arXiv subjects

Jian Kang

Publications and source records attributed to Jian Kang.

At least 145 records · Page 8Linked to original sources

arXiv2021

Lattice model for the Coulomb interacting chiral limit of the magic angle twisted bilayer graphene: symmetries, obstructions and excitations

We revisit the localized Wannier state description of the twisted bilayer graphene, focusing on the chiral limit. We provide a simple method for constructing such 2D exponentially localized -- yet valley polarized -- Wannier states, centered on the sites of the honeycomb lattice, paying particular attention to maintaining all the unobstructed symmetries. This includes the unitary particle-hole symmetry, and the combination of $C_2\mathcal{T}$ and the chiral particle-hole symmetry. The $C_2\mathcal{T}$ symmetry alone remains topologically obstructed and is not represented in a simple site-to-site fashion. We also analyze the gap and the dispersion of single particle and single hole excitations above a strong coupling ground state at integer fillings, which we find to be dominated by the on-site and the nearest neighbor terms of a triangular lattice hopping model, with a minimum at the center of the moire Brillouin zone. Finally, we use the insight gained from this real space description to understand the dependence of the gap and the effective mass on the range of the screened Coulomb interaction.

cond-mat.str-el↗

arXiv2021

Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene

We present a framework for understanding the recently observed cascade transitions and the Landau level degeneracies at every integer filling of twisted bilayer graphene. The Coulomb interaction projected onto narrow bands causes the charged excitations at an integer filling to disperse, forming new bands. If the excitation moves the filling away from the charge neutrality point, then it has a band minimum at the moire Brillouin zone center with a small mass that compares well with the experiment; if towards the charge neutrality point, then it has a much larger mass and a higher degeneracy. At a non-zero density away from an integer filling the excitations interact. The system on the small mass side has a large bandwidth and forms a Fermi liquid. On the large mass side the bandwidth is narrow, the compressibility is negative and the Fermi liquid is likely unstable. This explains the observed sawtooth features in compressibility, the Landau fans pointing away from charge neutrality as well as their degeneracies. By providing a description of the charge itineracy in the normal state this framework sets the stage for superconductivity at lower temperatures.

cond-mat.str-el↗

arXiv2021

Group Inverse-Gamma Gamma Shrinkage for Sparse Regression with Block-Correlated Predictors

Heavy-tailed continuous shrinkage priors, such as the horseshoe prior, are widely used for sparse estimation problems. However, there is limited work extending these priors to predictors with grouping structures. Of particular interest in this article, is regression coefficient estimation where pockets of high collinearity in the covariate space are contained within known covariate groupings. To assuage variance inflation due to multicollinearity we propose the group inverse-gamma gamma (GIGG) prior, a heavy-tailed prior that can trade-off between local and group shrinkage in a data adaptive fashion. A special case of the GIGG prior is the group horseshoe prior, whose shrinkage profile is correlated within-group such that the regression coefficients marginally have exact horseshoe regularization. We show posterior consistency for regression coefficients in linear regression models and posterior concentration results for mean parameters in sparse normal means models. The full conditional distributions corresponding to GIGG regression can be derived in closed form, leading to straightforward posterior computation. We show that GIGG regression results in low mean-squared error across a wide range of correlation structures and within-group signal densities via simulation. We apply GIGG regression to data from the National Health and Nutrition Examination Survey for associating environmental exposures with liver functionality.

stat.ME↗

arXiv2021

Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene

Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom -- charge, spin, and valley -- gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted hopping interaction that emerges due to the non-trivial topological properties of TBG. Such a non-local interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interaction. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.

cond-mat.str-el↗

arXiv2021

Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene

We propose an SU(4) spin-valley-fermion model to investigate the superconducting instabilities of twisted bilayer graphene (TBG). In this approach, bosonic fluctuations associated with an emergent SU(4) symmetry, corresponding to combined rotations in valley and spin spaces, couple to the low-energy fermions that comprise the flat bands. These fluctuations are peaked at zero wave-vector, reflecting the "ferromagnetic-like" SU(4) ground state recently found in strong-coupling solutions of microscopic models for TBG. Focusing on electronic states related to symmetry-imposed points of the Fermi surface, dubbed here "valley hot-spots" and "van Hove hot-spots", we find that the coupling to the itinerant electrons partially lifts the huge degeneracy of the ferro-SU(4) ground state manifold, favoring inter-valley order, spin-valley coupled order, ferromagnetic order, spin-current order, and valley-polarized order, depending on details of the band structure. These fluctuations, in turn, promote attractive pairing interactions in a variety of closely competing channels, including a nodeless $f$-wave state, a nodal $i$-wave state, and topological $d+id$ and $p+ip$ states with unusual Chern numbers $2$ and $4$, respectively. Nematic superconductivity, although not realized as a primary instability of the system, still appears as a consequence of the near-degeneracy of superconducting order parameters that transform as one-dimensional and two-dimensional irreducible representations of the point group $D_{6}$.

