I.V.
1985-08-01
The relevance of compact hyperbolic manifolds in the context of Kaluza-Klein theories is discussed. Examples of spontaneous compactification on hyperbolic manifolds including d dimensional (d>=8) Einstein-Yang-Mills gravity and 11-dimensional supergravity are considered. Some mathematical facts about hyperbolic manifolds essential for the physical content of the theory are briefly summarized. Non-linear σ-models based on hyperbolic manifolds are discussed. (author)
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
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.
Three-dimensional group manifold reductions of gravity
Linares, Román
2005-04-01
We review the three-dimensional group manifold reductions of pure Einstein gravity and we exhibit a new consistent group manifold reduction of gravity when the compactification group manifold is S3. The new reduction leads to a lower dimensional theory whose gauge group is SU(2).
Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds
Indian Academy of Sciences (India)
We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...
Classification of third-order symmetric Lorentzian manifolds
Galaev, Anton S.
2014-01-01
Third-order symmetric Lorentzian manifolds, i.e. Lorentzian manifold with zero third derivative of the curvature tensor, are classified. These manifolds are exhausted by a special type of pp-waves, they generalize Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.
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.
Topological quantum field theory and four manifolds
Marino, Marcos
2005-01-01
The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the ...
Heterogeneous massive feature fusion on grassmannian manifold
Huang, Haichao; Liu, Hongning; Kong, Xiaoyun; Lou, Xingdan; Wang, Zepeng
2017-08-01
Two issues remain unsolved on utilizing multimodal features for pattern recognition: the missing features and the curse of dimensionality. In this paper, we address the two issues by fusing the multimodal features on the Grassmann manifold. By defining grouping constrains on multimodal features, each multimodal feature vector is grouped into a set of subspaces, and is further represented as a point on the Grassmann manifold. To deal with missing features, L2-Hausdorff distance, a metric to compare multimodal feature vectors with different number of subspaces, is computed, and a kernel matrix can be obtained accordingly. Based on the kernel matrix, two feature selection criterions, one supervised and one unsupervised, are proposed to obtain a few representative features in the kernel space. Thus, the curse of dimensionality is alleviated. Experimental results on three multimodal dataset show the proposed feature fusion can outperforms the state-of -the-art by higher accuracy.
Incremental nonlinear dimensionality reduction by manifold learning.
Law, Martin H C; Jain, Anil K
2006-03-01
Understanding the structure of multidimensional patterns, especially in unsupervised cases, is of fundamental importance in data mining, pattern recognition, and machine learning. Several algorithms have been proposed to analyze the structure of high-dimensional data based on the notion of manifold learning. These algorithms have been used to extract the intrinsic characteristics of different types of high-dimensional data by performing nonlinear dimensionality reduction. Most of these algorithms operate in a "batch" mode and cannot be efficiently applied when data are collected sequentially. In this paper, we describe an incremental version of ISOMAP, one of the key manifold learning algorithms. Our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low-dimensional representation of the data in an efficient manner.
Echocardiogram enhancement using supervised manifold denoising.
Wu, Hui; Huynh, Toan T; Souvenir, Richard
2015-08-01
This paper presents data-driven methods for echocardiogram enhancement. Existing denoising algorithms typically rely on a single noise model, and do not generalize to the composite noise sources typically found in real-world echocardiograms. Our methods leverage the low-dimensional intrinsic structure of echocardiogram videos. We assume that echocardiogram images are noisy samples from an underlying manifold parametrized by cardiac motion and denoise images via back-projection onto a learned (non-linear) manifold. Our methods incorporate synchronized side information (e.g., electrocardiography), which is often collected alongside the visual data. We evaluate the proposed methods on a synthetic data set and real-world echocardiograms. Quantitative results show improved performance of our methods over recent image despeckling methods and video denoising methods, and a visual analysis of real-world data shows noticeable image enhancement, even in the challenging case of noise due to dropout artifacts. Copyright © 2015 Elsevier B.V. All rights reserved.
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...
Convex nonnegative matrix factorization with manifold regularization.
Hu, Wenjun; Choi, Kup-Sze; Wang, Peiliang; Jiang, Yunliang; Wang, Shitong
2015-03-01
Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
On complete manifolds supporting a weighted Sobolev type inequality
International Nuclear Information System (INIS)
Adriano, Levi; Xia Changyu
2011-01-01
Highlights: → We study manifolds supporting a weighted Sobolev or log-Sobolev inequality. → We investigate manifolds of asymptotically non-negative Ricci curvature. → The constant in the weighted Sobolev inequality on complete manifolds is studied. - Abstract: This paper studies the geometric and topological properties of complete open Riemannian manifolds which support a weighted Sobolev or log-Sobolev inequality. We show that the constant in the weighted Sobolev inequality on a complete open Riemannian manifold should be bigger than or equal to the optimal one on the Euclidean space of the same dimension and that a complete open manifold of asymptotically non-negative Ricci curvature supporting a weighted Sobolev inequality must have large volume growth. We also show that a complete manifold of non-negative Ricci curvature on which the log-Sobolev inequality holds is not very far from the Euclidean space.
On complete manifolds supporting a weighted Sobolev type inequality
Energy Technology Data Exchange (ETDEWEB)
Adriano, Levi, E-mail: levi@mat.ufg.br [Instituto de Matematica e Estatistica, Universidade Federal de Goias, 74001-900 Goiania, GO (Brazil); Xia Changyu, E-mail: xia@mat.unb.br [Departamento de Matematica, Universidade de Brasilia, 70910-900 Brasilia, DF (Brazil)
2011-11-15
Highlights: > We study manifolds supporting a weighted Sobolev or log-Sobolev inequality. > We investigate manifolds of asymptotically non-negative Ricci curvature. > The constant in the weighted Sobolev inequality on complete manifolds is studied. - Abstract: This paper studies the geometric and topological properties of complete open Riemannian manifolds which support a weighted Sobolev or log-Sobolev inequality. We show that the constant in the weighted Sobolev inequality on a complete open Riemannian manifold should be bigger than or equal to the optimal one on the Euclidean space of the same dimension and that a complete open manifold of asymptotically non-negative Ricci curvature supporting a weighted Sobolev inequality must have large volume growth. We also show that a complete manifold of non-negative Ricci curvature on which the log-Sobolev inequality holds is not very far from the Euclidean space.
Numerical Hermitian Yang-Mills connections and Kähler cone substructure
Anderson, Lara B.; Braun, Volker; Ovrut, Burt A.
2012-01-01
We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kähler cone substructure on manifolds with h 1;1 > 1. Since the computation depends only on a one-dimensional ray in the Kähler moduli space, it can probe slope-stability regardless of the size of h 1;1. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kähler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, a rapid computational check is proposed for probing the slope-stable stability properties of a given vector bundle.
Toric Sasaki-Einstein metrics on S2xS3
International Nuclear Information System (INIS)
Martelli, Dario; Sparks, James
2005-01-01
We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski-Demianski metrics one obtains a family of local toric Kahler-Einstein metrics. These can be used to construct local Sasaki-Einstein metrics in five dimensions which are generalisations of the Y p,q manifolds. In fact, we find that these metrics are diffeomorphic to those recently found by Cvetic, Lu, Page and Pope. We argue that the corresponding family of smooth Sasaki-Einstein manifolds all have topology S 2 xS 3 . We conclude by setting up the equations describing the warped version of the Calabi-Yau cones, supporting (2,1) three-form flux
Homological mirror symmetry and tropical geometry
Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia
2014-01-01
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...
Supersymmetry breaking and α'-corrections to flux induced potentials
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Haack, Michael; Louis, Jan
2002-01-01
We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant.We show that in the context of type-IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources α'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that α'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications. (author)
Nonsmoothable involutions on spin 4-manifolds
Indian Academy of Sciences (India)
[2] Bryan J, Seiberg-Witten theory and Z/2p actions on spin 4-manifolds, Math. Res. Lett. 5. (1998) 165–183. [3] Chen W and Kwasik S, Symmetries and exotic smooth structures on a K3 surface,. J. Topology 1(4) (2008) 923–962. [4] Edmonds A L and Ewing J H, Realizing forms and fixed point data in dimension four,.
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
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.
The geometry and physics of Abelian gauge groups in F-theory
Energy Technology Data Exchange (ETDEWEB)
Keitel, Jan
2015-07-14
In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.
Familial mild hyperglycemia associated with a novel ABCC8-V84I mutation within three generations
DEFF Research Database (Denmark)
Gonsorcikova, Lucie; Vaxillaire, Martine; Pruhova, Stepanka
2011-01-01
of the young genes (MODY1-4 and 6), we identified a novel ABCC8 V84I mutation, which segregated with autosomal dominant transmission of mild hyperglycemia within three generations. This mutation that is located in a conserved area of transmembrane domain TMD0 seems to be a rare cause of clinical phenotype...
Stafleu, A.
1994-01-01
In this thesis nutrition attitudes, beliefs, and fat intake in three generations of women are described. The aim of the study was twofold: the development of methods, and to study family resemblance in food habits. Based on literature study and qualitative pilot studies a questionnaire on
Learning Technology through Three Generations of Technology Enhanced Distance Education Pedagogy
Anderson, Terry; Dron, Jon
2012-01-01
This paper updates earlier work in which we defined three generations of distance education pedagogy. We then describe emerging technologies that are most conducive to instructional designs that evolve with each generation. Finally we discuss matching the pedagogies with learning outcomes. (Contains 3 figures.)
Cervantes, Richard C.; Padilla, Amado M.; Napper, Lucy E.; Goldbach, Jeremy T.
2013-01-01
Stress associated with acculturation and minority status among Hispanic youth is understudied. Using survey data from the Hispanic Stress Inventory-Adolescent Version (HSI-A), we examined psychosocial stress across eight domains including family economic stress and acculturation-gap stress in a national sample of three generations (first, second,…
Pope, Stacey; Kirk, David
2014-01-01
The experiences of female sports fans have been largely marginalised in academic research to date and little research has examined the formative sporting experiences of female spectators. This article draws on 51 semi-structured interviews with three generations of female fans of one (men's) professional football club (Leicester City), to consider…
Laplacian embedded regression for scalable manifold regularization.
Chen, Lin; Tsang, Ivor W; Xu, Dong
2012-06-01
Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real
Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds
Weeks, Jeffrey R.
2005-01-01
Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D...
Homotopy classification of contact foliations on open contact manifolds
Indian Academy of Sciences (India)
64
structures on a closed manifold M, then there exists an isotopy ψt, t ∈ I, of M such that ψt : (M,ξ0) → (M,ξt) is isocontact for all t ∈ I. Remark 2.6. Gray's stability theorem is not valid on non-closed manifolds. We shall see an extension of Theorem 2.5 for such manifolds in Theorem 1.1 which is one of the main results.
Some problems of dynamical systems on three dimensional manifolds
International Nuclear Information System (INIS)
Dong Zhenxie.
1985-08-01
It is important to study the dynamical systems on 3-dimensional manifolds, its importance is showing up in its close relation with our life. Because of the complication of topological structure of Dynamical systems on 3-dimensional manifolds, generally speaking, the search for 3-dynamical systems is not easier than 2-dynamical systems. This paper is a summary of the partial result of dynamical systems on 3-dimensional manifolds. (author)
Total Generalized Variation for Manifold-valued Data
Bredies, K.; Holler, M.; Storath, M.; Weinmann, A.
2017-01-01
In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data. We provide an axiomatic approach to formalize reasonable generalizations of TGV to the manifold setting and present two possible concrete instances that fulfill the proposed axioms. We provide well-posedness results and present algorithms for a numerical realization of these generalizations to the manifold setup. Further, we provide experimental results for syntheti...
CT Image Reconstruction in a Low Dimensional Manifold
Cong, Wenxiang; Wang, Ge; Yang, Qingsong; Hsieh, Jiang; Li, Jia; Lai, Rongjie
2017-01-01
Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a low-dimensional manifold model (LDMM) is investigated to characterize the low-dimensional patch manifold structure of natural images, where the manifold dimensionality characterizes structural information of an image. In this paper, we propose a CT image reconstruc...
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 ...
Geometry of manifolds with non-negative sectional curvature
Dearricott, Owen; Kennard, Lee; Searle, Catherine; Weingart, Gregor; Ziller, Wolfgang
2014-01-01
Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area. The lectures cover a wide range of topics such as general isometric group actions, circle actions on positively curved four manifolds, cohomogeneity one actions on Alexandrov spaces, isometric torus actions on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, contact CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. Also included is an introduction to the theory of exterior differential systems.
Variable area manifolds for ring mirror heat exchangers
Eng, Albert; Senterfitt, Donald R.
1988-05-01
A laser ring mirror assembly is disclosed which supports and cools an annular ring mirror of a high powered laser with a cooling manifold which has a coolant flow design which is intended to reduce thermal distortions of the ring mirror by minimizing azimuthal variations in temperature around its circumference. The cooling manifold has complementary pairs of cooling passages each of which conduct coolant in opposite flow directions. The manifold also houses adjusters which vary the depth between the annular ring mirror and each cooling, and which vary the flow area of the cooling passage to produce a control over the cooling characteristics of the cooling manifold.
Totally Contact Umbilical Lightlike Hypersurfaces of Indefinite -Manifolds
Directory of Open Access Journals (Sweden)
Rachna Rani
2013-01-01
Full Text Available We study totally contact umbilical lightlike hypersurfaces of indefinite -manifolds and prove the nonexistence of totally contact umbilical lightlike hypersurface in indefinite -space form.
Vousoura, Eleni; Verdeli, Helen; Warner, Virginia; Wickramaratne, Priya; Baily, Charles David Richard
2011-01-01
Research suggests a link between parental divorce and negative child outcomes; however, the presence of parental depression may confound this relationship. Studies exploring the simultaneous effects of depression and parents’ divorce on the adjustment of their children are scarce and rarely have a longitudinal design. This is the first three-generation study of the relative effects of depression and divorce on offspring psychopathology, based on data from a 25-year longitudinal study with fam...
Lopes, Fábio; Espirito-Santo, Helena; Vicente, Henrique
2013-01-01
Introduction The transmission of perceived parental rearing styles through generations has been proved in several studies, mostly in studies with two generations samples. Objectives/aims The main aim of this study is to investigate the intergenerational transmission of the perception of parental rearing styles in families composed by three generations. Methodology A convenience sample of 143 participants was collected, belonging to a female lineage subsystem, divided in three...
Evidence on the Long Shadow of Poor Mental Health across Three Generations
Johnston, David W.; Schurer, Stefanie; Shields, Michael A.
2011-01-01
Individuals suffering from mental health problems are often severely limited in their social and economic functioning. Mental health problems can develop early in life, are frequently chronic in nature, and have an established hereditary component. The extent to which mental illness runs in families could therefore help explain the widely discussed intergenerational transmission of socioeconomic disadvantage. Using data from three generations contained in the 1970 British Cohort Study, we est...
