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Qing Liu

Qing Liu appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Computer Visionmath.AGmath.APmath.NTastro-ph.GAphysics.comp-phphysics.flu-dynComputation and LanguageMachine Learningastro-ph.IMcond-mat.softq-fin.PRArtificial Intelligenceastro-ph.HEcond-mat.mes-hallcond-mat.mtrl-sciDatabasesDistributed, Parallel, and Cluster Computinghep-exInformation Retrievalmath.ACmath.DGmath.GRmath.GTmath.MGmath.QAmath.RAmath.STMethodologyNeurons and Cognitionphysics.ins-detphysics.opticsPopulations and Evolutionq-fin.RMquant-phQuantitative MethodsStatistics Theory

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Published work

54 published item(s)

preprint2026arXiv

CC-OCR V2: Benchmarking Large Multimodal Models for Literacy in Real-world Document Processing

Large Multimodal Models (LMMs) have recently shown strong performance on Optical Character Recognition (OCR) tasks, demonstrating their promising capability in document literacy. However, their effectiveness in real-world applications remains underexplored, as existing benchmarks adopt task scopes misaligned with practical applications and assume homogeneous acquisition conditions. To address this gap, we introduce CC-OCR V2, a comprehensive and challenging OCR benchmark tailored to real-world document processing. CC-OCR V2 focuses on practical enterprise document processing tasks and incorporates hard and corner cases that are critical yet underrepresented in prior benchmarks, covering 5 major OCR-centric tracks: text recognition, document parsing, document grounding, key information extraction, and document question answering, comprising 7,093 high-difficulty samples. Extensive experiments on 14 advanced LMMs reveal that current models fall short of real-world application requirements. Even state-of-the-art LMMs exhibit substantial performance degradation across diverse tasks and scenarios. These findings reveal a significant gap between performance on current benchmarks and effectiveness in real-world applications. We release the full dataset and evaluation toolkit at https://github.com/eioss/CC-OCR-V2.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Light-weight Interpretable Compositional Model for Nuclei Detection and Weakly-Supervised Segmentation

The field of computational pathology has witnessed great advancements since deep neural networks have been widely applied. These networks usually require large numbers of annotated data to train vast parameters. However, it takes significant effort to annotate a large histopathology dataset. We introduce a light-weight and interpretable model for nuclei detection and weakly-supervised segmentation. It only requires annotations on isolated nucleus, rather than on all nuclei in the dataset. Besides, it is a generative compositional model that first locates parts of nucleus, then learns the spatial correlation of the parts to further locate the nucleus. This process brings interpretability in its prediction. Empirical results on an in-house dataset show that in detection, the proposed method achieved comparable or better performance than its deep network counterparts, especially when the annotated data is limited. It also outperforms popular weakly-supervised segmentation methods. The proposed method could be an alternative solution for the data-hungry problem of deep learning methods.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Adaptive estimation for the nonparametric bivariate additive model in random design with long-memory dependent errors

We investigate the nonparametric bivariate additive regression estimation in the random design and long-memory errors and construct adaptive thresholding estimators based on wavelet series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function and its univariate additive components belong to Besov space. We consider the problem under two noise structures; (1) homoskedastic Gaussian long memory errors and (2) heteroskedastic Gaussian long memory errors. In the homoskedastic long-memory error case, the estimator is completely adaptive with respect to the long-memory parameter. In the heteroskedastic long-memory case, the estimator may not be adaptive with respect to the long-memory parameter unless the heteroskedasticity is of polynomial form. In either case, the convergence rates depend on the long-memory parameter only when long-memory is strong enough, otherwise, the rates are identical to those under i.i.d. errors. The proposed approach is extended to the general $r$-dimensional additive case, with $r>2$, and the corresponding convergence rates are free from the curse of dimensionality.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Context-aware Reranking with Utility Maximization for Recommendation

As a critical task for large-scale commercial recommender systems, reranking has shown the potential of improving recommendation results by uncovering mutual influence among items. Reranking rearranges items in the initial ranking lists from the previous ranking stage to better meet users' demands. However, rather than considering the context of initial lists as most existing methods do, an ideal reranking algorithm should consider the counterfactual context -- the position and the alignment of the items in the reranked lists. In this work, we propose a novel pairwise reranking framework, Context-aware Reranking with Utility Maximization for recommendation (CRUM), which maximizes the overall utility after reranking efficiently. Specifically, we first design a utility-oriented evaluator, which applies Bi-LSTM and graph attention mechanism to estimate the listwise utility via the counterfactual context modeling. Then, under the guidance of the evaluator, we propose a pairwise reranker model to find the most suitable position for each item by swapping misplaced item pairs. Extensive experiments on two benchmark datasets and a proprietary real-world dataset demonstrate that CRUM significantly outperforms the state-of-the-art models in terms of both relevance-based metrics and utility-based metrics.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Distributed D-core Decomposition over Large Directed Graphs

Given a directed graph $G$ and integers $k$ and $l$, a D-core is the maximal subgraph $H \subseteq G$ such that for every vertex of $H$, its in-degree and out-degree are no smaller than $k$ and $l$, respectively. For a directed graph $G$, the problem of D-core decomposition aims to compute the non-empty D-cores for all possible values of $k$ and $l$. In the literature, several \emph{peeling-based} algorithms have been proposed to handle D-core decomposition. However, the peeling-based algorithms that work in a sequential fashion and require global graph information during processing are mainly designed for \emph{centralized} settings, which cannot handle large-scale graphs efficiently in distributed settings. Motivated by this, we study the \emph{distributed} D-core decomposition problem in this paper. We start by defining a concept called \emph{anchored coreness}, based on which we propose a new H-index-based algorithm for distributed D-core decomposition. Furthermore, we devise a novel concept, namely \emph{skyline coreness}, and show that the D-core decomposition problem is equivalent to the computation of skyline corenesses for all vertices. We design an efficient D-index to compute the skyline corenesses distributedly. We implement the proposed algorithms under both vertex-centric and block-centric distributed graph processing frameworks. Moreover, we theoretically analyze the algorithm and message complexities. Extensive experiments on large real-world graphs with billions of edges demonstrate the efficiency of the proposed algorithms in terms of both the running time and communication overhead.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Exploring Contextual Relationships for Cervical Abnormal Cell Detection