cond-mat.supr-con↗

arXiv2021

Correlated Insulating Phases in the Twisted Bilayer Graphene

We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is $SU(4)$ symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are neglected, the ground states are found to be in the $SU(4)$ manifold with degeneracy. The kinetic terms, treated as perturbation, break this large $SU(4)$ symmetry and propel the appearance of intervalley coherent state, quantum topological insulators and other symmetry-breaking insulating states. We first present the theoretical analysis of moiré lattice model construction and then show how to solve the model with large-scale quantum Monte Carlo simulations in an unbiased manner. We further provide potential directions such that from the real-space model construction and its quantum many-body solutions how the perplexing yet exciting experimental discoveries in the correlation physics of twisted bilayer graphene can be gradually understood. This review will be helpful for the readers to grasp the fast growing field of the model study of twisted bilayer graphene.

cond-mat.str-el↗

arXiv2020

Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach

We develop a two stage renormalization group which connects the continuum Hamiltonian for twisted bilayer graphene at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only which is valid at distances much longer than the moire period. In the first stage, the Coulomb interaction renormalizes the Fermi velocity and the interlayer tunnelings in such a way as to suppress the ratio of the same sublattice to opposite sublatice tunneling, hence approaching the so-called chiral limit. In the second stage, the interlayer tunneling is treated non-perturbatively. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian is determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step. We also calculate exactly the exciton energy spectrum from the Coulomb interactions projected onto the renormalized narrow bands. The resulting softening of the collective modes marks the propinquity of the enlarged ("hidden") $U(4)\times U(4)$ symmetry in the magic angle twisted bilayer graphene.

cond-mat.str-el↗

arXiv2020

Bayesian Hierarchical Models for High-Dimensional Mediation Analysis with Coordinated Selection of Correlated Mediators

We consider Bayesian high-dimensional mediation analysis to identify among a large set of correlated potential mediators the active ones that mediate the effect from an exposure variable to an outcome of interest. Correlations among mediators are commonly observed in modern data analysis; examples include the activated voxels within connected regions in brain image data, regulatory signals driven by gene networks in genome data and correlated exposure data from the same source. When correlations are present among active mediators, mediation analysis that fails to account for such correlation can be sub-optimal and may lead to a loss of power in identifying active mediators. Building upon a recent high-dimensional mediation analysis framework, we propose two Bayesian hierarchical models, one with a Gaussian mixture prior that enables correlated mediator selection and the other with a Potts mixture prior that accounts for the correlation among active mediators in mediation analysis. We develop efficient sampling algorithms for both methods. Various simulations demonstrate that our methods enable effective identification of correlated active mediators, which could be missed by using existing methods that assume prior independence among active mediators. The proposed methods are applied to the LIFECODES birth cohort and the Multi-Ethnic Study of Atherosclerosis (MESA) and identified new active mediators with important biological implications.

stat.AP↗

arXiv2020

Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to estimate the model parameters, and carefully characterize their estimation precisions. We then construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Finally, we develop the testing procedures and establish their asymptotic guarantees. We study the finite-sample performance of our tests through intensive simulations, and illustrate with a brain connectivity analysis example.

stat.ME↗

arXiv2020

Bayesian Sparse Mediation Analysis with Targeted Penalization of Natural Indirect Effects

Causal mediation analysis aims to characterize an exposure's effect on an outcome and quantify the indirect effect that acts through a given mediator or a group of mediators of interest. With the increasing availability of measurements on a large number of potential mediators, like the epigenome or the microbiome, new statistical methods are needed to simultaneously accommodate high-dimensional mediators while directly target penalization of the natural indirect effect (NIE) for active mediator identification. Here, we develop two novel prior models for identification of active mediators in high-dimensional mediation analysis through penalizing NIEs in a Bayesian paradigm. Both methods specify a joint prior distribution on the exposure-mediator effect and mediator-outcome effect with either (a) a four-component Gaussian mixture prior or (b) a product threshold Gaussian prior. By jointly modeling the two parameters that contribute to the NIE, the proposed methods enable penalization on their product in a targeted way. Resultant inference can take into account the four-component composite structure underlying the NIE. We show through simulations that the proposed methods improve both selection and estimation accuracy compared to other competing methods. We applied our methods for an in-depth analysis of two ongoing epidemiologic studies: the Multi-Ethnic Study of Atherosclerosis (MESA) and the LIFECODES birth cohort. The identified active mediators in both studies reveal important biological pathways for understanding disease mechanisms.

