arXiv subjects

Rong Du

Publications and source records attributed to Rong Du.

At least 37 records · Page 2Linked to original sources

arXiv2022

Homogeneous ACM bundles on isotropic Grassmannians

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles over isotropic Grassmannians of types $B$, $C$ and $D$ in term of step matrices. We show that there are only finitely many irreducible homogeneous ACM bundles by twisting line bundles over these isotropic Grassmannians. So we classify all homogeneous ACM bundles over isotropic Grassmannians combining the results on usual Grassmannians by Costa and Mir{ó}-Roig. Moreover, if the irreducible initialized homogeneous ACM bundles correspond to some special highest weights, then they can be characterized by succinct forms.

math.AG↗

arXiv2022

Quench dynamics of Bose-Einstein condensates in boxlike traps

We investigate the nonequilibrium dynamics of two-dimensional Bose-Einstein condensates in boxlike traps with power-law potential boundaries by quenching the interatomic interactions. For both concave and convex potentials, we show that ring dark solitons can be excited during the quench dynamics. The modulation strength of the quench and the steepness of the boundary are two main factors affecting the evolution of the system. Five dynamic regimes are identified concerning the number of ring dark solitons excited in the condensate. For the situation without ring dark soliton excitations, the condensate undergoes damped radius oscillation. As far as the appearance of ring dark solitons, interesting structures arise from their decay. For the concave potential, the excitation patterns show a nested structure of vortex-antivortex pairs. For the convex potential, on the other hand, the dynamic excitation patterns display richer structures that have multiple transport behaviors.

nlin.PS↗

arXiv2021

TAGPerson: A Target-Aware Generation Pipeline for Person Re-identification

Nowadays, real data in person re-identification (ReID) task is facing privacy issues, e.g., the banned dataset DukeMTMC-ReID. Thus it becomes much harder to collect real data for ReID task. Meanwhile, the labor cost of labeling ReID data is still very high and further hinders the development of the ReID research. Therefore, many methods turn to generate synthetic images for ReID algorithms as alternatives instead of real images. However, there is an inevitable domain gap between synthetic and real images. In previous methods, the generation process is based on virtual scenes, and their synthetic training data can not be changed according to different target real scenes automatically. To handle this problem, we propose a novel Target-Aware Generation pipeline to produce synthetic person images, called TAGPerson. Specifically, it involves a parameterized rendering method, where the parameters are controllable and can be adjusted according to target scenes. In TAGPerson, we extract information from target scenes and use them to control our parameterized rendering process to generate target-aware synthetic images, which would hold a smaller gap to the real images in the target domain. In our experiments, our target-aware synthetic images can achieve a much higher performance than the generalized synthetic images on MSMT17, i.e. 47.5% vs. 40.9% for rank-1 accuracy. We will release this toolkit\footnote{\noindent Code is available at \href{https://github.com/tagperson/tagperson-blender}{https://github.com/tagperson/tagperson-blender}} for the ReID community to generate synthetic images at any desired taste.

cs.CV↗

arXiv2021

Convolutional discrete Fourier transform method for calculating thermal neutron cross section in liquids

Being exact at both short- and long-time limits, the Gaussian approximation is widely used to calculate neutron incoherent inelastic scattering functions in liquids. However, to overcome a few numerical difficulties, extra physical approximations are often employed to ease the evaluation. In this work, a new numerical method, called convolutional discrete Fourier transform, is proposed to perform Fourier transform of $\exp[-f(t)]$. We have applied this method to compute the differential cross sections of light water up to 10eV. The obtained results, thoroughly benchmarked against experimental data, showed a much higher dynamic range than conventional fast Fourier transform. The calculated integral cross sections agree closely with the light water data in the state-of-the-art nuclear data library. It is in evidence that this numerical method can be used in the place of the extra physical approximations.

