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

Solitons, Links and Knots

Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for solitons up to charge five the solutions have the structure of closed strings, which become increasingly twisted as the charge increases. However, for higher charge the solutions are more exotic and comprise linked loops and knots. We discuss the structure and formation of these solitons and demonstrate that the key property responsible for producing such a rich variety of solitons is that of string reconnection.Comment: 24 pages plus 14 figures in GIF forma

Non-Meissner electrodynamics and knotted solitons in two-component superconductors

I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in these systems remains an outstandingly difficult question both for analytical and numerical treatment. Here I propose a new perturbative approach to treat self-consistently all the degrees of freedom in the problem. I show that there exists a length scale for a Hopfion texture where the electrodynamics of a two-component superconductor is dominated by a self-induced Faddeev term, which is a stark contrast to the Meissner electrodynamics of single-component systems. I also show that at certain short length scales knotted solitons in two-component Ginzburg-Landau model are not described by a Faddeev-Skyrme-type model and are unstable. However these solitons can be stable at some intermediate length scales. I argue that configurations with a high topological charge may be more stable in this system than low-topological-charge configurations. In the second part of the paper I discuss qualitatively different physics of the stability of knotted solitons in a more general Ginzburg-Landau model and point out the physically relevant terms which enhance or suppress stability of the knotted solitons. With this argument it is demonstrated that the generalized Ginburg-Landau model possesses stable knotted solitons.Comment: In print in Phys. Rev. B. v2: a typo (missing factor) fixed. v3: discussion of some aspects made more detailed following a referee reques

Knot Solitons

The existence of ring-like and knotted solitons in O(3) non-linear sigma model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen.Comment: Latex 9 pages + 2 eps figure

Hopf Soliton Solutions from Low Energy Effective Action of SU(2) Yang-Mills Theory

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes the soliton solution. In this paper we derive an extended action including second derivative terms and obtain soliton solutions numerically. A new topological lower bound formula is infered for the extended action.Comment: 18 pages, 7 figure