Blocking central opiate function modulates hedonic impact and anterior cingulate response to rewards and losses.

Reward processing is linked to specific neuromodulatory systems with a dopaminergic contribution to reward learning and motivational drive being well established. Neuromodulatory influences on hedonic responses to actual receipt of reward, or punishment, referred to as experienced utility are less well characterized, although a link to the endogenous opioid system is suggested. Here, in a combined functional magnetic resonance imaging-psychopharmacological investigation, we used naloxone to block central opioid function while subjects performed a gambling task associated with rewards and losses of different magnitudes, in which the mean expected value was always zero. A graded influence of naloxone on reward outcome was evident in an attenuation of pleasure ratings for larger reward outcomes, an effect mirrored in attenuation of brain activity to increasing reward magnitude in rostral anterior cingulate cortex. A more striking effect was seen for losses such that under naloxone all levels of negative outcome were rated as more unpleasant. This hedonic effect was associated with enhanced activity in anterior insula and caudal anterior cingulate cortex, areas implicated in aversive processing. Our data indicate that a central opioid system contributes to both reward and loss processing in humans and directly modulates the hedonic experience of outcomes.

Contraction of monotone phase-coupled oscillators

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state. © 2012 Elsevier B.V. All rights reserved.

Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators

In this paper, we investigate the behavior of pulse-coupled integrate-and-fire oscillators. Because the stability analysis of finite populations is intricate, we investigate stability results in the approximation of infinite populations. In addition to recovering known stability results of finite populations, we also obtain new stability results for infinite populations. In particular, under a weak coupling assumption, we solve for the continuum model a conjecture still prevailing in the finite dimensional case. © 2011 IEEE.

Clustering behaviors in networks of integrate-and-fire oscillators

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse coupling. When considering a population of identical oscillators, the main result is a proof of global convergence to a phase-locked clustered behavior. The robustness of this clustering behavior is then investigated in a population of nonidentical oscillators by studying the transition from total clustering to the absence of clustering as the group coherence decreases. A robust intermediate situation of partial clustering, characterized by few oscillators traveling among nearly phase-locked clusters, is of particular interest. The analysis complements earlier studies of synchronization in a closely related model. © 2008 American Institute of Physics.

Analysis of interconnected oscillators by dissipativity theory

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators. © 2007 IEEE.

Dissipativity characterization of a class of oscillators and networks of oscillators

This paper uses dissipativity theory to provide the system-theoretic description of a basic oscillation mechanism. Elementary input-output tools are then used to prove the existence and stability of limit cycles in these "oscillators". The main benefit of the proposed approach is that it is well suited for the analysis and design of interconnections, thus providing a valuable mathematical tool for the study of networks of coupled oscillators.

Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Observation of locked phase dynamics and enhanced frequency stability in synchronized micromechanical oscillators

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references. © 2013 American Physical Society.

Noise and stability in giant-chirp oscillators mode-locked with a nanotube-based saturable absorber

We compare experimental results showing stable dissipative-soliton solutions exist in mode-locked lasers with ultra-large normal dispersion (as large as 21.5 ps2), with both the analytic framework provided by Haus' master-equation and full numerical simulations. © 2010 Optical Society of America.