arXiv subjects

Lu Wei

Publications and source records attributed to Lu Wei.

At least 55 records · Page 3Linked to original sources

arXiv2022

Spatio-Temporal Federated Learning for Massive Wireless Edge Networks

This paper presents a novel approach to conduct highly efficient federated learning (FL) over a massive wireless edge network, where an edge server and numerous mobile devices (clients) jointly learn a global model without transporting the huge amount of data collected by the mobile devices to the edge server. The proposed FL approach is referred to as spatio-temporal FL (STFL), which jointly exploits the spatial and temporal correlations between the learning updates from different mobile devices scheduled to join STFL in various training epochs. The STFL model not only represents the realistic intermittent learning behavior from the edge server to the mobile devices due to data delivery outage, but also features a mechanism of compensating loss learning updates in order to mitigate the impacts of intermittent learning. An analytical framework of STFL is proposed and employed to study the learning capability of STFL via its convergence performance. In particular, we have assessed the impact of data delivery outage, intermittent learning mitigation, and statistical heterogeneity of datasets on the convergence performance of STFL. The results provide crucial insights into the design and analysis of STFL-based wireless networks.

cs.LG↗

arXiv2022

Toward Ubiquitous and Flexible Coverage of UAV-IRS-Assisted NOMA Networks

This paper studies how to achieve a high and flexible coverage performance of a large-scale cellular network that enables unmanned aerial vehicles (UAVs) for non-orthogonal multiple access (NOMA) transmission to simultaneously serve multiple users. The considered cellular network consists of a tier of base stations and a tier of UAVs. Each UAV is mounted with an intelligent reflecting surface (IRS) in order to serve as an aerial IRS reflecting signals between a base station and a user in the network. All the UAVs in the network are deployed based on a newly proposed three-dimensional (3D) point process that leads to a tractable and accurate analysis of the association statistics, which is traditionally difficult to analyze due to the mobility of UAVs. In light of this, we are able to analyze the downlink coverage of UAV-IRS-assisted NOMA transmission for two users and derive the corresponding coverage probabilities. Our coverage analyses shed light on the optimal allocations of transmit power between NOMA users and UAVs to accomplish the goal of ubiquitous and flexible NOMA transmission. We also conduct numerical simulations to validate our coverage analytical results while demonstrating the improved coverage performance achieved by aerial IRSs.

cs.NI↗

arXiv2021

Second-order statistics of fermionic Gaussian states

We study the statistical behavior of entanglement in quantum bipartite systems over fermionic Gaussian states as measured by von Neumann entropy and entanglement capacity. The focus is on the variance of von Neumann entropy and the mean entanglement capacity that belong to the so-defined second-order statistics. The main results are the exact yet explicit formulas of the two considered second-order statistics for fixed subsystem dimension differences. We also conjecture the exact variance of von Neumann entropy valid for arbitrary subsystem dimensions. Based on the obtained results, we analytically study the numerically observed phenomena of Gaussianity of von Neumann entropy and linear growth of average capacity.

math-ph↗

arXiv2021

Systematic definition and classification of data anomalies in DBMS (English Version)

There is no unified definition of Data anomalies, which refers to the specific data operation mode that may violate the consistency of the database. Known data anomalies include Dirty Write, Dirty Read, Non-repeatable Read, Phantom, Read Skew and Write Skew, etc. In order to improve the efficiency of concurrency control algorithms, data anomalies are also used to define the isolation levels, because the weak isolation level can improve the efficiency of transaction processing systems. This paper systematically studies the data anomalies and the corresponding isolation levels. We report twenty-two new data anomalies that other papers have not reported, and all data anomalies are classified miraculously. Based on the classification of data anomalies, two new isolation levels systems with different granularity are proposed, which reveals the rule of defining isolation levels based on data anomalies and makes the cognition of data anomalies and isolation levels more concise.

cs.DB↗

arXiv2021

Kurtosis of von Neumann entanglement entropy

In this work, we study the statistical behavior of entanglement in quantum bipartite systems under the Hilbert-Schmidt ensemble as assessed by the standard measure - the von Neumann entropy. Expressions of the first three exact cumulants of von Neumann entropy are known in the literature. The main contribution of the present work is the exact formula of the corresponding fourth cumulant that controls the tail behavior of the distribution. As a key ingredient in deriving the result, we make use of newly observed unsimplifiable summation bases that lead to a complete cancellation. In addition to providing further evidence of the conjectured Gaussian limit of the von Neumann entropy, the obtained formula also provides an improved finite-size approximation to the distribution.

quant-ph↗

arXiv2021

Moments of quantum purity and biorthogonal polynomial recurrence

The Bures-Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statistical behavior of entanglement over the Bures-Hall ensemble as measured by the simplest form of an entanglement entropy - the quantum purity. The main results of this work are the exact second and third moment expressions of quantum purity valid for any subsystem dimensions, where the corresponding results in the literature are limited to the scenario of equal subsystem dimensions. In obtaining the results, we have derived recurrence relations of the underlying integrals over the Cauchy-Laguerre biorthogonal polynomials that may be of independent interest.

