We introduced a novel method for visualizing large diophantine datasets and in particular found that mapping the known integer triplets [Formula: see text] solving either equations of the type [Formula: see text] or [Formula: see text] on certain proper subgroups of the circle group exposed a very clear breaking in their symmetry and a strongly non-ergodic distribution of the solutions of sums of three cubes that had never been described before. This method could be further applied to a larger diversity of diophantine problems, informing both number-theoretical conjectures and novel methods in computer sciences on the way, along with paving the road for specific uses of machine learning in exploring diophantine datasets with possible applications in cryptography among others.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10762201 | PMC |
| http://dx.doi.org/10.1038/s41598-023-49960-y | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Electronic structure of superconducting infinite-layer lanthanum nickelates.
Sci Adv
January 2025
National Laboratory of Solid State Microstructures, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China.
Revealing the momentum-resolved electronic structure of infinite-layer nickelates is essential for understanding this class of unconventional superconductors but has been hindered by the formidable challenges in improving the sample quality. In this work, we report the angle-resolved photoemission spectroscopy of superconducting LaSrNiO films prepared by molecular beam epitaxy and in situ atomic-hydrogen reduction. The measured Fermi topology closely matches theoretical calculations, showing a large Ni [Formula: see text]-derived Fermi sheet that evolves from hole-like to electron-like along and a three-dimensional (3D) electron pocket centered at the Brillouin zone corner.
View Article and Find Full Text PDFIdentifying key genes in cancer networks using persistent homology.
Sci Rep
January 2025
University of São Paulo, ICMC, São Carlos, 13566-590, Brazil.
Identifying driver genes is crucial for understanding oncogenesis and developing targeted cancer therapies. Driver discovery methods using protein or pathway networks rely on traditional network science measures, focusing on nodes, edges, or community metrics. These methods can overlook the high-dimensional interactions that cancer genes have within cancer networks.
View Article and Find Full Text PDFPolymorphism and magnetism in a Kitaev honeycomb cobaltate KCoAsO.
Sci Rep
January 2025
Department of Applied Physics and Chemical Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo, 184-8588, Japan.
We report the synthesis, crystal structure, and magnetic properties of a new Kitaev honeycomb cobaltate, KCoAsO, which crystallizes in two distinct forms: P2/c and R[Formula: see text] space groups. Magnetic measurements reveal ordering temperatures of ~ 14 K for the P2/c structure and ~ 10.5 K for the R[Formula: see text] structure.
View Article and Find Full Text PDFMinimal sourced and lightweight federated transfer learning models for skin cancer detection.
Sci Rep
January 2025
School of Computer Science and AI, SR University, Warangal, Telangana, India.
One of the most fatal diseases that affect people is skin cancer. Because nevus and melanoma lesions are so similar and there is a high likelihood of false negative diagnoses challenges in hospitals. The aim of this paper is to propose and develop a technique to classify type of skin cancer with high accuracy using minimal resources and lightweight federated transfer learning models.
View Article and Find Full Text PDFOntogeny of energy use in harvester ant colonies, and the metabolic expense of colony growth.
Proc Biol Sci
January 2025
School of Life Sciences, Arizona State University, Tempe, AZ 85287, USA.
In animals, metabolic rates during ontogeny often scale differently from the way they do in cross-species or population comparisons, with near-isometric scaling patterns more often observed during juvenile growth. In multiple social insect taxa, colony metabolic rate scales hypometrically across species or populations at the same developmental stage, but metabolic patterns during ontogeny have not been examined for any social insect species. We performed the first ontogenetic study of social metabolic scaling in harvester ant colonies () over 3.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!