Catalog footprint

What is connected

99works
39topics
4close collaborators

Actions

Connect this record

Log in to claim

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

99 published item(s)

preprint2026arXiv

Revisiting Graph-Tokenizing Large Language Models: A Systematic Evaluation of Graph Token Understanding

The remarkable success of large language models (LLMs) has motivated researchers to adapt them as universal predictors for various graph tasks. As a widely recognized paradigm, Graph-Tokenizing LLMs (GTokenLLMs) compress complex graph data into graph tokens and treat them as prefix tokens for querying LLMs, leading many to believe that LLMs can understand graphs more effectively and efficiently. In this paper, we challenge this belief: \textit{Do GTokenLLMs fully understand graph tokens in the natural-language embedding space?} Motivated by this question, we formalize a unified framework for GTokenLLMs and propose an evaluation pipeline, \textbf{GTEval}, to assess graph-token understanding via instruction transformations at the format and content levels. We conduct extensive experiments on 6 representative GTokenLLMs with GTEval. The primary findings are as follows: (1) Existing GTokenLLMs do not fully understand graph tokens. They exhibit over-sensitivity or over-insensitivity to instruction changes, and rely heavily on text for reasoning; (2) Although graph tokens preserve task-relevant graph information and receive attention across LLM layers, their utilization varies across models and instruction variants; (3) Additional instruction tuning can improve performance on the original and seen instructions, but it does not fully address the challenge of graph-token understanding, calling for further improvement.

preprint2025arXiv

MiMo-Audio: Audio Language Models are Few-Shot Learners

Existing audio language models typically rely on task-specific fine-tuning to accomplish particular audio tasks. In contrast, humans are able to generalize to new audio tasks with only a few examples or simple instructions. GPT-3 has shown that scaling next-token prediction pretraining enables strong generalization capabilities in text, and we believe this paradigm is equally applicable to the audio domain. By scaling MiMo-Audio's pretraining data to over one hundred million of hours, we observe the emergence of few-shot learning capabilities across a diverse set of audio tasks. We develop a systematic evaluation of these capabilities and find that MiMo-Audio-7B-Base achieves SOTA performance on both speech intelligence and audio understanding benchmarks among open-source models. Beyond standard metrics, MiMo-Audio-7B-Base generalizes to tasks absent from its training data, such as voice conversion, style transfer, and speech editing. MiMo-Audio-7B-Base also demonstrates powerful speech continuation capabilities, capable of generating highly realistic talk shows, recitations, livestreaming and debates. At the post-training stage, we curate a diverse instruction-tuning corpus and introduce thinking mechanisms into both audio understanding and generation. MiMo-Audio-7B-Instruct achieves open-source SOTA on audio understanding benchmarks (MMSU, MMAU, MMAR, MMAU-Pro), spoken dialogue benchmarks (Big Bench Audio, MultiChallenge Audio) and instruct-TTS evaluations, approaching or surpassing closed-source models. Model checkpoints and full evaluation suite are available at https://github.com/XiaomiMiMo/MiMo-Audio.

preprint2024arXiv

Noise-Aware and Equitable Urban Air Traffic Management: An Optimization Approach

Urban air mobility (UAM), a transformative concept for the transport of passengers and cargo, faces several integration challenges in complex urban environments. Community acceptance of aircraft noise is among the most noticeable of these challenges when launching or scaling up a UAM system. Properly managing community noise is fundamental to establishing a UAM system that is environmentally and socially sustainable. In this work, we develop a holistic and equitable approach to manage UAM air traffic and its community noise impact in urban environments. The proposed approach is a hybrid approach that considers a mix of different noise mitigation strategies, including limiting the number of operations, cruising at higher altitudes, and ambient noise masking. We tackle the problem through the lens of network system control and formulate a multi-objective optimization model for managing traffic flow in a multi-layer UAM network while concurrently pursuing demand fulfillment, noise control, and energy saving. Further, we use a social welfare function in the optimization model as the basis for the efficiency-fairness trade-off in both demand fulfillment and noise control. We apply the proposed approach to a comprehensive case study in the city of Austin and perform design trade-offs through both visual and quantitative analyses.

preprint2024arXiv

The Fate of Simple Organics on Titan's Surface: A Theoretical Perspective

Atmospheric photochemistry on Titan continuously transforms methane and nitrogen gases into various organic compounds. This study explores the fate of these molecules when they land on Titan's surface. Our analytical exploration reveals that most simple organics found in Titan's atmosphere, including all nitriles, triple-bonded hydrocarbons, and benzene, land as solids. Only a few compounds are in the liquid phase, while only ethylene remains gaseous. For the simple organics that land as solids, we further examine their interactions with Titan's lake liquids. Utilizing principles of buoyancy, we found that flotation can be achieved via porosity-induced (25-60% porosity) or capillary force-induced buoyancy for HCN ices on ethane-rich lakes. Otherwise, these ices would sink and become lakebed sediments. By evaluating the timescale of flotation, our findings suggest that porosity-induced flotation of millimeter-sized and larger sediments is the only plausible mechanism for floating solids to explain the transient "magic islands" phenomena on Titan's lakes.

preprint2024arXiv

Training and Serving System of Foundation Models: A Comprehensive Survey

Foundation models (e.g., ChatGPT, DALL-E, PengCheng Mind, PanGu-$Σ$) have demonstrated extraordinary performance in key technological areas, such as natural language processing and visual recognition, and have become the mainstream trend of artificial general intelligence. This has led more and more major technology giants to dedicate significant human and financial resources to actively develop their foundation model systems, which drives continuous growth of these models' parameters. As a result, the training and serving of these models have posed significant challenges, including substantial computing power, memory consumption, bandwidth demands, etc. Therefore, employing efficient training and serving strategies becomes particularly crucial. Many researchers have actively explored and proposed effective methods. So, a comprehensive survey of them is essential for system developers and researchers. This paper extensively explores the methods employed in training and serving foundation models from various perspectives. It provides a detailed categorization of these state-of-the-art methods, including finer aspects such as network, computing, and storage. Additionally, the paper summarizes the challenges and presents a perspective on the future development direction of foundation model systems. Through comprehensive discussion and analysis, it hopes to provide a solid theoretical basis and practical guidance for future research and applications, promoting continuous innovation and development in foundation model systems.

preprint2023arXiv

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. Herein, we propose a learning framework to extract a peridynamic model as a mesoscale continuum surrogate from MD simulated material fracture datasets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in MD displacement dataset. Inspired by the Weighted Essentially Non-Oscillatory scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from datasets without material damage, to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. Our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our tests show that the proposed data-driven model is robust and generalizable: it is capable in modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

preprint2023arXiv

Uncertainty-Penalized Reinforcement Learning from Human Feedback with Diverse Reward LoRA Ensembles

Reinforcement learning from human feedback (RLHF) emerges as a promising paradigm for aligning large language models (LLMs). However, a notable challenge in RLHF is overoptimization, where beyond a certain threshold, the pursuit of higher rewards leads to a decline in human preferences. In this paper, we observe the weakness of KL regularization which is commonly employed in existing RLHF methods to address overoptimization. To mitigate this limitation, we scrutinize the RLHF objective in the offline dataset and propose uncertainty-penalized RLHF (UP-RLHF), which incorporates uncertainty regularization during RL-finetuning. To enhance the uncertainty quantification abilities for reward models, we first propose a diverse low-rank adaptation (LoRA) ensemble by maximizing the nuclear norm of LoRA matrix concatenations. Then we optimize policy models utilizing penalized rewards, determined by both rewards and uncertainties provided by the diverse reward LoRA ensembles. Our experimental results, based on two real human preference datasets, showcase the effectiveness of diverse reward LoRA ensembles in quantifying reward uncertainty. Additionally, uncertainty regularization in UP-RLHF proves to be pivotal in mitigating overoptimization, thereby contributing to the overall performance.

preprint2022arXiv

A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials

In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics for quantities of interest, such as the fracture toughness. To depict the material responses and naturally describe the nucleation and growth of fractures, we consider the peridynamics model. In particular, a stochastic state-based peridynamic model is developed, where the micromechanical parameters are modeled by a finite-dimensional random vector, or a combination of random variables truncating the Karhunen-Loève decomposition or the principle component analysis (PCA). To solve this stochastic peridynamic problem, probabilistic collocation method (PCM) is employed to sample the random field representing the micromechanical parameters. For each sample, the deterministic peridynamic problem is discretized with an optimization-based meshfree quadrature rule. We present rigorous analysis for the proposed scheme and demonstrate its convergence for a number of benchmark problems, showing that it sustains the asymptotic compatibility spatially and achieves an algebraic or sub-exponential convergence rate in the random space as the number of collocation points grows. Finally, to validate the applicability of this approach on real-world fracture problems, we consider the problem of crystallization toughening in glass-ceramic materials, in which the material at the microstructural scale contains both amorphous glass and crystalline phases. The proposed stochastic peridynamic solver is employed to capture the crack initiation and growth for glass-ceramics with different crystal volume fractions, and the averaged fracture toughness are calculated. The numerical estimates of fracture toughness show good consistency with experimental measurements.

preprint2022arXiv

A novel locking-free virtual element method for linear elasticity problems

This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one $\widetilde{K}$ with additional vertices consisting of interior points on edges of $K$, so that the discrete admissible space is taken as the $V_1$ type virtual element space related to the partition $\{\widetilde{K}\}$ instead of $\{K\}$. The method is shown to be uniformly convergent with the optimal rates both in $H^1$ and $L^2$ norms with respect to the Lamé constant $λ$. Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.