Cervical abnormal cell detection is a challenging task as the morphological discrepancies between abnormal and normal cells are usually subtle. To determine whether a cervical cell is normal or abnormal, cytopathologists always take surrounding cells as references to identify its abnormality. To mimic these behaviors, we propose to explore contextual relationships to boost the performance of cervical abnormal cell detection. Specifically, both contextual relationships between cells and cell-to-global images are exploited to enhance features of each region of interest (RoI) proposals. Accordingly, two modules, dubbed as RoI-relationship attention module (RRAM) and global RoI attention module (GRAM), are developed and their combination strategies are also investigated. We establish a strong baseline by using Double-Head Faster R-CNN with feature pyramid network (FPN) and integrate our RRAM and GRAM into it to validate the effectiveness of the proposed modules. Experiments conducted on a large cervical cell detection dataset reveal that the introduction of RRAM and GRAM both achieves better average precision (AP) than the baseline methods. Moreover, when cascading RRAM and GRAM, our method outperforms the state-of-the-art (SOTA) methods. Furthermore, we also show the proposed feature enhancing scheme can facilitate both image-level and smear-level classification. The code and trained models are publicly available at https://github.com/CVIU-CSU/CR4CACD.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Few-shot Named Entity Recognition with Self-describing Networks

Few-shot NER needs to effectively capture information from limited instances and transfer useful knowledge from external resources. In this paper, we propose a self-describing mechanism for few-shot NER, which can effectively leverage illustrative instances and precisely transfer knowledge from external resources by describing both entity types and mentions using a universal concept set. Specifically, we design Self-describing Networks (SDNet), a Seq2Seq generation model which can universally describe mentions using concepts, automatically map novel entity types to concepts, and adaptively recognize entities on-demand. We pre-train SDNet with large-scale corpus, and conduct experiments on 8 benchmarks from different domains. Experiments show that SDNet achieves competitive performances on all benchmarks and achieves the new state-of-the-art on 6 benchmarks, which demonstrates its effectiveness and robustness.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Global Weierstrass equations of hyperelliptic curves

Given a hyperelliptic curve $C$ of genus $g$ over a number field $K$ and a Weierstrass model $\mathscr{C}$ of $C$ over the ring of integers ${\mathcal O}_K$ (i.e. the hyperelliptic involution of $C$ extends to $\mathscr{C}$ and the quotient is a smooth model of ${\mathbb P}^1_K$ over ${\mathcal O}_K$), we give necessary and sometimes sufficient conditions for $\mathscr{C}$ to be defined by a global Weierstrass equation. In particular, if $C$ has everywhere good reduction, we prove that it is defined by a global Weierstrass equation with invertible discriminant if the class number $h_K$ is prime to $2(2g+1)$, confirming a conjecture of M. Sadek.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Learning Part Segmentation through Unsupervised Domain Adaptation from Synthetic Vehicles

Part segmentations provide a rich and detailed part-level description of objects. However, their annotation requires an enormous amount of work, which makes it difficult to apply standard deep learning methods. In this paper, we propose the idea of learning part segmentation through unsupervised domain adaptation (UDA) from synthetic data. We first introduce UDA-Part, a comprehensive part segmentation dataset for vehicles that can serve as an adequate benchmark for UDA (https://qliu24.github.io/udapart). In UDA-Part, we label parts on 3D CAD models which enables us to generate a large set of annotated synthetic images. We also annotate parts on a number of real images to provide a real test set. Secondly, to advance the adaptation of part models trained from the synthetic data to the real images, we introduce a new UDA algorithm that leverages the object's spatial structure to guide the adaptation process. Our experimental results on two real test datasets confirm the superiority of our approach over existing works, and demonstrate the promise of learning part segmentation for general objects from synthetic data. We believe our dataset provides a rich testbed to study UDA for part segmentation and will help to significantly push forward research in this area.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Modeling time evolving COVID-19 uncertainties with density dependent asymptomatic infections and social reinforcement

The COVID-19 pandemic has posed significant challenges in modeling its complex epidemic transmissions, infection and contagion, which are very different from known epidemics. The challenges in quantifying COVID-19 complexities include effectively modeling its process and data uncertainties. The uncertainties are embedded in implicit and high-proportional undocumented infections, asymptomatic contagion, social reinforcement of infections, and various quality issues in the reported data. These uncertainties become even more apparent in the first two months of the COVID-19 pandemic, when the relevant knowledge, case reporting and testing were all limited. Here we introduce a novel hybrid approach Susceptible-Undocumented infected-Documented infected-Recovered (SUDR) model. First, SUDR (1) characterizes and distinguishes Undocumented (U) and Documented (D) infections commonly seen during COVID-19 incubation periods and asymptomatic infections. Second, SUDR characterizes the probabilistic density of infections by capturing exogenous processes. Lastly, SUDR approximates the density likelihood of COVID-19 prevalence over time by incorporating Bayesian inference into SUDR. Different from existing COVID-19 models, SUDR characterizes the undocumented infections during unknown transmission processes. To capture the uncertainties of temporal transmission and social reinforcement during COVID-19 contagion, the transmission rate is modeled by a time-varying density function of undocumented infectious cases. By sampling from the mean-field posterior distribution with reasonable priors, SUDR handles the randomness, noise and sparsity of COVID-19 observations widely seen in the public COVID-19 case data. The results demonstrate a deeper quantitative understanding of the above uncertainties, in comparison with classic SIR, time-dependent SIR, and probabilistic SIR models.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Principal eigenvalue problem for infinity Laplacian in metric spaces

