arXiv subjects
Publications and source records attributed to Xiaonan Liu.
In this paper, we prove that any simple $\{C_3,C_5\}$-free non-empty connected graph $G$ with LLY curvature bounded below by $κ>0$ has the order at most $2^{\frac{2}κ}$. This upper bound is achieved if and only if $G$ is a hypercube $Q_d$ and $κ=\frac{2}{d}$ for some integer $d\geq 1$.
In this paper, we show that the oriented diameter of any $n$-vertex $2$-connected near triangulation is at most $\lceil{\frac{n}{2}}\rceil$ (except for seven small exceptions), and the upper bound is tight. This extends a result of Wang et.al. on the oriented diameter of maximal outerplanar graphs, and improves an upper bound of $n/2+O(\sqrt{n})$ on the oriented diameter of planar triangulations by Mondal, Parthiban and Rajasingh.
Over the past few years, significant advancements have been made in the field of machine learning (ML) to address resource management, interference management, autonomy, and decision-making in wireless networks. Traditional ML approaches rely on centralized methods, where data is collected at a central server for training. However, this approach poses a challenge in terms of preserving the data privacy of devices. To address this issue, federated learning (FL) has emerged as an effective solution that allows edge devices to collaboratively train ML models without compromising data privacy. In FL, local datasets are not shared, and the focus is on learning a global model for a specific task involving all devices. However, FL has limitations when it comes to adapting the model to devices with different data distributions. In such cases, meta learning is considered, as it enables the adaptation of learning models to different data distributions using only a few data samples. In this tutorial, we present a comprehensive review of FL, meta learning, and federated meta learning (FedMeta). Unlike other tutorial papers, our objective is to explore how FL, meta learning, and FedMeta methodologies can be designed, optimized, and evolved, and their applications over wireless networks. We also analyze the relationships among these learning algorithms and examine their advantages and disadvantages in real-world applications.
Federated Learning (FL) is a promising privacy-preserving distributed learning framework where a server aggregates models updated by multiple devices without accessing their private datasets. Hierarchical FL (HFL), as a device-edge-cloud aggregation hierarchy, can enjoy both the cloud server's access to more datasets and the edge servers' efficient communications with devices. However, the learning latency increases with the HFL network scale due to the increasing number of edge servers and devices with limited local computation capability and communication bandwidth. To address this issue, in this paper, we introduce model pruning for HFL in wireless networks to reduce the neural network scale. We present the convergence analysis of an upper on the l2 norm of gradients for HFL with model pruning, analyze the computation and communication latency of the proposed model pruning scheme, and formulate an optimization problem to maximize the convergence rate under a given latency threshold by jointly optimizing the pruning ratio and wireless resource allocation. By decoupling the optimization problem and using Karush Kuhn Tucker (KKT) conditions, closed-form solutions of pruning ratio and wireless resource allocation are derived. Simulation results show that our proposed HFL with model pruning achieves similar learning accuracy compared with the HFL without model pruning and reduces about 50 percent communication cost.
For any positive integer $t$, a \emph{$t$-broom} is a graph obtained from $K_{1,t+1}$ by subdividing an edge once. In this paper, we show that, for graphs $G$ without induced $t$-brooms, we have $χ(G) = o(ω(G)^{t+1})$, where $χ(G)$ and $ω(G)$ are the chromatic number and clique number of $G$, respectively. When $t=2$, this answers a question of Schiermeyer and Randerath. Moreover, for $t=2$, we strengthen the bound on $χ(G)$ to $7ω(G)^2$, confirming a conjecture of Sivaraman. For $t\geq 3$ and \{$t$-broom, $K_{t,t}$\}-free graphs, we improve the bound to $o(ω^{t})$.
In 1999, Katona and Kierstead conjectured that if a $k$-uniform hypergraph $\cal H$ on $n$ vertices has minimum co-degree $\lfloor \frac{n-k+3}{2}\rfloor$, i.e., each set of $k-1$ vertices is contained in at least $\lfloor \frac{n-k+3}{2}\rfloor$ edges, then it has a Hamiltonian cycle. Rödl, Ruciński and Szemerédi in 2011 proved that the conjecture is true when $k=3$ and $n$ is large. We show that this Katona-Kierstead conjecture holds if $k=4$, $n$ is large, and $V({\cal H})$ has a partition $A$, $B$ such that $|A|=\lceil n/2\rceil$, $|\{e\in E({\cal H}):|e \cap A|=2\}| <εn^4$ for a fixed small constant $ε>0$.