preprint2022arXiv

A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements

We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledges on the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on the phenomenological Fung-type model. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling.

preprint2022arXiv

A sparse grid discrete ordinate discontinuous Galerkin method for the radiative transfer equation

The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this bottleneck, we first use the discrete ordinate technique to discretize the scattering term, an integral with respect to the angular variables, resulting in a semi-discrete hyperbolic system. Then, we make the spatial discretization by means of the discontinuous Galerkin (DG) method combined with the sparse grid method. The final linear system is solved by the block Gauss-Seidal iteration method. The computational complexity and error analysis are developed in detail, which show the new method is more efficient than the original discrete ordinate DG method. A series of numerical results are performed to validate the convergence behavior and effectiveness of the proposed method.

preprint2022arXiv

A Survey on Programmatic Weak Supervision

Labeling training data has become one of the major roadblocks to using machine learning. Among various weak supervision paradigms, programmatic weak supervision (PWS) has achieved remarkable success in easing the manual labeling bottleneck by programmatically synthesizing training labels from multiple potentially noisy supervision sources. This paper presents a comprehensive survey of recent advances in PWS. In particular, we give a brief introduction of the PWS learning paradigm, and review representative approaches for each component within PWS's learning workflow. In addition, we discuss complementary learning paradigms for tackling limited labeled data scenarios and how these related approaches can be used in conjunction with PWS. Finally, we identify several critical challenges that remain under-explored in the area to hopefully inspire future research directions in the field.

preprint2022arXiv

Adaptive Constraint Satisfaction for Markov Decision Process Congestion Games: Application to Transportation Networks

Under the Markov decision process (MDP) congestion game framework, we study the problem of enforcing population distribution constraints on a population of players with stochastic dynamics and coupled congestion costs. Existing research demonstrates that the constraints on the players' population distribution can be satisfied by enforcing tolls. However, computing the minimum toll value for constraint satisfaction requires accurate modeling of the player's congestion costs. Motivated by settings where an accurate congestion cost model is unavailable (e.g. transportation networks), we consider an MDP congestion game with unknown congestion costs. We assume that a constraint-enforcing authority can repeatedly enforce tolls on a population of players who converges to an $ε$-optimal population distribution for any given toll. We then construct a myopic update algorithm to compute the minimum toll value while ensuring that the constraints are satisfied on average. We analyze how the players' sub-optimal responses to tolls impact the rates of convergence towards the minimum toll value and constraint satisfaction. Finally, we construct a congestion game model for Uber drivers in Manhattan, New York City (NYC) using data from the Taxi and Limousine Commission (TLC) to illustrate how to efficiently reduce congestion while minimizing the impact on driver earnings.

preprint2022arXiv

Bridging Pre-trained Models and Downstream Tasks for Source Code Understanding

With the great success of pre-trained models, the pretrain-then-finetune paradigm has been widely adopted on downstream tasks for source code understanding. However, compared to costly training a large-scale model from scratch, how to effectively adapt pre-trained models to a new task has not been fully explored. In this paper, we propose an approach to bridge pre-trained models and code-related tasks. We exploit semantic-preserving transformation to enrich downstream data diversity, and help pre-trained models learn semantic features invariant to these semantically equivalent transformations. Further, we introduce curriculum learning to organize the transformed data in an easy-to-hard manner to fine-tune existing pre-trained models. We apply our approach to a range of pre-trained models, and they significantly outperform the state-of-the-art models on tasks for source code understanding, such as algorithm classification, code clone detection, and code search. Our experiments even show that without heavy pre-training on code data, natural language pre-trained model RoBERTa fine-tuned with our lightweight approach could outperform or rival existing code pre-trained models fine-tuned on the above tasks, such as CodeBERT and GraphCodeBERT. This finding suggests that there is still much room for improvement in code pre-trained models.

preprint2022arXiv

Extrapolated Proportional-Integral Projected Gradient Method for Conic Optimization

Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named \emph{extrapolated proportional-integral projected gradient method (xPIPG)}, that automatically detects infeasibility. The iterates of xPIPG either asymptotically satisfy a set of primal-dual optimality conditions, or generate a proof of primal or dual infeasibility. We demonstrate the application of xPIPG using benchmark problems in model predictive control. xPIPG outperforms many state-of-the-art conic optimization solvers, especially when solving large-scale problems.

preprint2022arXiv

Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling

Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are present, these classical models may become inaccurate. In this work, we propose to use data-driven modeling, which directly utilizes high-fidelity simulation and/or experimental measurements to predict a material's response without using conventional constitutive models. Specifically, the material response is modeled by learning the implicit mappings between loading conditions and the resultant displacement and/or damage fields, with the neural network serving as a surrogate for a solution operator. To model the complex responses due to material heterogeneity and defects, we develop a novel deep neural operator architecture, which we coin as the Implicit Fourier Neural Operator (IFNO). In the IFNO, the increment between layers is modeled as an integral operator to capture the long-range dependencies in the feature space. As the network gets deeper, the limit of IFNO becomes a fixed point equation that yields an implicit neural operator and naturally mimics the displacement/damage fields solving procedure in material modeling problems. We demonstrate the performance of our proposed method for a number of examples, including hyperelastic, anisotropic and brittle materials. As an application, we further employ the proposed approach to learn the material models directly from digital image correlation (DIC) tracking measurements, and show that the learned solution operators substantially outperform the conventional constitutive models in predicting displacement fields.

preprint2022arXiv

MetaNOR: A Meta-Learnt Nonlocal Operator Regression Approach for Metamaterial Modeling

We propose MetaNOR, a meta-learnt approach for transfer-learning operators based on the nonlocal operator regression. The overall goal is to efficiently provide surrogate models for new and unknown material-learning tasks with different microstructures. The algorithm consists of two phases: (1) learning a common nonlocal kernel representation from existing tasks; (2) transferring the learned knowledge and rapidly learning surrogate operators for unseen tasks with a different material, where only a few test samples are required. We apply MetaNOR to model the wave propagation within 1D metamaterials, showing substantial improvements on the sampling efficiency for new materials.

preprint2022arXiv

Modality-Balanced Embedding for Video Retrieval

Video search has become the main routine for users to discover videos relevant to a text query on large short-video sharing platforms. During training a query-video bi-encoder model using online search logs, we identify a modality bias phenomenon that the video encoder almost entirely relies on text matching, neglecting other modalities of the videos such as vision, audio. This modality imbalanceresults from a) modality gap: the relevance between a query and a video text is much easier to learn as the query is also a piece of text, with the same modality as the video text; b) data bias: most training samples can be solved solely by text matching. Here we share our practices to improve the first retrieval stage including our solution for the modality imbalance issue. We propose MBVR (short for Modality Balanced Video Retrieval) with two key components: manually generated modality-shuffled (MS) samples and a dynamic margin (DM) based on visual relevance. They can encourage the video encoder to pay balanced attentions to each modality. Through extensive experiments on a real world dataset, we show empirically that our method is both effective and efficient in solving modality bias problem. We have also deployed our MBVR in a large video platform and observed statistically significant boost over a highly optimized baseline in an A/B test and manual GSB evaluations.

preprint2022arXiv

mVEM: A MATLAB Software Package for the Virtual Element Methods

This paper summarizes the development of mVEM, a MATLAB software package containing efficient and easy-following codes for various virtual element methods (VEMs) published in the literature. We explain in detail the numerical implementation of the mixed VEMs for the Darcy problem and the three-dimensional linear VEMs for the Poisson equation. For other model problems, we present the construction of the discrete methods and only provide the implementation of the elliptic projection matrices. Some mesh related functions are also given in the package, including the mesh generation and refinement in two or three dimensions. mVEM is free and open source software.

preprint2022arXiv

Nebula-I: A General Framework for Collaboratively Training Deep Learning Models on Low-Bandwidth Cloud Clusters

The ever-growing model size and scale of compute have attracted increasing interests in training deep learning models over multiple nodes. However, when it comes to training on cloud clusters, especially across remote clusters, huge challenges are faced. In this work, we introduce a general framework, Nebula-I, for collaboratively training deep learning models over remote heterogeneous clusters, the connections between which are low-bandwidth wide area networks (WANs). We took natural language processing (NLP) as an example to show how Nebula-I works in different training phases that include: a) pre-training a multilingual language model using two remote clusters; and b) fine-tuning a machine translation model using knowledge distilled from pre-trained models, which run through the most popular paradigm of recent deep learning. To balance the accuracy and communication efficiency, in Nebula-I, parameter-efficient training strategies, hybrid parallel computing methods and adaptive communication acceleration techniques are jointly applied. Meanwhile, security strategies are employed to guarantee the safety, reliability and privacy in intra-cluster computation and inter-cluster communication. Nebula-I is implemented with the PaddlePaddle deep learning framework, which can support collaborative training over heterogeneous hardware, e.g. GPU and NPU. Experiments demonstrate that the proposed framework could substantially maximize the training efficiency while preserving satisfactory NLP performance. By using Nebula-I, users can run large-scale training tasks over cloud clusters with minimum developments, and the utility of existed large pre-trained models could be further promoted. We also introduced new state-of-the-art results on cross-lingual natural language inference tasks, which are generated based upon a novel learning framework and Nebula-I.

