The Penetration of Mathematical Culture in Teaching Mathematics

Mathematical literacy constitutes an indispensable part of mathematical education. In order to prompt students' ability of solving problems, mathematical educators should take the responsibility to impart mathematical culture to students, guide them to grasp the mathematical thoughts and spirit, and provide corresponding practices. The reason lies on that one can extract the mathematical spirit and thinking patterns from such mathematic culture, which will benefit him throughout his life, even if he has forgotten mathematical concepts and corresponding properties

Stock Investment Value Analysis Model Based on AHP and Gray Relational Degree

The article presents a method for stock selection from the view of investors who contemplate stocks of a new investment. The AHP (Analytic Hierarchy Process) and Grey Relational Analysis are used as two integral parts of the method. By distilling information from the Judgment matrix, the AHP-GRA method provides a framework to assist investors in analyzing various investment factors, evaluating stock investment alternatives, and making final investment selections. The primary principle of the method is to match decision-makers’ preferences with stock characteristics. The model requires that a number of potential stocks have been proposed. Alternatives are then evaluated and compared under various factors. It allows investor to incorporate personal preference and judgement in the solution process. An example of evaluating eight listed companies in the steel industry of China is showed to illustrate the solution process, the results of which are promising.Key words: Stock Investment Decision; Judgment Matrix; AHP; Grey Relational Analysi

An Improved EMD and Its Applications to Find the Basis Functions of EMI Signals

A B-spline empirical mode decomposition (BEMD) method is proposed to improve the celebrated empirical mode decomposition (EMD) method. The improvement of BEMD on EMD mainly concentrates on the sifting process. First, instead of the curve that resulted from computing the average of upper and lower envelopes, the curve interpolated by the midpoints of local maximal and minimal points is used as the mean curve, which can reduce the cost of computation. Second, the cubic spline interpolation is replaced with cubic B-spline interpolation on account of the advantages of B-spline over polynomial spline. The effectiveness of BEMD compared with EMD is validated by numerical simulations and an application to find the basis functions of EMI signals

Indomethacin inhibits PGE2, regulates inflammatory response, participates in adipogenesis regulation, and improves success rate of fat transplantation in C57/B6 mice

Purpose: To investigate the effect of indomethacin on prostaglandin E2, regulation of inflammation and adipogenesis, and success of fat transplantation in mice. Methods: The mice were randomly divided into 4 groups: group A (free fat group), group B (free fat + stromal vascular fragments group (SVF)), group C (free fat + 200 μM indomethacin group), and group D (free fat + 200 μM indomethacin + SVF group), with 21 mice in each group. Expression levels of adipogenic genes CEBP-α, FABP4 and LPL in each group were determined. Changes in PGE2 level in transplanted adipose tissue, and changes in the expression of NF-κB in apoptotic stem cells induced by different pro-inflammatory treatments were assayed. Results: Compared with group B, the expression levels of adipogenic genes CEBP-α, FABP4 and LPL significantly decreased in groups A, C and D, with group A as the lowest (p < 0.05). Compared with the indomethacin treatment group, the level of inhibition of PGE2 in mice adipose tissue in the indomethacin-free group increased significantly (p < 0.01). The expression of NF-κB in the adipose stem cells from the indomethacin-treated group was significantly lower than that in the indomethacin-treated group after pretreatment with IL-17 or INF-γ + TNF-α. Conclusion: Indomethacin regulates adipogenesis by inhibiting the production of COX2 metabolite, PGE2. It also regulates the local microenvironment, inhibits the inflammatory process, and protects various stem cells. Therefore, it may improve the success rate of fat transplantation

Attacking Modulation Recognition With Adversarial Federated Learning in Cognitive Radio-Enabled IoT

Internet of Things (IoT) based on cognitive radio (CR) exhibits strong dynamic sensing and intelligent decision-making capabilities by effectively utilizing spectrum resources. The federal learning (FL) framework based modulation recognition (MR) is an essential component, but its use of uninterpretable deep learning (DL) introduces security risks. This paper combines traditional signal interference methods and data poisoning in FL to propose a new adversarial attack approach. The poisoning attack in distributed frameworks manipulates the global model by controlling malicious users, which is not only covert but also highly impactful. The carefully designed pseudo-noise in MR is also extremely difficult to detect. The combination of these two techniques can generate a greater security threat. We have further advanced our proposal with the introduction of the new adversarial attack method called "Chaotic Poisoning Attack" to reduce the recognition accuracy of the FL-based MR system. We establish effective attack conditions, and simulation results demonstrate that our method can cause a decrease of approximately 80% in the accuracy of the local model under weak perturbations and a decrease of around 20% in the accuracy of the global model. Compared to white-box attack methods, our method exhibits superior performance and transferability

Fast gradient method for Low-Rank Matrix Estimation

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction and tangent space projection. The subspace relationship between iterative and extrapolated sequences on the low-rank matrix manifold provides a computational convenience. With perturbation analysis of truncated singular value decomposition and two retractions, we systematically analyze the local convergence of gradient algorithms and Nesterov's variants in the Euclidean and Riemannian settings. Theoretically, we estimate the exact rate of local linear convergence under different parameters using the spectral radius in a closed form and give the optimal convergence rate and the corresponding momentum parameter. When the parameter is unknown, the adaptive restart scheme can avoid the oscillation problem caused by high momentum, thus approaching the optimal convergence rate. Extensive numerical experiments confirm the estimations of convergence rate and demonstrate that the proposed algorithm is competitive with first-order methods for matrix completion and matrix sensing.Comment: Accepted for publication in Journal of Scientific Computin

Observer-Based Robust Tracking Control for a Class of Switched Nonlinear Cascade Systems

This paper is devoted to robust output feedback tracking control design for a class of switched nonlinear cascade systems. The main goal is to ensure the global input-to-state stable (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. First, a nonlinear observer is constructed through state transformation to reconstruct the unavailable states, where only one parameter should be determined. Then, by virtue of the nonlinear sliding mode control (SMC), a discontinuous nonlinear output feedback controller is designed using a backstepping like design procedure to ensure the ISS property. Finally, an example is provided to show the effectiveness of the proposed approach