34,839 research outputs found
An Exploration of the Role of Principal Inertia Components in Information Theory
The principal inertia components of the joint distribution of two random
variables and are inherently connected to how an observation of is
statistically related to a hidden variable . In this paper, we explore this
connection within an information theoretic framework. We show that, under
certain symmetry conditions, the principal inertia components play an important
role in estimating one-bit functions of , namely , given an
observation of . In particular, the principal inertia components bear an
interpretation as filter coefficients in the linear transformation of
into . This interpretation naturally leads to the
conjecture that the mutual information between and is maximized when
all the principal inertia components have equal value. We also study the role
of the principal inertia components in the Markov chain , where and are binary
random variables. We illustrate our results for the setting where and
are binary strings and is the result of sending through an additive
noise binary channel.Comment: Submitted to the 2014 IEEE Information Theory Workshop (ITW
Relaxation of Wobbling Asteroids and Comets. Theoretical Problems. Perspectives of Experimental Observation
A body dissipates energy when it freely rotates about any axis different from
principal. This entails relaxation, i.e., decrease of the rotational energy,
with the angular momentum preserved. The spin about the major-inertia axis
corresponds to the minimal kinetic energy, for a fixed angular momentum. Thence
one may expect comets and asteroids (as well as spacecraft or cosmic-dust
granules) stay in this, so-called principal, state of rotation, unless they are
forced out of this state by a collision, or a tidal interaction, or cometary
jetting, or by whatever other reason. As is well known, comet P/Halley,
asteroid 4179 Toutatis, and some other small bodies exhibit very complex
rotational motions attributed to these objects being in non-principal states of
spin. Most probably, the asteroid and cometary wobble is quite a generic
phenomenon. The theory of wobble with internal dissipation has not been fully
developed as yet. In this article we demonstrate that in some spin states the
effectiveness of the inelastic-dissipation process is several orders of
magnitude higher than believed previously, and can be measured, by the
presently available observational instruments, within approximately a year
span. We also show that in some other spin states both the precession and
precession-relaxation processes slow down considerably. (We call it
near-separatrix lingering effect.) Such spin states may evolve so slowly that
they can mimic the principal-rotation state.Comment: 2 figure
Giant dipole resonance with exact treatment of thermal fluctuations
The shape fluctuations due to thermal effects in the giant dipole resonance
(GDR) observables are calculated using the exact free energies evaluated at
fixed spin and temperature. The results obtained are compared with Landau
theory calculations done by parameterizing the free energy. The Landau theory
is found to be insufficient when the shell effects are dominating.Comment: 5 pages, 2 figure
Behavior of the giant-dipole resonance in Sn and Pb at high excitation energ
The properties of the giant-dipole resonance (GDR) are calculated as a
function of excitation energy, angular momentum, and the compound nucleus
particle decay width in the nuclei Sn and Pb, and are compared
with recent experimental data. Differences observed in the behavior of the
full-width-at-half-maximum of the GDR for Sn and Pb are
attributed to the fact that shell corrections in Pb are stronger than
in Sn, and favor the spherical shape at low temperatures. The effects
shell corrections have on both the free energy and the moments of inertia are
discussed in detail. At high temperature, the FWHM in Sn exhibits
effects due to the evaporation width of the compound nucleus, while these
effects are predicted for Pb.Comment: 28 pages in RevTeX plus eight postscript figures. Submitted to Nucl.
Phys.
Enhanced flight performance by genetic manipulation of wing shape in Drosophila
Insect wing shapes are remarkably diverse and the combination of shape and kinematics determines both aerial capabilities and power requirements. However, the contribution of any specific morphological feature to performance is not known. Using targeted RNA interference to modify wing shape far beyond the natural variation found within the population of a single species, we show a direct effect on flight performance that can be explained by physical modelling of the novel wing geometry. Our data show that altering the expression of a single gene can significantly enhance aerial agility and that the Drosophila wing shape is not, therefore, optimized for certain flight performance characteristics that are known to be important. Our technique points in a new direction for experiments on the evolution of performance specialities in animals
Analysis of a data matrix and a graph: Metagenomic data and the phylogenetic tree
In biological experiments researchers often have information in the form of a
graph that supplements observed numerical data. Incorporating the knowledge
contained in these graphs into an analysis of the numerical data is an
important and nontrivial task. We look at the example of metagenomic
data---data from a genomic survey of the abundance of different species of
bacteria in a sample. Here, the graph of interest is a phylogenetic tree
depicting the interspecies relationships among the bacteria species. We
illustrate that analysis of the data in a nonstandard inner-product space
effectively uses this additional graphical information and produces more
meaningful results.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS402 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Applicability of shape parameterizations for giant dipole resonance in warm and rapidly rotating nuclei
We investigate how well the shape parameterizations are applicable for
studying the giant dipole resonance (GDR) in nuclei, in the low temperature
and/or high spin regime. The shape fluctuations due to thermal effects in the
GDR observables are calculated using the actual free energies evaluated at
fixed spin and temperature. The results obtained are compared with Landau
theory calculations done by parameterizing the free energy. We exemplify that
the Landau theory could be inadequate where shell effects are dominating. This
discrepancy at low temperatures and high spins are well reflected in GDR
observables and hence insists on exact calculations in such cases.Comment: 10 pages, 2 figure
The Ginger-shaped Asteroid 4179 Toutatis: New Observations from a Successful Flyby of Chang'e-2
On 13 December 2012, Chang'e-2 conducted a successful flyby of the near-Earth
asteroid 4179 Toutatis at a closest distance of 770 120 meters from the
asteroid's surface. The highest-resolution image, with a resolution of better
than 3 meters, reveals new discoveries on the asteroid, e.g., a giant basin at
the big end, a sharply perpendicular silhouette near the neck region, and
direct evidence of boulders and regolith, which suggests that Toutatis may bear
a rubble-pile structure. Toutatis' maximum physical length and width are (4.75
1.95 km) 10, respectively, and the direction of the + axis
is estimated to be (2505, 635) with respect to the
J2000 ecliptic coordinate system. The bifurcated configuration is indicative of
a contact binary origin for Toutatis, which is composed of two lobes (head and
body). Chang'e-2 observations have significantly improved our understanding of
the characteristics, formation, and evolution of asteroids in general.Comment: 21 pages, 3 figures, 1 tabl
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