Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs. 相似文献
An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by . The edge-forwarding index is the minimum of over all possible all-to-all routings R, and the arc-forwarding index is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colours. The optical index is defined to be the minimum of over all possible R, and the directed optical index is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for 4-regular circulant graphs with connection set , . We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of 4-regular circulant graphs. 相似文献
A compact 64‐channel hybrid demultiplexer based on silicon‐on‐insulator nanowires is proposed and demonstrated experimentally to enable wavelength‐division‐multiplexing and mode‐division‐multiplexing simultaneously in order to realize an ultra‐large capacity on‐chip optical‐interconnect link. The present hybrid demultiplexer consists of a 4‐channel mode multiplexer constructed with cascaded asymmetrical directional‐couplers and two bi‐directional 17 × 17 arrayed‐waveguide gratings (AWGs) with 16 channels. Here each bi‐directional AWG is equivalent as two identical 1 × 16 AWGs. The measured excess loss and the crosstalk for the monolithically integrated 64‐channel hybrid demultiplexer are about ‐5 dB and ‐14 dB, respectively. Better performance can be achieved by minimizing the imperfections (particularly in AWGs) during the fabrication processes.
In this paper, a spectrum-based wrinkling analysis method via two-dimensional Fourier transformation is proposed aiming to solve the difficulty of nanoscale wrinkle evaluation. It evaluates the wrinkle characteristics including wrinkling wavelength and direction simply using a single wrinkling image. Based on this method, the evaluation results of nanoscale wrinkle characteristics show agreement with the open experimental results within an error of 6%. It is also verified to be appropriate for the macro wrinkle evaluation without scale limitations. The spectrum-based wrinkling analysis is an effective method for nanoscale evaluation, which contributes to reveal the mechanism of nanoscale wrinkling. 相似文献
A G‐design of order n is a decomposition of the complete graph on n vertices into edge‐disjoint subgraphs isomorphic to G. Grooming uniform all‐to‐all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The existence spectrum problem of G‐designs for five‐vertex graphs is a long standing problem posed by Bermond, Huang, Rosa and Sotteau in 1980, which is closely related to traffic groomings in optical networks. Although considerable progress has been made over the past 30 years, the existence problems for such G‐designs and their related traffic groomings in optical networks are far from complete. In this paper, we first give a complete solution to this spectrum problem for five‐vertex graphs by eliminating all the undetermined possible exceptions. Then, we determine almost completely the minimum drop cost of 8‐groomings for all orders n by reducing the 37 possible exceptions to 8. Finally, we show the minimum possible drop cost of 9‐groomings for all orders n is realizable with 14 exceptions and 12 possible exceptions. 相似文献
We present a facile approach to make aptamer‐conjugated FRET (fluorescent resonance energy transfer) nanoflowers (NFs) through rolling circle replication for multiplexed cellular imaging and traceable targeted drug delivery. The NFs can exhibit multi‐fluorescence emissions by a single‐wavelength excitation as a result of the DNA matrix covalently incorporated with three dye molecules able to perform FRET. Compared with the conventional DNA nanostructure assembly, NF assembly is independent of template sequences, avoiding the otherwise complicated design of DNA building blocks assembled into nanostructures by base‐pairing. The NFs were uniform and exhibited high fluorescence intensity and excellent photostability. Combined with the ability of traceable targeted drug delivery, these colorful DNA NFs provide a novel system for applications in multiplex fluorescent cellular imaging, effective screening of drugs, and therapeutic protocol development. 相似文献