The dichotomy of Nikodym sets and local smoothing estimates for wave equations

We show that Nikodym sets and local smoothing estimates for linear wave equations form a dichotomy: If Nikodym sets for a family of curves exist, then the related maximal operator is not bounded on $L^p(\mathbb{R}^2)$ for any $p<\infty$; if Nikodym sets do not exist, then local smoothing estimates hold, and the related maximal operator is bounded on $L^p(\mathbb{R}^2)$ for some $p<\infty$. Whenever the maximal operator is bounded on $L^p(\mathbb{R}^2)$ for some $p<\infty$, we also determine the sharp exponent for $L^p(\mathbb{R}^2)$ bounds

A multi-parameter cinematic curvature

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

FedBRB: An Effective Solution to the Small-to-Large Scenario in Device-Heterogeneity Federated Learning

Recently, the success of large models has demonstrated the importance of scaling up model size. This has spurred interest in exploring collaborative training of large-scale models from federated learning perspective. Due to computational constraints, many institutions struggle to train a large-scale model locally. Thus, training a larger global model using only smaller local models has become an important scenario (i.e., the \textbf{small-to-large scenario}). Although recent device-heterogeneity federated learning approaches have started to explore this area, they face limitations in fully covering the parameter space of the global model. In this paper, we propose a method called \textbf{FedBRB} (\underline{B}lock-wise \underline{R}olling and weighted \underline{B}roadcast) based on the block concept. FedBRB can uses small local models to train all blocks of the large global model, and broadcasts the trained parameters to the entire space for faster information interaction. Experiments demonstrate FedBRB yields substantial performance gains, achieving state-of-the-art results in this scenario. Moreover, FedBRB using only minimal local models can even surpass baselines using larger local models

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

Factors Associated with Thrombosis in Primary Immune Thrombocytopenia

BackgroundPatients with primary immune thrombocytopenia (ITP) , a hemorrhagic disease characterized by thrombocytopenia, have increased incidence of thrombotic events, which increases the treatment difficulty. Therefore, it is necessary to determine the risk factors for thrombosis in ITP.ObjectiveTo identify the factors associated with thrombosis in ITP.MethodsSeven hundred and twenty-five ITP inpatients (including individuals with and without thrombosis) were recruited from the First People&apos;s Hospital of Shangqiu. Demographics and results of testing for antiphospholipid antibodies and thrombosis type were collected retrospectively. Multivariate Logistic regression analysis was used to explore the influencing factors of thrombosis.ResultsPatients with thrombosis (n=704, 97.1%) had higher rates of 50-year-olds and above, having hypertension history, diabetes history, and splenectomy, and higher prevalence of use of hormone over 8 weeks, lupus anticoagulant positivity, as well as anticardiolipin antibody positivity than those without (n=21, 2.9%) (P&lt;0.05) . The difference of disease status between patients with and without thrombosis was statistically significant (P&lt;0.05) . Multivariate Logistic regression analysis showed that older age (≥50 years) 〔OR=4.466, 95%CI (1.008, 19.797) , P=0.049) 〕, chronic ITP 〔OR=3.046, 95%CI (1.067, 8.699) , P=0.037) 〕, history of hypertension 〔OR=9.031, 95%CI (1.930, 42.272) , P=0.005〕, history of diabetes〔OR=5.919, 95%CI (2.078, 16.863) , P=0.001〕, hormone use &gt;8 weeks 〔OR=4.119, 95%CI (1.465, 11.580) , P=0.007〕, lupus anticoagulant positivity 〔OR=3.426, 95%CI (1.145, 10.254) , P=0.028〕, anticardiolipin antibody positivity〔OR=4.064, 95%CI (1.357, 12.169) , P=0.021〕 were independently associated with increased risk of thrombosis in ITP. Among the 725 participants, 12 (1.7%) had arterial thrombosis, 8 (1.1%) had venous thrombosis, and 1 (0.1%) had arteriovenous thrombosis.ConclusionFifty years old and above, chronic ITP, history of hypertension, history of diabetes, hormone use &gt;8 weeks, lupus anticoagulant positivity, and anticardiolipin antibody positivity may be independent risk factors for thrombosis in ITP. Special attention should be paid to the prevention of thrombosis in clinical treatment of ITP patients

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