stat.AP↗

arXiv2020

Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene

We use the DMRG to study the correlated electron states favored by the Coulomb interaction projected onto the narrow bands of twisted bilayer graphene within a spinless one-valley model. The Hilbert space of the narrow bands is constructed from a pair of hybrid Wannier states with opposite Chern numbers. Depending on the parameters in the BM model, the DMRG in this basis determines the ground state at one particle per unit cell to be either QAH state or a state with no Hall effect which is nearly a product state. Based on this form, we then apply the variational method to study their competition, thus identifying three states: the QAH, a gapless $C_2T$ symmetric nematic, and a gapped $C_2T$ symmetric stripe. All three states are nearly degenerate at the realistic parameters of the BM model. The single particle spectrum of the nematic contains either a quadratic node or two close Dirac nodes near $Γ$. Motivated by the Landau level degeneracy found in this state, we propose it to be the state observed at the charge neutrality point once spin and valley degeneracies are restored. The optimal period for the $C_2T$ stripe state is found to be $2$ unit cells. In addition, using the fact that the topological charge of the nodes in the $C_2T$ nematic phase is no longer described simply by their winding numbers once the translation symmetry is broken, but rather by certain elements of a non-Abelian group that was recently pointed out, we identify the mechanism of the gap opening within the $C_2T$ stripe state. Although the nodes at the Fermi energy are locally stable, they can be annihilated after braiding with other nodes connecting them to adjacent (folded) bands. Therefore, if the translation symmetry is broken, the gap at one particle per unit cell can open even if the system preserves the $C_2T$ and valley $U(1)$ symmetries, and the gap to remote bands remains open.

cond-mat.str-el↗

arXiv2020

Deep Learning for Image Search and Retrieval in Large Remote Sensing Archives

This chapter presents recent advances in content based image search and retrieval (CBIR) systems in remote sensing (RS) for fast and accurate information discovery from massive data archives. Initially, we analyze the limitations of the traditional CBIR systems that rely on the hand-crafted RS image descriptors. Then, we focus our attention on the advances in RS CBIR systems for which deep learning (DL) models are at the forefront. In particular, we present the theoretical properties of the most recent DL based CBIR systems for the characterization of the complex semantic content of RS images. After discussing their strengths and limitations, we present the deep hashing based CBIR systems that have high time-efficient search capability within huge data archives. Finally, the most promising research directions in RS CBIR are discussed.

cs.CV↗

arXiv2020

Learning Shared Cross-modality Representation Using Multispectral-LiDAR and Hyperspectral Data

Due to the ever-growing diversity of the data source, multi-modality feature learning has attracted more and more attention. However, most of these methods are designed by jointly learning feature representation from multi-modalities that exist in both training and test sets, yet they are less investigated in absence of certain modality in the test phase. To this end, in this letter, we propose to learn a shared feature space across multi-modalities in the training process. By this way, the out-of-sample from any of multi-modalities can be directly projected onto the learned space for a more effective cross-modality representation. More significantly, the shared space is regarded as a latent subspace in our proposed method, which connects the original multi-modal samples with label information to further improve the feature discrimination. Experiments are conducted on the multispectral-Lidar and hyperspectral dataset provided by the 2018 IEEE GRSS Data Fusion Contest to demonstrate the effectiveness and superiority of the proposed method in comparison with several popular baselines.

cs.CV↗

arXiv2020

Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe$_2$

We present a microscopic calculation of the phase diagram of the Ising superconductor NbSe$_{2}$ in presence of both in-plane magnetic field and Rashba spin-orbit coupling (SOC). Repulsive interactions lead to two distinct instabilities, in singlet- and triplet- interaction channels. While we recover the previously predicted nodal topological superconducting state in the absence of Rashba SOC at large magnetic field with six pairs of nodes along $Γ$-$M$ lines, a finite Rashba SOC breaks the symmetry that protects these nodes and therefore generally lifts them, resulting in a topologically trivial phase. There is an exception when the field is applied along one of the three $Γ$-$K$ lines, however. In that case, a single mirror symmetry remains that can protect two pairs of nodes out of the original six, resulting in a \emph{crystalline} topological superconducting phase. Depending on the Cooper pairs' center-of-mass momentum, this superconducting state displays either Bogolyubov Fermi surfaces or point nodes. Moreover, a chiral topological superconducting phase with Chern number of 6 is realized in the regime of large Rashba SOC and dominant triplet interactions, spontaneously breaking time-reversal symmetry.

cond-mat.str-el↗

arXiv2020

Learning Convolutional Sparse Coding on Complex Domain for Interferometric Phase Restoration

