Fast B-spline Curve Fitting by L-BFGS

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods

The crossing number of locally twisted cubes

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.Comment: 17 pages, 12 figure

Performance comparison of medium access control in wireless LAN IEEE-802.11 and HIPERLAN

There are two principal wireless LAN standards: IEEE 802.11 and ETSI HIPERLAN, which define the specification of physical and media access control layer. WLAN medium access control protocols describe the rules for orderly access to the shared wireless medium and play a crucial role in the efficient and fair sharing of scarce wireless bandwidth resource. IEEE 802.11 MAC layer employs CSMA/CA protocol to access medium, whereas ETSI HIPERLAN uses EY-NPMA protocol to control the medium access. In this thesis, the two standards are introduced first. Then, the simulation models are presented for various network architectures and environmental parameters in order to obtain comparable performance results regarding the buffer size, the packet lifetime period and the traffic load of terminal stations. After that, the simulation results are presented for different simulation models with analyzing and evaluating the performance for both standards in different criteria and various input parameters

Threshold for the Outbreak of Cascading Failures in Degree-degree Uncorrelated Networks

In complex networks, the failure of one or very few nodes may cause cascading failures. When this dynamical process stops in steady state, the size of the giant component formed by remaining un-failed nodes can be used to measure the severity of cascading failures, which is critically important for estimating the robustness of networks. In this paper, we provide a cascade of overload failure model with local load sharing mechanism, and then explore the threshold of node capacity when the large-scale cascading failures happen and un-failed nodes in steady state cannot connect to each other to form a large connected sub-network. We get the theoretical derivation of this threshold in degree-degree uncorrelated networks, and validate the effectiveness of this method in simulation. This threshold provide us a guidance to improve the network robustness under the premise of limited capacity resource when creating a network and assigning load. Therefore, this threshold is useful and important to analyze the robustness of networks.Comment: 11 pages, 4 figure