Piecewise affine models provide a qualitative description of the dynamics of a system, and are often used to study genetic regulatory networks. The state space of a piecewise affine system is partitioned into hyperrectangles, which can be represented as nodes in a directed graph, so that the system's trajectories follow a path in a transition graph. This paper proposes and compares two definitions of probability of transition between two nodes A and B of the graph, based on the volume of the initial conditions on the hyperrectangle A whose trajectories cross to B. The parameters of the system can thus be compared to the observed transitions between two hyperrectangles. This property may become useful to identify sets of parameters for which the system yields a desired periodic orbit with a high probability, or to predict the most likely periodic orbit given a set of parameters, as illustrated by a gene regulatory system composed of two intertwined negative loops.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1007/s11538-012-9773-6 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Analytic solutions for the circadian oscillator characterize cycle dynamics and its robustness.
J Math Biol
December 2024
Macbes team, INRAE, CNRS, Centre Inria d'Université Côte d'Azur, Sophia Antipolis, France.
Circadian clocks form a fundamental mechanism that promotes the correct behavior of many cellular and molecular processes by synchronizing them on a 24 h period. However, the circadian cycles remain difficult to describe mathematically. To overcome this problem, we first propose a segmentation of the circadian cycle into eight stages based on the levels of expression of the core clock components CLOCK:BMAL1, REV-ERB and PER:CRY.
View Article and Find Full Text PDFBifurcation analysis of a two-neuron central pattern generator model for both oscillatory and convergent neuronal activities.
Chaos
September 2024
Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
The neural oscillator model proposed by Matsuoka is a piecewise affine system that exhibits distinctive periodic solutions. Although such typical oscillation patterns have been widely studied, little is understood about the dynamics of convergence to certain fixed points and bifurcations between the periodic orbits and fixed points in this model. We performed fixed point analysis on a two-neuron version of the Matsuoka oscillator model, the result of which explains the mechanism of oscillation and the discontinuity-induced bifurcations such as subcritical/supercritical Hopf-like, homoclinic-like and grazing bifurcations.
View Article and Find Full Text PDFDeep Generative Models (DGMs) are versatile tools for learning data representations while adequately incorporating domain knowledge such as the specification of conditional probability distributions. Recently proposed DGMs tackle the important task of comparing data sets from different sources. One such example is the setting of contrastive analysis that focuses on describing patterns that are enriched in a target data set compared to a background data set.
View Article and Find Full Text PDFA full-body transcription factor expression atlas with completely resolved cell identities in C. elegans.
Nat Commun
January 2024
College of Life Sciences, Capital Normal University, Beijing, 100048, China.
Invariant cell lineage in C. elegans enables spatiotemporal resolution of transcriptional regulatory mechanisms controlling the fate of each cell. Here, we develop RAPCAT (Robust-point-matching- And Piecewise-affine-based Cell Annotation Tool) to automate cell identity assignment in three-dimensional image stacks of L1 larvae and profile reporter expression of 620 transcription factors in every cell.
View Article and Find Full Text PDFLocally linear attributes of ReLU neural networks.
Front Artif Intell
November 2023
Department of Computer Science, Colorado State University, Fort Collins, CO, United States.
A ReLU neural network functions as a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a partitioning of the input space into convex polytopes, where each polytope is associated with a distinct affine mapping. The structure of this partitioning, together with the affine map attached to each polytope, can be analyzed to investigate the behavior of the associated neural network.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!