A note on the generalized min-sum set cover problem

In this paper, we consider the generalized min-sum set cover problem, introduced by Azar, Gamzu, and Yin (STOC 2009). Bansal, Gupta, and Krishnaswamy (SODA 2010) give a 485-approximation algorithm for the problem. We are able to alter their algorithm and analysis to obtain a 28-approximation algorithm, improving the performance guarantee by an order of magnitude. We use concepts from α-point scheduling to obtain our improvements.     

Single electron charging effects in semiconductor quantum dots

We have studied charging effects in a lateral split-gate quantum dot defined by metal gates in the two dimensional electron gas (2 DEG) of a GaAs/AlGaAs heterostructure. The gate structure allows an independent control of the conductances of the two tunnel barriers separating the quantum dot from the two 2 DEG leads, and enables us to vary the number of electrons that are localized in the dot. We have measured Coulomb oscillations in the conductance and the Coulomb staircase in current-voltage characteristics and studied their dependence on the conductances of the tunnel barriers. We show experimentally that at zero magnetic field charging effects start to affect the transport properties when both barrier conductances are smaller than the first quantized conductance value of a point contact at 2e ²/h. The experiments are described by a simple model in terms of electrochemical potentials, which includes both the discreteness of the electron charge and the quantum energy states due to confinement.     

Synthesis of Poly(1,3-cyclohexadiene) Containing Star-Shaped Elastomers

The synthesis of high molecular weight star-shaped polymers comprising poly(1,3-cyclohexadiene-block-isoprene) diblock arms coupled to a divinyl benzene (DVB) core is reported. The number average molecular weights of the diblock arms were varied from 30000 to 50000 and the ratio of DVB to n-butyllithium (nBuLi) was systematically varied from 3:1 to 12:1. Size exclusion chromatography coupled with light scattering detection was utilized to detect the formation of star-shaped polymers and the presence of star-star coupling. The molecular weight distribution (<M_w>/<M_n>) of the star polymers ranged from 1.25 to 1.50. The effect of poly(1,3-cyclohexadiene) content on the mechanical properties of these novel elastomers is reported. The elastic modulus, elongation at break, and tensile strength of these elastomers were all found to be a function of the percentage of poly(1,3-cyclohexadiene). The glass transition temperatures were determined using both differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA). Atomic force microscopy was performed in the tapping mode (TMAFM) to verify the presence of microphase separation.