Do logarithmic proximity measures outperform plain ones in graph clustering?

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.Comment: 11 pages, 5 tables, 9 figures. Accepted for publication in the Proceedings of 6th International Conference on Network Analysis, May 26-28, 2016, Nizhny Novgorod, Russi

Structural peculiarities of the Quadrantid meteor shower

Systematic radio observations to investigate the Quadrantid meteor shower structure are regularly carried out. They have now been conducted annually in the period of its maximum activity, January 1 to 6, since 1966. The latest results of these investigations are presented, on the basis of 1981 to 1984 data obtained using new equipment with a limiting sensitivity of +7.7 sup m which make it possible to draw some conclusions on the Quadrantids shower structure both for transverse and lengthwise directions

Analysis of Collectivism and Egoism Phenomena within the Context of Social Welfare

Comparative benefits provided by the basic social strategies including collectivism and egoism are investigated within the framework of democratic decision-making. In particular, we study the mechanism of growing "snowball" of cooperation.Comment: 12 pages, 5 figures. Translated from Russian. Original Russian Text published in Problemy Upravleniya, 2008, No. 4, pp. 30-3

Planetary Trojans - the main source of short period comets?

We present a short review of the impact regime experienced by the terrestrial planets within our own Solar system, describing the three populations of potentially hazardous objects which move on orbits that take them through the inner Solar system. Of these populations, the origins of two (the Near-Earth Asteroids and the Long-Period Comets) are well understood, with members originating in the Asteroid belt and Oort cloud, respectively. By contrast, the source of the third population, the Short-Period Comets, is still under debate. The proximate source of these objects is the Centaurs, a population of dynamically unstable objects that pass perihelion between the orbits of Jupiter and Neptune. However, a variety of different origins have been suggested for the Centaur population. Here, we present evidence that at least a significant fraction of the Centaur population can be sourced from the planetary Trojan clouds, stable reservoirs of objects moving in 1:1 mean-motion resonance with the giant planets (primarily Jupiter and Neptune). Focusing on simulations of the Neptunian Trojan population, we show that an ongoing flux of objects should be leaving that region to move on orbits within the Centaur population. With conservative estimates of the flux from the Neptunian Trojan clouds, we show that their contribution to that population could be of order ~3%, while more realistic estimates suggest that the Neptune Trojans could even be the main source of fresh Centaurs. We suggest that further observational work is needed to constrain the contribution made by the Neptune Trojans to the ongoing flux of material to the inner Solar system, and believe that future studies of the habitability of exoplanetary systems should take care not to neglect the contribution of resonant objects (such as planetary Trojans) to the impact flux that could be experienced by potentially habitable worlds.Comment: 16 pages, 4 figures, published in the International Journal of Astrobiology (the arXiv.org's abstract was shortened, but the original one can be found in the manuscript file

Quantum scattering in one dimension

A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concept of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.Comment: 8 page

Origin and Dynamical Evolution of Neptune Trojans - I: Formation and Planetary Migration

We present the results of detailed dynamical simulations of the effect of the migration of the four giant planets on both the transport of pre-formed Neptune Trojans, and the capture of new Trojans from a trans-Neptunian disk. We find that scenarios involving the slow migration of Neptune over a large distance (50Myr to migrate from 18.1AU to its current location) provide the best match to the properties of the known Trojans. Scenarios with faster migration (5Myr), and those in which Neptune migrates from 23.1AU to its current location, fail to adequately reproduce the current day Trojan population. Scenarios which avoid disruptive perturbation events between Uranus and Neptune fail to yield any significant excitation of pre-formed Trojans (transported with efficiencies between 30 and 98% whilst maintaining the dynamically cold nature of these objects). Conversely, scenarios with periods of strong Uranus-Neptune perturbation lead to the almost complete loss of such pre-formed objects. In these cases, a small fraction (~0.15%) of these escaped objects are later recaptured as Trojans prior to the end of migration, with a wide range of eccentricities (<0.35) and inclinations (<40 deg). In all scenarios (including those with such disruptive interaction between Uranus and Neptune) the capture of objects from the trans-Neptunian disk (through which Neptune migrates) is achieved with efficiencies between ~0.1 and ~1%. The captured Trojans display a wide range of inclinations (<40 deg for slow migration, and <20 deg for rapid migration) and eccentricities (<0.35), and we conclude that, given the vast amount of material which undoubtedly formed beyond the orbit of Neptune, such captured objects may be sufficient to explain the entire Neptune Trojan population. (Shortened version)Comment: 25 pages, 6 figure

Non-equilibrium states of a photon cavity pumped by an atomic beam

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.Comment: Corrected energy production calculations and made some changes to ease the readin