138 research outputs found
Non-Factorizable Branes on the Torus
This work discusses string compactifications on the torus with optional Z_4 x
Z_4 or Z_2 x Z_2 orbifold action from the perspective of matrix factorizations.
The method is brought to a level where model building on these backgrounds is
possible. Whereas branes discussed in the literature typically wrap
factorizable cycles, that is cycles which are products of 1-cycles, branes
studied here can be in generic homology classes, can have arbitrary position
and Wilson line, have full complex structure respectively Kahler moduli
dependence and can be subject to any consistent orientifold action. It is shown
how any desired D-brane can be constructed systematically. Three-point
correlators can be computed as is demonstrated at hand of an example. Their
normalization is not discussed.Comment: 41 pages, references added, typos corrected, modified introductio
Barycentric Subspace Analysis on Manifolds
This paper investigates the generalization of Principal Component Analysis
(PCA) to Riemannian manifolds. We first propose a new and general type of
family of subspaces in manifolds that we call barycentric subspaces. They are
implicitly defined as the locus of points which are weighted means of
reference points. As this definition relies on points and not on tangent
vectors, it can also be extended to geodesic spaces which are not Riemannian.
For instance, in stratified spaces, it naturally allows principal subspaces
that span several strata, which is impossible in previous generalizations of
PCA. We show that barycentric subspaces locally define a submanifold of
dimension k which generalizes geodesic subspaces.Second, we rephrase PCA in
Euclidean spaces as an optimization on flags of linear subspaces (a hierarchy
of properly embedded linear subspaces of increasing dimension). We show that
the Euclidean PCA minimizes the Accumulated Unexplained Variances by all the
subspaces of the flag (AUV). Barycentric subspaces are naturally nested,
allowing the construction of hierarchically nested subspaces. Optimizing the
AUV criterion to optimally approximate data points with flags of affine spans
in Riemannian manifolds lead to a particularly appealing generalization of PCA
on manifolds called Barycentric Subspaces Analysis (BSA).Comment: Annals of Statistics, Institute of Mathematical Statistics, A
Para\^itr
Optimal load balancing techniques for block-cyclic decompositions for matrix factorization
In this paper, we present a new load balancing technique, called panel scattering, which is generally applicable for parallel block-partitioned dense linear algebra algorithms, such as matrix factorization. Here, the panels formed in such computation are divided across their length, and evenly (re-)distributed among all processors. It is shown how this technique can be eÆciently implemented for the general block-cyclic matrix distribution, requiring only the collective communication primitives that required for block-cyclic parallel BLAS. In most situations, panel scattering yields optimal load balance and cell computation speed across all stages of the computation. It has also advantages in naturally yielding good memory access patterns. Compared with traditional methods which minimize communication costs at the expense of load balance, it has a small (in some situations negative) increase in communication volume costs. It however incurs extra communication startup costs, but only by a factor not exceeding 2. To maximize load balance and minimize the cost of panel re-distribution, storage block sizes should be kept small; furthermore, in many situations of interest, there will be no significant communication startup penalty for doing so. Results will be given on the Fujitsu AP+ parallel computer, which will compare the performance of panel scattering with previously established methods, for LU, LLT and QR factorization. These are consistent with a detailed performance model for LU factorization for each method that is developed here
Branes: from free fields to general backgrounds
Motivated by recent developments in string theory, we study the structure of
boundary conditions in arbitrary conformal field theories. A boundary condition
is specified by two types of data: first, a consistent collection of reflection
coefficients for bulk fields on the disk; and second, a choice of an
automorphism of the fusion rules that preserves conformal weights.
Non-trivial automorphisms correspond to D-brane configurations for
arbitrary conformal field theories. The choice of the fusion rule automorphism
amounts to fixing the dimension and certain global topological
features of the D-brane world volume and the background gauge field on it. We
present evidence that for fixed choice of the boundary conditions are
classified as the irreducible representations of some commutative associative
algebra, a generalization of the fusion rule algebra. Each of these irreducible
representations corresponds to a choice of the moduli for the world volume of
the D-brane and the moduli of the flat connection on it.Comment: 56 pages, LaTeX2e. Typos corrected; two references adde
Must linear algebra be block cyclic? : and other explorations into the expressivity of data parallel and task parallel languages
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (leaves 68-69).Prevailing Parallel Linear Algebra software block cyclically distributes data across its processors for good load balancing and communication between its nodes. The block cyclic distribution schema characterized by cyclic order allocation of row and column data blocks followed by consecutive elimination is widely used in scientific computing and is the default approach in ScaLA-PACK. The fact that we are not familiar with any software outside of linear algebra that has considered cyclic distributions for their execution presents incompatibility. This calls for possible change in approach as advanced computing platforms like Star-P are emerging allowing for interoperability of algorithms. This work demonstrates a data parallel column block cyclic elimination technique for LU and QR factorization. This technique yields good load balance and communication between nodes, and also eliminates superfluous overheads. The algorithms are implemented with consecutive allocation and cyclic elimination using the high level platform, Star-P. Block update tenders extensive performance enhancement making use of Basic Linear Algebra Subroutine-3 for delivering tremendous speedup. This project also provides an overview of threading in parallel systems through implementation of important task parallel algorithms: prefix, hexadecimal Pi digits and Monte-Carlo simulation.by Harish Peruvamba Sundaresh.S.M
Topological Strings and Quantum Curves
This thesis presents several new insights on the interface between
mathematics and theoretical physics, with a central role for fermions on
Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW
models is embedded into string theory. Secondly, this model is generalized to a
web of dualities connecting topological string theory and N=2 supersymmetric
gauge theories to a configuration of D-branes that intersect over a Riemann
surface. This description yields a new perspective on topological string theory
in terms of a KP integrable system based on a quantum curve. Thirdly, this
thesis describes a geometric analysis of wall-crossing in N=4 string theory.
And lastly, it offers a novel approach to construct metastable vacua in type
IIB string theory.Comment: PhD thesis, July 2009, 308 pages, 65 figure
- …