Our Work

This is AI-generated research: the results, proofs and code were found and written by AI. Credit goes to all the humans whose work it builds on.We prove that the largest possible minimal angular dista…

This is AI-generated research: the results, proofs and code were found and written by AI. Credit goes to all the humans whose work it builds on.We prove that the largest possible minimal angular distance between fifteen points on the unit sphere is $\arccos u\approx 53.65785^\circ$, where $u$ is the root in $(1/2,7/10)$ of $13u^5-u^4+6u^3+2u^2-3u-1$. This value is attained by two configurations described by Buddenhagen and Kottwitz, whose contact graphs are not isomorphic, so the optimum is not unique. As Musin and Tarasov did for thirteen and fourteen points, a written reduction leads to plane graphs with at most fifteen vertices, and an interval computation rules out each of them except near the two known optima, where a local rigidity estimate concludes. The computation records certificates, and a second program written independently confirms it. Lean 4 proves every step except the enumeration of the plane graphs and their refutation by the program, which enter the formal proof as hypotheses.Corollary 1.2 of the paper answers in the negative, for $N=15$, Question 2 of Section 6 of Musin and Tarasov, Extremal problems of circle packings on a sphere and irreducible contact graphs, Proc. Steklov Inst. Math. 288 (2015), 117–131 (doi:10.1134/S0081543815010095), numbered as in its Russian version arXiv:1410.0744: is the contact graph of a maximal configuration of $N>5$ points unique up to isomorphism?Lean 4 with Mathlib proves the main theorem and Corollary 1.2, with only the standard axioms, from two hypotheses checked by computation: D2, the completeness of the list of plane graphs, which plantri enumerates, and the search trees of the program, accepted by interval procedures that it computes and whose certificates the repository replays. Two steps are proved on paper: that the program computes these procedures, and D2 from the description of plantri. A second program, written separately, refutes every graph that the first level of the search leaves. Code, Lean proofs and certificates: github.com/mt0-svg/tammes-15

This is the code to process and analyse the data of the twaite shad (Alosa fallax) migration study in the Schelde Estuary as under review in Movement Ecology.

Ushbu maqolada ta’lim muassasalarida o‘qituvchilar faoliyatini samarali boshqarishning mazmuni, asosiy tamoyillari va usullari yoritilgan. O‘qituvchilarning kasbiy faoliyatini to&lsq…

Ushbu maqolada ta’lim muassasalarida o‘qituvchilar faoliyatini samarali boshqarishning mazmuni, asosiy tamoyillari va usullari yoritilgan. O‘qituvchilarning kasbiy faoliyatini to‘g‘ri tashkil etish, ularni rag‘batlantirish, jamoada sog‘lom muhit yaratish hamda zamonaviy boshqaruv usullaridan foydalanish ta’lim sifatini oshirishning muhim omillari sifatida ko‘rib chiqiladi.

This collection brings together teaching materials developed by Boris Vázquez-Calvo (Universidad de Sevilla) for the opening weeks of Didáctica de la Lengua Inglesa / English Language Te…

This collection brings together teaching materials developed by Boris Vázquez-Calvo (Universidad de Sevilla) for the opening weeks of Didáctica de la Lengua Inglesa / English Language Teaching in the 2026–2027 academic year. It is intended for students, teacher educators, and teachers interested in analysing and designing communicative language teaching activities.  The materials address language systems, skills and use; communicative competence; the Common European Framework of Reference for Languages (CEFR); information gaps, choice and feedback; and Communicative Language Teaching (CLT). They connect communication with opportunities for learning through input, output, interaction and repair, attention to language, practice, and fluency development. Nation’s Four Strands provide a framework for examining course balance, while classroom examples distinguish successful task performance from evidence of lasting learning. The consolidated PDF contains 370 pages from 11 documents, organized by week in the sequence T1>Seminar>T2 (T standing for theory), with navigation bookmarks. Both complementary Week 4 T1 decks are retained. Week 4 T2 was taught by the next teacher and falls outside this collection. The accompanying README and study guide provides a page map, key concepts and figures, conceptual associations, suggested readings, and APA 7 references.