This paper is concerned with the Dirichlet eigenvalue problem associated to the $\infty$-Laplacian in metric spaces. We establish a direct PDE approach to find the principal eigenvalue and eigenfunctions in a proper geodesic space without assuming any measure structure. We provide an appropriate notion of solutions to the $\infty$-eigenvalue problem and show the existence of solutions by adapting Perron's method. Our method is different from the standard limit process via the variational eigenvalue formulation for $p$-Laplacian in the Euclidean space.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Recent Advances for Quantum Neural Networks in Generative Learning

Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relation and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Stellar halos from The Dragonfly Edge-on Galaxies Survey

We present the primary results from the Dragonfly Edge-on Galaxies Survey (DEGS), an exploration of the stellar halos of twelve nearby ($d < 25$ Mpc) edge-on disc galaxies with the Dragonfly Telephoto Array. The edge-on orientation of these galaxies allows their stellar halos to be explored with minimal obscuration by or confusion with the much brighter disc light. Galaxies in the sample span a range of stellar masses from $10^{9.68} - 10^{10.88} M_\odot$. We confirm that the wide range of stellar halo mass fractions previously seen for Milky Way-mass galaxies is also found among less massive spiral galaxies. The scatter in stellar halo mass fraction is large but we do find a significant positive correlation between stellar halo mass fraction and total stellar mass when the former is measured beyond five half-mass radii. Reasonably good agreement is found with predictions from cosmological hydrodynamical simulations, although observed stellar halo fractions appear to be somewhat lower than expected from these simulations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Takagi Topological Insulator on the Honeycomb Lattice

Recently, real topological phases protected by $PT$ symmetry have been actively investigated. In two dimensions, the corresponding topological invariant is the Stiefel-Whitney number. A recent theoretical advance is that in the presence of the sublattice symmetry, the Stiefel-Whitney number can be equivalently formulated in terms of Takagi's factorization. The topological invariant gives rise to a novel second-order topological insulator with odd $PT$-related pairs of corner zero modes. In this article, we review the elements of this novel second-order topological insulator, and demonstrate the essential physics by a simple model on the honeycomb lattice.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Tidal Distortions in NGC1052-DF2 and NGC1052-DF4: Independent Evidence for a Lack of Dark Matter

Two ultra diffuse galaxies in the same group, NGC1052-DF2 and NGC1052-DF4, have been found to have little or no dark matter and to host unusually luminous globular cluster populations. Such low mass diffuse objects in a group environment are easily disrupted and are expected to show evidence of tidal distortions. In this work we present deep new imaging of the NGC1052 group, obtained with the Dragonfly Telephoto Array, to test this hypothesis. We find that both galaxies show strong position angle twists and are significantly more elongated at their outskirts than in their interiors. The group's central massive elliptical NGC1052 is the most likely source of these tidal disturbances. The observed distortions imply that the galaxies have a low total mass or are very close to NGC1052. Considering constraints on the galaxies' relative distances, we infer that the dark matter halo masses of these galaxies cannot be much greater than their stellar masses. Calculating pericenters from the distortions, we find that the galaxies are on highly elliptical orbits, with a ratio of pericenter to present-day radius Rperi/R0~0.1 if the galaxies are dark matter-free and Rperi/R0~0.01 if they have a normal dark halo. Our findings provide strong evidence, independent of kinematic constraints, that both galaxies are dark matter deficient. Furthermore, the similarity of the tidal features in NGC1052-DF2 and NGC1052-DF4 strongly suggests that they arose at comparable distances from NGC1052. In Appendix A, we describe sbcontrast, a robust method to determine the surface brightness limit of images.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Time Resolution of the 4H-SiC PIN Detector

We address the determination of the time resolution for the $\rm 100~μm$ 4H-SiC PIN detectors fabricated by Nanjing University (NJU). The time response to $\rm β$ particles from a $\rm ^{90}$Sr source is investigated for the detection of the minimum ionizing particles (MIPs). We study the influence of different reverse voltages, which correspond to different carrier velocities and device sizes, and how this correlates with the detector capacitance. We determine a time resolution $\rm (94\pm1)~ps$ for $\rm 100~μm$ 4H-SiC PIN detector. A fast simulation software, termed RASER (RAdiation SEmiconductoR), is developed, and validated by comparing the waveform obtained from simulated and measured data. The simulated time resolution is $\rm (73\pm 1)~ps$ after considering the intrinsic leading contributions of the detector to time resolution.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Unified Structure Generation for Universal Information Extraction

Information extraction suffers from its varying targets, heterogeneous structures, and demand-specific schemas. In this paper, we propose a unified text-to-structure generation framework, namely UIE, which can universally model different IE tasks, adaptively generate targeted structures, and collaboratively learn general IE abilities from different knowledge sources. Specifically, UIE uniformly encodes different extraction structures via a structured extraction language, adaptively generates target extractions via a schema-based prompt mechanism - structural schema instructor, and captures the common IE abilities via a large-scale pre-trained text-to-structure model. Experiments show that UIE achieved the state-of-the-art performance on 4 IE tasks, 13 datasets, and on all supervised, low-resource, and few-shot settings for a wide range of entity, relation, event and sentiment extraction tasks and their unification. These results verified the effectiveness, universality, and transferability of UIE.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A Method To Characterize the Wide-Angle Point Spread Function of Astronomical Images

