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Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional$$O(log_{2}{N})$$$O\left(lo{g}_{2}N\right)$quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications.

 

Instance-level tooth segmentation extracts abundant localization and shape information from panoramic radiographs (PRs). The aim of this study was to evaluate the performance of a mask refinement network that extracts precise tooth edges.

A public dataset which consists of 543 PRs and 16211 labelled teeth was utilized. The structure of a typical Mask Region-based Convolutional Neural Network (Mask RCNN) was used as the baseline. A novel loss function was designed focus on producing accurate mask edges. In addition to our proposed method, 3 existing tooth segmentation methods were also implemented on the dataset for comparative analysis. The average precisions (APs), mean intersection over union (mIoU), and mean Hausdorff distance (mHAU) were exploited to evaluate the performance of the network.

A novel mask refinement region-based convolutional neural network was designed based on Mask RCNN architecture to extract refined masks for individual tooth on PRs. A total of 3311 teeth were correctly detected from 3382 tested teeth in 111 PRs. The AP, precision, and recall were 0.686, 0.979, and 0.952, respectively. Moreover, the mIoU and mHAU achieved 0.941 and 9.7, respectively, which are significantly better than the other existing segmentation methods.

This study proposed an efficient deep learning algorithm for accurately extracting the mask of any individual tooth from PRs. Precise tooth masks can provide valuable reference for clinical diagnosis and treatment. This algorithm is a fundamental basis for further automated processing applications.

 

We present efficient algorithms for solving systems of linear equations in 1-Laplacians of well-shaped simplicial complexes. 1-Laplacians, or higher-dimensional Laplacians, generalize graph Laplacians to higher-dimensional simplicial complexes and play a key role in computational topology and topological data analysis. Previously, nearly-linear time solvers were developed for simplicial complexes with known collapsing sequences and bounded Betti numbers, such as those triangulating a three-ball in ℝ³ (Cohen, Fasy, Miller, Nayyeri, Peng, and Walkington [SODA'2014], Black, Maxwell, Nayyeri, and Winkelman [SODA'2022], Black and Nayyeri [ICALP'2022]). Furthermore, Nested Dissection provides quadratic time solvers for more general systems with nonzero structures representing well-shaped simplicial complexes embedded in ℝ³. We generalize the specialized solvers for 1-Laplacians to simplicial complexes with additional geometric structures but without collapsing sequences and bounded Betti numbers, and we improve the runtime of Nested Dissection. We focus on simplicial complexes that meet two conditions: (1) each individual simplex has a bounded aspect ratio, and (2) they can be divided into "disjoint" and balanced regions with well-shaped interiors and boundaries. Our solvers draw inspiration from the Incomplete Nested Dissection for stiffness matrices of well-shaped trusses (Kyng, Peng, Schwieterman, and Zhang [STOC'2018]). 

Blockchain and distributed ledger technologies (DLT) are emerging decentralized infrastructures touted by researchers to improve existing systems that have been limited by centralized governance and proprietary control. These technologies have shown continued success in sustaining the operational models of modern cryptocurrencies and decentralized finance applications (DeFi). These applications has incentivized growing discussions in their potential applications and adoption in other sectors such as healthcare, which has a high demand for data liquidity and interoperability. Despite the increasing research efforts in adopting blockchain and DLT in healthcare with conceptual designs and prototypes, a major research gap exists in literature: there is a lack of design recommendations that discuss concrete architectural styles and domain-specific considerations that are necessary for implementing health data exchange systems based on these technologies. This paper aims to address this gap in research by introducing a collection of design patterns for constructing blockchain and DLT-based healthcare systems that support secure and scalable data sharing. Our approach adapts traditional software patterns and proposes novel patterns that take into account both the technical requirements specific to healthcare systems and the implications of these requirements on naive blockchain-based solutions. 

Patients often have their healthcare data stored in centralized systems, leading to challenges when reconciling or consolidating their data across providers due to centralized databases that store patient identities. The challenges disrupt the flow of patient care where time is sensitive for both patients and providers. Decentralized technologies have enabled a new identity model–Self-Sovereign Identity (SSI)–that grants individuals the right to freely control, access, and share their own data. This work proposes a system that achieves SSI in a semi-permissioned blockchain network using an open protocol as the certificate of authority and several guidelines for securely handling transactions in the network. Open protocols like Keccak can grant access to a permission-based network such as Hyperledger Fabric. The network architecture ensures data security and privacy through mechanisms of multi-signature transactions and guidelines for storing transactions locally, making this architecture ideal for privacy-centered use cases, such as healthcare data-sharing applications. The ultimate goal is to give patients full control over their identity and other data derived from their identity within a semi-permissioned network. 

We use 3653 (2661 RRab, 992 RRc) RR Lyrae stars (RRLs) with 7D (3D position, 3D velocity, and metallicity) information selected from Sloan Digital Sky Survey, Large Sky Area Multi-Object Fiber Spectroscopic Telescope, and Gaia EDR3, and divide the sample into two Oosterhoff groups (Oo I and Oo II) according to their amplitude–period behaviour in the Bailey diagram. We present a comparative study of these two groups based on chemistry, kinematics, and dynamics. We find that Oo I RRLs are relatively more metal-rich, with predominately radially dominated orbits and large eccentricities, while Oo II RRLs are relatively more metal-poor, and have mildly radially dominated orbits. The Oosterhoff dichotomy of the Milky Way’s halo is more apparent for the inner-halo region than for the outer-halo region. Additionally, we also search for this phenomenon in the haloes of the two largest satellite galaxies, the Large and Small Magellanic clouds, and compare over different bins in metallicity. We find that the Oosterhoff dichotomy is not immutable, and varies based on position in the Galaxy and from galaxy to galaxy. We conclude that the Oosterhoff dichotomy is the result of a combination of stellar and galactic evolution, and that it is much more complex than the dichotomy originally identified in Galactic globular clusters.

 

In multilayered magnetic topological insulator structures, magnetization reversal processes can drive topological phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Here we report an examination of the critical behavior of two such transitions: the quantum anomalous Hall to normal insulator (QAH-NI), and quantum anomalous Hall to axion insulator (QAH-AXI) transitions. By introducing a new analysis protocol wherein temperature dependent variations in the magnetic coercivity are accounted for, the critical behavior of the QAH-NI and QAH-AXI transitions are evaluated over a wide range of temperature and magnetic field. Despite the uniqueness of these different transitions, quantized longitudinal resistance and Hall conductance are observed at criticality in both cases. Furthermore, critical exponents were extracted for QAH-AXI transitions occurring at magnetization reversals of two different magnetic layers. The observation of consistent critical exponents and resistances in each case, independent of the magnetic layer details, demonstrates critical behaviors in quantum anomalous Hall transitions to be of electronic rather than magnetic origin. Our finding offers a new avenue for studies of phase transition and criticality in QAH insulators.