The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plug-and-play property. Our work builds on recently developed plug-and-play inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A

When designing decentralised autonomic computing systems, a fundamental engineering issue is to assess system-wide behaviour. Such decentralised systems are characterised by the lack of global control, typically consist of autonomous cooperating entities, and often rely on self-organised emergent behaviour to achieve the requirements. A well-founded and practically feasible approach to study overall system behaviour is a prerequisite for successful deployment. On one hand, formal proofs of correct behaviour and even predictions of the exact system-wide behaviour are practically infeasible due to the complex, dynamic, and often non-deterministic nature of self-organising emergent systems. On the other hand, simple simulations give no convincing arguments for guaranteeing system-wide properties. We describe an alternative approach that allows to analyse and assess trends in system-wide behaviour, based on so-called “equation-free” macroscopic analysis. This technique yields more reliable results about the system-wide behaviour, compared to mere observation of simulation results, at an affordable computational cost. Numerical algorithms act at the system-wide level and steer the simulations. This allows to limit the amount of simulations considerably. We illustrate the approach by studying a particular system-wide property of a decentralised control system for Automated Guided Vehicles and we outline a road map towards a general methodology for studying decentralised autonomic computing systems.

The goal of engineering self-organising emergent systems is to acquire a macroscopic system behaviour solely from autonomous local activity and interaction. Due to the non-deterministic nature of such systems, it is hard to guarantee that the required macroscopic behaviour is achieved and maintained. Before even considering a self-organising emergent system in an industrial context, e.g. for Automated Guided Vehicle (AGV) transportation systems, such guarantees are needed. An empirical analysis approach is proposed that combines realistic agent-based simulations with existing scientific numerical algorithms for analysing the macroscopic behaviour. The numerical algorithm itself obtains the analysis results on the fly by steering and accelerating the simulation process according to the algorithm’s goal. The approach is feasible, compared to formal proofs, and leads to more reliable and valuable results, compared to mere observation of simulation results. Also, the approach allows to systematically analyse the macroscopic behaviour to acquire macroscopic guarantees and feedback that can be used by an engineering process to iteratively shape a self-organising emergent solution.

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We present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [Chemical Oscillations, Waves, and Turbulence, Springer-Verlag (1984)], a prototype model for coupled oscillator populations. Our study takes place in a reduced phase space of coarse-grained “observables ” of the system: the first few moments of the oscillator phase angle distribution. We circumvent the derivation of explicit dynamical equations (approximately) governing the evolution of these coarse-grained macroscopic variables; instead we use the equationfree framework [Kevrekidis et al., Comm. Math. Sci. 1(4), 715 (2003)] to computationally solve these equations without obtaining them in closed form. In this approach, the numerical tasks for the conceptually existing but unavailable coarse-grained equations are implemented through short bursts of appropriately initialized simulations of the “fine-scale”, detailed coupled oscillator model. Coarse projective integration and coarse fixed point computations are illustrated. Coupled nonlinear oscillators can exhibit spontaneous emergence of order, a fundamental qualitative feature of many complex dynamical systems [Manrubia et al., 2004]. The collective,

Why do we seek to quantify and understand disease dynamics? • Prevention and control of emerging infectious diseases (SARS, HIV/AIDS, H5N1 influenza “bird flu”) • Understanding the development and spread of drug resistant strains (malaria, tuberculosis, MRSA “the hospital super-bug”) Ed Ionides Infectious disease dynamics: a statistical perspective 4 Disease dynamics: epidemiology or ecology, or both? • Environmental host/pathogen dynamics are close to predator/prey relationships which are a central topic of ecology. • Analysis of diseases as ecosystems complements more traditional epidemiology (risk factors etc). • Ecologists typically seek to avoid extinctions, whereas epidemiologists typically seek the reverse. Things are not always this simple... – Helicobacter pylori bacteria used to live in the stomach of most humans. Some strains cause stomach ulcers and cancer. It is almost extinct in the developed world due to widespread use of

modeling and inference for ecological systems

Time series analysis for nonlinear dynamical systems with applications to modeling of infectious diseases by

Why do we seek to quantify and understand disease dynamics? • Prevention and control of emerging infectious diseases (SARS, HIV/AIDS, H5N1 “bird flu ” influenza, H1N1 “swine flu ” influenza) • Understanding the development and spread of drug resistant strains (malaria, tuberculosis, MRSA) Ed Ionides Infectious disease dynamics: a statistical perspective 4 Disease dynamics: epidemiology or ecology, or both? • Environmental host/pathogen dynamics are close to predator/prey relationships which are a central topic of ecology. • Analysis of diseases as ecosystems complements more traditional epidemiology (risk factors etc). • Ecologists typically seek to avoid extinctions, whereas epidemiologists typically seek the reverse. Ed Ionides Infectious disease dynamics: a statistical perspective 5 Infectious disease transmission: the statistical challenge • Time series data of sufficient quantity and quality to support investigations of disease dynamics are increasingly available.

Multiscale analysis of re-entrant production lines: An equation-free approach