Uncertainty in the wide-angle Point Spread Function (PSF) at large angles (tens of arcseconds and beyond) is one of the dominant sources of error in a number of important quantities in observational astronomy. Examples include the stellar mass and shape of galactic halos and the maximum extent of starlight in the disks of nearby galaxies. However, modeling the wide-angle PSF has long been a challenge in astronomical imaging. In this paper, we present a self-consistent method to model the wide-angle PSF in images. Scattered light from multiple bright stars is fitted simultaneously with a background model to characterize the extended wing of the PSF using a Bayesian framework operating on pixel-by-pixel level. The method is demonstrated using our software elderflower and is applied to data from the Dragonfly Telephoto Array to model its PSF out to 20-25 arcminutes. We compare the wide-angle PSF of Dragonfly to that of a number of other telescopes, including the SDSS PSF, and show that on scales of arcminutes the scattered light in the Dragonfly PSF is markedly lower than that of other wide-field imaging telescopes. The energy in the wings of the Dragonfly point-spread function is sufficiently low that optical cleanliness plays an important role in defining the PSF. This component of the PSF can be modelled accurately, highlighting the power of our self-contained approach.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput -- 83% of theoretical peak -- on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Analyzing the Spatiotemporal Interaction and Propagation of ATN Biomarkers in Alzheimer's Disease using Longitudinal Neuroimaging Data

Three major biomarkers: beta-amyloid (A), pathologic tau (T), and neurodegeneration (N), are recognized as valid proxies for neuropathologic changes of Alzheimer's disease. While there are extensive studies on cerebrospinal fluids biomarkers (amyloid, tau), the spatial propagation pattern across brain is missing and their interactive mechanisms with neurodegeneration are still unclear. To this end, we aim to analyze the spatiotemporal associations between ATN biomarkers using large-scale neuroimaging data. We first investigate the temporal appearances of amyloid plaques, tau tangles, and neuronal loss by modeling the longitudinal transition trajectories. Second, we propose linear mixed-effects models to quantify the pathological interactions and propagation of ATN biomarkers at each brain region. Our analysis of the current data shows that there exists a temporal latency in the build-up of amyloid to the onset of tau pathology and neurodegeneration. The propagation pattern of amyloid can be characterized by its diffusion along the topological brain network. Our models provide sufficient evidence that the progression of pathological tau and neurodegeneration share a strong regional association, which is different from amyloid.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Class Knowledge Overlay to Visual Feature Learning for Zero-Shot Image Classification

New categories can be discovered by transforming semantic features into synthesized visual features without corresponding training samples in zero-shot image classification. Although significant progress has been made in generating high-quality synthesized visual features using generative adversarial networks, guaranteeing semantic consistency between the semantic features and visual features remains very challenging. In this paper, we propose a novel zero-shot learning approach, GAN-CST, based on class knowledge to visual feature learning to tackle the problem. The approach consists of three parts, class knowledge overlay, semi-supervised learning and triplet loss. It applies class knowledge overlay (CKO) to obtain knowledge not only from the corresponding class but also from other classes that have the knowledge overlay. It ensures that the knowledge-to-visual learning process has adequate information to generate synthesized visual features. The approach also applies a semi-supervised learning process to re-train knowledge-to-visual model. It contributes to reinforcing synthesized visual features generation as well as new category prediction. We tabulate results on a number of benchmark datasets demonstrating that the proposed model delivers superior performance over state-of-the-art approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Cross Knowledge-based Generative Zero-Shot Learning Approach with Taxonomy Regularization

Although zero-shot learning (ZSL) has an inferential capability of recognizing new classes that have never been seen before, it always faces two fundamental challenges of the cross modality and crossdomain challenges. In order to alleviate these problems, we develop a generative network-based ZSL approach equipped with the proposed Cross Knowledge Learning (CKL) scheme and Taxonomy Regularization (TR). In our approach, the semantic features are taken as inputs, and the output is the synthesized visual features generated from the corresponding semantic features. CKL enables more relevant semantic features to be trained for semantic-to-visual feature embedding in ZSL, while Taxonomy Regularization (TR) significantly improves the intersections with unseen images with more generalized visual features generated from generative network. Extensive experiments on several benchmark datasets (i.e., AwA1, AwA2, CUB, NAB and aPY) show that our approach is superior to these state-of-the-art methods in terms of ZSL image classification and retrieval.

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preprint2021arXiv

Observation of an Unusual Colossal Anisotropic Magnetoresistance Effect in an Antiferromagnetic Semiconductor

Searching for novel antiferromagnetic materials with large magnetotransport response is highly demanded for constructing future spintronic devices with high stability, fast switching speed, and high density. Here we report a colossal anisotropic magnetoresistance effect in an antiferromagnetic binary compound with layered structure rare-earth dichalcogenide EuTe2. The AMR reaches 40000%, which is 4 orders of magnitude larger than that in conventional antiferromagnetic alloys. Combined magnetization, resistivity, and theoretical analysis reveal that the colossal AMR effect is attributed to a novel mechanism of vector-field tunable band structure, rather than the conventional spin-orbit coupling mechanism. Moreover, it is revealed that the strong hybridization between orbitals of Eu-layer with localized spin and Te-layer with itinerant carriers is extremely important for the large AMR effect. Our results suggest a new direction towards exploring AFM materials with prominent magnetotransport properties, which creates an unprecedented opportunity for AFM spintronics applications.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Observation of optical gyromagnetic properties in a magneto-plasmonic metamaterial

Metamaterials with artificial optical properties have attracted significant research interest. In particular, artificial magnetic resonances in non-unity permeability tensor at optical frequencies in metamaterials have been reported. However, only non-unity diagonal elements of the permeability tensor have been demonstrated to date. A gyromagnetic permeability tensor with non-zero off-diagonal elements has not been observed at the optical frequencies. Here we report the observation of gyromagnetic properties in the near-infrared wavelength range in a magneto-plasmonic metamaterial. The non-zero off-diagonal permeability tensor element causes the transverse magneto-optical Kerr effect (TMOKE) under s-polarized incidence that otherwise vanishes if the permeability tensor is not gyromagnetic. By retrieving the permeability tensor elements from reflection, transmission, and TMOKE spectra, we show that the effective off-diagonal permeability tensor elements reach the 10-3 level at the resonance wavelength (~900 nm) of the split-ring resonators that is at least two orders of magnitude higher than that of magneto-optical materials at the same wavelength. The artificial gyromagnetic permeability is attributed to the change in the local electric field direction modulated by the split-ring resonators. Our study demonstrates the possibility of engineering the permeability and permittivity tensors in metamaterials at arbitrary frequencies, thereby promising a variety of applications of next-generation nonreciprocal photonic devices, magneto-plasmonic sensors, and active metamaterials.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

