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Xiaomin Chen

Publications and source records attributed to Xiaomin Chen.

At least 37 records · Page 2Linked to original sources
arXiv2018

Einstein-Weyl structures on almost cosymplectic manifolds

In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(κ,μ)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. Next for a three dimensional compact almost $α$-cosymplectic manifold admitting closed Einstein-Weyl structures, we prove that it is Ricc-flat. Further, we show that an almost $α$-cosymplectic admitting two Einstein-Weyl structures is either Einstein or $α$-cosymplectic, provided that its Ricci tensor is commuting. Finally, we prove that a compact $K$-cosymplectic manifold with a closed Einstein-Weyl structure or two special Einstein-Weyl structures is cosymplectic.

math.DG↗
arXiv2018

Proportional fairness in wireless powered CSMA/CA based IoT networks

This paper considers the deployment of a hybrid wireless data/power access point in an 802.11-based wireless powered IoT network. The proportionally fair allocation of throughputs across IoT nodes is considered under the constraints of energy neutrality and CPU capability for each device. The joint optimization of wireless powering and data communication resources takes the CSMA/CA random channel access features, e.g. the backoff procedure, collisions, protocol overhead into account. Numerical results show that the optimized solution can effectively balance individual throughput across nodes, and meanwhile proportionally maximize the overall sum throughput under energy constraints.

cs.NI↗
arXiv2018

Notes on Ricci solitons in $f$-cosymplectic manifolds

The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class of gradient Ricci solitons, for which we give the local classifications of $M$. Meanwhile, we also give some properties of $f$-cosymplectic manifolds.

math.DG↗
arXiv2017

Multi-destination Aggregation with Binary Symmetric Broadcast Channel Based Coding in 802.11 WLANs

In this paper we consider the potential benefits of adopting a binary symmetric broadcast channel paradigm for multi-destination aggregation in 802.11 WLANs, as opposed to a more conventional packet erasure channel paradigm. We propose two approaches for multi-destination aggregation, i.e. superposition coding and a simpler time-sharing coding. Theoretical and simulation results for both unicast and multicast traffic demonstrate that increases in network throughput of more than 100% are possible over a wide range of network conditions and that the much simpler time-sharing scheme yields most of these gains and have minimal loss of performance. Importantly, these performance gains are achieved exclusively through software rather than hardware changes.

cs.NI↗
arXiv2017

Real hypersurfaces with $^{*}$-Ricci solitons of non-flat complex space forms

Kaimakamis and Panagiotidou in \cite{KP} introduced the notion of $^*$-Ricci soliton and studied the real hypersurfaces of a non-flat complex space form admitting a $^*$-Ricci soliton whose potential vector field is the structure vector field. In this article, we consider that a real hypersurface of a non-flat complex space form admits a $^*$-Ricci soliton whose potential vector field belongs to the principal curvature space and the holomorphic distribution.

math.DG↗
arXiv2017

Real hypersurfaces of complex quadric in terms of star-Ricci tensor

In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric $Q^m$. It is proved that there exist no Hopf hypersurfaces in $Q^m,m\geq3$, with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on $M$ are considered. In this case we show that $M$ is an open part of a tube around a totally geodesic $\mathbb{C}P^\frac{m}{2}\subset Q^{m},m\geq4$.

math.DG↗
arXiv2017

Real hypersurfaces with Miao-Tam critical metrics of complex space forms

Let $M$ be a real hypersurface of a complex space form with constant curvature $c$. In this paper, we study the hypersurface $M$ admitting Miao-Tam critical metric, i.e. the induced metric $g$ on $M$ satisfies the equation:$-(Δ_gλ)g+\nabla^2_gλ-λRic=g$, where $λ$ is a smooth function on $M$. At first, for the case where $M$ is Hopf, $c=0$ and $c\neq0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with $λ>0$ or $λ<0$ is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

math.DG↗
arXiv2015

A control theoretic approach to achieve proportional fairness in 802.11e EDCA WLANs

This paper considers proportional fairness amongst ACs in an EDCA WLAN for provision of distinct QoS requirements and priority parameters. A detailed theoretical analysis is provided to derive the optimal station attempt probability which leads to a proportional fair allocation of station throughputs. The desirable fairness can be achieved using a centralised adaptive control approach. This approach is based on multivariable statespace control theory and uses the Linear Quadratic Integral (LQI) controller to periodically update CWmin till the optimal fair point of operation. Performance evaluation demonstrates that the control approach has high accuracy performance and fast convergence speed for general network scenarios. To our knowledge this might be the first time that a closed-loop control system is designed for EDCA WLANs to achieve proportional fairness.

cs.NI↗
arXiv2015

Achieving proportional fairness with a control theoretic approach in error-prone 802.11e WLANs

This letter proposes a control theoretic approach to achieve proportional fairness amongst access categories (ACs) in an error-prone EDCA WLAN for provision of distinct QoS requirements and priority parameters. The approach adaptively adjusts the minimum contention window of each AC to derive the station attempt probability to its optimum which leads to a proportional fair allocation of station throughputs. Evaluation results demonstrate that the proposed control approach has high accuracy performance and fast convergence speed for general network scenarios.

cs.NI↗
arXiv2014

Lines, betweenness and metric spaces

A classic theorem of Euclidean geometry asserts that any noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chvátal conjectured that this holds for an arbitrary finite metric space, with a certain natural definition of lines in a metric space. We prove that in any metric space with $n$ points, either there is a line containing all the points or there are at least $Ω(\sqrt{n})$ lines. This is the first polynomial lower bound on the number of lines in general finite metric spaces. In the more general setting of pseudometric betweenness, we prove a corresponding bound of $Ω(n^{2/5})$ lines. When the metric space is induced by a connected graph, we prove that either there is a line containing all the points or there are $Ω(n^{4/7})$ lines, improving the previous $Ω(n^{2/7})$ bound. We also prove that the number of lines in an $n$-point metric space is at least $n / 5w$, where $w$ is the number of different distances in the space, and we give an $Ω(n^{4/3})$ lower bound on the number of lines in metric spaces induced by graphs with constant diameter, as well as spaces where all the positive distances are from \{1, 2, 3\}.

