Related papers: Quantifying energy landscape of high-dimensional o…
Complex biological systems have been successfully modeled by biochemical and genetic interaction networks, typically gathered from high-throughput (HTP) data. These networks can be used to infer functional relationships between genes or…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…
The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The…
To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…
Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including cell-fate decision in developmental processes as well as genesis and progression of cancers. While various attempts have…
Stochastic gradient descent (SGD) is a key ingredient in the training of deep neural networks and yet its geometrical significance appears elusive. We study a deterministic model in which the trajectories of our dynamical systems are…
The dynamics of individual colloidal particles in random potential energy landscapes were investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a…
Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include phase transitions of…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
Formulating quantitative and predictive models for tissue development requires consideration of the complex, stochastic gene expression dynamics, its regulation via cell-to-cell interactions, and cell proliferation. Including all of these…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
In this article, we propose a general framework to study the dynamics and topology of cellular networks that capture the geometry of cell packings in two-dimensional tissues. Such epithelia undergo large-scale deformation during…
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…
Gaussian macroscopic fluctuation theory underpins the understanding of noise in a broad class of nonequilibrium systems. We derive exact fluctuation-response relations linking the power spectral density of stationary fluctuations to the…
Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these…
This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…