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We study the quantum dynamics of interstitials and vacancies in a two-dimensional Wigner crystal (WC) using a semi-classical instanton method that is asymptotically exact at low density, i.e., in the $r_s\to \infty$ limit. The dynamics of these point defects mediates magnetism with much higher energy scales than the exchange energies of the pure WC. Via exact diagonalization of the derived effective Hamiltonians in the single-defect sectors, we find the dynamical corrections to the defect energies. The resulting expression for the interstitial (vacancy) energy extrapolates to 0 at $r_s = r_{\rm mit} \approx 70$ ($r_s \approx 30$), suggestive of a self-doping instability to a partially melted WC for some range of $r_s$ below $r_{\rm mit}$. We thus propose a "metallic electron crystal'' phase of the two-dimensional electron gas at intermediate densities between a low density insulating WC and a high density Fermi fluid., Comment: 9+3 pages, 7 figures and 1 table

We propose a two-fluid description of fractional quantum Hall systems, in which one component is a condensate of composite bosons and the other a Fermi liquid formed by composite fermions (or simply electrons). We employ the theory to model the interface between a fractional quantum Hall liquid and a (composite) Fermi liquid metal, where we find a penetration of quantum Hall condensate into the metallic region reminiscent of the proximity effect in superconductor-metal interfaces. We also find a novel and physically reasonable set of gapped quasielectron and neutral modes in fractional quantum Hall liquids., Comment: 17 pages, 6 figures

We analyze the transition temperature $T_c$ of bipolaronic superconductivity in a bond Su-Schrieffer-Heeger (bond-SSH) model -- also known as a bond Peierls model -- where the electron hoppings are modulated by bond phonons. Using a semiclassical instanton approximation justifiable in the adiabatic limit of slow phonons, we find that the bipolaron mass is only weakly enhanced, in contrast to the typical large mass enhancement found in standard (Holstein) electron-phonon models. Specifically, in the strong coupling limit, the bipolarons can freely slide within a degenerate manifold rather than become self-trapped. A gas of these bipolarons can undergo a superfluid transition at a critical temperature for which we obtain an upper bound. We find that this bound is exponentially larger than that in the Holstein model. Our study provides an analytical understanding of the mechanism behind the high-$T_c$ bipolaronic superconductivity numerically observed in [Phys. Rev. X 13, 011010 (2023)]., Comment: 5 pages, 4 figures

We prove that the motion of a single hole induces $SU(N)$ flavor-singlets in the $U=\infty$ $SU(N)$ (Fermi) Hubbard model on a Husimi-like tree graph. The result is also generalized to certain $t$-$J$ models with antiferromagnetic interactions and singlet hopping terms typically neglected in the literature. This is an $SU(N)$ generalization of the "counter-Nagaoka theorem" introduced in [Phys. Rev. B 107, L140401 (2023)]. Our results suggest the existence of antiferromagnetic or resonating-valence-bond (RVB)-like polarons in the $t$-$J$ models on a more realistic non-bipartite lattice. Such antiferromagnetic/RVB polarons may be relevant for a novel strong-coupling mechanism of superconductivity or other exotic fractionalized phases of matter., Comment: 5 + 1 pages, 4 figures. Exact diagonalization result added

Automated segmentation and volumetry of brain magnetic resonance imaging (MRI) scans are essential for the diagnosis of Parkinson's disease (PD) and Parkinson's plus syndromes (P-plus). To enhance the diagnostic performance, we adopt deep learning (DL) models in brain segmentation and compared their performance with the gold-standard non-DL method. We collected brain MRI scans of healthy controls (n=105) and patients with PD (n=105), multiple systemic atrophy (n=132), and progressive supranuclear palsy (n=69) at Samsung Medical Center from January 2017 to December 2020. Using the gold-standard non-DL model, FreeSurfer (FS), we segmented six brain structures: midbrain, pons, caudate, putamen, pallidum, and third ventricle, and considered them as annotating data for DL models, the representative V-Net and UNETR. The Dice scores and area under the curve (AUC) for differentiating normal, PD, and P-plus cases were calculated. The segmentation times of V-Net and UNETR for the six brain structures per patient were 3.48 +- 0.17 and 48.14 +- 0.97 s, respectively, being at least 300 times faster than FS (15,735 +- 1.07 s). Dice scores of both DL models were sufficiently high (>0.85), and their AUCs for disease classification were superior to that of FS. For classification of normal vs. P-plus and PD vs. multiple systemic atrophy (cerebellar type), the DL models and FS showed AUCs above 0.8. DL significantly reduces the analysis time without compromising the performance of brain segmentation and differential diagnosis. Our findings may contribute to the adoption of DL brain MRI segmentation in clinical settings and advance brain research., Comment: Joomee Song and Juyoung Hahm contributed equally to this work as the co-first author. Jong Hyeon Ahn and Kyung-Su Kim (kskim.doc@gmail.com) contributed equally to this work as the co-corresponding author

