2,268 research outputs found
Algorithmic Solution for Systems of Linear Equations, in time
We present a novel algorithm attaining excessively fast, the sought solution
of linear systems of equations. The algorithm is short in its basic formulation
and, by definition, vectorized, while the memory allocation demands are
trivial, because, for each iteration, only one dimension of the given input
matrix is utilized. The execution time is very short compared with
state-of-the-art methods, exhibiting speed-up and low memory
allocation demands, especially for non-square Systems of Linear Equations, with
ratio of equations versus features high (tall systems), or low (wide systems)
accordingly. The accuracy is high and straightforwardly controlled, and the
numerical results highlight the efficiency of the proposed algorithm, in terms
of computation time, solution accuracy and memory demands. The paper also
comprises a theoretical proof for the algorithmic convergence, and we extend
the implementation of the proposed algorithmic rationale to feature selection
tasks
Gradient flows and instantons at a Lifshitz point
I provide a broad framework to embed gradient flow equations in
non-relativistic field theory models that exhibit anisotropic scaling. The
prime example is the heat equation arising from a Lifshitz scalar field theory;
other examples include the Allen-Cahn equation that models the evolution of
phase boundaries. Then, I review recent results reported in arXiv:1002.0062
describing instantons of Horava-Lifshitz gravity as eternal solutions of
certain geometric flow equations on 3-manifolds. These instanton solutions are
in general chiral when the anisotropic scaling exponent is z=3. Some general
connections with the Onsager-Machlup theory of non-equilibrium processes are
also briefly discussed in this context. Thus, theories of Lifshitz type in d+1
dimensions can be used as off-shell toy models for dynamical vacuum selection
of relativistic field theories in d dimensions.Comment: 19 pages, 1 figure, contribution to conference proceedings (NEB14);
minor typos corrected in v
Rational algebras from composite operators
Factoring out the spin subalgebra of a algebra leads to a new
structure which can be seen either as a rational finitely generated
algebra or as a polynomial non-linear realization.Comment: 11 pages, LATEX, preprint ENSLAPP-AL-429/93 and NORDITA-93/47-
Rational vs Polynomial Character of W-Algebras
The constraints proposed recently by Bershadsky to produce algebras
are a mixture of first and second class constraints and are degenerate. We show
that they admit a first-class subsystem from which they can be recovered by
gauge-fixing, and that the non-degenerate constraints can be handled by
previous methods. The degenerate constraints present a new situation in which
the natural primary field basis for the gauge-invariants is rational rather
than polynomial. We give an algorithm for constructing the rational basis and
converting the base elements to polynomials.Comment: 18 page
BPS Solutions and New Phases of Finite-Temperature Strings
All high-temperature phases of the known N=4 superstrings in five dimensions
can be described by the universal thermal potential of an effective
four-dimensional supergravity. This theory, in addition to three moduli s, t,
u, contains non-trivial winding modes that become massless in certain regions
of the thermal moduli space, triggering the instabilities at the Hagedorn
temperature. In this context, we look for exact domain wall solutions of first
order BPS equations. These solutions preserve half of the supersymmetries, in
contrast to the usual finite-temperature weak-coupling approximation, and as
such may constitute a new phase of finite-temperature superstrings. We present
exact solutions for the type-IIA and type-IIB theories and for a self-dual
hybrid type-II theory. While for the heterotic case the general solution cannot
be given in closed form, we still present a complete picture and a detailed
analysis of the behaviour around the weak and strong coupling limits and around
certain critical points. In all cases these BPS solutions have no instabilities
at any temperature. Finally, we address the physical meaning of the resulting
geometries within the contexts of supergravity and string theory.Comment: 47 pages, 3 eps figures, Latex, version to be published in Nucl.
Phys. B, one refernce added, minor correction
Nonholonomic Ricci Flows and Running Cosmological Constant: I. 4D Taub-NUT Metrics
In this work we construct and analyze exact solutions describing Ricci flows
and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It
is outlined a new geometric techniques of constructing Ricci flow solutions.
Some conceptual issues on spacetimes provided with generic off-diagonal metrics
and associated nonlinear connection structures are analyzed. The limit from
gravity/Ricci flow models with nontrivial torsion to configurations with the
Levi-Civita connection is allowed in some specific physical circumstances by
constraining the class of integral varieties for the Einstein and Ricci flow
equations.Comment: latex2e, final variant to be published in IJMP
An N=1 Supersymmetric Coulomb Flow
We find a three-parameter family of solutions to IIB supergravity that
corresponds to N=1 supersymmetric holographic RG flows of N=4 supersymmetric
Yang Mills theory. This family of solutions allows one to give a mass to a
single chiral superfield, and to probe a two-dimensional subspace of the
Coulomb branch. In particular, we examine part of the Coulomb branch of the
Leigh-Strassler fixed point. We look at the infra-red asymptotics of these
flows from the ten-dimensional perspective. We also make general conjectures
for the lifting Ansatz of five-dimensional scalar configurations to
ten-dimensional tensor gauge fields. Our solution provides a highly non-trivial
test of these conjectures.Comment: 13 pages; harvma
Supersymmetry and finite-temperature strings
We describe finite temperature N=4 superstrings in D=5 by an effective
four-dimensional supergravity of the thermal winding modes that can become
tachyonic and trigger the instabilities at the Hagedorn temperature. Using a
domain-wall ansatz, exact solutions to special BPS-type first order equations
are found. They preserve half of the supersymmetries, contrary to the standard
perturbative superstring at finite temperature that breaks all supersymmetries.
Our solutions show no indication of any tachyonic instability and provide
evidence for a new BPS phase of finite temperature superstrings that is stable
for all temperatures. This would have important consequences for a stringy
description of the early universe.Comment: 6 pages, Latex, To appear in the proceedings of The Ninth Marcel
Grossmann Meeting, Rome, July 2-8, 200
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