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Ligong Wang

Publications and source records attributed to Ligong Wang.

At least 109 records · Page 6Linked to original sources
arXiv2016

Some upper bounds for the signless Laplacian spectral radius of digraphs

Let $G=(V(G) ,E(G))$ be a digraph without loops and multiarcs, where $V(G)=\{v_1,v_2,\ldots,v_n\}$ and $E(G)$ are the vertex set and the arc set of $G$, respectively. Let $d_i^{+}$ be the outdegree of the vertex $v_i$. Let $A(G)$ be the adjacency matrix of $G$ and $D(G)=\textrm{diag}(d_1^{+},d_2^{+},\ldots,d_n^{+})$ be the diagonal matrix with outdegrees of the vertices of $G$. Then we call $Q(G)=D(G)+A(G)$ the signless Laplacian matrix of $G$. The spectral radius of $Q(G)$ is called the signless Laplacian spectral radius of $G$, denoted by $q(G)$. In this paper, some upper bounds for $q(G)$ are obtained. Furthermore, some upper bounds on $q(G)$ involving outdegrees and the average 2-outdegrees of the vertices of $G$ are also derived.

math.CO↗
arXiv2016

Distance signless Laplacian spectral radius and Hamiltonian properties of graphs

In this paper, first, we establish a sufficient condition for a bipartite graph to be Hamilton-connected. Furthermore, we also give two sufficient conditions on distance signless Laplacian spectral radius for a graph to be Hamilton-connected and traceable from every vertex, respectively. Last, we obtain a sufficient condition for a graph to be Hamiltonian in terms of the distance signless Laplacian spectral radius of $G^{C}$.

math.CO↗
arXiv2016

Minimal Skew energy of oriented bicyclic graphs with a given diameter

Let $S(G^σ)$ be the skew-adjacency matrix of the oriented graph $G^σ$, which is obtained from a simple undirected graph $G$ by assigning an orientation $σ$ to each of its edges. The skew energy of an oriented graph $G^σ$ is defined as the sum of absolute values of all eigenvalues of $S(G^σ)$. For any positive integer $d$ with $3\leq d\leq n-3$, we determine the graph with minimal skew energy among all oriented bicyclic graphs that contain no vertex disjoint odd cycle of lengths $s$ and $l$ with $s+l\equiv 2(mod 4)$ on $n$ vertices with a given diameter $d$.

math.CO↗
arXiv2016

Fundamental Limits of Communication with Low Probability of Detection

This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. Specifically, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the "off" input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.

cs.IT↗
arXiv2016

5-regular oriented graphs with optimum skew energy

Let $G$ be a simple undirected graph and $G^σ$ be the corresponding oriented graph of $G$ with the orientation $σ$. The skew energy of $G^σ$, denoted by $\varepsilon_s(G^σ)$, is defined as the sum of the singular values of the skew adjacency matrix $S(G^σ)$. In 2010, Adiga et al. certified that $\varepsilon_s(G^σ) \leq n\sqrtΔ$, where $Δ$ is the maximum degree of $G$ of order $n$. In this paper, we determine all connected 5-regular oriented graphs of order $n$ with maximum skew-energy.

math.CO↗
arXiv2016

On the second smallest and the largest normalized Laplacian eigenvalues of a graph

Let $G$ be a simple connected graph with order $n$. Let $\mathcal{L}(G)$ be the normalized Laplacian matrix of $G$. Let $λ_{k}(G)$ be the $k$-th smallest normalized Laplacian eigenvalue of $G$. Denote $ρ(A)$ the spectral radius of the matrix $A$. In this paper, we study the behaviors of $λ_{2}(G)$ and $ρ(\mathcal{L}(G))$ when the graph is perturbed by three operations.