We prove that the motion of a single hole induces the nearest-neighbor resonating-valence-bond ground state in the $U=\infty$ Hubbard model on a triangular cactus - a tree-like variant of a kagome lattice. The result can be easily generalized to $t-J$ models with antiferromagnetic interactions $J\geq 0$ on the same graphs. This is a weak converse of Nagaoka's theorem of ferromagnetism on a bipartite lattice., Comment: 4 pages + references, a revised version

Compared with chest X-ray (CXR) imaging, which is a single image projected from the front of the patient, chest digital tomosynthesis (CDTS) imaging can be more advantageous for lung lesion detection because it acquires multiple images projected from multiple angles of the patient. Various clinical comparative analysis and verification studies have been reported to demonstrate this, but there were no artificial intelligence (AI)-based comparative analysis studies. Existing AI-based computer-aided detection (CAD) systems for lung lesion diagnosis have been developed mainly based on CXR images; however, CAD-based on CDTS, which uses multi-angle images of patients in various directions, has not been proposed and verified for its usefulness compared to CXR-based counterparts. This study develops/tests a CDTS-based AI CAD system to detect lung lesions to demonstrate performance improvements compared to CXR-based AI CAD. We used multiple projection images as input for the CDTS-based AI model and a single-projection image as input for the CXR-based AI model to fairly compare and evaluate the performance between models. The proposed CDTS-based AI CAD system yielded sensitivities of 0.782 and 0.785 and accuracies of 0.895 and 0.837 for the performance of detecting tuberculosis and pneumonia, respectively, against normal subjects. These results show higher performance than sensitivities of 0.728 and 0.698 and accuracies of 0.874 and 0.826 for detecting tuberculosis and pneumonia through the CXR-based AI CAD, which only uses a single projection image in the frontal direction. We found that CDTS-based AI CAD improved the sensitivity of tuberculosis and pneumonia by 5.4% and 8.7% respectively, compared to CXR-based AI CAD without loss of accuracy. Therefore, we comparatively prove that CDTS-based AI CAD technology can improve performance more than CXR, enhancing the clinical applicability of CDTS., Comment: Kyung-Su Kim, Ju Hwan Lee, and Seong Je Oh have contributed equally to this work as the co-first author. Kyung-Su Kim (kskim.doc@gmail.com) and Myung Jin Chung (mj1.chung@samsung.com) have contributed equally to this work as the co-corresponding author

Computer-aided diagnosis for low-dose computed tomography (CT) based on deep learning has recently attracted attention as a first-line automatic testing tool because of its high accuracy and low radiation exposure. However, existing methods rely on supervised learning, imposing an additional burden to doctors for collecting disease data or annotating spatial labels for network training, consequently hindering their implementation. We propose a method based on a deep neural network for computer-aided diagnosis called virtual multi-view projection and reconstruction for unsupervised anomaly detection. Presumably, this is the first method that only requires data from healthy patients for training to identify three-dimensional (3D) regions containing any anomalies. The method has three key components. Unlike existing computer-aided diagnosis tools that use conventional CT slices as the network input, our method 1) improves the recognition of 3D lung structures by virtually projecting an extracted 3D lung region to obtain two-dimensional (2D) images from diverse views to serve as network inputs, 2) accommodates the input diversity gain for accurate anomaly detection, and 3) achieves 3D anomaly/disease localization through a novel 3D map restoration method using multiple 2D anomaly maps. The proposed method based on unsupervised learning improves the patient-level anomaly detection by 10% (area under the curve, 0.959) compared with a gold standard based on supervised learning (area under the curve, 0.848), and it localizes the anomaly region with 93% accuracy, demonstrating its high performance., Comment: Kyung-Su Kim and Seong Je Oh have contributed equally to this work as the co-first author. Kyung-Su Kim (kskim.doc@gmail.com) and Myung Jin Chung (mj1.chung@samsung.com) have contributed equally to this work as the co-corresponding author