preprint2022arXiv

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN's optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

preprint2022arXiv

Nonparametric learning of kernels in nonlocal operators

Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant. In this work, we provide a rigorous identifiability analysis and convergence study for the learning of kernels in nonlocal operators. It is found that the kernel learning is an ill-posed or even ill-defined inverse problem, leading to divergent estimators in the presence of modeling errors or measurement noises. To resolve this issue, we propose a nonparametric regression algorithm with a novel data adaptive RKHS Tikhonov regularization method based on the function space of identifiability. The method yields a noisy-robust convergent estimator of the kernel as the data resolution refines, on both synthetic and real-world datasets. In particular, the method successfully learns a homogenized model for the stress wave propagation in a heterogeneous solid, revealing the unknown governing laws from real-world data at microscale. Our regularization method outperforms baseline methods in robustness, generalizability and accuracy.

preprint2022arXiv

On The Low Speed Limits of Lorentz's Transformation

This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the conventional language. We show that even under low speed limits, the relativistic effects should not be neglected to get a self-consistent theory of the electromagnetic fields, unless the intrinsic dynamics of these fields has been omitted completely. The quasi-static limits, where the relativistic effects can be partly neglected are also reviewed, to clarify some common misunderstandings and imprecise use of the theory in presence of moving media and other related situations. The discussion presented in this paper provide a clear view of why classical electromagnetic theory is relativistic in its essence.

preprint2022arXiv

OpenMedIA: Open-Source Medical Image Analysis Toolbox and Benchmark under Heterogeneous AI Computing Platforms

In this paper, we present OpenMedIA, an open-source toolbox library containing a rich set of deep learning methods for medical image analysis under heterogeneous Artificial Intelligence (AI) computing platforms. Various medical image analysis methods, including 2D/3D medical image classification, segmentation, localisation, and detection, have been included in the toolbox with PyTorch and/or MindSpore implementations under heterogeneous NVIDIA and Huawei Ascend computing systems. To our best knowledge, OpenMedIA is the first open-source algorithm library providing compared PyTorch and MindSpore implementations and results on several benchmark datasets. The source codes and models are available at https://git.openi.org.cn/OpenMedIA.

preprint2022arXiv

Overpotential decomposition enabled decoupling of complex kinetic processes in battery electrodes

Identifying overpotential components of electrochemical systems enables quantitative analysis of polarization contributions of kinetic processes under practical operating conditions. However, the inherently coupled kinetic processes lead to an enormous challenge in measuring individual overpotentials, particularly in composite electrodes of lithium-ion batteries. Herein, the full decomposition of electrode overpotential is realized by the collaboration of single-layer structured particle electrode (SLPE) constructions and time-resolved potential measurements, explicitly revealing the evolution of kinetic processes. Perfect prediction of the discharging profiles is achieved via potential measurements on SLPEs, even in extreme polarization conditions. By decoupling overpotentials in different electrode/cell structures and material systems, the dominant limiting processes of battery rate performance are uncovered, based on which the optimization of electrochemical kinetics can be conducted. Our study not only shades light on decoupling complex kinetics in electrochemical systems, but also provides vitally significant guidance for the rational design of high-performance batteries.

preprint2022arXiv

Physics-Informed Deep Neural Operator Networks

Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black box, e.g., a system-of-systems. The first neural operator was the Deep Operator Network (DeepONet), proposed in 2019 based on rigorous approximation theory. Since then, a few other less general operators have been published, e.g., based on graph neural networks or Fourier transforms. For black box systems, training of neural operators is data-driven only but if the governing equations are known they can be incorporated into the loss function during training to develop physics-informed neural operators. Neural operators can be used as surrogates in design problems, uncertainty quantification, autonomous systems, and almost in any application requiring real-time inference. Moreover, independently pre-trained DeepONets can be used as components of a complex multi-physics system by coupling them together with relatively light training. Here, we present a review of DeepONet, the Fourier neural operator, and the graph neural operator, as well as appropriate extensions with feature expansions, and highlight their usefulness in diverse applications in computational mechanics, including porous media, fluid mechanics, and solid mechanics.

preprint2022arXiv

PolyU-BPCoMa: A Dataset and Benchmark Towards Mobile Colorized Mapping Using a Backpack Multisensorial System

Constructing colorized point clouds from mobile laser scanning and images is a fundamental work in surveying and mapping. It is also an essential prerequisite for building digital twins for smart cities. However, existing public datasets are either in relatively small scales or lack accurate geometrical and color ground truth. This paper documents a multisensorial dataset named PolyU-BPCoMA which is distinctively positioned towards mobile colorized mapping. The dataset incorporates resources of 3D LiDAR, spherical imaging, GNSS and IMU on a backpack platform. Color checker boards are pasted in each surveyed area as targets and ground truth data are collected by an advanced terrestrial laser scanner (TLS). 3D geometrical and color information can be recovered in the colorized point clouds produced by the backpack system and the TLS, respectively. Accordingly, we provide an opportunity to benchmark the mapping and colorization accuracy simultaneously for a mobile multisensorial system. The dataset is approximately 800 GB in size covering both indoor and outdoor environments. The dataset and development kits are available at https://github.com/chenpengxin/PolyU-BPCoMa.git.

preprint2022arXiv

PRBoost: Prompt-Based Rule Discovery and Boosting for Interactive Weakly-Supervised Learning

Weakly-supervised learning (WSL) has shown promising results in addressing label scarcity on many NLP tasks, but manually designing a comprehensive, high-quality labeling rule set is tedious and difficult. We study interactive weakly-supervised learning -- the problem of iteratively and automatically discovering novel labeling rules from data to improve the WSL model. Our proposed model, named PRBoost, achieves this goal via iterative prompt-based rule discovery and model boosting. It uses boosting to identify large-error instances and then discovers candidate rules from them by prompting pre-trained LMs with rule templates. The candidate rules are judged by human experts, and the accepted rules are used to generate complementary weak labels and strengthen the current model. Experiments on four tasks show PRBoost outperforms state-of-the-art WSL baselines up to 7.1% and bridges the gaps with fully supervised models. Our Implementation is available at \url{https://github.com/rz-zhang/PRBoost}.

preprint2022arXiv

Quenched randomness, thermal fluctuations and reentrant superconductivity: application to UTe$_2$

Reentrant superconductivity has been observed in the candidate spin-triplet superconductor UTe$_2$ as a function of the magnetic field applied along the hard axis. Resistivity measurements have shown, a broadened superconducting transition appears near the minimal $T_c$, highlighting the importance of superconducting fluctuations in this regime. We present a phenomenological study assuming a field-driven first-order transition between two superconducting states. We show that with quenched randomness, inhomogeneity-enhanced superconducting fluctuations near the transition could naturally account for both the reentrant superconductivity as well as the broadened superconducting transition.

preprint2022arXiv

Real-Time Quadrotor Trajectory Optimization with Time-Triggered Corridor Constraints

One of the keys to flying quadrotors is to optimize their trajectories within the set of collision-free corridors. These corridors impose nonconvex constraints on the trajectories, making real-time trajectory optimization challenging. We introduce a novel numerical method that approximates the nonconvex corridor constraints with time-triggered convex corridor constraints. This method combines bisection search and repeated infeasibility detection. We further develop a customized C++ implementation of the proposed method, based on a first-order conic optimization method that detects infeasibility and exploits problem structure. We demonstrate the efficiency and effectiveness of the proposed method using numerical simulation on randomly generated problem instances as well as indoor flight experiments with hoop obstacles. Compared with mixed integer programming, the proposed method is about 50--200 times faster.

preprint2022arXiv

Self-Training with Differentiable Teacher

Self-training achieves enormous success in various semi-supervised and weakly-supervised learning tasks. The method can be interpreted as a teacher-student framework, where the teacher generates pseudo-labels, and the student makes predictions. The two models are updated alternatingly. However, such a straightforward alternating update rule leads to training instability. This is because a small change in the teacher may result in a significant change in the student. To address this issue, we propose DRIFT, short for differentiable self-training, that treats teacher-student as a Stackelberg game. In this game, a leader is always in a more advantageous position than a follower. In self-training, the student contributes to the prediction performance, and the teacher controls the training process by generating pseudo-labels. Therefore, we treat the student as the leader and the teacher as the follower. The leader procures its advantage by acknowledging the follower's strategy, which involves differentiable pseudo-labels and differentiable sample weights. Consequently, the leader-follower interaction can be effectively captured via Stackelberg gradient, obtained by differentiating the follower's strategy. Experimental results on semi- and weakly-supervised classification and named entity recognition tasks show that our model outperforms existing approaches by large margins.

preprint2022arXiv

Smart Tracking Tray System for A Smart and Sustainable Wet Lab Community

The laboratories and research institutes are the major places for cutting-edge scientific exploration. Hundreds of millions of research papers were formed from front-line labs. Behind this glorious achievement were unsustainable facts. More and more human investment is required in innovative experimental design and analysis of results. However, the laboratory operating environment has not been subversively transformed for centuries. This abstract proposed a smart tracking system, consisting of IoT and Data Visualization technologies, to track the chemicals in an automatic and timely approach. Positive feedback has been collected from pilot tests in several labs. The system benefits various lab users in their daily work and improves their working efficiency. In the long run, it will play an essential role in promoting the efficient use of lab resources and achieving the goal of sustainable labs.

