49,540 research outputs found
Discovering Evolutionary Stepping Stones through Behavior Domination
Behavior domination is proposed as a tool for understanding and harnessing
the power of evolutionary systems to discover and exploit useful stepping
stones. Novelty search has shown promise in overcoming deception by collecting
diverse stepping stones, and several algorithms have been proposed that combine
novelty with a more traditional fitness measure to refocus search and help
novelty search scale to more complex domains. However, combinations of novelty
and fitness do not necessarily preserve the stepping stone discovery that
novelty search affords. In several existing methods, competition between
solutions can lead to an unintended loss of diversity. Behavior domination
defines a class of algorithms that avoid this problem, while inheriting
theoretical guarantees from multiobjective optimization. Several existing
algorithms are shown to be in this class, and a new algorithm is introduced
based on fast non-dominated sorting. Experimental results show that this
algorithm outperforms existing approaches in domains that contain useful
stepping stones, and its advantage is sustained with scale. The conclusion is
that behavior domination can help illuminate the complex dynamics of
behavior-driven search, and can thus lead to the design of more scalable and
robust algorithms.Comment: To Appear in Proceedings of the Genetic and Evolutionary Computation
Conference (GECCO 2017
From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index
{Let be a -dimensional fractional Brownian motion
with Hurst index , or more generally a Gaussian process whose paths
have the same local regularity. Defining properly iterated integrals of is
a difficult task because of the low H\"older regularity index of its paths. Yet
rough path theory shows it is the key to the construction of a stochastic
calculus with respect to , or to solving differential equations driven by
.
We intend to show in a series of papers how to desingularize iterated
integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure
defined by a limit in law procedure. Convergence is proved by using "standard"
tools of constructive field theory, in particular cluster expansions and
renormalization. These powerful tools allow optimal estimates, and call for an
extension of Gaussian tools such as for instance the Malliavin calculus.
After a first introductory paper \cite{MagUnt1}, this one concentrates on the
details of the constructive proof of convergence for second-order iterated
integrals, also known as L\'evy area
Energy composition of the Universe: time-independent internal symmetry
The energy composition of the Universe, as emerged from the Type Ia supernova
observations and the WMAP data, looks preposterously complex, -- but only at
the first glance. In fact, its structure proves to be simple and regular. An
analysis in terms of the Friedmann integral enables to recognize a remarkably
simple time-independent covariant robust recipe of the cosmic mix: the
numerical values of the Friedmann integral for vacuum, dark matter, baryons and
radiation are approximately identical. The identity may be treated as a
symmetry relation that unifies cosmic energies into a regular set, a quartet,
with the Friedmann integral as its common genuine time-independent physical
parameter. Such cosmic internal (non-geometrical) symmetry exists whenever
cosmic energies themselves exist in nature. It is most natural for a finite
Universe suggested by the WMAP data. A link to fundamental theory may be found
under the assumption about a special significance of the electroweak energy
scale in both particle physics and cosmology. A freeze-out model developed on
this basis demonstrates that the physical nature of new symmetry might be due
to the interplay between electroweak physics and gravity at the cosmic age of a
few picoseconds. The big `hierarchy number' of particle physics represents the
interplay in the model. This number quantifies the Friedmann integral and gives
also a measure to some other basic cosmological figures and phenomena
associated with new symmetry. In this way, cosmic internal symmetry provides a
common ground for better understanding of old and recent problems that
otherwise seem unrelated; the coincidence of the observed cosmic densities, the
flatness of the co-moving space, the initial perturbations and their amplitude,
the cosmic entropy are among them.Comment: 32 page
Observational Consequences of a Landscape
In this paper we consider the implications of the "landscape" paradigm for
the large scale properties of the universe. The most direct implication of a
rich landscape is that our local universe was born in a tunnelling event from a
neighboring vacuum. This would imply that we live in an open FRW universe with
negative spatial curvature. We argue that the "overshoot" problem, which in
other settings would make it difficult to achieve slow roll inflation, actually
favors such a cosmology.
We consider anthropic bounds on the value of the curvature and on the
parameters of inflation. When supplemented by statistical arguments these
bounds suggest that the number of inflationary efolds is not very much larger
than the observed lower bound. Although not statistically favored, the
likelihood that the number of efolds is close to the bound set by observations
is not negligible. The possible signatures of such a low number of efolds are
briefly described.Comment: 21 pages, 4 figures v2: references adde
Black Hole Genesis of Dark Matter
We present a purely gravitational infra-red-calculable production mechanism
for dark matter (DM). The source of both the DM relic abundance and the hot
Standard Model (SM) plasma is a primordial density of micro black holes (BHs),
which evaporate via Hawking emission into both the dark and SM sectors. The
mechanism has four qualitatively different regimes depending upon whether the
BH evaporation is `fast' or `slow' relative to the initial Hubble rate, and
whether the mass of the DM particle is `light' or `heavy' compared to the
initial BH temperature. For each of these regimes we calculate the DM yield,
, as a function of the initial state and DM mass and spin. In the `slow'
regime depends on only the initial BH mass over a wide range of initial
conditions, including scenarios where the BHs are a small fraction of the
initial energy density. The DM is produced with a highly non-thermal energy
spectrum, leading in the `light' DM mass regime ( and
above depending on DM spin) to a strong constraint from free-streaming, but
also possible observational signatures in structure formation in the spin 3/2
and 2 cases. The `heavy' regime ( to
depending on spin) is free of these constraints and provides
new possibilities for DM detection. In all cases there is a dark radiation
component predicted.Comment: 16 pages, 8 figures. Fixed typos and added reference
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