494,567 research outputs found
Problem Understanding through Landscape Theory
In order to understand the structure of a problem we need to measure some features of the problem. Some examples of measures suggested in the past are autocorrelation and fitness-distance correlation. Landscape theory, developed in the last years in the field of combinatorial optimization, provides mathematical expressions to efficiently compute statistics on optimization problems. In this paper we discuss how can we use optimización combinatoria in the context of problem understanding and present two software tools that can be used to efficiently compute the mentioned measures.Ministerio de EconomÃa y Competitividad (TIN2011-28194
Non-singular AdS-dS transitions in a landscape scenario
Understanding transitions between different vacua of a multiverse allowing
eternal inflation is an open problem whose resolution is important to gain
insights on the global structure of the spacetime as well as the problem of
measure. In the classical theory, transitions from the anti-deSitter to
deSitter vacua are forbidden due to the big crunch singularity. In this
article, we consider toy landscape potentials: a double well and a triple well
potential allowing anti-deSitter and de-Sitter vacua, in the effective dynamics
of loop quantum cosmology for the FRW model. We show that due to the
non-perturbative quantum gravity effects as understood in loop quantum
cosmology, non-singular anti-deSitter to de-Sitter transitions are possible. In
the future evolution, an anti-deSitter bubble universe does not encounter a big
crunch singularity but undergoes a big bounce occurring at a scale determined
by the underlying quantum geometry. These non-singular transitions provide a
mechanism through which a probe or a `watcher', used to define a local measure,
can safely evolve through the bounce and geodesics can be smoothly extended
from anti-deSitter to de-Sitter vacua.Comment: Revised version. Appendix on results in k=0 model added. To appear in
PR
Density Perturbations and the Cosmological Constant from Inflationary Landscapes
An anthropic understanding of the cosmological constant requires that the
vacuum energy at late time scans from one patch of the universe to another. If
the vacuum energy during inflation also scans, the various patches of the
universe acquire exponentially differing volumes. In a generic landscape with
slow-roll inflation, we find that this gives a steeply varying probability
distribution for the normalization of the primordial density perturbations,
resulting in an exponentially small fraction of observers measuring the COBE
value of 10^-5. Inflationary landscapes should avoid this "\sigma problem", and
we explore features that can allow them to do that. One possibility is that,
prior to slow-roll inflation, the probability distribution for vacua is
extremely sharply peaked, selecting essentially a single anthropically allowed
vacuum. Such a selection could occur in theories of eternal inflation. A second
possibility is that the inflationary landscape has a special property: although
scanning leads to patches with volumes that differ exponentially, the value of
the density perturbation does not vary under this scanning. This second case is
preferred over the first, partly because a flat inflaton potential can result
from anthropic selection, and partly because the anthropic selection of a small
cosmological constant is more successful.Comment: 23 page
Credimus
We believe that economic design and computational complexity---while already
important to each other---should become even more important to each other with
each passing year. But for that to happen, experts in on the one hand such
areas as social choice, economics, and political science and on the other hand
computational complexity will have to better understand each other's
worldviews.
This article, written by two complexity theorists who also work in
computational social choice theory, focuses on one direction of that process by
presenting a brief overview of how most computational complexity theorists view
the world. Although our immediate motivation is to make the lens through which
complexity theorists see the world be better understood by those in the social
sciences, we also feel that even within computer science it is very important
for nontheoreticians to understand how theoreticians think, just as it is
equally important within computer science for theoreticians to understand how
nontheoreticians think
A perspective on the landscape problem
I discuss the historical roots of the landscape problem and propose criteria
for its successful resolution. This provides a perspective to evaluate the
possibility to solve it in several of the speculative cosmological scenarios
under study including eternal inflation, cosmological natural selection and
cyclic cosmologies.Comment: Invited contribution for a special issue of Foundations of Physics
titled: Forty Years Of String Theory: Reflecting On the Foundations. 31
pages, no figure
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