math.CO↗
arXiv2016

A new S-type eigenvalue localization set for tensors and its applications

A new \emph{S}-type eigenvalue localization set for tensors is derived by breaking $N=\{1,2,\cdots,n\}$ into disjoint subsets $S$ and its complement. It is proved that this new set is tighter than those presented by Qi (Journal of Symbolic Computation 40 (2005) 1302-1324), Li et al. (Numer. Linear Algebra Appl. 21 (2014) 39-50) and Li et al. (Linear Algebra Appl. 493 (2016) 469-483). As applications, checkable sufficient conditions for the positive definiteness and the positive semi-definiteness of tensors are proposed. Moreover, based on this new set, we establish a new upper bound for the spectral radius of nonnegative tensors and a lower bound for the minimum \emph{H}-eigenvalue of weakly irreducible strong \emph{M}-tensors in this paper. We demonstrate that these bounds are sharper than those obtained by Li et al. (Numer. Linear Algebra Appl. 21 (2014) 39-50) and He and Huang (J. Inequal. Appl. 114 (2014) 2014). Numerical examples are also given to illustrate this fact.

math.CO↗
arXiv2015

Complex unit gain bicyclic graphs with rank 2, 3 or 4

A $\mathbb{T}$-gain graph is a triple $Φ=(G,\mathbb{T},φ)$ consisting of a graph $G=(V,E)$, the circle group $\mathbb{T}=\{z\in C: |z|=1\}$ and a gain function $φ:\overrightarrow{E}\rightarrow \mathbb{T}$ such that $φ(e_{ij})=φ(e_{ji})^{-1}=\overline{φ(e_{ji})}$. The rank of $\mathbb{T}$-gain graph $Φ$, denoted by $r(Φ)$, is the rank of the adjacency matrix of $Φ$. In 2015, Yu, Qu and Tu [ G. H. Yu, H. Qu, J. H. Tu, Inertia of complex unit gain graphs, Appl. Math. Comput. 265(2015) 619--629 ] obtained some properties of inertia of a $\mathbb{T}$-gain graph. They characterized the $\mathbb{T}$-gain unicyclic graphs with small positive or negative index. Motivated by above, in this paper, we characterize the complex unit gain bicyclic graphs with rank 2, 3 or 4.

math.CO↗
arXiv2015

Distance integral complete multipartite graphs with $s=5,6$

Let $D(G)=(d_{ij})_{n\times n}$ denote the distance matrix of a connected graph $G$ with order $n$, where $d_{ij}$ is equal to the distance between vertices $v_{i}$ and $v_{j}$ in $G$. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete $r$-partite graphs $K_{p_{1},p_{2},\ldots,p_{r}}=K_{a_{1}\cdot p_{1},a_{2}\cdot p_{2},\ldots,a_{s}\cdot p_{s}}$ to be distance integral and obtained such distance integral graphs with $s=1,2,3,4$. However distance integral complete multipartite graphs $K_{a_{1}\cdot p_{1},a_{2}\cdot p_{2},\ldots,a_{s}\cdot p_{s}}$ with $s>4$ have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs $K_{a_{1}\cdot p_{1},a_{2}\cdot p_{2},\ldots,a_{s}\cdot p_{s}}$ with $s=5,6$. The problem of the existence of such distance integral graphs $K_{a_{1}\cdot p_{1},a_{2}\cdot p_{2},\ldots,a_{s}\cdot p_{s}}$ with arbitrarily large number $s$ remains open.

math.CO↗
arXiv2015

Photon-efficient quantum cryptography with pulse-position modulation

The binary (one-bit-per-photon) encoding that most existing quantum key distribution (QKD) protocols employ puts a fundamental limit on their achievable key rates, especially under high channel loss conditions associated with long-distance fiber-optic or satellite-to-ground links. Inspired by the pulse-position-modulation (PPM) approach to photon-starved classical communications, we design and demonstrate the first PPM-QKD, whose security against collective attacks is established through continuous-variable entanglement measurements that also enable a novel decoy-state protocol performed conveniently in post processing. We achieve a throughput of 8.0 Mbit/s (2.5 Mbit/s for loss equivalent to 25 km of fiber) and secret-key capacity up to 4.0 bits per detected photon, thus demonstrating the significant enhancement afforded by high-dimensional encoding. These results point to a new avenue for realizing high-throughput satellite-based or long-haul fiber-optic quantum communications beyond their photon-reception-rate limits.

