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We introduce a new method to jointly reduce the dimension of the input and output space of a high-dimensional function. Choosing a reduced input subspace influences which output subspace is relevant and vice versa. Conventional methods focus on reducing either the input or output space, even though both are often reduced simultaneously in practice. Our coupled approach naturally supports goal-oriented dimension reduction, where either an input or output quantity of interest is prescribed. We consider, in particular, goal-oriented sensor placement and goal-oriented sensitivity analysis, which can be viewed as dimension reduction where the most important output or, respectively, input components are chosen. Both applications present difficult combinatorial optimization problems with expensive objectives such as the expected information gain and Sobol indices. By optimizing gradient-based bounds, we can determine the most informative sensors and most sensitive parameters as the largest diagonal entries of some diagnostic matrices, thus bypassing the combinatorial optimization and objective evaluation.

Rare-earth-based triangular-lattice magnets provide the fertile ground to explore the exotic quantum magnetic state. Herein, we report a new family of RE-based triangular-lattice magnets Ba6RE2Ti4O17(RE= rare earth ions) crystallized into the hexagonal structure with space group of P63 mmc, where magnetic rare earth ions form an ideal triangular lattice within the ab-plane and stack in an AA -type fashion along the c-axis. The low-temperature magnetic susceptibility results reveal all the serial compounds have the dominant antiferromagnetic interactions and an absence of magnetic ordering down to 1.8 K. The magnetization and electron spin resonance results indicate distinct magnetic anisotropy for the compounds with different RE ions. Moreover, Ba6Nd2Ti4O17 single crystal is successfully grown and it exhibits strong Ising like anisotropy with magnetic easy-axis perpendicular to the triangle-lattice plane, being a candidate to explore quantum spin liquid state with dominant Ising-type interaction., Comment: 20 pages, 8 figures

In many applications, piecewise continuous functions are commonly interpolated over meshes. However, accurate high-order manipulations of such functions can be challenging due to potential spurious oscillations known as the Gibbs phenomena. To address this challenge, we propose a novel approach, Robust Discontinuity Indicators (RDI), which can efficiently and reliably detect both C^{0} and C^{1} discontinuities for node-based and cell-averaged values. We present a detailed analysis focusing on its derivation and the dual-thresholding strategy. A key advantage of RDI is its ability to handle potential inaccuracies associated with detecting discontinuities on non-uniform meshes, thanks to its innovative discontinuity indicators. We also extend the applicability of RDI to handle general surfaces with boundaries, features, and ridge points, thereby enhancing its versatility and usefulness in various scenarios. To demonstrate the robustness of RDI, we conduct a series of experiments on non-uniform meshes and general surfaces, and compare its performance with some alternative methods. By addressing the challenges posed by the Gibbs phenomena and providing reliable detection of discontinuities, RDI opens up possibilities for improved approximation and analysis of piecewise continuous functions, such as in data remap., Comment: 37 pages, 37 figures, submitted to Computational and Applied Mathematics (COAM)

Interfacial coupling between graphene and other 2D materials can give rise to intriguing physical phenomena. In particular, several theoretical studies predict that the interplay between graphene and an antiferromagnetic insulator could lead to the emergence of quantum anomalous Hall phases. However, such phases have not been observed experimentally yet, and further experimental studies are needed to reveal the interaction between graphene and antiferromagnetic insulators. Here, we report the study in heterostructures composed of graphene and the antiferromagnetic insulator MnPSe$_3$. It is found that the MnPSe$_3$ has little impact on the quantum Hall phases apart from doping graphene via interfacial charge transfer. However, the magnetic order can contribute indirectly via process like Kondo effect, as evidenced by the observed minimum in the temperature-resistance curve between 20-40 K, far below the N\'eel temperature (70 K).

The study of the interaction between superconductivity and charge ordering is helpful to resolve the pairing mechanism in high-temperature superconductors. Recently, several resistance oscillations studies trigger the speculation that a long-range charge ordering, with an enormous mesh size of several tens of nanometer, can possibly emerge in underdoped high Tc superconductor. However, spectroscopy studies have not traced this kind of long-range charge ordering. Here, we clarify the disagreement between the transport and spectroscopy studies on the mysterious long-range charge ordering by investigating the magneto-oscillations in underdoped Bi2Sr2CaCu2O8+{\delta} flakes. Inspired by the observation that the oscillations evolve from a periodic to an aperiodic one with decreasing doping level, we conclude that the magneto-oscillations can be generated by the interaction between vortices and superconducting loops that enclose randomly distributed underdoped puddles while an assumption of long-range charge ordering is not necessary.