Interferometric phase restoration has been investigated for decades and most of the state-of-the-art methods have achieved promising performances for InSAR phase restoration. These methods generally follow the nonlocal filtering processing chain aiming at circumventing the staircase effect and preserving the details of phase variations. In this paper, we propose an alternative approach for InSAR phase restoration, i.e. Complex Convolutional Sparse Coding (ComCSC) and its gradient regularized version. To our best knowledge, this is the first time that we solve the InSAR phase restoration problem in a deconvolutional fashion. The proposed methods can not only suppress interferometric phase noise, but also avoid the staircase effect and preserve the details. Furthermore, they provide an insight of the elementary phase components for the interferometric phases. The experimental results on synthetic and realistic high- and medium-resolution datasets from TerraSAR-X StripMap and Sentinel-1 interferometric wide swath mode, respectively, show that our method outperforms those previous state-of-the-art methods based on nonlocal InSAR filters, particularly the state-of-the-art method: InSAR-BM3D. The source code of this paper will be made publicly available for reproducible research inside the community.

eess.IV↗

arXiv2020

Bayesian Symbolic Regression

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical expressions composed of some basic functions. However, the search space of all possible expressions grows exponentially with the length of the expression, making it infeasible for enumeration. Genetic programming (GP) has been traditionally and commonly used in SR to search for the optimal solution, but it suffers from several limitations, e.g. the difficulty in incorporating prior knowledge; overly-complicated output expression and reduced interpretability etc. To address these issues, we propose a new method to fit SR under a Bayesian framework. Firstly, Bayesian model can naturally incorporate prior knowledge (e.g., preference of basis functions, operators and raw features) to improve the efficiency of fitting SR. Secondly, to improve interpretability of expressions in SR, we aim to capture concise but informative signals. To this end, we assume the expected signal has an additive structure, i.e., a linear combination of several concise expressions, whose complexity is controlled by a well-designed prior distribution. In our setup, each expression is characterized by a symbolic tree, and the proposed SR model could be solved by sampling symbolic trees from the posterior distribution using an efficient Markov chain Monte Carlo (MCMC) algorithm. Finally, compared with GP, the proposed BSR(Bayesian Symbolic Regression) method saves computer memory with no need to keep an updated 'genome pool'. Numerical experiments show that, compared with GP, the solutions of BSR are closer to the ground truth and the expressions are more concise. Meanwhile we find the solution of BSR is robust to hyper-parameter specifications such as the number of trees.

stat.ME↗

arXiv2020

Multipass SAR Interferometry Based on Total Variation Regularized Robust Low Rank Tensor Decomposition

Multipass SAR interferometry (InSAR) techniques based on meter-resolution spaceborne SAR satellites, such as TerraSAR-X or COSMO-Skymed, provide 3D reconstruction and the measurement of ground displacement over large urban areas. Conventional method such as Persistent Scatterer Interferometry (PSI) usually requires a fairly large SAR image stack (usually in the order of tens), in order to achieve reliable estimates of these parameters. Recently, low rank property in multipass InSAR data stack was explored and investigated in our previous work. By exploiting this low rank prior, more accurate estimation of the geophysical parameters can be achieved, which in turn can effectively reduce the number of interferograms required for a reliable estimation. Based on that, this paper proposes a novel tensor decomposition method in complex domain, which jointly exploits low rank and variational prior of the interferometric phase in InSAR data stacks. Specifically, a total variation (TV) regularized robust low rank tensor decomposition method is exploited for recovering outlier-free InSAR stacks. We demonstrate that the filtered InSAR data stacks can greatly improve the accuracy of geophysical parameters estimated from real data. Moreover, this paper demonstrates for the first time in the community that tensor-decomposition-based methods can be beneficial for large-scale urban mapping problems using multipass InSAR. Two TerraSAR-X data stacks with large spatial areas demonstrate the promising performance of the proposed method.

eess.SP↗

arXiv2019

Minorization-Maximization-based Steepest Ascent for Large-scale Survival Analysis with Time-Varying Effects: Application to the National Kidney Transplant Dataset

The time-varying effects model is a flexible and powerful tool for modeling the dynamic changes of covariate effects. However, in survival analysis, its computational burden increases quickly as the number of sample sizes or predictors grows. Traditional methods that perform well for moderate sample sizes and low-dimensional data do not scale to massive data. Analysis of national kidney transplant data with a massive sample size and large number of predictors defy any existing statistical methods and software. In view of these difficulties, we propose a Minorization-Maximization-based steepest ascent procedure for estimating the time-varying effects. Leveraging the block structure formed by the basis expansions, the proposed procedure iteratively updates the optimal block-wise direction along which the approximate increase in the log-partial likelihood is maximized. The resulting estimates ensure the ascent property and serve as refinements of the previous step. The performance of the proposed method is examined by simulations and applications to the analysis of national kidney transplant data.

stat.CO↗