Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the \textit{Code Usage Frequency} of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit \uline{c}ode-based \uline{s}elf-\uline{v}erification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset \textbf{(53.9\% $\to$ 84.3\%)}.Comment: Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verificatio

Effects of facet joint degeneration on stress alterations in cervical spine C5–C6: A finite element analysis

It has been demonstrated that articular facet degeneration can cause local strain alterations and induce neck pain. This study aims to quantify the biomechanical effects of normal and degenerated C5–C6 articular facets, and evaluate the correlation of mechanical strain between healthy and degenerated spine. A 3-dimensional finite element (FE) model of the C5–C6 cervical spine was developed [Model 0 (M0)]. The asymmetric models of C5–C6 bilateral articular facet joint were established separately to mimic articular facet joint degeneration. The capsule ligament stiffness of C5–C6 unilateral facet joint was altered with minimum and maximum threshold to simulate capsule ligaments' lesion and calcification [Model 1 (M1) and Model 2 (M2), respectively]. Besides, the cervical C5–C6 unilateral articular facet joint direction was changed by 5° and 10° forward to imitate the moderate joint hyperplasia and severe osteophyte (Model 3 and Model 4 respectively). M1 increased the rotation range of ipsilateral side (left), while M2 reduced, and both had limited effect on the contralateral side (right). The angle increased in Model 3 (M3) (61°) and Model 4 (M4) (55°) comparing to M0 during the axial rotation, and the angle of M4 was larger. M3 and M4 increased the nucleus pulposus pressure with and without controlled angular displacement during axial rotation. The pressure of nucleus pulpous increased during M1 rotating to the abnormal side but decreased when rotating to the other side, but the results of M2 were opposite. The capsule ligament stiffness made an impact on segmental mobility and vertebral spatial position, and the sagittal angle of articular facet joint exerted an influence on disc pressure distribution

Exploring the optimal impact force for chronic skeletal muscle injury induced by drop-mass technique in rats

Introduction: Skeletal muscle injuries are widespread in sports, traffic accidents and natural disasters and some of them with poor prognoses can lead to chronic skeletal muscle damage in the clinic. We induced a chronic skeletal muscle injury by controlling time and contusion force using an acute blunt trauma model that will help us better comprehend the pathological features of chronic skeletal muscle injury.Methods: Several levels of injury were induced by repeatedly striking in 5, 10, and 15 times the gastrocnemius muscle from the same height with 200 g weights. After injury, the markers of muscle injury were assessed at 2 and 4 weeks by serum elisa. Electron microscopy, histologic and immunohistochemical staining, and mRNA analysis were used to evaluate the ultrastructure, inflammation, extracellular matrix decomposition, and anabolism of injured muscle in 2 and 4 weeks.Results: All three different kinetic energies can result in skeletal muscle injuries. However, the injured skeletal muscles of rats in each group could not recover within 2 weeks. After 4 weeks, tissue self-repair and reconstruction caused the damage induced by 5 J kinetic energy to almost return to normal. In contrast, damage induced by 10 J kinetic energy displayed slight improvement compared to that at 2 weeks. Despite this, collagen fibers on the surface of the tissue were disorganized, directionally ambiguous, and intertwined with each other. Myofilaments within the tissue were also arranged disorderly, with blurry and broken Z-lines. Damage caused by 15 J kinetic energy was the most severe and displayed no improvements at 4 weeks compared to 2 weeks. At 4 weeks, IL-1β, IL-6, Collagen I, and Collagen III, MMP2 expressions in the 10 J group were lower than those at 2 weeks, showing a tendency towards injury stabilization.Conclusion: After 4 weeks of remodeling and repair, the acute skeletal muscle injury model induced by 10 J kinetic energy can stabilize pathological manifestations, inflammatory expression, and extracellular matrix synthesis and catabolism, making it an appropriate model for studying chronic skeletal muscle injuries caused by acute injury

Traditional Chinese Herbal Patch for Short-Term Management of Knee Osteoarthritis: A Randomized, Double-Blind, Placebo-Controlled Trial