math.CO↗
arXiv2014

A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions

Motivated by the paper (Beals, Sattinger and Szmigielski, Adv. Math. 154 (2000) 229--257), we propose an extension of the Camassa-Holm equation, which also admits the multipeakon solutions. The novel aspect is that our approach is mainly based on classic determinant technique. Furthermore, the proposed equation is shown to possess a nonisospectral Lax pair.

math-ph↗
arXiv2014

About several classes of bi-orthogonal polynomials and discrete integrable systems

By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hungry Lotka-Volterra (QD-type dhLV) system, together with their Lax pairs. These two known equations can be regarded as extensions of the QD algorithm. When this idea is applied to a higher analogue of the discrete-time Toda (HADT) equation and the quotient-quotient-difference (QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems are constructed. We call these systems the hungry forms of the higher analogue discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD) scheme, respectively. In addition, the corresponding Lax pairs are provided.

math-ph↗
arXiv2014

Nordhaus-Gaddum-type problems for lines in hypergraphs

We study the number of lines in hypergraphs in a more symmetric setting, where both the hypergraph and its complement are considered. In the general case and in some special cases, the lower bounds on the number of lines are much higher than their counterparts in single hypergraph setting or admit more elegant proofs. We show that the minimum value of product of the number of lines in both hypergraphs on $n$ points is easily determined as $\binom{n}{2}$; and the minimum value of their sum is between $Ω(n)$ and $O(n \log n)$. We also study some restricted classes of hypergraphs; and determine the tight bounds on the minimum sum when the hypergraph is derived from an Euclidean space, a real projective plane, or a tree.

math.CO↗
arXiv2014

Graph metric with no proper inclusion between lines

In trying to generalize the classic Sylvester-Gallai theorem and De Bruijn-Erdős theorem in plane geometry, lines and closure lines were previously defined for metric spaces and hypergraphs. Both definitions do not obey the geometric intuition in the sense that two lines (closure lines) may intersect at more than one point, and one line (closure line) might be the proper subset of another. In this work, we study the systems where one or both of the configurations are forbidden. We note that when any two lines intersect in at most one point, the two classic theorems extend in any metric space. We study the metric spaces induced by simple graphs where no line is a proper subset of another, and show that the least number of lines for such a graph with $n$ vertices is between the order of $n^{4/3}$ and $n^{4/3} \ln^{2/3} n$.

math.MG↗
arXiv2013

Number of lines in hypergraphs

Chen and Chvátal introduced the notion of lines in hypergraphs; they proved that every 3-uniform hypergraph with $n$ vertices either has a line that consists of all $n$ vertices or else has at least $\log_2 n$ distinct lines. We improve this lower bound by a factor of $2-o(1)$.

math.CO↗
arXiv2013

Optimized Parallel Transmission in Elastic Optical Networks to Support High-Speed Ethernet

The need for optical parallelization is driven by the imminent optical capacity crunch, where the spectral efficiency required in the coming decades will be beyond the Shannon limit. To this end, the emerging high-speed Ethernet services at 100 Gbps, have already standardized options to utilize parallel optics to parallelize interfaces referred to as Multi-lane Distribution (MLD). OFDM-based optical network is a promising transmission option towards the goal of Ethernet parallelization. It can allocate optical resource tailored for a variety of bandwidth requirements and that in a fundamentally parallel fashion with each sub-carrier utilizing a frequency slot at a lower rate than if serial transmission was used. In this paper, we propose a novel parallel transmission framework designed for elastic (OFDM-based) optical networks to support high-speed Ethernet services, in-line with IEEE and ITU-T standards. We formulate an ILP optimization model based on integer linear programming, with consideration of various constraints, including spectrum fragmentation, differential delay and guard-band constraints. We also propose a heuristic algorithm which can be applied when the optimization model becomes intractable. The numerical results show the effectiveness and high suitability of elastic optical networks to support parallel transmission in high-speed Ethernet. To the best of our knowledge, this is the first attempt to investigate the parallel transmission in elastic optical networks to support standardized high-speed Ethernet.

cs.NI↗
arXiv2013

A Novel Network Coded Parallel Transmission Framework for High-Speed Ethernet

Parallel transmission, as defined in high-speed Ethernet standards, enables to use less expensive optoelectronics and offers backwards compatibility with legacy Optical Transport Network (OTN) infrastructure. However, optimal parallel transmission does not scale to large networks, as it requires computationally expensive multipath routing algorithms to minimize differential delay, and thus the required buffer size, optimize traffic splitting ratio, and ensure frame synchronization. In this paper, we propose a novel framework for high-speed Ethernet, which we refer to as network coded parallel transmission, capable of effective buffer management and frame synchronization without the need for complex multipath algorithms in the OTN layer. We show that using network coding can reduce the delay caused by packet reordering at the receiver, thus requiring a smaller overall buffer size, while improving the network throughput. We design the framework in full compliance with high-speed Ethernet standards specified in IEEE802.3ba and present solutions for network encoding, data structure of coded parallel transmission, buffer management and decoding at the receiver side. The proposed network coded parallel transmission framework is simple to implement and represents a potential major breakthrough in the system design of future high-speed Ethernet.

cs.NI↗