physics.comp-ph↗

arXiv2020

Vector Bundles on Rational Homogeneous Spaces

We consider a uniform $r$-bundle $E$ on a complex rational homogeneous space $X$ %over complex number field $\mathbb{C}$ and show that if $E$ is poly-uniform with respect to all the special families of lines and the rank $r$ is less than or equal to some number that depends only on $X$, then $E$ is either a direct sum of line bundles or $δ_i$-unstable for some $δ_i$. So we partially answer a problem posted by Muñoz-Occhetta-Solá Conde. In particular, if $X$ is a generalized Grassmannian $\mathcal{G}$ and the rank $r$ is less than or equal to some number that depends only on $X$, then $E$ splits as a direct sum of line bundles. We improve the main theorem of Muñoz-Occhetta-Solá Conde when $X$ is a generalized Grassmannian by considering the Chow rings. Moreover, by calculating the relative tangent bundles between two rational homogeneous spaces, we give explicit bounds for the generalized Grauert-Mülich-Barth theorem on rational homogeneous spaces.

math.AG↗

arXiv2020

Meta-Key: A Secure Data-Sharing Protocol under Blockchain-Based Decentralised Storage Architecture

In this letter we propose Meta-key, a data-sharing mechanism that enables users share their encrypted data under a blockchain-based decentralized storage architecture. All the data-encryption keys are encrypted by the owner's public key and put onto the blockchain for safe and secure storage and easy key-management. Encrypted data are stored in dedicated storage nodes and proxy re-encryption mechanism is used to ensure secure data-sharing in the untrusted environment. Security analysis of our model shows that the proxy re-encryption adopted in our system is naturally free from collusion-attack due to the specific architecture of Meta-key.

cs.DC↗

arXiv2020

The Internet of Things as a Deep Neural Network

An important task in the Internet of Things (IoT) is field monitoring, where multiple IoT nodes take measurements and communicate them to the base station or the cloud for processing, inference, and analysis. This communication becomes costly when the measurements are high-dimensional (e.g., videos or time-series data). The IoT networks with limited bandwidth and low power devices may not be able to support such frequent transmissions with high data rates. To ensure communication efficiency, this article proposes to model the measurement compression at IoT nodes and the inference at the base station or cloud as a deep neural network (DNN). We propose a new framework where the data to be transmitted from nodes are the intermediate outputs of a layer of the DNN. We show how to learn the model parameters of the DNN and study the trade-off between the communication rate and the inference accuracy. The experimental results show that we can save approximately 96% transmissions with only a degradation of 2.5% in inference accuracy. Our findings have the potentiality to enable many new IoT data analysis applications generating large amount of measurements.

cs.LG↗

arXiv2020

Vector Bundles on Flag varieties

We study vector bundles on flag varieties over an algebraically closed field $k$. In the first part, we suppose $G=G_k(d,n)$ $(2\le d\leq n-d)$ to be the Grassmannian manifold parameterizing linear subspaces of dimension $d$ in $k^n$, where $k$ is an algebraically closed field of characteristic $p>0$. Let $E$ be a uniform vector bundle over $G$ of rank $r\le d$. We show that $E$ is either a direct sum of line bundles or a twist of a pull back of the universal bundle $H_d$ or its dual $H_d^{\vee}$ by a series of absolute Frobenius maps. In the second part, splitting properties of vector bundles on general flag varieties $F(d_1,\cdots,d_s)$ in characteristic zero are considered. We prove a structure theorem for bundles over flag varieties which are uniform with respect to the $i$-th component of the manifold of lines in $F(d_1,\cdots,d_s)$. Furthermore, we generalize the Grauert-M$\ddot{\text{u}}$lich-Barth theorem to flag varieties. As a corollary, we show that any strongly uniform $i$-semistable $(1\le i\le n-1)$ bundle over the complete flag variety splits as a direct sum of special line bundles.

math.AG↗

arXiv2020

Wirelessly-powered Sensor Networks Power Allocation for Channel Estimation and Energy Beamforming