Energy Technology Data Exchange (ETDEWEB)
McGreevy, John Austen; /Stanford U., Phys. Dept.
2005-07-06
This thesis is a study of D-branes in string compactifications. In this context, D-branes are relevant as an important component of the nonperturbative spectrum, as an incisive probe of these backgrounds, and as a natural stringy tool for localizing gauge interactions. In the first part of the thesis, we discuss half-BPS D-branes in compactifications of type II string theory on Calabi-Yau threefolds. The results we describe for these objects are pertinent both in their role as stringy brane-worlds, and in their role as solitonic objects. In particular, we determine couplings of these branes to the moduli determining the closed-string geometry, both perturbatively and non-perturbatively in the worldsheet expansion. We provide a local model for transitions in moduli space where the BPS spectrum jumps, and discuss the extension of mirror symmetry between Calabi-Yau manifolds to the case when D-branes are present. The next section is an interlude which provides some applications of D-branes to other curved backgrounds of string theory. In particular, we discuss a surprising phenomenon in which fundamental strings moving through background Ramond-Ramond fields dissolve into large spherical D3-branes. This mechanism is used to explain a previously-mysterious fact discovered via the AdS-CFT correspondence. Next, we make a connection between type IIA string vacua of the type discussed in the first section and M-theory compactifications on manifolds of G{sub 2} holonomy. Finally we discuss constructions of string vacua which do not have large radius limits. In the final part of the thesis, we develop techniques for studying the worldsheets of open strings ending on the curved D-branes studied in the first section. More precisely, we formulate a large class of massive two-dimensional gauge theories coupled to boundary matter, which flow in the infrared to the relevant boundary conformal field theories. Along with many other applications, these techniques are used to describe
Geometric Transitions, Topological Strings, and Generalized Complex Geometry
Energy Technology Data Exchange (ETDEWEB)
Chuang, Wu-yen; /SLAC /Stanford U., Phys. Dept.
2007-06-29
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.
Directory of Open Access Journals (Sweden)
Daniele Fabiana Glaeser
2014-06-01
Full Text Available The successive rearing of parasitoids in factitious hosts may affect its biological quality. Trichospilus diatraeae Cherian & Margabandhu, 1942 (Hymenoptera: Eulophidae has been studied for the biological control of sugarcane borer [Diatraea saccharalis (Fabricius, 1794 (Lepidoptera: Crambidae]. This study aimed to evaluate whether the rearing of T. diatraeae for three generations in the factitious host Tenebrio molitor Linnaeus, 1758 (Coleoptera: Tenebrionidae affects its reproductive performance, when subsequently reared in the natural host pupae D. saccharalis. Two groups of T. diatraeae were reared separately for three generations: one in pupae of T. molitor and the other in pupae of D. saccharalis. Subsequently, 20 pupae of D. saccharalis were exposed, for 72 hours, to the parasitism of T. diatraeae females reared earlier in pupae of T. molitor or D. saccharalis. The successive rearing of T. diatraeae in the factitious host did not affect the number of pupae parasitized and the number of pupae in which the emergence of parasitoids occurred in the natural host D. saccharalis, and increased the longevity of females and the sex ratio of T. diatraeae. The progeny, duration of developmental cycle (egg to adult, width of head capsule of males and females and longevity of males of T. diatraeae were similar on both treatments. T. diatraeae can be reared in the factitious host T. molitor for three generations without compromising its reproductive performance, when subsequently reared in the natural host D. saccharalis.
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.
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)PRLTAO0031-900710.1103/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.
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...... }, with the corresponding realization B = (P + G)T, we de¿ne the sectorial projection ¿¿,¿(B) and the residue of this projection. We discuss whether this residue is always zero, through various analyses of the structure of the pro jection. The question is interesting since ¿¿(B, 0) is independent of ¿ exactly when...
Efficient orbit integration by manifold correction methods.
Fukushima, Toshio
2005-12-01
Triggered by a desire to investigate, numerically, the planetary precession through a long-term numerical integration of the solar system, we developed a new formulation of numerical integration of orbital motion named manifold correct on methods. The main trick is to rigorously retain the consistency of physical relations, such as the orbital energy, the orbital angular momentum, or the Laplace integral, of a binary subsystem. This maintenance is done by applying a correction to the integrated variables at each integration step. Typical methods of correction are certain geometric transformations, such as spatial scaling and spatial rotation, which are commonly used in the comparison of reference frames, or mathematically reasonable operations, such as modularization of angle variables into the standard domain [-pi, pi). The form of the manifold correction methods finally evolved are the orbital longitude methods, which enable us to conduct an extremely precise integration of orbital motions. In unperturbed orbits, the integration errors are suppressed at the machine epsilon level for an indefinitely long period. In perturbed cases, on the other hand, the errors initially grow in proportion to the square root of time and then increase more rapidly, the onset of which depends on the type and magnitude of the perturbations. This feature is also realized for highly eccentric orbits by applying the same idea as used in KS-regularization. In particular, the introduction of time elements greatly enhances the performance of numerical integration of KS-regularized orbits, whether the scaling is applied or not.
Manifold-Based Visual Object Counting.
Wang, Yi; Zou, Yuexian; Wang, Wenwu
2018-07-01
Visual object counting (VOC) is an emerging area in computer vision which aims to estimate the number of objects of interest in a given image or video. Recently, object density based estimation method is shown to be promising for object counting as well as rough instance localization. However, the performance of this method tends to degrade when dealing with new objects and scenes. To address this limitation, we propose a manifold-based method for visual object counting (M-VOC), based on the manifold assumption that similar image patches share similar object densities. Firstly, the local geometry of a given image patch is represented linearly by its neighbors using a predefined patch training set, and the object density of this given image patch is reconstructed by preserving the local geometry using locally linear embedding. To improve the characterization of local geometry, additional constraints such as sparsity and non-negativity are also considered via regularization, nonlinear mapping, and kernel trick. Compared with the state-of-the-art VOC methods, our proposed M-VOC methods achieve competitive performance on seven benchmark datasets. Experiments verify that the proposed M-VOC methods have several favorable properties, such as robustness to the variation in the size of training dataset and image resolution, as often encountered in real-world VOC applications.
Three-generation reproduction study with dioctyl sodium sulfosuccinate in rats.
MacKenzie, K; Henwood, S; Foster, G; Akin, F; Davis, R; DeBaecke, P; Sisson, G; McKinney, G
1990-07-01
Groups of 30 male and 30 female rats (F0) were fed diets containing 0, 0.1, 0.5, or 1.0% dioctyl sodium sulfosuccinate (DSS) for 10 and 2 weeks, respectively. The F0 animals were then mated to produce an F1 litter. Groups of 30 male and 30 female F1 animals were fed the same dose levels for at least 10 weeks postweaning, and the breeding program was repeated to produce F2 animals. F3 animals were produced from F2 animals by the same procedure. The study was terminated with the F3 weanlings. Test diets were fed continuously throughout the study. All F0, F1, and F2 adults and F3 weanlings (one/sex/litter) were necropsied and given a macroscopic examination. There were no effects on reproductive function for parental animals of either sex during any of the three generations in this study. At the highest dose level (1.0% DSS), body weights were lower than those of controls during the premating phase for males in all three generations and for F1 and F2 females. Body weights for F1 and F2 males and females in the 0.5% dose group were also low during the premating phase. Pup weights on Lactation Day 0 were significantly lower than those of controls only for the high-dose group during the third generation. However, lower pup weight gains in the mid- and high-dose groups resulted in significantly lower pup weights on Day 21 for all three generations. Perinatal pup survival across three generations ranged from 96 to 100% for the control and treated groups. Pup survival ranged from 95 to 100% for controls, from 98 to 100% for low- and mid-dose groups, and from 91 to 99% for the high-dose group. There were no treatment-related mortality and antemortem or macroscopic observations. In summary, DSS administered in the diet to three successive generations of rats at levels of 0.5 and 1.0% caused a reduction in body weights for parental males in all generations and for F1 and F2 females. Pup weights at the 0.5 and 1.0% dose levels were also lower than those of the control in all
Manifold corrections on spinning compact binaries
International Nuclear Information System (INIS)
Zhong Shuangying; Wu Xin
2010-01-01
This paper deals mainly with a discussion of three new manifold correction methods and three existing ones, which can numerically preserve or correct all integrals in the conservative post-Newtonian Hamiltonian formulation of spinning compact binaries. Two of them are listed here. One is a new momentum-position scaling scheme for complete consistency of both the total energy and the magnitude of the total angular momentum, and the other is the Nacozy's approach with least-squares correction of the four integrals including the total energy and the total angular momentum vector. The post-Newtonian contributions, the spin effects, and the classification of orbits play an important role in the effectiveness of these six manifold corrections. They are all nearly equivalent to correct the integrals at the level of the machine epsilon for the pure Kepler problem. Once the third-order post-Newtonian contributions are added to the pure orbital part, three of these corrections have only minor effects on controlling the errors of these integrals. When the spin effects are also included, the effectiveness of the Nacozy's approach becomes further weakened, and even gets useless for the chaotic case. In all cases tested, the new momentum-position scaling scheme always shows the optimal performance. It requires a little but not much expensive additional computational cost when the spin effects exist and several time-saving techniques are used. As an interesting case, the efficiency of the correction to chaotic eccentric orbits is generally better than one to quasicircular regular orbits. Besides this, the corrected fast Lyapunov indicators and Lyapunov exponents of chaotic eccentric orbits are large as compared with the uncorrected counterparts. The amplification is a true expression of the original dynamical behavior. With the aid of both the manifold correction added to a certain low-order integration algorithm as a fast and high-precision device and the fast Lyapunov
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...
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.
Conformal Vector Fields on Doubly Warped Product Manifolds and Applications
Directory of Open Access Journals (Sweden)
H. K. El-Sayied
2016-01-01
Full Text Available This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.
The quantum equivariant cohomology of toric manifolds through mirror symmetry
Baptista, J. M.
2008-01-01
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.
Flow and Pressure Distribution in Fuel Cell Manifolds
DEFF Research Database (Denmark)
Lebæk, Jesper; Bang, Mads; Kær, Søren Knudsen
2010-01-01
The manifold is an essential part of the fuel cell stack. Evidently, evenly distributed reactants are a prerequisite for an efficient fuel cell stack. In this study, the cathode manifold ability to distribute air to the cells of a 70 cell stack is investigated experimentally. By means of 20...
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.
Variable volume combustor with nested fuel manifold system
McConnaughhay, Johnie Franklin; Keener, Christopher Paul; Johnson, Thomas Edward; Ostebee, Heath Michael
2016-09-13
The present application provides a combustor for use with a gas turbine engine. The combustor may include a number of micro-mixer fuel nozzles, a fuel manifold system in communication with the micro-mixer fuel nozzles to deliver a flow of fuel thereto, and a linear actuator to maneuver the micro-mixer fuel nozzles and the fuel manifold system.
Submanifolds in manifolds with metric mixed 3-structures
Ianus, Stere; Ornea, Liviu; Vilcu, Gabriel Eduard
2010-01-01
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. Particular attention is given to two cases of ambient space: mixed 3-Sasakian and mixed 3-cosymplectic.
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, ...
A new proof of the theorem: Harmonic manifolds with minimal ...
Indian Academy of Sciences (India)
In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem.
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
The structure of some classes of K-contact manifolds
Indian Academy of Sciences (India)
metric manifold satisfying the case (1), (2) and (3) is said to be conformally symmetric. [8], ξ-conformally flat [9] and ϕ-conformally flat [3] respectively. In [8], it is proved that a conformally symmetric K-contact manifold is locally isometric to the unit sphere. In ... derivative of ϕ in the characteristic direction ξ vanishes.
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
We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use...... ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer...... “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...
Contact manifolds, Lagrangian Grassmannians and PDEs
Directory of Open Access Journals (Sweden)
Eshkobilov Olimjon
2018-02-01
Full Text Available In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a Ph.D course given by two of the authors (G. M. and G. M.. As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections.
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
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....
Manifold Adaptive Label Propagation for Face Clustering.
Pei, Xiaobing; Lyu, Zehua; Chen, Changqing; Chen, Chuanbo
2015-08-01
In this paper, a novel label propagation (LP) method is presented, called the manifold adaptive label propagation (MALP) method, which is to extend original LP by integrating sparse representation constraint into regularization framework of LP method. Similar to most LP, first of all, MALP also finds graph edges from given data and gives weights to the graph edges. Our goal is to find graph weights matrix adaptively. The key advantage of our approach is that MALP simultaneously finds graph weights matrix and predicts the label of unlabeled data. This paper also derives efficient algorithm to solve the proposed problem. Extensions of our MALP in kernel space and robust version are presented. The proposed method has been applied to the problem of semi-supervised face clustering using the well-known ORL, Yale, extended YaleB, and PIE datasets. Our experimental evaluations show the effectiveness of our method.
Consistent Pauli reduction on group manifolds
Baguet, A.; Pope, C. N.; Samtleben, H.
2016-01-01
We prove an old conjecture by Duff, Nilsson, Pope and Warner asserting that the NSsbnd NS sector of supergravity (and more general the bosonic string) allows for a consistent Pauli reduction on any d-dimensional group manifold G, keeping the full set of gauge bosons of the G × G isometry group of the bi-invariant metric on G. The main tool of the construction is a particular generalised Scherk-Schwarz reduction ansatz in double field theory which we explicitly construct in terms of the group's Killing vectors. Examples include the consistent reduction from ten dimensions on S3 ×S3 and on similar product spaces. The construction is another example of globally geometric non-toroidal compactifications inducing non-geometric fluxes.
On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
Jockers, Hans; Walcher, Johannes
2009-01-01
We show that certain superpotential and Kahler potential couplings of N=1 supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry. This applies to F-theory on a Calabi-Yau four-fold and three-fold compactifications of type II and heterotic strings with branes. The heterotic case includes a class of bundles on elliptic manifolds constructed by Friedmann, Morgan and Witten. Mirror symmetry of the four-fold computes non-perturbative corrections to mirror symmetry on the three-folds, including D-instanton corrections. We also propose a physical interpretation for the observation by Warner that relates the deformation spaces of certain matrix factorizations and the periods of non-compact 4-folds that are ALE fibrations.
Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
Lerche, Wolfgang
2003-01-01
We review an approach for computing non-perturbative, exact superpotentials for Type II strings compactified on Calabi-Yau manifolds, with extra fluxes and D-branes on top. The method is based on an open string generalization of mirror symmetry, and takes care of the relevant sphere and disk instanton contributions. We formulate a framework based on relative (co)homology that uniformly treats the flux and brane sectors on a similar footing. However, one important difference is that the brane induced potentials are of much larger functional diversity than the flux induced ones, which have a hidden N=2 structure and depend only on the bulk geometry. This lecture is meant for an audience unfamiliar with mirror symmetry
On stability of Kummer surfaces' tangent bundle
International Nuclear Information System (INIS)
Bozhkov, Y.D.
