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Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just…
Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
While the behavior of double stranded DNA at mesoscopic scales is fairly well understood, less is known about its relation to the rich mechanical properties in the base-pair scale, which is crucial, for instance, to understand DNA-protein…
The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a…
With the continued improvement of sequencing technologies, the prospect of genome-based medicine is now at the forefront of scientific research. To realize this potential, however, we need a revolutionary sequencing method for the…
We investigate kinetic pathways of the DNA melting transition using variable-range versions of the Poland-Scheraga (PS) and Peyrard-Dauxois-Bishop (PDB) models of DNA. In the PS model, we construct a phi^4-field theory to calculate the…
This paper investigates the connection between discrete and continuous models describing prion proliferation. The scaling parameters are interpreted on biological grounds and we establish rigorous convergence statements. We also discuss,…
We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can…
DNA denaturation has long been a subject of intense study due to its relationship to DNA transcription and its fundamental importance as a nonlinear, structural transition. Many aspects of this phenomenon, however, remain poorly understood.…
Single-molecule experiments provide new insights into biological processes hitherto not accessible by measurements performed on bulk systems. We report on a study of the kinetics of a triple-branch DNA molecule with four conformational…
A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a…
The mechanism allowing a protein to search of a target sequence on DNA is currently described as an intermittent process composed of 3D diffusion in bulk and 1D diffusion along the DNA molecule. Due to the relevant charge of protein and…
Nuclear pore complexes (NPCs) are very selective filters that monitor the transport between the cytoplasm and the nucleoplasm. Two models have been suggested for the plug of the NPC. They are (i) it is a reversible hydrogel or (ii) it is a…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other…
The repton model is a simple model of the "reptation" motion by which DNA diffuses through a gel during electrophoresis. In this paper we show that the model can be mapped onto a system consisting of two types of particles with hard-sphere…
The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a…
We report a study of DNA (150 bp fragments) conformations in very low added salt $<0.05$mM, across wide DNA concentration range $0.0015\leq c \leq 8$~mM (bp). We found an intermediate DNA conformation in the region $0.05 < c < 1$~mM, by…
Denoising Diffusion Probabilistic models have become increasingly popular due to their ability to offer probabilistic modeling and generate diverse outputs. This versatility inspired their adaptation for image segmentation, where multiple…