Algorithmic Reduction of Biological Networks With Multiple Time Scales
We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting. The existence of invariant manifolds is subject to hyperbolicity conditions, for which we propose an algorithmic test based on Hurwitz criteria. We finally obtain a sequence of nested invariant manifolds and respective reduced systems on those manifolds. Our theoretical results are generally accompanied by rigorous algorithmic descriptions suitable for direct implementation based on existing off-the-shelf software systems, specifically symbolic computation libraries and Satisfiability Modulo Theories solvers. We present computational examples taken from the well-known BioModels database using our own prototypical implementations.
Code (0)
등록된 구현이 없습니다.
Tasks
EpidemiologySimilar Papers 제목 키워드 기반
Tikhonov-Fenichel Reductions and their Application to a Novel Modelling Approach for Mutualism
When formulating a model there is a trade-off between model complexity and (biological) realism. In the present paper we demonstrate how model reduction from a precise mechanistic "super model" to simpler conceptual mode…
Similarity Matching Networks: Hebbian Learning and Convergence Over Multiple Time Scales
A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biologica…
Dimensionality ReductionApproximate Hamilton-Jacobi Reachability Analysis for a Class of Two-Timescale Systems, with Application to Biological Models
Hamilton-Jacobi reachability (HJR) is an exciting framework used for control of safety-critical systems with nonlinear and possibly uncertain dynamics. However, HJR suffers from the curse of dimensionality, with computat…
A time-causal and time-recursive analogue of the Gabor transform
This paper presents a time-causal analogue of the Gabor filter, as well as a both time-causal and time-recursive analogue of the Gabor transform, where the proposed time-causal representations obey both temporal scale co…
Computational principles of biological memory
Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct …