Related papers: A new approach to multi-modal diffusions with appl…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing…
Using Wang-Landau sampling with suitable Monte Carlo trial moves (pull moves and bond-rebridging moves combined) we have determined the density of states and thermodynamic properties for a short sequence of the HP protein model. For free…
We consider a class of conditional forward-backward diffusion models for conditional generative modeling, that is, generating new data given a covariate (or control variable). To formally study the theoretical properties of these…
We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
A method that reconstructs protein residue networks using suitable node selection and edge recovery policies produced numerical observations that correlate strongly (Pearson's correlation coefficient < -0.83) with published folding rates…
This chapter shows how toroidal diffusions are convenient methodological tools for modelling protein evolution in a probabilistic framework. The chapter addresses the construction of ergodic diffusions with stationary distributions equal to…
The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Folding and aggregation of proteins, the interaction between proteins and membranes, as well as the adsorption of organic soft matter to inorganic solid substrates belong to the most interesting challenges in understanding structure and…
This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
A transfer-matrix formalism is introduced to evaluate exactly the partition function of the Munoz-Eaton model, relating the folding kinetics of proteins of known structure to their thermodynamics and topology. This technique can be used for…
We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active Ornstein-Uhlenbeck process. We focus on the diffusivity properties of the…
The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force are characterized by explicit dynamics of their integer moments and by explicit relaxation spectral properties towards their steady state.…
To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplifed protein chain model that embodies a cooperative…
Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…
A novel combination of discontinuous molecular dynamics and the Langevin equation, together with an intermediate-resolution model, are used to carry out long (several $\mu$s) simulation and study folding transition and transport of proteins…
Cloth manipulation is challenging due to its highly complex dynamics, near-infinite degrees of freedom, and frequent self-occlusions, which complicate both state estimation and dynamics modeling. Inspired by recent advances in generative…
Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic ``burnt-bridge'' models. The transport of the particles is viewed…