2,151 research outputs found
An implementation of Deflate in Coq
The widely-used compression format "Deflate" is defined in RFC 1951 and is
based on prefix-free codings and backreferences. There are unclear points about
the way these codings are specified, and several sources for confusion in the
standard. We tried to fix this problem by giving a rigorous mathematical
specification, which we formalized in Coq. We produced a verified
implementation in Coq which achieves competitive performance on inputs of
several megabytes. In this paper we present the several parts of our
implementation: a fully verified implementation of canonical prefix-free
codings, which can be used in other compression formats as well, and an elegant
formalism for specifying sophisticated formats, which we used to implement both
a compression and decompression algorithm in Coq which we formally prove
inverse to each other -- the first time this has been achieved to our
knowledge. The compatibility to other Deflate implementations can be shown
empirically. We furthermore discuss some of the difficulties, specifically
regarding memory and runtime requirements, and our approaches to overcome them
Remarks on the Classical Size of D-Branes
We discuss different criteria for `classical size' of extremal Dirichlet
p-branes in type-II supergravity. Using strong-weak coupling duality, we find
that the size of the strong-coupling region at the core of the (p<3)-branes, is
always given by the asymptotic string scale, if measured in the weakly coupled
dual string metric. We also point out how the eleven-dimensional Planck scale
arises in the classical 0-brane solution, as well as the ten-dimensional Planck
scale in the D-instanton solution.Comment: 8 pp, harvma
The information paradox and the locality bound
Hawking's argument for information loss in black hole evaporation rests on
the assumption of independent Hilbert spaces for the interior and exterior of a
black hole. We argue that such independence cannot be established without
incorporating strong gravitational effects that undermine locality and
invalidate the use of quantum field theory in a semiclassical background
geometry. These considerations should also play a role in a deeper
understanding of horizon complementarity.Comment: 21 pages, harvmac; v2-3. minor corrections, references adde
Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes
We obtain exact expressions for the quasi-normal modes of various spin for
the BTZ black hole. These modes determine the relaxation time of black hole
perturbations. Exact agreement is found between the quasi-normal frequencies
and the location of the poles of the retarded correlation function of the
corresponding perturbations in the dual conformal field theory. This then
provides a new quantitative test of the AdS/CFT correspondence.Comment: 4 pages, RevTeX, references adde
CMB quadrupole suppression: II. The early fast roll stage
Within the effective field theory of inflation, an initialization of the
classical dynamics of the inflaton with approximate equipartition between the
kinetic and potential energy of the inflaton leads to a brief fast roll stage
that precedes the slow roll regime. The fast roll stage leads to an attractive
potential in the wave equations for the mode functions of curvature and tensor
perturbations. The evolution of the inflationary perturbations is equivalent to
the scattering by this potential and a useful dictionary between the scattering
data and observables is established.Implementing methods from scattering theory
we prove that this attractive potential leads to a suppression of the
quadrupole moment for CMB and B-mode angular power spectra. The scale of the
potential is determined by the Hubble parameter during slow roll. Within the
effective field theory of inflation at the grand unification (GUT) energy scale
we find that if inflation lasts a total number of efolds N_{tot} ~ 59, there is
a 10-20% suppression of the CMB quadrupole and about 2-4% suppression of the
tensor quadrupole. The suppression of higher multipoles is smaller, falling off
as 1/l^2. The suppression is much smaller for N_{tot} > 59, therefore if the
observable suppression originates in the fast roll stage, there is the upper
bound N_{tot} ~ 59.Comment: Some comments and references adde
Symmetries of Large N Matrix Models for Closed Strings
We obtain the symmetry algebra of multi-matrix models in the planar large N
limit. We use this algebra to associate these matrix models with quantum spin
chains. In particular, certain multi-matrix models are exactly solved by using
known results of solvable spin chain systems.Comment: 12 pages, 1 eps figure, RevTex, some minor typos in the publised
version are correcte
Modification to the power spectrum in the brane world inflation driven by the bulk inflaton
We compute the cosmological perturbations generated in the brane world
inflation driven by the bulk inflaton. Different from the model that the
inflation is a brane effect, we exhibit the modification of the power spectrum
of scalar perturbations due to the existence of the fifth dimension. With the
change of the initial vacuum, we investigate the dependence of the correction
of the power spectrum on the choice of the vacuum.Comment: replaced with the revised version, accepted for publication in PR
Lectures on string theory and cosmology
In these lectures I review recent attempts to apply string theory to
cosmology, including string cosmology and various models of brane cosmology. In
addition, the review includes an introduction to inflation as well as a
discussion of transplanckian signatures. I also provide a critical discussion
of the possible role of holography. The material is based on lectures given in
January 2004 at the RTN String School in Barcelona, but also contain some
additional material.Comment: Lectures given in January 2004 at the RTN Barcelona String School, 50
pages, 9 figure
Holographic bounds on the UV cutoff scale in inflationary cosmology
We discuss how holographic bounds can be applied to the quantum fluctuations
of the inflaton. In general the holographic principle will lead to a bound on
the UV cutoff scale of the effective theory of inflation, but it will depend on
the coarse-graining prescription involved in calculating the entropy. We
propose that the entanglement entropy is a natural measure of the entropy of
the quantum perturbations, and show which kind of bound on the cutoff it leads
to. Such bounds are related to whether the effects of new physics will show up
in the CMB.Comment: 19 pages, 2 figures;(V3):Comments and references adde
(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame
We formulate and analyze the Hamiltonian dynamics of a pair of massive
spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the
system to a conical infinity, isometric to the infinity generated by a single
massive but possibly spinning particle. The reduced phase space \Gamma_{red}
has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the
phase space of a Newtonian two-body system in the centre-of-mass frame, and we
find on \Gamma_{red} a canonical chart that makes this analogue explicit and
reduces to the Newtonian chart in the appropriate limit. Prospects for
quantization are commented on.Comment: 38 pages, REVTeX v3.1 with amsfonts and epsf, 12 eps figures. (v2:
Presentational improvement, references added, typos corrected.
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