Cocycle deformations and Galois objects of semisimple Hopf algebras of dimension 1616

In this article, we determine cocycle deformations and Galois objects of non-commutative and non-cocommutative semisimple Hopf algebras of dimension $16$. We show that these Hopf algebras are pairwise twist inequivalent mainly by calculating their higher Frobenius-Schur indicators, and that except three Hopf algebras which are cocycle deformations of dual group algebras, none of them admit non-trivial cocycle deformations.Comment: 22 page

On the realization of a class of SL(2,Z)\text{SL}(2,\mathbb{Z})-representations

Let $p<q$ be odd primes, $\rho_1$ and $\rho_2$ be irreducible representations of $\text{SL}(2,\mathbb{Z}_p)$ and $\text{SL}(2,\mathbb{Z}_q)$ of dimensions $\frac{p+1}{2}$ and $\frac{q+1}{2}$, respectively. We show that if $\rho_1\oplus\rho_2$ can be realized as modular representation associated to a modular fusion category $\mathcal{C}$, then $q-p=4$. Moreover, if $\mathcal{C}$ contains a non-trivial \'{e}tale algebra, then $\mathcal{C}\boxtimes\mathcal{C}(\mathbb{Z}_p,\eta)\cong\mathcal{Z}(\mathcal{A})$ as braided fusion category, where $\mathcal{A}$ is a near-group fusion category of type $(\mathbb{Z}_p,p)$. And we show that there exists a non-trivial $\mathbb{Z}_2$-extension of $\mathcal{A}$ that contains simple objects of Frobenius-Perron dimension $\frac{\sqrt{p}+\sqrt{q}}{2}$.Comment: 20pages; comments are welcome

Adaptive Multiscale Weighted Permutation Entropy for Rolling Bearing Fault Diagnosis

© 2020 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.Bearing vibration signals contain non-linear and non-stationary features due to instantaneous variations in the operation of rotating machinery. It is important to characterize and analyze the complexity change of the bearing vibration signals so that bearing health conditions can be accurately identified. Entropy measures are non-linear indicators that are applicable to the time series complexity analysis for machine fault diagnosis. In this paper, an improved entropy measure, termed Adaptive Multiscale Weighted Permutation Entropy (AMWPE), is proposed. Then, a new rolling bearing fault diagnosis method is developed based on the AMWPE and multi-class SVM. For comparison, experimental bearing data are analyzed using the AMWPE, compared with the conventional entropy measures, where a multi-class SVM is adopted for fault type classification. Moreover, the robustness of different entropy measures is further studied for the analysis of noisy signals with various Signal-to-Noise Ratios (SNRs). The experimental results have demonstrated the effectiveness of the proposed method in fault diagnosis of rolling bearing under different fault types, severity degrees, and SNR levels.Peer reviewedFinal Accepted Versio

Iterative Object and Part Transfer for Fine-Grained Recognition

The aim of fine-grained recognition is to identify sub-ordinate categories in images like different species of birds. Existing works have confirmed that, in order to capture the subtle differences across the categories, automatic localization of objects and parts is critical. Most approaches for object and part localization relied on the bottom-up pipeline, where thousands of region proposals are generated and then filtered by pre-trained object/part models. This is computationally expensive and not scalable once the number of objects/parts becomes large. In this paper, we propose a nonparametric data-driven method for object and part localization. Given an unlabeled test image, our approach transfers annotations from a few similar images retrieved in the training set. In particular, we propose an iterative transfer strategy that gradually refine the predicted bounding boxes. Based on the located objects and parts, deep convolutional features are extracted for recognition. We evaluate our approach on the widely-used CUB200-2011 dataset and a new and large dataset called Birdsnap. On both datasets, we achieve better results than many state-of-the-art approaches, including a few using oracle (manually annotated) bounding boxes in the test images.Comment: To appear in ICME 2017 as an oral pape