Newton polygons of L functions of polynomials x+ax

Ouyang, Yi; Yang, Jinbang

doi:10.1016/j.jnt.2015.09.020

Cited by 10 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For f (x) = x d + ax, Zhu, Liu-Niu and Ouyang-J. Yang obtained the slopes in [Z2, Theorem 1.1], [LN1,Theorem 1.10] and [OY,Theorem 1.1], see also R. Yang [Y,§1 Theorem] for earlier results.…”

Section: Resultsmentioning

confidence: 99%

“…In [N], Niu gave a lower bound of the Newton polygon NP q (f, χ, t). In [OY,Theorem 4.3], Ouyang-Yang showed that if the Newton polygon of L * (f, t) is sufficiently close to its Hodge polygon, the slopes of NP q (f, χ, t) for χ in general follow from the slopes of NP q (f, t). As a consequence they obtained the slopes of NP q (x d + ax, χ, t) when p is bigger than an explicit bound depending only on d and h.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Newton polygons of $L$-functions of polynomials $x^d+ax^{d-1}$ with $p\equiv-1\bmod d$

Ouyang,

Zhang

2015

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Newton polygons of $L$-functions of polynomials $x^d+ax^{d-1}$ with $p\equiv-1\bmod d$

Ouyang,

Zhang

2015

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Instruction-tuned large language models (LLMs) have been successful at knowledge retrieval, text extraction, summarization, and reasoning tasks without requiring domain-specific fine-tuning. Prompting LLMs with instruction and data contexts described in natural language has emerged as a means for task and domain specification as well as controllability of model behaviors .…”

Section: Introductionmentioning

confidence: 99%

Large Language Model Capabilities in Perioperative Risk Prediction and Prognostication

Chung,

Fong,

Walters

et al. 2024

JAMA Surg

View full text Add to dashboard Cite

ImportanceGeneral-domain large language models may be able to perform risk stratification and predict postoperative outcome measures using a description of the procedure and a patient’s electronic health record notes.ObjectiveTo examine predictive performance on 8 different tasks: prediction of American Society of Anesthesiologists Physical Status (ASA-PS), hospital admission, intensive care unit (ICU) admission, unplanned admission, hospital mortality, postanesthesia care unit (PACU) phase 1 duration, hospital duration, and ICU duration.Design, Setting, and ParticipantsThis prognostic study included task-specific datasets constructed from 2 years of retrospective electronic health records data collected during routine clinical care. Case and note data were formatted into prompts and given to the large language model GPT-4 Turbo (OpenAI) to generate a prediction and explanation. The setting included a quaternary care center comprising 3 academic hospitals and affiliated clinics in a single metropolitan area. Patients who had a surgery or procedure with anesthesia and at least 1 clinician-written note filed in the electronic health record before surgery were included in the study. Data were analyzed from November to December 2023.ExposuresCompared original notes, note summaries, few-shot prompting, and chain-of-thought prompting strategies.Main Outcomes and MeasuresF1 score for binary and categorical outcomes. Mean absolute error for numerical duration outcomes.ResultsStudy results were measured on task-specific datasets, each with 1000 cases with the exception of unplanned admission, which had 949 cases, and hospital mortality, which had 576 cases. The best results for each task included an F1 score of 0.50 (95% CI, 0.47-0.53) for ASA-PS, 0.64 (95% CI, 0.61-0.67) for hospital admission, 0.81 (95% CI, 0.78-0.83) for ICU admission, 0.61 (95% CI, 0.58-0.64) for unplanned admission, and 0.86 (95% CI, 0.83-0.89) for hospital mortality prediction. Performance on duration prediction tasks was universally poor across all prompt strategies for which the large language model achieved a mean absolute error of 49 minutes (95% CI, 46-51 minutes) for PACU phase 1 duration, 4.5 days (95% CI, 4.2-5.0 days) for hospital duration, and 1.1 days (95% CI, 0.9-1.3 days) for ICU duration prediction.Conclusions and RelevanceCurrent general-domain large language models may assist clinicians in perioperative risk stratification on classification tasks but are inadequate for numerical duration predictions. Their ability to produce high-quality natural language explanations for the predictions may make them useful tools in clinical workflows and may be complementary to traditional risk prediction models.