Peripherally inserted central catheters (PICCs) have been widely used as one of the representative central venous lines (CVCs) due to their long-term intravascular access with low infectivity. However, PICCs have a fatal drawback of a high frequency of tip mispositions, increasing the risk of puncture, embolism, and complications such as cardiac arrhythmias. To automatically and precisely detect it, various attempts have been made by using the latest deep learning (DL) technologies. However, even with these approaches, it is still practically difficult to determine the tip location because the multiple fragments phenomenon (MFP) occurs in the process of predicting and extracting the PICC line required before predicting the tip. This study aimed to develop a system generally applied to existing models and to restore the PICC line more exactly by removing the MFs of the model output, thereby precisely localizing the actual tip position for detecting its disposition. To achieve this, we proposed a multi-stage DL-based framework post-processing the PICC line extraction result of the existing technology. The performance was compared by each root mean squared error (RMSE) and MFP incidence rate according to whether or not MFCN is applied to five conventional models. In internal validation, when MFCN was applied to the existing single model, MFP was improved by an average of 45%. The RMSE was improved by over 63% from an average of 26.85mm (17.16 to 35.80mm) to 9.72mm (9.37 to 10.98mm). In external validation, when MFCN was applied, the MFP incidence rate decreased by an average of 32% and the RMSE decreased by an average of 65\%. Therefore, by applying the proposed MFCN, we observed the significant/consistent detection performance improvement of PICC tip location compared to the existing model., Comment: Subin Park and Yoon Ki Cha have contributed equally to this work as the co-first author. Kyung-Su Kim (kskim.doc@gmail.com) and Myung Jin Chung (mj1.chung@samsung.com) have contributed equally to this work as the co-corresponding author

The two-dimensional Wigner crystal (WC) occurs in the strongly interacting regime ($r_s \gg 1$) of the two-dimensional electron gas (2DEG). The magnetism of a pure WC is determined by tunneling processes that induce multi-spin ring-exchange interactions, resulting in fully polarized ferromagnetism for large enough $r_s$. Recently, Hossain et al. [PNAS 117 (51) 32244-32250] reported the occurrence of a fully polarized ferromagnetic insulator at $r_s \gtrsim 35$ in an AlAs quantum well, but at temperatures orders of magnitude larger than the predicted exchange energies for the pure WC. Here, we analyze the large $r_s$ dynamics of an interstitial defect in the WC, and show that it produces local ferromagnetism with much higher energy scales. Three hopping processes are dominant, which favor a large, fully polarized ferromagnetic polaron. Based on the above results, we speculate concerning the phenomenology of the magnetism near the metal-insulator transition of the 2DEG., Comment: 4 pages + references & Supplementary (5 pages), 2+4 figures, 1 table. Minor revision based on comments

This is a commentary on two papers (PNAS 117 (51) 32244-32250 (2020) and arXiv:2011.06721), which observed a series of ordering transitions in a strongly correlated two-dimensional electron system confined to a AlAs quantum well. We summarize the main discoveries (electron nematicity, insulating ferromagnetism, etc.) of them and speculate on $T-r_s$ phase diagram based on theoretical considerations., Comment: 5 pages, 1 figure, published in PNAS

It is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e. for the existence of `plateaus' in the quantum Hall effect. Here, we show that the existence of a quasi-particle Wigner crystal results in the persistence of plateaus of finite extent even in the limit of vanishing disorder. Several experimentally detectable features that characterize the behavior in the zero disorder limit are also explored., Comment: 7 pages, 2 figures

Recent theoretical works based on the neural tangent kernel (NTK) have shed light on the optimization and generalization of over-parameterized networks, and partially bridge the gap between their practical success and classical learning theory. Especially, using the NTK-based approach, the following three representative results were obtained: (1) A training error bound was derived to show that networks can fit any finite training sample perfectly by reflecting a tighter characterization of training speed depending on the data complexity. (2) A generalization error bound invariant of network size was derived by using a data-dependent complexity measure (CMD). It follows from this CMD bound that networks can generalize arbitrary smooth functions. (3) A simple and analytic kernel function was derived as indeed equivalent to a fully-trained network. This kernel outperforms its corresponding network and the existing gold standard, Random Forests, in few shot learning. For all of these results to hold, the network scaling factor $\kappa$ should decrease w.r.t. sample size n. In this case of decreasing $\kappa$, however, we prove that the aforementioned results are surprisingly erroneous. It is because the output value of trained network decreases to zero when $\kappa$ decreases w.r.t. n. To solve this problem, we tighten key bounds by essentially removing $\kappa$-affected values. Our tighter analysis resolves the scaling problem and enables the validation of the original NTK-based results., Comment: We spotted an error in the proof of Lemma A.4 and are investigating whether this can be corrected. Furthermore, the authors of the original paper have informed us that they are fixing the lemma upon which our theorem 3.2 builds. Therefore, we are removing the current version of our paper

A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the generator to utilize additional information from a given measurement for prior learning, thereby yielding more accurate prediction for signals. As our framework has a simple form, it is easily applied to existing CS methods using pre-trained generators. We demonstrate through extensive experiments that our framework exhibits uniformly superior performances by large margin and can reduce the reconstruction error up to an order of magnitude for some applications. We also explain the experimental success in theory by showing that our framework can slightly relax the stringent signal presence condition, which is required to guarantee the success of signal recovery.