math-ph↗

arXiv2021

Exploring the effect of social media and spatial characteristics during the COVID-19 pandemic in China

The declaration of COVID-19 as a pandemic has largely amplified the spread of related information on social media, such as Twitter, Facebook, and WeChat.Unlike the previous studies which focused on how to detect the misinformation or fake news related toCOVID-19, we investigate how the disease and information co-evolve in the population. We focus onCOVID-19and its information during the period when the disease was widely spread in China, i.e., from January 25th to March 24th, 2020. We first explore how the disease and information co-evolve via the spatial analysis of the two spreading processes. We visualize the geo-location of both disease and information at the province level and find that disease is more geo-localized compared to information. We find a high correlation between the disease and information data, and also people care about the spread only when it comes to their neighborhood. Regard to the content of the information, we find that positive messages are more negatively correlated with the disease compared to negative and neutral messages. Additionally, we introduce machine learning algorithms, i.e., linear regression and random forest, to further predict the number of infected using different disease spatial related and information-related characteristics. We obtain that the disease spatial related characteristics of nearby cities can help to improve the prediction accuracy. Meanwhile, information-related characteristics can also help to improve the prediction performance, but with a delay, i.e., the improvement comes from using, for instance, the number of messages 10 days ago, for disease prediction. The methodology proposed in this paper may shed light on new clues of emerging infections

physics.soc-ph↗

arXiv2021

Quantum advantages of communication complexity from Bell nonlocality

Communication games are crucial tools for investigating the limitations of physical theories. The communication complexity (CC) problem is a typical example, for which several distributed parties attempt to jointly calculate a given function with limited classical communications. In this work, we present a method to construct CC problems from Bell tests in a graph-theoretic way. Starting from an experimental compatibility graph and the corresponding Bell test function, a target function which encodes the information of each edge can be constructed, then using this target function we could construct an CC function for which by pre-sharing entangled states, the success probability will exceed that for arbitrary classical strategy. The non-signaling protocol based on Popescu-Rohrlich box is also discussed, and the success probability in this case would reach one.

quant-ph↗

arXiv2020

Exact variance of von Neumann entanglement entropy over the Bures-Hall measure

The Bures-Hall distance metric between quantum states is a unique measure that satisfies various useful properties for quantum information processing. In this work, we study the statistical behavior of quantum entanglement over the Bures-Hall ensemble as measured by von Neumann entropy. The average von Neumann entropy over such an ensemble has been recently obtained, whereas the main result of this work is an explicit expression of the corresponding variance that specifies the fluctuation around its average. The starting point of the calculations is the connection between correlation functions of the Bures-Hall ensemble and these of the Cauchy-Laguerre ensemble. The derived variance formula, together with the known mean formula, leads to a simple but accurate Gaussian approximation to the distribution of von Neumann entropy of finite-size systems. This Gaussian approximation is also conjectured to be the limiting distribution for large dimensional systems.

math-ph↗

arXiv2020

Entanglement Area Law for Shallow and Deep Quantum Neural Network States

A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understanding the power of neural networks and show that image classification problems which can be efficiently solved must obey the area law.

quant-ph↗

arXiv2020

Proof of Sarkar-Kumar's Conjectures on Average Entanglement Entropies over the Bures-Hall Ensemble

Sarkar and Kumar recently conjectured [J. Phys. A: Math. Theor. $\textbf{52}$, 295203 (2019)] that for a bipartite system of Hilbert dimension $mn$, the mean values of quantum purity and von Neumann entropy of a subsystem of dimension $m\leq n$ over the Bures-Hall measure are given by \begin{equation*} \frac{2n(2n+m)-m^{2}+1}{2n(2mn-m^2+2)} \end{equation*} and \begin{equation*} ψ_{0}\left(mn-\frac{m^2}{2}+1\right)-ψ_{0}\left(n+\frac{1}{2}\right), \end{equation*} respectively, where $ψ_{0}(\cdot)$ is the digamma function. We prove the above conjectured formulas in this work. A key ingredient of the proofs is Forrester and Kieburg's discovery on the connection between the Bures-Hall ensemble and the Cauchy-Laguerre biorthogonal ensemble studied by Bertola, Gekhtman, and Szmigielski.

math-ph↗

arXiv2019

Skewness of von Neumann entanglement entropy

We study quantum bipartite systems in a random pure state, where von Neumann entropy is considered as a measure of the entanglement. Expressions of the first and second exact cumulants of von Neumann entropy, relevant respectively to the average and fluctuation behavior, are known in the literature. The focus of this paper is on its skewness that specifies the degree of asymmetry of the distribution. Computing the skewness requires additionally the third cumulant, an exact formula of which is the main result of this work. In proving the main result, we obtain as a byproduct various summation identities involving polygamma and related functions. The derived third cumulant also leads to an improved approximation to the distribution of von Neumann entropy.

