arXiv subjects

Alexander Hoffmann

Publications and source records attributed to Alexander Hoffmann.

4 recordsLinked to original sources

arXiv2026

Diagram of Geodesic Intervals in $C'(1/8)$-Groups

Let $Γ$ be a group characterized by a small cancellation $C'(1/8)$-presentation. We study the structure of its Cayley graph, specifically geodesic intervals and digons. We prove that all geodesic segments $[x,y]$ of length $n$ can be covered by finitely many simple geodesic digons with pairwise $C'(1/8)$-short lower intersections whose lower sides lie on a common geodesic segment $[x,y]$. This is a generalization of a proposition of Kharlampovich-Sklinos (arXiv:2106.05461) for random groups. We then bound this resulting diagram of digons, showing that the total perimeter of its cells and its edge count is bounded by $n$, and the cycle rank is equal to the number of distinct cell contours. Thus, although there may be many different geodesics, the size of their union is bounded linearly in the distance between their endpoints. The constant is independent of the number and lengths of the defining relators. In particular, the estimate applies to infinite presentations with unbounded relator lengths. From this we get a consequence for growth, allowing us to compare the number of geodesic words with the number of group elements of the same length.

math.GM↗

arXiv2026

BioEVAL: A global, multi-institutional benchmark of large language and multimodal models for bioengineering

Large Language Models (LLMs) have demonstrated historic breakthroughs in general reasoning with early successes in biomedical science. However, existing LLM benchmarking emphasizes factual recall, offering limited insight into model performance on frontier and multimodal tasks. We assembled BioEVAL (BioEngineering Validation of AI and LLMs), a global, multi-institutional initiative designed to assess experimental reasoning capability across bioengineering (BE) subfields. BioEVAL spans 11 major BE subfields plus a set of uncategorized items, bringing together 22 research groups to create a PhD-level benchmark comprising 608 evaluation items: 1) 380 multiple-choice questions (MCQs, 359 retained after audit), 2) 218 literature synthesis tasks, and 3) 10 multimodal problems with experimental image interpretation. Benchmark items underwent authoring-group expert review and centralized quality control before evaluation. Following evaluation, a blinded cross-group consensus audit of the highest- and lowest-accuracy MCQ items flagged 21 questions for revision or removal; these were withheld, and all reported MCQ results are computed on the 359 retained items. We evaluated diverse cloud-scale foundation/multimodal models (e.g., ChatGPT, Gemini, and Grok) and locally deployable models suitable for inference on consumer-grade GPUs. Models achieved the highest accuracy of up to 90% on MCQs, similarity score of 0.72 on literature synthesis, and accuracy of 80% on a small sample of multimodal reasoning questions, with substantial performance variation across subfields. Leaderboard rankings characterize current capabilities, limitations, and development priorities across the evaluated BE task categories. BioEVAL is maintained as an extensible benchmark with standardized protocols for continuing expert item contribution and model evaluation.

cs.AI↗

arXiv2025

Teaching RDM in a smart advanced inorganic lab course and its provision in the DALIA platform

Research data management (RDM) is a key data literacy skill that chemistry students must acquire. Concepts such as the FAIR data principles (Findable, Accessible, Interoperable, Reusable) should be taught and applied in undergraduate studies already. Traditionally, research data from labs, theses, and internships were handwritten and stored in inaccessible formats such as PDFs, limiting reuse and machine learning applications. At RWTH Aachen University, a fifth-semester lab course introduces students to the electronic laboratory notebook (ELN) Chemotion, an open-source DFG-funded tool linked to the national NFDI4Chem initiative. Students plan, document, and evaluate experiments digitally, ensuring metadata and analysis are captured for long-term reuse. Chemotion's intuitive interface and repository enable sustainable data sharing. To reinforce RDM, students receive a seminar and access to online training videos with interactive Moodle elements. Herein we highlight the use of the DALIA platform as a discovery tool for the students.

cs.DB↗

arXiv2008

Visibility of Cold Atomic Gases in Optical Lattices for Finite Temperatures

In nearly all experiments with ultracold atoms time-of-flight pictures are the only data available. In this paper we present an analytical strong-coupling calculation for those time-of-flight pictures of bosons in an optical lattice in the Mott phase. This allows us to determine the visibility, which quantifies the contrast of peaks in the time-of-flight pictures, and we suggest how to use it as a thermometer.

cond-mat.stat-mech↗