SITELLE Hα Imaging Spectroscopy of z~0.25 Clusters: Emission Line Galaxy Detection and Ionized Gas Offset in Abell 2390 & Abell 2465

Environmental effects are crucial to the understanding of the evolution of galaxies in dense environments, such as galaxy clusters. Using the large field-of-view of SITELLE, the unique imaging fourier transform spectrograph at CFHT, we are able to obtain 2D spectral information for a large and complete sample of cluster galaxies out to the infall region. We describe a pipeline developed to identify emission line galaxies (ELGs) from the datacube using cross-correlation techniques. We present results based on the spatial offsets between the emission-line regions and stellar continua in ELGs from two z$\sim$0.25 galaxy clusters, Abell 2390 and Abell 2465. We find a preference in the offsets being pointed away from the cluster center. Combining the two clusters, there is a 3$σ$ excess for high-velocity galaxies within the virial radius having the offsets to be pointed away from the cluster center. Assuming the offset being a proxy for the velocity vector of a galaxy, as expected from ram pressure stripping, this excess indicates that ram pressure stripping occurs most effectively during the first passage of an infalling galaxy, leading to the quenching of its star formation. We also find that, outside the virial region, the continuum-normalized H$α$ line flux for infalling galaxies with large offsets are on average lower than those with small or no measurable offset, further supporting ram pressure as a dominant quenching mechanism during the initial infall stages.

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preprint2020arXiv

A Deep Retinal Image Quality Assessment Network with Salient Structure Priors

Retinal image quality assessment is an essential prerequisite for diagnosis of retinal diseases. Its goal is to identify retinal images in which anatomic structures and lesions attracting ophthalmologists' attention most are exhibited clearly and definitely while reject poor quality fundus images. Motivated by this, we mimic the way that ophthalmologists assess the quality of retinal images and propose a method termed SalStructuIQA. First, two salient structures for automated retinal quality assessment. One is the large-size salient structures including optic disc region and exudates in large-size. The other is the tiny-size salient structures which mainly include vessels. Then we incorporate the proposed two salient structure priors with deep convolutional neural network (CNN) to shift the focus of CNN to salient structures. Accordingly, we develop two CNN architectures: Dual-branch SalStructIQA and Single-branch SalStructIQA. Dual-branch SalStructIQA contains two CNN branches and one is guided by large-size salient structures while the other is guided by tiny-size salient structures. Single-branch SalStructIQA contains one CNN branch, which is guided by the concatenation of salient structures in both large-size and tiny-size. Experimental results on Eye-Quality dataset show that our proposed Dual-branch SalStructIQA outperforms the state-of-the-art methods for retinal image quality assessment and Single-branch SalStructIQA is much light-weight comparing with state-of-the-art deep retinal image quality assessment methods and still achieves competitive performances.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Combining Compositional Models and Deep Networks For Robust Object Classification under Occlusion

Deep convolutional neural networks (DCNNs) are powerful models that yield impressive results at object classification. However, recent work has shown that they do not generalize well to partially occluded objects and to mask attacks. In contrast to DCNNs, compositional models are robust to partial occlusion, however, they are not as discriminative as deep models. In this work, we combine DCNNs and compositional object models to retain the best of both approaches: a discriminative model that is robust to partial occlusion and mask attacks. Our model is learned in two steps. First, a standard DCNN is trained for image classification. Subsequently, we cluster the DCNN features into dictionaries. We show that the dictionary components resemble object part detectors and learn the spatial distribution of parts for each object class. We propose mixtures of compositional models to account for large changes in the spatial activation patterns (e.g. due to changes in the 3D pose of an object). At runtime, an image is first classified by the DCNN in a feedforward manner. The prediction uncertainty is used to detect partially occluded objects, which in turn are classified by the compositional model. Our experimental results demonstrate that combining compositional models and DCNNs resolves a fundamental problem of current deep learning approaches to computer vision: The combined model recognizes occluded objects, even when it has not been exposed to occluded objects during training, while at the same time maintaining high discriminative performance for non-occluded objects.

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preprint2020arXiv

Compositional Convolutional Neural Networks: A Deep Architecture with Innate Robustness to Partial Occlusion

Recent findings show that deep convolutional neural networks (DCNNs) do not generalize well under partial occlusion. Inspired by the success of compositional models at classifying partially occluded objects, we propose to integrate compositional models and DCNNs into a unified deep model with innate robustness to partial occlusion. We term this architecture Compositional Convolutional Neural Network. In particular, we propose to replace the fully connected classification head of a DCNN with a differentiable compositional model. The generative nature of the compositional model enables it to localize occluders and subsequently focus on the non-occluded parts of the object. We conduct classification experiments on artificially occluded images as well as real images of partially occluded objects from the MS-COCO dataset. The results show that DCNNs do not classify occluded objects robustly, even when trained with data that is strongly augmented with partial occlusions. Our proposed model outperforms standard DCNNs by a large margin at classifying partially occluded objects, even when it has not been exposed to occluded objects during training. Additional experiments demonstrate that CompositionalNets can also localize the occluders accurately, despite being trained with class labels only. The code used in this work is publicly available.