cs.IT↗

arXiv2019

A note on Bianchi-Donà's proof to the variance formula of von Neumann entropy

Bianchi and Donà [1] have recently reported a proof to the variance formula of von Neumann entropy, which was conjectured in [2] and firstly proved in [3]. The purpose of this short note is to show that, despite having a different starting point, the subsequent calculations (omitted in [1]) leading to the result are essentially the same as in [3].

cs.IT↗

arXiv2019

Ergodic MIMO Mutual Information: Twenty Years After Emre Telatar

In the celebrated work of Emre Telatar in the year 1999 (14274 citations to date), it was shown that the expected value of the mutual information \begin{equation*} \mathrm{I} = \ln\det\left( \mathbf{I}_m + \frac{1}{t} \mathbf{HH}^{\dagger} \right) \end{equation*} of an $m\times n$ MIMO Rayleigh channel matrix $\mathbf{H}$ with a SNR $1/t$ can be represented as an integral involving Laguerre polynomials. We show, in this work, that Telatar's integral representation can be explicitly evaluated to a finite sum of the form \begin{equation*} \mathbb{E}\!\left[\mathrm{I}\right]=\sum_{k=0}^{n+m-3}a_{k}t^{k}+\rm e^{t}~\text{Ei}(-t)\sum_{k=0}^{n+m-2}b_{k}t^{k},, \end{equation*} where $\text{Ei}(-t)$ is the exponential integral and $a_{k}$, $b_{k}$ are known constants that do not dependent on $t$. The renewed interest in this classical information theory problem came from, quite surprisingly, the recent development in quantum information theory.

cs.IT↗

arXiv2018

On the exact variance of Tsallis entropy in a random pure state

Tsallis entropy is a useful one-parameter generalization of the standard von Neumann entropy in information theory. We study the variance of Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proved variance formula of von Neumann entropy based on the derived moment relation to the Tsallis entropy.

math-ph↗

arXiv2017

Density of Spherically-Embedded Stiefel and Grassmann Codes

The density of a code is the fraction of the coding space covered by packing balls centered around the codewords. This paper investigates the density of codes in the complex Stiefel and Grassmann manifolds equipped with the chordal distance. The choice of distance enables the treatment of the manifolds as subspaces of Euclidean hyperspheres. In this geometry, the densest packings are not necessarily equivalent to maximum-minimum-distance codes. Computing a code's density follows from computing: i) the normalized volume of a metric ball and ii) the kissing radius, the radius of the largest balls one can pack around the codewords without overlapping. First, the normalized volume of a metric ball is evaluated by asymptotic approximations. The volume of a small ball can be well-approximated by the volume of a locally-equivalent tangential ball. In order to properly normalize this approximation, the precise volumes of the manifolds induced by their spherical embedding are computed. For larger balls, a hyperspherical cap approximation is used, which is justified by a volume comparison theorem showing that the normalized volume of a ball in the Stiefel or Grassmann manifold is asymptotically equal to the normalized volume of a ball in its embedding sphere as the dimension grows to infinity. Then, bounds on the kissing radius are derived alongside corresponding bounds on the density. Unlike spherical codes or codes in flat spaces, the kissing radius of Grassmann or Stiefel codes cannot be exactly determined from its minimum distance. It is nonetheless possible to derive bounds on density as functions of the minimum distance. Stiefel and Grassmann codes have larger density than their image spherical codes when dimensions tend to infinity. Finally, the bounds on density lead to refinements of the standard Hamming bounds for Stiefel and Grassmann codes.

cs.IT↗

arXiv2017

A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy

It was recently conjectured by Vivo, Pato, and Oshanin [Phys. Rev. E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\leq n$ is given by \begin{equation*} -ψ_{1}\left(mn+1\right)+\frac{m+n}{mn+1}ψ_{1}\left(n\right)-\frac{(m+1)(m+2n+1)}{4n^{2}(mn+1)}, \end{equation*} where $ψ_{1}(\cdot)$ is the trigamma function. We give a proof of this formula.

math-ph↗

arXiv2016

Asymptotic Matrix Variate von-Mises Fisher and Bingham Distributions with Applications

Probability distributions in Stiefel manifold such as the von-Mises Fisher and Bingham distributions find diverse applications in signal processing and other applied sciences. Use of these statistical models in practice is complicated by the difficulties in numerical evaluation of their normalization constants. In this letter, we derive asymptotical approximations to the normalization constants via recent results in random matrix theory. The derived approximations take simple forms and are reasonably accurate in regimes of practical interest. As an application, we show that the proposed analytical results lead to a remarkably reduction of the sampling complexity compared to existing simulation based approaches.

math.ST↗