Related papers: A Physics-informed Sheaf Model
We propose a new approach for modelling the process of RNA folding as a graph transformation guided by the global value of free energy. Since the folding process evolves towards a configuration in which the free energy is minimal, the…
Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…
It has been suggested in Hoyng (2009) that dynamo action can be analysed by expansion of the magnetic field into dynamo modes and statistical evaluation of the mode coefficients. We here validate this method by analysing a numerical…
Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions,…
We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially…
As a step toward analyzing second-harmonic generation (SHG) from crystalline Si nanospheres in glass, we develop an anisotropic bond model (ABM) that expresses SHG in terms of physically meaningful parameters and provides a detailed…
Developing microscopic understanding of the thermal properties of liquids is challenging due to their strong dynamic disorder, which prevents characterization of the atomic degrees of freedom. There have been significant research interests…
We develop a quasi-normal mode theory (QNMT) to calculate a system's scattering $S$ matrix, simultaneously satisfying both energy conservation and reciprocity even for a small truncated set of resonances. It is a practical reduced-order…
We review the ab initio symmetry-adapted (SA) framework for determining the structure of stable and unstable nuclei, along with related electroweak, decay and reaction processes. This framework utilizes the dominant symmetry of nuclear…
A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have…
Recent developments in elastic shape analysis (ESA) are motivated by the fact that it provides comprehensive frameworks for simultaneous registration, deformation, and comparison of shapes. These methods achieve computational efficiency…
Mechanical metamaterials designed around a zero-energy pathway of deformation, known as a mechanism, have repeatedly challenged the conventional picture of elasticity. However, the complex spatial deformations these structures are able to…
The normal modes, i.e., the eigen solutions to the dispersion relation equation, are the most fundamental properties of a plasma, which also of key importance to many nonlinear effects such as parametric and two-plasmon decay, and Raman…
We propose a novel technique for sampling particle physics model parameter space. The main sampling method applied is Nested Sampling (NS), which is boosted by the application of multiple Machine Learning (ML) networks, e.g.,…
The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system.…
Background: Previous studies have used different methods in an effort to extract the modular organization of transcriptional regulatory networks (TRNs). However, these approaches are not natural, as they try to cluster highly connected…
This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us…
We generalize normal mode expansion of Green's tensor $\bar{\bar{G}}(\bf{r},\bf{r}')$ to lossy resonators in open systems, resolving a longstanding open challenge. We obtain a simple yet robust formulation, whereby radiation of energy to…
What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…