Objective. To assess the short-term efficacy and safety of two kinds of Traditional Chinese herbal patches, Fufang Nanxing Zhitong Gao (FNZG) and Shangshi Jietong Gao (SJG), for painful knee osteoarthritis (OA). Methods. Patients were randomly enrolled in a double-blind, placebo-controlled study to receive FNZG (n=60), SJG (n=60), or placebo patch (n=30) for 7 days. Outcome measures included visual analogue scale (VAS), Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC), and Traditional Chinese Medicine Syndrome Questionnaire (TCMSQ) subscale. Results. Although there was no significant difference among, three groups in short-term pain management, patients receiving FNZG got significant improvement in symptom of fear of coldness as compared with placebo patch (P=0.029). The most common local adverse events of rash, itching, erythema, and slightly damaged skin were observed in 7% of participants. Conclusions. FNZG may be a useful treatment for symptom of knee OA and merits long-term study in broader populations

Effectiveness, Medication Patterns, and Adverse Events of Traditional Chinese Herbal Patches for Osteoarthritis: A Systematic Review

Objective. The aim of this study is to systematically evaluate the evidence whether traditional Chinese herbal patches (TCHPs) for osteoarthritis (OA) are effective and safe and analyze their medication patterns. Methods. A systematic literature search was performed using all the possible Medical Subject Headings (MeSH) and keywords from January 1979 to July 2013. Both randomized controlled trials (RCTs) and observational studies were included. Estimated effects were analyzed using mean difference (MD) or relative risk (RR) with 95% confidence intervals (CI) and meta-analysis. Results. 86 kinds of TCHPs were identified. RCTs and controlled clinical trials (CCTs) which were mostly of low quality favored TCHPs for local pain and dysfunction relief. TCHPs, compared with diclofenac ointment, had significant effects on global effectiveness rate (RR = 0.50; 95% CI (0.29, 0.87)). Components of formulae were mainly based on the compounds “Xiao Huo Luo Dan” (Minor collateral-freeing pill) and “Du Huo Ji Sheng Tang” (Angelicae Pubescentis and Loranthi decoction). Ten kinds of adverse events (AEs), mainly consisting of itching and/or local skin rashes, were identified after 3-4 weeks of follow-up. Conclusions. TCHPs have certain evidence in improving global effectiveness rate for OA; however, more rigorous studies are warranted to support their use

Origin of anomalous instability of grid‐forming converters tied to stiff grid

Abstract Grid‐forming (GFM) converter is believed to be highly promising in the future power systems, due to its ability of providing voltage and frequency support. However, some recent studies have shown that the GFM converter may suffer from instability in stiff grids, which seriously hampers its application. In this paper, the mechanism of this anomalous effect is studied by using the small‐signal stability analysis in detail. First, a detailed state‐space model of a single converter grid‐tied system is established from the first principle, and by using the participation factor analysis, the interaction between the terminal voltage loop and the power synchronization loop is identified as the major cause for the system instability. Then relying on a reduced‐order model containing only these two controls and using two classical analytical methods including the Routh criterion analysis and the Phillips– Heffron model of complex torque analysis, the origin of this anomalous instability of GFM converters tied to stiff grid coming from the negative damping provided by the terminal voltage loop is well uncovered and the critical grid strength is well predicted. In addition, these results may provide ideas for subsequent control optimization and stability improvement of GFM converters under various situations

The Influence of Natural Head Position on the Cervical Sagittal Alignment

Introduction. This study investigated the relationship between the parameters related to the natural head position and cervical segmental angles and alignment of patients with neck pain. Material and Methods. The lateral radiographs of the cervical spine were collected from 103 patients and were used to retrospectively analyze the correlation between the natural head position, cervical local sagittal angles, and alignment. Sagittal measurements were as follows: cervical curvature classification, slope of McGregor’s line (McGS), local sagittal angles (C0–C2 angle, C2–C5 angle, C5–C7 angle, and C2–C7 angle), T1 slope, center of gravity of the head to sagittal vertical axis (CG–C7 SVA), and local sagittal alignment (C0–C2 SVA and C2–C7 SVA). Results. McGS was significantly correlated to C0–C2 angle (r=0.57), C0–C2 SVA (r=−0.53), C2–C7 SVA (r=−0.28), and CG–C7 SVA (r=−0.47). CG–C7 SVA was also significantly correlated to curvature type (r=0.27), C5–C7 angle (r=−0.37), and C2–C7 angle (r=−0.39). Conclusions. A backward shift with an extended head position may accompany a relatively normal curvature of the cervical spine. The effect of posture control in relieving abnormal mechanical state of the cervical spine needs to be further confirmed by biomechanical analysis