Synchronization of weakly perturbed Markov chain oscillators

Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained, symbolic dynamics. In contrast to limit cycle oscillators which are weakly perturbed by noise, the stochasticity in such systems may be strong and more complicated system topologies than the circle can be considered. Here we employ second order, time dependent perturbation theory to derive expressions for the mean frequency and phase diffusion constant of discrete state oscillators coupled or driven through weakly time dependent transition rates. We also describe a method of global control to optimize the response of the mean frequency in complex transition networks.Comment: 16 pages, 7 figure

Coherence resonance in influencer networks

Complex networks are abundant in nature and many share an important structural property: they contain a few nodes that are abnormally highly connected (hubs). Some of these hubs are called influencers because they couple strongly to the network and play fundamental dynamical and structural roles. Strikingly, despite the abundance of networks with influencers, little is known about their response to stochastic forcing. Here, for oscillatory dynamics on influencer networks, we show that subjecting influencers to an optimal intensity of noise can result in enhanced network synchronization. This new network dynamical effect, which we call coherence resonance in influencer networks, emerges from a synergy between network structure and stochasticity and is highly nonlinear, vanishing when the noise is too weak or too strong. Our results reveal that the influencer backbone can sharply increase the dynamical response in complex systems of coupled oscillators.Comment: this pdf includes supplementary note

Synchronization Transition in the Kuramoto Model with Colored Noise

We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and analytically solvable cases of white noise and quenched random frequencies.Comment: 4 pages, 2 figure

Characterization of Human Endogenous Retrovirus Type K Virus-like Particles Generated from Recombinant Baculoviruses

AbstractThe family of human endogenous retrovirus type K (HERV-K) comprises members with long open reading frames (ORF) for retroviral proteins. The existence of a biologically active provirus with replicative capacities has not yet been demonstrated. To confirm the assumption that HERV-K codes for the previously observed retrovirus-like particles (human teratocarcinoma-derived virus, HTDV) in human teratocarcinoma cells, we have constructed recombinant full-length HERV-K cDNA-based baculoviruses withgag, pro, pol,andenvORFs. Two viral constructs were used for infections of insect cells, one bearing 67 bp of the 5′ untranslated region upstream of the 5′ splice donor (SD) site and of the retroviral genes, the second omitting the SD sequence. For both recombinant viruses, indirect immunofluorescence and laser scan analyses revealed expression of HERV-K Gag protein. Electron microscopy studies demonstrated efficient production of virus-like particles (VLPs) at the cytoplasmic cell membranes. These VLPs are morphologically identical with the HTDV phenotype. In immunoelectron microscopy of ultrathin frozen sections, anti-HERV-K Gag antibodies specifically reacted with HERV-K VLPs. In Western blots, in addition to the 76-kDa precursor protein, the putative major core protein with an apparent molecular mass of 32 kDa exhibited predominant immunoreactivity with anti-Gag antiserum. In contrast, neither HERV-K Env nor cORF proteins could be detected due to inefficient mRNA splicing. Purified particles from insect cell culture supernatants tested in an ultrasensitive reverse transcriptase assay revealed weak polymerase activity. The data demonstrate that HERV-K codes for retroviral particles of the HTDV phenotype

Survey of context provisioning middleware

In the scope of ubiquitous computing, one of the key issues is the awareness of context, which includes diverse aspects of the user's situation including his activities, physical surroundings, location, emotions and social relations, device and network characteristics and their interaction with each other. This contextual knowledge is typically acquired from physical, virtual or logical sensors. To overcome problems of heterogeneity and hide complexity, a significant number of middleware approaches have been proposed for systematic and coherent access to manifold context parameters. These frameworks deal particularly with context representation, context management and reasoning, i.e. deriving abstract knowledge from raw sensor data. This article surveys not only related work in these three categories but also the required evaluation principles. © 2009-2012 IEEE

Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder

The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in form of dispersion, leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second order perturbation terms. We apply the theory to simple topologies, like a line or the sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter the synchronized state may become quasi degenerate. We demonstrate how perturbation theory fails at such a critical point.Comment: 22 pages, 5 figure

Quasi regular concentric waves in heterogeneous lattices of coupled oscillators

We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one-dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.Comment: 4 pages, 3 figures, submitted to PR