preprint2022arXiv

The Development and Prospect of Code Clone

The application of code clone technology accelerates code search, improves code reuse efficiency, and assists in software quality assessment and code vulnerability detection. However, the application of code clones also introduces software quality issues and increases the cost of software maintenance. As an important research field in software engineering, code clone has been extensively explored and studied by researchers, and related studies on various sub-research fields have emerged, including code clone detection, code clone evolution, code clone analysis, etc. However, there lacks a comprehensive exploration of the entire field of code clone, as well as an analysis of the trend of each sub-research field. This paper collects related work of code clones in the past ten years. In summary, the contributions of this paper mainly include: (1) summarize and classify the sub-research fields of code clone, and explore the relative popularity and relation of these sub-research fields; (2) analyze the overall research trend of code clone and each sub-research field; (3) compare and analyze the difference between academy and industry regarding code clone research; (4) construct a network of researchers, and excavate the major contributors in code clone research field; (5) The list of popular conferences and journals was statistically analyzed. The popular research directions in the future include clone visualization, clone management, etc. For the clone detection technique, researchers can optimize the scalability and execution efficiency of the method, targeting particular clone detection tasks and contextual environments, or apply the technology to other related research fields continuously.

preprint2022arXiv

Theory of superconductivity in doped quantum paraelectrics

Recent experiments on Nb-doped SrTiO$_3$ have shown that the superconducting energy gap to the transition temperature ratio maintains the Bardeen-Cooper-Schrieffer (BCS) value throughout its superconducting dome. Motivated by these and related studies, we show that the Cooper pairing mediated by a single soft transverse-optical phonon is the most natural mechanism for such a superconducting dome given experimental constraints, and present the microscopic theory for this pairing mechanism. Furthermore, we show that this mechanism is consistent with the $T^2$ resistivity in the normal state. Lastly, we discuss what physical insights SrTiO$_3$ provides for superconductivity in other quantum paraelectrics such as KTaO$_3$.

preprint2022arXiv

Universal topological quantum computation with strongly correlated Majorana edge modes

Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In Ref. \cite{hukane}, it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibobacci anyon $τ$ and a thermal operator anyon $\varepsilon$ in the tricritical Ising model. The deconfinement of $τ$ and $\varepsilon$ via the interaction between the fermion modes yields the anyon {collisions} and gives the braiding of either $τ$ or $\varepsilon$. With these braidings, the complete members {of} a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for 1-qubit as well as controlled-not gate for 2-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit {where the controlled-not gate turns out { to be} a probabilistic gate} and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor's integer factorization algorithm.

preprint2022arXiv

Vertiport Selection in Hybrid Air-Ground Transportation Networks via Mathematical Programs with Equilibrium Constraints

Urban air mobility is a concept that promotes aerial modes of transport in urban areas. In these areas, the location and capacity of the vertiports--where the travelers embark and disembark the aircraft--not only affect the flight delays of the aircraft, but can also aggravate the congestion of ground vehicles by creating extra ground travel demands. We introduce a mathematical model for selecting the location and capacity of the vertiports that minimizes the traffic congestion in hybrid air-ground transportation networks. Our model is based on a mathematical program with bilinear equilibrium constraints. Furthermore, we show how to compute a global optimal solution of this mathematical program by solving a mixed integer linear program. We demonstrate our results via the Anaheim transportation network model, which contains more than 400 nodes and 900 links.

preprint2021arXiv

A data-driven peridynamic continuum model for upscaling molecular dynamics

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials' behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

preprint2021arXiv

A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems

We develop a lowest-order nonconforming virtual element method for planar linear elasticity, which can be viewed as an extension of the idea in Falk (1991) to the virtual element method (VEM), with the family of polygonal meshes satisfying a very general geometric assumption. The method is shown to be uniformly convergent for the nearly incompressible case with optimal rates of convergence. The crucial step is to establish the discrete Korn's inequality, yielding the coercivity of the discrete bilinear form. We also provide a unified locking-free scheme both for the conforming and nonconforming VEMs in the lowest order case. Numerical results validate the feasibility and effectiveness of the proposed numerical algorithms.

preprint2021arXiv

A physics-informed variational DeepONet for predicting the crack path in brittle materials

Failure trajectories, identifying the probable failure zones, and damage statistics are some of the key quantities of relevance in brittle fracture applications. High-fidelity numerical solvers that reliably estimate these relevant quantities exist but they are computationally demanding requiring a high resolution of the crack. Moreover, independent intensive simulations need to be carried out even for a small change in domain parameters and/or material properties. Therefore, fast and generalizable surrogate models are needed to alleviate the computational burden but the discontinuous nature of fracture mechanics presents a major challenge to developing such models. We propose a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis. V-DeepONet is trained to map the initial configuration of the defect to the relevant fields of interests (e.g., damage and displacement fields). Once the network is trained, the entire global solution can be rapidly obtained for any initial crack configuration and loading steps on that domain. While the original DeepONet is solely data-driven, we take a different path to train the V-DeepONet by imposing the governing equations in variational form and we also use some labelled data. We demonstrate the effectiveness of V-DeepOnet through two benchmarks of brittle fracture, and we verify its accuracy using results from high-fidelity solvers. Encoding the physical laws and also some data to train the network renders the surrogate model capable of accurately performing both interpolation and extrapolation tasks, considering that fracture modeling is very sensitive to fluctuations. The proposed hybrid training of V-DeepONet is superior to state-of-the-art methods and can be applied to a wide array of dynamical systems with complex responses.

preprint2021arXiv

An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems

In this paper we present an asymptotically compatible meshfree method for solving nonlocal equations with random coefficients, describing diffusion in heterogeneous media. In particular, the random diffusivity coefficient is described by a finite-dimensional random variable or a truncated combination of random variables with the Karhunen-Loève decomposition, then a probabilistic collocation method (PCM) with sparse grids is employed to sample the stochastic process. On each sample, the deterministic nonlocal diffusion problem is discretized with an optimization-based meshfree quadrature rule. We present rigorous analysis for the proposed scheme and demonstrate convergence for a number of benchmark problems, showing that it sustains the asymptotic compatibility spatially and achieves an algebraic or sub-exponential convergence rate in the random coefficients space as the number of collocation points grows. Finally, to validate the applicability of this approach we consider a randomly heterogeneous nonlocal problem with a given spatial correlation structure, demonstrating that the proposed PCM approach achieves substantial speed-up compared to conventional Monte Carlo simulations.

preprint2021arXiv

Majorana fermion arcs and the local density of states of UTe$_2$

$\text{UTe}_2$ is a leading candidate for chiral p-wave superconductivity, and for hosting exotic Majorana fermion quasiparticles. Motivated by recent STM experiments in this system, we study particle-hole symmetry breaking in chiral p-wave superconductors. We compute the local density of states from Majorana fermion surface states in the presence of Rashba surface spin-orbit coupling, which is expected to be sizeable in heavy-fermion materials like UTe$_2$. We show that time-reversal and surface reflection symmetry breaking lead to a natural pairing tendency towards a triplet pair density wave state, which naturally can account for broken particle-hole symmetry.

preprint2020arXiv

$T_c$ and Pauli limited critical field of $\text{Sr}_2\text{Ru}\text{O}_4$: uniaxial strain dependence

Variations of critical temperature $T_c$ and in-plane critical field $H_{c2}$ of $\text{Sr}_2\text{Ru}\text{O}_4$ under uniaxial stress have recently been reported. We compare the strain dependence of $T_c$ and $H_{c2}$ in various pairing channels ($d$-wave, extended s-wave and $p$-wave) with the experimental observations, by studying a three-band tight-binding model that includes effects of spin-orbit and Zeeman couplings and a separable pairing interaction. Our study helps narrow down the possibility of pairing channels. The importance of the multi-band nature of $\text{Sr}_2\text{Ru}\text{O}_4$ is also highlighted.

preprint2020arXiv

BOND: BERT-Assisted Open-Domain Named Entity Recognition with Distant Supervision

We study the open-domain named entity recognition (NER) problem under distant supervision. The distant supervision, though does not require large amounts of manual annotations, yields highly incomplete and noisy distant labels via external knowledge bases. To address this challenge, we propose a new computational framework -- BOND, which leverages the power of pre-trained language models (e.g., BERT and RoBERTa) to improve the prediction performance of NER models. Specifically, we propose a two-stage training algorithm: In the first stage, we adapt the pre-trained language model to the NER tasks using the distant labels, which can significantly improve the recall and precision; In the second stage, we drop the distant labels, and propose a self-training approach to further improve the model performance. Thorough experiments on 5 benchmark datasets demonstrate the superiority of BOND over existing distantly supervised NER methods. The code and distantly labeled data have been released in https://github.com/cliang1453/BOND.

preprint2020arXiv

Phases of frustrated quantum antiferromagnets on the square and triangular lattices

We analyze the zero temperature phase diagrams of the spin S quantum antiferromagnet on square and triangular lattices with competing nearest and next-nearest exchange interactions as well as biquadratic couplings. We approach the problem from the large S limit. Our primary focus is on determining the extent to which the existence and character of any quantum disordered phases can be inferred from this approach.

preprint2020arXiv

Quantum chaos associated with emergent ergosurface in transition layer between type-I and type-II Weyl semimetals

