235,504 research outputs found
Numerical algebraic geometry for model selection and its application to the life sciences
Researchers working with mathematical models are often confronted by the
related problems of parameter estimation, model validation, and model
selection. These are all optimization problems, well-known to be challenging
due to non-linearity, non-convexity and multiple local optima. Furthermore, the
challenges are compounded when only partial data is available. Here, we
consider polynomial models (e.g., mass-action chemical reaction networks at
steady state) and describe a framework for their analysis based on optimization
using numerical algebraic geometry. Specifically, we use probability-one
polynomial homotopy continuation methods to compute all critical points of the
objective function, then filter to recover the global optima. Our approach
exploits the geometric structures relating models and data, and we demonstrate
its utility on examples from cell signaling, synthetic biology, and
epidemiology.Comment: References added, additional clarification
An Iterative Procedure for the Estimation of Drift and Diffusion Coefficients of Langevin Processes
A general method is proposed which allows one to estimate drift and diffusion
coefficients of a stochastic process governed by a Langevin equation. It
extends a previously devised approach [R. Friedrich et al., Physics Letters A
271, 217 (2000)], which requires sufficiently high sampling rates. The analysis
is based on an iterative procedure minimizing the Kullback-Leibler distance
between measured and estimated two time joint probability distributions of the
process.Comment: 4 pages, 5 figure
Stationary probability density of stochastic search processes in global optimization
A method for the construction of approximate analytical expressions for the
stationary marginal densities of general stochastic search processes is
proposed. By the marginal densities, regions of the search space that with high
probability contain the global optima can be readily defined. The density
estimation procedure involves a controlled number of linear operations, with a
computational cost per iteration that grows linearly with problem size
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