The Reconstruction Conjecture due to Kelly and Ulam states that every graph with at least 3 vertices is uniquely determined by its multiset of subgraphs $\{G-v: v\in V(G)\}$. Let $diam(G)$ and $κ(G)$ denote the diameter and the connectivity of a graph $G$, respectively, and let $\mathcal{G}_2:=\{G: \textrm{diam}(G)=2\}$ and $\mathcal{G}_3:=\{G:\textrm{diam}(G)=\textrm{diam}(\overline{G})=3\}$. It is known that the Reconstruction Conjecture is true if and only if it is true for every 2-connected graph in $\mathcal{G}_2\cup \mathcal{G}_3$. Balakumar and Monikandan showed that the Reconstruction Conjecture holds for every triangle-free graph $G$ in $\mathcal{G}_2\cup \mathcal{G}_3$ with $κ(G)=2$. Moreover, they asked whether the result still holds if $κ(G)\ge 3$. (If yes, the class of graphs critical for solving the Reconstruction Conjecture is restricted to 2-connected graphs in $\mathcal{G}_2\cup\mathcal{G}_3$ which contain triangles.) In this paper, we give a partial solution to their question by showing that the Reconstruction Conjecture holds for every triangle-free graph $G$ in $\mathcal{G}_3$ and every triangle-free graph $G$ in $\mathcal{G}_2$ with $κ(G)=3$. We also prove similar results about the Edge Reconstruction Conjecture.
Hakimi, Schmeichel, and Thomassen in 1979 conjectured that every $4$-connected planar triangulation $G$ on $n$ vertices has at least $2(n-2)(n-4)$ Hamiltonian cycles, with equality if and only if $G$ is a double wheel. In this paper, we show that every $4$-connected planar triangulation on $n$ vertices has $Ω(n^2)$ Hamiltonian cycles. Moreover, we show that if $G$ is a $4$-connected planar triangulation on $n$ vertices and the distance between any two vertices of degree $4$ in $G$ is at least $3$, then $G$ has $2^{Ω(n^{1/4})}$ Hamiltonian cycles.
We present a phenomenological analysis of the $q_{\mathrm{T}}$-weighted transverse spin dependent azimuthal asymmetry recently measured by the COMPASS Collaboration in polarized pion-proton Drell-Yan process. In the kinematical regimes explored by experiments, we consider the leading-twist contributions from the Boer-Mulders distribution functions $h_{1}^{\perp}(x,k_{\mathrm{T}}^{2})$ of both the pion and the proton, the transversity distribution $h_{1}(x,k_{\mathrm{T}}^{2})$ and the pretzelosity distribution $h_{1\mathrm{T}}^{\perp}(x,k_{\mathrm{T}}^{2})$ of the proton, with the unpolarized transverse-momentum-dependent distribution function $f_{1}(x,k_{\mathrm{T}}^{2})$ of the proton being also involved in the calculation. By comparing the data reported by the COMPASS Collaboration with theoretical calculated results, we find that the COMPASS measurements represent the first experimental evidence of the Boer-Mulders effect in polarized Drell-Yan process. We also test the universality between proton and pion Boer-Mulders functions.
The planar Turan number $\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$ is the largest number of edges in an $n$-vertex planar graph with no $\ell$-cycle. For $\ell\in \{3,4,5,6\}$, upper bounds on $\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$ are known that hold with equality infinitely often. Ghosh, Györi, Martin, Paulo, and Xiao [arxiv:2004.14094] conjectured an upper bound on $\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$ for every $\ell\ge 7$ and $n$ sufficiently large. We disprove this conjecture for every $\ell\ge 11$. We also propose two revised versions of the conjecture.
The quality of experience (QoE) requirements of wireless Virtual Reality (VR) can only be satisfied with high data rate, high reliability, and low VR interaction latency. This high data rate over short transmission distances may be achieved via abundant bandwidth in the terahertz (THz) band. However, THz waves suffer from severe signal attenuation, which may be compensated by the reconfigurable intelligent surface (RIS) technology with programmable reflecting elements. Meanwhile, the low VR interaction latency may be achieved with the mobile edge computing (MEC) network architecture due to its high computation capability. Motivated by these considerations, in this paper, we propose a MEC-enabled and RIS-assisted THz VR network in an indoor scenario, by taking into account the uplink viewpoint prediction and position transmission, MEC rendering, and downlink transmission. We propose two methods, which are referred to as centralized online Gated Recurrent Unit (GRU) and distributed Federated Averaging (FedAvg), to predict the viewpoints of VR users. In the uplink, an algorithm that integrates online Long-short Term Memory (LSTM) and Convolutional Neural Networks (CNN) is deployed to predict the locations and the line-of-sight and non-line-of-sight statuses of the VR users over time. In the downlink, we further develop a constrained deep reinforcement learning algorithm to select the optimal phase shifts of the RIS under latency constraints. Simulation results show that our proposed learning architecture achieves near-optimal QoE as that of the genie-aided benchmark algorithm, and about two times improvement in QoE compared to the random phase shift selection scheme.
