56,995 research outputs found
Decision Making for Rapid Information Acquisition in the Reconnaissance of Random Fields
Research into several aspects of robot-enabled reconnaissance of random
fields is reported. The work has two major components: the underlying theory of
information acquisition in the exploration of unknown fields and the results of
experiments on how humans use sensor-equipped robots to perform a simulated
reconnaissance exercise.
The theoretical framework reported herein extends work on robotic exploration
that has been reported by ourselves and others. Several new figures of merit
for evaluating exploration strategies are proposed and compared. Using concepts
from differential topology and information theory, we develop the theoretical
foundation of search strategies aimed at rapid discovery of topological
features (locations of critical points and critical level sets) of a priori
unknown differentiable random fields. The theory enables study of efficient
reconnaissance strategies in which the tradeoff between speed and accuracy can
be understood. The proposed approach to rapid discovery of topological features
has led in a natural way to to the creation of parsimonious reconnaissance
routines that do not rely on any prior knowledge of the environment. The design
of topology-guided search protocols uses a mathematical framework that
quantifies the relationship between what is discovered and what remains to be
discovered. The quantification rests on an information theory inspired model
whose properties allow us to treat search as a problem in optimal information
acquisition. A central theme in this approach is that "conservative" and
"aggressive" search strategies can be precisely defined, and search decisions
regarding "exploration" vs. "exploitation" choices are informed by the rate at
which the information metric is changing.Comment: 34 pages, 20 figure
Entropy production and isotropization in Yang-Mills theory with use of quantum distribution function
We investigate thermalization process in relativistic heavy ion collisions in
terms of the Husimi-Wehrl (HW) entropy defined with the Husimi function, a
quantum distribution function in a phase space. We calculate the semiclassical
time evolution of the HW entropy in Yang-Mills field theory with the
phenomenological initial field configuration known as the McLerran-Venugopalan
model in a non-expanding geometry, which has instabilty triggered by initial
field fluctuations. HW-entropy production implies the thermalization of the
system and it reflects the underlying dynamics such as chaoticity and
instability. By comparing the production rate with the Kolmogorov-Sina\"i rate,
we find that the HW entropy production rate is significantly larger than that
expected from chaoticity. We also show that the HW entropy is finally saturated
when the system reaches a quasi-stationary state. The saturation time of the HW
entropy is comparable with that of pressure isotropization, which is around
fm/c in the present calculation in the non-expanding geometry.Comment: 17 pages, 5 figure
From Wires to Cosmology
We provide a statistical framework for characterizing stochastic particle
production in the early universe via a precise correspondence to current
conduction in wires with impurities. Our approach is particularly useful when
the microphysics is uncertain and the dynamics are complex, but only
coarse-grained information is of interest. We study scenarios with multiple
interacting fields and derive the evolution of the particle occupation numbers
from a Fokker-Planck equation. At late times, the typical occupation numbers
grow exponentially which is the analog of Anderson localization for disordered
wires. Some statistical features of the occupation numbers show hints of
universality in the limit of a large number of interactions and/or a large
number of fields. For test cases, excellent agreement is found between our
analytic results and numerical simulations.Comment: v3: minor changes and references added; matches published version in
JCA
A stroll along the gamma
We provide the first in-depth study of the "smart path" interpolation between
an arbitrary probability measure and the gamma-
distribution. We propose new explicit representation formulae for the ensuing
process as well as a new notion of relative Fisher information with a gamma
target distribution. We use these results to prove a differential and an
integrated De Bruijn identity which hold under minimal conditions, hereby
extending the classical formulae which follow from Bakry, Emery and Ledoux's
-calculus. Exploiting a specific representation of the "smart path", we
obtain a new proof of the logarithmic Sobolev inequality for the gamma law with
as well as a new type of HSI inequality linking relative
entropy, Stein discrepancy and standardized Fisher information for the gamma
law with .Comment: Typos correcte
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