Related papers: A Physics-informed Sheaf Model

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynam- ics simulation. Best…

The aim of this article is a comprehensive description of normal modes of molecular vibrations. The starting point is chosen to be a general molecular system with separated center of mass and an arbitrary embedding of body-fixed axes. This…

Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical…

A ternary/binary data coding algorithm and conditions under which Hopfield networks implement optimal convolutional or Hamming decoding algorithms has been described. Using the coding/decoding approach (an optimal Binary Signal Detection…

Interpretable representation learning is a central challenge in modern machine learning, particularly in high-dimensional settings such as neuroimaging, genomics, and text analysis. Current methods often struggle to balance the competing…

We propose the Neural Functional Alignment Space (NFAS), a brain-referenced representational framework for characterizing artificial neural networks on equal functional grounds. NFAS departs from conventional alignment approaches that rely…

Gaussian network model(GNM) and anisotropic network model(ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM(gGNM) and ANM methods and show that the…

We construct the molecular model and the tensor model for the dynamics of the nematic phases of bent-core molecules and star molecules in incompressible fluid. We start from the molecular interaction and the molecule--fluid friction, and…

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by the…

Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear…

Magnetic resonance imaging (MRI) is the method of choice for noninvasive studies of micrometer-scale structures in biological tissues via their effects on the time/frequency-dependent ("restricted") and anisotropic self-diffusion of water.…

We study how the optimization landscape of a neural network deforms as a non-linear activation is introduced through a smooth homotopy. Working first in an abstract local setting - a smooth one-parameter family of objective functions…

The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets…

Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA),…

Normal mode analysis is a widely used technique for reconstructing conformational changes of proteins from the knowledge of native structures. In this Letter, we investigate to what extent normal modes capture the salient features of the…

The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent…

Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight…

Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their…

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they…