Rigidity of stable Lyapunov exponents for codimension one Anosov covering maps on nilmanifolds

Let $\Psi$ be an endomorphism of a nilmanifold $M = N/\Gamma$. We show that the preimages of a point under $\Psi$ become dense exponentially if and only if $\Psi$ is totally non-invertible, which means $(M, \Psi)$ has no invertible factors of quotients of factors. As an application, let $f$ be a non-invertible Anosov covering map on $M$ with one-dimensional stable bundle, if $f$ has such linear part $\Psi$ and is topologically conjugate to $\Psi$, then every periodic point of $f$ admits the same stable Lyapunov exponent with $\Psi$, and hence the conjugacy is automatically smooth along each stable leaf. Conversely, if $\Psi$ is horizontally irreducible, which means the induced horizontal toral endomorphism is irreducible, then $f$ admitting a constant periodic stable Lyapunov exponent implies that there exists a topological conjugacy to $\Psi$. In summary, for an Anosov covering map on a nilmanifold with one-dimensional stable bundle and totally non-invertible, horizontally irreducible linear part, we get the equivalence among the existence of invariant unstable bundle, the existence of topological conjugacy to linear part, and a constant periodic stable Lyapunov exponent

Evolution-Peak based Evolutionary Control and Analysis on Carbon Emission System of the United States

AbstractBased on the status quo of carbon emissions in USA and the international crude oil price fluctuations, this paper introduces control index and critical time of carbon emissions to find a new dynamic evolutionary model of carbon emissions of the States, deducing relative theories, such as Change Trends Theorem and Evolutionary Theorem. The critical time in the economic period is determined based on the evolutionary situation of the international crude oil price peaks, and it can be divided into four time intervals. Least-square method is used to analyze the dynamic evolutionary system of carbon emissions in the four time intervals with data provided by the international energy agency (IEA). Based on the nonlinear dynamic evolutionary model, the paper predicts carbon emissions by means of control index and control function, which facilitates carbon policy regulation and the system's external influence, and creates unique dynamic evolutionary factors of carbon emissions corresponding with the real situation of the United States. The financial crisis and shale gas large-scale mining have significantly changed America's energy supply structure. With the economy running upward, carbon emissions have a tendency to increase again. To achieve the goal of its reduction, different policies should be adopted by the US government. In this essay, the influence of the control index and the effect of critical time of carbon emissions to control function are analyzed. In addition, the dynamic evolutionary model is introduced and evolutionary scenario analysis is also conducted by modulating evolutionary coefficient and critical time

BASIC:A Comprehensive Model for so _xFormation Mechanism and Optimization in Municipal Solid Waste (MSW) Combustion

[Image: see text] Municipal solid waste (MSW) incineration is one of the main techniques currently used for waste to energy (WTE) conversion in China. Although the sulfur content in MSW is lower than that in coal, its emission cannot be neglected due to environmental pollution, malodor, health problems, and global climate change. Therefore, it is particularly important to effectively predict and control the sulfur pollutants. In this study, a comprehensive model was developed and coupled with the full combustion process bed model bulk accumulated solids incineration code (BASIC) to investigate the formation and transformation processes of sulfur in MSW incineration. The submodels of the four stages in the MSW combustion processes; governing equations of mass, momentum, and energy conservation; and various chemical reactions were included in the model. Based on this model, the effects of different parameters on the formation of sulfur pollutants during the incineration process were studied under different operating conditions. The study finds that for SO(X) formation, initial temperature, primary air volume, and material particle size have significant impacts, whereas pressure shows a less significant effect. This article also considers H(2)S, COS, and CS(2) formation under different conditions. An optimization study was performed to reduce SO(X) pollutants