quant-ph↗
arXiv2014

Toward Photon-Efficient Key Distribution over Optical Channels

This work considers the distribution of a secret key over an optical (bosonic) channel in the regime of high photon efficiency, i.e., when the number of secret key bits generated per detected photon is high. While in principle the photon efficiency is unbounded, there is an inherent tradeoff between this efficiency and the key generation rate (with respect to the channel bandwidth). We derive asymptotic expressions for the optimal generation rates in the photon-efficient limit, and propose schemes that approach these limits up to certain approximations. The schemes are practical, in the sense that they use coherent or temporally-entangled optical states and direct photodetection, all of which are reasonably easy to realize in practice, in conjunction with off-the-shelf classical codes.

cs.IT↗
arXiv2014

A refined analysis of the Poisson channel in the high-photon-efficiency regime

We study the discrete-time Poisson channel under the constraint that its average input power (in photons per channel use) must not exceed some constant E. We consider the wideband, high-photon-efficiency extreme where E approaches zero, and where the channel's "dark current" approaches zero proportionally with E. Improving over a previously obtained first-order capacity approximation, we derive a refined approximation, which includes the exact characterization of the second-order term, as well as an asymptotic characterization of the third-order term with respect to the dark current. We also show that pulse-position modulation is nearly optimal in this regime.

cs.IT↗
arXiv2013

One-Shot Classical-Quantum Capacity and Hypothesis Testing

The one-shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold. In this work, we show that this capacity is well approximated by a relative-entropy-type measure defined via hypothesis testing. Combined with a quantum version of Stein's lemma, our results give a conceptually simple proof of the well-known Holevo-Schumacher-Westmoreland theorem for the capacity of memoryless channels. More generally, we obtain tight capacity formulas for arbitrary (not necessarily memoryless) channels.

quant-ph↗
arXiv2012

The State-Dependent Semideterministic Broadcast Channel

We derive the capacity region of the state-dependent semideterministic broadcast channel with noncausal state-information at the transmitter. One of the two outputs of this channel is a deterministic function of the channel input and the channel state, and the state is assumed to be known noncausally to the transmitter but not to the receivers. We show that appending the state to the deterministic output does not increase capacity. We also derive an outer bound on the capacity of general (not necessarily semideterministic) state-dependent broadcast channels.

cs.IT↗
arXiv2012

Private-Capacity Bounds for Bosonic Wiretap Channels

We prove an upper bound on the private capacity of the single-mode noiseless bosonic wiretap channel. Combined with a previous lower bound, we obtain the low photon-number asymptotic expression for the private capacity. We then show that the multiple-mode noiseless bosonic wiretap channel is equivalent to parallel single-mode channels, hence the single-mode bounds can be applied. Finally, we consider multiple-spatial-mode propagation through atmospheric turbulence, and derive a private-capacity lower bound that only requires second moments of the channel matrix.

quant-ph↗
arXiv2011

Covering Point Patterns

An encoder observes a point pattern---a finite number of points in the interval $[0,T]$---which is to be described to a reconstructor using bits. Based on these bits, the reconstructor wishes to select a subset of $[0,T]$ that contains all the points in the pattern. It is shown that, if the point pattern is produced by a homogeneous Poisson process of intensity $λ$, and if the reconstructor is restricted to select a subset of average Lebesgue measure not exceeding $DT$, then, as $T$ tends to infinity, the minimum number of bits per second needed by the encoder is $-λ\log D$. It is also shown that, as $T$ tends to infinity, any point pattern on $[0,T]$ containing no more than $λT$ points can be successfully described using $-λ\log D$ bits per second in this sense. Finally, a Wyner-Ziv version of this problem is considered where some of the points in the pattern are known to the reconstructor.

cs.IT↗
arXiv2010

Simple Channel Coding Bounds

New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel. Both bounds are expressed using a quantity called the "smooth 0-divergence", which is a generalization of Renyi's divergence of order 0. The bounds are also studied in the limit of large block-lengths. In particular, they combine to give a general capacity formula which is equivalent to the one derived by Verdu and Han.

cs.IT↗