Related papers: Topological Methods for Exploring Low-density Stat…
Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…
One among several advantages of measure transport methods is that they allow for a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results…
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold…
Topological photonics and acoustics have recently garnered wide research interests for their topological ability to manipulate the light and sound at surfaces. Conventionally, the supercell technique is the standard approach to calculating…
Markov state models represent a popular means to interpret molecular dynamics trajectories in terms of memoryless transitions between metastable conformational states. To provide a mechanistic understanding of the considered biomolecular…
Developing accurate and efficient coarse-grained representations of proteins is crucial for understanding their folding, function, and interactions over extended timescales. Our methodology involves simulating proteins with molecular…
Simplified representations of macromolecules help in rationalising and understanding the outcome of atomistic simulations, and serve to the construction of effective, coarse-grained models. The number and distribution of coarse-grained…
Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…
A model of quasistationary states is constructed for the one-dimensional edge states propagating along the edge of a two-dimensional topological insulator based on HgTe/CdTe quantum well in the presence of magnetic barriers with finite…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
Our world is ambiguous and this is reflected in the data we use to train our algorithms. This is particularly true when we try to model natural processes where collected data is affected by noisy measurements and differences in measurement…
We propose a regularization framework inspired by thermodynamic work for guiding pre-trained probability flow generative models (e.g., continuous normalizing flows or diffusion models) by minimizing excess work, a concept rooted in…
Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…
Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
The study of the rare transitions that take place between long lived metastable states is a major challenge in molecular dynamics simulations. Many of the methods suggested to address this problem rely on the identification of the slow…
The discovery of the topological insulators has fueled a surge of interests in the topological phases in periodic systems. Topological insulators have bulk energy gap and topologically protected gapless edge states. The edge states in…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network…
Quantifying population dynamics is a fundamental challenge in ecology and evolutionary biology, particularly for species that are cryptic, microscopic, or extinct. Traditional approaches rely on continuous representations of population…