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

Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator subjected to weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise.Comment: 16 pages, 6 figure

Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators

We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven synchronizing state. The result shows that such a synchronization can be achieved in a broad class of oscillators with little constraint on their intrinsic property. On the other hand, the leaky integrate-and-fire neuron oscillators do not belong to this class, generating intermittent phase slips according to a power low distribution of their intervals.Comment: 10 pages, 3 figure

Appetite suppressants and valvular heart disease - a systematic review

Background Although appetite suppressants have been implicated in the development of valvular heart disease, the exact level of risk is still uncertain. Initial studies suggested that as many as 1 in 3 exposed patients were affected, but subsequent research has yielded substantially different figures. Our objective was to systematically assess the risk of valvular heart disease with appetite suppressants. Methods We accepted studies involving obese patients treated with any of the following appetite suppressants: fenfluramine, dexfenfluramine, and phentermine. Three types of studies were reviewed: controlled and uncontrolled observational studies, and randomized controlled trials. Outcomes of interest were echocardiographically detectable aortic regurgitation of mild or greater severity, or mitral regurgitation of moderate or greater severity. Results Of the 1279 patients evaluated in seven uncontrolled cohort studies, 236 (18%) and 60 (5%) were found to have aortic and mitral regurgitation, respectively. Pooled data from six controlled cohort studies yielded, for aortic regurgitation, a relative risk ratio of 2.32 (95% confidence intervals 1.79 to 3.01, p < 0.00001) and an attributable rate of 4.9%, and for mitral regurgitation, a relative risk ratio of 1.55 (95% confidence intervals 1.06 to 2.25, p = 0.02) with an attributable rate of 1.0%. Only one case of valvular heart disease was detected in 57 randomized controlled trials, but this was judged unrelated to drug therapy. Conclusions The risk of valvular heart disease is significantly increased by the appetite suppressants reviewed here. Nevertheless, when considering all the evidence, valvulopathy is much less common than suggested by the initial, less methodologically rigorous studies

Ab initio many-body calculations on infinite carbon and boron-nitrogen chains

In this paper we report first-principles calculations on the ground-state electronic structure of two infinite one-dimensional systems: (a) a chain of carbon atoms and (b) a chain of alternating boron and nitrogen atoms. Meanfield results were obtained using the restricted Hartree-Fock approach, while the many-body effects were taken into account by second-order M{\o}ller-Plesset perturbation theory and the coupled-cluster approach. The calculations were performed using 6-31$G^{**}$ basis sets, including the d-type polarization functions. Both at the Hartree-Fock (HF) and the correlated levels we find that the infinite carbon chain exhibits bond alternation with alternating single and triple bonds, while the boron-nitrogen chain exhibits equidistant bonds. In addition, we also performed density-functional-theory-based local density approximation (LDA) calculations on the infinite carbon chain using the same basis set. Our LDA results, in contradiction to our HF and correlated results, predict a very small bond alternation. Based upon our LDA results for the carbon chain, which are in agreement with an earlier LDA calculation calculation [ E.J. Bylaska, J.H. Weare, and R. Kawai, Phys. Rev. B 58, R7488 (1998).], we conclude that the LDA significantly underestimates Peierls distortion. This emphasizes that the inclusion of many-particle effects is very important for the correct description of Peierls distortion in one-dimensional systems.Comment: 3 figures (included). To appear in Phys. Rev.

Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise

We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.Comment: 10 pages, 5 figure

A Measurement of the D∗±D^{*\pm} Cross Section in Two-Photon Processes

We have measured the inclusive $D^{*\pm}$ production cross section in a two-photon collision at the TRISTAN $e^+e^-$ collider. The mean $\sqrt{s}$ of the collider was 57.16 GeV and the integrated luminosity was 150 $pb^{-1}$. The differential cross section ($d\sigma(D^{*\pm})/dP_T$) was obtained in the $P_T$ range between 1.6 and 6.6 GeV and compared with theoretical predictions, such as those involving direct and resolved photon processes.Comment: 8 pages, Latex format (article), figures corrected, published in Phys. Rev. D 50 (1994) 187

Finite-size and correlation-induced effects in Mean-field Dynamics

The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon two recent approaches that include correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We introduce a new model, the infinite model, which arises from both equations by a rescaling of the variables and, which is invertible for finite-size networks, and hence, provides equivalent equations to those previously derived models. The study of this model allows us to understand qualitative behavior of such large-scale networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field. The origin of all these behaviors is then explored in finite-size networks where interesting mesoscopic scale effects appear. This study leads us to show that the infinite-size system appears as a singular limit of the network equations, and for any finite network, the system will differ from the infinite system

Emergent complex neural dynamics

A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain's hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain

Risk of valvular heart disease associated with use of fenfluramine

BACKGROUND: Estimates of excess risk of valvular heart disease among prior users of fenfluramine and dexfenfluramine have varied widely. Two major forms of bias appear to contribute to this variability and also result in a systematic under-estimation of risk. The first, a form of nondifferential misclassification, is the result of including background, prevalent cases among both exposed and unexposed persons in calculations of risk. The second bias results from not considering the relatively short duration of exposure to drugs. METHODS: We examined data from all available echocardiographic studies reporting the prevalence of aortic regurgitation (AR) and mitral regurgitation (MR) among persons exposed to fenfluramine or dexfenfluramine and a suitable control group. We also included one study in which previously existing AR or MR had been excluded. We corrected for background prevalent cases, estimated incidence rates in unexposed persons, and performed a person-years analysis of apparent incidence rates based on exposure time to provide an unbiased estimate of relative risk. RESULTS: Appearance of new AR was strongly related to duration of exposure (R(2 )= 0.75, p < 0.0001). The summary relative risk for mild or greater AR was 19.6 (95% CI 16.3 – 23.5, p < 0.00001); for moderate or greater MR it was 5.9 (95% CI 4.0 – 8.6, p < 0.00001). CONCLUSION: These findings provide strong support for the view that fenfluramine and dexfenfluramine are potent causal factors in the development of both aortic and mitral valvular heart disease