11,871 research outputs found
Computation of epidemic final size distributions
We develop a new methodology for the efficient computation of epidemic final
size distributions for a broad class of Markovian models. We exploit a
particular representation of the stochastic epidemic process to derive a method
which is both computationally efficient and numerically stable. The algorithms
we present are also physically transparent and so allow us to extend this
method from the basic SIR model to a model with a phase-type infectious period
and another with waning immunity. The underlying theory is applicable to many
Markovian models where we wish to efficiently calculate hitting probabilities.Comment: final published versio
Lattices of hydrodynamically interacting flapping swimmers
Fish schools and bird flocks exhibit complex collective dynamics whose
self-organization principles are largely unknown. The influence of
hydrodynamics on such collectives has been relatively unexplored theoretically,
in part due to the difficulty in modeling the temporally long-lived
hydrodynamic interactions between many dynamic bodies. We address this through
a novel discrete-time dynamical system (iterated map) that describes the
hydrodynamic interactions between flapping swimmers arranged in one- and
two-dimensional lattice formations. Our 1D results exhibit good agreement with
previously published experimental data, in particular predicting the
bistability of schooling states and new instabilities that can be probed in
experimental settings. For 2D lattices, we determine the formations for which
swimmers optimally benefit from hydrodynamic interactions. We thus obtain the
following hierarchy: while a side-by-side single-row "phalanx" formation offers
a small improvement over a solitary swimmer, 1D in-line and 2D rectangular
lattice formations exhibit substantial improvements, with the 2D diamond
lattice offering the largest hydrodynamic benefit. Generally, our
self-consistent modeling framework may be broadly applicable to active systems
in which the collective dynamics is primarily driven by a fluid-mediated
memory
Evaluating the role of quantitative modeling in language evolution
Models are a flourishing and indispensable area of research in language evolution. Here we highlight critical issues in using and interpreting models, and suggest viable approaches. First, contrasting models can explain the same data and similar modelling techniques can lead to diverging conclusions. This should act as a reminder to use the extreme malleability of modelling parsimoniously when interpreting results. Second, quantitative techniques similar to those used in modelling language evolution have proven themselves inadequate in other disciplines. Cross-disciplinary fertilization is crucial to avoid mistakes which have previously occurred in other areas. Finally, experimental validation is necessary both to sharpen models' hypotheses, and to support their conclusions. Our belief is that models should be interpreted as quantitative demonstrations of logical possibilities, rather than as direct sources of evidence. Only an integration of theoretical principles, quantitative proofs and empirical validation can allow research in the evolution of language to progress
Iterated filtering methods for Markov process epidemic models
Dynamic epidemic models have proven valuable for public health decision
makers as they provide useful insights into the understanding and prevention of
infectious diseases. However, inference for these types of models can be
difficult because the disease spread is typically only partially observed e.g.
in form of reported incidences in given time periods. This chapter discusses
how to perform likelihood-based inference for partially observed Markov
epidemic models when it is relatively easy to generate samples from the Markov
transmission model while the likelihood function is intractable. The first part
of the chapter reviews the theoretical background of inference for partially
observed Markov processes (POMP) via iterated filtering. In the second part of
the chapter the performance of the method and associated practical difficulties
are illustrated on two examples. In the first example a simulated outbreak data
set consisting of the number of newly reported cases aggregated by week is
fitted to a POMP where the underlying disease transmission model is assumed to
be a simple Markovian SIR model. The second example illustrates possible model
extensions such as seasonal forcing and over-dispersion in both, the
transmission and observation model, which can be used, e.g., when analysing
routinely collected rotavirus surveillance data. Both examples are implemented
using the R-package pomp (King et al., 2016) and the code is made available
online.Comment: This manuscript is a preprint of a chapter to appear in the Handbook
of Infectious Disease Data Analysis, Held, L., Hens, N., O'Neill, P.D. and
Wallinga, J. (Eds.). Chapman \& Hall/CRC, 2018. Please use the book for
possible citations. Corrected typo in the references and modified second
exampl
On the effects of firing memory in the dynamics of conjunctive networks
Boolean networks are one of the most studied discrete models in the context
of the study of gene expression. In order to define the dynamics associated to
a Boolean network, there are several \emph{update schemes} that range from
parallel or \emph{synchronous} to \emph{asynchronous.} However, studying each
possible dynamics defined by different update schemes might not be efficient.
In this context, considering some type of temporal delay in the dynamics of
Boolean networks emerges as an alternative approach. In this paper, we focus in
studying the effect of a particular type of delay called \emph{firing memory}
in the dynamics of Boolean networks. Particularly, we focus in symmetric
(non-directed) conjunctive networks and we show that there exist examples that
exhibit attractors of non-polynomial period. In addition, we study the
prediction problem consisting in determinate if some vertex will eventually
change its state, given an initial condition. We prove that this problem is
{\bf PSPACE}-complete
Efficient likelihood estimation in state space models
Motivated by studying asymptotic properties of the maximum likelihood
estimator (MLE) in stochastic volatility (SV) models, in this paper we
investigate likelihood estimation in state space models. We first prove, under
some regularity conditions, there is a consistent sequence of roots of the
likelihood equation that is asymptotically normal with the inverse of the
Fisher information as its variance. With an extra assumption that the
likelihood equation has a unique root for each , then there is a consistent
sequence of estimators of the unknown parameters. If, in addition, the supremum
of the log likelihood function is integrable, the MLE exists and is strongly
consistent. Edgeworth expansion of the approximate solution of likelihood
equation is also established. Several examples, including Markov switching
models, ARMA models, (G)ARCH models and stochastic volatility (SV) models, are
given for illustration.Comment: With the comments by Jens Ledet Jensen and reply to the comments.
Published at http://dx.doi.org/10.1214/009053606000000614;
http://dx.doi.org/10.1214/09-AOS748A; http://dx.doi.org/10.1214/09-AOS748B in
the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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