Flexible and robust networks

We consider networks with two types of nodes. The v-nodes, called centers, are hyper- connected and interact one to another via many u-nodes, called satellites. This central- ized architecture, widespread in gene networks, possesses two fundamental properties. Namely, this organization creates feedback loops that are capable to generate practically any prescribed patterning dynamics, chaotic or periodic, or having a number of equilib- rium states. Moreover, this organization is robust with respect to random perturbations of the system.Comment: Journal of Bioinformatics and Computational Biology, in pres

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.Comment: 17 pages, 2 figures, 3 tables; a version accepted for publication in J. Phys. A: Math. Gen.; Sect. 2 and sect. 5 (old sect. 4) are modified. Sect. 4, Tables 1 and Table 3 are adde

Toroidal Soliton Solutions in O(3)^N Nonlinear Sigma Model

A set of N three component unit scalar fields in (3+1) Minkowski space-time is investigated. The highly nonlinear coupling between them is chosen to omit the scaling instabilities. The multi-soliton static configurations with arbitrary Hopf numbers are found. Moreover, the generalized version of the Vakulenko-Kapitansky inequality is obtained. The possibility of attractive, repulsing and noninteracting channels is discussed.Comment: to be published in Mod. Phys. Lett.

Soliton in Gravitating Gas. Hoag's Object

We explore the possibility of creating of solitons in gravitating gas. It is shown that the virial arguments does not put an obstacle for the existence of localized static solutions. The simplest toroidal soliton of gravitating gas could be the explanation of the peculiar galaxy named Hoag's object.Comment: 14 pages, 1 Figur

Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers

In this paper we construct explicitly an infinite number of Hopfions (static, soliton solutions with non-zero Hopf topological charges) within the recently proposed 3+1-dimensional, integrable and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are constructed explicitly in terms of the toroidal coordinates and shown to have a form of linked closed vortices.Comment: LaTeX, 7 pg

The influence of environmental forcing on biodiversity and extinction in a resource competition model

In this paper, we study a model of many species that compete, directly or indirectly, for a pool of common resources under the influence of periodic, stochastic, and/or chaotic environmental forcing. Using numerical simulations, we find the number and sequence of species going extinct when the community is initially packed with a large number of species of random initial densities. Thereby, any species with a density below a given threshold is regarded to be extinct