Glaucoma is a chronic eye disease that leads to irreversible vision loss. The cup to disc ratio (CDR) plays an important role in the screening and diagnosis of glaucoma. Thus, the accurate and automatic segmentation of optic disc (OD) and optic cup (OC) from fundus images is a fundamental task. Most existing methods segment them separately, and rely on hand-crafted visual feature from fundus images. In this paper, we propose a deep learning architecture, named M-Net, which solves the OD and OC segmentation jointly in a one-stage multi-label system. The proposed M-Net mainly consists of multi-scale input layer, U-shape convolutional network, side-output layer, and multi-label loss function. The multi-scale input layer constructs an image pyramid to achieve multiple level receptive field sizes. The U-shape convolutional network is employed as the main body network structure to learn the rich hierarchical representation, while the side-output layer acts as an early classifier that produces a companion local prediction map for different scale layers. Finally, a multi-label loss function is proposed to generate the final segmentation map. For improving the segmentation performance further, we also introduce the polar transformation, which provides the representation of the original image in the polar coordinate system. The experiments show that our M-Net system achieves state-of-the-art OD and OC segmentation result on ORIGA dataset. Simultaneously, the proposed method also obtains the satisfactory glaucoma screening performances with calculated CDR value on both ORIGA and SCES datasets.

Glaucoma is a chronic eye disease that leads to irreversible vision loss. Most of the existing automatic screening methods firstly segment the main structure, and subsequently calculate the clinical measurement for detection and screening of glaucoma. However, these measurement-based methods rely heavily on the segmentation accuracy, and ignore various visual features. In this paper, we introduce a deep learning technique to gain additional image-relevant information, and screen glaucoma from the fundus image directly. Specifically, a novel Disc-aware Ensemble Network (DENet) for automatic glaucoma screening is proposed, which integrates the deep hierarchical context of the global fundus image and the local optic disc region. Four deep streams on different levels and modules are respectively considered as global image stream, segmentation-guided network, local disc region stream, and disc polar transformation stream. Finally, the output probabilities of different streams are fused as the final screening result. The experiments on two glaucoma datasets (SCES and new SINDI datasets) show our method outperforms other state-of-the-art algorithms.

We present improved quantum circuit for modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. While previous work mostly focuses on minimizing the number of qubits or the depth of circuit, we try to minimize the number of CNOT gate which primarily determines the running time on a ion trap quantum computer. First, we give the implementation of basic arithmetic with known lowest number of CNOT gate and the construction of improved modular exponentiation of a constant by accumulating intermediate date and windowing technique. Then, we precisely estimate the number of improved quantum circuit to perform Shor's algorithm for factoring a $n$-bit integer, which is $217\frac{n^3}{\log_2n}+4n^2+n$. According to the number of CNOT gates, we analyze the running time and feasibility of Shor's algorithm on a ion trap quantum computer. Finally, we discuss the lower bound of CNOT numbers needed to implement Shor's algorithm.

This note analyzed the angle-distribution of the probabilities of two-photon states come out of a single-photon's stimulated emission amplification, show that one can exploit EPR photon pairs combined with stimulated emission to realize superluminal signaling.

Existing deraining Transformers employ self-attention mechanisms with fixed-range windows or along channel dimensions, limiting the exploitation of non-local receptive fields. In response to this issue, we introduce a novel dual-branch hybrid Transformer-Mamba network, denoted as TransMamba, aimed at effectively capturing long-range rain-related dependencies. Based on the prior of distinct spectral-domain features of rain degradation and background, we design a spectral-banded Transformer blocks on the first branch. Self-attention is executed within the combination of the spectral-domain channel dimension to improve the ability of modeling long-range dependencies. To enhance frequency-specific information, we present a spectral enhanced feed-forward module that aggregates features in the spectral domain. In the second branch, Mamba layers are equipped with cascaded bidirectional state space model modules to additionally capture the modeling of both local and global information. At each stage of both the encoder and decoder, we perform channel-wise concatenation of dual-branch features and achieve feature fusion through channel reduction, enabling more effective integration of the multi-scale information from the Transformer and Mamba branches. To better reconstruct innate signal-level relations within clean images, we also develop a spectral coherence loss. Extensive experiments on diverse datasets and real-world images demonstrate the superiority of our method compared against the state-of-the-art approaches.