TRIGO: Benchmarking Formal Mathematical Proof Reduction for Generative Language Models

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve the understanding of complex number combination reasoning. In this work, we propose TRIGO, an ATP benchmark that not only requires a model to reduce a trigonometric expression with step-by-step proofs but also evaluates a generative LM's reasoning ability on formulas and its capability to manipulate, group, and factor number terms. We gather trigonometric expressions and their reduced forms from the web, annotate the simplification process manually, and translate it into the Lean formal language system. We then automatically generate additional examples from the annotated samples to expand the dataset. Furthermore, we develop an automatic generator based on Lean-Gym to create dataset splits of varying difficulties and distributions in order to thoroughly analyze the model's generalization ability. Our extensive experiments show our proposed TRIGO poses a new challenge for advanced generative LM's including GPT-4 which is pre-trained on a considerable amount of open-source formal theorem-proving language data, and provide a new tool to study the generative LM's ability on both formal and mathematical reasoning.Comment: Accepted by EMNLP 2023. Code is available at https://github.com/menik1126/TRIG

LEGO-Prover: Neural Theorem Proving with Growing Libraries

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results, but they still struggle to prove even middle school level theorems. One common limitation of these methods is that they assume a fixed theorem library during the whole theorem proving process. However, as we all know, creating new useful theorems or even new theories is not only helpful but crucial and necessary for advancing mathematics and proving harder and deeper results. In this work, we present LEGO-Prover, which employs a growing skill library containing verified lemmas as skills to augment the capability of LLMs used in theorem proving. By constructing the proof modularly, LEGO-Prover enables LLMs to utilize existing skills retrieved from the library and to create new skills during the proving process. These skills are further evolved (by prompting an LLM) to enrich the library on another scale. Modular and reusable skills are constantly added to the library to enable tackling increasingly intricate mathematical problems. Moreover, the learned library further bridges the gap between human proofs and formal proofs by making it easier to impute missing steps. LEGO-Prover advances the state-of-the-art pass rate on miniF2F-valid (48.0% to 57.0%) and miniF2F-test (45.5% to 47.1%). During the proving process, LEGO-Prover also manages to generate over 20,000 skills (theorems/lemmas) and adds them to the growing library. Our ablation study indicates that these newly added skills are indeed helpful for proving theorems, resulting in an improvement from a success rate of 47.1% to 50.4%. We also release our code and all the generated skills

Activation of the STAT3 Signaling Pathway by the RNA-Dependent RNA Polymerase Protein of Arenavirus

Arenaviruses cause chronic and asymptomatic infections in their natural host, rodents, and several arenaviruses cause severe hemorrhagic fever that has a high mortality in infected humans, seriously threatening public health. There are currently no FDA-licensed drugs available against arenaviruses; therefore, it is important to develop novel antiviral strategies to combat them, which would be facilitated by a detailed understanding of the interactions between the viruses and their hosts. To this end, we performed a transcriptomic analysis on cells infected with arenavirus lymphocytic choriomeningitis virus (LCMV), a neglected human pathogen with clinical significance, and found that the signal transducer and activator of transcription 3 (STAT3) signaling pathway was activated. A further investigation indicated that STAT3 could be activated by the RNA-dependent RNA polymerase L protein (Lp) of LCMV. Our functional analysis found that STAT3 cannot affect LCMV multiplication in A549 cells. We also found that STAT3 was activated by the Lp of Mopeia virus and Junin virus, suggesting that this activation may be conserved across certain arenaviruses. Our study explored the interactions between arenaviruses and STAT3, which may help us to better understand the molecular and cell biology of arenaviruses