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preprint2020arXiv

Compositional Convolutional Neural Networks: A Robust and Interpretable Model for Object Recognition under Occlusion

Computer vision systems in real-world applications need to be robust to partial occlusion while also being explainable. In this work, we show that black-box deep convolutional neural networks (DCNNs) have only limited robustness to partial occlusion. We overcome these limitations by unifying DCNNs with part-based models into Compositional Convolutional Neural Networks (CompositionalNets) - an interpretable deep architecture with innate robustness to partial occlusion. Specifically, we propose to replace the fully connected classification head of DCNNs with a differentiable compositional model that can be trained end-to-end. The structure of the compositional model enables CompositionalNets to decompose images into objects and context, as well as to further decompose object representations in terms of individual parts and the objects' pose. The generative nature of our compositional model enables it to localize occluders and to recognize objects based on their non-occluded parts. We conduct extensive experiments in terms of image classification and object detection on images of artificially occluded objects from the PASCAL3D+ and ImageNet dataset, and real images of partially occluded vehicles from the MS-COCO dataset. Our experiments show that CompositionalNets made from several popular DCNN backbones (VGG-16, ResNet50, ResNext) improve by a large margin over their non-compositional counterparts at classifying and detecting partially occluded objects. Furthermore, they can localize occluders accurately despite being trained with class-level supervision only. Finally, we demonstrate that CompositionalNets provide human interpretable predictions as their individual components can be understood as detecting parts and estimating an objects' viewpoint.

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preprint2020arXiv

Equivalence of solutions of eikonal equation in metric spaces

In this paper we prove the equivalence between some known notions of solutions to the eikonal equation and more general analogs of the Hamilton-Jacobi equations in complete and rectifiably connected metric spaces. The notions considered are that of curve-based viscosity solutions, slope-based viscosity solutions, and Monge solutions. By using the induced intrinsic (path) metric, we reduce the metric space to a length space and show the equivalence of these solutions to the associated Dirichlet boundary problem. Without utilizing the boundary data, we also localize our argument and directly prove the equivalence for the definitions of solutions. Regularity of solutions related to the Euclidean semi-concavity is discussed as well.

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preprint2020arXiv

Incremental Meta-Learning via Indirect Discriminant Alignment

Majority of the modern meta-learning methods for few-shot classification tasks operate in two phases: a meta-training phase where the meta-learner learns a generic representation by solving multiple few-shot tasks sampled from a large dataset and a testing phase, where the meta-learner leverages its learnt internal representation for a specific few-shot task involving classes which were not seen during the meta-training phase. To the best of our knowledge, all such meta-learning methods use a single base dataset for meta-training to sample tasks from and do not adapt the algorithm after meta-training. This strategy may not scale to real-world use-cases where the meta-learner does not potentially have access to the full meta-training dataset from the very beginning and we need to update the meta-learner in an incremental fashion when additional training data becomes available. Through our experimental setup, we develop a notion of incremental learning during the meta-training phase of meta-learning and propose a method which can be used with multiple existing metric-based meta-learning algorithms. Experimental results on benchmark dataset show that our approach performs favorably at test time as compared to training a model with the full meta-training set and incurs negligible amount of catastrophic forgetting

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preprint2020arXiv

Maps on the Morse boundary

For a proper geodesic metric space $X$, the Morse boundary $\partial_*X$ focuses on the hyperbolic-like directions in the space $X$. It is a quasi-isometry invariant. That is, a quasi-isometry between two hyperbolic spaces induces a homeomorphism on their boundaries. In this paper, we investigate additional structures on the Morse boundary $\partial_*X$ which determine $X$ up to a quasi-isometry. We prove that, for $X$ and $Y$ proper, cocompact spaces, a homeomorphism $f$ between their Morse boundaries is induced by a quasi-isometry if and only if $f$ and $f^{-1}$ are bihölder, or quasi-symmetric, or strongly quasi-conformal.

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preprint2020arXiv

The Dragonfly Wide Field Survey. I. Telescope, Survey Design and Data Characterization

We present a description of the Dragonfly Wide Field Survey (DWFS), a deep photometric survey of a wide area of sky. The DWFS covers 330 $\mathrm{deg}^2$ in the equatorial GAMA fields and the Stripe 82 fields in the SDSS $g$ and $r$ bands. It is carried out with the 48-lens Dragonfly Telephoto Array, a telescope that is optimized for the detection of low surface brightness emission. The main goal of the survey is to study the dwarf galaxy population beyond the Local Group. In this paper, we describe the survey design and show early results. We reach $1σ$ depths of $μ_g\approx 31$ mag arcsec$^{-2}$ on arcminute scales and show that Milky Way satellites such as Sextans, Bootes, and Ursa Major should be detectable out to $D\gtrsim 10$ Mpc. We also provide an overview of the elements and operation of the 48-lens Dragonfly telescope and a detailed description of its data reduction pipeline. The pipeline is fully automated, with individual frames subjected to a rigorous series of quality tests. The sky subtraction is performed in two stages, ensuring that emission features with spatial scales up to $\sim 0.^{\circ}9 \times 0.^{\circ}6$ are preserved. The DWFS provides unparalleled sensitivity to low surface brightness features on arcminute scales.

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preprint2016arXiv

A multiple-relaxation-time lattice Boltzmann model for simulating incompressible axisymmetric thermal flows in porous media

In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating incompressible axisymmetric thermal flows in porous media at the representative elementary volume (REV) scale. In the model, a D2Q9 MRT-LB equation is proposed to solve the flow field in addition to the D2Q5 LB equation for the temperature field. The source terms of the model are simple and contain no velocity and temperature gradient terms. The generalized axisymmetric Navier-Stokes equations for axisymmetric flows in porous media are correctly recovered from the MRT-LB model through the Chapman-Enskog analysis in the moment space. The present model is validated by numerical simulations of several typical axisymmetric thermal problems in porous media. The numerical results agree well with the data reported in the literature, demonstrating the effectiveness and accuracy of the present MRT-LB model for simulating axisymmetric thermal flows in porous media.