A density map-based method for counting wheat ears

IntroductionField wheat ear counting is an important step in wheat yield estimation, and how to solve the problem of rapid and effective wheat ear counting in a field environment to ensure the stability of food supply and provide more reliable data support for agricultural management and policy making is a key concern in the current agricultural field.MethodsThere are still some bottlenecks and challenges in solving the dense wheat counting problem with the currently available methods. To address these issues, we propose a new method based on the YOLACT framework that aims to improve the accuracy and efficiency of dense wheat counting. Replacing the pooling layer in the CBAM module with a GeM pooling layer, and then introducing the density map into the FPN, these improvements together make our method better able to cope with the challenges in dense scenarios.ResultsExperiments show our model improves wheat ear counting performance in complex backgrounds. The improved attention mechanism reduces the RMSE from 1.75 to 1.57. Based on the improved CBAM, the R2 increases from 0.9615 to 0.9798 through pixel-level density estimation, the density map mechanism accurately discerns overlapping count targets, which can provide more granular information.DiscussionThe findings demonstrate the practical potential of our framework for intelligent agriculture applications

Personalized Federated Learning under Mixture of Distributions

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.Comment: International Conference on Machine Learning (ICML'23

Heat stress affects tassel development and reduces the kernel number of summer maize

Maize grain yield is drastically reduced by heat stress (HTS) during anthesis and early grain filling. However, the mechanism of HTS in reproductive organs and kernel numbers remains poorly understood. From 2018 to 2020, two maize varieties (ND372, heat tolerant; and XY335, heat sensitive) and two temperature regimens (HTS, heat stress; and CK, natural control) were evaluated, resulting in four treatments (372CK, 372HTS, 335CK, and 335HTS). HTS was applied from the nine-leaf stage (V9) to the anthesis stage. Various morphological traits and physiological activities of the tassels, anthers, and pollen from the two varieties were evaluated to determine their correlation with kernel count. The results showed that HTS reduced the number of florets, tassel volume, and tassel length, but increased the number of tassel branches. HTS accelerates tassel degradation and reduces pollen weight, quantity, and viability. Deformation and reduction in length and volume due to HTS were observed in both the Nongda 372 (ND372) and Xianyu 335 (XY335) varieties, with the average reductions being 22.9% and 35.2%, respectively. The morphology of the anthers changed more conspicuously in XY335 maize. The number of kernels per spike was reduced in the HTS group compared with the CK group, with the ND372 and XY335 varieties showing reductions of 47.3% and 59.3%, respectively. The main factors underlying the decrease in yield caused by HTS were reductions in pollen quantity and weight, tassel rachis, and branch length. HTS had a greater effect on the anther shape, pollen viability, and phenotype of XY335 than on those of ND372. HTS had a greater impact on anther morphology, pollen viability, and the phenotype of XY335 but had no influence on the appearance or dissemination of pollen from tassel

Comparison of Diagnostic Performance of Three-Dimensional Positron Emission Mammography versus Whole Body Positron Emission Tomography in Breast Cancer

Objective. To compare the diagnostic performance of three-dimensional (3D) positron emission mammography (PEM) versus whole body positron emission tomography (WBPET) for breast cancer. Methods. A total of 410 women with normal breast or benign or highly suspicious malignant tumors were randomized at 1 : 1 ratio to undergo 3D-PEM followed by WBPET or WBPET followed by 3D-PEM. Lumpectomy or mastectomy was performed on eligible participants after the scanning. Results. The sensitivity and specificity of 3D-PEM were 92.8% and 54.5%, respectively. WBPET showed a sensitivity of 95.7% and specificity of 56.8%. After exclusion of the patients with lesions beyond the detecting range of the 3D-PEM instrument, 3D-PEM showed higher sensitivity than WBPET (97.0% versus 95.5%, P = 0.913), particularly for small lesions (<1 cm) (72.0% versus 60.0%, P = 0.685). Conclusions. The 3D-PEM appears more sensitive to small lesions than WBPET but may fail to detect lesions that are beyond the detecting range. This study was approved by the Ethics Committee (E2012052) at the Tianjin Medical University Cancer Institute and Hospital (Tianjin, China). The instrument positron emission mammography (PEMi) was approved by China State Food and Drug Administration under the registration number 20153331166