Related papers: A new approach to multi-modal diffusions with appl…
Despite the growing interest in diffusion models, gaining a deep understanding of the model class remains an elusive endeavour, particularly for the uninitiated in non-equilibrium statistical physics. Thanks to the rapid rate of progress in…
Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools.…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
The thermodynamic properties for three different types of off-lattice four-strand beta-sheet protein models interacting via a hybrid Go-type potential have been investigated. Discontinuous molecular dynamic simulations have been performed…
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
We derive a new theoretical interpretation of the reweighted losses that are widely used for training diffusion models. Our method is based on constructing a cascade of time-dependent variational lower bounds on the data log-likelihood,…
We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since…
Biomolecular folding and function are often coupled. During molecular recognition events, one of the binding partners may transiently or partially unfold, allowing more rapid access to a binding site. We describe a simple model for this…
The protein folding is regarded as a quantum transition between torsion states on polypeptide chain. The deduction of the folding rate formula in our previous studies is reviewed. The rate formula is generalized to the case of frequency…
A simple way to get insights about the possible functional motions of a protein is to perform a normal mode analysis (NMA). Indeed, it has been shown that low-frequency modes thus obtained are often closely related to domain motions…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
A phenomenological model hamiltonian to describe the folding of a protein with any given sequence is proposed. The protein is thought of as a collection of pieces of helices; as a consequence its configuration space increases with the…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
Recently, a new formalism describing the anomalous diffusion processes, based on the Onsager-Machlup fluctuation theory, has been suggested \cite{Smain, Spub}. We study particles performing this new type of motion, under the action of…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…