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Modelling gene regulatory networks not only requires a thorough understanding of the biological system depicted but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to…
Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…
Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems…
In this paper, we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular dynamics. The latter are ubiquitous in physicochemical and biological…
Generative methods for graphs need to be sufficiently flexible to model complex dependencies between sets of nodes. At the same time, the generated graphs need to satisfy domain-dependent feasibility conditions, that is, they should not…
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…
Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are…
Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance but also the distribution of protein numbers. We assume…
Transcriptional regulation of gene expression is one of the main processes that affect cell diversification from a single set of genes. Regulatory proteins often interact with DNA regions located distally from the transcription start sites…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
A recent article by Weidner et al. [2021] presents a method to extract graph properties that are predictive of the dynamical behavior of multivariate, discrete models of biochemical regulation. In other words, a method that uses only…
A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general but they satisfy an overdamped…
In many far-from-equilibrium biological systems, energy injected by irreversible processes at microscopic scales propagates to larger scales to fulfill important biological functions. But given dissipative dynamics at the microscale, how…
Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks.…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…
In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…