1988-10-01
In this paper we propose an explicit approximation of the Kaehler-Einstein-Calabi-Yau metric on the Kummer surfaces, which are manifolds of type K3. It is constructed by gluing 16 pieces of the Eguchi-Hanson metric and 16 pieces of the Euclidean metric. Two estimates on its curvature are proved. Then we prove an estimate on the first eigenvalue of a covariant differential operator of second order. This enables us to apply Taubes' iteration procedure to obtain that there exists an anti-self-dual connection on the considered Kummer surface. In fact, it is a Hermitian-Einstein connection from which we conclude that Kummer surfaces' co-tangent bundle is stable and therefore their tangent bundle is stable too. (author). 40 refs
Sasakian quiver gauge theories and instantons on cones over lens 5-spaces
Lechtenfeld, Olaf; Popov, Alexander D.; Sperling, Marcus; Szabo, Richard J.
2015-10-01
We consider SU (3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU (3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as Kähler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces.
Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
Hosseini, Seyed Morteza; Mekareeya, Noppadol
2016-08-01
In this paper, we calculate the topological free energy for a number of {N} ≥ 2 Yang-Mills-Chern-Simons-matter theories at large N and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the partition function of the theory on S 2 × S 1 with a topological A-twist along S 2 and can be reduced to a matrix integral by exploiting the localization technique. The theories of our interest are dual to a variety of Calabi-Yau four-fold singularities, including a product of two asymptotically locally Euclidean singularities and the cone over various well-known homogeneous Sasaki-Einstein seven-manifolds, N 0,1,0, V 5,2, and Q 1,1,1. We check that the large N topological free energy can be matched for theories which are related by dualities, including mirror symmetry and SL(2,{Z}) duality.
International Nuclear Information System (INIS)
Tyurin, A N
2000-01-01
The special geometry of calibrated cycles, which is closely related to the mirror symmetry among Calabi-Yau 3-manifolds, is in fact only a specialization of a more general geometry, which may naturally be called slightly deformed algebraic geometry or phase geometry. On the other hand, both of these geometries are parallel to classical gauge theory and its complexification. This article explains this parallelism. Hence the appearance of new invariants in complexified gauge theory is accompanied by the appearance of analogous invariants in the theory of special Lagrangian cycles, whose development is at present much more modest. Algebraic geometry is transformed into special Lagrangian geometry by the geometric Fourier transform (GFT). Roughly speaking, this construction coincides with the well-known 'spectral curve' constructions plus phase geometry
Vertex operator algebras and conformal field theory
International Nuclear Information System (INIS)
Huang, Y.Z.
1992-01-01
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics
Multiple dark matter scenarios from ubiquitous stringy throats
DEFF Research Database (Denmark)
Chialva, D.; Dev, P.S.B.; Mazumdar, A.
2013-01-01
We discuss the possibility of having multiple Kaluza-Klein dark matter candidates which arise naturally in generic type-IIB string theory compactification scenarios. These dark matter candidates reside in various throats of the Calabi-Yau manifold. In principle, they can come with a varied range......, we find that the mass scales allowed for the Kaluza-Klein dark matter particles in various throats can vary between 0.1 eV and 10 TeV, depending upon the throat geometry. Thus, there could be simultaneously more than one kind of cold (and possibly warm and hot) dark matter components residing...... in the Universe. This multiple dark matter scenario could weaken the bound on a conventional supersymmetric dark matter candidate and could also account for extra relativistic degrees of freedom in our Universe....
Testing R-parity with geometry
Energy Technology Data Exchange (ETDEWEB)
He, Yang-Hui [Department of Mathematics, City University, London,Northampton Square, London EC1V 0HB (United Kingdom); School of Physics, NanKai University,94 Weijin Road, Tianjin, 300071 (China); Merton College, University of Oxford,Merton Street, OX1 4JD (United Kingdom); Jejjala, Vishnu [Mandelstam Institute for Theoretical Physics, NITheP, and School of Physics,University of the Witwatersrand,1 Jan Smuts Avenue, Johannesburg, WITS 2050 (South Africa); Matti, Cyril [Department of Mathematics, City University, London,Northampton Square, London EC1V 0HB (United Kingdom); Mandelstam Institute for Theoretical Physics, NITheP, and School of Physics,University of the Witwatersrand,1 Jan Smuts Avenue, Johannesburg, WITS 2050 (South Africa); Nelson, Brent D. [Department of Physics, Northeastern University,360 Huntington Avenue, Boston, MA 02115 (United States)
2016-03-14
We present a complete classification of the vacuum geometries of all renormalizable superpotentials built from the fields of the electroweak sector of the MSSM. In addition to the Severi and affine Calabi-Yau varieties previously found, new vacuum manifolds are identified; we thereby investigate the geometrical implication of theories which display a manifest matter parity (or R-parity) via the distinction between leptonic and Higgs doublets, and of the lepton number assignment of the right-handed neutrino fields. We find that the traditional R-parity assignments of the MSSM more readily accommodate the neutrino see-saw mechanism with non-trivial geometry than those superpotentials that violate R-parity. However there appears to be no geometrical preference for a fundamental Higgs bilinear in the superpotential, with operators that violate lepton number, such as νHH̄, generating vacuum moduli spaces equivalent to those with a fundamental bilinear.
International Nuclear Information System (INIS)
Schimmrigk, R.
1989-01-01
The vacuum structure of the Heterotic String is investigated. Methods from fleld theory and critical systems are being used to map out part of the moduli space of the (2,2)-configuration space of the Heterotic String. This configuration space breaks up into different Multidimensional spaces, each leading to a different physical particle spectrum. After explicitly constructing parts of the subspace of all (2,2)-vacua corresponding to complete intersection Calabi-Yau manifolds and tensor models of the N = 2 superconformal discrete minimal series, the spectrum of these models is computed and a search for phenomenological viable models is conducted. It turns out that there are only very few such models. In the second part of the thesis the construction of a new threegeneration model is explained and a detailed phenomenological analysis is presented
Asymmetric Gepner models III. B-L lifting
Energy Technology Data Exchange (ETDEWEB)
Gato-Rivera, B. [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); Schellekens, A.N., E-mail: t58@nikhef.n [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); IMAPP, Radboud Universiteit, Nijmegen (Netherlands)
2011-06-21
In the same spirit as heterotic weight lifting, B-L lifting is a way of replacing the superfluous and ubiquitous U(1){sub B-L} with something else with the same modular properties, but different conformal weights and ground state dimensions. This method works in principle for all variants of (2,2) constructions, such as orbifolds, Calabi-Yau manifolds, free bosons and fermions and Gepner models, since it only modifies the universal SO(10)xE{sub 8} part of the CFT. However, it can only yield chiral spectra if the 'internal' sector of the theory provides a simple current of order 5. Here we apply this new method to Gepner models. Including exceptional invariants, 86 of them have the required order 5 simple current, and 69 of these yield chiral spectra. Three family spectra occur abundantly.
Non-extremal instantons and wormholes in string theory
International Nuclear Information System (INIS)
Bergshoeff, E.; Collinucci, A.; Gran, U.; Roest, D.; Vandoren, S.
2005-01-01
We construct the most general non-extremal spherically symmetric instanton solution of a gravity-dilaton-axion system with SL(2,R) symmetry, for arbitrary euclidean spacetime dimension D≥3. A subclass of these solutions describe completely regular wormhole geometries, whose size is determined by an invariant combination of the SL(2,R) charges. Our results can be applied to four-dimensional effective actions of type II strings compactified on a Calabi-Yau manifold, and in particular to the universal hypermultiplet coupled to gravity. We show that these models contain regular wormhole solutions, supported by regular dilaton and RR scalar fields of the universal hypermultiplet. (Abstract Copyright [2005], Wiley Periodicals, Inc.)
Creutzfeldt-Jakob disease segregating in a three generation Danish family.
Holm, I E; Abelskov, K; Bojsen-Møller, M; Nielsen, A L; Jørgensen, A L
2001-03-01
A three generation family is presented in which rapidly progressive, early-onset Creutzfeldt-Jakob disease without typical EEG changes segregates as an autosomal dominant disease. An aspartic acid to asparagine mutation at codon 178 of the prion gene, PRNP, co-segregates with the disease. As expected, the disease allele also carries the valine codon of the polymorphic valine/methionine codon 129 of the gene. In family members homozygous for this valine codon the disease was more rapidly progressive than in a heterozygous family member, who had a variant clinical phenotype. Definite neuropathological diagnosis required prion staining with specific antibodies.
Geometric transitions and integrable systems
Diaconescu, D.-E.; Dijkgraaf, R.H.; Donagi, R.; Hofman, C.; Pantev, T.
2006-01-01
We consider B-model large N duality for a new class of noncompact Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a Calabi-Yau threefold. The closed string side of the transition is governed at genus zero by an A(1) Hitchin integrable system on a genus g Riemann surface Sigma.
Hu, Yichun; Zhuo, Qin; Gong, Zhaolong; Piao, Jianhua; Yang, Xiaoguang
2017-01-01
In the present work, we evaluated the three generation reproductive toxicity of the genetically modified rice with insectresistant cry1Ac and sck genes. 120 Sprague-Dawley (SD) rats were divided into three groups which were fed with genetically modified rice diet (GM group), parental control rice diet (PR group) and AIN-93 control diet (both used as negative control) respectively. Bodyweight, food consumption, reproductive data, hematological parameters, serum chemistry, relative organ weights and histopathology for each generation were examined respectively. All the hematology and serum chemistry parameters, organ/body weight indicators were within the normal range or no change to the adverse direction was observed, although several differences in hematology and serum chemistry parameters (WBC, BUN, LDH of male rat, PLT, PCT, MPV of female rats), reproductive data (rate of morphologically abnormal sperm) were observed between GM rice group and two control groups. No macroscopic or histological adverse effects were found or considered as treatment-related, either. Overall, the three generation study of genetically modified rice with cry1Ac and sck genes at a high level showed no unintended adverse effects on rats's reproductive system. Copyright © 2016. Published by Elsevier Ltd.
Solar and atmospheric neutrinos in three generations with a magnetic moment
International Nuclear Information System (INIS)
Pulido, J.; Tao, Z.
1995-01-01
A solution to the solar and atomospheric neutrino problems in three generations in the joint context of matter oscillations and the magnetic moment is investigated. An appropriate rotation of the evolution Hamiltonian reduces the three generation case to a two generation one. A convenient background for such a scenario with small neutrino masses and large magnetic moments is given by the Zee-type models, in which the mass generation mechanism leads to a pair of separate orders of magnitude for the mass square differences between neutrino species. We obtain a ratio var-epsilon congruent 10 -2 --10 -3 between these orders of magnitude, so that one of them [(0.3--3)x10 -2 eV 2 ] is suitable for the atmospheric neutrino solution and the other (∼10 -5 eV 2 ) for the solar neutrino solution. The magnetic moment leads to a decrease of the survival probability with solar neutrino energy. Such a decrease is consistent with the experimental situation
Directory of Open Access Journals (Sweden)
Isabelle Roskam
2013-07-01
Full Text Available "Why do parents parent the way they do?" is a very important question. The aim of the current research is to study whether and to what extent the way parents have been parented influences the way they parent. Original data were collected from 48 families across three generations. Grandparents, parents and young adults were asked to report on how they had been parented, how they themselves had parented in the case of the grandparents' and parents' generations, or how they were planning to parent in the case of young adults without children. We tested the hypothesis of a "childrearing tradition" across three generations of respondents in a cross-sectional study with a non-clinical sample. Some arguments in favour of continuities have been found, in particular for supportive rather than for controlling parenting. The results hence suggest that reports on parenting behaviour correlate from one generation to the next and even across two non-consecutive generations. The similarities that have been displayed result from the influence of the parenting individuals have received on the way they themselves parent. Our results also suggest that such an influence may be higher for childrearing attitudes such as warmth that have consistently been regarded as desirable, than for those that have been regarded as more controversial in society, such as harsh discipline.
Grassmann manifolds and the Grassmann image of submanifolds
Borisenko, A. A.; Nikolaevskii, Yu A.
1991-04-01
CONTENTS I. Introduction II. Topology of Grassmann manifolds 1. Local coordinates 2. The cell decomposition and basic topological characteristics 3. Plücker coordinates III. Riemannian geometry of Grassmann manifolds: geometric approach 1. The metric and angles between planes 2. Curvature tensor, sectional curvature, closed geodesics, the limit set 3. More about Plücker embeddings 4. G+(2,n) as a Kähler manifold IV. Grassmann manifolds as symmetric spaces 1. The structure of a symmetric space 2. Totally geodesic and totally umbilical submanifolds 3. Standard embeddings of Grassmann manifolds in Euclidean space 4. Generalization of Grassmann manifolds V. Grassmann image. Intrinsic geometry 1. Induced metric. Homothety 2. Volume of the Grassmann image 3. Grassmann image of minimal surfaces 4. Harmonicity of the Grassmann map VI. Extrinsic geometry of the Grassmann image 1. Curvature of a Grassmann manifold along the Grassmann image of a surface 2. Reconstruction of a surface from the Grassmann image 3. Second fundamental form of the Grassmann image. Surfaces with totally geodesic and totally umbilical Grassmann image VII. Notes References
Introduction to global analysis minimal surfaces in riemannian manifolds
Moore, John Douglas
2017-01-01
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...
Introduction to global analysis minimal surfaces in Riemannian manifolds
Moore, John Douglas
2017-01-01
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...
Directory of Open Access Journals (Sweden)
Badaruddoza
2015-09-01
Full Text Available The current study focused to determine significant cardiovascular risk factors through principal component factor analysis (PCFA among three generations on 1827 individuals in three generations including 911 males (378 from offspring, 439 from parental and 94 from grand-parental generations and 916 females (261 from offspring, 515 from parental and 140 from grandparental generations. The study performed PCFA with orthogonal rotation to reduce 12 inter-correlated variables into groups of independent factors. The factors have been identified as 2 for male grandparents, 3 for male offspring, female parents and female grandparents each, 4 for male parents and 5 for female offspring. This data reduction method identified these factors that explained 72%, 84%, 79%, 69%, 70% and 73% for male and female offspring, male and female parents and male and female grandparents respectively, of the variations in original quantitative traits. The factor 1 accounting for the largest portion of variations was strongly loaded with factors related to obesity (body mass index (BMI, waist circumference (WC, waist to hip ratio (WHR, and thickness of skinfolds among all generations with both sexes, which has been known to be an independent predictor for cardiovascular morbidity and mortality. The second largest components, factor 2 and factor 3 for almost all generations reflected traits of blood pressure phenotypes loaded, however, in male offspring generation it was observed that factor 2 was loaded with blood pressure phenotypes as well as obesity. This study not only confirmed but also extended prior work by developing a cumulative risk scale from factor scores. Till today, such a cumulative and extensive scale has not been used in any Indian studies with individuals of three generations. These findings and study highlight the importance of global approach for assessing the risk and need for studies that elucidate how these different cardiovascular risk factors
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...... 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...