Wirelessly-powered sensor networks (WPSNs) are becoming increasingly important in different monitoring applications. We consider a WPSN where a multiple-antenna base station, which is dedicated for energy transmission, sends pilot signals to estimate the channel state information and consequently shapes the energy beams toward the sensor nodes. Given a fixed energy budget at the base station, in this paper, we investigate the novel problem of optimally allocating the power for the channel estimation and for the energy transmission. We formulate this non-convex optimization problem for general channel estimation and beamforming schemes that satisfy some qualification conditions. We provide a new solution approach and a performance analysis in terms of optimality and complexity. We also present a closed-form solution for the case where the channels are estimated based on a least square channel estimation and a maximum ratio transmit beamforming scheme. The analysis and simulations indicate a significant gain in terms of the network sensing rate, compared to the fixed power allocation, and the importance of improving the channel estimation efficiency.

cs.NI↗

arXiv2019

Matrix Bloom Filter: An Efficient Probabilistic Data Structure for 2-tuple Batch Lookup

With the growing scale of big data, probabilistic structures receive increasing popularity for efficient approximate storage and query processing. For example, Bloom filters (BF) can achieve satisfactory performance for approximate membership existence query at the expense of false positives. However, a standard Bloom filter can only handle univariate data and single membership existence query, which is insufficient for OLAP and machine learning applications. In this paper, we focus on a common multivariate data type, namely, 2-tuples, or equivalently, key-value pairs. We design the matrix Bloom filter as a high-dimensional extension of the standard Bloom filter. This new probabilistic data structure can not only insert and lookup a single 2-tuple efficiently, but also support these operations efficiently in batches --- a key requirement for OLAP and machine learning tasks. To further balance the insertion and query efficiency for different workload patterns, we propose two variants, namely, the maximum adaptive matrix BF and minimum storage matrix BF. Through both theoretical and empirical studies, we show the performance of matrix Bloom filter is superior on datasets with common statistical distributions; and even without them, it just degrades to a standard Bloom filter.

cs.DS↗

arXiv2018

Inequalities of Chern classes on nonsingular projective $n$-folds of Fano and general type with ample canonical bundle

Let $X$ be a nonsingular projective $n$-fold $(n\ge 2)$ of Fano or of general type with ample canonical bundle $K_X$ over an algebraic closed field $κ$ of any characteristic. We produce a new method to give a bunch of inequalities in terms of all the Chern classes $c_1, c_2, \cdots, c_n$ by pulling back Schubert classes in the Chow group of Grassmannian under the Gauss map. Moreover, we show that if the characteristic of $κ$ is $0$, then the Chern ratios $(\frac{c_{2,1^{n-2}}}{c_{1^n}}, \frac{c_{2,2,1^{n-4}}}{c_{1^n}}, \cdots, \frac{c_{n}}{c_{1^n}})$ are contained in a convex polyhedron for all $X$. So we give an affirmative answer to a generalized open question, that whether the region described by the Chern ratios is bounded, posted by Hunt (\cite{Hun}) to all dimensions. As a corollary, we can get that there exist constants $d_1$, $d_2$, $d_3$ and $d_4$ depending only on $n$ such that $d_1K_X^n\leχ_{top}(X)\le d_2 K_X^n$ and $d_3K_X^n\leχ(X, \mathscr{O}_X)\le d_4 K_X^n$. If the characteristic of $κ$ is positive, $K_X$ (or $-K_X$) is ample and $\mathscr{O}_X(K_X)$ ($\mathscr{O}_X(-K_X)$, respectively) is globally generated, then the same results hold.

math.AG↗

arXiv2018

Normal bundles on the exceptional sets of simple small resolutions

We study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $\mathbb{Z}$ and the normal bundle of it has some good filtration. In particular, for the exceptional set is a projective space with the split normal bundle, we generalized Nakayama and Ando's results to higher dimension. Moreover, we also generalize Laufer's results of rationality and embedding dimension to higher dimension.

