Euler-Rodrigues frames on spatial Pythagorean-hodograph curves
We investigate the properties of a special kind of frame, which we call the Euler–Rodrigues frame (ERF), defined on the spatial Pythagorean-hodograph (PH) curves. It is a frame that can be naturally constructed from the PH condition. It turns out that this ERF enjoys some nice properties. In particular, a close examination of its angular velocity against a rotation-minimizing frame yields a characterization of PH curves whose ERF achieves rotation-minimizing property. This computation leads into a new fact that this ERF is equivalent to the Frenet frame on cubic PH curves. Furthermore, we prove that the minimum degree of non-planar PH curves whose ERF is an rotation-minimizing frame is seven, and provide a parameterization of the coefficients of those curves.

title: Almost rotation-minimizing rational parametrization of canal surfaces
abstract: Almost rotation minimizing parametrization of the canal surface is given. The basic building block of our approach is the curve approximation scheme that enables us to construct a curve, called the parameter curve, on the canal surface that produces, when projected and rescaled, an almost parallel normal vector field on the spine curve. Its construction relies on our earlier methods and results on relating the geometry of the canal surface to the Lorentzian geometry of the Minkowski geometry via the Clifford algebra formalism. We then iteratively construct patches out of the parameter curves via suitable interpolation procedure. Furthermore, its rotational deviation, i.e., the angle deviation from the parallel (no rotation) frame along the spine curve, can be controlled with the use of the rotation deviation estimate of the parameter curves. Our numerical experiment shows that the rotation deviation is minuscule. When compared with other earlier results including our earlier one, our result fares extremely favorably. To facilitate the implement, a practitioners' summary is given in the appendix.

title: Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
abstract: We present a new approach toward the rational parametrization of canal surfaces. According to our previous work, every canal surface with rational (respectively polynomial) spine curve and rational (respectively polynomial) radius function is a rational (respectively polynomial) Pythagorean hodograph curve in R3,1. Drawing upon this formalism and utilizing the underlying Lorentzian geometry, the problem is reduced to simple algebraic manipulations.We also illustrate how our work related to the previous work of pottmann and Peternell. Finally, we give an outline of an approach toward the rotation minimizing parametrization of canal surfaces.

title: Hardness on IP-subnet Aware Routing in WDM Network
abstract: In this paper, we study the hardness of the IP-subnet aware routing problem in WDM network. IP-subnet aware routing attempts to reduce routing overhead by grouping a set of addresses under a single subnet. However, routing in WDM network with subnets imposes neighboring IP interfaces along the path to be on the same subnet. This subnet constraint forces the routing path to be longer unless routing permits reconfiguration of subnets. The hardness of this routing problem is first studied in . We investigate further the problem of finding paths accounting for subnets and its hardness. Regardless of subnets, we argue that a shortest IP hop path can be constructed in a polynomial time. We provide efficient routing algorithms to justify our argument.

title: The Optimum Network on Chip Architectures for Video Object Plane Decoder Design
abstract: On Chip Network (OCN) has been proposed as a new methodology for addressing the design challenges of future massly integrated system in nanoscale. In this paper, three differently heterogenous Tree-based network topologies are proposed as the OCN architectures for Video Object Plane Decoder (VOPD). The topologies are designed in order to maximize the system throughput. This paper also evaluates the proposed topologies by comparing them to other conventional topologies such as 2-D Mesh and Fat-Tree with respects to throughput, power consumption and size. We use the power modelling tool, known as Orion model to calculate the static powers, areas, and dynamic energies of three topologies. The experiment results show that our Tree-based topologies offer similar throughputs as Fat-Tree does and much higher throughputs compared to 2-D Mesh while use less chip areas and power consumptions.

title: Robust kernel Isomap
abstract: Isomap is one of widely used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). In this paper we pay our attention to two critical issues that were not considered in Isomap, such as: (1) generalization property (projection property); (2) topological stability. Then we present a robust kernel Isomap method, armed with such two properties. We present a method which relates the Isomap to Mercer kernel machines, so that the generalization property naturally emerges, through kernel principal component analysis. For topological stability, we investigate the network flow in a graph, providing a method for eliminating critical outliers. The useful behavior of the robust kernel Isomap is confirmed through numerical experiments with several data sets.

title: On monitoring transparent optical networks
abstract: Fault identification and localization problems in optical networks have become crucial. Due to network transparency and high data rates, optical networks are vulnerable to sophisticated attacks on the physical infrastructure, and hence require adequate fault monitoring in order to accurately identify and locate network failures. In transparent optical networks, faults may propagate to various parts of the network from the origin, and multiple alarms can be generated for a single failure. In order to reduce the number of redundant alarms, simplify fault localization, as well as lower financial investment in network monitoring equipment, fault monitor placement should be optimized for a given network. In this paper, we formulate a problem on the optimal placement of network monitoring devices and propose a solution approach. We provide a brief summary of available physical-layer monitoring devices, and present a scheme for optimal monitor placement.

title: Realization of Video Object Plane Decoder on On-Chip Network Architecture
abstract: System-on-chip (SoC) designs provide integrated solutions to challenging design problems in the telecommunications, multimedia, and so on. Present and future SoC are designed using pre-existing components which we call cores. Communication between the cores will become a major bottleneck for system performance as standard hardwired bus-based communication architectures will be inefficient in terms of throughput, latency and power consumption. To solve this problem, a packet switched platform that considers the delay and reliability issues of wires so called Network-on-Chip (NoC) has been proposed. In this paper, we present interconnected network topologies and analyze their performances with a particular application under bandwidth constrains. Then we compare the performances among different ways of mapping the cores onto a Mesh NoC architecture. The comparison between Mesh and Fat-Tree topology is also presented. These evaluations are done by utilizing NS-2, a tool that has been widely used in the computer network design.