We present emergent ergosurfaces (ES) in a transition layer between type-I and type-II Weyl semimetals (WSMs). The Hawking temperature defined by the surface gravity at the acoustic event horizon which coincides with the ES when the tangent velocity $v_{\parallel}$ is small is in a measurable interval. On the type-II WSM side, i.e., inside the {ES when $v_{\parallel}$ is large}, the motion of the quasiparticles may be chaotic {after} a critical surface as they are governed by an effective inverted oscillator potential induced by the mismatch between the type-I and type-II Weyl nodes. In a relevant lattice model, we calculate out of time ordered correlators (OTOCs). We find that the OTOCs are fast scrambling with a quantum Lyapunov exponent in high temperature and the scrambling is saturated after the Ehrenfest time. This confirms the quantum chaotic behavior.

preprint2020arXiv

RC Circuits based Distributed Conditional Gradient Method

We consider distributed optimization on undirected connected graphs. We propose a novel distributed conditional gradient method with (O(1/\sqrt{k})) convergence. Compared with existing methods, each iteration of our method uses both communication and linear minimization step only once rather than multiple times. We further extend our results to cases with composite local constraints. We demonstrate our results via examples on distributed matrix completion problem.

preprint2020arXiv

RLC Circuits based Distributed Mirror Descent Method

We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with mirror-prox method, our algorithm achieves the same \(\mathcal{O}(1/k)\) iteration complexity with only half the computation cost per iteration. We further extend our results to cases where a) gradients are corrupted by stochastic noise, and b) objective function is composed of both smooth and non-smooth terms. We demonstrate our theoretical results via numerical experiments.

preprint2020arXiv

SPAN: A Stochastic Projected Approximate Newton Method

Second-order optimization methods have desirable convergence properties. However, the exact Newton method requires expensive computation for the Hessian and its inverse. In this paper, we propose SPAN, a novel approximate and fast Newton method. SPAN computes the inverse of the Hessian matrix via low-rank approximation and stochastic Hessian-vector products. Our experiments on multiple benchmark datasets demonstrate that SPAN outperforms existing first-order and second-order optimization methods in terms of the convergence wall-clock time. Furthermore, we provide a theoretical analysis of the per-iteration complexity, the approximation error, and the convergence rate. Both the theoretical analysis and experimental results show that our proposed method achieves a better trade-off between the convergence rate and the per-iteration efficiency.

preprint2020arXiv

STEAM: Self-Supervised Taxonomy Expansion with Mini-Paths

Taxonomies are important knowledge ontologies that underpin numerous applications on a daily basis, but many taxonomies used in practice suffer from the low coverage issue. We study the taxonomy expansion problem, which aims to expand existing taxonomies with new concept terms. We propose a self-supervised taxonomy expansion model named STEAM, which leverages natural supervision in the existing taxonomy for expansion. To generate natural self-supervision signals, STEAM samples mini-paths from the existing taxonomy, and formulates a node attachment prediction task between anchor mini-paths and query terms. To solve the node attachment task, it learns feature representations for query-anchor pairs from multiple views and performs multi-view co-training for prediction. Extensive experiments show that STEAM outperforms state-of-the-art methods for taxonomy expansion by 11.6\% in accuracy and 7.0\% in mean reciprocal rank on three public benchmarks. The implementation of STEAM can be found at \url{https://github.com/yueyu1030/STEAM}.

preprint2020arXiv

Three Jahn-Teller states of matter in the spin-crossover system Mn(taa)

Three high-spin phases recently discovered in the spin-crossover system Mn(taa) are identified through analysis by a combination of first-principles calculations and Monte Carlo simulation as a low-temperature Jahn-Teller ordered (solid) phase, an intermediate-temperature dynamically correlated (liquid) phase, and an uncorrelated (gas) phase. In particular, the Jahn-Teller liquid phase arises from competition between mixing with low-spin impurities, which drive the disorder, and inter-molecular strain interactions. The latter are a key factor in both the spin-crossover phase transition and the magnetoelectric coupling. Jahn-Teller liquids may exist in other spin-crossover materials and materials that have multiple equivalent Jahn-Teller axes.

preprint2020arXiv

Topological superconductor from superconducting topological surface states and fault-tolerant quantum computing

The chiral $p$-wave superconductor/superfluid in two dimensions (2D) is the simplest and most robust system for topological quantum computation . Candidates for such topological superconductors/superfluids in nature are very rare. A widely believed chiral $p$-wave superfluid is the Moore-Read state in the $ν=\frac{5}2$ fractional quantum Hall effect, although experimental evidence are not yet conclusive. Experimental realizations of chiral $p$-wave superconductors using quantum anomalous Hall insulator-superconductor hybrid structures have been controversial. Here we report a new mechanism for realizing 2D chiral $p$-wave superconductors on the surface of 3D $s$-wave superconductors that have a topological band structure and support superconducting topological surface states (SC-TSS), such as the iron-based superconductor Fe(Te,Se). We find that tunneling and pairing between the SC-TSS on the top and bottom surfaces in a thin film or between two opposing surfaces of two such superconductors can produce an emergent 2D time-reversal symmetry breaking chiral topological superconductor. The topologically protected anyonic vortices with Majorana zero modes as well as the chiral Majorana fermion edge modes can be used as a platform for more advantageous non-abelian braiding operations. We propose a novel device for the CNOT gate with six chiral Majorana fermion edge modes, which paves the way for fault-tolerant universal quantum computing.

preprint2020arXiv

Urban Anomaly Analytics: Description, Detection, and Prediction

Urban anomalies may result in loss of life or property if not handled properly. Automatically alerting anomalies in their early stage or even predicting anomalies before happening are of great value for populations. Recently, data-driven urban anomaly analysis frameworks have been forming, which utilize urban big data and machine learning algorithms to detect and predict urban anomalies automatically. In this survey, we make a comprehensive review of the state-of-the-art research on urban anomaly analytics. We first give an overview of four main types of urban anomalies, traffic anomaly, unexpected crowds, environment anomaly, and individual anomaly. Next, we summarize various types of urban datasets obtained from diverse devices, i.e., trajectory, trip records, CDRs, urban sensors, event records, environment data, social media and surveillance cameras. Subsequently, a comprehensive survey of issues on detecting and predicting techniques for urban anomalies is presented. Finally, research challenges and open problems as discussed.

preprint2019arXiv

An Asymptotically Compatible Formulation for Local-to-Nonlocal Coupling Problems without Overlapping Regions

In this paper we design and analyze an explicit partitioned procedure for a 2D dynamic local-to-nonlocal (LtN) coupling problem, based on a new nonlocal Robin-type transmission condition. The nonlocal subproblem is modeled by the nonlocal heat equation with a finite horizon parameter $δ$ characterizing the range of nonlocal interactions, and the local subproblem is described by the classical heat equation. We consider a heterogeneous system where the local and nonlocal subproblems present different physical properties, and employ no overlapping region between the two subdomains. We first propose a new generalization of classical local Neumann-type condition by converting the local flux to a correction term in the nonlocal model, and show that the proposed Neumann-type boundary formulation recovers the local case as $O(δ^2)$ in the $L^{\infty}$ norm. We then extend the nonlocal Neumann-type boundary condition to a Robin-type boundary condition, and develop a local-to-nonlocal coupling formulation with Robin-Dirichlet transmission conditions. To stabilize the explicit coupling procedure and to achieve asymptotic compatibility, the choice of the coefficient in the Robin condition is obtained via amplification factor analysis for the discretized system with coarse grids. Employing a high-order meshfree discretization method in the nonlocal solver and a linear finite element method in the local solver, the selection of optimal Robin coefficients are verified with numerical experiments on heterogeneous and complicated domains. With the developed optimal coupling strategy, we numerically demonstrate the coupling framework's asymptotic convergence to the local limit with an $O(δ)=O(h)$ rate, when there is a fixed ratio between the horizon size $δ$ and the spatial discretization size $h$.

preprint2018arXiv

Aurora: Providing Trusted System Services for Enclaves On an Untrusted System

Intel SGX provisions shielded executions for security-sensitive computation, but lacks support for trusted system services (TSS), such as clock, network and filesystem. This makes \textit{enclaves} vulnerable to Iago attacks~\cite{DBLP:conf/asplos/CheckowayS13} in the face of a powerful malicious system. To mitigate this problem, we present Aurora, a novel architecture that provides TSSes via a secure channel between enclaves and devices on top of an untrusted system, and implement two types of TSSes, i.e. clock and end-to-end network. We evaluate our solution by porting SQLite and OpenSSL into Aurora, experimental results show that SQLite benefits from a \textit{microsecond} accuracy trusted clock and OpenSSL gains end-to-end secure network with about 1ms overhead.

preprint2016arXiv

Field Induced Oscillation of Two Majorana Modes for a finite Quantum Wire

The evolution of quantum walk on a finite wire under a small increment of vector potential $α$ can exhibit intrinsic quantum oscillation of the two topologically protected bound states corresponding to the Majorana modes. By tuning an external electric field corresponding to the addition of an $α$ impulse at the end of each intrinsic period, the intrinsic oscillation is enveloped by a beat modulation with a longer period. This beat oscillation is useful in the preparation of decoherence-free qubit in trapped ion chain and may be observed in several experiments.

preprint2016arXiv

Gauge fermions with flat bands and anomalous transport via chiral modes from breaking gauge symmetry

