Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation

We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation, instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed auto-inhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.Comment: 21 pages, 7 figure

Generating functionals and Gaussian approximations for interruptible delay reactions

We develop a generating functional description of the dynamics of non-Markovian individual-based systems, in which delay reactions can be terminated before completion. This generalises previous work in which a path-integral approach was applied to dynamics in which delay reactions complete with certainty. We construct a more widely applicable theory, and from it we derive Gaussian approximations of the dynamics, valid in the limit of large, but finite population sizes. As an application of our theory we study predator-prey models with delay dynamics due to gestation or lag periods to reach the reproductive age. In particular we focus on the effects of delay on noise-induced cycles.Comment: 18 pages, 4 figure

Developing educational iPhone, Android and Windows smartphone cross-platform apps to facilitate understanding of clinical genomics terminology

No abstract available

The instanton method and its numerical implementation in fluid mechanics

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional fluid dynamical problems. We illustrate these ideas using the two-dimensional Burgers equation and the three-dimensional Navier-Stokes equations

Invariant Solution underlying Oblique Stripe Patterns in Plane Couette Flow

When subcritical shear flows transition to turbulence, laminar and turbulent flow often coexists in space, giving rise to turbulent-laminar patterns. Most prominent are regular stripe patterns with large-scale periodicity and oblique orientation. Oblique stripes are a robust phenomenon, observed in experiments and flow simulations, yet their origin remains unclear. We demonstrate the existence of an invariant equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles the oblique pattern of turbulent-laminar stripes in plane Couette flow. We uncover the origin of the stripe equilibrium and show how it emerges from the well-studied Nagata equilibrium via two successive symmetry-breaking bifurcations

Keynesian government spending multipliers and spillovers in the euro area

The global financial crisis has lead to a renewed interest in discretionary fiscal stimulus. Advocates of discretionary measures emphasize that government spending can stimulate additional private spending — the so-called Keynesian multiplier effect. Thus, we investigate whether the discretionary spending announced by Euro area governments for 2009 and 2010 is likely to boost euro area GDP by more than one for one. Because of modeling uncertainty, it is essential that such policy evaluations be robust to alternative modeling assumptions and different parameterizations. Therefore, we use five different empirical macroeconomic models with Keynesian features such as price and wage rigidities to evaluate the impact of fiscal stimulus. Four of them suggest that the planned increase in government spending will reduce private spending for consumption and investment purposes significantly. If announced government expenditures are implemented with delay the initial effect on euro area GDP, when stimulus is most needed, may even be negative. Traditional Keynesian multiplier effects only arise in a model that ignores the forward-looking behavioral response of consumers and firms. Using a multi-country model, we find that spillovers between euro area countries are negligible or even negative, because direct demand effects are offset by the indirect effect of euro appreciation