How to Couple from the Past Using a Read-Once Source of Randomness

We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related to an idea known as PASTA (Poisson arrivals see time averages) in the operations research literature. Because the new algorithm can be run using a read-once stream of randomness, we call it read-once CFTP. The memory and time requirements of read-once CFTP are on par with the requirements of the usual form of CFTP, and for a variety of applications the requirements may be noticeably less. Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a read-once version of coupling into and from the past, but it remains unpractical. For these point process applications, we give an alternative coupling method with which read-once CFTP may be efficiently used.Comment: 28 pages, 2 figure

Transport in partially hyperbolic fast-slow systems

I will discuss, from a dynamical systems point of view, some recent attempts to rigorously derive the macroscopic laws of transport (e.g. the heat equation) from deterministic microscopic dynamics.Comment: Contribution to the ICM 201

Dynamische Systeme

This workshop, organized by Hakan Eliasson (Paris), Helmut Hofer (Princeton) and Jean-Christophe Yoccoz (Paris), continued the biannual series at Oberwolfach on Dynamical Systems that started as the “Moser– Zehnder meeting” in 1981. The workshop was attended by more than 50 participants from 12 countries. The main theme of the workshop were the new results and developments in the area of classical dynamical systems, in particular in celestial mechanics and Hamiltonian systems. Among the main topics were KAM theory in finite and infinite dimensions, and new developments in Floer homology (Rabinowitz-Floer homology)

Stochastic average-cost control, with energy-related applications

In this thesis we present a new stochastic optimisation model arising from supplyside management of power networks. We provide the exact optimal solution under assumption that the environment is Markovian. For the semi-Markovian environment we establish existence of an optimal policy in an important subclass of policies. Finally, we solve the problem for a number of particular examples of environment

Applying Mean-field Approximation to Continuous Time Markov Chains

The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and uid model checking analysis techniques

Nutritional Value of Pulses and Whole Grains

Pulses and whole grains have a rich history as part of healthy and sustainable dietary patterns. There is ongoing interest in the use of these foods, and their ingredient derivatives, to delineate effects on multiple aspects of human health and quantify their individual and societal benefits. In additional to an editorial synopsis, this Special Issue “Nutritional Value of Pulses and Whole Grains” adds 11 manuscripts, including 7 studies, 2 reviews, and 2 communications that touch on a variety of topics including the efficacy of pulses and whole grains on cardiometabolic risk factors, consumer preferences and the changing retail landscape, effects on health and societal economic outcomes, and a proposed consensus to effectively integrate and evaluate whole grains and pulses within dietary patterns. The works presented herein touch on various topics and themes that are relevant to a changing food landscape aimed at incorporating more pulses and whole grains into diets. They identify near and future benefits of pulses and whole grains on health, but also underscore some of the underlying challenges around their dietary incorporation. The latter could be critical for leveraging whole grains and pulses in a manner that aligns with global dietary objectives

Geometric Numerical Integration (hybrid meeting)

The topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects