Related papers: Quantifying energy landscape of high-dimensional o…

Cells use genetic switches to shift between alternate stable gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Conceptually, these stable phenotypes can be considered as attractive states on an…

Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). However, there exists a pathology of deep Gaussian processes that their learning…

Generative models, such as GANs and diffusion models, have been used to augment training sets and boost performances in different tasks. We focus on generative models for cell detection instead, i.e., locating and classifying cells in given…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy…

Occupancy prediction infers fine-grained 3D geometry and semantics from camera images of the surrounding environment, making it a critical perception task for autonomous driving. Existing methods either adopt dense grids as scene…

Understanding how the structure of within-system interactions affects the dynamics of the system is important in many areas of science. We extend a network dynamics modeling platform DSGRN, which combinatorializes both dynamics and…

Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental…

Scenario-based probabilistic forecasts have become vital for decision-makers in handling intermittent renewable energies. This paper presents a recent promising deep learning generative approach called denoising diffusion probabilistic…

Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard…

Molecules in dense environments, such as biological cells, are subjected to forces that fluctuate both in time and in space. While spatial fluctuations are captured by Lifson-Jackson-Zwanzig's model of "diffusion in a rough potential", and…

Advances in deep learning have greatly improved structure prediction of molecules. However, many macroscopic observations that are important for real-world applications are not functions of a single molecular structure, but rather…

Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…

Free energy landscapes encode the kinetics, intermediates, and transition states that govern molecular processes and are thus a key target of single biomolecule research. Typical approaches to deriving optimal, error-minimizing,…

Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as for example the energy dissipation field of fully developed turbulence. A dynamical generalisation of these models is…

Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the…

Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…

The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that…

We measure different contributions to entropy production in a living functional epithelial tissue. We do this by extracting the functional dynamics of development while at the same time quantifying fluctuations. Using the translucent…