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preprint2016arXiv

Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group

In this paper we study viscosity solutions of semilinear parabolic equations in the Heisenberg group. We show uniqueness of viscosity solutions with exponential growth at space infinity. We also study Lipschitz and horizontal convexity preserving properties under appropriate assumptions. Counterexamples show that in general such properties that are well-known for semilinear and fully nonlinear parabolic equations in the Euclidean spaces do not hold in the Heisenberg group.

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preprint2016arXiv

Non-orthogonal multiple-relaxation-time lattice Boltzmann method for incompressible thermal flows

In this paper, a non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method for simulating incompressible thermal flows is presented. In the method, the incompressible Navier-Stokes equations and temperature equation are solved separately by two different MRT-LB equations, which are developed based on non-orthogonal basis vectors obtained from the combinations of the lattice velocity components. The macroscopic governing equations of incompressible thermal flows can be recovered from the method through the Chapman-Enskog analysis in the incompressible limit. Numerical simulations of several typical two-dimensional problems are carried out to validate the proposed method. It is found that the present results are in good agreement with the analytical solutions and/or other numerical results reported in the literature. Furthermore, the non-orthogonal MRT-LB model shows better numerical stability in comparison with the BGK-LB model, and the grid convergence tests indicate that the present MRT-LB method has a second-order convergence rate in space.

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preprint2016arXiv

Numerical modelling of microchannel gas flows in the transition flow regime using the cascaded lattice Boltzmann method

In the CLB method, a Bosanquet-type effective viscosity is employed to account for the rarefaction effect on the gas viscosity. To gain accurate simulations and to match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection boundary scheme with a modified second-order slip boundary condition is adopted in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel (the ratio of the length to the height L/H=100) with pressure boundary condition over a wide range of Knudsen numbers. The influence of the rarefaction effect on the velocity profile, the mass flow rate, and the non-linear pressure deviation distribution along the long microchannel are investigated.

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preprint2015arXiv

Double multiple-relaxation-time lattice Boltzmann model for solid-liquid phase change with natural convection in porous media

In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid phase change interface is traced through the liquid fraction which is determined by the enthalpy method. The model is validated by numerical simulations of conduction melting in a semi-infinite space, solidification in a semi-infinite corner, and convection melting in a square cavity filled with porous media. The numerical results demonstrate the efficiency and accuracy of the present model for simulating transient solid-liquid phase change problems in porous media.

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preprint2015arXiv

Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media

In this paper, a two-dimensional eight-velocity (D2Q8) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman-Forchheimer-extended Darcy formulation. In the model, the porosity is included into the pressure-based equilibrium moments, and the linear and nonlinear drag forces of the porous media are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. Through the Chapman-Enskog analysis, the generalized Navier-Stokes equations can be recovered exactly without artificial compressible errors. Numerical simulations of several typical two-dimensional porous flows are carried out to validate the present MRT-LB model. The numerical results of the present MRT-LB model are in good agreement with the analytical solutions and/or other numerical solutions reported in the literature.

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preprint2014arXiv

Hypersurfaces in projective schemes and a moving lemma

Let X/S be a quasi-projective morphism over an affine base. We develop in this article a technique for proving the existence of closed subschemes H/S of X/S with various favorable properties. We offer several applications of this technique, including the existence of finite quasi-sections in certain projective morphisms, and the existence of hypersurfaces in X/S containing a given closed subscheme C, and intersecting properly a closed set F. Assume now that the base S is the spectrum of a ring R such that for any finite morphism Z -> S, Pic(Z) is a torsion group. This condition is satisfied if R is the ring of integers of a number field, or the ring of functions of a smooth affine curve over a finite field. We prove in this context a moving lemma pertaining to horizontal 1-cycles on a regular scheme X quasi-projective and flat over S. We also show the existence of a finite surjective S-morphism to the projective space P_S^d for any scheme X projective over S when X/S has all its fibers of a fixed dimension d.

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preprint2014arXiv

Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes

We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a general pricing equation where Credit, Debit, Liquidity and Funding Valuation Adjustments (CVA, DVA, LVA and FVA) are introduced by simply modifying the payout cash-flows of the deal. Funding costs and specific close-out procedures at default break the bilateral nature of the deal price and render the valuation problem a non-linear and recursive one. CVA and FVA are in general not really additive adjustments, and the risk for double counting is concrete. We introduce a new adjustment, called a Non-linearity Valuation Adjustment (NVA), to address double-counting. The theoretical risk free rate disappears from our final equations. The framework can be tailored also to CCP trading under initial and variation margins, as explained in detail in Brigo and Pallavicini (2014). In particular, we allow for asymmetric collateral and funding rates, replacement close-out and re-hypothecation. The valuation equation takes the form of a backward stochastic differential equation or semi-linear partial differential equation, and can be cast as a set of iterative equations that can be solved by least-squares Monte Carlo. We propose such a simulation algorithm in a case study involving a generalization of the benchmark model of Black and Scholes for option pricing. Our numerical results confirm that funding risk has a non-trivial impact on the deal price, and that double counting matters too. We conclude the article with an analysis of large scale implications of non-linearity of the pricing equations.

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preprint2014arXiv

The THU-NAOC Transient Survey: the Performance and the First-year Result

The Tsinghua University-National Astronomical Observatories of China (NAOC) Transient Survey (TNTS) is an automatic survey for a systematic exploration of optical transients (OTs), conducted with a 60/90 cm Schmidt telescope at Xinglong station of NAOC. This survey repeatedly covers ~ 1000 square degrees of the north sky with a cadence of 3-4 days. With an exposure of 60 s, the survey reaches a limited unfiltered magnitude of about 19.5 mag. This enables us to discover supernovae at their relatively young stages. In this paper, we describe the overall performance of our survey during the first year and present some preliminary results.

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preprint2014arXiv

Very strong approximation for certain algebraic varieties

Let F be a global field. In this work, we show that the Brauer-Manin condition on adelic points for subvarieties of a torus T over F cuts out exactly the rational points, if either F is a function field or, if F is the field of rational numbers and T is split. As an application, we prove a conjecture of Harari-Voloch over global function fields which states, roughly speaking, that on any rational hyperbolic curve, the local integral points with the Brauer-Manin condition are the global integral points. Finally we prove for tori over number fields a theorem of Stoll on adelic points of zero-dimensional subvarieties in abelian varieties.

