where c(E(S, S̄)) is the sum of the weights of the edges that cross the cut, and D(S, S̄) is the sum of the demands of the pairs (si, ti) that are separated by the cut. We recall that optimizing over the set of cuts is equivalent to optimizing over `1 metrics, and is NP-hard. Instead, we may optimize over the set of all metrics. In this lecture, we bound the gap introduced by this relaxation by s...

We have studied the bronchial hyperresponsiveness (BHR) of children with normal controls and asthma by methacholine inhalation challenge, using a forced oscillation method. Four parameters, respiratory conductance (Grs), bronchial responsiveness (PD35Grs), bronchial sensitivity (Dmin) and reactivity (SGrs) were studied. There were three patterns of dose-response curves identified in this study,...

Double minutes (dmin), the cytogenetic hallmark of genomic amplification, are found in approximately 1% of karyotypically abnormal acute myeloid leukemias (AML) and myelodysplastic syndromes (MDS). The MYC gene at 8q24 has been reported to be amplified in the majority of the cases, and generally it has been assumed that MYC is the target gene. However, only a few studies have focused on the ext...

The graphene interlayer spacing in pure graphite is known to have a minimum value of dmin=0.3354 nm, while defective graphites typically have larger interlayer spacings. Using x-ray diffraction, we find that the graphene interlayer spacing in multi-walled carbon nanofibers heat treated above 2800 K is distinctly smaller than dmin. To explain this unusual observation, we investigate the structur...

For a secret sharing scheme, two parameters dmin and dcheat are defined in [12] and [13]. These two parameters measure the errorcorrecting capability and the secret-recovering capability of the secret sharing scheme against cheaters. Some general properties of the parameters have been studied in [12],[9] and [13]. The MDS secretsharing scheme was defined in [13] and it was proved that MDS perfe...

We present a unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the concurrence, and the robustness of entanglement. We then introduce an infinite family of new entanglement quantifiers, having as its limits the best separable approximation measure and the generalized r...