Related papers: Semi-quantitative diagram about temporal evolution…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
We study the classical and semiclassical time evolutions of subsystems of a Hamiltonian system; this is done using a generalization of Heller's thawed Gaussian approximation introduced by Littlejohn. The key tool in our study is an…
Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…
The teaching of matrix multiplication in secondary education is often limited to the mechanical application of the row-by-column algorithm, leaving aside its interpretation as a geometric transformation. This study analyzes the impact of a…
Morphological development is part of the way any human or animal learns. The learning processes starts with the morphology at birth and progresses through changing morphologies until adulthood is reached. Biologically, this seems to…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…
We study the homogenization of a linear kinetic equation which models the evolution of the density of charged particles submitted to a highly oscillating electric field. The electric field and the initial density are assumed to be random…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
Understanding how learners conceptualise complex scientific systems remains a key challenge in geoscience education. We investigate the evolution of conceptual understanding of cloud physics among 153 learners, ranging from bachelor…
As children grow older, they develop an intuitive understanding of the physical processes around them. They move along developmental trajectories, which have been mapped out extensively in previous empirical research. We investigate how…
We demonstrate that the update of weight matrices in learning algorithms can be described in the framework of Dyson Brownian motion, thereby inheriting many features of random matrix theory. We relate the level of stochasticity to the ratio…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…
Hypergraphs provide a natural framework for modeling higher-order interactions, yet their theoretical underpinnings in semi-supervised learning remain limited. We provide an asymptotic consistency analysis of variational learning on random…
Urban transportation systems face increasing resilience challenges from extreme weather events, but current assessment methods rely on surface-level recovery indicators that miss hidden structural damage. Existing approaches cannot…
Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity…
This paper introduces a SSSUMO, semi-supervised deep learning approach for submovement decomposition that achieves state-of-the-art accuracy and speed. While submovement analysis offers valuable insights into motor control, existing methods…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
Traditional problem-based exams are not efficient instruments for assessing the "structure" of physics students' conceptual knowledge or for providing diagnostically detailed feedback to students and teachers. We present the Free Term Entry…