An Exploration of the Role of Principal Inertia Components in Information Theory

The principal inertia components of the joint distribution of two random variables $X$ and $Y$ are inherently connected to how an observation of $Y$ is statistically related to a hidden variable $X$. 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 $X$, namely $f(X)$, given an observation of $Y$. In particular, the principal inertia components bear an interpretation as filter coefficients in the linear transformation of $p_{f(X)|X}$ into $p_{f(X)|Y}$. This interpretation naturally leads to the conjecture that the mutual information between $f(X)$ and $Y$ 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 $B\rightarrow X\rightarrow Y\rightarrow \widehat{B}$, where $B$ and $\widehat{B}$ are binary random variables. We illustrate our results for the setting where $X$ and $Y$ are binary strings and $Y$ is the result of sending $X$ 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 120^{120}Sn and 208^{208}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 $^{120}$Sn and $^{208}$Pb, and are compared with recent experimental data. Differences observed in the behavior of the full-width-at-half-maximum of the GDR for $^{120}$Sn and $^{208}$Pb are attributed to the fact that shell corrections in $^{208}$Pb are stronger than in $^{120}$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 $^{120}$Sn exhibits effects due to the evaporation width of the compound nucleus, while these effects are predicted for $^{208}$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 $\pm$ 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 $\times$ 1.95 km) $\pm$10$\%$, respectively, and the direction of the +$z$ axis is estimated to be (250$\pm$5$^\circ$, 63$\pm$5$^\circ$) 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