An official website of the United States government
We analyze the spectrum of a discrete Schrödinger operator with a potential given by a periodic variant of the Anderson model. In order to do so, we study the uniform hyperbolicity of a Schrödinger cocycle generated by the SL(2,R) transfer matrices. In the specific case of the potential generated by an alternating sequence of random values, we show that the almost sure spectrum consists of at most 4 intervals.
more »
« less
On the quotient of the homology cobordism group by Seifert spaces
We prove that the quotient of the integer homology cobordism group by the subgroup generated by the Seifert fibered spaces is infinitely generated.
more »
« less
- PAR ID:
- 10413988
- Date Published:
- Journal Name:
- Transactions of the American Mathematical Society, Series B
- Volume:
- 9
- Issue:
- 25
- ISSN:
- 2330-0000
- Page Range / eLocation ID:
- 757 to 781
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Recently, there have been significant advances and wide-scale use of generative AI in natural language generation. Models such as OpenAI’s GPT3 and Meta’s LLaMA are widely used in chatbots, to summarize documents, and to generate creative content. These advances raise concerns about abuses of these models, especially in social media settings, such as large-scale generation of disinformation, manipulation campaigns that use AI-generated content, and personalized scams. We used stylometry (the analysis of style in natural language text) to analyze the style of AI-generated text. Specifically, we applied an existing authorship verification (AV) model that can predict if two documents are written by the same author on texts generated by GPT2, GPT3, ChatGPT and LLaMA. Our AV model was trained only on human-written text and was effectively used in social media settings to analyze cases of abuse. We generated texts by providing the language models with fanfiction snippets and prompting them to complete the rest of it in the same writing style as the original snippet. We then applied the AV model across the texts generated by the language models and the human written texts to analyze the similarity of the writing styles between these texts. We found that texts generated with GPT2 had the highest similarity to the human texts. Texts generated by GPT3 and ChatGPT were very different from the human snippet, and were similar to each other. LLaMA-generated texts had some similarity to the original snippet but also has similarities with other LLaMA-generated texts and texts from other models. We then conducted a feature analysis to identify the features that drive these similarity scores. This analysis helped us answer questions like which features distinguish the language style of language models and humans, which features are different across different models, and how these linguistic features change over different language model versions. The dataset and the source code used in this analysis have been made public to allow for further analysis of new language models.more » « less
-
Abstract Let $${\mathrm{Diff}}_{0}(N)$$ represent the subgroup of diffeomorphisms that are homotopic to the identity. We show that if $$N$$ is a closed hyperbolic 4-manifold, then $$\pi _{0}{\mathrm{Diff}}_{0}(N)$$ is not finitely generated with similar results holding topologically. This proves in dimension-4 results previously known for $$n$$-dimensional hyperbolic manifolds of dimension $$n\ge 11$$ by Farrell and Jones in 1989 and $$n\ge 10$$ by Farrell and Ontaneda in 2010. Our proof relies on the technical result that $$\pi _{0}{\mathrm{Homeo}}(S^{1}\times D^{3})$$ is not finitely generated, which extends to the topological category smooth results of the authors. We also show that $$\pi _{n-4} {\mathrm{Homeo}}(S^{1} \times D^{n-1})$$ is not finitely generated for $$n \geq 4$$ and in particular $$\pi _{0}{\mathrm{Homeo}}(S^{1}\times D^{3})$$ is not finitely generated. These results are new for $n=4, 5$ and $$7$$. We also introduce higher dimensional barbell maps and establish some of their basic properties.more » « less
-
Rambow, Owen; Wanner, Leo; Apidianaki, Marianna; Khalifa, Hend; Eugenio, Barbara; Schockaert, Steven (Ed.)We propose a novel framework that leverages Visual Question Answering (VQA) models to automate the evaluation of LLM-generated data visualizations. Traditional evaluation methods often rely on human judgment, which is costly and unscalable, or focus solely on data accuracy, neglecting the effectiveness of visual communication. By employing VQA models, we assess data representation quality and the general communicative clarity of charts. Experiments were conducted using two leading VQA benchmark datasets, ChartQA and PlotQA, with visualizations generated by OpenAI’s GPT-3.5 Turbo and Meta’s Llama 3.1 70B-Instruct models. Our results indicate that LLM-generated charts do not match the accuracy of the original non-LLM-generated charts based on VQA performance measures. Moreover, while our results demonstrate that few-shot prompting significantly boosts the accuracy of chart generation, considerable progress remains to be made before LLMs can fully match the precision of human-generated graphs. This underscores the importance of our work, which expedites the research process by enabling rapid iteration without the need for human annotation, thus accelerating advancements in this field.more » « less
-
We propose a novel framework that leverages Visual Question Answering (VQA) models to automate the evaluation of LLM-generated data visualizations. Traditional evaluation methods often rely on human judgment, which is costly and unscalable, or focus solely on data accuracy, neglecting the effectiveness of visual communication. By employing VQA models, we assess data representation quality and the general communicative clarity of charts. Experiments were conducted using two leading VQA benchmark datasets, ChartQA and PlotQA, with visualizations generated by OpenAI’s GPT-3.5 Turbo and Meta’s Llama 3.1 70B-Instruct models. Our results indicate that LLM-generated charts do not match the accuracy of the original non-LLM-generated charts based on VQA performance measures. Moreover, while our results demonstrate that few-shot prompting significantly boosts the accuracy of chart generation, considerable progress remains to be made before LLMs can fully match the precision of human-generated graphs. This underscores the importance of our work, which expedites the research process by enabling rapid iteration without the need for human annotation, thus accelerating advancements in this field.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1090/btran/110
