Related papers: SMART: Spatial Modeling Algorithms for Reaction an…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…
While 2D occupancy maps commonly used in mobile robotics enable safe navigation in indoor environments, in order for robots to understand and interact with their environment and its inhabitants representing 3D geometry and semantic…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
From optical sensors to microwave radars, leveraging the complementary strengths of remote sensing (RS) sensors is crucial for achieving dense spatio-temporal monitoring of our planet. In contrast, recent deep learning models, whether…
Proteins are essential biological macromolecules that execute life functions. Local structural motifs, such as active sites, are the most critical components for linking structure to function and are key to understanding protein evolution…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
The study of physiology demonstrates that the form (shape)of anatomical structures dictates their functions, and analyzing the form of anatomies plays a crucial role in clinical research. Statistical shape modeling (SSM) is a widely used…
Motivation: Modeling biological signaling networks using ordinary differential equations (ODEs) has proven to be a powerful technique for generating insight into cellular dynamics, but it typically requires estimating rate parameters based…
Many transport processes in nature take place on substrates, often considered as unidimensional lanes. These unidimensional substrates are typically non-static: affected by a fluctuating environment, they can undergo conformational changes.…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…
We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on intrinsic kernel-based meshless collocation methods. The…
The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit…
Previous models of the cerebrovascular smooth muscle cell have not addressed the interaction between the electrical, chemical and mechanical components of cell function during the development of active tension. These models are primarily…
The interpretation of ligand-target interactions at atomistic resolution is central to most efforts in computational drug discovery and optimization. However, the highly dynamic nature of protein targets, as well as possible induced fit…
Signalling pathways are abstractions that help life scientists structure the coordination of cellular activity. Cross-talk between pathways accounts for many of the complex behaviours exhibited by signalling pathways and is often critical…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…