Optimal decay rates and asymptotic profiles for the nonlinear acoustic wave equation with fractional Laplacians

In this paper, we study the Cauchy problem for the nonlinear acoustic wave equation with the Cattaneo law involving fractional Laplacians $(-\Delta)^{\alpha}$ of the viscosity with $\alpha\in[0,1]$, which is established by applying the Lighthill approximation of the fractional Navier-Stokes-Cattaneo equations under irrotational flows. Exploring structures of the nonlinearities, we rigorously demonstrate optimal decay rates of the global (in time) small datum Sobolev solutions with suitable regularities. Furthermore, by introducing a threshold $\alpha=1/2$, we derive the anomalous diffusion profiles when $\alpha\in[0,1/2)$ and the diffusion wave profiles when $\alpha\in[1/2,1]$ as large time. These results show influences of the fractional index $\alpha$ on large time behaviors of the solutions

The High-dimensional Phase Diagram and the Large CALPHAD Model

When alloy systems comprise more than three elements, the visualization of the entire phase space becomes not only daunting but is also accompanied by a data surge. Addressing this complexity, we delve into the FeNiCrMn alloy system and introduce the Large CALPHAD Model (LCM). The LCM acts as a computational conduit, capturing the entire phase space. Subsequently, this enormous data is systematically structured using a high-dimensional phase diagram, aided by hash tables and Depth-first Search (DFS), rendering it both digestible and programmatically accessible. Remarkably, the LCM boasts a 97% classification accuracy and a mean square error of 4.80*10-5 in phase volume prediction. Our methodology successfully delineates 51 unique phase spaces in the FeNiCrMn system, exemplifying its efficacy with the design of all 439 eutectic alloys. This pioneering methodology signifies a monumental shift in alloy design techniques or even multi-variable problems

Asymptotic behavior of solutions for the thermoviscous acoustic systems

We study some asymptotic properties of solutions for the acoustic coupled systems in thermoviscous fluids which was proposed by [Karlsen-Bruus, \emph{Phys. Rev. E} (2015)]. Basing on the WKB analysis and the Fourier analysis, we derive optimal estimates and large time asymptotic profiles of the energy term via diagonalization procedure, and of the velocity potential via reduction methodology. We found that the wave effect has a dominant influence for lower dimensions comparing with thermal-viscous effects. Moreover, by employing suitable energy methods, we rigorously demonstrate global (in time) inviscid limits as the momentum diffusion coefficient vanishes, whose limit model can be regarded as the thermoelastic acoustic systems in isotropic solids. These results explain some influence of the momentum diffusion on asymptotic behavior of solutions

Clinical Study of Endocrine Hormone Combined with Trastuzumab in Maintenance Treatment of HR and HER-2 Positive Advanced Breast Cancer

Objective: To analyze the clinical effect of endocrine hormone combined with trastuzumab in maintenance therapy of HR (hormone receptor) and HER-2 (human epidermal growth factor receptor) positive advanced breast cancer. Methods: A total of 80 patients with HR and HER-2 positive advanced breast cancer admitted to our hospital from January 2020 to December 2022 were selected, and the 80 patients were divided into 2 groups by random number table method, the control group (N= 40) The patients in the observation group (N=40) were treated with trastuzumab, and the patients in the observation group (N=40) were treated with endocrine hormones and trastuzumab for maintenance. The therapeutic effects of the two groups were compared. Results: The two groups of patients had similar serum CD8+, CD4+, CD3+ before treatment and CD8+ after treatment (P>0.05). After treatment, the CD4+ and CD3+ in the observation group were higher than those in the control group (P<0.05). The total effective rate of the observation group was significantly higher than that of the control group. It was higher in the control group (P<0.05); the incidence of adverse reactions in the observation group was lower than that in the control group (P<0.05). Conclusion: Endocrine hormone combined with trastuzumab maintenance therapy for HR and HER-2 positive advanced breast cancer has significant clinical effect, can effectively improve the immune indexes of patients, and has less adverse reactions, which is worthy of clinical application

RepBNN: towards a precise Binary Neural Network with Enhanced Feature Map via Repeating

Binary neural network (BNN) is an extreme quantization version of convolutional neural networks (CNNs) with all features and weights mapped to just 1-bit. Although BNN saves a lot of memory and computation demand to make CNN applicable on edge or mobile devices, BNN suffers the drop of network performance due to the reduced representation capability after binarization. In this paper, we propose a new replaceable and easy-to-use convolution module RepConv, which enhances feature maps through replicating input or output along channel dimension by $\beta$ times without extra cost on the number of parameters and convolutional computation. We also define a set of RepTran rules to use RepConv throughout BNN modules like binary convolution, fully connected layer and batch normalization. Experiments demonstrate that after the RepTran transformation, a set of highly cited BNNs have achieved universally better performance than the original BNN versions. For example, the Top-1 accuracy of Rep-ReCU-ResNet-20, i.e., a RepBconv enhanced ReCU-ResNet-20, reaches 88.97% on CIFAR-10, which is 1.47% higher than that of the original network. And Rep-AdamBNN-ReActNet-A achieves 71.342% Top-1 accuracy on ImageNet, a fresh state-of-the-art result of BNNs. Code and models are available at:https://github.com/imfinethanks/Rep_AdamBNN.Comment: This paper has absolutely nothing to do with repvgg, rep means repeatin

Stock Volatility Prediction Based on Transformer Model Using Mixed-Frequency Data

With the increasing volume of high-frequency data in the information age, both challenges and opportunities arise in the prediction of stock volatility. On one hand, the outcome of prediction using tradition method combining stock technical and macroeconomic indicators still leaves room for improvement; on the other hand, macroeconomic indicators and peoples' search record on those search engines affecting their interested topics will intuitively have an impact on the stock volatility. For the convenience of assessment of the influence of these indicators, macroeconomic indicators and stock technical indicators are then grouped into objective factors, while Baidu search indices implying people's interested topics are defined as subjective factors. To align different frequency data, we introduce GARCH-MIDAS model. After mixing all the above data, we then feed them into Transformer model as part of the training data. Our experiments show that this model outperforms the baselines in terms of mean square error. The adaption of both types of data under Transformer model significantly reduces the mean square error from 1.00 to 0.86.Comment: Accepted by the 7th APWeb-WAIM International Joint Conference on Web and Big Data. (APWeb 2023

Elimination of the confrontation between theory and experiment in flexoelectric Bi2GeO5

In this paper, we have investigated the flexoelectric effect of Bi2GeO5(BGO), successfully predicted the maximum flexoelectric coefficient of BGO, and tried to explore the difference between experimental and simulated flexoelectric coefficients.Comment: 16 pages,6 figure