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Fred Cohen

Publications and source records attributed to Fred Cohen.

5 recordsLinked to original sources

Configuration Spaces and Braid Groups

The main thrust of these notes is 3-fold: (1) An analysis of certain $K(\pi,1)$'s that arise from the connections between configuration spaces, braid groups, and mapping class groups, (2) a function space interpretation of these results, and (3) a homological analysis of the cohomology of some of these groups for genus zero, one, and two surfaces possibly with marked points, as well as the cohomology of certain associated function spaces. An example of the type of results given here is an analysis of the space k particles moving on a punctured torus up to equivalence by the natural $SL(2,\mathbb{Z})$ action.

math.AT

Ten Headache Specialists versus Artificial Intelligence for Clinical Literature Summarization: A Critical Evaluation and Comparison

Summarizing the latest medical literature to guide clinical decision-making is essential for evidence-based medicine and high-quality patient care. Yet clinicians face increasing challenges due to limited time with patients and a rapidly growing volume of published articles. Although retrieval-augmented large language models (LLMs) have shown promise in clinical summarization, human evaluations of their effectiveness in synthesizing broader scientific literature and direct comparisons to expert-written syntheses remain scarce. We constructed a RAG-based agentic AI framework using three state-of-the-art LLMs: Sonnet, GPT-4o, and Llama 3.1. A headache specialist created 13 questions, three for prompt optimization and ten for evaluation. Ten headache specialists across the United States and Canada each wrote a summary for one question, yielding four summaries per question (expert, Sonnet, GPT-4o, and Llama). The experts, blinded to authorship, critically evaluated the summaries, excluding the topic for which they wrote a summary, based on correctness, completeness, conciseness, and clinical utility, scoring each from 1 to 10 using standardized rubrics. They also ranked the summaries by preference and indicated whether they believed each summary was written by an expert or an LLM. Our study, comparing LLM- and expert-written literature summaries evaluated by headache specialists, showed that expert-written summaries were preferred, although experts sometimes found it challenging to distinguish between human- and AI-generated summaries. We also identified key expert-valued features beyond standard evaluation metrics that can guide future refinement of both human and AI literature summarization pipelines.

cs.AI

Bounds on Multiple Sensor Fusion

We consider the problem of fusing measurements from multiple sensors, where the sensing regions overlap and data are non-negative---possibly resulting from a count of indistinguishable discrete entities. Because of overlaps, it is, in general, impossible to fuse this information to arrive at an accurate estimate of the overall amount or count of material present in the union of the sensing regions. Here we study the range of overall values consistent with the data. Posed as a linear programming problem, this leads to interesting questions associated with the geometry of the sensor regions, specifically, the arrangement of their non-empty intersections. We define a computational tool called the fusion polytope and derive a condition for this to be in the positive orthant thus simplifying calculations. We show that, in two dimensions, inflated tiling schemes based on rectangular regions fail to satisfy this condition, whereas inflated tiling schemes based on hexagons do.

eess.SY

Cohomology of braids, principal congruence subgroups and geometric representations

The main purpose of this article is to give the integral cohomology of classical principal congruence subgroups in SL(2,Z) as well as their analogues in the third braid group with local coefficients in symmetric powers of the natural symplectic representation. The resulting answers (1) correspond to certain modular forms in characteristic zero, and (2) the cohomology of certain spaces in homotopy theory in characteristic p. The torsion is given in terms of the structure of a "p-divided power algebra". The work is an extension of the work in arXiv:1204.5390v1 as well as extensions of a classical computation of Shimura to integral coefficients. The results here contrast the local coefficients such as that in [Looijenga, J. Alg. Geom., 5, '96] and [Tillmann, Q. J. Math., 61, '10].

math.AT

The cohomology of the braid group B_3 and of SL_2(Z) with coefficients in a geometric representation

The purpose of this article is to describe the integral cohomology of the braid group B_3 and SL_2(Z) with local coefficients in a classical geometric representation given by symmetric powers of the natural symplectic representation. These groups have a description in terms of the so called "divided polynomial algebra". The results show a strong relation between torsion part of the computed cohomology and fibrations related to loop spaces of spheres.

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