show abstract

“…Among these models, ChatGPT (OpenAI) has emerged as a particularly powerful tool based on GPT-3.5 that was designed specifically for the task of generating natural and contextually appropriate responses in a conversational setting. Building on the GPT-3 model, GPT-3.5 was trained on a larger corpus of textual data and with additional training techniques like Reinforcement Learning from Human Feedback (RLHF), which incorporates human knowledge and expertise into the model . This chatbot is an implementation of GPT-3.5 fine-tuned on conversational data, allowing it to generate appropriate responses to user input in a conversational context .…”

Section: Introductionmentioning

confidence: 99%

Comparison of Ophthalmologist and Large Language Model Chatbot Responses to Online Patient Eye Care Questions

Bernstein,

Zhang,

Govil

et al. 2023

JAMA Netw Open

View full text Add to dashboard Cite

ImportanceLarge language models (LLMs) like ChatGPT appear capable of performing a variety of tasks, including answering patient eye care questions, but have not yet been evaluated in direct comparison with ophthalmologists. It remains unclear whether LLM-generated advice is accurate, appropriate, and safe for eye patients.ObjectiveTo evaluate the quality of ophthalmology advice generated by an LLM chatbot in comparison with ophthalmologist-written advice.Design, Setting, and ParticipantsThis cross-sectional study used deidentified data from an online medical forum, in which patient questions received responses written by American Academy of Ophthalmology (AAO)–affiliated ophthalmologists. A masked panel of 8 board-certified ophthalmologists were asked to distinguish between answers generated by the ChatGPT chatbot and human answers. Posts were dated between 2007 and 2016; data were accessed January 2023 and analysis was performed between March and May 2023.Main Outcomes and MeasuresIdentification of chatbot and human answers on a 4-point scale (likely or definitely artificial intelligence [AI] vs likely or definitely human) and evaluation of responses for presence of incorrect information, alignment with perceived consensus in the medical community, likelihood to cause harm, and extent of harm.ResultsA total of 200 pairs of user questions and answers by AAO-affiliated ophthalmologists were evaluated. The mean (SD) accuracy for distinguishing between AI and human responses was 61.3% (9.7%). Of 800 evaluations of chatbot-written answers, 168 answers (21.0%) were marked as human-written, while 517 of 800 human-written answers (64.6%) were marked as AI-written. Compared with human answers, chatbot answers were more frequently rated as probably or definitely written by AI (prevalence ratio [PR], 1.72; 95% CI, 1.52-1.93). The likelihood of chatbot answers containing incorrect or inappropriate material was comparable with human answers (PR, 0.92; 95% CI, 0.77-1.10), and did not differ from human answers in terms of likelihood of harm (PR, 0.84; 95% CI, 0.67-1.07) nor extent of harm (PR, 0.99; 95% CI, 0.80-1.22).Conclusions and RelevanceIn this cross-sectional study of human-written and AI-generated responses to 200 eye care questions from an online advice forum, a chatbot appeared capable of responding to long user-written eye health posts and largely generated appropriate responses that did not differ significantly from ophthalmologist-written responses in terms of incorrect information, likelihood of harm, extent of harm, or deviation from ophthalmologist community standards. Additional research is needed to assess patient attitudes toward LLM-augmented ophthalmologists vs fully autonomous AI content generation, to evaluate clarity and acceptability of LLM-generated answers from the patient perspective, to test the performance of LLMs in a greater variety of clinical contexts, and to determine an optimal manner of utilizing LLMs that is ethical and minimizes harm.

show abstract

Newton polygons of L functions of polynomials x+ax

Cited by 10 publications

References 9 publications

Newton polygons of $L$-functions of polynomials $x^d+ax^{d-1}$ with $p\equiv-1\bmod d$

Newton polygons of $L$-functions of polynomials $x^d+ax^{d-1}$ with $p\equiv-1\bmod d$

Large Language Model Capabilities in Perioperative Risk Prediction and Prognostication

Comparison of Ophthalmologist and Large Language Model Chatbot Responses to Online Patient Eye Care Questions

Contact Info

Product

Resources

About