arXiv subjects

Yong Ji

Publications and source records attributed to Yong Ji.

5 recordsLinked to original sources

arXiv2024

On the metric mean dimensions of saturated sets

From a geometric perspective, we employ metric mean dimension to investigate the set of generic points of invariant measures and saturated sets in infinite entropy systems. For systems with the specification property, we establish certain variational principles for the Bowen and packing metric mean dimensions of saturated sets in terms of Kolmogorov-Sinai $\epsilon$-entropy, and prove that the upper capacity metric mean dimension of saturated sets has full metric mean dimension. Consequently, the Bowen and packing metric mean dimensions of the set of generic points of invariant measures coincide with the mean R\'enyi information dimension, and the upper capacity metric mean dimension of the set of generic points of invariant measures also has full metric mean dimension. As applications, for systems with the specification property, we present the qualitative characterization of the metric mean dimensions of level sets, the set of mean Li-Yorke pairs in infinite-entropy systems, and the set of generic points of invariant measures in full shifts over compact metric spaces.

math.DS↗

arXiv2024

Depth-induced Saliency Comparison Network for Diagnosis of Alzheimer's Disease via Jointly Analysis of Visual Stimuli and Eye Movements

Early diagnosis of Alzheimer's Disease (AD) is very important for following medical treatments, and eye movements under special visual stimuli may serve as a potential non-invasive biomarker for detecting cognitive abnormalities of AD patients. In this paper, we propose an Depth-induced saliency comparison network (DISCN) for eye movement analysis, which may be used for diagnosis the Alzheimers disease. In DISCN, a salient attention module fuses normal eye movements with RGB and depth maps of visual stimuli using hierarchical salient attention (SAA) to evaluate comprehensive saliency maps, which contain information from both visual stimuli and normal eye movement behaviors. In addition, we introduce serial attention module (SEA) to emphasis the most abnormal eye movement behaviors to reduce personal bias for a more robust result. According to our experiments, the DISCN achieves consistent validity in classifying the eye movements between the AD patients and normal controls.

cs.CV↗

arXiv2023

Deep Learning-based Eye-Tracking Analysis for Diagnosis of Alzheimer's Disease Using 3D Comprehensive Visual Stimuli

Alzheimer's Disease (AD) causes a continuous decline in memory, thinking, and judgment. Traditional diagnoses are usually based on clinical experience, which is limited by some realistic factors. In this paper, we focus on exploiting deep learning techniques to diagnose AD based on eye-tracking behaviors. Visual attention, as typical eye-tracking behavior, is of great clinical value to detect cognitive abnormalities in AD patients. To better analyze the differences in visual attention between AD patients and normals, we first conduct a 3D comprehensive visual task on a non-invasive eye-tracking system to collect visual attention heatmaps. We then propose a multi-layered comparison convolution neural network (MC-CNN) to distinguish the visual attention differences between AD patients and normals. In MC-CNN, the multi-layered representations of heatmaps are obtained by hierarchical convolution to better encode eye-movement behaviors, which are further integrated into a distance vector to benefit the comprehensive visual task. Extensive experimental results on the collected dataset demonstrate that MC-CNN achieves consistent validity in classifying AD patients and normals with eye-tracking data.

eess.IV↗

arXiv2021

High pointwise emergence and Katok's conjecture for systems with non-uniform structure

Recently, Kiriki, Nakano and Soma introduced a concept called pointwise emergence as a new quantitative perspective into the study of non-existence of averages for dynamical systems. In the present paper, we consider the set of points with high pointwise emergence for systems with non-uniform structure and prove that this set carries full topological pressure. For the proof of this result, we show that such systems have ergodic measures of arbitrary intermediate pressures.

math.DS↗

arXiv2020

Entropy and Emergence of Topological Dynamical Systems

A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it coincides with topological entropy of $(X,f)$. We also consider the entropy order of an invariant measure and a variational principle is established.

math.DS↗