math.AG↗

arXiv2018

Modular quotient varieties and singularities by the cyclic group of order $2p$

We classify all $n$-dimensional reduced Cohen-Macaulay modular quotient variety $\mathbb{A}_\mathbb{F}^n/C_{2p}$ and study their singularities, where $p$ is a prime number and $C_{2p}$ denotes the cyclic group of order $2p$. In particular, we present an example that demonstrates that the problem proposed by Yasuda \cite[Problem 6.6]{Yas2015} has a negative answer if the condition that "$G$ is a small subgroup" was dropped.

math.AG↗

arXiv2017

Smooth solution to higher dimensional complex Plateau problem

Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\mathbb{C}^{N}$. For $n\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups in 1981. In this paper, we generalize Yau's conjecture on some numerical invariant of every isolated surface singularity defined by Yau and the author to any dimension and prove that the conjecture is true for local complete intersection singularities of dimension $n\ge 3$. As a direct application, we solved complex Plateau problem of hypersurface type for any dimension $n\ge 3$ by checking only one numerical invariant.

math.AG↗

arXiv2017

On Maximizing Sensor Network Lifetime by Energy Balancing

Many physical systems, such as water/electricity distribution networks, are monitored by battery-powered Wireless Sensor Networks (WSNs). Since battery replacement of sensor nodes is generally difficult, long-term monitoring can be only achieved if the operation of the WSN nodes contributes to a long WSN lifetime. Two prominent techniques to long WSN lifetime are i) optimal sensor activation and ii) efficient data gathering and forwarding based on compressive sensing. These techniques are feasible only if the activated sensor nodes establish a connected communication network (connectivity constraint), and satisfy a compressive sensing decoding constraint (cardinality constraint). These two constraints make the problem of maximizing network lifetime via sensor node activation and compressive sensing NP-hard. To overcome this difficulty, an alternative approach that iteratively solves energy balancing problems is proposed. However, understanding whether maximizing network lifetime and energy balancing problems are aligned objectives is a fundamental open issue. The analysis reveals that the two optimization problems give different solutions, but the difference between the lifetime achieved by the energy balancing approach and the maximum lifetime is small when the initial energy at sensor nodes is significantly larger than the energy consumed for a single transmission. The lifetime achieved by the energy balancing is asymptotically optimal, and that the achievable network lifetime is at least $50$\% of the optimum. Analysis and numerical simulations quantify the efficiency of the proposed energy balancing approach.

eess.SY↗

arXiv2017

Data Reduction for Time-of-Flight Small-Angle Neutron Scattering with Virtual Neutrons

Small-angle neutron scattering (SANS) is an experimental technique to detect material structures in the nanometer to micrometer range. The solution of the structural model constructed from SANS strongly depends on the accuracy of the reduced data. The time-of-flight (TOF) SANS data are dependent on the wavelength of the pulsed neutron source. Therefore, data reduction must be handled very carefully to transform measured neutron events into neutron scattering intensity. In this study, reduction algorithms for TOF SANS data are developed and optimized using simulated data from a virtual neutron experiment. Each possible effect on the measured data is studied systematically, and suitable corrections are performed to obtain high-quality data. This work will facilitate scientific research and the instrument design at China Spallation Neutron Source.

physics.ins-det↗

arXiv2017

The Virtual Neutron Experiment for TOF Neutron Reflectometer

A general virtual neutron experiment for TOF neutron reflectometer was introduced, including instrument simulation, sample modeling, detector simulation and data reduction to mimic the routine of real experimental process and data reduction. The reduced data fit quite well with the sample simulation, confirming the reliability of our algorithm and the smearing effect was analyzed. Methodology and algorithms developed in this study paves the way for the future development of data processing and data reduction software for the TOF neutron reflectometers in China Spallation Neutron Source (CSNS). Details of the virtual experiment and performance of the instrument was demonstrated.

physics.ins-det↗

arXiv2016

On the canonical maps of nonsingular threefolds of general type

Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric genus of $S$ and discussed the canonical degrees for these two cases. We generalize his results to nonsingular minimal complex projective threefolds.

math.AG↗