arXiv subjects

Sheng Chen

Publications and source records attributed to Sheng Chen.

193 records · Page 11Linked to original sources

arXiv2015

Super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras

The purpose of this paper is to introduce and study super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing super Hom-Gel'fand-Dorfman bialgebras and obtain some infinite-dimensional Hom-Lie superalgebras from affinization of super Hom-Gel'fand-Dorfman bialgebras. Also, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish equivalence of quadratic Hom-Lie conformal superalgebras and super Hom-Gel'fand-Dorfman bialgebras. Finally, we characterize one-dimensional central extensions of quadratic Hom-Lie conformal superalgebras by using certain bilinear forms of super Hom-Gel'fand-Dorfman bialgebras.

math.QA↗

arXiv2015

Soft Pilot Reuse and Multi-Cell Block Diagonalization Precoding for Massive MIMO Systems

The users at cell edge of a massive multiple-input multiple-output (MIMO) system suffer from severe pilot contamination, which leads to poor quality of service (QoS). In order to enhance the QoS for these edge users, soft pilot reuse (SPR) combined with multi-cell block diagonalization (MBD) precoding are proposed. Specifically, the users are divided into two groups according to their large-scale fading coefficients, referred to as the center users, who only suffer from modest pilot contamination and the edge users, who suffer from severe pilot contamination. Based on this distinction, the SPR scheme is proposed for improving the QoS for the edge users, whereby a cell-center pilot group is reused for all cell-center users in all cells, while a cell-edge pilot group is applied for the edge users in the adjacent cells. By extending the classical block diagonalization precoding to a multi-cell scenario, the MBD precoding scheme projects the downlink transmit signal onto the null space of the subspace spanned by the inter-cell channels of the edge users in adjacent cells. Thus, the inter-cell interference contaminating the edge users' signals in the adjacent cells can be efficiently mitigated and hence the QoS of these edge users can be further enhanced. Our theoretical analysis and simulation results demonstrate that both the uplink and downlink rates of the edge users are significantly improved, albeit at the cost of the slightly decreased rate of center users.

cs.IT↗

arXiv2015

Generalized Dantzig Selector: Application to the k-support norm

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS, and non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian width of unit norm ball and suitable set encompassing estimation error. Further, we consider a non-trivial example of the GDS using $k$-support norm. We derive an efficient method to compute the proximal operator for $k$-support norm since existing methods are inapplicable in this setting. For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the $k$-support norm. The experimental results confirm our theoretical analysis.

stat.ML↗

arXiv2015

A Survey of directed graphs invariants

In this paper, various kinds of invariants of directed graphs are summarized. In the first topic, the invariant w(G) for a directed graph G is introduced, which is primarily defined by S. Chen and X.M. Chen to solve a problem of weak connectedness of tensor product of two directed graphs. Further, we present our recent studies on the invariant w(G) in categorical view. In the second topic, Homology theory on directed graph is introduced, and we also cast on categorical view of the definition. The third topic mainly focuses on Laplacians on graphs, including traditional work and latest result of 1-laplacian by K.C.Chang. Finally, Zeta functions and Graded graphs are introduced, inclduing Bratteli-Vershik diagram, dual graded graphs and differential posets, with some applications in dynamic system.

math.CO↗

arXiv2014

Cross-Layer Software-Defined 5G Network

In the past few decades, the world has witnessed a rapid growth in mobile communication and reaped great benefits from it. Even though the fourth generation (4G) mobile communication system is just being deployed worldwide, proliferating mobile demands call for newer wireless communication technologies with even better performance. Consequently, the fifth generation (5G) system is already emerging in the research field. However, simply evolving the current mobile networks can hardly meet such great expectations, because over the years the infrastructures have generally become ossified, closed, and vertically constructed. Aiming to establish a new paradigm for 5G mobile networks, in this article, we propose a cross-layer software-defined 5G network architecture. By jointly considering both the network layer and the physical layer together, we establish the two software-defined programmable components, the control plane and the cloud computing pool, which enable an effective control of the mobile network from the global perspective and benefit technological innovations. Specifically, by the cross-layer design for software-defining, the logically centralized and programmable control plane abstracts the control functions from the network layer down to the physical layer, through which we achieve the fine-grained controlling of mobile network, while the cloud computing pool provides powerful computing capability to implement the baseband data processing of multiple heterogeneous networks. We discuss the main challenges of our architecture, including the fine-grained control strategies, network virtualization, and programmability. The architecture significantly benefits the convergence towards heterogeneous networks and it enables much more controllable, programmable and evolvable mobile networks.

cs.NI↗

arXiv2014

Generalized Jacobi Functions and Their Applications to Fractional Differential Equations

