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Jinsong Wu

Publications and source records attributed to Jinsong Wu.

At least 55 records · Page 3Linked to original sources
arXiv2020

Quantum Fourier Analysis

{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform $\FS$, as a map between suitably defined $L^{p}$ spaces, leading to a new uncertainty principle for relative entropy. We cite several applications of the quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a new topological inequality, and we outline several open problems.

math.OA↗
arXiv2020

Intelligent Reflecting Surface Assisted Secure Wireless Communications with Multiple-Transmit and Multiple-Receive Antennas

In this paper, we propose intelligent reflecting surfaces (IRS) assisted secure wireless communications with multi-input and multi-output antennas (IRS-MIMOME). The considered scenario is an access point (AP) equipped with multiple antennas communicates with a multi-antenna enabled legitimate user in the downlink at the present of an eavesdropper configured with multiple antennas. Particularly, the joint optimization of the transmit covariance matrix at the AP and the reflecting coefficients at the IRS to maximize the secrecy rate for the IRS-MIMOME system is investigated, with two different assumptions on the phase shifting capabilities at the IRS, i.e., the IRS has the continuous reflecting coefficients and the IRS has the discrete reflecting coefficients. For the former case, due to the non-convexity of the formulated problem, an alternating optimization (AO)-based algorithm is proposed, i.e., for given the reflecting coefficients at the IRS, the successive convex approximation (SCA)-based algorithm is used to solve the transmit covariance matrix optimization, while given the transmit covariance matrix at the AP, alternative optimization is used again in individually optimizing of each reflecting coefficient at the IRS with other fixed reflecting coefficients. For the individual reflecting coefficient optimization, the close-form or an interval of the optimal solution is provided. Then, the proposed algorithm is extended to the discrete reflecting coefficient model at the IRS. Finally, some numerical simulations have been done to demonstrate that the proposed algorithm outperforms other benchmark schemes.

cs.IT↗
arXiv2019

Antisymmetric characters and Fourier duality

Inspired by the quantum McKay correspondence, we consider the classical $ADE$ Lie theory as a quantum theory over $\mathfrak{sl}_2$. We introduce anti-symmetric characters for representations of quantum groups and investigate the Fourier duality to study the spectral theory. In the $ADE$ Lie theory, there is a correspondence between the eigenvalues of the Coxeter element and the eigenvalues of the adjacency matrix. We formalize related notions and prove such a correspondence for representations of Verlinde algebras of quantum groups: this includes the quiver of any module category acted on by the representation category of any simple Lie algebra $\mathfrak{g}$ at any level $\ell$. This answers an old question posed by Victor Kac in 1994 and a recent comment by Terry Gannon.

math.QA↗
arXiv2019

Similarity Invariants of Essentially normal Cowen-Douglas Operators and Chern Polynomials

In this paper, we systematically study a class of essentially normal operators by using the geometry method from the Cowen-Douglas theory and prove a Brown-Douglas-Fillmore theorem in the Cowen-Douglas theory. More precisely, the Chern polynomials and the second fundamental forms are the similarity invariants (in the sense of Herrero) of this class of essentially normal operators.

math.FA↗
arXiv2019

De Finetti Theorems for Braided Parafermions

The classical de Finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables. This result has application in quantum information. Here we study states that are invariant with respect to a natural action of the braid group, and we emphasize the pictorial formulation and interpretation of our results. We prove a new type of de Finetti theorem for the four-string, double-braid group acting on the parafermion algebra to braid qudits, a natural symmetry in the quon language for quantum information. We prove that a braid-invariant state is extremal if and only if it is a product state. Furthermore, we provide an explicit characterization of braid-invariant states on the parafermion algebra, including finding a distinction that depends on whether the order of the parafermion algebra is square free. We characterize the extremal nature of product states (an inverse de Finetti theorem).

math-ph↗
arXiv2019

Non-commutative Rényi Entropic Uncertainty Principles

In this paper, we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters $0<p,q\leq \infty$. Furthermore, we establish Rényi entropic uncertainty principles for subfactor planar algebras.

math.OA↗
arXiv2019

Analysis on the Empirical Spectral Distribution of Large Sample Covariance Matrix and Applications for Large Antenna Array Processing

This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the channel are fixed. We prove that the empirical spectral distribution (ESD) of the large dimension sample covariance matrix and a well-studied spiked central Wishart matrix converge to the same distribution. As an application, an asymptotic power function is presented for the general likelihood ratio statistics for testing the presence of signal in large array signal processing.

cs.IT↗
arXiv2018

Big Data Meet Cyber-Physical Systems: A Panoramic Survey

The world is witnessing an unprecedented growth of cyber-physical systems (CPS), which are foreseen to revolutionize our world {via} creating new services and applications in a variety of sectors such as environmental monitoring, mobile-health systems, intelligent transportation systems and so on. The {information and communication technology }(ICT) sector is experiencing a significant growth in { data} traffic, driven by the widespread usage of smartphones, tablets and video streaming, along with the significant growth of sensors deployments that are anticipated in the near future. {It} is expected to outstandingly increase the growth rate of raw sensed data. In this paper, we present the CPS taxonomy {via} providing a broad overview of data collection, storage, access, processing and analysis. Compared with other survey papers, this is the first panoramic survey on big data for CPS, where our objective is to provide a panoramic summary of different CPS aspects. Furthermore, CPS {require} cybersecurity to protect {them} against malicious attacks and unauthorized intrusion, which {become} a challenge with the enormous amount of data that is continuously being generated in the network. {Thus, we also} provide an overview of the different security solutions proposed for CPS big data storage, access and analytics. We also discuss big data meeting green challenges in the contexts of CPS.