Geometric transitions, flops and non-Kahler manifolds: I
International Nuclear Information System (INIS)
Becker, Melanie; Dasgupta, Keshav; Knauf, Anke; Tatar, Radu
2004-01-01
We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G2 manifolds that are circle fibrations over non-Kahler manifolds is presented
Scientific data interpolation with low dimensional manifold model
International Nuclear Information System (INIS)
Zhu, Wei; Wang, Bao; Barnard, Richard C.; Hauck, Cory D.
2017-01-01
Here, 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.
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.
Directory of Open Access Journals (Sweden)
Ledimo Ophillia
2015-06-01
Full Text Available Despite several reviews of generational differences across cohorts regarding their career stages in organizations, relatively few empirical investigations have been conducted to understand cohorts’ perceptions. Hence, there is paucity of studies that explored differences on the construct organizational justice across generational cohorts. The objective of this study was to explore the differences across three generational cohorts (Millennials, Generation X, and Baby Boomers on dimensions of the organizational justice measurement instrument (OJMI. Data was collected through the administration of OJMI to a random sample size of organizational employees (n = 289. Descriptive statistics and analysis of variance were conducted to interpret the data. These findings provide evidence that differences do exist across cohorts on dimensions of organizational justice. In terms of contributions and practical implications, insight gained from the findings may be used in proposing organizational development interventions to manage multigenerational employees as well as to conduct future research.
Sterile neutrino in a minimal three-generation see-saw model
Indian Academy of Sciences (India)
Sterile neutrino in a minimal three-generation see-saw model. Table 1. Relevant right-handed fermion and scalar fields and their transformation properties. Here we have defined Y. I3R· (B–L)/2. SU´2µL ¢U´1µI3R ¢U´1µB L. SU´2µL ¢UY ´1µ. Le ·Lµ Lτ. Seµ. 2R ν R. (1,1/2, 1). (1,0). 1. 1 ν·R. (1,1/2, 1). (1,0). 1. 1. ντR. (1, 1/2, 1).
Solution path for manifold regularized semisupervised classification.
Wang, Gang; Wang, Fei; Chen, Tao; Yeung, Dit-Yan; Lochovsky, Frederick H
2012-04-01
Traditional learning algorithms use only labeled data for training. However, labeled examples are often difficult or time consuming to obtain since they require substantial human labeling efforts. On the other hand, unlabeled data are often relatively easy to collect. Semisupervised learning addresses this problem by using large quantities of unlabeled data with labeled data to build better learning algorithms. In this paper, we use the manifold regularization approach to formulate the semisupervised learning problem where a regularization framework which balances a tradeoff between loss and penalty is established. We investigate different implementations of the loss function and identify the methods which have the least computational expense. The regularization hyperparameter, which determines the balance between loss and penalty, is crucial to model selection. Accordingly, we derive an algorithm that can fit the entire path of solutions for every value of the hyperparameter. Its computational complexity after preprocessing is quadratic only in the number of labeled examples rather than the total number of labeled and unlabeled examples.
Quantization of a symplectic manifold associated to a manifold with projective structure
International Nuclear Information System (INIS)
Biswas, Indranil
2009-01-01
Let X be a complex manifold equipped with a projective structure P. There is a holomorphic principal C*-bundle L P ' over X associated with P. We show that the holomorphic cotangent bundle of the total space of L P ' equipped with the Liouville symplectic form has a canonical deformation quantization. This generalizes the construction in the work of and Ben-Zvi and Biswas [''A quantization on Riemann surfaces with projective structure,'' Lett. Math. Phys. 54, 73 (2000)] done under the assumption that dim C X=1.
Spatial context driven manifold learning for hyperspectral image classification
CSIR Research Space (South Africa)
Zhang, Y
2014-06-01
Full Text Available Department of Electrical and Computer Engineering, University of Houston. 2 Meraka Institute, Council for Scientific and Industrial Research, South Africa. 3 School of Civil Engineering, Purdue University, US. Abstract Manifold learning techniques have...
Manifold learning based feature extraction for classification of hyperspectral data
CSIR Research Space (South Africa)
Lunga, D
2014-01-01
Full Text Available of Electrical and Computer Engineering, University of Houston. 3. Schools of Civil Engineering and Electrical and Computer Engineering, Purdue University. Interest in manifold learning for representing the topology of large, high dimensional nonlinear data sets...
46 CFR 153.285 - Valving for cargo pump manifolds.
2010-10-01
... SHIPS CARRYING BULK LIQUID, LIQUEFIED GAS, OR COMPRESSED GAS HAZARDOUS MATERIALS Design and Equipment Piping Systems and Cargo Handling Equipment § 153.285 Valving for cargo pump manifolds. (a) When cargo...
Supervised learning for neural manifold using spatiotemporal brain activity.
Kuo, Po-Chih; Chen, Yong-Sheng; Chen, Li-Fen
2015-12-01
Determining the means by which perceived stimuli are compactly represented in the human brain is a difficult task. This study aimed to develop techniques for the construction of the neural manifold as a representation of visual stimuli. We propose a supervised locally linear embedding method to construct the embedded manifold from brain activity, taking into account similarities between corresponding stimuli. In our experiments, photographic portraits were used as visual stimuli and brain activity was calculated from magnetoencephalographic data using a source localization method. The results of 10 × 10-fold cross-validation revealed a strong correlation between manifolds of brain activity and the orientation of faces in the presented images, suggesting that high-level information related to image content can be revealed in the brain responses represented in the manifold. Our experiments demonstrate that the proposed method is applicable to investigation into the inherent patterns of brain activity.
Some functional inequalities on non-reversible Finsler manifolds
Indian Academy of Sciences (India)
SHIN-ICHI OHTA
2017-11-13
). Finsler manifolds, based on the Bochner inequality established by Ohta and Sturm. Following the approach of the -calculus of Bakry et al (2014), we show the dimensional versions of the Poincaré–Lichnerowicz inequality, ...
Example-driven manifold priors for image deconvolution.
Ni, Jie; Turaga, Pavan; Patel, Vishal M; Chellappa, Rama
2011-11-01
Image restoration methods that exploit prior information about images to be estimated have been extensively studied, typically using the Bayesian framework. In this paper, we consider the role of prior knowledge of the object class in the form of a patch manifold to address the deconvolution problem. Specifically, we incorporate unlabeled image data of the object class, say natural images, in the form of a patch-manifold prior for the object class. The manifold prior is implicitly estimated from the given unlabeled data. We show how the patch-manifold prior effectively exploits the available sample class data for regularizing the deblurring problem. Furthermore, we derive a generalized cross-validation (GCV) function to automatically determine the regularization parameter at each iteration without explicitly knowing the noise variance. Extensive experiments show that this method performs better than many competitive image deconvolution methods.
Manopt, a Matlab toolbox for optimization on manifolds
Boumal, Nicolas; Mishra, Bamdev; Absil, P. -A.; Sepulchre, Rodolphe
2013-01-01
Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design effcient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, in...
Ideal triangulations of 3-manifolds II: taut and angle structures
Kang, Ensil; Rubinstein, J. Hyam
2005-01-01
This is the second in a series of papers in which we investigate ideal triangulations of the interiors of compact 3-manifolds with tori or Klein bottle boundaries. Such triangulations have been used with great effect, following the pioneering work of Thurston. Ideal triangulations are the basis of the computer program SNAPPEA of Weeks and the program SNAP of Coulson, Goodman, Hodgson and Neumann. Casson has also written a program to find hyperbolic structures on such 3-manifolds, by solving T...
Reduction of Nambu-Poisson Manifolds by Regular Distributions
Das, Apurba
2018-03-01
The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.
Integrated high pressure manifold for thermoplastic microfluidic devices
Aghvami, S. Ali; Fraden, Seth
2017-11-01
We introduce an integrated tubing manifold for thermoplastic microfluidic chips that tolerates high pressure. In contrast to easy tubing in PDMS microfluidic devices, tube connection has been challenging for plastic microfluidics. Our integrated manifold connection tolerates 360 psi while conventional PDMS connections fail at 50 psi. Important design considerations are incorporation of a quick-connect, leak-free and high-pressure manifold for the inlets and outlets on the lid and registration marks that allow the precise alignment of the inlets and outlets. In our method, devices are comprised of two molded pieces joined together to create a sealed device. The first piece contains the microfluidic features and the second contains the inlet and outlet manifold, a frame for rigidity and a viewing window. The mold for the lid with integrated manifold is CNC milled from aluminium. A cone shape PDMS component which acts as an O-ring, seals the connection between molded manifold and tubing. The lid piece with integrated inlet and outlets will be a standard piece and can be used for different chips and designs. Sealing the thermoplastic device is accomplished by timed immersion of the lid in a mixture of volatile and non-volatile solvents followed by application of heat and pressure.
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.
Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.
Sun, Shiliang; Xie, Xijiong
2016-09-01
Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.
International Nuclear Information System (INIS)
Bersimbaev, R.I.
2002-01-01
The objectives of this work are as follows: to establish a Blood Bio-sample Database of three generations families living close to the Semipalatinsk test site (STS) and control families in three generation from clean areas; to determine the mini-satellite mutations rates in the three generation of radiation exposed people and control families of the same ethnic origin; to definition the chromosomal translocation frequencies by FISH chromosome painting in the lymphocytes of the exposed and control people in order to determine the radiation exposure. The following criteria for select to examined groups were used: the people from control group should be permanently living at clean area (far from STS or any places where the nuclear tests occur and far from any chemical industrial plants), e.g. they should not been exposed to radiation during their life (including a radiotherapy and cytostatics); the people of both examined groups should be matched regard to structure of families, age, ethnic background, parental age of P 0 and F 1 to the moment children birth, smoking habit, lifestyle and occupation. The maximum of available families by appropriate criteria in villages were chosen. As exposed inhabitation serves residents of following villages: Dolon, Mostik, Bodene, Cheremushki, Kanonerka, Karamyrza (all these villages are situated in Beskargai district). The inhabitants of Dzerzhinsk, Zhanatalap and Ushtobe villages of former Taldy-Kurgan oblast were included for study as a control group. The Bio-sample Bank consists of the frozen EDTA blood (at - 20 deg C), and isolated whole blood DNA (at - 70 deg C), the fixated erythrocytes (at - 70 deg C), isolated lymphocytes (in liquid nitrogen container) and lymphocyte cultures (at - 20 deg C). The Bio-sample Bank is supplement with a computerized database identifying the samples and number of vial stored, and information on individuals studied (all questionnaire data) and family tree. Results from the translocation FISH
Physical activity level of three generation families. Genetic and environmental factors
Directory of Open Access Journals (Sweden)
Raquel Nichele de Chaves
2010-09-01
Full Text Available This study aims (1 to investigate the presence of familial aggregation in physical activity (PA levels and sedentary behavior (SB among members of three generations families and (2 to estimate the magnitude of additive genetic influences on PA and SB phenotypes. The sample consisted of 100 extended families covering three generations (n=1034, from the Lisbon area, Portugal. Phenotypes were assessed via the short version of the self-administered International Physical Activity Questionnaire (IPAQ-SF. Measured phenotypes: total physical activity (TPA; vigorous (VPA; moderate (MPA; walking; time spent in sitting time (ST, watching television (WT and PA levels classification. Body mass index (BMI was calculated. Exploratory family analysis in all phenotypes was conducted in PEDSTATS software. The genetic component (h2 and shared environmental effect were estimated using maximum likelihood implemented in the SOLAR software package. All graphs were done in HLM software. Sex, age, sex*age, age2, sex*age2 and BMI were used as covariates. Significant level was set at 0,05. Genetic component estimates (h2 were as follows: TPA h2=0,28±0,06 (p<0.0001; VPA h2=0,35±0,06 (p<0.0001; MPA h2=0,29±0,06 (p<0.0001; walking h2=0,40±0,06 (p<0.0001; ST h2=0,29±0,06 (p<0.0001; WT h2=0,15±0,06 (p<0.003 and determination of the level physical activity h2=0,35±0,14 (p<0.007. Shared environmental effect was not significant. These results showed a low-to-moderate genetic contribution, between 15% to 40% of the total variability, in the PA and SB phenotypes. The genetic factors have low to moderate influence in this sample. Non-shared environmental factors appear to have the major contribution in these phenotypes.
STAR CLUSTERS, GALAXIES, AND THE FUNDAMENTAL MANIFOLD
International Nuclear Information System (INIS)
Zaritsky, Dennis; Zabludoff, Ann I.; Gonzalez, Anthony H.
2011-01-01
We explore whether global observed properties, specifically half-light radii, mean surface brightness, and integrated stellar kinematics, suffice to unambiguously differentiate galaxies from star clusters, which presumably formed differently and lack dark matter halos. We find that star clusters lie on the galaxy scaling relationship referred to as the fundamental manifold (FM), on the extension of a sequence of compact galaxies, and so conclude that there is no simple way to differentiate star clusters from ultracompact galaxies. By extending the validity of the FM over a larger range of parameter space and a wider set of objects, we demonstrate that the physics that constrains the resulting baryon and dark matter distributions in stellar systems is more general than previously appreciated. The generality of the FM implies (1) that the stellar spatial distribution and kinematics of one type of stellar system do not arise solely from a process particular to that set of systems, such as violent relaxation for elliptical galaxies, but are instead the result of an interplay of all processes responsible for the generic settling of baryons in gravitational potential wells, (2) that the physics of how baryons settle is independent of whether the system is embedded within a dark matter halo, and (3) that peculiar initial conditions at formation or stochastic events during evolution do not ultimately disturb the overall regularity of baryonic settling. We also utilize the relatively simple nature of star clusters to relate deviations from the FM to the age of the stellar population and find that stellar population models systematically and significantly overpredict the mass-to-light ratios of old, metal-rich clusters. We present an empirical calibration of stellar population mass-to-light ratios with age and color. Finally, we use the FM to estimate velocity dispersions for the low surface brightness, outer halo clusters that lack such measurements.
