The Octonions

The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.Comment: 56 pages LaTeX, 11 Postscript Figures, some small correction

Orthopedic Surgery Planning Based on the Integration of Reverse Engineering and Rapid Prototyping

This paper describes orthopedic surgical planning based on the integration of RE and RP. Using symmetrical characteristics of the human body, CAD data of the original bone without damages for the injured extent are generated from a mirror transformation of undamaged bone data for the uninjured extent. The physical model before the injury is manufactured from RP apparatus. Surgical planning, such as the selection of the proper implant, pre-forming of the implant, decision of fixation positions and incision sizes, etc., is determined by a physical simulation using the physical model. In order to examine the applicability and efficiency of surgical planning technology for orthopedics, various case studies, such as a proximal tibia plateau fracture, a distal tibia comminuted fracture and an iliac wing fracture of pelvis, are carried out. As a result of the examination, it has been shown that the orthopedic surgical planning based on the integration of RE and RP is an efficient surgical tool.Mechanical Engineerin

A Practical Cooperative Multicell MIMO-OFDMA Network Based on Rank Coordination

An important challenge of wireless networks is to boost the cell edge performance and enable multi-stream transmissions to cell edge users. Interference mitigation techniques relying on multiple antennas and coordination among cells are nowadays heavily studied in the literature. Typical strategies in OFDMA networks include coordinated scheduling, beamforming and power control. In this paper, we propose a novel and practical type of coordination for OFDMA downlink networks relying on multiple antennas at the transmitter and the receiver. The transmission ranks, i.e.\ the number of transmitted streams, and the user scheduling in all cells are jointly optimized in order to maximize a network utility function accounting for fairness among users. A distributed coordinated scheduler motivated by an interference pricing mechanism and relying on a master-slave architecture is introduced. The proposed scheme is operated based on the user report of a recommended rank for the interfering cells accounting for the receiver interference suppression capability. It incurs a very low feedback and backhaul overhead and enables efficient link adaptation. It is moreover robust to channel measurement errors and applicable to both open-loop and closed-loop MIMO operations. A 20% cell edge performance gain over uncoordinated LTE-A system is shown through system level simulations.Comment: IEEE Transactions or Wireless Communications, Accepted for Publicatio