The dispersionless longitudinal photon in Maxwell theory is thought of as a redundant degree of freedom due to the gauge symmetry. We find that when there exist exactly flat bands with zero energy in a condensed matter system, the fermion field may locally transform as a gauge field and the system possesses a gauge symmetry. As the longitudinal photon, the redundant degrees of freedom from the flat bands must be gauged away from the physical states. As an example, we study spinless fermions on a generalized Lieb lattice in three dimensions. The flat band of the longitudinal fermion induces a gauge symmetry. An external magnetic field breaks this gauge symmetry and emerges a bunch of non-topologically chiral modes. Combining these emergent chiral modes with the chiral anomaly mode which is of an opposite chirality, rich anomalous electric transport phenomena exhibit and are expected to be observed in Pd$_3$Bi$_2$S$_2$ and Ag$_3$Se$_2$Au.

preprint2016arXiv

Hybrid Weyl Semimetal

We construct a tight-binding model realizing one pair of Weyl nodes and three distinct Weyl semimetals. In the type-I (type-II) Weyl semimetal, both nodes belong to type-I (type-II) Weyl nodes. In addition, there exists a novel type, dubbed "hybrid Weyl semimetal", in which one Weyl node is of type-I while the other is of type-II. For the hybrid Weyl semimetal, we further demonstrate the bulk Fermi surfaces and the topologically protected surface states, analyze the unique Landau level structure and quantum oscillation, and discuss the material realization.

preprint2016arXiv

Initial and Eventual Software Quality Relating to Continuous Integration in GitHub

The constant demand for new features and bug fixes are forcing software projects to shorten cycles and deliver updates ever faster, while sustaining software quality. The availability of inexpensive, virtualized, cloud-computing has helped shorten schedules, by enabling continuous integration (CI) on demand. Platforms like GitHub support CI in-the-cloud. In projects using CI, a user submitting a pull request triggers a CI step. Besides speeding up build and test, this fortuitously creates voluminous archives of build and test successes and failures. CI is a relatively new phenomenon, and these archives allow a detailed study of CI. How many problems are exposed? Where do they occur? What factors affect CI failures? Does the "initial quality" as ascertained by CI predict how many bugs will later appear ("eventual quality") in the code? In this paper, we undertake a large-scale, fine resolution study of these records, to better understand CI processes, the nature, and predictors of CI failures, and the relationship of CI failures to the eventual quality of the code. We find that: a) CI failures appear to be concentrated in a few files, just like normal bugs; b) CI failures are not very highly correlated with eventual failures; c) The use of CI in a pull request doesn't necessarily mean the code in that request is of good quality.

preprint2016arXiv

Noncommutative Chern-Simons theory and exotic geometry emerging from the lowest Landau level

We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $ν=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in two-dimensional guiding center space emerges from these internal geometric modes. Using the Dirac bracket method, we find that this quantum geometric field theory is a topological non-commutative Chern-Simons theory.Topological indices, such as the guiding center angular momentum (also called the shift) and the guiding center spin, which characterize the fractional quantum Hall (FQH) states besides the filling factor, are naturally defined. A noncommutative K-matrix Chern-Simons theory is proposed as a generalization to a large class of Abelian FQH topological orders.

preprint2016arXiv

Nonlinear Quantum Hall effects in Rarita-Schwinger gas

Emergence of higher spin relativistic fermionic materials becomes a new favorite in the study of condensed matter physics. Massive Rarita-Schwinger 3/2-spinor was known owning very exotic properties, such as the superluminal fermionic modes and even being unstable in an external magnetic field. Due to the superluminal modes and the non-trivial constraints on the Rarita-Schwinger gas, we exposit anomalous properties of the Hall effects in (2+1)-dimensions which subvert the well-known quantum Hall paradigms. First, the Hall conductance of a pure Rarita-Schwinger gas is step-like but not plateau-quantized, instead of the linear dependence on the filling factor for a pure spin-1/2 Dirac gas. In reality, the Hall conductance of the Dirac gas is of quantized integer plateaus with the unit $\frac{e^2}h$ due to the localization away from the Landau level centers. If the general localization rule is applicable to the disordered Rarita-Schwinger gas, the Hall plateaus are also expected to appear but they are nonlinearly dependent on the Landau level index. Furthermore, there is a critical magnetic field beyond which higher Landau levels become unstable. This confines the filling factor of the system. We also show that the non-hermitness of the effective Hamiltonian is not crucial to the nonlinearity of the quantum Hall conductance.

preprint2016arXiv

Quantum spin ice on the breathing pyrochlore lattice

The Coulombic quantum spin liquid in quantum spin ice is an exotic quantum phase of matter that emerges on the pyrochlore lattice and is currently actively searched for. Motivated by recent experiments on the Yb-based breathing pyrochlore material Ba$_3$Yb$_2$Zn$_5$O$_{11}$, we theoretically study the phase diagram and magnetic properties of the relevant spin model. The latter takes the form of a quantum spin ice Hamiltonian on a breathing pyrochlore lattice, and we analyze the stability of the quantum spin liquid phase in the absence of the inversion symmetry which the lattice breaks explicitly at lattice sites. Using a gauge mean-field approach, we show that the quantum spin liquid occupies a finite region in parameter space. Moreover, there exists a direct quantum phase transition between the quantum spin liquid phase and featureless paramagnets, even though none of theses phases break any symmetry. At nonzero temperature, we show that breathing pyrochlores provide a much broader finite temperature spin liquid regime than their regular counterparts. We discuss the implications of the results for current experiments and make predictions for future experiments on breathing pyrochlores.

preprint2016arXiv

Seiberg-Witten monopoles: Weyl metal coupled to chiral magnets

We study a Weyl (semi)metal which couples to local magnets. In the continuum limit, the Hamiltonian of the system matches the Chern-Simons-Maxwell-Dirac functional and then the ground state is governed by generalized Seiberg-Witten (SW) or Freund equations in terms of the sign of Dzyaloshinskii-Moriya coupling. The ground states determined by the Freund equations may either be monopolar Weyl semimetal accompanied by the ferromagnetic magnets (MWFM) or SW monopoles which consist of spheric Weyl fermions coupled to chiral magnets, depending on the strength of the Kondo coupling. In the latter phase, the topological ground state is characterized by SW invariants and with a Weyl surface on which the Weyl metal is of an exotic dispersion $\propto \sqrt k$. There are also the metastable SW monopole solutions carrying an opposite SW invariant for the SW equations while the ground state in this case is the MWFM state.

preprint2015arXiv

Collective modes in a Dirac insulator with short range interactions

We study a Haldane model with nearest neighbor interactions. We find one-dimensional like collective modes arising due to the interplay of pseudo-spin and valley degrees of freedom. In the large band gap or moderate interaction limit, these excitations are low energy modes lying in the band gap. The dispersion relations are qualitatively different in trivial insulator phase and Chern insulator phase, thus can be used to identify the topology of the Haldane model with the bulk property. We also discuss how to detect these modes in cold atom systems. An abelian gauge theory will emerge when a physical current-current interaction is introduced to the Haldane model or the Kane-Mele model.

preprint2015arXiv

Global Phase Diagram of the Extended Kitaev-Heisenberg Model on Honeycomb Lattice

We study the extended Kitaev-Heisenberg (EKH) quantum spin model by adding bond-dependent off-diagonal Heisenberg term into the original KH model, which was recently proposed to describe the honeycomb Iridates. A rigorous mathematical mapping of spin operators reveals the intrinsic symmetry of the model Hamiltonian. By employing an unbiased numerical entanglement renormalization method based on tensor network ansatz, we obtain the global phase diagram containing eight distinct quantum phases. By using the dual mapping of spin operators, each of the individual magnetic phase in the global phase diagram can be clearly understood. At last, we show that a valence solid state emerges as the ground state in the quadro-critical region where multiple magnetic phases compete most intensively.

preprint2015arXiv

Rarita-Schwinger-Weyl semimetal in Jeff=3/2 electron systems

We propose a relativistic Jeff=3/2 semimetal with 4d1 or 5d1 electrons on a cubic lattice when the strong spin-orbital coupling takes over the Hunds' coupling. A relativistic spinor with spin 3/2 is historically called Rarita-Schwinger spinor. In the massless case, the right- and left-handed chiral degrees of freedom of the Rarita-Schwinger spinors are independent. In the lattice model that we propose, the right- and left- handed gapless points in Brillouin zone are separated. We call this linearly dispersed semimetal Rarita-Schwinger-Weyl semimetal, similar to Weyl semimetal for spin 1/2 systems. There is a network of gapless Fermi arcs in the surface Brillouin zone if n1+n2+n3 is even for the normal vector (n1,n2,n3) of the surface while the surface is insulator if n1+n2+n3 is odd.

preprint2015arXiv

Symmetry Protected Topological Phases and Majorana Mode in One-dimensional Quantum Walk with Boundary

The topological phases in one-dimensional quantum walk can be classified by the coin parameters. By solving for the general exact solutions of bound states in one-dimensional quantum walk with boundaries specified by different coin parameters, we show that these bound states are Majorana modes with quasi-energy $E=0,π$. These modes are qualitatively different for different boundary conditions used. For two-boundary system with symmetric boundary conditions, the interaction energy between two Majorana bound states can be computed, as in the case of a finite wire. Suggestion of observing these modes are provided.