Energy Technology Data Exchange (ETDEWEB)
San Martin Diaz, Jose Ignacio; Aperribay Maiztegui, Victor; San Martin Diaz, Jose Javier [Escuela Universitaria de Ingenieria Tecnica Industrial de Eibar, Guipuzcoa, Pais Vasco (Spain); Zamora Belver, Inmaculada; Eguia Lopez, Pablo [Escuela Tecnica Superior de Ingenieria de Bilbao (Spain)
2010-10-15
The three generation includes production processes and simultaneous use oe electric power, heat and cold from a fuel source providing global high energy efficiency, reduction of emission of gases in the atmosphere, losses of investments, and more reliability in the supply. This paper approaches the use of fuel cells for three generation, and presents different subsystems of generation with the main characteristics and applications. (author)
Genealogy Study of Three Generations of Patients with Bipolar Mood Disorder Type I.
Salehi, Bahman; Khoz, Sara; Sadeghi, Bahman; Amanat, Manouchehr; Salehi, Mona
2017-01-01
The purpose of this research is genealogy examination of three generation of bipolar mood disorder Type I patients. Patients selected using Poisson sampling method from 100 patients with bipolar mood disorder Type I, referring to a psychiatric center of Amir Kabir Hospital of Arak, Iran. Examine issues such as physical ailments, psychological review of living and deceased family members of each patient, drawn family pedigree using pedigree chart, check the relationship of the different pattern of the autosomal dominant and recessive disease, sex-linked dominant and recessive and linked to Y chromosome have been performed on patients. Different methods used in this study are pedigree chart and young mania rating scale and SPSS and Pearson's correlation test for analyzing the data collected. Among the studied inheritance patterns, the most common inheritance pattern was autosomal recessive. There was a significant relationship between age, number of generation, and inheritance patterns with physical ailments in families of patients with bipolar mood disorder ( P 0.05). Furthermore, there was a significant relation between generation and skin, gastrointestinal, ovarian, lung, coronary heart disease, diabetes mellitus, hypertension, Cerebrovascular accident (CVA), hyperlipidemia, cardiomyopathy, hypothyroidism, and kidney disease in patients with bipolar affective disorder Type I ( P generation and some physical disorders in patients with bipolar mood disorder Type I.
Fitness Consequences of Advanced Ancestral Age over Three Generations in Humans.
Directory of Open Access Journals (Sweden)
Adam D Hayward
Full Text Available A rapid rise in age at parenthood in contemporary societies has increased interest in reports of higher prevalence of de novo mutations and health problems in individuals with older fathers, but the fitness consequences of such age effects over several generations remain untested. Here, we use extensive pedigree data on seven pre-industrial Finnish populations to show how the ages of ancestors for up to three generations are associated with fitness traits. Individuals whose fathers, grandfathers and great-grandfathers fathered their lineage on average under age 30 were ~13% more likely to survive to adulthood than those whose ancestors fathered their lineage at over 40 years. In addition, females had a lower probability of marriage if their male ancestors were older. These findings are consistent with an increase of the number of accumulated de novo mutations with male age, suggesting that deleterious mutations acquired from recent ancestors may be a substantial burden to fitness in humans. However, possible non-mutational explanations for the observed associations are also discussed.
Vousoura, Eleni; Verdeli, Helen; Warner, Virginia; Wickramaratne, Priya; Baily, Charles David Richard
2012-10-01
Research suggests a link between parental divorce and negative child outcomes; however, the presence of parental depression may confound this relationship. Studies exploring the simultaneous effects of depression and parents' divorce on the adjustment of their children are scarce and rarely have a longitudinal design. This is the first three-generation study of the relative effects of depression and divorce on offspring psychopathology, based on data from a 25-year longitudinal study with families at high and low risk for depression. One hundred seventy-eight grandchildren (mean age = 13.9 years) of depressed and nondepressed parents and grandparents were evaluated by raters blind to their parents' and grandparents' clinical status. We found that in both low and high-risk children, divorce had a limited impact on child adjustment over and above familial risk for depression. Divorce had a significant effect on child outcomes only among high-risk grandchildren with a depressed grandparent and non-depressed parents, with this group showing a threefold risk for anxiety disorders. Results support previous findings suggesting that familial risk for depression largely overshadows the effect of parental divorce on child psychopathology. Possible reasons for the lack of association between divorce and child psychopathology among low-risk offspring are discussed.
Very large intermediate breaking scale in the Gepner/Schimmrigk three generation model
International Nuclear Information System (INIS)
Wu Jizhi; Arnowitt, Richard
1994-01-01
A detailed study of the intermediate symmetry breaking scale, via the renormalization group equations, for a three generation heterotic string model arising from the N=2 superconformal construction is reported. The numerical study shows that the model admits a very large intermediate breaking scale > or ∼1.0x10 16 GeV. The role of the gauge singlets in this model is studied, and it is found that these fields play a crucial role in determining the directions and the scale of the intermediate symmetry breaking. The importance of the mixing in generation space is also studied. The generation mixing terms are found to have special effects in the intermediate symmetry breaking. Remarkably these terms can produce some new Yukawa couplings (not present at the Planck scale) through loops. These couplings are in general very small compared to the ones with non-vanishing tree level values and thus offer a new mechanism to solve the lepton/quark mass hierarchy problem. ((orig.))
Directory of Open Access Journals (Sweden)
Arturo Ramirez-Miranda
2011-05-01
Full Text Available Background: Congenital microcoria (CMC is due to a maldevelopment of the dilator pupillae muscle of the iris, with a pupil diameter of less than 2 mm. It is associated with juvenile open angle glaucoma and myopia. We report on a three-generation Mexican-Mestizo family with CMC. The eldest member’s iris biopsy proved muscle anomalies. Further, we analyzed novel ultrasound biomicroscopy findings in the family members who did not require surgery. Patients and Methods: A 62-year-old woman, her 41-year-old son and her 9-year-old grandson affected with microcoria since birth, documented by clinical examination and ultrasound biomicroscopy. The eldest member underwent phacoemulsification, and a biopsy of the iris and the anterior capsule of the lens was taken. Results: Ultrasound biomicroscopy confirmed the CMC diagnosis showing iris thinning and a pupil diameter of less than 2 mm. Histopathology of the iris showed a significant reduction of smooth muscle cells, but no alterations of the anterior lens capsule. Discussion: Although CMC is a rare disorder, which is due to a maldevelopment of the dilator pupillae muscle of the iris, it could be associated with juvenile open angle glaucoma and myopia; therefore, precise diagnosis is required. Ultrasound biomicroscopy could be a great option to confirm the disorder.
Zhou, Xing Hua; Dong, Ying; Zhao, Yan Sheng; Xiao, Xiang; Wang, Yun; He, Yuan Qing; Liu, Qiao Quan
2014-12-01
The transgenic rice line (TRS) enriched with amylose and resistant starch (RS) was developed by antisense RNA inhibition of starch-branching enzymes. Cereal starch with high amylose has a great benefit on human health through its resistant starch. In order to evaluate the effect of transgenic rice on rats, the rats were fed diets containing 70% TRS rice flour, its near-isogenic rice flour or the standard diet as the control through three generations. In the present study, clinical performance, reproductive capacity and pathological responses including body weight, food consumption, reproductive data, hematological parameters, serum chemistry components, organ relative weights and histopathology were examined. Some statistically significant differences were observed in rats consuming the high amylose rice diet when compared to rats fed the near-isogenic control rice diet or the conventional (non-rice) standard diet. These differences were generally of small magnitude, appeared to be random in nature, and were within normal limits for the strain of rat used, and were therefore not considered to be biologically meaningful or treatment related. Crown Copyright © 2014. Published by Elsevier Ltd. All rights reserved.
Kobayashi-Maskawa type of hard-CP-violation model with three-generation Majorana neutrinos
International Nuclear Information System (INIS)
Cheng, H.
1986-01-01
Within the framework of the Kobayashi-Maskawa (KM) type of hard CP-violation model with three-generation Majorana neutrinos, we point out that on-shell CP-violation phenomena (i.e., CP-violating effects taking place in on-shell processes), which are characteristic of Majorana neutrinos, can only occur in total-lepton-number-conserving reactions, and are unobservably small. Off-shell CP-nonconserving effects which arise from gauge bosons are undetectable, but those which are mediated by Higgs bosons could be seen in certain rare decays. It is emphasized that CP-odd effects intrinsic to Majorana behavior depend not only on the two CP-violating Majorana phases but also on the KM phase. We then demonstrate why the KM model, which has rich implications in the hadronic sector, leads to no observable CP-violating effects in leptonic processes (except in neutrino oscillations) directly related to the CP-odd KM phase
The world problem: on the computability of the topology of 4-manifolds
vanMeter, J. R.
2005-01-01
Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.
Wilson loops, instantons and quantum mechanics
International Nuclear Information System (INIS)
Schiereck, Marc
2014-05-01
In this thesis we examine two different problems. The first is the computation of vacuum expectation values of Wilson loop operators in ABJM theory, the other problem is finding the instanton series of the refined topological string on certain local Calabi-Yau geometries in the Nekrasov-Shatashvili limit. Based on the description of ABJM theory as a matrix model, it is possible to find a description of it in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. The vacuum-expectation-values of Wilson loop operators in ABJM theory correspond to averages of operators in the statistical-mechanical problem. Using the WKB expansion, it is possible to extract the full 1/N expansion of the vevs, up to exponentially small contributions, for arbitrary Chern-Simons coupling. We compute these vevs for the 1/6 and 1/2 BPS Wilson loops at any winding number. These can be written in terms of the Airy function. The expressions we found reproduce the low genus results previously obtained in the 't Hooft expansion. In another problem we use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies, given in terms of an instanton sum, in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum geometry here is to be understood as a quantum deformed version of rigid special geometry, which has its origin in the quantum mechanical behavior of branes in the topological string B-model. We argue that in the Seiberg-Witten picture only the Coulomb parameters lead to quantum corrections, while the mass parameters remain uncorrected. In certain cases we also compute the expansion of the free energies at the orbifold point and the conifold locus. We compute the quantum corrections order by order on ℎ by deriving second order differential operators, which act on the classical periods.
Aspects of NT ≥ 2 topological gauge theories and D-branes
International Nuclear Information System (INIS)
Blau, M.; Thompson, G.
1996-12-01
Recently, topological field theories with extended N T > 1 topological symmetries have appeared in various contexts, e.g. in the discussion of S-duality in supersymmetry gauge theories, as world volume theories of Dirichlet p-branes in string theory, and in a general discussion of 'balanced' or critical topological theories. Here we will comment on, explain, or expand on various aspects of these theories, thus complementing the already existing discussions of such models in the literature. We comment on various aspects of topological gauge theories possessing N T ≥ 2 topological symmetry: 1. We show that the construction of Vafa-Witten and Dijkgraaf-Moore of 'balanced' topological field theories is equivalent to an earlier construction in terms of N T = 2 superfields inspired by supersymmetric quantum mechanics. 2. We explain the relation between topological field theories calculating signed and unsigned sums of Euler numbers of moduli spaces. 3. We show that the topological twist of N = 4 d = 4 Yang-Mills theory recently constructed by Marcus is formally a deformation of four-dimensional super-BF theory. 4. We construct a novel N T = 2 topological twist of N = 4 d = 3 Yang-Mills theory, a 'mirror' of the Casson invariant model, with certain unusual features (e.g. no bosonic scalar field and hence no underlying equivariant cohomology). 5. We give a complete classification of the topological twists of N = 8 d = 3 Yang-Mills theory and show that they are realized as world-volume theories of Dirichlet two-brane instantons wrapping supersymmetric three-cycles of Calabi-Yau three-folds and G 2 -holonomy Joyce manifolds. 6. We describe the topological gauge theories associated to D-string instantons on holomorphic curves in K3s and Calabi-Yau 3-folds. 48 refs
Directory of Open Access Journals (Sweden)
Long Cui
Full Text Available We present the genetic analyses conducted on a three-generation family (14 individuals with three members affected with isolated-Hirschsprung disease (HSCR and one with HSCR and heterochromia iridum (syndromic-HSCR, a phenotype reminiscent of Waardenburg-Shah syndrome (WS4. WS4 is characterized by pigmentary abnormalities of the skin, eyes and/or hair, sensorineural deafness and HSCR. None of the members had sensorineural deafness. The family was screened for copy number variations (CNVs using Illumina-HumanOmni2.5-Beadchip and for coding sequence mutations in WS4 genes (EDN3, EDNRB, or SOX10 and in the main HSCR gene (RET. Confocal microscopy and immunoblotting were used to assess the functional impact of the mutations. A heterozygous A/G transition in EDNRB was identified in 4 affected and 3 unaffected individuals. While in EDNRB isoforms 1 and 2 (cellular receptor the transition results in the abolishment of translation initiation (M1V, in isoform 3 (only in the cytosol the replacement occurs at Met91 (M91V and is predicted benign. Another heterozygous transition (c.-248G/A; -predicted to affect translation efficiency- in the 5'-untranslated region of EDN3 (EDNRB ligand was detected in all affected individuals but not in healthy carriers of the EDNRB mutation. Also, a de novo CNVs encompassing DACH1 was identified in the patient with heterochromia iridum and HSCR Since the EDNRB and EDN3 variants only coexist in affected individuals, HSCR could be due to the joint effect of mutations in genes of the same pathway. Iris heterochromia could be due to an independent genetic event and would account for the additional phenotype within the family.
Lessons Learned From Developing Three Generations of Remote Sensing Science Data Processing Systems
Tilmes, Curt; Fleig, Albert J.