This research investigates the systemic interplay between Grade 6 teachers’ profiles, their mathematical dispositions, and the academic performance of students in mathematics within public eleme…

This research investigates the systemic interplay between Grade 6 teachers’ profiles, their mathematical dispositions, and the academic performance of students in mathematics within public elementary schools in the DepEd-Schools Division of Bohol, Philippines. Grounded in the Triadic Framework of Mathematical Dispositions and Mastery Learning Theory, the study employs a quantitative, descriptive-correlational research design to evaluate how teacher characteristics—such as age, gender, civil status, educational attainment, years of teaching experience, and relevant professional development—alongside their cognitive, affective, and conative mathematical dispositions, influence student outcomes measured through classroom grades and Rapid Mathematics Assessment (RMA) results. The findings reveal that while procedural compliance remains steady across demographic profiles, teachers with highly positive mathematical dispositions and advanced postgraduate training significantly foster conceptual understanding, continuous formative growth, and emotional support in the classroom. Conversely, pronounced gaps persist in student performance regarding complex arithmetic applications and spatial reasoning, which are heavily mitigated by targeted teacher upskilling and scaffolded instructional designs. Ultimately, the study underscores that integrating teacher structural stability with robust affective architecture is vital for learning recovery, providing an empirical basis for strategic institutional interventions and localized curriculum policies aligned with the Department of Education’s recent academic recovery mandates.

Code for the PNAS Nexus paper below: PINN (pinn_jax/) and PIKAN (PIKAN_jax/) parameter inference for the macrophage signaling model, and the Monte Carlo inference for Fig. S4 (learnerUQ/). If you use …

Code for the PNAS Nexus paper below: PINN (pinn_jax/) and PIKAN (PIKAN_jax/) parameter inference for the macrophage signaling model, and the Monte Carlo inference for Fig. S4 (learnerUQ/). If you use this code, please cite: Zhaojie Chai, Nazanin Ahmadi Daryakenari, and George Em Karniadakis. A Multiscale Signaling–Biophysical Framework Reveals Mechanisms of Macrophage-Mediated RBC Clearance in Sickle Cell and Gaucher Disease. PNAS Nexus (2026), in press. Zhaojie Chai, Guansheng Li, Papa Alioune Ndour, Philippe Connes, Pierre A. Buffet, Melanie Franco, and George Em Karniadakis. In silico biophysics and rheology of blood and red blood cells in Gaucher Disease. PLOS Computational Biology 21(9): e1012705 (2025). https://doi.org/10.1371/journal.pcbi.1012705 Changes from v1.1.0: the README now lists these references; the code is unchanged.

The RSC Organic Chemistry Community Ireland Regional Meeting took place on Friday 12 June 2026 at University College Cork. The meeting in Cork followed successful recent iterations in Queens Universit…

The RSC Organic Chemistry Community Ireland Regional Meeting took place on Friday 12 June 2026 at University College Cork. The meeting in Cork followed successful recent iterations in Queens University Belfast (2025) and University of Galway (2024). Presentations at the meeting ranged in theme from traditional synthetic chemistry, medicinal chemistry, chemical biology to enabling synthetic technologies. The plenary lecture, delivered by Associate Professor Becky Greenaway (Royal Society University Research Fellow at Imperial College London), was a thought-provoking look at high-throughput automation in the synthesis of molecular organic materials and supramolecular assemblies.

A 20 kW class Hall Thruster featuring two coaxial channels has been designed at the University of Pisa and manufactured by Aerospazio Tecnologie. The thruster was preliminarily characterized in 2024 i…

A 20 kW class Hall Thruster featuring two coaxial channels has been designed at the University of Pisa and manufactured by Aerospazio Tecnologie. The thruster was preliminarily characterized in 2024 in the framework of the ESA TANDEM program. The following paper outlines the findings from the recent characterization test campaign performed on the TANDEM thruster coupled with the new cathode developed within the CHEOPS-VHP-BB program. This test was carried out at AEROSPAZIO Tecnologie in 2025 in the LVTF-3 test facility. The TANDEM thruster was operated with three different propellants (Xenon, Krypton, and Argon) in four operating points (from 4.5 to 20 kW) at discharge voltages of 300 and 400 V. Thermal assessments were performed using an infrared thermal camera. This document presents the experimental results collected throughout the testing.