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Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
Predicting materials properties from composition or structure is of great interest to the materials science community. Deep learning has recently garnered considerable interest in materials predictive tasks with low model errors when…
A key problem in computational material science deals with understanding the effect of material distribution (i.e., microstructure) on material performance. The challenge is to synthesize microstructures, given a finite number of…
Molecular structure elucidation is a fundamental step in understanding chemical phenomena, with applications in identifying molecules in natural products, lab syntheses, forensic samples, and the interstellar medium. We consider the task of…
Spatial transcriptomics (ST) bridges gene expression and tissue morphology but faces clinical adoption barriers due to technical complexity and prohibitive costs. While computational methods predict gene expression from H&E-stained…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
A system-level genetic code is a hypothetical genetic code that exclusively or preferentially codes systems of interacting coadapted parts. System-level genetic codes differ from part-level genetic codes in which each discrete part is coded…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
A new model is proposed for fusion mechanisms of massive nuclear systems where so-called fusion hindrance exists. The model describes two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into…
Motivation: Molecular interaction networks summarize complex biological processes as graphs, whose structure is informative of biological function at multiple scales. Simultaneously, omics technologies measure the variation or activity of…
The mechanical properties of metal matrix fiber-reinforced composites depend on many aspects of their structure in a complicated way. In this paper, we propose a \emph{minimalistic} approach to study interface debonding, matrix cracking,…
Mechanically interlocked molecules have marked a breakthrough in the field of topological chemistry and boosted the vigorous development of molecular machinery. As an archetypal example of the interlocked molecules, catenanes comprise…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
Despite their impressive performance, generative image models trained on large-scale datasets frequently fail to produce images with seemingly simple concepts -- e.g., human hands or objects appearing in groups of four -- that are…
Using density-functional theory and a tight-binding approach we investigate the physical origin of distinct favourable geometries of adsorbed hydrogen atoms in various graphyne structures, and the relation with electronic properties. In…
We present a model-centric diagnostic framework that treats training state as a latent variable and unifies a family of internal readouts -- head-gradient norms, confidence, entropy, margin, and related signals -- as anchor-relative…
Cancer diagnosis, prognosis, and therapeutic response predictions are based on morphological information from histology slides and molecular profiles from genomic data. However, most deep learning-based objective outcome prediction and…