A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is proposed to estimate a sparse signal vector and its support given $m$ linear measurements. Unlike the maximum a posteriori (MAP) support detection, which was proposed by Lee to estimate the support by selecting an index with the maximum likelihood ratio of the correlation given by a normalized version of the orthogonal matching pursuit (OMP), the proposed method uses the correlation given by the matching pursuit proposed by Davies and Eldar. BMMP exploits the diversity gain to estimate the support by considering multiple support candidates, each of which is obtained by iteratively selecting an index set with a size different for each candidate. In particular, BMMP considers an extended support estimate whose maximal size is $m$ in the process to obtain each of the support candidates. It is observed that BMMP outperforms other state-of-the-art methods and approaches the ideal limit of the signal sparsity in our simulation setting.

We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover the $k$-sparse signal vector and its support $\mathcal{T}$. We exploit extended support estimate $\mathcal{E}$ with size larger than $k$ satisfying $\mathcal{E} \supseteq \mathcal{T}$ and obtained by a trained deep neural network (DNN). To make the DNN learnable, it provides $\mathcal{E}$ as the union of equivalent solutions of $\mathcal{T}$ by utilizing modulo Fourier invariances. Set $\mathcal{E}$ can be estimated with short running time via the DNN, and support $\mathcal{T}$ can be determined from the DNN output rather than from the full index set by applying hard thresholding to $\mathcal{E}$. Thus, the DNN-based extended support estimation improves the reconstruction performance of the signal with a low complexity burden dependent on $k$. Numerical results verify that the proposed scheme has a superior performance with lower complexity compared to local search-based greedy sparse phase retrieval and a state-of-the-art variant of the Fienup method.

We consider the classical sparse regression problem of recovering a sparse signal $x_0$ given a measurement vector $y = \Phi x_0+w$. We propose a tree search algorithm driven by the deep neural network for sparse regression (TSN). TSN improves the signal reconstruction performance of the deep neural network designed for sparse regression by performing a tree search with pruning. It is observed in both noiseless and noisy cases, TSN recovers synthetic and real signals with lower complexity than a conventional tree search and is superior to existing algorithms by a large margin for various types of the sensing matrix $\Phi$, widely used in sparse regression.

The non-trivial magnon band topology and its consequent responses have been extensively studied in two-dimensional magnetisms. However, the triangular lattice antiferromagnet (TLAF), the best-known frustrated two-dimensional magnet, has received less attention than the closely related Kagome system, because of the spin-chirality cancellation in the umbrella ground state of the undistorted TLAF. In this work, we study the band topology and the thermal Hall effect (THE) of the TLAF with (anti-)trimerization distortion under the external perpendicular magnetic field using the linearized spin wave theory. We show that the spin-chirality cancellation is removed in such case, giving rise to the non-trivial magnon band topology and the finite THE. Moreover, the magnon bands exhibit band topology transitions tuned by the magnetic field. We demonstrate that such transitions are accompanied by the logarithmic divergence of the first derivative of the thermal Hall conductivity. Finally, we examine the above consequences by calculating the THE in the hexagonal manganite YMnO$_3$, well known to have anti-trimerization., Comment: 6 + 7 pages, 3 + 5 figures, 0 + 1 table; Journal reference added

In this paper, we address the sparse multiple measurement vector (MMV) problem where the objective is to recover a set of sparse nonzero row vectors or indices of a signal matrix from incomplete measurements. Ideally, regardless of the number of columns in the signal matrix, the sparsity (k) plus one measurements is sufficient for the uniform recovery of signal vectors for almost all signals, i.e., excluding a set of Lebesgue measure zero. To approach the "k+1" lower bound with computational efficiency even when the rank of signal matrix is smaller than k, we propose a greedy algorithm called Two-stage orthogonal Subspace Matching Pursuit (TSMP) whose theoretical results approach the lower bound with less restriction than the Orthogonal Subspace Matching Pursuit (OSMP) and Subspace-Augmented MUltiple SIgnal Classification (SA-MUSIC) algorithms. We provide non-asymptotical performance guarantees of OSMP and TSMP by covering both noiseless and noisy cases. Variants of restricted isometry property and mutual coherence are used to improve the performance guarantees. Numerical simulations demonstrate that the proposed scheme has low complexity and outperforms most existing greedy methods. This shows that the minimum number of measurements for the success of TSMP converges more rapidly to the lower bound than the existing methods as the number of columns of the signal matrix increases., Comment: 55 pages, 8 figures, to be submitted to IEEE Transactions on Information theory, a shorter version was submitted to Proc. IEEE ISIT 2016