Reduced Power Graphs of PGL3(Fq)\mathrm{PGL}_3(\mathbb{F}_q)

Given a group $G$, let us connect two non-identity elements by an edge if and only if one is a power of another. This gives a graph structure on $G$ minus identity, called the reduced power graph. In this paper, we shall find the exact number of connected components and the exact diameter of each component for the reduced power graphs of $\mathrm{PGL}_3(\mathbb{F}_q)$ for all prime power $q$

Deep-neural-network solution of the ab initio nuclear structure

Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving condensed matter and chemistry problems, while for atomic nuclei, it is still quite challenging because of the complicated nucleon-nucleon interactions, which strongly couples the spatial, spin, and isospin degrees of freedom. By combining essential physics of the nuclear wave functions and the strong expressive power of artificial neural networks, we develop FeynmanNet, a novel deep-learning variational quantum Monte Carlo approach for \emph{ab initio} nuclear structure. We show that FeynmanNet can provide very accurate ground-state energies and wave functions for $^4$He, $^6$Li, and even up to $^{16}$O as emerging from the leading-order and next-to-leading-order Hamiltonians of pionless effective field theory. Compared to the conventional diffusion Monte Carlo approaches, which suffer from the severe inherent fermion-sign problem, FeynmanNet reaches such a high accuracy in a variational way and scales polynomially with the number of nucleons. Therefore, it paves the way to a highly accurate and efficient \emph{ab initio} method for predicting nuclear properties based on the realistic interactions between nucleons.Comment: 13 pages, 3 figure

Rotation-Scale Equivariant Steerable Filters

Incorporating either rotation equivariance or scale equivariance into CNNs has proved to be effective in improving models' generalization performance. However, jointly integrating rotation and scale equivariance into CNNs has not been widely explored. Digital histology imaging of biopsy tissue can be captured at arbitrary orientation and magnification and stored at different resolutions, resulting in cells appearing in different scales. When conventional CNNs are applied to histopathology image analysis, the generalization performance of models is limited because 1) a part of the parameters of filters are trained to fit rotation transformation, thus decreasing the capability of learning other discriminative features; 2) fixed-size filters trained on images at a given scale fail to generalize to those at different scales. To deal with these issues, we propose the Rotation-Scale Equivariant Steerable Filter (RSESF), which incorporates steerable filters and scale-space theory. The RSESF contains copies of filters that are linear combinations of Gaussian filters, whose direction is controlled by directional derivatives and whose scale parameters are trainable but constrained to span disjoint scales in successive layers of the network. Extensive experiments on two gland segmentation datasets demonstrate that our method outperforms other approaches, with much fewer trainable parameters and fewer GPU resources required. The source code is available at: https://github.com/ynulonger/RSESF.Comment: Accepted by MIDL 202

Finger Vein Recognition Based on (2D)2 PCA and Metric Learning

Finger vein recognition is a promising biometric recognition technology, which verifies identities via the vein patterns in the fingers. In this paper, (2D)2 PCA is applied to extract features of finger veins, based on which a new recognition method is proposed in conjunction with metric learning. It learns a KNN classifier for each individual, which is different from the traditional methods where a fixed threshold is employed for all individuals. Besides, the SMOTE technology is adopted to solve the class-imbalance problem. Our experiments show that the proposed method is effective by achieving a recognition rate of 99.17%

Scale-Equivariant UNet for Histopathology Image Segmentation

Digital histopathology slides are scanned and viewed under different magnifications and stored as images at different resolutions. Convolutional Neural Networks (CNNs) trained on such images at a given scale fail to generalise to those at different scales. This inability is often addressed by augmenting training data with re-scaled images, allowing a model with sufficient capacity to learn the requisite patterns. Alternatively, designing CNN filters to be scale-equivariant frees up model capacity to learn discriminative features. In this paper, we propose the Scale-Equivariant UNet (SEUNet) for image segmentation by building on scale-space theory. The SEUNet contains groups of filters that are linear combinations of Gaussian basis filters, whose scale parameters are trainable but constrained to span disjoint scales through the layers of the network. Extensive experiments on a nuclei segmentation dataset and a tissue type segmentation dataset demonstrate that our method outperforms other approaches, with much fewer trainable parameters.Comment: This paper was accepted by GeoMedIA 202

ADS_UNet: A Nested UNet for Histopathology Image Segmentation

The UNet model consists of fully convolutional network (FCN) layers arranged as contracting encoder and upsampling decoder maps. Nested arrangements of these encoder and decoder maps give rise to extensions of the UNet model, such as UNete and UNet++. Other refinements include constraining the outputs of the convolutional layers to discriminate between segment labels when trained end to end, a property called deep supervision. This reduces feature diversity in these nested UNet models despite their large parameter space. Furthermore, for texture segmentation, pixel correlations at multiple scales contribute to the classification task; hence, explicit deep supervision of shallower layers is likely to enhance performance. In this paper, we propose ADS UNet, a stage-wise additive training algorithm that incorporates resource-efficient deep supervision in shallower layers and takes performance-weighted combinations of the sub-UNets to create the segmentation model. We provide empirical evidence on three histopathology datasets to support the claim that the proposed ADS UNet reduces correlations between constituent features and improves performance while being more resource efficient. We demonstrate that ADS_UNet outperforms state-of-the-art Transformer-based models by 1.08 and 0.6 points on CRAG and BCSS datasets, and yet requires only 37% of GPU consumption and 34% of training time as that required by Transformers.Comment: To be published in Expert Systems With Application