1,850 research outputs found
Turing machines can be efficiently simulated by the General Purpose Analog Computer
The Church-Turing thesis states that any sufficiently powerful computational
model which captures the notion of algorithm is computationally equivalent to
the Turing machine. This equivalence usually holds both at a computability
level and at a computational complexity level modulo polynomial reductions.
However, the situation is less clear in what concerns models of computation
using real numbers, and no analog of the Church-Turing thesis exists for this
case. Recently it was shown that some models of computation with real numbers
were equivalent from a computability perspective. In particular it was shown
that Shannon's General Purpose Analog Computer (GPAC) is equivalent to
Computable Analysis. However, little is known about what happens at a
computational complexity level. In this paper we shed some light on the
connections between this two models, from a computational complexity level, by
showing that, modulo polynomial reductions, computations of Turing machines can
be simulated by GPACs, without the need of using more (space) resources than
those used in the original Turing computation, as long as we are talking about
bounded computations. In other words, computations done by the GPAC are as
space-efficient as computations done in the context of Computable Analysis
A Curvature Principle for the interaction between universes
We propose a Curvature Principle to describe the dynamics of interacting
universes in a multi-universe scenario and show, in the context of a simplified
model, how interaction drives the cosmological constant of one of the universes
toward a vanishingly small value. We also conjecture on how the proposed
Curvature Principle suggests a solution for the entropy paradox of a universe
where the cosmological constant vanishes.Comment: Essay selected for an honorable mention by the Gravity Research
Foundation, 2007. Plain latex, 8 page
Kaehler forms and cosmological solutions in type II supergravities
We consider cosmological solutions to type II supergravity theories where the
spacetime is split into a FRW universe and a K\"ahler space, which may be taken
to be Calabi-Yau. The various 2-forms present in the theories are taken to be
proportional to the K\"ahler form associated to the K\"ahler space.Comment: 6 pages, LaTeX2
New properties of scalar field dynamics in brane isotropic cosmological models
Several aspects of scalar field dynamics on a brane which differs from
corresponding regimes in the standard cosmology are investigated. We consider
asymptotic solution near a singularity, condition for inflation and bounces and
some detail of chaotic behavior in the brane model. Each results are compared
with those known in the standard cosmology.Comment: 13 pages with 2 eps figures, submitted to Astronomy Letter
Bianchi Type I Cosmologies in Arbitrary Dimensional Dilaton Gravities
We study the low energy string effective action with an exponential type
dilaton potential and vanishing torsion in a Bianchi type I space-time
geometry. In the Einstein and string frames the general solution of the
gravitational field equations can be expressed in an exact parametric form.
Depending on the values of some parameters the obtained cosmological models can
be generically divided into three classes, leading to both singular and
nonsingular behaviors. The effect of the potential on the time evolution of the
mean anisotropy parameter is also considered in detail, and it is shown that a
Bianchi type I Universe isotropizes only in the presence of a dilaton field
potential or a central deficit charge.Comment: REVTEX, 10 pages, 8 figure
Collisions of Cosmic F- and D-strings
Recent work suggests that fundamental and Dirichlet strings, and their (p,q)
bound states, may be observed as cosmic strings. The evolution of cosmic string
networks, and therefore their observational signals, depends on what happens
when two strings collide. We study this in string perturbation theory for
collisions between all possible pairs of strings; different cases involve
sphere, disk, and annulus amplitudes. The result also depends on the details of
compactification; the dependence on ratios of scales is only logarithmic, but
this is still numerically important. We study a range of models and parameters,
and find that in most cases these strings can be distinguished from cosmic
strings that arise as gauge theory solitons.Comment: 42 pages, 7 figures; v.2: added references, expanded discussion of
reconnection in field theor
A Hedged Monte Carlo Approach to Real Option Pricing
In this work we are concerned with valuing optionalities associated to invest
or to delay investment in a project when the available information provided to
the manager comes from simulated data of cash flows under historical (or
subjective) measure in a possibly incomplete market. Our approach is suitable
also to incorporating subjective views from management or market experts and to
stochastic investment costs. It is based on the Hedged Monte Carlo strategy
proposed by Potters et al (2001) where options are priced simultaneously with
the determination of the corresponding hedging. The approach is particularly
well-suited to the evaluation of commodity related projects whereby the
availability of pricing formulae is very rare, the scenario simulations are
usually available only in the historical measure, and the cash flows can be
highly nonlinear functions of the prices.Comment: 25 pages, 14 figure
Growth of Inflaton Perturbations and the Post-Inflation Era in Supersymmetric Hybrid Inflation Models
It has been shown that hybrid inflation may end with the formation of
non-topological solitons of inflaton field. As a first step towards a fully
realistic picture of the post-inflation era and reheating in supersymmetric
hybrid inflation models, we study the classical scalar field equations of a
supersymmetric hybrid inflation model using a semi-analytical ansatz for the
spatial dependence of the fields. Using the minimal D-term inflation model as
an example, the inflaton field is evolved using the full 1-loop effective
potential from the slow-rolling era to the U(1)_{FI} symmetry-breaking phase
transition. Spatial perturbations of the inflaton corresponding to quantum
fluctuations are introduced for the case where there is spatially coherent
U(1)_{FI} symmetry breaking. The maximal growth of the dominant perturbation is
found to depend only on the ratio of superpotential coupling \lambda to the
gauge coupling g. The inflaton condensate fragments to non-topological solitons
for \lambda/g > 0.09. Possible consequences of non-topological soliton
formation in fully realistic SUSY hybrid inflation models are discussed.Comment: 27 pages LaTeX, 8 figures. Additional references and discussio
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