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Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low-rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non-Gaussian. We thus propose a new method called Robust Principal Component Analysis for Exponential Family distributions ($e^{\text{RPCA}}$), which can perform the desired decomposition into low-rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient $e^{\text{RPCA}}$ decomposition. The effectiveness of $e^{\text{RPCA}}$ is then demonstrated in two applications: the first for steel sheet defect detection, and the second for crime activity monitoring in the Atlanta metropolitan area.

Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a wide range of applications, including signal processing, neuroscience and network analysis. In these applications, the online detection of changes is of crucial importance, but this can be highly challenging since such changes often occur in a low-dimensional embedding within high-dimensional data streams. We thus propose a new method, called PERsistence diagram-based ChangE-PoinT detection (PERCEPT), which leverages the learned topological structure from TDA to sequentially detect changes. PERCEPT follows two key steps: it first learns the embedded topology as a point cloud via persistence diagrams, then applies a non-parametric monitoring approach for detecting changes in the resulting point cloud distributions. This yields a non-parametric, topology-aware framework which can efficiently detect online changes from high-dimensional data streams. We investigate the effectiveness of PERCEPT over existing methods in a suite of numerical experiments where the data streams have an embedded topological structure. We then demonstrate the usefulness of PERCEPT in two applications in solar flare monitoring and human gesture detection.

Pressure not only provides a powerful way to tune the crystal structure of transition metal dichalcogenides (TMDCs) but also promotes the discovery of exotic electronic states and intriguing phenomena. Structural transitions from the quasi-two-dimensional layered orthorhombic phase to three-dimensional cubic pyrite phase, metallization, and superconductivity under high pressure have been observed experimentally in TMDCs materials PdS2 and PdSe2. Here, we report a theoretical prediction of the pressure-induced evolutions of crystal structure and electronic structure of PdSSe, an isomorphous intermediate material of the orthorhombic PdS2 and PdSe2. A series of pressure-induced structural phase transitions from the layered orthorhombic structure into an intermediate phase, then to a cubic phase are revealed. The intermediate phase features the same structure symmetry as the ambient orthorhombic phase, except for drastic collapsed interlayer distances and striking changes of the coordination polyhedron. Furthermore, the structural phase transitions are accompanied by electronic structure variations from semiconductor to semimetal, which are attributed to bandwidth broaden and orbital-selective mechanisms. Especially, the cubic phase PdSSe is distinct from the cubic PdS2 and PdSe2 materials by breaking inversion and mirror-plane symmetries, but showing similar superconductivity under high pressure, which is originated from strong electron-phonon coupling interactions concomitant with topologically nontrivial Weyl and high-fold Fermions. The intricate interplay between lattice, charge, and orbital degrees of freedom as well as the topologically nontrivial states in these compounds will further stimulate wide interest to explore the exotic physics of the TMDCs materials., Comment: 21 pages main text, 6 figures,and Supplemental Material including 12 figures

Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric structures for a wide range of applications, including protein classification, neuroscience, and time-series analysis. However, in many such applications, one is also interested in sequentially detecting changes in this topological structure. We propose a new method called Persistence Diagram based Change-Point (PD-CP), which tackles this problem by integrating the widely-used persistence diagrams in TDA with recent developments in nonparametric change-point detection. The key novelty in PD-CP is that it leverages the distribution of points on persistence diagrams for online detection of topological changes. We demonstrate the effectiveness of PD-CP in an application to solar flare monitoring.

Single-parameter persistent homology, a key tool in topological data analysis, has been widely applied to data problems along with statistical techniques that quantify the significance of the results. In contrast, statistical techniques for two-parameter persistence, while highly desirable for real-world applications, have scarcely been considered. We present three statistical approaches for comparing geometric data using two-parameter persistent homology; these approaches rely on the Hilbert function, matching distance, and barcodes obtained from two-parameter persistence modules computed from the point-cloud data. Our statistical methods are broadly applicable for analysis of geometric data indexed by a real-valued parameter. We apply these approaches to analyze high-dimensional point-cloud data obtained from Simple English Wikipedia articles. In particular, we show how our methods can be utilized to distinguish certain subsets of the Wikipedia data and to compare with random data. These results yield insights into the construction of null distributions and stability of our methods with respect to noisy data., Comment: 17 pages, 13 figures

Charge-density-wave (CDW) instability and pressure-induced superconductivity in bulk 1T-NbS2 are predicted theoretically by first-principles calculations. We reveal a CDW instability towards the formation of a stable commensurate CDW order, resulting in a sqart(13)*sqart(13) structural reconstruction featured with star-of-David clusters. The CDW phase exhibits one-dimensional metallic behavior with in-plane flat-band characteristics, and coexists with an orbital-density-wave order predominantly contributed by 4d_(z^2-r^2 ) orbital from the inner Nb atoms of the star-of-David cluster. By doubling the cell of the CCDW phase along the layer stacking direction, a metal-insulator transition may be realized in the CDW phase in case the interlayer antiferromagnetic ordering and Coulomb correlation effect have been considered simultaneously. Bare electron susceptibility, phonon linewidth and electron-phonon coupling calculations suggest that the CDW instability is driven by softened phonon modes due to the strong electron-phonon coupling interactions. CDW order can be suppressed by pressure, concomitant with appearance of superconductivity. Our theoretical predictions call for experimental investigations to further clarify the transport and magnetic properties of 1T-NbS2. Furthermore, it would also be very interesting to explore the possibility to realize the CDW order coexisting with the superconductivity in bulk 1T-NbS2., Comment: 24 pages,9 figures +supplemental material,submitted to PRB

