Scaling properties in dynamics of non-analytic complex maps near the accumulation point of the period-tripling cascade

The accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett. A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps, not necessary satisfying the Cauchy - Riemann equations, the scaling properties associated with the period-tripling are governed by two relevant universal complex constants. The first one is $\delta_1 = 4.6002-8.9812i$ (in accordance with the mentioned works), while the other one, responsible for the violation of the analyticity, is found to be $\delta_2 = 2.5872+1.8067i$. It means that in the extended parameter space the critical behaviour associated with the period-tripling cascade is a phenomenon of codimension four. Scaling properties of the parameter space are illustrated by diagrams in special local coordinates. We emphasize a necessity for a nonlinear parameter change to observe the parameter space scaling.Comment: 22 pages, 3 figures, 4 table

Period tripling accumulation point for complexified Henon map

Accumulation point of period-tripling bifurcations for complexified Henon map is found. Universal scaling properties of parameter space and Fourier spectrum intrinsic to this critical point is demonstrated.Comment: 5 pages, 2 figure

Constraining heavy decaying dark matter with the high energy gamma-ray limits

We consider decaying dark matter with masses $10^{7} \lesssim M \lesssim 10^{16}$ GeV, as a source of ultra-high energy (UHE) gamma rays. Using recent limits on UHE gamma-ray flux for energies $E_\gamma > 2 \cdot 10^{14}$ eV, provided by extensive air shower observatories, we put limits on masses and lifetimes of the dark matter. We also discuss possible dark matter decay origin of tentative 100 PeV photon flux detected with EAS-MSU experiment.Comment: Journal version, to appear in PRD, 12 pages, 5 figure

On possibility of realization of the phenomena of complex analytic dynamics in physical systems. Novel mechanism of the synchronization loss in coupled period-doubling systems

The possibility of realization of the phenomena of complex analytic dynamics for the realistic physical models are investigated. Observation of the Mandelbrot and Julia sets in the parameter and phase spaces both for the discrete maps and non-autonomous continuous systems is carried out. For these purposes, the method, based on consideration of coupled systems, demonstrating period-doubling cascade is suggested. Novel mechanism of synchronization loss in coupled systems corresponded to the dynamical behavior intrinsic to the complex analytic maps is offered.Comment: 14 pages, 9 figure

Concept-based Recommendations for Internet Advertisement

The problem of detecting terms that can be interesting to the advertiser is considered. If a company has already bought some advertising terms which describe certain services, it is reasonable to find out the terms bought by competing companies. A part of them can be recommended as future advertising terms to the company. The goal of this work is to propose better interpretable recommendations based on FCA and association rules.Comment: D.I.Ignatov, S.O. Kuznetsov. Concept-based Recommendations for Internet Advertisement//In proceedings of The Sixth International Conference Concept Lattices and Their Applications (CLA'08), Olomouc, Czech Republic, 2008 ISBN 978-80-244-2111-

On possibility of realization of the Mandelbrot set in coupled continuous systems

According to the method, suggested in our previous work (nlin/0509012) and based on the consideration of the specially coupled systems, the possibility of physical realization of the phenomena of complex analytic dynamics (such as Mandelbrot and Julia sets) is discussed. It is shown, that unlike the case of discrete maps or differential systems with periodic driving, investigated in mentioned work, there are some difficulties in attempts to obtain the Mandelbrot set for the coupled autonomous continuous systems. A system of coupled autonomous R\"{o}ssler oscillators is considered as an example.Comment: 18 pages, 16 picture

Dualization in Lattices Given by Ordered Sets of Irreducibles

Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and join irreducibles (i.e., as a concept lattice of a formal context). We show that in this case dualization is equivalent to the enumeration of so-called minimal hypotheses. In contrast to usual dualization setting, where a lattice is given by the ordered set of its elements, dualization in this case is shown to be impossible in output polynomial time unless P = NP. However, if the lattice is distributive, dualization is shown to be possible in subexponential time

Concept Stability for Constructing Taxonomies of Web-site Users

Owners of a web-site are often interested in analysis of groups of users of their site. Information on these groups can help optimizing the structure and contents of the site. In this paper we use an approach based on formal concepts for constructing taxonomies of user groups. For decreasing the huge amount of concepts that arise in applications, we employ stability index of a concept, which describes how a group given by a concept extent differs from other such groups. We analyze resulting taxonomies of user groups for three target websites.Comment: Sergei O. Kuznetsov, D.I. Ignatov, Concept Stability for Constructing Taxonomies of Web-site users, in Proc. Social Network Analysis and Conceptual Structures: Exploring Opportunities, S. Obiedkov, C. Roth (Eds.), Clermont-Ferrand (France), February 16, 200

Heavy decaying dark matter and large-scale anisotropy of high-energy cosmic rays

We examine the role of the large--scale anisotropy of the high--energy cosmic ray distribution in a search for the heavy decaying dark matter (DM) signal. Using recent anisotropy measurements from the extensive air shower (EAS) observatories we constrain the lifetime of the DM particles with masses $10^{7}~\leq~M_X~\leq~10^{16}$ GeV. These constraints appear to be weaker than that obtained with the high energy gamma-ray limits. We also estimate the desired precision level for the anisotropy measurements to discern the decaying DM signal marginally allowed by the gamma-ray limits and discuss the prospects of the DM search with the modern EAS facilities.Comment: matches the journal version, 19 pages, 5 figure

Subquandles of free quandles

We prove that a subquandle of a free quandle is free