Alternative determinism principle for topological analysis of chaos

The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Comment: Accepted for publication as Rapid Communication in Physical Review

Stochastic Oscillations Induced by Intrinsic Fluctuations in a Self-Repressing Gene

AbstractBiochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified

Topological signature of deterministic chaos in short nonstationary signals from an optical parametric oscillator

Although deterministic chaos has been predicted to occur in the triply resonant optical parametric oscillator (TROPO) fifteen years ago, experimental evidence of chaotic behavior in this system has been lacking so far, in marked contrast with most nonlinear systems, where chaos has been actively tracked and found. This situation is probably linked to the high sensitivity of the TROPO to perturbations, which adversely affects stationary operation at high power. We report the experimental observation in this system of a burst of irregular behavior of duration 80 microseconds. Although the system is highly nonstationary over this time interval, a topological analysis allows us to extract a clearcut signature of deterministic chaos from a time series segment of only 9 base cycles (3 microseconds). This result suggests that nonstationarity is not necessarily an obstacle to the characterization of chaos

Does the management of regulatory compliance and occupational risk have an impact on safety culture?

International audienceCompanies try to improve risk management in the field of Occupational Health and Safety (OHS). In recent years this has translated into the introduction of safety management systems (SMS). These management tools bring together personnel, policies and resources aimed at improving the performance of a company in the area of OHS. SMS provide a structured, global framework for risk management based on compliance with existing repositories. An SMS consists of various stages or processes, notably concerned with the management of regulatory compliance and risk analysis. Various tools are deployed in order to meet these SMS requirements. At the same time, the concept of safety culture has progressively taken hold in organizations. The idea has numerous benefits and can contribute to a reduction in occupational accidents and illness. However, these benefits are presented as self-evident facts which have not really been tested and proven. It is therefore appropriate to study the nature and strength of relationships between safety culture and two explanatory variables; namely compliance management and risk assessment. In other words, it is necessary to assess the respective contributions of these two variables to the creation, deployment and running of safety culture within a company. This paper is organized into three parts. The first part describes the definition of safety culture and looks at its various components as described in the literature. The second part presents ways to model the processes of regulatory compliance, risk assessment and safety climate and provides a further, descriptive model that uses common variables to identify the relationships between these three components in terms of nature and degree. Finally, the third section details the results of an experiment carried out in a company. The experiment demonstrates the deployment of models to evaluate the interactions between components, and its results are discussed and analysed