16,381 research outputs found
Persistence and First-Passage Properties in Non-equilibrium Systems
In this review we discuss the persistence and the related first-passage
properties in extended many-body nonequilibrium systems. Starting with simple
systems with one or few degrees of freedom, such as random walk and random
acceleration problems, we progressively discuss the persistence properties in
systems with many degrees of freedom. These systems include spins models
undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces
etc. Persistence properties are nontrivial in these systems as the effective
underlying stochastic process is non-Markovian. Several exact and approximate
methods have been developed to compute the persistence of such non-Markov
processes over the last two decades, as reviewed in this article. We also
discuss various generalisations of the local site persistence probability.
Persistence in systems with quenched disorder is discussed briefly. Although
the main emphasis of this review is on the theoretical developments on
persistence, we briefly touch upon various experimental systems as well.Comment: Review article submitted to Advances in Physics: 149 pages, 21
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Networks and the epidemiology of infectious disease
The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues
A Multi-scale View of the Emergent Complexity of Life: A Free-energy Proposal
We review some of the main implications of the free-energy principle (FEP) for the study of the self-organization of living systems – and how the FEP can help us to understand (and model) biotic self-organization across the many temporal and spatial scales over which life exists. In order to maintain its integrity as a bounded system, any biological system - from single cells to complex organisms and societies - has to limit the disorder or dispersion (i.e., the long-run entropy) of its constituent states. We review how this can be achieved by living systems that minimize their variational free energy. Variational free energy is an information theoretic construct, originally introduced into theoretical neuroscience and biology to explain perception, action, and learning. It has since been extended to explain the evolution, development, form, and function of entire organisms, providing a principled model of biotic self-organization and autopoiesis. It has provided insights into biological systems across spatiotemporal scales, ranging from microscales (e.g., sub- and multicellular dynamics), to intermediate scales (e.g., groups of interacting animals and culture), through to macroscale phenomena (the evolution of entire species). A crucial corollary of the FEP is that an organism just is (i.e., embodies or entails) an implicit model of its environment. As such, organisms come to embody causal relationships of their ecological niche, which, in turn, is influenced by their resulting behaviors. Crucially, free-energy minimization can be shown to be equivalent to the maximization of Bayesian model evidence. This allows us to cast natural selection in terms of Bayesian model selection, providing a robust theoretical account of how organisms come to match or accommodate the spatiotemporal complexity of their surrounding niche. In line with the theme of this volume; namely, biological complexity and self-organization, this chapter will examine a variational approach to self-organization across multiple dynamical scales
Generalized structured additive regression based on Bayesian P-splines
Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM's and extensions to generalized structured additive regression based on one or two dimensional P-splines as the main building block. The approach extends previous work by Lang und Brezger (2003) for Gaussian responses. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. Our approach covers the most common univariate response distributions, e.g. the Binomial, Poisson or Gamma distribution, as well as multicategorical responses. For the first time, we present Bayesian semiparametric inference for the widely used multinomial logit models. As we will demonstrate through two applications on the forest health status of trees and a space-time analysis of health insurance data, the approach allows realistic modelling of complex problems. We consider the enormous flexibility and extendability of our approach as a main advantage of Bayesian inference based on MCMC techniques compared to more traditional approaches. Software for the methodology presented in the paper is provided within the public domain package BayesX
ToyArchitecture: Unsupervised Learning of Interpretable Models of the World
Research in Artificial Intelligence (AI) has focused mostly on two extremes:
either on small improvements in narrow AI domains, or on universal theoretical
frameworks which are usually uncomputable, incompatible with theories of
biological intelligence, or lack practical implementations. The goal of this
work is to combine the main advantages of the two: to follow a big picture
view, while providing a particular theory and its implementation. In contrast
with purely theoretical approaches, the resulting architecture should be usable
in realistic settings, but also form the core of a framework containing all the
basic mechanisms, into which it should be easier to integrate additional
required functionality.
In this paper, we present a novel, purposely simple, and interpretable
hierarchical architecture which combines multiple different mechanisms into one
system: unsupervised learning of a model of the world, learning the influence
of one's own actions on the world, model-based reinforcement learning,
hierarchical planning and plan execution, and symbolic/sub-symbolic integration
in general. The learned model is stored in the form of hierarchical
representations with the following properties: 1) they are increasingly more
abstract, but can retain details when needed, and 2) they are easy to
manipulate in their local and symbolic-like form, thus also allowing one to
observe the learning process at each level of abstraction. On all levels of the
system, the representation of the data can be interpreted in both a symbolic
and a sub-symbolic manner. This enables the architecture to learn efficiently
using sub-symbolic methods and to employ symbolic inference.Comment: Revision: changed the pdftitl
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