preprint2014arXiv

Distinct-symmetry spin liquid states and phase diagram of Kitaev-Hubbard model

We report the finding of a series of symmetry distinct spin liquid (SL) states and a rich phase diagram in a half-filled honeycomb lattice Hubbard model with spin-dependent hopping amplitude t'. We first study the magnetic instability of the system and find two antiferromagnetic orders beyond a critical Hubbard U which increases with the ratio t'/t . For $t'$ approaching to $t$, the semimetal (SM) transforms to a U(1) SL and then to the Kitaev Z_2 SL as U increases. In a wide middle range of t'/t, the latter is replaced by a U(1) SL to $SU(2)$ SL transition. The physical properties of the stable SL phases are discussed.

preprint2014arXiv

Effects of dipole-dipole interaction between cigar-shaped BECs of cold alkali atoms: Towards inverse-squared interactions

We show that the dipole-dipole coupling between Wannier modes in cigar-shaped Bose-Einstein condensates (BECs) is significantly enhanced while the short-range coupling strongly suppressed. As a result, the dipole-dipole interaction can become the dominant interaction between ultracold alkali Bose atoms. In the long length limit of a cigar-shaped BEC, the resulting effective one-dimensional models possess an effective inverse squared interacting potential, the Calogero-Sutherland potential, which plays a fundamental role in many fields of contemporary physics; but its direct experimental realization has been a challenge for a long time. We propose to realize the Calogero-Sutherland model in ultracold alkali Bose atoms and study the effects of the dipole-dipole interaction.

preprint2013arXiv

Cluster-Based Regularized Sliced Inverse Regression for Forecasting Macroeconomic Variables

This article concerns the dimension reduction in regression for large data set. We introduce a new method based on the sliced inverse regression approach, called cluster-based regularized sliced inverse regression. Our method not only keeps the merit of considering both response and predictors' information, but also enhances the capability of handling highly correlated variables. It is justified under certain linearity conditions. An empirical application on a macroeconomic data set shows that our method has outperformed the dynamic factor model and other shrinkage methods.

preprint2013arXiv

Dynamical Mass Generation of Composite Dirac Fermions and Fractional Quantum Hall Effects near Charge Neutrality in Graphene

We develop a composite Dirac fermion theory for the fractional quantum Hall effects (QHE) near charge neutrality in graphene. We show that the interactions between the composite Dirac fermions lead to dynamical mass generation through exciton condensation. The four-fold spin-valley degeneracy is fully lifted due to the mass generation and the exchange effects such that the odd-denominator fractional QHE observed in the vicinity of charge neutrality can be understood in terms of the integer QHE of the composite Dirac fermions. At the filling factor $ν=1/2$, we show that the massive composite Dirac fermion liquid is unstable against chiral p-wave pairing for weak Coulomb interactions and the ground state is a paired nonabelian state described by the Moore-Read Pfaffian in the long wavelength limit.

preprint2013arXiv

Tuning into the Kitaev spin liquid phase:A spin model on the honeycomb lattice with two types of Heisenberg exchange couplings

We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, $J$ and $\tilde J$, where $J$ is for the conventional spin and and $\tilde J$ for rotated spin. When $\tilde J=0$, this is the conventional Heisenberg model. When J=0, the system is either in a stripy antiferromagnetic order($\tilde J<0$, ferromagnetic for rotated spin) or a zig-zag antiferromagnetic order ($\tilde J>0$, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or two antiferromagnetic orders induces Kitaev's spin liquid phase characterized by the exactly solvable Kitaev model ($J=\tilde J$). Our model can be applied to layered Mott insulators A$_2$IrO$_3$ (A=Li, Na). For a monolayer of Li$_2$IrO$_3$, we show that it is possible to tune the controlling parameter into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital coupling.

preprint2012arXiv

Isotropic Landau levels of Dirac fermions in high dimensions

We generalize the Landau levels of two-dimensional Dirac fermions to three dimensions and above with the full rotational symmetry. Similarly to the two-dimensional case, there exists a branch of zero energy Landau levels of fractional fermion modes for the massless Dirac fermions. The spectra of other Landau levels distribute symmetrically with respect to the zero energy scaling with the square root of the Landau-level indices. This mechanism is a nonminimal coupling of Dirac fermions to the background fields. This high dimensional relativistic Landau-level problem is a square-root problem of its previous studied nonrelativistic version investigated in Li and Wu [arXiv:1103.5422 (2011)].

preprint2012arXiv

Partial Sliced Inverse Regression for Quality-Relevant Multivariate Statistical Process Monitoring

This paper introduces a popular dimension reduction method, sliced inverse regression (SIR), into multivariate statistical process monitoring. Provides an extension of SIR for the single-index model by adopting the idea from partial least squares (PLS). Our partial sliced inverse regression (PSIR) method has the merit of incorporating information from both predictors (x) and responses (y), and it has capability of handling large, nonlinear, or "n<p" dataset. Two statistics with their corresponding distributions and control limits are given based on the X-space decomposition of PSIR for the purpose of fault detection in process monitoring. Simulations showed PSIR outperformed over PLS and SIR for both linear and nonlinear model.

preprint2011arXiv

Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect

We study the quantum anomalous Hall effect described by a class of two-component Haldane models on square lattices. We show that the latter can be transformed into a pseudospin triplet p+ip-wave paired superfluid. In the long wave length limit, the ground state wave function is described by Halperin's (1,1,-1) state of neutral fermions analogous to the double layer quantum Hall effect. The vortex excitations are charge e/2 abelian anyons which carry a neutral Dirac fermion zero mode. The superconducting proximity effect induces `tunneling' between `layers' which leads to topological phase transitions whereby the Dirac fermion zero mode fractionalizes and Majorana fermions emerge in the edge states. The charge e/2 vortex excitation carrying a Majorana zero mode is a non-abelian anyon. The proximity effect can also drive a conventional insulator into a quantum anomalous Hall effect state with a Majorana edge mode and the non-abelian vortex excitations.

preprint2011arXiv

Spin superconductor in ferromagnetic graphene

We show a spin superconductor (SSC) in ferromagnetic graphene as the counterpart to the charge superconductor, in which a spin-polarized electron-hole pair plays the role of the spin $2 (\hbar/2)$ `Cooper pair' with a neutral charge. We present a BCS-type theory for the SSC. With the `London-type equations' of the super-spin-current density, we show the existence of an electric `Meissner effect' against a spatial varying electric field. We further study a SSC/normal conductor/SSC junction and predict a spin-current Josephson effect.

preprint2011arXiv

Supersolid phase transitions for hardcore bosons on a triangular lattice

Hard-core bosons on a triangular lattice with nearest neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical Quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.

preprint2011arXiv

Three-body interactions on a triangular lattice

We analyze the hard-core Bose-Hubbard model with both the three-body and nearest neighbor repulsions on the triangular lattice. The phase diagram is achieved by means of the semi-classical approximation and the quantum Monte Carlo simulation. For a system with only the three-body interactions, both the supersolid phase and one third solid disappear while the two thirds solid stably exists. As the thermal behavior of the bosons with nearest neighbor repulsion, the solid and the superfluid undergo the 3-state Potts and the Kosterlitz-Thouless type phase transitions, respectively. In a system with both the frustrated nearest neighbor two-body and three-body interactions, the supersolid and one third solid revive. By tuning the strength of the three-body interactions, the phase diagram is distorted, because the one-third solid and the supersolid are suppressed.

preprint2010arXiv

An anyon model in a toric honeycomb lattice

We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wigner transformation. We discuss the equivalence between these two models in the low-lying sector and realize these anyon excitations in a conventional fermion system.

preprint2010arXiv

Correlation-hole induced paired quantum Hall states in lowest Landau level

A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. Two canonically dual pairing gap functions are related by the bosonic Laughlin wavefunction (Jastraw factor) due to the correlation holes. We find that the ground state is the Moore-Read pfaffian in the long wavelength limit for weak Coulomb interactions, a new pfaffian of an oscillatory pairing function for intermediate interactions, and a Read-Rezayi composite Fermi liquid beyond a critical interaction strength. Our findings are consistent with recent experimental observations of the 1/2 and 1/4 fractional quantum Hall effects in asymmetric wide quantum wells.

preprint2010arXiv

Simulating Wess-Zumino Supersymmetry Model in Optical Lattices

We study a cold atom-molecule mixture in two-dimensional optical lattices, in which fermionic atoms have a Dirac-type dispersion. We show that by fine-tuning the atomic and molecular interactions, such mixtures can simulate Wess-Zumino supersymmetry (SUSY) model, the first example of SUSY theories. At zero temperature, SUSY is not spontaneously broken for this simplest SUSY model, which implies identical relativistic dispersions of the atom and its superpartner, bosonic diatom molecule. This defining signature of SUSY can be probed by single particle spectroscopies. Thermal breaking of SUSY at finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.

preprint2010arXiv

Supersymmetric Response of Bose-Fermi Mixture to Photoassociation

We study supersymmetric (SUSY) responses to a photoassociation process in a mixture of Bose molecules $b$ and Fermi atoms $f$ which turn to mutual superpartners for a set of proper parameters. We consider the molecule $b$ to be a bound state of the atom $f$ and another Fermi atom $F$ with different species. The $b$-$f$ mixture and a free $F$ atom gas are loaded in an optical lattice. The SUSY nature of the mixture can be signaled in the response to a photon induced atom-molecule transition: While two new types of fermionic excitations, an individual $b$ particle-$f$ hole pair continuum and the Goldstino-like collective mode, are concomitant for a generic $b$-$f$ mixture, the former is completely suppressed in the SUSY $b$-$f$ mixture and the zero-momentum mode of the latter approaches to an exact eigenstate. This SUSY response can be detected by means of the spectroscopy method, e.g., the photoassociation spectrum which displays the molecular formation rate of $% Ff\to b$.

