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

A topological interpretation of the walk distances

The walk distances in graphs have no direct interpretation in terms of walk weights, since they are introduced via the \emph{logarithms} of walk weights. Only in the limiting cases where the logarithms vanish such representations follow straightforwardly. The interpretation proposed in this paper rests on the identity \ln\det B=\tr\ln B applied to the cofactors of the matrix $I-tA,$ where $A$ is the weighted adjacency matrix of a weighted multigraph and $t$ is a sufficiently small positive parameter. In addition, this interpretation is based on the power series expansion of the logarithm of a matrix. Kasteleyn (1967) was probably the first to apply the foregoing approach to expanding the determinant of $I-A$. We show that using a certain linear transformation the same approach can be extended to the cofactors of $I-tA,$ which provides a topological interpretation of the walk distances.Comment: 13 pages, 1 figure. Version #

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

Influence of environment factors on the morbidity rate with temporary disability of working in oil refinery workers

There was performed a comprehensive assessment of working conditions of refinery workers on the results of the carrying out of certification of workplaces on working conditions. An analysis of the sample materials laboratory control over the content of harmful substances in the working area of industrial premises refinery. The prolonged exposure to harmful factors on the health of workers of the main production throughout the length of service was established to be a major risk factor for the development of somatic and malignant diseases, to the gain in the morbidity rate and can become a cause of the emergency of malignancies