The rise and prospects of medical aesthetics

Since the 1980s, Chinese scholars have been trying to expound and synthethise elementary aesthetical ideas which occur in medicine, in order to treat this area of study as a defined branch of medicine-'medical aesthetics'. It is in this context that the points discussed in this paper arise. We set forth in detail the ideas, objectives and methods adopted within the framework of medical aesthetics and its applied branch-medical cosmetology and expound the relations between them. We think the task of medical aesthetics is to study the human body in its entirety, concentrating on both internal and external beauty and put the findings into practice, whereas the task of medical cosmetology is to study and assess only the external beauty of the human body and to take action on that basis. Medical cosmetology is the enforcement of medical aesthetics, practised in order to give positive results connected with physical beauty, and is therefore easily understood by the layman. It is known that the development of medical cosmetology represents an important breakthrough in the development of medical aesthetics. We think that beauty should not be measured mechanically, always following the same pattern, but that it should be considered individually with everyone's own particular characteristics. The quality of physical attractiveness should be assessed jointly by the doctor and his patient or client, not solely by either of these individuals nor even by a group of doctors. The necessity of defining and developing both medical aesthetics and medical cosmetology arises largely as a result of the increasing numbers of people who pursue beauty and health and is in accordance with the trend for consolidating different aspects of modern science. A main objective of medical advance is to improve the quality of health and beauty; to enhance the quality of life and encourage human beings toward achieving perfection in both health and beauty. We predict that in the future medical aesthetics and medical cosmetology will be amongst those subjects considered to be of major importance in the medical field. We have at last reached a stage where we can define the intentions and applied measures of medical aesthetics and medical cosmetology which differ from those of clinical medicine, preventive medicine, or recuperative medicine.medical aesthetics medical cosmetology medical beauty the beauty of the human body

Design project on controlled-release drug delivery devices: Implementation, management, and learning experiences

Chemical Engineering Education444289-298CHED

Keep Moving to Retain the Healthy Self: The Influence of Physical Exercise in Health Anxiety among Chinese Menopausal Women

Menopause is a period of high incidence of chronic diseases. Women experience various physical and psychological discomforts during menopause, and hormonal changes exacerbate mood swings in menopausal women and also cause them to begin to experience excessive worry and anxiety about their health problems. This study was a cross-sectional survey investigating the relationship between physical activity and women’s health anxiety. Using cluster sampling, a valid sample of 455 females aged 45–50 was collected from 78 communities in five municipal districts in Changsha, China, and AMOS v.23 was adopted to construct a structural equation model to verify the hypotheses. The results indicate that interpersonal competence and emotional intelligence are negatively associated with health anxiety. Furthermore, interpersonal competence and emotional intelligence mediate the relationship between physical exercise and health anxiety, which means that menopausal women with more physical exercise, higher interpersonal competence, and higher emotional intelligence reported lower health anxiety. Finally, to alleviate menopausal women’s health anxiety and reduce their risk of chronic diseases, the government, community, and family should create conditions and opportunities for women to participate in group physical activities

Nonlinear parameterized model order reduction method for synthesis and optimization of VLSI circuits

A parameterized model order reduction technique for nonlinear VLSI circuit system is presented in this paper, which combines the Proper Orthogonal Decomposition (POD) with the interpolation method and hence overcomes the inefficiency of POD in representing parameterized nonlinear functions. In order to capture the accuracy of the parameterized reduced model over a large range of parameter values, a training scheme is proposed to automatically select the training parameter points by the greedy sampling method. Results show that the accuracy and efficacy are improved in the proposed nonlinear parameterized reduction method. ? 2013 IEEE.EI

Frontier Materials for Adsorption of Antimony and Arsenic in Aqueous Environments: A Review

As highly toxic and carcinogenic substances, antimony and arsenic often coexist and cause compound pollution. Heavy metal pollution in water significantly threatens human health and the ecological environment. This article elaborates on the sources and hazards of compound antimony and arsenic contamination and systematically discusses the research progress of treatment technology to remove antimony and arsenic in water. Due to the advantages of simple operation, high removal efficiency, low economic cost, and renewable solid and sustainable utilization, adsorption technology for removing antimony and arsenic from sewage stand out among many treatment technologies. The adsorption performance of adsorbent materials is the key to removing antimony and arsenic in water. Therefore, this article focused on summarizing frontier adsorption materials’ characteristics, adsorption mechanism, and performance, including MOFs, COFs, graphene, and biomass materials. Then, the research and application progress of antimony and arsenic removal by frontier materials were described. The adsorption effects of various frontier adsorption materials were objectively analyzed and comparatively evaluated. Finally, the characteristics, advantages, and disadvantages of various frontier adsorption materials in removing antimony and arsenic from water were summarized to provide ideas for improving and innovating adsorption materials for water pollution treatment