preprint2009arXiv

Anyons from fermions with conventional two-body interactions

Emergent anyons are the key elements of the topological quantum computation and topological quantum memory. We study a two-component fermion model with conventional two-body interaction in an open boundary condition and show that several subsets in the low-lying excitations obey the same fusion rules as those of the toric code model. Those string-like non-local excitations in a given subset obey mutual semionic statistics. We show how to peel off one of such subset from other degenerate subsets and manipulate anyons in cold dipolar Fermi atoms or cold dipolar fermionic heteronuclear molecules in optical lattices by means of the established techniques.

preprint2009arXiv

Quantized squeezing and even-odd asymmetry of trapped bosons

We investigate the exact nature of the superfluid-to-Mott-insulator crossover for interacting bosons on an optical lattice in a one-dimensional, harmonic trap by high-precision density-matrix renormalization-group calculations. The results reveal an intermediate regime characterized by a cascade of microscopic steps. These arise as a consequence of individual boson "squeezing" events and display an even-odd alternation dependent on the trap symmetry. We discuss the experimental observation of this behavior, which is generic in an external trapping potential.

preprint2009arXiv

Topological quantum phase transition in an extended Kitaev spin model

We study the quantum phase transition between Abelian and non-Abelian phases in an extended Kitaev spin model on the honeycomb lattice, where the periodic boundary condition is applied by placing the lattice on a torus. Our analytical results show that this spin model exhibits a continuous quantum phase transition. Also, we reveal the relationship between bipartite entanglement and the ground-state energy. Our approach directly shows that both the entanglement and the ground-state energy can be used to characterize the topological quantum phase transition in the extended Kitaev spin model.

preprint2008arXiv

Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid

We established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-abelian statistics. We characterize this kind of statistics by non-abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.

preprint2008arXiv

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

We construct an exactly soluble spin-$\frac{1}2$ model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore-Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess-Zumino term of SO(3) group through an index theorem in 2+1 dimensions.

preprint2007arXiv

Exactly soluble spin-1/2 models on three-dimensional lattices and non-abelian statistics of closed string excitations

Exactly soluble spin-$\frac{1}2$ models on three-dimensional lattices are proposed by generalizing Kitaev model on honeycomb lattice to three dimensions with proper periodic boundary conditions. The simplest example is spins on a diamond lattice which is exactly soluble. The ground state sector of the model may be mapped into a p-wave paired state on cubic lattice. We observe for the first time a topological phase transition from a gapless phase to a gapped phase in an exactly soluble spin model. Furthermore, the gapless phase can not be gapped by a perturbation breaking the time reversal symmetry. Unknotted and unlinked Wilson loops arise as eigen excitations, which may evolute into linked and knotted loop excitations. We show that these closed string excitations obey abelian statistics in the gapped phase and non-abelian statistics in the gapless phase.

preprint2007arXiv

Nature of Intermediate States between Superfluid and Mott insulator for Interacting Bosons in One-dimension with a Harmonic Trapping Potential

Successive quantum transitions in an intermediate regime are shown to exist between the superfluid and Mott insulating states for interacting bosonic atoms in one dimension with a trapping potential. These transitions, which are caused by the interplay of the trapping potential with the competition between the kinetic energy and the interaction, reveal novel many-body effects as reflected by low-lying excitation behavior, unconventional long-range correlations and an even-odd alternating squeezing process of superfluid bosons into the Mott insulating state. These features, most likely being generic for all dimensions when a trapping potential is involved, are relevant for both experimental observations and physical interpretation of the Mott insulator transition.

preprint2007arXiv

The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice

We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large scale quantum Monte Carlo simulations. We present the ground state phase diagrams for both the hard-core case and the soft-core case. For the hard-core case, the transition between $ρ=1/2$ solid and the superfluid is first order and the supersolid state is unstable towards phase separation. For the soft-core case, due to the presence of the multiple occupation, a stable particle induced supersolid (SS-p) phase emerges when $1/2<ρ<1$. The transition from the solid at $ρ=1/2$ to the SS-p is second order with the superfluid density scaling as $ ρ_{s} \sim ρ-1/2 $. The SS-p has the same diagonal order as the solid at $ ρ=1/2 $. As the chemical potential increasing further, the SS-p will turn into a solid where two bosons occupying each site of a sublattice through a first order transition. We also calculate the critical exponents of the transition between $ρ=1/2$ solid and superfluid at the Heisenberg point for the hard core case. We find the dynamical critical exponent $z=0.15$, which is smaller than results obtained on smaller lattices. This indicates that $ z $ approaches zero in the thermodynamic limit, so the transition is also first order even at the Heisenberg point.

preprint2006arXiv

Interaction broadening of Wannier functions and Mott transitions in atomic BEC

Superfluid to Mott-insulator transitions in atomic BEC in optical lattices are investigated for the case of number of atoms per site larger than one. To account for mean field repulsion between the atoms in each well, we construct an orthogonal set of Wannier functions. The resulting hopping amplitude and on-site interaction may be substantially different from those calculated with single-atom Wannier functions. As illustrations of the approach we consider lattices of various dimensionality and different mean occupations. We find that in three-dimensional optical lattices the correction to the critical lattice depth is significant to be measured experimentally even for small number of atoms. Finally, we discuss validity of the single band model.

preprint2005arXiv

Interaction of a surface acoustic wave with a two-dimensional electron gas

When a surface acoustic wave propagates on the surface of a GaAs semiconductor, coupling between electrons in the two-dimensional electron gas beneath the interface and the elastic host crystal through piezoelectric interaction will attenuate the SAW. The coupling coefficient is calculated for the SAW propagating along an arbitrary direction. It is found that the coupling strength is largely dependent on the propagating direction. When the SAW propagates along the [011] direction, the coupling becomes quite weak.

preprint2004arXiv

Density-induced reorientation of the stripe at half-filled high Landau levels

The effect of a unidirectional periodic potential on the orientation of the stripe state is studied for the two-dimensional electron system at half-filled high Landau levels. By considering a quantum well with two electric subbands, it is found that the stripe is parallel to the external potential for weak modulation and is orthogonal for strong modulation. In the intermediate range, the orientation of the stripe changes from orthogonal to parallel as the electron density is increased. This result explains the recent experiment performed by J. Zhu {\it et al} that the anisotropy axis at half-filled high Landau levels rotates by $90^0$ by increasing the electron density. It also supports the suggestion that the stripes is pinned by the native surface morphology at the interface of the heterojunction.

preprint2004arXiv

Luttinger liquid with strong spin-orbital coupling and Zeeman splitting in quantum wires

We study a one-dimensional interacting electron gas with the strong Rashba spin-orbit coupling and Zeeman splitting in a quantum well. A bosonization theory is developed for this system. The tunneling current may deviate from a simple power law which is that in an ordinary Luttinger liquid. The microscopic interacting coupling and the spin-orbital parameter may be measured by varying the external magnetic field in the tunneling experiment.

preprint2003arXiv

Electron space charge effect on spin injection into semiconductors

We consider spin polarized transport in a ferromagnet-insulator/semiconductor/insulator-ferromagnet (F1-I-S-I-F2) junction. We find that the spin current is strongly dependent on the spin configurations, the doping and space charge distribution in the semiconductor. When the ferromagnet-semiconductor interface resistance is comparable to the semiconductor resistance, the magnetoresistance ratio of this junction can be greatly enhanced under appropriate doping when the space charge effect in the nonequilibrium transport processes is taken into consideration.

preprint2002arXiv

A Novel Meron-induced Pseudospin Wave in Bilayer Quantum Hall Coherent State and the Residual Zero-bias Peak in Tunneling Conductance

In the bilayer quantum Hall coherent state for $ν_T$ deviating slightly from one, we show that, instead of the global order parameter, the spontaneous breaking of the pseudospin U(1) rotational symmetry is reflected by the periodic domain structure accompanying with the charged meron pairs. The motion of meron pairs induces a novel pseudospin wave. The long range order of the periodic domains in a low bias voltage range leads to the residual zero-bias peak in the tunneling conductance even when the pseudopsin Goldstone feature in a high bias voltage range can be distinct from it.

preprint2002arXiv

The Effect of the Tilted Field in the Fractional Quantum Hall Systems: Numerical Studies for the Solid-liquid Transition

We construct a generalized Laughlin-liquid wave function and a variational electron solid wave function when the magnetic field is tilted. The energy of the liquid state is evaluated by Monte Carlo methods while the energy of the solid state is calculated by the optimization. Comparing these two energies for a given tilted angle $θ$, it is seen that the critical filling factor $ν_c$ of $θ$ of the solid-liquid transition increases as the tilted angle. The implication to the experiment is that: i) the insulating phase may harder be melt as $ν\to 1/5$ such that the width of the valley of the longitudinal resistance may become narrow as the filed is tilted; ii) it is expected that even in the vicinity of $ν=1/3$ for the electron system in the presence of the tilted field, the insulating phase may be observed.