Sammüller, Florian Hermann, Sophie Schmidt, Matthias
Published in
Journal of Physics: Condensed Matter

We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammüller et al (2023 Proc. Natl Acad. Sci. 120 e2312484120) gives a functional representation of direct correl...

Shi, Cheng Pan, Liming Hu, Hong Dokmanić, Ivan
Published in
Proceedings of the National Academy of Sciences of the United States of America

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical learning theory fail to account for observed phenomena like the double descent or the impact of relational semantics ...

DeLuca, Marcello Sensale, Sebastian Lin, Po-An Arya, Gaurav
Published in
ACS applied bio materials

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nan...

Marino, Raffaele Ricci-Tersenghi, Federico
Published in
Machine Learning: Science and Technology

The use of mini-batches of data in training artificial neural networks is nowadays very common. Despite its broad usage, theories explaining quantitatively how large or small the optimal mini-batch size should be are missing. This work presents a systematic attempt at understanding the role of the mini-batch size in training two-layer neural networ...

Ord, G. N.
Published in
Frontiers in Physics

The chessboard model was Feynman’s adaptation of his path integral method to a two-dimensional relativistic domain. It is shown that chessboard paths encode information about the contiguous pairs of paths in a spacetime plane, as required by discrete worldlines in Minkowski space. The application of coding by pairs in a four-dimensional spacetime i...

Wu, Tong David, Tomos Bos, Wouter J T
Published in
Journal of Statistical Mechanics: Theory and Experiment

In turbulent systems with inverse cascades, energy will pile up at large scales if no large-scale sink is present. We observe that in forced-dissipative three-dimensional turbulence from which vortex-stretching is removed, such condensation is observed, associated with an inverse cascade of helicity. The large-scale structure of this condensate is ...

Fernández, Francisco M
Published in
European Journal of Physics

We argue that the approximate analytical expression for the canonical partition function for a particle in a box proposed recently was derived earlier by other authors in a more straightforward and efficient way. We also show that the canonical partition function for the particle in a finite box derived by the same authors is incorrect because they...

Falkner, Sebastian Coretti, Alessandro Romano, Salvatore Geissler, Phillip L Dellago, Christoph
Published in
Machine Learning: Science and Technology

Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of transition paths using a random walk in trajectory space. This, however, comes with the drawback of strong correlat...

Lewis, Greyson R Marshall, Wallace F

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and funct...

Zhdankin, Vladimir
Published in
Journal of Physics A: Mathematical and Theoretical

Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond the additive definition pioneered by Boltzmann, Gibbs, and Shannon (applicable to thermodynamic equilibria). F...