cs.LG↗
arXiv2018

Information and Communications Technologies for Sustainable Development Goals: State-of-the-Art, Needs and Perspectives

In September 2015, the United Nations General Assembly accepted the 2030 Development Agenda, which has included 92 paragraphs, and the Paragraph 91 defined 17 sustainable development goals (SDGs) and 169 associated targets. The goal of this paper is to discover the correlations among SDGs and information and communications technologies (ICTs). This paper discusses the roles and opportunities that ICTs play in pursuing the SDGs. We identify a number of research gaps to those three pillars, social, economic, and environmental perspectives, of sustainable development. After extensive literature reviews on the SDG-related research initiatives and activities, we find that the majority of contributions to SDGs recognized by the IEEE and ACM research communities have mainly focused on the technical aspects, while there are lack of the holistic social good perspectives. Therefore, there are essential and urgent needs to raise the awareness and call for attentions on how to innovate and energize ICTs in order to best assist all nations to achieve the SDGs by 2030.

cs.CY↗
arXiv2017

Achieve Sustainable Ultra-Dense Heterogeneous Networks for 5G

Due to the exponentially increased demands of mobile data traffic, e.g., a 1000-fold increase in traffic demand from 4G to 5G, network densification is considered as a key mechanism in the evolution of cellular networks, and ultra-dense heterogeneous network (UDHN) is a promising technique to meet the requirements of explosive data traffic in 5G networks. In the UDHN, base station is brought closer and closer to users through densely deploying small cells, which would result in extremely high spectral efficiency and energy efficiency. In this article, we first present a potential network architecture for the UDHN, and then propose a generalized orthogonal/non-orthogonal random access scheme to improve the network efficiency while reducing the signaling overhead. Simulation results demonstrate the effectiveness of the proposed scheme. Finally, we present some of the key challenges of the UDHN.

cs.NI↗
arXiv2017

Local Core Members Aided Community Structure Detection

The relationship of friends in social networks can be strong or weak. Some research works have shown that a close relationship between friends conducts good community structure. Based on this result, we propose an effective method in detecting community structure in social networks based on the closeness of relations among neighbors. This method calculates the gravity between each neighbor node to core nodes, then makes judgement if the node should be classified in the community or not, and finally form the process of community detection. The experimental results show that the proposed method can mine the social structure efficiently with a low computational complexity

cs.SI↗
arXiv2017

A Prediction Model of the Project Life-span in Open Source Software Ecosystem

In nature ecosystems, animal life-spans are determined by genes and some other biological characteristics. Similarly, the software project life-spans are related to some internal or external characteristics. Analyzing the relations between these characteristics and the project life-span, may help developers, investors, and contributors to control the development cycle of the software project. The paper provides an insight on the project life-span for a free open source software ecosystem. The statistical analysis of some project characteristics in GitHub is presented, and we find that the choices of programming languages, the number of files, the label format of the project, and the relevant membership expressions can impact the life-span of a project. Based on these discovered characteristics, we also propose a prediction model to estimate the project life-span in open source software ecosystems. These results may help developers reschedule the project in open source software ecosystem.

cs.SE↗
arXiv2017

Topic-based Integrator Matching for Pull Request

Pull Request (PR) is the main method for code contributions from the external contributors in GitHub. PR review is an essential part of open source software developments to maintain the quality of software. Matching a new PR for an appropriate integrator will make the PR reviewing more effective. However, PR and integrator matching are now organized manually in GitHub. To make this process more efficient, we propose a Topic-based Integrator Matching Algorithm (TIMA) to predict highly relevant collaborators(the core developers) as the integrator to incoming PRs . TIMA takes full advantage of the textual semantics of PRs. To define the relationships between topics and collaborators, TIMA builds a relation matrix about topic and collaborators. According to the relevance between topics and collaborators, TIMA matches the suitable collaborators as the PR integrator.

cs.SE↗
arXiv2017

DevRank: Mining Influential Developers In Github

As the social coding is becoming increasingly popular, understanding the influence of developers can benefit various applications, such as advertisement for new projects and innovations. However, most existing works have focused only on ranking influential nodes in non-weighted and homogeneous networks, which are not able to transfer proper importance scores to the real important node. To rank developers in Github, we define developer's influence on the capacity of attracting attention which can be measured by the number of followers obtained in the future. We further defined a new method, DevRank, which ranks the developers by influence propagation through heterogeneous network constructed according to user behaviors, including "commit" and "follow". Our experiment compares the performance between DevRank and some other link analysis algorithms, the results have shown that DevRank can improve the ranking accuracy.

cs.SI↗
arXiv2017

Block maps and Fourier analysis

We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For the Z2 case, the asymptotic phenomenon of the block map coincides with that of that 2D Ising model. The study of block maps requires a further development of the recent work of the authors on the Fourier analysis of subfactors. We generalize the notion of sum set estimates in additive combinatorics for subfactors and prove the exact inverse sum set theorem. Using this new method, we characterize the extremal pairs of Young's inequality for subfactors, as well as the extremal operators of the Hausdorff-Young inequality.

math.OA↗
arXiv2016

Uncertainty Principles for Kac Algebras

In this paper, we introduce the notation of bi-shift of biprojections in subfactor theory to unimodular Kac algebras. We characterize the minimizers of Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for unimodular Kac algebras with biprojections and prove Hardy's uncertainty principle in terms of minimizers.

math.OA↗
arXiv2015

M$\ddot{o}$bius Disjointness for Exact C$^*$ Algebras

In this paper we introduce the Möbius disjointness for C$^*$-algebras with their automorphisms and studied the Möbius disjointness for finite dimensional C$^*$ algebras, finite von Neumann algebras, reduced free group algebra and canonical anticommutation relation algebra etc.

math.OA↗