2005-01-01
The Biospheric Information Systems Branch at NASA s Goddard Space Flight Center has developed three generations of Science Investigator-led Processing Systems for use with various remote sensing instruments. The first system is used for data from the MODIS instruments flown on NASA s Earth Observing Systems @OS) Terra and Aqua Spacecraft launched in 1999 and 2002 respectively. The second generation is for the Ozone Measuring Instrument flying on the EOS Aura spacecraft launched in 2004. We are now developing a third generation of the system for evaluation science data processing for the Ozone Mapping and Profiler Suite (OMPS) to be flown by the NPOESS Preparatory Project (NPP) in 2006. The initial system was based on large scale proprietary hardware, operating and database systems. The current OMI system and the OMPS system being developed are based on commodity hardware, the LINUX Operating System and on PostgreSQL, an Open Source RDBMS. The new system distributes its data archive across multiple server hosts and processes jobs on multiple processor boxes. We have created several instances of this system, including one for operational processing, one for testing and reprocessing and one for applications development and scientific analysis. Prior to receiving the first data from OMI we applied the system to reprocessing information from the Solar Backscatter Ultraviolet (SBUV) and Total Ozone Mapping Spectrometer (TOMS) instruments flown from 1978 until now. The system was able to process 25 years (108,000 orbits) of data and produce 800,000 files (400 GiB) of level 2 and level 3 products in less than a week. We will describe the lessons we have learned and tradeoffs between system design, hardware, operating systems, operational staffing, user support and operational procedures. During each generational phase, the system has become more generic and reusable. While the system is not currently shrink wrapped we believe it is to the point where it could be readily
Cui, Long; Wong, Emily Hoi-Man; Cheng, Guo; Firmato de Almeida, Manoel; So, Man-Ting; Sham, Pak-Chung; Cherny, Stacey S; Tam, Paul Kwong-Hang; Garcia-Barceló, Maria-Mercè
2013-01-01
We present the genetic analyses conducted on a three-generation family (14 individuals) with three members affected with isolated-Hirschsprung disease (HSCR) and one with HSCR and heterochromia iridum (syndromic-HSCR), a phenotype reminiscent of Waardenburg-Shah syndrome (WS4). WS4 is characterized by pigmentary abnormalities of the skin, eyes and/or hair, sensorineural deafness and HSCR. None of the members had sensorineural deafness. The family was screened for copy number variations (CNVs) using Illumina-HumanOmni2.5-Beadchip and for coding sequence mutations in WS4 genes (EDN3, EDNRB, or SOX10) and in the main HSCR gene (RET). Confocal microscopy and immunoblotting were used to assess the functional impact of the mutations. A heterozygous A/G transition in EDNRB was identified in 4 affected and 3 unaffected individuals. While in EDNRB isoforms 1 and 2 (cellular receptor) the transition results in the abolishment of translation initiation (M1V), in isoform 3 (only in the cytosol) the replacement occurs at Met91 (M91V) and is predicted benign. Another heterozygous transition (c.-248G/A; -predicted to affect translation efficiency-) in the 5'-untranslated region of EDN3 (EDNRB ligand) was detected in all affected individuals but not in healthy carriers of the EDNRB mutation. Also, a de novo CNVs encompassing DACH1 was identified in the patient with heterochromia iridum and HSCR Since the EDNRB and EDN3 variants only coexist in affected individuals, HSCR could be due to the joint effect of mutations in genes of the same pathway. Iris heterochromia could be due to an independent genetic event and would account for the additional phenotype within the family.
Algebras and manifolds: Differential, difference, simplicial and quantum
International Nuclear Information System (INIS)
Finkelstein, D.; Rodriguez, E.
1986-01-01
Generalized manifolds and Clifford algebras depict the world at levels of resolution ranging from the classical macroscopic to the quantum microscopic. The coarsest picture is a differential manifold and algebra (dm), direct integral of familiar local Clifford algebras of spin operators in curved time-space. Next is a finite difference manifold (Δm) of Regge calculus. This is a subalgebra of the third, a Minkowskian simplicial manifold (Σm). The most detailed description is the quantum manifold (Qm), whose algebra is the free Clifford algebra S of quantum set theory. We surmise that each Σm is a classical 'condensation' of a Qm. Quantum simplices have both integer and half-integer spins in their spectrum. A quantum set theory of nature requires a series of reductions leading from the Qm and a world descriptor W up through the intermediate Σm and Δm to a dm and an action principle. What may be a new algebraic language for topology, classical or quantum, is a by-product of the work. (orig.)
Hierarchical discriminant manifold learning for dimensionality reduction and image classification
Chen, Weihai; Zhao, Changchen; Ding, Kai; Wu, Xingming; Chen, Peter C. Y.
2015-09-01
In the field of image classification, it has been a trend that in order to deliver a reliable classification performance, the feature extraction model becomes increasingly more complicated, leading to a high dimensionality of image representations. This, in turn, demands greater computation resources for image classification. Thus, it is desirable to apply dimensionality reduction (DR) methods for image classification. It is necessary to apply DR methods to relieve the computational burden as well as to improve the classification accuracy. However, traditional DR methods are not compatible with modern feature extraction methods. A framework that combines manifold learning based DR and feature extraction in a deeper way for image classification is proposed. A multiscale cell representation is extracted from the spatial pyramid to satisfy the locality constraints for a manifold learning method. A spectral weighted mean filtering is proposed to eliminate noise in the feature space. A hierarchical discriminant manifold learning is proposed which incorporates both category label and image scale information to guide the DR process. Finally, the image representation is generated by concatenating dimensionality reduced cell representations from the same image. Extensive experiments are conducted to test the proposed algorithm on both scene and object recognition datasets in comparison with several well-established and state-of-the-art methods with respect to classification precision and computational time. The results verify the effectiveness of incorporating manifold learning in the feature extraction procedure and imply that the multiscale cell representations may be distributed on a manifold.
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.
Enhanced manifold regularization for semi-supervised classification.
Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong
2016-06-01
Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.
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.
Differential forms and the Wodzicki residue for manifolds with boundary
Wang, Yong
2006-05-01
In [A. Connes, Quantized calculus and applications, XIth International Congress of Mathematical Physics (Paris,1994), 15-36, Internat Press, Cambridge, MA, 1995], Connes found a conformal invariant using Wodzicki's 1-density and computed it in the case of 4-dimensional manifold without boundary. In [W. J. Ugalde, Differential forms and the Wodzicki residue, arXiv: Math, DG/0211361], Ugalde generalized the Connes' result to n-dimensional manifold without boundary. In this paper, we generalize the results of [A. Connes, Quantized calculus and applications, XIth International Congress of Mathematical Physics (Paris,1994), 15-36, Internat Press, Cambridge, MA, 1995] and [W. J. Ugalde, Differential forms and the Wodzicki residue, arXiv: Math, DG/0211361] to the case of manifolds with boundary.
Rigidity of complete noncompact bach-flat n-manifolds
Chu, Yawei; Feng, Pinghua
2012-11-01
Let (Mn,g) be a complete noncompact Bach-flat n-manifold with the positive Yamabe constant and constant scalar curvature. Assume that the L2-norm of the trace-free Riemannian curvature tensor R∘m is finite. In this paper, we prove that (Mn,g) is a constant curvature space if the L-norm of R∘m is sufficiently small. Moreover, we get a gap theorem for (Mn,g) with positive scalar curvature. This can be viewed as a generalization of our earlier results of 4-dimensional Bach-flat manifolds with constant scalar curvature R≥0 [Y.W. Chu, A rigidity theorem for complete noncompact Bach-flat manifolds, J. Geom. Phys. 61 (2011) 516-521]. Furthermore, when n>9, we derive a rigidity result for R<0.
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.
Spherical formulation for diagrammatic evaluations on a manifold with boundary
Tsoupros, G
2002-01-01
The mathematical formalism necessary for the diagrammatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of quantum corrections to the effective action past one-loop necessitates diagrammatic techniques. Diagrammatic evaluations and higher loop-order renormalization can be best accomplished on a Riemannian manifold of constant curvature accommodating a boundary of constant extrinsic curvature. In such a context, the stated evaluations can be accomplished through a consistent interpretation of the Feynman rules within the spherical formulation of the theory which the method of images allows. To this effect, the mathematical consequences of such an interpretation are analysed and the spherical formulation of the Feynman rules on the bounded manifold is, as a result, developed.
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.
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...
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.
Unimodularity criteria for Poisson structures on foliated manifolds
Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury
2018-03-01
We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.
Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds
Directory of Open Access Journals (Sweden)
Nülifer ÖZDEMİR
2017-02-01
Full Text Available It is known that there exist canonical and nearly parallel $G_2$ structures on 7-dimensional 3-Sasakian manifolds. In this paper, we investigate the existence of $G_2$ structures which are neither canonical nor nearly parallel. We obtain eight new $G_2$ structures on 7-dimensional 3-Sasakian manifolds which are of general type according to the classification of $G_2$ structures by Fernandez and Gray. Then by deforming the metric determined by the $G_2$ structure, we give integrable $G_2$ structures. On a manifold with integrable $G_2$ structure, there exists a uniquely determined metric covariant derivative with anti-symetric torsion. We write torsion tensors corresponding to metric covariant derivatives with skew-symmetric torsion. In addition, we investigate some properties of torsion tensors.
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.
Postoperative 3D spine reconstruction by navigating partitioning manifolds
International Nuclear Information System (INIS)
Kadoury, Samuel; Labelle, Hubert; Parent, Stefan
2016-01-01
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
Spectral invariants of operators of Dirac type on partitioned manifolds
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Bleecker, D.
2004-01-01
We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators of Dirac type on closed manifolds and manifolds...... with boundary. We emphasize various (occasionally overlooked) aspects of rigorous definitions and explain the quite different stability properties. Moreover, we utilize the heat equation approach in various settings and show how these topological and spectral invariants are mutually related in the study...
Gauge groups and topological invariants of vacuum manifolds
International Nuclear Information System (INIS)
Golo, V.L.; Monastyrsky, M.I.
1978-01-01
The paper is concerned with topological properties of the vacuum manifolds in the theories with the broken gauge symmetry for the groups of the type SO(k) x U(n), SO(k) x SO(p) x U(r). For the Ginsburg-Landau theory of the superfluid 3 He the gauge transformations are discussed. They provide the means to indicate all possible types of the vacuum manifolds, which are likely to correspond to distinct phases of the superfluid 3 He. Conditions on the existence of the minimums of the Ginsburg-Landau functional are discussed
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....
Distributed mean curvature on a discrete manifold for Regge calculus
International Nuclear Information System (INIS)
Conboye, Rory; Miller, Warner A; Ray, Shannon
2015-01-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)
Spontaneous compactification and Ricci-flat manifolds with torsion
International Nuclear Information System (INIS)
McInnes, B.
1985-06-01
The Freund-Rubin mechanism is based on the equation Rsub(ik)=lambdagsub(ik) (where lambda>0), which, via Myers' Theorem, implies ''spontaneous'' compactification. The difficulties connected with the cosmological constant in this approach can be resolved if torsion is introduced and lambda set equal to zero, but then compactification ''by hand'' is necessary, since the equation Rsub(ik)=0 can be satisfied both on compact and on non-compact manifolds. In this paper we discuss the global geometry of Ricci-flat manifolds with torsion, and suggest ways of restoring the ''spontaneity'' of the compactification. (author)
Rotation vectors for homeomorphisms of non-positively curved manifolds
International Nuclear Information System (INIS)
Lessa, Pablo
2011-01-01
Rotation vectors, as defined for homeomorphisms of the torus that are isotopic to the identity, are generalized to such homeomorphisms of any complete Riemannian manifold with non-positive sectional curvature. These generalized rotation vectors are shown to exist for almost every orbit of such a dynamical system with respect to any invariant measure with compact support. The concept is then extended to flows and, as an application, it is shown how non-null rotation vectors can be used to construct a measurable semi-conjugacy between a given flow and the geodesic flow of a manifold
Silke, Wiegand-Grefe; Möller, Birgit
2012-01-01
The paper presents some reflections on the transgenerational transmission of traumatic experiences of war and in particular bombing during Second World War. These theoretical considerations are based on a case study (family interview) deriving from the research project "Kriegskindheit im Hamburger Feuersturm" additionally illustrated and complemented with impressions based on interviews with three generations in context of the project.
DEFF Research Database (Denmark)
Larsen, Christian Grønhøj; Gyldenløve, Mette; Jønch, Aia Elise
2015-01-01
Idiopathic facial palsy (IFP), also known as Bell's palsy, is a common neurologic disorder, but recurrent and familial forms are rare. This case series presents a three-generation family with idiopathic facial palsy. The mode of inheritance of IFP has previously been suggested as autosomal dominant...
Nonparametric Bayes Classification and Hypothesis Testing on Manifolds
Bhattacharya, Abhishek; Dunson, David
2012-01-01
Our first focus is prediction of a categorical response variable using features that lie on a general manifold. For example, the manifold may correspond to the surface of a hypersphere. We propose a general kernel mixture model for the joint distribution of the response and predictors, with the kernel expressed in product form and dependence induced through the unknown mixing measure. We provide simple sufficient conditions for large support and weak and strong posterior consistency in estimating both the joint distribution of the response and predictors and the conditional distribution of the response. Focusing on a Dirichlet process prior for the mixing measure, these conditions hold using von Mises-Fisher kernels when the manifold is the unit hypersphere. In this case, Bayesian methods are developed for efficient posterior computation using slice sampling. Next we develop Bayesian nonparametric methods for testing whether there is a difference in distributions between groups of observations on the manifold having unknown densities. We prove consistency of the Bayes factor and develop efficient computational methods for its calculation. The proposed classification and testing methods are evaluated using simulation examples and applied to spherical data applications. PMID:22754028
Riemannian multi-manifold modeling and clustering in brain networks
Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.
2017-08-01
This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.
Sampling from Determinantal Point Processes for Scalable Manifold Learning.
Wachinger, Christian; Golland, Polina
2015-01-01
High computational costs of manifold learning prohibit its application for large datasets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire dataset with the Nyström method. The two main challenges that arise are: (i) the landmarks selected in non-Euclidean geometries must result in a low reconstruction error, (ii) the graph constructed from sparsely sampled landmarks must approximate the manifold well. We propose to sample the landmarks from determinantal distributions on non-Euclidean spaces. Since current determinantal sampling algorithms have the same complexity as those for manifold learning, we present an efficient approximation with linear complexity. Further, we recover the local geometry after the sparsification by assigning each landmark a local covariance matrix, estimated from the original point set. The resulting neighborhood selection .based on the Bhattacharyya distance improves the embedding of sparsely sampled manifolds. Our experiments show a significant performance improvement compared to state-of-the-art landmark selection techniques on synthetic and medical data.
Holomorphic two-spheres in complex Grassmann manifold
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 118; Issue 3. Holomorphic Two-Spheres in Complex Grassmann Manifold (2, 4). Xiaowei Xu ... Author Affiliations. Xiaowei Xu1 Xiaoxiang Jiao1. School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China ...
Sparse discriminant manifold projections for bearing fault diagnosis
Chen, Gang; Liu, Fenglin; Huang, Wei
2017-07-01
The monitored vibration signal of bearing is usually nonlinear and nonstationary, and may be corrupted by background noise. Thus, it is very difficult to accurately extract sensitive and reliable characteristics information from the vibration signal to diagnose bearing health conditions. This paper proposes a novel bearing fault diagnosis method based on sparse discriminant manifold projections (SDMP). The SDMP was developed based on sparsity preserving projections, and sparse manifold clustering and embedding. The SDMP can effectively extract the meaningful low-dimensional intrinsic features that hidden in a high-dimensional feature dataset. After dimensionality reduction with the SDMP, the least squares support vector machine (LS-SVM) is utilized to classify the different low-dimensional feature data for fault recognition. The effectiveness and superiorities of the proposed method are demonstrated through several comparative experiments with other three manifold learning methods. The experimental results validate that the SDMP is more effective than the other three manifold learning methods for implementation bearing fault diagnosis, and it is more robust when deal with noise interference signal.
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 s...
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 descri...
Growth of fundamental group for Finsler manifolds with integral Ricci ...
