Optimization of Amplifier Placements in Switch-Based Optical Networks

Wavelength division multiplexing (WDM) offers a solution to the problem of exploiting the large bandwidth on optical links; it is the current favorite multiplexing technology for optical communication networks. Due to the high cost of an optical amplifier, it is desirable to strategically place the amplifiers throughout the network in a way that guarantees that all the signals are adequately amplified while minimizing the total number amplifiers being used. Previous studies all consider a star-based network. This paper demonstrates an original approach for solving the problem in switch-based WDM optical network assuming the traffic matrix is always the permutation of the nodes. First we formulate the problem by choosing typical permutations which can maximize traffic load on individual links; then a GA (Genetic Algorithm) is used to search for feasible amplifier placements. Finally, by setting up all the lightpaths without violating the power constaints we confirm the feasibility of the solution.

Rhodium-Catalyzed Hydroboration: Directed Asymmetric Desymmetrization

Rhodium-catalyzed asymmetric hydroboration in conjunction with directing groups can be used control relative and absolute stereochemistry. Hydroboration has the potential to create new C–C, C–O, and C–N bonds from an intermediate C–B bond with retention of stereochemistry. Desymmetrization resulting in the loss of one or more symmetry elements can give rise to molecular chirality, i.e., the conversion of a prochiral molecule to one that is chiral. Unsaturated amides and esters hold the potential for two-point binding to the rhodium catalyst and have been shown to direct the regiochemistry and impact stereochemistry in asymmetric hydroborations of acyclic β,γ-unsaturated substrates. In the present study, the pendant amide functionality directs the hydroboration cis in the cyclic substrates studied; the corresponding ester substrates do so to a lesser extent. The enantioselectivity is determined by regioselective addition to the re or si site of the rhodium-complexed alkene. The effect of catalyst, ligand and borane on the observed diastereoselectivity and enantioselectivity for a variety of cyclopentenyl ester and amide substrates is discussed.