Noise-controlled dynamics runs counter to usual intuition: the larger the noise the more regular the solutions. We present numerical and analytical results for a set of three stochastic partial differential equations in one space dimension, motivated by the intermittent destabilization of tall thin convection cells by horizontal shear. Time-series are predictable in the sense that they follow l...

We extend the cosmological linear perturbation theory code CMBFAST to closed geometries. This completes the implementation of CMBFAST to all types of geometries and allows the user to perform an unlimited search in the parameter space of models. This will be specially useful for placing confidence limits on cosmological parameters from existing and future data. We discuss some of the technical ...

This paper presents a study on the limit cycles of Zq -equivariant polynomial vector fields with degree 3 or 4. Previous studies have shown that when q = 2, cubic-order systems can have 12 small amplitude limit cycles. In this paper, particular attention is focused on the cases of q 3. It is shown that for cubicorder systems, when q = 3 there exist 3 small limit cycles and 1 big limit cycle; wh...

We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrödinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the numerical solutions keep a WKB structure, on a time interval independent of the Planck constant. We prove error estimates, which show that the quadratic observables can be comp...

IEEE 802.15.4 low-rate Wireless Personal Area Networks (WPAN) are expected to provide ubiquitous networking between small personal/home devices and sensors with low power consumption and low cost features. The technology employs special CSMA/CA to save power consumption for batterypowered small or portable WPAN devices. In this letter, we present a new model for the slotted CSMA/CA of IEEE 802....

The objective of this paper is to investigate the stability of limit cycles of a mathematical model with a distributed delay which describes the interaction between p53 and mdm2. Choosing the delay as a bifurca-tion parameter we study the direction and stability of the bifurcating periodic solutions using the normal form and the center manifold theorem. Some numerical examples are finally made ...

Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic system. As a practical application, we numerically demonstrate that this method can retrieve all the interaction functions from the fluctuating rhythmic neurona...

Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the...

This paper develops the concept of reduction-based control, which is founded on a controlled form of geometric reduction known as functional Routhian reduction. We prove a geometric property of general serial-chain robots termed recursive cyclicity, identifying the inherent robot symmetries that we exploit with the Subrobot Theorem. This shows that any serial-chain robot can be decomposed for a...