A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.

Thomas H. Otway

In the paper we introduce the notions of bounded invariance complexity, bounded invariance complexity in the mean and mean L-stability for control systems. Then we characterize these notions by introducing six types of equi-invariability. As by product, two new dichotomy theorems for control system on control sets are established.

Xingfu Zhong Zhijing Chen Yu Huang

The dynamic Jahn-Teller splitting of the six equivalent $D_{5d}$ polarons due to quantum fluctuations is studied in the framework of the Bogoliubov-de Gennes formalism. The tunneling induced level splittings are determined to be $^2 T_{1u} \bigoplus ^2 T_{2u}$ and $^1 A_g \bigoplus ^1 H_g$ for $C_{60}^{1-}$ and $C_{60}^{2-}$, respectively, which should give rise to observable effects in experiments.

Chui-Lin Wang Wen-Zheng Wang Yu-Liang Liu Zhao-Bin Su Lu Yu

In this paper, we study the integrability and linearization of a class of quadratic quasi-analytic switching systems. We improve an existing method to compute the focus values and periodic constants of quasi-analytic switching systems. In particular, with our method, we demonstrate that the dynamical behaviors of quasi-analytic switching systems are more complex than that of continuous quasi-analytic systems, by showing the existence of six and seven limit cycles in the neighborhood of the origin and infinity, respectively, in a quadratic quasi-analytic switching system. Moreover, explicit conditions are obtained for classifying the centers and isochronous centers of the system.

Feng Li Pei Yu Yirong Liu Yuanyuan Liu

The fate of the Ising ferromagnet and antiferromagnet by the zero-temperature Glauber dynamics from random initial spin configuration is investigated in the two-dimensional Archimedean and 2-uniform lattices. Blinker states are found in addition to the ground state and metastable state. We show that an even-coordinated lattice can arrive at a blinker state or a metastable state without stripe structure, in contrast to common expectation. The universal relationship between the critical percolation and the probability of stripe final state is confirmed for six lattices. Results about the fate of the antiferromagnetic Ising model show that the geometric frustration suppresses ordering more and promotes blinker state.

Unjong Yu

Kadomtsev-Petviashvili (KP) equation, who can describe different models in fluids and plasmas, has drawn investigation for its solitonic solutions with various methods. In this paper, we focus on the periodic parabola solitons for the (2+1) dimensional nonautonomous KP equations where the necessary constraints of the parameters are figured out. With Painleve analysis and Hirota bilinear method, we find that the solution has six undetermined parameters as well as analyze the features of some typical cases of the solutions. Based on the constructed solutions, the conditions of their convergence are also discussed.

Yingyou Ma Zhiqiang Chen Xin Yu

Erd\H{o}s and Fishburn studied the maximum number of points in the plane that span $k$ distances and classified these configurations, as an inverse problem of the Erd\H{o}s distinct distances problem. We consider the analogous problem for triangles. Past work has obtained the optimal sets for one and two distinct triangles in the plane. In this paper, we resolve a conjecture that at most six points in the plane can span three distinct triangles, and obtain the hexagon as the unique configuration that achieves this. We also provide evidence that optimal sets cannot be on the square lattice in the general case.

Eyvindur A. Palsson Edward Yu

Feature selection (FS) is an important research topic in machine learning. Usually, FS is modelled as a+ bi-objective optimization problem whose objectives are: 1) classification accuracy; 2) number of features. One of the main issues in real-world applications is missing data. Databases with missing data are likely to be unreliable. Thus, FS performed on a data set missing some data is also unreliable. In order to directly control this issue plaguing the field, we propose in this study a novel modelling of FS: we include reliability as the third objective of the problem. In order to address the modified problem, we propose the application of the non-dominated sorting genetic algorithm-III (NSGA-III). We selected six incomplete data sets from the University of California Irvine (UCI) machine learning repository. We used the mean imputation method to deal with the missing data. In the experiments, k-nearest neighbors (K-NN) is used as the classifier to evaluate the feature subsets. Experimental results show that the proposed three-objective model coupled with NSGA-III efficiently addresses the FS problem for the six data sets included in this study.

Yu Xue Yihang Tang Xin Xu Jiayu Liang Ferrante Neri

Model compression is an essential technique for deploying deep neural networks (DNNs) on power and memory-constrained resources. However, existing model-compression methods often rely on human expertise and focus on parameters' local importance, ignoring the rich topology information within DNNs. In this paper, we propose a novel multi-stage graph embedding technique based on graph neural networks (GNNs) to identify DNN topologies and use reinforcement learning (RL) to find a suitable compression policy. We performed resource-constrained (i.e., FLOPs) channel pruning and compared our approach with state-of-the-art model compression methods. We evaluated our method on various models from typical to mobile-friendly networks, such as ResNet family, VGG-16, MobileNet-v1/v2, and ShuffleNet. Results show that our method can achieve higher compression ratios with a minimal fine-tuning cost yet yields outstanding and competitive performance.

Sixing Yu Arya Mazaheri Ali Jannesari

The capability of linear optics to generate entangled states is exploited in photonic quantum information processing, however, it is challenging to obtain entangled logical qubit states. We report, to the best of our knowledge, the most compact scheme producing the dual-rail-encoded Bell states out of four single photons. Our scheme requires a five-mode interferometer and a single photon detector, while the previously known schemes use six-mode interferometers and two photon detectors. Using computer optimization, we have found a decomposition of the five-mode interferometer with a minimum number of beam-splitters and phase-shift elements. Besides compactness, our scheme also offers a success probability of $1/9$, which is higher than $2/27$ provided by the six-mode counterparts. The analysis suggests that the elevated success probability is connected to higher order of photon interference realized by our scheme, in particular, four-photon interference is implemented in our scheme, while three-photon interference was implemented in previous counterparts.

Suren A. Fldzhyan Mikhail Yu. Saygin Sergei P. Kulik