A multi-parameter cinematic curvature

We state a multi-parameter cinematic curvature condition, and prove $L^p$ bounds for related maximal operators

Comprehensive ab initio study of effects of alloying elements on generalized stacking fault energies of Ni and Ni3_3Al

Excellent high-temperature mechanical properties of Ni-based single crystal superalloys (NSCSs) are attributed to the yield strength anomaly of Ni$_{3}$Al that is intimately related to generalized stacking fault energies (GSFEs). Therefore, clarifying the effects of alloying elements on the GSFEs is of great significance for alloys design. Here, by means of ab initio density functional theory calculations, we systematically calculated the GSFEs of different slip systems of Ni and Ni$_{3}$Al without and with alloying elements using the alias shear method. We obtained that for Ni, except for magnetic elements Mn, Fe, and Co, most of alloying elements decrease the unstable stacking fault energy ($\gamma_{usf}$) of the $[01\bar{1}](111)$ and $[11\bar{2}](111)$ slip systems and also decrease the stable stacking fault energy ($\gamma_{sf}$) of the $[11\bar{2}](111)$ slip system. For Ni$_{3}$Al, most of alloying elements in groups IIIB-VIIB show a strong Al site preference. Except for Mn and Fe, the elements in groups VB-VIIB and the first column of group VIII increase the values of $\gamma_{usf}$ of different slip systems of Ni$_{3}$Al. On the other hand, the elements in groups IIIB-VIIB also increase the value of $\gamma_{sf}$. We found that Re is an excellent strengthening alloying element that significantly increases the slip barrier of the tailing slip process for Ni, and also enhances the slip barrier of the leading slip process of three slip systems for Ni$_{3}$Al. W and Mo exhibit similar effects as Re. We predicted that Os, Ru, and Ir are good strengthening alloying elements as well, since they show the strengthening effects on both the leading and tailing slip process for Ni and Ni$_{3}$Al

Development and Validation of a Prognostic Nomogram for Extremity Soft Tissue Leiomyosarcoma

Background: Extremity soft tissue leiomyosarcoma (LMS) is a rare disease with a poor prognosis. The aim of this study is to develop nomograms to predict the overall survival (OS) and cancer-specific survival (CSS) of patients with extremity soft tissue LMS.Methods: Based on the Surveillance, Epidemiology, and End Results (SEER) database, 1,528 cases of extremity soft tissue LMS diagnosed between 1983 and 2015 were included. Cox proportional hazards regression modeling was used to analyze prognosis and obtain independent predictors. The independent predictors were integrated to develop nomograms predicting 5- and 10-year OS and CSS. Nomogram performance was evaluated by a concordance index (C-index) and calibration plots using R software version 3.5.0.Results: Multivariate analysis revealed that age ≥60 years, high tumor grade, distant metastasis, tumor size ≥5 cm, and lack of surgery were significantly associated with decreased OS and CSS. These five predictors were used to construct nomograms for predicting 5- and 10-year OS and CSS. Internal and external calibration plots for the probability of 5- and 10-year OS and CSS showed excellent agreement between nomogram prediction and observed outcomes. The C-index values for internal validation of OS and CSS prediction were 0.776 (95% CI 0.752–0.801) and 0.835 (95% CI 0.810–0.860), respectively, whereas those for external validation were 0.748 (95% CI 0.721–0.775) and 0.814 (95% CI 0.785–0.843), respectively.Conclusions: The proposed nomogram is a reliable and robust tool for accurate prognostic prediction in patients with extremity soft tissue LMS

Assessing Hidden Risks of LLMs: An Empirical Study on Robustness, Consistency, and Credibility

The recent popularity of large language models (LLMs) has brought a significant impact to boundless fields, particularly through their open-ended ecosystem such as the APIs, open-sourced models, and plugins. However, with their widespread deployment, there is a general lack of research that thoroughly discusses and analyzes the potential risks concealed. In that case, we intend to conduct a preliminary but pioneering study covering the robustness, consistency, and credibility of LLMs systems. With most of the related literature in the era of LLM uncharted, we propose an automated workflow that copes with an upscaled number of queries/responses. Overall, we conduct over a million queries to the mainstream LLMs including ChatGPT, LLaMA, and OPT. Core to our workflow consists of a data primitive, followed by an automated interpreter that evaluates these LLMs under different adversarial metrical systems. As a result, we draw several, and perhaps unfortunate, conclusions that are quite uncommon from this trendy community. Briefly, they are: (i)-the minor but inevitable error occurrence in the user-generated query input may, by chance, cause the LLM to respond unexpectedly; (ii)-LLMs possess poor consistency when processing semantically similar query input. In addition, as a side finding, we find that ChatGPT is still capable to yield the correct answer even when the input is polluted at an extreme level. While this phenomenon demonstrates the powerful memorization of the LLMs, it raises serious concerns about using such data for LLM-involved evaluation in academic development. To deal with it, we propose a novel index associated with a dataset that roughly decides the feasibility of using such data for LLM-involved evaluation. Extensive empirical studies are tagged to support the aforementioned claims

Structure-driven intercalated architecture of septuple-atomic-layer MA2Z4MA_2Z_4 family with diverse properties from semiconductor to topological insulator to Ising superconductor

Motivated by the fact that septuple-atomic-layer MnBi$_2$Te$_4$ can be structurally viewed as the combination of double-atomic-layer MnTe intercalating into quintuple-atomic-layer Bi$_2$Te$_3$, we present a general approach of constructing twelve septuple-atomic-layer $\alpha_i$- and $\beta_i$-$MA_2Z_4$ monolayer family (\emph{i} = 1 to 6) by intercalating MoS$_2$-type $MZ$$_2$ monolayer into InSe-type A$_2$Z$_2$ monolayer. Besides reproducing the experimentally synthesized $\alpha_1$-MoSi$_2$N$_4$, $\alpha_1$-WSi$_2$N$_4$ and $\beta_5$-MnBi$_2$Te$_4$ monolayer materials, another 66 thermodynamically and dynamically stable $MA_2Z_4$ were predicted, which span a wide range of properties upon the number of valence electrons (VEC). $MA_2Z_4$ with the rules of 32 or 34 VEC are mostly semiconductors with direct or indirect band gap and, however, with 33 VEC are generally metal, half-metal ferromagnetism, or spin-gapless semiconductor upon whether or not an unpaired electron is spin polarized. Moreover, we propose $\alpha_2$-WSi$_2$P$_4$ for the spin-valley polarization, $\alpha_1$-TaSi$_2$N$_4$ for Ising superconductor and $\beta_2$-SrGa$_2$Se$_4$ for topological insulator.Comment: Maintext 9 pages; 5 figures; Supplementary Materials 8 figures and 4 table