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preprint2013arXiv

A Game-Tree approach to discrete infinity Laplacian with running costs

We give a self-contained and elementary proof for boundedness, existence, and uniqueness of solutions to dynamic programming principles (DPP) for biased tug-of-war games with running costs. The domain we work in is very general, and as a special case contains metric spaces. Technically, we introduce game-trees and show that a discretized flow converges uniformly, from which we obtain not only the existence, but also the uniqueness. Our arguments are entirely deterministic, and also do not rely on (semi-)continuity in any way; in particular, we do not need to mollify the DPP at the boundary for well-posedness.

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preprint2013arXiv

A multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media

In this paper, a two-dimensional (2D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating convection heat transfer in porous media at the representative elementary volume scale. In the model, a MRT-LB equation is used to simulate the flow field, while another MRT-LB equation is employed to simulate the temperature field. The effect of the porous media is considered by introducing the porosity into the equilibrium moments, and adding a forcing term to the MRT-LB equation of the flow field in the moment space. The present MRT-LB model is validated by numerical simulations of several 2D convection problems in porous media. The numerical results are in good agreement with the well-documented data reported in the literature.

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preprint2013arXiv

Néron models of algebraic curves

Let S be a Dedekind scheme with field of functions K. We show that if X_K is a smooth connected proper curve of positive genus over K, then it admits a Néron model over S, i.e., a smooth separated model of finite type satisfying the usual Néron mapping property. It is given by the smooth locus of the minimal proper regular model of X_K over S, as in the case of elliptic curves. When S is excellent, a similar result holds for connected smooth affine curves different from the affine line, with locally finite type Néron models.

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preprint2012arXiv

Illustrating a problem in the self-financing condition in two 2010-2011 papers on funding, collateral and discounting

We illustrate a problem in the self-financing condition used in the papers "Funding beyond discounting: collateral agreements and derivatives pricing" (Risk Magazine, February 2010) and "Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs" (The Journal of Credit Risk, 2011). These papers state an erroneous self-financing condition. In the first paper, this is equivalent to assuming that the equity position is self-financing on its own and without including the cash position. In the second paper, this is equivalent to assuming that a subportfolio is self-financing on its own, rather than the whole portfolio. The error in the first paper is avoided when clearly distinguishing between price processes, dividend processes and gain processes. We present an outline of the derivation that yields the correct statement of the self-financing condition, clarifying the structure of the relevant funding accounts, and show that the final result in "Funding beyond discounting" is correct, even if the self-financing condition stated is not.

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preprint2012arXiv

On the Characterization of p-Harmonic Functions on the Heisenberg Group by Mean Value Properties

We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1<p<\infty$, following the scheme described in Manfredi et al. (2009) for the Euclidean case. The new tool that allows us to consider the subelliptic case is a geometric lemma, Lemma 3.2 below, that relates the directions of the points of maxima and minima of a function on a small subelliptic ball with the unit horizontal gradient of that function.

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preprint2012arXiv

On the horizontal Mean Curvature Flow for Axisymmetric surfaces in the Heisenberg Group

We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set equation. An explicit solution is given for the motion starting from a subelliptic sphere. We also give several properties of the level-set method and the mean curvature flow in the Heisenberg group.

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preprint2012arXiv

The index of an algebraic variety

Let K be the field of fractions of a Henselian discrete valuation ring O_K. Let X_K/K be a smooth proper geometrically connected scheme admitting a regular model X/O_K. We show that the index δ(X_K/K) of X_K/K can be explicitly computed using data pertaining only to the special fiber X_k/k of the model X. We give two proofs of this theorem, using two moving lemmas. One moving lemma pertains to horizontal 1-cycles on a regular projective scheme X over the spectrum of a semi-local Dedekind domain, and the second moving lemma can be applied to 0-cycles on an FA-scheme X which need not be regular. The study of the local algebra needed to prove these moving lemmas led us to introduce an invariant γ(A) of a singular local ring (A, \m): the greatest common divisor of all the Hilbert-Samuel multiplicities e(Q,A), over all \m-primary ideals Q in \m. We relate this invariant γ(A) to the index of the exceptional divisor in a resolution of the singularity of Spec(A), and we give a new way of computing the index of a smooth subvariety X_K/K of P^n_K over any field K, using the invariant γof the local ring at the vertex of a cone over X.

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preprint2011arXiv

PostLie algebra structures on the Lie algebra sl(2,C)

The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and integrable systems. We give a complete classification of PostLie algebra structures on the Lie algebra sl(2,C) up to isomorphism. We first reduce the classification problem to solving an equation of 3 x 3 matrices. To solve the latter problem, we make use of the classification of complex symmetric matrices up to the congruent action of orthogonal groups.

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preprint2005arXiv

Stable reduction of finite covers of curves

Let K be the function field of a connected regular scheme S of dimension 1, and let f : X -> Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) greater or equal to 2. Suppose that f can be extended to a finite cover {\mathcal X} -> {\mathcal Y} of semi-stable models over S (it is known that this is always possible up to finite separable extension of K). We prove that there then exists a (unique) minimal such cover. This gives a canonical way to extend X -> Y to a finite cover of semi-stable models over S.

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preprint1998arXiv

Rational points of the group of components of a Neron model

Let A_K be an abelian variety over a discrete valuation field K. Let A be the Neron model of A_K over the ring of integers O_K of K and A_k its special fibre. We study the set of rational points of the group of components ϕ_A of A_k. In particular, we look at the cases where A_K is a Jacobian or where A_K is an abelian variety having semi-stable reduction. We also consider algebraic tori over K instead of abelian varieties.

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