Whitney proved in 1931 that 4-connected planar triangulations are Hamiltonian. Hakimi, Schmeichel, and Thomassen conjectured in 1979 that if $G$ is a 4-connected planar triangulation with $n$ vertices then $G$ contains at least $2(n-2)(n-4)$ Hamiltonian cycles, with equality if and only if $G$ is a double wheel. On the other hand, a recent result of Alahmadi, Aldred, and Thomassen states that there are exponentially many Hamiltonian cycles in 5-connected planar triangulations. In this paper, we consider 4-connected planar $n$-vertex triangulations $G$ that do not have too many separating 4-cycles or have minimum degree 5. We show that if $G$ has $O(n/{\log}_2 n)$ separating 4-cycles then $G$ has $Ω(n^2)$ Hamiltonian cycles, and if $δ(G)\ge 5$ then $G$ has $2^{Ω(n^{1/4})}$ Hamiltonian cycles. Both results improve previous work. Moreover, the proofs involve a "double wheel" structure, providing further evidence to the above conjecture.
A challenge for rescue teams when fighting against wildfire in remote areas is the lack of information, such as the size and images of fire areas. As such, live streaming from Unmanned Aerial Vehicles (UAVs), capturing videos of dynamic fire areas, is crucial for firefighter commanders in any location to monitor the fire situation with quick response. The 5G network is a promising wireless technology to support such scenarios. In this paper, we consider a UAV-to-UAV (U2U) communication scenario, where a UAV at a high altitude acts as a mobile base station (UAV-BS) to stream videos from other flying UAV-users (UAV-UEs) through the uplink. Due to the mobility of the UAV-BS and UAV-UEs, it is important to determine the optimal movements and transmission powers for UAV-BSs and UAV-UEs in real-time, so as to maximize the data rate of video transmission with smoothness and low latency, while mitigating the interference according to the dynamics in fire areas and wireless channel conditions. In this paper, we co-design the video resolution, the movement, and the power control of UAV-BS and UAV-UEs to maximize the Quality of Experience (QoE) of real-time video streaming. To learn the Deep Q-Network (DQN) and Actor-Critic (AC) to maximize the QoE of video transmission from all UAV-UEs to a single UAVBS. Simulation results show the effectiveness of our proposed algorithm in terms of the QoE, delay and video smoothness as compared to the Greedy algorithm.
Wireless Virtual Reality (VR) users are able to enjoy immersive experience from anywhere at anytime. However, providing full spherical VR video with high quality under limited VR interaction latency is challenging. If the viewpoint of the VR user can be predicted in advance, only the required viewpoint is needed to be rendered and delivered, which can reduce the VR interaction latency. Therefore, in this paper, we use offline and online learning algorithms to predict viewpoint of the VR user using real VR dataset. For the offline learning algorithm, the trained learning model is directly used to predict the viewpoint of VR users in continuous time slots. While for the online learning algorithm, based on the VR user's actual viewpoint delivered through uplink transmission, we compare it with the predicted viewpoint and update the parameters of the online learning algorithm to further improve the prediction accuracy. To guarantee the reliability of the uplink transmission, we integrate the Proactive retransmission scheme into our proposed online learning algorithm. Simulation results show that our proposed online learning algorithm for uplink wireless VR network with the proactive retransmission scheme only exhibits about 5% prediction error.
Wireless-connected Virtual Reality (VR) provides immersive experience for VR users from any-where at anytime. However, providing wireless VR users with seamless connectivity and real-time VR video with high quality is challenging due to its requirements in high Quality of Experience (QoE) and low VR interaction latency under limited computation capability of VR device. To address these issues,we propose a MEC-enabled wireless VR network, where the field of view (FoV) of each VR user can be real-time predicted using Recurrent Neural Network (RNN), and the rendering of VR content is moved from VR device to MEC server with rendering model migration capability. Taking into account the geographical and FoV request correlation, we propose centralized and distributed decoupled Deep Reinforcement Learning (DRL) strategies to maximize the long-term QoE of VR users under the VR interaction latency constraint. Simulation results show that our proposed MEC rendering schemes and DRL algorithms substantially improve the long-term QoE of VR users and reduce the VR interaction latency compared to rendering at VR devices
We calculate the inclusive production of a polarized $Λ$ or $\barΛ$ hyperon from the single longitudinally polarized proton and proton ($pp$) collision at RHIC. By comparing the data reported by the STAR Collaboration, we find that this process is sensitive to the polarization of strange and antistrange quarks of the proton in the experimental range. By introducing asymmetric coefficients with the minimization of $χ^2$, we further identify the asymmetry of the polarized strange-antistrange quarks in the proton sea and find that the first moment is $Δs \approx -0.025\pm 0.019$ for strange quark and $Δ\bar s \approx -0.001\pm 0.012$ for antistrange quark, with central values agreeing with the light-cone meson-baryon fluctuation model prediction, the recent lattice QCD determination of strangeness polarization and results from a global QCD analysis given by the Jefferson Lab Angular Momentum (JAM) Collaboration.