Additive noise quenches delay-induced oscillations

Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interfere with the linear stability of scalar nonlinear systems when these are subject to time delay. We show this by performing a recently designed time-dependent delayed center manifold (DCM) reduction around an Hopf bifurcation in a model of nonlinear negative feedback. Using this, we show that noise intensity must be considered as a bifurcation parameter and thus shifts the threshold at which emerge delay-induced rhythmic solutions.Comment: pre-print submitted versio

An Empirical Analysis of Legal Insider Trading in the Netherlands

In this paper, we employ a registry of legal insider trading for Dutch listed firms to investigate the information content of trades by corporate insiders. Using a standard event-study methodology, we examine short-term stock price behavior around trades. We find that purchases are followed by economically large abnormal returns. This result is strongest for purchases by top executives and for small market capitalization firms, which is consistent with the hypothesis that legal insider trading is an important channel through which information flows to the market. We analyze also the impact of the implementation of the Market Abuse Directive (European Union Directive 2003/6/EC), which strengthens the existing regulation in the Netherlands. We show that the new regulation reduced the information content of sales by top executives.insider trading, financial market regulation

The Bootstrap in Event Study Methodology

Numéro de référence interne originel : a1.1 g 107

Arousal fluctuations govern oscillatory transitions between dominant gamma and alpha occipital activity during eyes open/closed conditions

Arousal results in widespread activation of brain areas to increase their response in task and behavior relevant ways. Mediated by the Ascending Reticular Arousal System (ARAS), arousal-dependent inputs interact with neural circuitry to shape their dynamics. In the occipital cortex, such inputs may trigger shifts between dominant oscillations, where α activity is replaced by γ activity, or vice versa. A salient example of this are spectral power alternations observed while eyes are opened and/or closed. These transitions closely follow fluctuations in arousal, suggesting a common origin.To better understand the mechanisms at play, we developed and analyzed a computational model composed of two modules: a thalamocortical feedback circuit coupled with a superficial cortical network. Upon activation by noise-like inputs originating from the ARAS, our model is able to demonstrate that noise-driven nonlinear interactions mediate transitions in dominant peak frequency, resulting in the simultaneous suppression of α limit cycle activity and the emergence of γ oscillations through coherence resonance. Reduction in input provoked the reverse effect-leading to anticorrelated transitions between α and γ power. Taken together, these results shed a new light on how arousal shapes oscillatory brain activity

Periodic external input tunes the stability of delayed nonlinear systems: from the slaving principle to center manifolds

The work illustrates a recent analysis technique that demon- strates that external periodic input affects the stability of the time- averaged nonlinear dynamics of a delayed system. At first, the article introduces the fundamental elements of delayed differential equations and then applies these to a nonlinear delayed problem close to a trans- critical bifurcation. We observe a shift of stability in the system induced by the fast periodic driving

Stochastic center manifold analysis in scalar nonlinear systems involving distributed delays and additive noise

International audienceThis study reviews and extends a recent center manifold analysis technique developped to characterize stochastic bifurcations in delayed systems induced by additive noise. Motivated by the dynamics of spatially extended neural field models with finite propagation velocity, we revealed and fully characterized codimension 1 stochastic bifurcations induced by additive white noise. In contrast to previous studies, we here extended our analysis to the case of distributed delays while applying our results to the stochastic Hopf bifurcation. Taken together, our results provide further insight on the conjugate role of noise and delays in the genesis non-linear phenomena

Procedural Voronoi Foams for Additive Manufacturing

International audienceMicrostructures at the scale of tens of microns change the physical properties of objects, making them lighter or more flexible. While traditionally difficult to produce, additive manufacturing now lets us physically realize such microstructures at low cost.In this paper we propose to study procedural, aperiodic microstructures inspired by Voronoi open-cell foams. The absence of regularity affords for a simple approach to grade the foam geometry - and thus its mechanical properties - within a target object and its surface. Rather than requiring a global optimization process, the microstructures are directly generated to exhibit a specified elastic behavior. The implicit evaluation is akin to procedural textures in computer graphics, and locally adapts to follow the elasticity field. This allows very detailed structures to be generated in large objects without having to explicitly produce a full representation - mesh or voxels - of the complete object: the structures are added on the fly, just before each object slice is manufactured.We study the elastic behavior of the microstructures and provide a complete description of the procedure generating them. We explain how to determine the geometric parameters of the microstructures from a target elasticity, and evaluate the result on printed samples. Finally, we apply our approach to the fabrication of objects with spatially varying elasticity, including the implicit modeling of a frame following the object surface and seamlessly connecting to the microstructures

Delay stabilizes stochastic systems near an non-oscillatory instability

International audienceThe work discovers a stochastic bifurcation in delayed systems in the presence of both delay and additive noise. To understand this phenomenon we present a stochastic center manifold method to compute a non-delayed stochastic order parameter equation for a scalar delayed system driven by additive uncorrelated noise. The derived order parameter equation includes additive and multiplicative white and coloured noise. An illustrative neural system with delayed self-excitation reveals stationary states that are postponed by combined additive noise and delay. A nal brief analytical treatment of the derived order parameter equation reveals analytically the shift of the stationary states which depends on the delay and the noise strength

Persistent Entrainment in Non-linear Neural Networks With Memory

We investigate the dynamics of a non-linear network with noise, periodic forcing and delayed feedback. Our model reveals that there exist forcing regimes—called persistent entrainment regimes—in which the system displays oscillatory responses that outlast the termination of the forcing. Our analysis shows that in presence of delays, periodic forcing can selectively excite components of an infinite reservoir of intrinsic modes and hence display a wide range of damped frequencies. Mean-field and linear stability analysis allows a characterization of the magnitude and duration of these persistent oscillations, as well as their dependence on noise intensity and time delay. These results provide new perspectives on the control of non-linear delayed system using periodic forcing