7,042 research outputs found
Simulation-based model selection for dynamical systems in systems and population biology
Computer simulations have become an important tool across the biomedical
sciences and beyond. For many important problems several different models or
hypotheses exist and choosing which one best describes reality or observed data
is not straightforward. We therefore require suitable statistical tools that
allow us to choose rationally between different mechanistic models of e.g.
signal transduction or gene regulation networks. This is particularly
challenging in systems biology where only a small number of molecular species
can be assayed at any given time and all measurements are subject to
measurement uncertainty. Here we develop such a model selection framework based
on approximate Bayesian computation and employing sequential Monte Carlo
sampling. We show that our approach can be applied across a wide range of
biological scenarios, and we illustrate its use on real data describing
influenza dynamics and the JAK-STAT signalling pathway. Bayesian model
selection strikes a balance between the complexity of the simulation models and
their ability to describe observed data. The present approach enables us to
employ the whole formal apparatus to any system that can be (efficiently)
simulated, even when exact likelihoods are computationally intractable.Comment: This article is in press in Bioinformatics, 2009. Advance Access is
available on Bioinformatics webpag
Training Echo State Networks with Regularization through Dimensionality Reduction
In this paper we introduce a new framework to train an Echo State Network to
predict real valued time-series. The method consists in projecting the output
of the internal layer of the network on a space with lower dimensionality,
before training the output layer to learn the target task. Notably, we enforce
a regularization constraint that leads to better generalization capabilities.
We evaluate the performances of our approach on several benchmark tests, using
different techniques to train the readout of the network, achieving superior
predictive performance when using the proposed framework. Finally, we provide
an insight on the effectiveness of the implemented mechanics through a
visualization of the trajectory in the phase space and relying on the
methodologies of nonlinear time-series analysis. By applying our method on well
known chaotic systems, we provide evidence that the lower dimensional embedding
retains the dynamical properties of the underlying system better than the
full-dimensional internal states of the network
Determining Structurally Identifiable Parameter Combinations Using Subset Profiling
Identifiability is a necessary condition for successful parameter estimation
of dynamic system models. A major component of identifiability analysis is
determining the identifiable parameter combinations, the functional forms for
the dependencies between unidentifiable parameters. Identifiable combinations
can help in model reparameterization and also in determining which parameters
may be experimentally measured to recover model identifiability. Several
numerical approaches to determining identifiability of differential equation
models have been developed, however the question of determining identifiable
combinations remains incompletely addressed. In this paper, we present a new
approach which uses parameter subset selection methods based on the Fisher
Information Matrix, together with the profile likelihood, to effectively
estimate identifiable combinations. We demonstrate this approach on several
example models in pharmacokinetics, cellular biology, and physiology
Stochastic ordinary differential equations in applied and computational mathematics
Using concrete examples, we discuss the current and potential use of stochastic ordinary differential equations (SDEs) from the perspective of applied and computational mathematics. Assuming only a minimal background knowledge in probability and stochastic processes, we focus on aspects that distinguish SDEs from their deterministic counterparts. To illustrate a multiscale modelling framework, we explain how SDEs arise naturally as diffusion limits in the type of discrete-valued stochastic models used in chemical kinetics, population dynamics, and, most topically, systems biology. We outline some key issues in existence, uniqueness and stability that arise when SDEs are used as physical models, and point out possible pitfalls. We also discuss the use of numerical methods to simulate trajectories of an SDE and explain how both weak and strong convergence properties are relevant for highly-efficient multilevel Monte Carlo simulations. We flag up what we believe to be key topics for future research, focussing especially on nonlinear models, parameter estimation, model comparison and multiscale simulation
Estimating Threshold Effects of Generic Fluid Milk and Cheese Advertising
Replaced with revised version of paper 08/01/06.Livestock Production/Industries, Marketing,
Survey of decentralized control methods
An overview is presented of the types of problems that are being considered by control theorists in the area of dynamic large scale systems with emphasis on decentralized control strategies. Approaches that deal directly with decentralized decision making for large scale systems are discussed. It is shown that future advances in decentralized system theory are intimately connected with advances in the stochastic control problem with nonclassical information pattern. The basic assumptions and mathematical tools associated with the latter are summarized, and recommendations concerning future research are presented
A comparison of methods to determine neuronal phase-response curves
The phase-response curve (PRC) is an important tool to determine the
excitability type of single neurons which reveals consequences for their
synchronizing properties. We review five methods to compute the PRC from both
model data and experimental data and compare the numerically obtained results
from each method. The main difference between the methods lies in the
reliability which is influenced by the fluctuations in the spiking data and the
number of spikes available for analysis. We discuss the significance of our
results and provide guidelines to choose the best method based on the available
data.Comment: PDFLatex, 16 pages, 7 figures
- …