On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures

Periodicities in Solar Coronal Mass Ejections

Mid-term quasi-periodicities in solar coronal mass ejections (CMEs) during the most recent solar maximum cycle 23 are reported here for the first time using the four-year data (February 5, 1999 to February 10, 2003) of the Large Angle Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric Observatory (SOHO). In parallel, mid-term quasi-periodicities in solar X-ray flares (class >M5.0) from the Geosynchronous Operational Environment Satellites (GOES) and in daily averages of Ap index for geomagnetic disturbances from the World Data Center (WDC) at the International Association for Geomagnetism and Aeronomy (IAGA) are also examined for the same four-year time span. Several conceptual aspects of possible equatorially trapped Rossby-type waves at and beneath the solar photosphere are discussed.Comment: Accepted by MNRAS, 6 figure

Localization of tyrosine kinase-coding region in v-abl oncogene by the expression of v-abl-encoded proteins in bacteria

A series of plasmids containing different segments of the v-abl oncogene have been constructed to express different portions of the v- abl protein in bacteria. The tyrosine kinase activity of these proteins was determined by an in vitro assay employing histones or angiotensin II as substrates for the v-abl-encoded tyrosine kinase. These experiments show that the 5'-1.2 kilobases of v-abl is necessary and sufficient to produce an active tyrosine kinase which is functional as a monomeric soluble protein. The kinase-coding region corresponds to the minimal region of v-abl required for the transformation of fibroblasts. The kinase-coding region also coincides with the conserved protein sequences which are found in other tyrosine kinases. A compact domain of the v-abl protein including this kinase-coding region can accumulate to high levels in bacteria. The C-terminal region of the v- abl protein is not needed for the kinase activity and is rapidly degraded in bacteria

Synchronization in an array of linearly stochastically coupled networks with time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2007 Elsevier LtdIn this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.This work was jointly supported by the National Natural Science Foundation of China under Grant 60574043, the Royal Society of the United Kingdom, the Natural Science Foundation of Jiangsu Province of China under Grant BK2006093, and International Joint Project funded by NSFC and the Royal Society of the United Kingdom

Ising-model description of the SU(2)_1 quantum critical point in a dimerized two-leg spin-1/2 ladder

A nonperturbative analytical description of the SU(2)_1 quantum critical point in an explicitly dimerized two-leg spin-1/2 Heisenberg ladder is presented. It is shown that this criticality essentially coincides with that emerging in a weakly dimerized spin-1 chain with a small Haldane gap. The approach is based on the mapping onto an SO(3)-symmetric model of three strongly coupled quantum Ising chains. This mapping is used to establish the correspondence between all physical fields of the spin ladder and those characterizing the SU(2)_1 criticality at the infrared fixed point.Comment: 22 page

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

Environmental Dependence of Cold Dark Matter Halo Formation

We use a high-resolution $N$-body simulation to study how the formation of cold dark matter (CDM) halos is affected by their environments, and how such environmental effects produce the age-dependence of halo clustering observed in recent $N$-body simulations. We estimate, for each halo selected at redshift $z=0$, an `initial' mass $M_{\rm i}$ defined to be the mass enclosed by the largest sphere which contains the initial barycenter of the halo particles and within which the mean linear density is equal to the critical value for spherical collapse at $z=0$. For halos of a given final mass, $M_{\rm h}$, the ratio $M_{\rm i}/M_{\rm h}$ has large scatter, and the scatter is larger for halos of lower final masses. Halos that form earlier on average have larger $M_{\rm i}/M_{\rm h}$, and so correspond to higher peaks in the initial density field than their final masses imply. Old halos are more strongly clustered than younger ones of the same mass because their initial masses are larger. The age-dependence of clustering for low-mass halos is entirely due to the difference in the initial/final mass ratio. Low-mass old halos are almost always located in the vicinity of big structures, and their old ages are largely due to the fact that their mass accretions are suppressed by the hot environments produced by the tidal fields of the larger structure. The age-dependence of clustering is weaker for more massive halos because the heating by large-scale tidal fields is less important.Comment: 18 pages,19 figures, accepted by MNRA