On the Use of Matrix Factorization Techniques in Penalty Function Methods for Structured Linear Programs

An algorithm converging to an optimal solution of a linear program in a finite number of steps is proposed. The algorithm is based on the use of smooth penalty functions as well as on matrix factorization techniques. It consists of finding corner points of the piece-wise linear unconstrained minima trajectory. The application of the algorithm to dynamic linear programs and block-angular programs is described

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

S\mathcal{S}-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and plots edited, references and acknowledgments added; prepared for the special issue of the journal Particles in memory of G.V. Efimo

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

Communication Society and Security: Current Threats and Legal Maintenance

Over many centuries, human societies across the globe have established progressively closer contacts. Recently, the pace of globalization has dramatically increased. Unprecedented changes in communications, transportation, and computer technology have given the process new impetus and made the world more interdependent than ever. Information resources and structures have become a tool for achieving a strategic advantage. The authenticity, credibility, and an adequate reflection of information realities represent the key challenges for the communication society. Our research aims to analyze the possibilities of establishing a profound system for countering legalization of proceeds from crime (money laundering) and creating efficient barriers against cybercrimes, such as hacking of personal data. The sphere of security of online communication processes has become an objective element of our life, and it couldn’t be ignored, especially due to further development of securing biometric personal data mechanisms

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