Indian Academy of Sciences (India)
tant to reveal the relationship between the topology and geometry invariants for Finsler manifolds. As for the ... Ricci curvature bound was established and the integral Ricci curvature and topology was studied [13]. .... star-shaped at x ∈ T if for all y ∈ T there exists a minimal geodesic from x to y contained in T . For r > 0, let T ...
Rigid Body Energy Minimization on Manifolds for Molecular Docking.
Mirzaei, Hanieh; Beglov, Dmitri; Paschalidis, Ioannis Ch; Vajda, Sandor; Vakili, Pirooz; Kozakov, Dima
2012-11-13
Virtually all docking methods include some local continuous minimization of an energy/scoring function in order to remove steric clashes and obtain more reliable energy values. In this paper, we describe an efficient rigid-body optimization algorithm that, compared to the most widely used algorithms, converges approximately an order of magnitude faster to conformations with equal or slightly lower energy. The space of rigid body transformations is a nonlinear manifold, namely, a space which locally resembles a Euclidean space. We use a canonical parametrization of the manifold, called the exponential parametrization, to map the Euclidean tangent space of the manifold onto the manifold itself. Thus, we locally transform the rigid body optimization to an optimization over a Euclidean space where basic optimization algorithms are applicable. Compared to commonly used methods, this formulation substantially reduces the dimension of the search space. As a result, it requires far fewer costly function and gradient evaluations and leads to a more efficient algorithm. We have selected the LBFGS quasi-Newton method for local optimization since it uses only gradient information to obtain second order information about the energy function and avoids the far more costly direct Hessian evaluations. Two applications, one in protein-protein docking, and the other in protein-small molecular interactions, as part of macromolecular docking protocols are presented. The code is available to the community under open source license, and with minimal effort can be incorporated into any molecular modeling package.
Analytical and numerical manifolds in a symplectic 4-D map
Delis, N.; Contopoulos, G.
2016-05-01
We study analytically the orbits along the asymptotic manifolds from a complex unstable periodic orbit in a symplectic 4-D Froeschlé map. The orbits are given as convergent series. We compare the analytic results by truncating the series at various orders with the corresponding numerical results and we find agreement along a more extended length, as the order of truncation increases. The agreement is improved when the parameters approach those of the stability domain. Along the manifolds no terms with small divisors appear in the series. The same result is found if we use a parametrization method along the asymptotic curves. In the case of orbits starting close to the manifolds small divisors appear, but the orbits remain close to the manifolds for an extended period of time. If the parameters of the map are close to the stable domain the orbits recede and approach the origin several times and remain confined in a certain volume around the origin for a long time before escaping to large distances. For special sets of parameters we see resonance phenomena and the orbits take particular forms near every resonance.
An algorithmic approach to construct crystallizations of 3-manifolds ...
Indian Academy of Sciences (India)
dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely ..... from the construction of ˜r as in eq. (2.3) and Definition 2.2. D. DEFINITION 2.8. A crystallization ( , γ ) of a 3-manifold is called minimal with respect to the pair (〈S | R〉 ...
Geometry and physics of pseudodifferential operators on manifolds
DEFF Research Database (Denmark)
Esposito, Giampiero; Napolitano, George M.
2015-01-01
A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: existence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic...
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 ...
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.
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 ...
Deformations of coisotropic submanifolds in locally conformal symplectic manifolds
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van; Oh, Y.-G.
2016-01-01
Roč. 20, č. 3 (2016), s. 553-596 ISSN 1093-6106 Institutional support: RVO:67985840 Keywords : locally conformal symplectic manifold * coisotropic submanifold * b-twisted differential * bulk deformation Subject RIV: BA - General Mathematics Impact factor: 0.895, year: 2016 http://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0020/0003/a007/index.html
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
Quantum cohomology of flag manifolds and Toda lattices
International Nuclear Information System (INIS)
Givental, A.; Kim, B.
1995-01-01
We discuss relations of Vafa's quantum cohomology with Floer's homology theory, introduce equivariant quantum cohomology, formulate some conjectures about its general properties and, on the basis of these conjectures, compute quantum cohomology algebras of the flag manifolds. The answer turns out to coincide with the algebra of regular functions on an invariant lagrangian variety of a Toda lattice. (orig.)
Enhancing Low-Rank Subspace Clustering by Manifold Regularization.
Liu, Junmin; Chen, Yijun; Zhang, JiangShe; Xu, Zongben
2014-07-25
Recently, low-rank representation (LRR) method has achieved great success in subspace clustering (SC), which aims to cluster the data points that lie in a union of low-dimensional subspace. Given a set of data points, LRR seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself. However, LRR only considers the global Euclidean structure, while the local manifold structure, which is often important for many real applications, is ignored. In this paper, to exploit the local manifold structure of the data, a manifold regularization characterized by a Laplacian graph has been incorporated into LRR, leading to our proposed Laplacian regularized LRR (LapLRR). An efficient optimization procedure, which is based on alternating direction method of multipliers (ADMM), is developed for LapLRR. Experimental results on synthetic and real data sets are presented to demonstrate that the performance of LRR has been enhanced by using the manifold regularization.
Robust Semi-Supervised Manifold Learning Algorithm for Classification
Directory of Open Access Journals (Sweden)
Mingxia Chen
2018-01-01
Full Text Available In the recent years, manifold learning methods have been widely used in data classification to tackle the curse of dimensionality problem, since they can discover the potential intrinsic low-dimensional structures of the high-dimensional data. Given partially labeled data, the semi-supervised manifold learning algorithms are proposed to predict the labels of the unlabeled points, taking into account label information. However, these semi-supervised manifold learning algorithms are not robust against noisy points, especially when the labeled data contain noise. In this paper, we propose a framework for robust semi-supervised manifold learning (RSSML to address this problem. The noisy levels of the labeled points are firstly predicted, and then a regularization term is constructed to reduce the impact of labeled points containing noise. A new robust semi-supervised optimization model is proposed by adding the regularization term to the traditional semi-supervised optimization model. Numerical experiments are given to show the improvement and efficiency of RSSML on noisy data sets.
Manifold regularization for sparse unmixing of hyperspectral images.
Liu, Junmin; Zhang, Chunxia; Zhang, Jiangshe; Li, Huirong; Gao, Yuelin
2016-01-01
Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression , ignore the intrinsic geometric structure in the hyperspectral data. In this paper, we propose a novel model, called manifold regularized collaborative sparse regression , by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model. Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.
Morphological appearance manifolds for group-wise morphometric analysis.
Lian, Nai-Xiang; Davatzikos, Christos
2011-12-01
Computational anatomy quantifies anatomical shape based on diffeomorphic transformations of a template. However, different templates warping algorithms, regularization parameters, or templates, lead to different representations of the same exact anatomy, raising a uniqueness issue: variations of these parameters are confounding factors as they give rise to non-unique representations. Recently, it has been shown that learning the equivalence class derived from the multitude of representations of a given anatomy can lead to improved and more stable morphological descriptors. Herein, we follow that approach, by approximating this equivalence class of morphological descriptors by a (nonlinear) morphological appearance manifold fitting to the data via a locally linear model. Our approach parallels work in the computer vision field, in which variations lighting, pose and other parameters lead to image appearance manifolds representing the exact same figure in different ways. The proposed framework is then used for group-wise registration and statistical analysis of biomedical images, by employing a minimum variance criterion to perform manifold-constrained optimization, i.e. to traverse each individual's morphological appearance manifold until group variance is minimal. The hypothesis is that this process is likely to reduce aforementioned confounding effects and potentially lead to morphological representations reflecting purely biological variations, instead of variations introduced by modeling assumptions and parameter settings. Copyright © 2011 Elsevier B.V. All rights reserved.
On equations of motion on complex grassman manifold
International Nuclear Information System (INIS)
Berceanu, S.; Gheorghe, A.
1989-02-01
We investigate the equations of motion on the 'classical' phase space which corresponds to quantum state space in the case of the complex Grassmann manifold appearing in the Hartree-Fock problem. First and second degree polynomial Hamiltonians in bifermion operators are considered. The 'classical' motion corresponding to linear Hamiltonians is described by a Matrix Riccati equation.(authors)
The Geometry of Slow Manifolds near a Folded Node
Desroches, M.; Krauskopf, B.; Osinga, H.M.
2008-01-01
This paper is concerned with the geometry of slow manifolds of a dynamical system with one fast and two slow variables. Specifically, we study the dynamics near a folded-node singularity, which is known to give rise to so-called canard solutions. Geometrically, canards are intersection curves of
Invariant Distributionally Scrambled Manifolds for an Annihilation Operator
Directory of Open Access Journals (Sweden)
Xinxing Wu
2014-01-01
Full Text Available This note proves that the annihilation operator of a quantum harmonic oscillator admits an invariant distributionally ε-scrambled linear manifold for any 0<ε<2. This is a positive answer to Question 1 by Wu and Chen (2013.
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...
On some properties of the superposition operator on topological manifolds
Directory of Open Access Journals (Sweden)
Janusz Dronka
2010-01-01
Full Text Available In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
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.
Quantum invariants of knots and 3-manifolds. 2. rev. ed.
International Nuclear Information System (INIS)
Turaev, Vladimir G.
2010-01-01
Due to the strong appeal and wide use of this monograph, it is now available in its second revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. From the contents: - Invariants of graphs in Euclidean 3-space and of closed 3-manifolds - Foundations of topological quantum field theory - Three-dimensional topological quantum field theory - Two-dimensional modular functors - 6j-symbols - Simplicial state sums on 3-manifolds - Shadows of manifolds and state sums on shadows - Constructions of modular categories. (orig.)
Action-angle variables and a KAM theorem for b-Poisson manifolds
Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey
2015-01-01
In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.
30 CFR 250.444 - What are the choke manifold requirements?
2010-07-01
... 30 Mineral Resources 2 2010-07-01 2010-07-01 false What are the choke manifold requirements? 250... Blowout Preventer (bop) System Requirements § 250.444 What are the choke manifold requirements? (a) Your BOP system must include a choke manifold that is suitable for the anticipated surface pressures...
Naturalness of three generations in free fermionic Z2n direct-product Z4 string models
International Nuclear Information System (INIS)
Faraggi, A.E.; Nanopoulos, D.V.
1993-01-01
We study the construction of free fermionic spin structure models with Z 2 n direct-product Z 4 boundary-condition vectors. We argue that requiring chiral space-time fermions in the massless spectrum and the existence of a well-defined hidden gauge group severely constrain the allowed boundary-condition vectors. We show that the minimal way to obtain these requirements is given by a unique set of Z 2 5 boundary-condition vectors. We classify the possible extensions to this basic set. We argue that a result of this fundamental set is that obtaining three generations in this construction is correlated with projecting out all the enhanced gauge symmetries which arise from nonzero vacuum expectation values of background fields. We propose that this correlation and the properties of the fundamental Z 2 5 subset suggest that three generations is natural in this construction
Birkhoff’s theorem in Lovelock gravity for general base manifolds
Ray, Sourya
2015-10-01
We extend the Birkhoff’s theorem in Lovelock gravity for arbitrary base manifolds using an elementary method. In particular, it is shown that any solution of the form of a warped product of a two-dimensional transverse space and an arbitrary base manifold must be static. Moreover, the field equations restrict the base manifold such that all the non-trivial intrinsic Lovelock tensors of the base manifold are constants, which can be chosen arbitrarily, and the metric in the transverse space is determined by a single function of a spacelike coordinate which satisfies an algebraic equation involving the constants characterizing the base manifold along with the coupling constants.
Birdal, Sevcan
2014-01-01
Ankara : The Department of International Relations İhsan Doğramacı Bilkent University, 2014. Thesis (Master's) -- Bilkent University, 2014. Includes bibliographical references leaves 129-142 This thesis focuses on the generations of human rights of women based on Vasak’s notion of three generations of human rights - in which the first generation rights refer political and civil rights; the second generation rights include economic, social and cultural rights while the third ...
Out-of-sample extrapolation of learned manifolds.
Chin, Tat-Jun; Suter, David
2008-09-01
We investigate the problem of extrapolating the embedding of a manifold learned from finite samples to novel out-of-sample data. We concentrate on the manifold learning method called Maximum Variance Unfolding (MVU) for which the extrapolation problem is still largely unsolved. Taking the perspective of MVU learning being equivalent to Kernel PCA, our problem reduces to extending a kernel matrix generated from an unknown kernel function to novel points. Leveraging on previous developments, we propose a novel solution which involves approximating the kernel eigenfunction using Gaussian basis functions. We also show how the width of the Gaussian can be tuned to achieve extrapolation. Experimental results which demonstrate the effectiveness of the proposed approach are also included.
Slow manifold and Hannay angle in the spinning top
Energy Technology Data Exchange (ETDEWEB)
Berry, M V [H H Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Shukla, P [Department of Physics, Indian Institute of Technology, Kharagpur (India)
2011-01-15
The spin of a top can be regarded as a fast variable, coupled to the motion of the axis which is slow. In pure precession, the rotation of the axis round a cone (without nutation), can be considered as the result of a reaction from the fast spin. The resulting restriction of the total state space of the top is an illustrative example, at graduate-student level, of the general dynamical concept of the slow manifold. For this case, the slow manifold can be calculated exactly, and expanded as a series of reaction forces (of magnetic type) in powers of slowness, corresponding to a modified precession frequency. The forces correspond to a series for the Hannay angle for the fast motion, describing the location of a point on the top.
Manifold: a Custom Analytics Platform to Visualize Research Impact
Directory of Open Access Journals (Sweden)
Steven Braun
2015-10-01
Full Text Available The use of research impact metrics and analytics has become an integral component to many aspects of institutional assessment. Many platforms currently exist to provide such analytics, both proprietary and open source; however, the functionality of these systems may not always overlap to serve uniquely specific needs. In this paper, I describe a novel web-based platform, named Manifold, that I built to serve custom research impact assessment needs in the University of Minnesota Medical School. Built on a standard LAMP architecture, Manifold automatically pulls publication data for faculty from Scopus through APIs, calculates impact metrics through automated analytics, and dynamically generates report-like profiles that visualize those metrics. Work on this project has resulted in many lessons learned about challenges to sustainability and scalability in developing a system of such magnitude.
Lattice Dirac fermions on a simplicial Riemannian manifold
Brower, Richard C.; Weinberg, Evan S.; Fleming, George T.; Gasbarro, Andrew D.; Raben, Timothy G.; Tan, Chung-I.
2017-06-01
The lattice Dirac equation is formulated on a simplicial complex which approximates a smooth Riemann manifold by introducing a lattice vierbein on each site and a lattice spin connection on each link. Care is taken so the construction applies to any smooth D-dimensional Riemannian manifold that permits a spin connection. It is tested numerically in 2D for the projective sphere S2 in the limit of an increasingly refined sequence of triangles. The eigenspectrum and eigenvectors are shown to converge rapidly to the exact result in the continuum limit. In addition comparison is made with the continuum Ising conformal field theory on S2. Convergence is tested for the two point, ⟨ɛ (x1)ɛ (x2)⟩, and the four point, ⟨σ (x1)ɛ (x2)ɛ (x3)σ (x4)⟩, correlators for the energy, ɛ (x )=i ψ ¯(x )ψ (x ), and twist operators, σ (x ), respectively.
