Research on Genetic Algorithm and Data Information based on Combined Framework for Nonlinear Functions Optimization

AbstractIn recent years, piecewise linear change has become an attractive tools, used for all kinds of complicated nonlinear system. Piecewise linear individual function to provide the platform segmental affine nonlinear system contains a large amount of counter approximate nonlinear function value. Even if section of linearization method widely used the best approximation of the nonlinear function of continuous time a minimum number of piecewise functions did not mention liveried with appropriate literature. This paper presents a method of optimization based on clustering evolution get optimal piecewise linear approximation of a class of nonlinear function. The technology is based on the balance between the approximate precision and simplified, and improves the approximate Linear A minimum number of department. The technology has been successfully applied in some common nonlinear function

Competing Magnetic Orderings and Tunable Topological States in Two-Dimensional Hexagonal Organometallic Lattices

The exploration of topological states is of significant fundamental and practical importance in contemporary condensed matter physics, for which the extension to two-dimensional (2D) organometallic systems is particularly attractive. Using first-principles calculations, we show that a 2D hexagonal triphenyl-lead lattice composed of only main group elements is susceptible to a magnetic instability, characterized by a considerably more stable antiferromagnetic (AFM) insulating state rather than the topologically nontrivial quantum spin Hall state proposed recently. Even though this AFM phase is topologically trivial, it possesses an intricate emergent degree of freedom, defined by the product of spin and valley indices, leading to Berry curvature-induced spin and valley currents under electron or hole doping. Furthermore, such a trivial band insulator can be tuned into a topologically nontrivial matter by the application of an out-of-plane electric field, which destroys the AFM order, favoring instead ferrimagnetic spin ordering and a quantum anomalous Hall state with a non-zero topological invariant. These findings further enrich our understanding of 2D hexagonal organometallic lattices for potential applications in spintronics and valleytronics.Comment: 9 pages, 8 figure

Optimal control-based inverse determination of electrode distribution for electroosmotic micromixer

This paper presents an optimal control-based inverse method used to determine the distribution of the electrodes for the electroosmotic micromixers with external driven flow from the inlet. Based on the optimal control method, one Dirichlet boundary control problem is constructed to inversely find the optimal distribution of the electrodes on the sidewalls of electroosmotic micromixers and achieve the acceptable mixing performance. After solving the boundary control problem, the step-shaped distribution of the external electric potential imposed on the sidewalls can be obtained and the distribution of electrodes can be inversely determined according to the obtained external electric potential. Numerical results are also provided to demonstrate the effectivity of the proposed method

Decoupled Federated Learning on Long-Tailed and Non-IID data with Feature Statistics

Federated learning is designed to enhance data security and privacy, but faces challenges when dealing with heterogeneous data in long-tailed and non-IID distributions. This paper explores an overlooked scenario where tail classes are sparsely distributed over a few clients, causing the models trained with these classes to have a lower probability of being selected during client aggregation, leading to slower convergence rates and poorer model performance. To address this issue, we propose a two-stage Decoupled Federated learning framework using Feature Statistics (DFL-FS). In the first stage, the server estimates the client's class coverage distributions through masked local feature statistics clustering to select models for aggregation to accelerate convergence and enhance feature learning without privacy leakage. In the second stage, DFL-FS employs federated feature regeneration based on global feature statistics and utilizes resampling and weighted covariance to calibrate the global classifier to enhance the model's adaptability to long-tailed data distributions. We conducted experiments on CIFAR10-LT and CIFAR100-LT datasets with various long-tailed rates. The results demonstrate that our method outperforms state-of-the-art methods in both accuracy and convergence rate

Dual-Branch Temperature Scaling Calibration for Long-Tailed Recognition

The calibration for deep neural networks is currently receiving widespread attention and research. Miscalibration usually leads to overconfidence of the model. While, under the condition of long-tailed distribution of data, the problem of miscalibration is more prominent due to the different confidence levels of samples in minority and majority categories, and it will result in more serious overconfidence. To address this problem, some current research have designed diverse temperature coefficients for different categories based on temperature scaling (TS) method. However, in the case of rare samples in minority classes, the temperature coefficient is not generalizable, and there is a large difference between the temperature coefficients of the training set and the validation set. To solve this challenge, this paper proposes a dual-branch temperature scaling calibration model (Dual-TS), which considers the diversities in temperature parameters of different categories and the non-generalizability of temperature parameters for rare samples in minority classes simultaneously. Moreover, we noticed that the traditional calibration evaluation metric, Excepted Calibration Error (ECE), gives a higher weight to low-confidence samples in the minority classes, which leads to inaccurate evaluation of model calibration. Therefore, we also propose Equal Sample Bin Excepted Calibration Error (Esbin-ECE) as a new calibration evaluation metric. Through experiments, we demonstrate that our model yields state-of-the-art in both traditional ECE and Esbin-ECE metrics

A Simple Statistical Energy Analysis Technique on Modeling Continuous Coupling Interfaces

In statistical energy analysis (SEA) modeling, it is desirable that the SEA coupling loss factors (CLFs) between two continuously connected subsystems can be estimated in a convenient way. A simple SEA modeling technique is recommended in that continuous coupling interfaces may be replaced by sets of discrete points, provided the points are spaced at an appropriate distance apart. Consequently, the simple CLF formulae derived from discretelyconnected substructures can be applied for continuous coupling cases. Based on the numerical investigations on SEA modeling of two thin plates connected along a line, a point-spacing criterion is recommended by fitting the point-and line-connection data of the two plates. It shows that the point spacing depends on not only the wavelengths but also the wavelength ratio of the two coupled subsystems