Van der Waals (vdW) Josephson junctions can possibly accelerate the development of advanced superconducting device that utilizes the unique properties of two-dimensional (2D) transition metal dichalcogenide (TMD) superconductors such as spin-orbit coupling, spin-valley locking. Here, we fabricate vertically stacked NbS$_{2}$/NbS$_{2}$ Josephson junctions using a modified all-dry transfer technique and characterize the device performance via systematic low-temperature transport measurements. The experimental results show that the superconducting transition temperature of the NbS$_{2}$/NbS$_{2}$ Josephson junction is 5.84 K, and the critical current density reaches 3975 A/cm$^{2}$ at 2K. Moreover, we extract a superconducting energy gap $\Delta=0.58$ meV, which is considerably smaller than that expected from the single band s-wave Bardeen-Cooper-Schrieffer (BCS) model ($\Delta=0.89$ meV).

Image-based 3D reconstruction is one of the most important tasks in Computer Vision with many solutions proposed over the last few decades. The objective is to extract metric information i.e. the geometry of scene objects directly from images. These can then be used in a wide range of applications such as film, games, virtual reality, etc. Recently, deep learning techniques have been proposed to tackle this problem. They rely on training on vast amounts of data to learn to associate features between images through deep convolutional neural networks and have been shown to outperform traditional procedural techniques. In this paper, we improve on the state-of-the-art two-view structure-from-motion(SfM) approach of [11] by incorporating 4D correlation volume for more accurate feature matching and reconstruction. Furthermore, we extend it to the general multi-view case and evaluate it on the complex benchmark dataset DTU [4]. Quantitative evaluations and comparisons with state-of-the-art multi-view 3D reconstruction methods demonstrate its superiority in terms of the accuracy of reconstructions., Comment: IEEE International Conference on Signal Processing, Sensors, and Intelligent Systems (SPSIS 2022)

Large displacement optical flow is an integral part of many computer vision tasks. Variational optical flow techniques based on a coarse-to-fine scheme interpolate sparse matches and locally optimize an energy model conditioned on colour, gradient and smoothness, making them sensitive to noise in the sparse matches, deformations, and arbitrarily large displacements. This paper addresses this problem and presents HybridFlow, a variational motion estimation framework for large displacements and deformations. A multi-scale hybrid matching approach is performed on the image pairs. Coarse-scale clusters formed by classifying pixels according to their feature descriptors are matched using the clusters' context descriptors. We apply a multi-scale graph matching on the finer-scale superpixels contained within each matched pair of coarse-scale clusters. Small clusters that cannot be further subdivided are matched using localized feature matching. Together, these initial matches form the flow, which is propagated by an edge-preserving interpolation and variational refinement. Our approach does not require training and is robust to substantial displacements and rigid and non-rigid transformations due to motion in the scene, making it ideal for large-scale imagery such as Wide-Area Motion Imagery (WAMI). More notably, HybridFlow works on directed graphs of arbitrary topology representing perceptual groups, which improves motion estimation in the presence of significant deformations. We demonstrate HybridFlow's superior performance to state-of-the-art variational techniques on two benchmark datasets and report comparable results with state-of-the-art deep-learning-based techniques.

The Luttinger's theorem has long been taken as the key feature of Landau's Fermi liquid, which signals the presence of quasiparticles. Here, by the unbiased Monte Carlo method, violation of Luttinger's theorem is clearly revealed in the Falicov-Kimball (FK) model, indicating the robust correlation-driven non-Fermi liquid characteristic under any electron density. Introducing hole carriers to the half-filled FK leads to Mott insulator-metal transition, where the Mott quantum criticality manifests unconventional scaling behavior in transport properties. Further insight on the violation of the Luttinger's theorem is examined by combining Hubbard-I approximation with a composite fermion picture, which emphasizes the importance of a mixed excitation of the itinerant electron and the composite fermion. Interestingly, when compared FK model with a binary disorder system, it suggests that the two-peak band structure discovered by Monte Carlo and Hubbard-I approaches is underlying the violation of Luttinger's theorem., Comment: 10 pages, 9 figures