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.
Multiview vector-valued manifold regularization for multilabel image classification.
Luo, Yong; Tao, Dacheng; Xu, Chang; Xu, Chao; Liu, Hong; Wen, Yonggang
2013-05-01
In computer vision, image datasets used for classification are naturally associated with multiple labels and comprised of multiple views, because each image may contain several objects (e.g., pedestrian, bicycle, and tree) and is properly characterized by multiple visual features (e.g., color, texture, and shape). Currently, available tools ignore either the label relationship or the view complementarily. Motivated by the success of the vector-valued function that constructs matrix-valued kernels to explore the multilabel structure in the output space, we introduce multiview vector-valued manifold regularization (MV(3)MR) to integrate multiple features. MV(3)MR exploits the complementary property of different features and discovers the intrinsic local geometry of the compact support shared by different features under the theme of manifold regularization. We conduct extensive experiments on two challenging, but popular, datasets, PASCAL VOC' 07 and MIR Flickr, and validate the effectiveness of the proposed MV(3)MR for image classification.
Gravity and supergravity as gauge theories on a group manifold
Directory of Open Access Journals (Sweden)
Yuval Ne'eman
1978-03-01
Full Text Available We construct generalizations of gravity, including supergravity, by writing the theory on the group manifold (Poincaré for gravity, the graded-Poincaré group for supergravity. The action involves forms over the group, restricted to a 4-dimensional submanifold. The equations of motion produce a Lorentz gauge in gravity and supergravity, and an additional anholonomic supersymmetric coordinate transformation which reduces to the “local supersymmetry” of supergravity.
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.
Particle Spaces on Manifolds and Generalized Poincar\\'e Dualities
Kallel, Sadok
1998-01-01
It is quite an interesting phenomenon in Topology that configuration spaces on a manifold M are intrinsically related to certain mapping spaces from M. In this paper we interpret and greatly expand on this relationship. Building (mainly) on work of Segal, we introduce a new class of configuration spaces; the particle spaces, and these include the classical configuration spaces of distinct points, symmetric products, truncated products, divisor spaces, positive and negative particles of McDuff...
On symplectomorphisms of the symplectisation of a compact contact manifold
International Nuclear Information System (INIS)
Banyaga, A.
2004-03-01
Let (N, α) be a compact contact manifold and (N x R, d(e t α)) its symplectisation. We show that the group G which is the identity component in the group of symplectic diffeomorphisms Φ of (N x R, d(e t α)) that cover diffeomorphisms of Φ of N x S 1 is simple, by showing that G is isomorphic to the kernel of the Calabi homomorphism of the associated locally conformal symplectic structure. (author)
A note on generalized metrics on complex manifolds
International Nuclear Information System (INIS)
Rastogi, S.C.
1986-08-01
In 1981, Hojo introduced a generalized metric function Φ (P) , p(≠1) is a real number in a Finsler space and studied some beautiful consequences of such a metric function. The aim of this paper is to investigate the possibility of introducing a similar metric function on a complex manifold studied by Rund. It is interesting to note that such an introduction is unnatural for values of p other than 2, which corresponds to the metric function introduced by Rund. (author)
Homotopy classification of contact foliations on open contact manifolds
Indian Academy of Sciences (India)
64
Abstract. We give a homotopy classification of foliations on open contact manifolds whose leaves are contact ... The inverse images of FN under an f ∈ Trα(M, FN ), namely f−1FN , is a contact foliation on (M,α). ..... Let Γ be the graph of H; then the image of ϕ is contained in Γ. By Lemma 3.2 there exists a diffeomorphism Φ ...
Curved manifolds with conserved Runge-Lenz vectors
International Nuclear Information System (INIS)
Ngome, J.-P.
2009-01-01
van Holten's algorithm is used to construct Runge-Lenz-type conserved quantities, induced by Killing tensors, on curved manifolds. For the generalized Taub-Newman-Unti-Tamburino metric, the most general external potential such that the combined system admits a conserved Runge-Lenz-type vector is found. In the multicenter case, the subclass of two-center metric exhibits a conserved Runge-Lenz-type scalar.
One-loop effective potential on hyperbolic manifolds
International Nuclear Information System (INIS)
Cognola, G.; Kirsten, K.; Zerbini, S.
1993-01-01
The one-loop effective potential for a scalar field defined on an ultrastatic space-time whose spatial part is a compact hyperbolic manifold is studied using ζ-function regularization for the one-loop effective action. Other possible regularizations are discussed in detail. The renormalization group equations are derived, and their connection with the conformal anomaly is pointed out. The symmetry breaking and the topological mass generation are also discussed
Ultrasonic defect characterization using parametric-manifold mapping
Velichko, A.; Bai, L.; Drinkwater, B. W.
2017-06-01
The aim of ultrasonic non-destructive evaluation includes the detection and characterization of defects, and an understanding of the nature of defects is essential for the assessment of structural integrity in safety critical systems. In general, the defect characterization challenge involves an estimation of defect parameters from measured data. In this paper, we explore the extent to which defects can be characterized by their ultrasonic scattering behaviour. Given a number of ultrasonic measurements, we show that characterization information can be extracted by projecting the measurement onto a parametric manifold in principal component space. We show that this manifold represents the entirety of the characterization information available from far-field harmonic ultrasound. We seek to understand the nature of this information and hence provide definitive statements on the defect characterization performance that is, in principle, extractable from typical measurement scenarios. In experiments, the characterization problem of surface-breaking cracks and the more general problem of elliptical voids are studied, and a good agreement is achieved between the actual parameter values and the characterization results. The nature of the parametric manifold enables us to explain and quantify why some defects are relatively easy to characterize, whereas others are inherently challenging.
The α ' expansion on a compact manifold of exceptional holonomy
Becker, Katrin; Robbins, Daniel; Witten, Edward
2014-06-01
In the approximation corresponding to the classical Einstein equations, which is valid at large radius, string theory compactification on a compact manifold M of G 2 or Spin(7) holonomy gives a supersymmetric vacuum in three or two dimensions. Do α ' corrections to the Einstein equations disturb this statement? Explicitly analyzing the leading correction, we show that the metric of M can be adjusted to maintain supersymmetry. Beyond leading order, a general argument based on low energy effective field theory in spacetime implies that this is true exactly (not just to all finite orders in α '). A more elaborate field theory argument that includes the massive Kaluza-Klein modes matches the structure found in explicit calculations. In M-theory compactification on a manifold M of G 2 or Spin(7) holonomy, similar results hold to all orders in the inverse radius of M — but not exactly. The classical moduli space of G 2 metrics on a manifold M is known to be locally a Lagrangian submanifold of H 3( M,) ⊕ H 4( M,). We show that this remains valid to all orders in the α ' or inverse radius expansion.
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.
Robust head pose estimation via supervised manifold learning.
Wang, Chao; Song, Xubo
2014-05-01
Head poses can be automatically estimated using manifold learning algorithms, with the assumption that with the pose being the only variable, the face images should lie in a smooth and low-dimensional manifold. However, this estimation approach is challenging due to other appearance variations related to identity, head location in image, background clutter, facial expression, and illumination. To address the problem, we propose to incorporate supervised information (pose angles of training samples) into the process of manifold learning. The process has three stages: neighborhood construction, graph weight computation and projection learning. For the first two stages, we redefine inter-point distance for neighborhood construction as well as graph weight by constraining them with the pose angle information. For Stage 3, we present a supervised neighborhood-based linear feature transformation algorithm to keep the data points with similar pose angles close together but the data points with dissimilar pose angles far apart. The experimental results show that our method has higher estimation accuracy than the other state-of-art algorithms and is robust to identity and illumination variations. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
GPU accelerated manifold correction method for spinning compact binaries
Ran, Chong-xi; Liu, Song; Zhong, Shuang-ying
2018-04-01
The graphics processing unit (GPU) acceleration of the manifold correction algorithm based on the compute unified device architecture (CUDA) technology is designed to simulate the dynamic evolution of the Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries. The feasibility and the efficiency of parallel computation on GPU have been confirmed by various numerical experiments. The numerical comparisons show that the accuracy on GPU execution of manifold corrections method has a good agreement with the execution of codes on merely central processing unit (CPU-based) method. The acceleration ability when the codes are implemented on GPU can increase enormously through the use of shared memory and register optimization techniques without additional hardware costs, implying that the speedup is nearly 13 times as compared with the codes executed on CPU for phase space scan (including 314 × 314 orbits). In addition, GPU-accelerated manifold correction method is used to numerically study how dynamics are affected by the spin-induced quadrupole-monopole interaction for black hole binary system.
Quantum fields on manifolds: PCT and gravitationally induced thermal states
International Nuclear Information System (INIS)
Sewell, G.L.
1982-01-01
We formulate an axiomatic scheme, designed to provide a framework for a general, rigorous theory of relativistic quantum fields on a class of manifolds, that includes Kruskal's extension of Schwarzchild space-time, as well as Minkowski space-time. The scheme is an adaptation of Wightman's to this class of manifolds. We infer from it that, given an arbitrary field (in general, interacting) on a manifold X, the restriction of the field to a certain open submanifold X/sup( + ), whose boundaries are event horizons, satisfies the Kubo--Martin--Schwinger (KMS) thermal equilibrium conditions. This amounts to a rigorous, model-independent proof of a generalized Hawking--Unruh effect. Further, in cases where the field enjoys a certain PCT symmetry, the conjugation governing the KMS condition is just the PCT operator. The key to these results is an analogue, that we prove, of the Bisognano--Wichmann theorem [J. Math. Phys. 17, (1976), Theorem 1]. We also construct an alternative scheme by replacing a regularity condition at an event horizon by the assumption that the field in X/sup( + ) is in a ground, rather then a thermal, state. We show that, in this case, the observables in X/sup( + ) are uncorrelated to those in its causal complement, X/sup( - ), and thus that the event horizons act as physical barriers. Finally, we argue that the choice between the two schemes must be dictated by the prevailing conditions governing the state of the field
Analyticity of the Free Energy of a Closed 3-Manifold
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Stavros Garoufalidis
2008-11-01
Full Text Available The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant of a closed 3-manifold with gauge group U(N for arbitrary N. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a corollary, it follows that the genus g part of the free energy is convergent in a neighborhood of zero, independent of the genus. Our results follow from an estimate of the LMO invariant, in a particular gauge, and from recent results of Bender-Gao-Richmond on the asymptotics of the number of rooted maps for arbitrary genus. We illustrate our results with an explicit formula for the free energy of a Lens space. In addition, using the Painlevé differential equation, we obtain an asymptotic expansion for the number of cubic graphs to all orders, stengthening the results of Bender-Gao-Richmond.
Differential geometry in the large and compactification of higher-dimensional gravity
Muzinich, I. J.
1986-05-01
Some well-known results from differential geometry are applied to some of the major issues of compactification of higher-dimensional gravity. The results apply both to the theories generally known as Kaluza-Klein and the recently more promising super string theories. These results are primarily due to Yano [K. Yano, Integral Formulas in Differential Geometry (Marcel Dekker, New York, 1970); Differential Geometry on Complex and Almost Complex Manifolds (Macmillian, New York, 1965)] and have profound implications for the Kaluza-Klein scenario with respect to the cosmological constant problem and the massless sector of the theory. While the results are well known in the mathematical literature, the present author has only seen a fragmentary account presented by a few physicists. The necessary introduction to complex manifolds is also provided including Kähler manifolds and their possible relevance to the problem of compactification. The Ricci tensor provides the central role in the discussion of metric isometries, holomorphy, and holonomy. The incumbent role of Calabi-Yau manifolds with Ricci flat curvature and SU(n) holonomy, which have been recently conjectured in regard to super string compactification, is also mentioned.
Squashed Toric Sigma Models and Mock Modular Forms
Gupta, Rajesh Kumar; Murthy, Sameer
2018-01-01
We study a class of two-dimensional N}=(2,2)} sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global {U(1)} symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold in which the torus fibration maintains a constant size in the interior of the manifold, thus producing a neck-like region. We compute the elliptic genus of these models, using localization, in the case when the unsquashed vacuum manifolds obey the Calabi-Yau condition. The elliptic genera have a non-holomorphic dependence on the modular parameter {τ} coming from the continuum produced by the neck. In the simplest case corresponding to squashed {C / Z_{2 the elliptic genus is a mixed mock Jacobi form which coincides with the elliptic genus of the {N=(2,2)} {SL(2,R) / U(1)} cigar coset.
Boukraa, S.; Hassani, S.; Maillard, J.-M.
2012-12-01
Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard-Fuchs systems of two-variables ‘above’ Calabi-Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ(n), corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ(3) and χ(4), that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ(n)s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi-Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non-holonomic anisotropic full
Energy Technology Data Exchange (ETDEWEB)
Coelho, Celso Roberto Molinaro [PETROBRAS S.A., Sao Jose dos Campos, SP (Brazil). Refinaria Henrique Lage (REVAP)
2004-07-01
Digital Control System are three generations of hardware and software platforms in process automation , but DCS is using the same functions and presents the reliability and availability . The challenge in automation has to maintain the old and the newest system operating and integrated perhaps the different times of platforms to guarantee the actual investments and in the future. A new generation of DCS using field equipment to control or the actual architecture with a lot of new information are coming with the technologies. (author)
Kaalep, Tõnu, 1966-
2003-01-01
Heliplaatidest: Mihkel Kleis "Quest For Fire/Visit To Minotaur", Andrew W. K. "The Wolf",Client "Client", Bubba Sparxxx "Deliverance", Yes "The Ultimate Yes - 35th Anniversary Collection", Joseph Suchy "calabi.yau", Luomo "Present Lover"
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.
Toward Optimal Manifold Hashing via Discrete Locally Linear Embedding.
Rongrong Ji; Hong Liu; Liujuan Cao; Di Liu; Yongjian Wu; Feiyue Huang
2017-11-01
Binary code learning, also known as 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 first needs to build the local linear embedding in the original feature space, and then quantize such embedding to binary codes. Such a two-step coding is problematic and less optimized. Besides, the off-line 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. The 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 embeddingcodes, we further propose a discrete optimization algorithm with an iterative parameters updating scheme. Moreover, an anchor-based acceleration scheme, termed Anchor-DLLH, is further introduced, which approximates the large similarity matrix by the product of two low-rank matrices. Experimental results on three widely used benchmark data sets, i.e., CIFAR10, NUS-WIDE, and YouTube Face, have shown superior performance of the proposed DLLH over the state-of-the-art approaches.