Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators

We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the phase difference between oscillators for weak noise intensity. We demonstrate that in addition to synchronization, clustering, or more generally coherence, always results from arbitrary initial conditions, irrespective of the details of the oscillators.Comment: 6 pages, 2 figure

Abnormal prothrombin (DES-y-Carboxy Prothrombin) in hepatocellular carcinoma

Des-γ-carboxy prothrombin (DCP), a protein induced by vitamin K absence or antagonist-II (PIVKA-II) was measured by an enzyme immunoassay (E-1023) using anti-DCP monoclonal antibody in 92 patients with various hepatobiliary diseases. Thirty-six of the 38 patients (94.7%) with hepatocellular carcinoma (HCC) had abnormal DCP levels greater than 0.1 arbitrary unit (AU)/ml, but only 18 of the 35 patients (51.4%) had AFP greater than 100 ng/ml (suspicious levels for HCC). There was no correlation between plasma or serum DCP and serum alpha-fetoprotein (AFP) levels. Serum alpha fetoprotein was elevated (above 20 ng/ml) in 23 of the 35 patients (65.7%), and DCP was elevated in all of the remaining 12 patients with normal AFP. DCP levels returned to normal levels following curative hepatic resection or orthotopic liver transplantation for HCC. DCP is a useful tumor marker in the diagnosis and postoperative monitoring of patients with HCC

A Comparison of the Gingival Health of Children with Down Syndrome to Healthy Children Residing in an Institution

The purpose of this study was to compare the onset and severity of gingivitis in children with Down syndrome, when compared to a healthy control group of children. The subjects included 41 children with Down syndrome ages two to 14 years (mean age: 7.6 years) and 112 age-matched healthy controls. We assessed the gingival health of all subjects using the gingival inflammation (M-PMA) index and periodontal probing depth (PD). Children were divided into three age categories: <5 years (AD, 5 to <10 years (AID, and 10 to <17 years (AIII). Supragingival plaque was measured using the Oral Hygiene Index (OHI) and the subjects were screened with the BANA test (Perioscan-Oral-B). Measurement of the M-PMA index in the healthy children showed an age-related increase (F = 10.369. p<0.001), and the M-PMA index at the younger age group <5 year (AD was significantly lower than that for the other two age groups AII or AIII (p<0.005, p<0.001). In contrast, the M-PMA index values at AI and AIII in the subjects with Down syndrome were significantly higher than those for healthy children (p<0.001, p<0.001). Both groups had an age-related increase in PD (F=3.388, p<0.05 & F= 10.806, p<0.001). and PD at AIII was significantly higher than that at AI in both groups (p<0.01, p<0.001). The children with Down syndrome showed an age-related increase in the BANA test score (F=3.452, p<0.05), and the BANA test score at AIII was significantly higher than that at AI (p<0.02). The BANA test score in the healthy children was not age-related but was significantly higher than that in the children with Down syndrome (p<0.02, p<0.05).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72264/1/j.1754-4505.2006.tb01504.x.pd

Independent Component Analysis of Spatiotemporal Chaos

Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude patterns, ICA extracts localized one-humped basis vectors that reflect the characteristic hole structures of the system, and for nonlocally coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns, ICA extracts localized basis vectors with characteristic gap structures. Statistics of the decomposed signals also provide insight into the complex dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.

Gravitational Mass in Asymptotically de Sitter Space-Times with Compactified Dimensions

We define gravitational mass in asymptotically de Sitter space-times with compactified dimension. It was shown that the mass can be negative for space-time with matter spreading beyond the cosmological horizon scale or large outward `momentum' in four dimension. We give simple examples with negative energy in higher dimensions even if the matter is not beyond horizon or system does not have large `momentum'. They do not have the lower bound on the mass. We also give a positive energy argument in higher dimensions and realise that elementary fermion cannot exist in our examples.Comment: 7 pages, the version to be published in Phys. Rev.

Collective dynamical response of coupled oscillators with any network structure

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is also developed. General formulae for the collective phase sensitivity and the effective phase coupling between the oscillator networks are found. Our theory is applicable to a wide variety of oscillator networks undergoing frequency synchronization. Any network structure can systematically be treated. A few examples are given to illustrate our theory.Comment: 4 pages, 2 figure

Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase difference from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example

Synchronization of uncoupled oscillators by common gamma impulses: from phase locking to noise-induced synchronization

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by Poisson random impulses, but their difference has not been fully quantified. Here we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between regular periodic and random Poisson impulses. Their dynamics are charac- terized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.Comment: 18 page

Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise

A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment