On hypergraph Lagrangians

It is conjectured by Frankl and F\"uredi that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform hypergraphs with $m$ edges in \cite{FF}. Motzkin and Straus' theorem confirms this conjecture when $r=2$. For $r=3$, it is shown by Talbot in \cite{T} that this conjecture is true when $m$ is in certain ranges. In this paper, we explore the connection between the clique number and Lagrangians for $r$-uniform hypergraphs. As an implication of this connection, we prove that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform graphs with $t$ vertices and $m$ edges satisfying ${t-1\choose r}\leq m \leq {t-1\choose r}+ {t-2\choose r-1}-[(2r-6)\times2^{r-1}+2^{r-3}+(r-4)(2r-7)-1]({t-2\choose r-2}-1)$ for $r\geq 4.$Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.7529, arXiv:1211.7057, arXiv:1211.6508, arXiv:1311.140

Generalized Parity-Time Symmetry Condition for Enhanced Sensor Telemetry

Wireless sensors based on micro-machined tunable resonators are important in a variety of applications, ranging from medical diagnosis to industrial and environmental monitoring.The sensitivity of these devices is, however, often limited by their low quality (Q) factor.Here, we introduce the concept of isospectral party time reciprocal scaling (PTX) symmetry and show that it can be used to build a new family of radiofrequency wireless microsensors exhibiting ultrasensitive responses and ultrahigh resolution, which are well beyond the limitations of conventional passive sensors. We show theoretically, and demonstrate experimentally using microelectromechanical based wireless pressure sensors, that PTXsymmetric electronic systems share the same eigenfrequencies as their parity time (PT)-symmetric counterparts, but crucially have different circuit profiles and eigenmodes. This simplifies the electronic circuit design and enables further enhancements to the extrinsic Q factor of the sensors

RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomalies

Time series forecasting is an important and forefront task in many real-world applications. However, most of time series forecasting techniques assume that the training data is clean without anomalies. This assumption is unrealistic since the collected time series data can be contaminated in practice. The forecasting model will be inferior if it is directly trained by time series with anomalies. Thus it is essential to develop methods to automatically learn a robust forecasting model from the contaminated data. In this paper, we first statistically define three types of anomalies, then theoretically and experimentally analyze the loss robustness and sample robustness when these anomalies exist. Based on our analyses, we propose a simple and efficient algorithm to learn a robust forecasting model. Extensive experiments show that our method is highly robust and outperforms all existing approaches. The code is available at https://github.com/haochenglouis/RobustTSF.Comment: Accepted by the 12th International Conference on Learning Representations (ICLR 2024

Design and analysis of genetic algorithm and BP neural network based PID control for boost converter applied in renewable power generations

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DFPENet-geology: A Deep Learning Framework for High Precision Recognition and Segmentation of Co-seismic Landslides

The following lists two main reasons for withdrawal for the public. 1. There are some problems in the method and results, and there is a lot of room for improvement. In terms of method, "Pre-trained Datasets (PD)" represents selecting a small amount from the online test set, which easily causes the model to overfit the online test set and could not obtain robust performance. More importantly, the proposed DFPENet has a high redundancy by combining the Attention Gate Mechanism and Gate Convolution Networks, and we need to revisit the section of geological feature fusion, in terms of results, we need to further improve and refine. 2. arXiv is an open-access repository of electronic preprints without peer reviews. However, for our own research, we need experts to provide comments on my work whether negative or positive. I then would use their comments to significantly improve this manuscript. Therefore, we finally decided to withdraw this manuscript in arXiv, and we will update to arXiv with the final accepted manuscript to facilitate more researchers to use our proposed comprehensive and general scheme to recognize and segment seismic landslides more efficiently.Comment: 1. There are some problems in the method and results, and there is a lot of room for improvement. Overall, the proposed DFPENet has a high redundancy by combining the Attention Gate Mechanism and Gate Convolution Networks, and we need to further improve and refine the results. 2. For our own research, we need experts to provide comments on my work whether negative or positiv