Based on first-principles simulations and calculations, we explore the evolution of crystal structure, electronic structure and transport properties of quasi 2D layered PdS2 under uniaxial stress and hydrostatic pressure. The coordination of the Pd ions plays crucial roles in the structural transition, electronic structure and transport properties of PdS2. An interesting ferroelastic phase transition with lattice reorientation is revealed under uniaxial compressive stress, which originates from the bond reconstructions of the unusual PdS4 square-planar coordination. By contrast, the layered structure transforms to 3D cubic pyrite-type structure under hydrostatic pressure. In contrast to the experimental proposed coexistence of layered PdS2-type structure with cubic pyrite-type structure at intermediate pressure range, we predict that the compression-induced intermediate phase showing the same structural symmetry with the ambient phase, except of sharply contracted interlayer-distances. The coordination environments of the Pd ions have changed from square-planar to distorted octahedra in the intermediate phase, which results in the bandwidth broaden and orbital-selective metallization. In addition, the superconductivity comes from the cubic pyrite-type structure protected topological nodal-line states. The strong correlations between structural transition, electronic structure and transport properties in PdS2 provide a platform to study the fundamental physics of the interplay between crystal structure and transport behavior, and the competition between diverse phases., Comment: 40pages,20figures

Iridium oxides (iridates) provide a good platform to study the delicate interplay between spin-orbit coupling (SOC) interactions, electron correlation effects, Hund's coupling and lattice degree of freedom. However, overwhelming investigations primarily focus on tetravalent (Ir4+, 5d5) and pentavalent (Ir5+, 5d4) iridates, far less attention has been paid to iridates with other valence states. Here, we pay our attention to a less-explored trivalent (Ir3+, 5d6) iridates, K0.75Na0.25IrO2, crystalizing in a triangular lattice with edge-sharing IrO6 octahedra and alkali metal ions intercalated [IrO2]- layers. We theoretically determine the preferred occupied positions of the alkali metal ions from energetic viewpoints and reproduce the experimentally observed semiconducting behavior and nonmagnetic (NM) properties. The SOC interactions play a critical role in the band dispersion, resulting in NM Jeff = 0 states. More intriguingly, our electronic structure not only uncovers the presence of in-gap states and explains the abnormal low activation energy in K0.75Na0.25IrO2, but also predicts the band edge can be effectively modulated by mechanical strain. Especially, the in-gap states feature with enhanced band-convergence characteristics by 6% compressive strain, which will greatly enhance the electrical conductivity of K0.75Na0.25IrO2. Present work sheds new lights on the unconventional electronic structures of the trivalent iridates, indicating its promising application as nanoelectronic and thermoelectric material., Comment: 17pages,8figures

Using constrained-path quantum Monte Carlo method, we systematically study the Hubbard model on AA-stacked honeycomb lattices with electric field. Our simulation demonstrates a dominant chiral d+id wave pairing induced by the electric field at half filling. In particular, as the on-site Coulomb interaction increases, the effective pairing correlation of chiral d+id superconducting state exhibits increasing behavior. We attribute the electric field induced d+id superconductivity to an increased density of states near the Fermi energy and an suppressed antiferromagnetic spin correlation after turning on the electric field. Our results strongly suggest the AA-stacked graphene system with electric field is a good candidate for chiral d+id superconductors.

In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on statistical techniques for single-parameter persistence, the case of two-parameter persistence, which is highly desirable for real-world applications, has been less studied. This paper provides an accessible introduction to two-parameter persistent homology and presents results about matching distance between 2-D persistence modules obtained from families of point clouds. Results include observations of how differences in geometric structure of point clouds affect the matching distance between persistence modules. We offer these results as a starting point for the investigation of more complex data., Comment: 21 pages, 14 figures

To understand the interplay between nematic fluctuation and superconductivity in iron-based superconductors, we performed a systematic study of the realistic two-orbital Hubbard model by using the constrained-path quantum Monte Carlo method. Our numerical results showed that the on-site nematic interaction induces a strong enhancement of nematic fluctuations at various momentums, especially at ($\pi$,$\pi$). Simultaneously, it was found that the on-site nematic interaction suppresses the ($\pi$,0)/(0,$\pi$) antiferromagnetic order and long-range electron pairing correlations for dominant pairing channels in iron-based superconductors. Our findings suggest that nematic fluctuation seems to compete with superconductivity in iron-based superconductors., Comment: 6 figures

The spin-orbit coupling (SOC) interactions, electron correlation effects and Hund coupling cooperate and compete with each other, leading to novel properties, quantum phase and non-trivial topological electronic behavior in iridium oxides. Because of the well separated IrO6 octahedra approaching cubic crystal-field limit, the hexagonal iridates Sr3MIrO6 (M = Sr, Na and Li) serves as a canonical model system to investigate the underlying physical properties that arises from the novel Jeff state. Based on density functional theory calculations complemented by Green's function methods, we systematically explore the critical role of SOC on the electronic structure and magnetic properties of Sr3MIrO6. The crystal-field splitting combined with correlation effects are insufficient to account for the insulating nature, but the SOC interactions is the intrinsic source to trigger the insulating ground states in these hexagonal iridates. The decreasing geometry connectivity of IrO6 octahedra gives rise to the increasing of effective electronic correlations and SOC interactions, tuning the hexagonal iridates from low-spin Jeff = 1/2 states with large local magnetic moments for the Ir4+ (5d5) ions in Sr4IrO6 to nonmagnetic singlet Jeff = 0 states without magnetic moments for the Ir5+ (5d4) ions in Sr3NaIrO6 and Sr3LiIrO6. The theoretical calculated results are in good agreement with available experimental data, and explain the magnetic properties of Sr3MIrO6 well., Comment: 21