A linkage is a collection of line segments, called bars, possibly joined at their ends, called joints. We consider flattening a tree-like linkage, that is, a continuous motion of their bars from an initial configuration to a final configuration looking like a"straight line segment," preserving the length of each bar and not crossing any two bars. In this paper, we introduce a new class of linkages, called "radial trees," and show that there exists a radial tree which cannot be flattened.

This paper quantitatively analyzes thermal gradient of SoC and proposes a thermal flattening procedure. First, the impact of dominant parameters, such as area occupancy of memory/logic block, power density, and floorplan on thermal gradient are studied quantitatively. Temperature difference is also evaluated from timing and reliability standpoints. Important results obtained here are 1) the maximum temperature difference increases with higher memory area occupancy and 2) the difference is very floorplan sensitive. Then, we propose a procedure to amend thermal gradient. A slight floorplan modification using the proposed procedure improves on-chip thermal gradient significantly.

The Lorentzian-shape filter response of a microring resonator filter is not suitable to the practical use in WDM systems, because of the lack of pass band flatness, high cross talk, and the large wing in the stop band. Therefore, the tailoring of filter response shape is required to improve the performance. In this paper, the authors designed and demonstrated the box-like filter response of microring resonator filter by using the supermodes of stacked double microring resonators. The thicknesses of microrings and the separation between them were optimally designed to give the maximally flat response. A fine fabrication process was developed to achieve the deep and very smooth side wall. The shape factor, which is defined by the ratio of -1 dB bandwidth to -10 dB bandwidth, was successfully improved by three factors from 0.17 of Lorentzian shape to 0.51.