In this paper, we consider spectral approximation of fractional differential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi functions (GJFs), which is intrinsically related to fractional calculus, and can serve as natural basis functions for properly designed spectral methods for FDEs. We establish spectral approximation results for these GJFs in weighted Sobolev spaces involving fractional derivatives. We construct efficient GJF-Petrov-Galerkin methods for a class of prototypical fractional initial value problems (FIVPs) and fractional boundary value problems (FBVPs) of general order, and show that with an appropriate choice of the parameters in GJFs, the resulted linear systems can be sparse and well-conditioned. Moreover, we derive error estimates with convergence rate only depending on the smoothness of data, so truly spectral accuracy can be attained if the data are smooth enough. The idea and results presented in this paper will be useful to deal with more general FDEs associated with Riemann-Liouville or Caputo fractional derivatives.

math.NA↗

arXiv2010

Generalized Ehrhart polynomials

Let $P$ be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations $P(n) = nP$ is a quasi-polynomial in $n$. We generalize this theorem by allowing the vertices of P(n) to be arbitrary rational functions in $n$. In this case we prove that the number of lattice points in P(n) is a quasi-polynomial for $n$ sufficiently large. Our work was motivated by a conjecture of Ehrhart on the number of solutions to parametrized linear Diophantine equations whose coefficients are polynomials in $n$, and we explain how these two problems are related.

math.CO↗

arXiv2010

Radiation-driven Implosion in the Cepheus B Molecular Cloud

We analyze large scale mapping observations of the molecular lines in the 12CO (J=2-1), 12CO (J=3-2), 13CO (J=2-1), and 13CO (J=3-2) transition emissions toward the Cepheus B molecular cloud with the KOSMA 3m-telescope. The integrated intensity map of the 12CO (J=2-1) transition has shown a structure with a compact core and a compact ridge extended in the north-west of the core. The cloud is surrounded by an optically bright rim, where the radiation-driven implosion (RDI) may greatly change the gas properties. The intensities of the CO (J=3-2) transition are higher than those of the CO (J=2-1) transition along the rim area.We find characteristic RDI structure in positionvelocity diagrams. Non-LTE Large velocity gradient (LVG) model analysis shows that the density and temperature at the edge are higher than that in the center. Our results provide evidences that RDI is taking place in Cepheus B molecular cloud.

astro-ph.SR↗

arXiv2008

High-Resolution Observations of Molecular Lines toward the Hot Core G28.20-0.04N

We present the results from arcsecond resolution observations of various line transitions at 1.3 mm toward hypercompact HII region G28.20-0.04N. With the SMA data, we have detected and mapped the transitions in the CH$_{3}$CN, CO, $^{13}$CO, SO$_{2}$, OCS, and CH$_{3}$OH molecular lines as well as the radio recombination line H30$α$. The observations and analysis indicate a hot core associated with G28.20-0.04N. The outflow and possible rotation are detected in this region.

astro-ph↗

arXiv2007

On Algebraic Shift Equivalence of Matrices over Polynomial Rings

The paper studies algebraic strong shift equivalence of matrices over $n$-variable polynomial rings over a principal ideal domain $D$($n\leq 2$). It is proved that in the case $n=1$, every non-zero matrix over $D[x]$ has a full rank factorization and every non-nilpotent matrix over $D[x]$ is algebraically strong shift equivalent to a nonsingular matrix. In the case $n=2$, an example of non-nilpotent matrix over $\mathbb{R}[x,y,z]=\mathbb{R}[x][y,z]$, which can not be algebraically shift equivalent to a nonsingular matrix, is given.

math.RA↗

arXiv2007

On a Conjecture about the Number of Solutions to Linear Diophantine Equations with a Positive Integer Parameter

Let A(n) be a $k\times s$ matrix and $m(n)$ be a $k$ dimensional vector, where all entries of A(n) and $m(n)$ are integer-valued polynomials in $n$. Suppose that $$t(m(n)|A(n))=#\{x\in\mathbb{Z}_{+}^{s}\mid A(n)x=m(n)\}$$ is finite for each $n\in \mathbb{N}$, where $Z_+$ is the set of nonnegative integers. This paper conjectures that $t(m(n)|A(n))$ is an integer-valued quasi-polynomial in $n$ for $n$ sufficiently large and verifies the conjecture in several cases.

math.CO↗

arXiv2007

On Popoviciu type tormulas for generalized restricted partition function

Suppose that $a_1(n),a_2(n),...,a_s(n),m(n)$ are integer-valued polynomials in $n$ with positive leading coefficients. This paper presents Popoviciu type formulas for the generalized restricted partition function $$p_{A(n)}(m(n)):=#\{(x_1,...,x_s)\in \mathbb{Z}^{s}: all x_j\geqslant 0, x_1a_1(n)+...+x_sa_s(n)=m(n) \}$$ when $s=2$ or 3. In either case, the formula implies that the function is an integer-valued quasi-polynomial. The main result is proved by a reciprocity law for a class of fractional part sums and the theory of generalized Euclidean division.

math.NT↗

arXiv2007

On the Ring of Integer-valued Quasi-polynomials

The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and Smith normal form of integral matrices with integer parameters are also given.

math.NT↗