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Xiaomin Zhou

Publications and source records attributed to Xiaomin Zhou.

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Local stable and unstable sets for random dynamical systems

We study local stable and unstable sets for two-sided continuous bundle random dynamical systems. For an ergodic invariant measure with positive fiber measure-theoretic entropy and positive fiberwise maximal Lyapunov exponent, we show that the fiber entropy is determined by the action of the random maps on local unstable sets, and establish a lower bound for the Hausdorff dimension of local unstable sets in terms of the ratio of entropy to the maximal fiber Lyapunov exponent. If the upper box dimension of the phase space is finite, we obtain a weak form of Ruelle's inequality.

math.DS

Discrete spectrum of probability measures for locally compact group actions

In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum if and only if it has bounded measure-max-mean-complexity. As applications: 1) An invariant measure for a locally compact amenable group action has a discrete spectrum if and only if it has bounded mean-complexity along Følner sequences; 2) An invariant measure for a locally compact amenable group action has a discrete spectrum if and only if it is mean equicontinuous along a tempered Følner sequence, or equicontinuous in the mean along a tempered Følner sequence.

math.DS

Application of Transfer Learning and Ensemble Learning in Image-level Classification for Breast Histopathology

Background: Breast cancer has the highest prevalence in women globally. The classification and diagnosis of breast cancer and its histopathological images have always been a hot spot of clinical concern. In Computer-Aided Diagnosis (CAD), traditional classification models mostly use a single network to extract features, which has significant limitations. On the other hand, many networks are trained and optimized on patient-level datasets, ignoring the application of lower-level data labels. Method: This paper proposes a deep ensemble model based on image-level labels for the binary classification of benign and malignant lesions of breast histopathological images. First, the BreaKHis dataset is randomly divided into a training, validation and test set. Then, data augmentation techniques are used to balance the number of benign and malignant samples. Thirdly, considering the performance of transfer learning and the complementarity between each network, VGG16, Xception, ResNet50, DenseNet201 are selected as the base classifiers. Result: In the ensemble network model with accuracy as the weight, the image-level binary classification achieves an accuracy of $98.90\%$. In order to verify the capabilities of our method, the latest Transformer and Multilayer Perception (MLP) models have been experimentally compared on the same dataset. Our model wins with a $5\%-20\%$ advantage, emphasizing the ensemble model's far-reaching significance in classification tasks. Conclusion: This research focuses on improving the model's classification performance with an ensemble algorithm. Transfer learning plays an essential role in small datasets, improving training speed and accuracy. Our model has outperformed many existing approaches in accuracy, providing a method for the field of auxiliary medical diagnosis.

cs.CV

Packing topological entropy for amenable group actions

Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for a continuous $G$-action dynamical system $(X,G)$, where $X$ is a compact metric space and $G$ is a countable discrete amenable group. We first prove a variational principle for amenable packing topological entropy: for any Borel subset $Z$ of $X$, the packing topological entropy of $Z$ equals the supremum of upper local entropy over all Borel probability measures for which the subset $Z$ has full measure. And then we obtain an entropy inequality concerning amenable packing entropy. Finally we show that the packing topological entropy of the set of generic points for any invariant Borel probability measure $μ$ coincides with the metric entropy if either $μ$ is ergodic or the system satisfies a kind of specification property.

math.DS

A Comprehensive Review for Breast Histopathology Image Analysis Using Classical and Deep Neural Networks

Breast cancer is one of the most common and deadliest cancers among women. Since histopathological images contain sufficient phenotypic information, they play an indispensable role in the diagnosis and treatment of breast cancers. To improve the accuracy and objectivity of Breast Histopathological Image Analysis (BHIA), Artificial Neural Network (ANN) approaches are widely used in the segmentation and classification tasks of breast histopathological images. In this review, we present a comprehensive overview of the BHIA techniques based on ANNs. First of all, we categorize the BHIA systems into classical and deep neural networks for in-depth investigation. Then, the relevant studies based on BHIA systems are presented. After that, we analyze the existing models to discover the most suitable algorithms. Finally, publicly accessible datasets, along with their download links, are provided for the convenience of future researchers.

eess.IV

Auslander-Yorkes type dichotomy theorems for stronger version r-sensitivity

In this paper, for r in N with r>=2 we consider several stronger version r-sensitivities and measure-theoretical r-sensitivities by analysing subsets of nonnegative integers, for which the r-sensitivity occurs. We obtain an Auslander-Yorke's type dichotomy theorem: a minimal topological dynamical system is either thickly r-sensitive or an almost m to one extension of its maximal equicontinuousfactor for some m in {1,2,...,r-1}.

math.DS

Preimage entropy dimension of topological dynamical systems

We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated systems have the same preimage entropy dimension. Also, we discuss the relation between the preimage entropy dimension and the preimage entropy.

math.DS