Electronic states in a magnetic quantum-dot molecule: phase transitions and spontaneous symmetry breaking

We show that a double quantum-dot system made of diluted magnetic semiconductor behaves unlike usual molecules. In a semiconductor double quantum dot or in a diatomic molecule, the ground state of a single carrier is described by a symmetric orbital. In a magnetic material molecule, new ground states with broken symmetry can appear due the competition between the tunnelling and magnetic polaron energy. With decreasing temperature, the ground state changes from the normal symmetric state to a state with spontaneously broken symmetry. Interestingly, the symmetry of a magnetic molecule is recovered at very low temperatures. A magnetic double quantum dot with broken-symmetry phases can be used a voltage-controlled nanoscale memory cell.Comment: 4 pages, 5 figure

Two-sample Behrens--Fisher problems for high-dimensional data: a normal reference F-type test

The problem of testing the equality of mean vectors for high-dimensional data has been intensively investigated in the literature. However, most of the existing tests impose strong assumptions on the underlying group covariance matrices which may not be satisfied or hardly be checked in practice. In this article, an F-type test for two-sample Behrens--Fisher problems for high-dimensional data is proposed and studied. When the two samples are normally distributed and when the null hypothesis is valid, the proposed F-type test statistic is shown to be an F-type mixture, a ratio of two independent chi-square-type mixtures. Under some regularity conditions and the null hypothesis, it is shown that the proposed F-type test statistic and the above F-type mixture have the same normal and non-normal limits. It is then justified to approximate the null distribution of the proposed F-type test statistic by that of the F-type mixture, resulting in the so-called normal reference F-type test. Since the F-type mixture is a ratio of two independent chi-square-type mixtures, we employ the Welch--Satterthwaite chi-square-approximation to the distributions of the numerator and the denominator of the F-type mixture respectively, resulting in an approximation F-distribution whose degrees of freedom can be consistently estimated from the data. The asymptotic power of the proposed F-type test is established. Two simulation studies are conducted and they show that in terms of size control, the proposed F-type test outperforms two existing competitors. The proposed F-type test is also illustrated by a real data example

Robust Core-Periphery Constrained Transformer for Domain Adaptation

Unsupervised domain adaptation (UDA) aims to learn transferable representation across domains. Recently a few UDA works have successfully applied Transformer-based methods and achieved state-of-the-art (SOTA) results. However, it remains challenging when there exists a large domain gap between the source and target domain. Inspired by humans' exceptional transferability abilities to adapt knowledge from familiar to uncharted domains, we try to apply the universally existing organizational structure in the human functional brain networks, i.e., the core-periphery principle to design the Transformer and improve its UDA performance. In this paper, we propose a novel brain-inspired robust core-periphery constrained transformer (RCCT) for unsupervised domain adaptation, which brings a large margin of performance improvement on various datasets. Specifically, in RCCT, the self-attention operation across image patches is rescheduled by an adaptively learned weighted graph with the Core-Periphery structure (CP graph), where the information communication and exchange between images patches are manipulated and controlled by the connection strength, i.e., edge weight of the learned weighted CP graph. Besides, since the data in domain adaptation tasks can be noisy, to improve the model robustness, we intentionally add perturbations to the patches in the latent space to ensure generating robust learned weighted core-periphery graphs. Extensive evaluations are conducted on several widely tested UDA benchmarks. Our proposed RCCT consistently performs best compared to existing works, including 88.3\% on Office-Home, 95.0\% on Office-31, 90.7\% on VisDA-2017, and 46.0\% on DomainNet.Comment: Core-Periphery, ViT, Unsupervised domain adaptatio

Asymptotic enumeration of some RNA secondary structures

AbstractIn this paper, we derive recursions of some RNA secondary structures with certain properties under two new representations. Furthermore, by making use of methods of asymptotic analysis and generating functions we present asymptotic enumeration of these RNA secondary structures

Unidirectional Photonic Reflector Using a Defective Atomic Lattice

Based on the broken spatial symmetry, we propose a novel scheme for engineering a unidirectional photonic reflector using a one-dimensional atomic lattice with defective cells that have been specifically designed to be vacant. By trapping three-level atoms and driving them into the regime of electromagnetically induced transparency, and through the skillful design of the number and position of vacant cells in the lattice, numerical simulations demonstrate that a broad and high unidirectional reflection region can be realized within EIT window. This proposed unidirectional reflector scheme provides a new platform for achieving optical nonreciprocity and has potential applications for designing optical circuits and devices of nonreciprocity at extremely low energy levels

Research on railway track edge detection based on BM3D and Zernike moments

With the rapid development of intelligent rail transportation, the realization of intelligent detection of railroad foreign body intrusion has become an important topic of current research. Accurate detection of rail edge location, and then delineate the danger area is the premise and basis for railroad track foreign object intrusion detection. The application of a single edge detection algorithm in the process of rail identification is likely to cause the problem of missing important edges and weak gradient change edges of railroad tracks. It will affect the subsequent detection of track foreign objects. A combined global and local edge detection method is proposed to detect the edges of railroad tracks. In the global pixel-level edge detection, an improved blok-matching and 3D filtering (BM3D) algorithm combined with bilateral filtering is used for denoising to eliminate the interference information in the complex environment. Then the gradient direction is added to the Canny operator, the computational template is increased to achieve non-extreme value suppression, and the Otsu thresholding segmentation algorithm is used for thresholding improvement. It can effectively suppress noise while preserving image details, and improve the accuracy and efficiency of detection at the pixel level. For local subpixel-level edge detection, the improved Zernike moment algorithm is used to extract the edges of the obtained pixel-level images and obtain the corresponding subpixel-level images. It can enhance the extraction of tiny feature edges, effectively reduce the computational effort and obtain the subpixel edges of the orbit images. The experimental results show that compared with other improved algorithms, the method proposed in this paper can effectively extract the track edges of the detected images with higher accuracy, better preserve the track edge features, reduce the appearance of pseudo-edges, and shorten the edge detection time with certain noise immunity, which provides a reliable basis for subsequent track detection and analysis

Exploring the Influence of Information Entropy Change in Learning Systems

In this work, we explore the influence of entropy change in deep learning systems by adding noise to the inputs/latent features. The applications in this paper focus on deep learning tasks within computer vision, but the proposed theory can be further applied to other fields. Noise is conventionally viewed as a harmful perturbation in various deep learning architectures, such as convolutional neural networks (CNNs) and vision transformers (ViTs), as well as different learning tasks like image classification and transfer learning. However, this paper aims to rethink whether the conventional proposition always holds. We demonstrate that specific noise can boost the performance of various deep architectures under certain conditions. We theoretically prove the enhancement gained from positive noise by reducing the task complexity defined by information entropy and experimentally show the significant performance gain in large image datasets, such as the ImageNet. Herein, we use the information entropy to define the complexity of the task. We categorize the noise into two types, positive noise (PN) and harmful noise (HN), based on whether the noise can help reduce the complexity of the task. Extensive experiments of CNNs and ViTs have shown performance improvements by proactively injecting positive noise, where we achieved an unprecedented top 1 accuracy of over 95% on ImageNet. Both theoretical analysis and empirical evidence have confirmed that the presence of positive noise can benefit the learning process, while the traditionally perceived harmful noise indeed impairs deep learning models. The different roles of noise offer new explanations for deep models on specific tasks and provide a new paradigm for improving model performance. Moreover, it reminds us that we can influence the performance of learning systems via information entropy change.Comment: Information Entropy, CNN, Transforme