Related papers: Topological Methods for Exploring Low-density Stat…
When clustering molecular dynamics (MD) trajectories into a few metastable conformational states, the Markov state models (MSMs) assumption of timescale separation between fast intrastate fluctuations and rarely occurring interstate…
Tumor heterogeneity is a complex and widely recognized trait that poses significant challenges in developing effective cancer therapies. In particular, many tumors harbor a variety of subpopulations with distinct therapeutic response…
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…
This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation…
Understanding the merging behavior patterns at freeway on-ramps is important for assistanting the decisions of autonomous driving. This study develops a primitive-based framework to identify the driving patterns during merging processes and…
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects…
The 3D folding of a mammalian gene can be studied by a polymer model, where the chromatin fibre is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors…
Protein folding cooperativity is defined by the nature of the finite-size thermodynamic transition exhibited upon folding: two-state transitions show a free energy barrier between the folded and unfolded ensembles, while downhill folding is…
We introduce a new model to study the oscillations of opposite flows sharing a common bottleneck and moving on two Totally Asymmetric Simple Exclusion Process (TASEP) lanes. We provide a theoretical analysis of the phase diagram, valid when…
We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
The biomolecules in and around a living cell -- proteins, nucleic acids, lipids, carbohydrates -- continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given…
Semiflexible polymers in poor solvents exhibit a rich variety of collapsed morphologies, including globules, toroids, and rodlike bundles, arising from the competition between attractive interactions and chain stiffness. Computer…
We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the…
We describe a systematic approach to construct coarse-grained Markov state models from molecular dynamics data of systems driven into a non-equilibrium steady state. We apply this method to study the globule-stretch transition of a single…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Markov community models have been applied to sessile organisms because such models facilitate estimation of transition probabilities by tracking species occupancy at many fixed observation points over multiple periods of time. Estimation of…
In contrast to the usual bulk-boundary correspondence, topological states localized within the bulk of the system have been numerically identified in quasicrystalline structures, termed bulk localized transport (BLT) states. These states…
Topological magnetic textures are particle-like spin configurations stabilized by competing interactions. Their formation is commonly attributed to fluctuation-driven, first-order nucleation processes requiring activation over a topological…