Factoring Algorithms for Computing K-Terminal Network Reliability

Let GK denote a graph G whose edges can fail and with a set K ? V specified. Edge failures are independent and have known probabilities. The K-terminal reliability of GK, R(GK), is the probability that all vertices in K are connected by working edges. A factoring algorithm for computing network reliability recursively applies the formula R(GK) = piR(GK * ei) + qiR(GK - ei) where GK * ei is GK, with edge ei contracted, GK - ei is GK with ei deleted and pi ? 1 - qi is the reliability of edge ei. Various reliability-preserving reductions can be performed after each factoring operation in order to reduce computation. A unified framework is provided for complexity analysis and for determining optimal factoring strategies. Recent results are reviewed and extended within this framework.     

Base-catalyzed tritium exchange between tritium-containing heavy water and deuterated chloroform–kinetics and equilibrium

We develop a kinetic model for the exchange of tritium and deuteriumbetween tritium-containing heavy water and deuterated chloroform in a two-phase liquid system, catalyzed by hydroxide ion (sodium hydroxide). For the exchange reaction yielding tritiated chloroform andheavy water, the measured equilibrium constant is 0.518 at 25–45°C, independent of temperature. The rate constant (for the controlling step, deuteron abstraction from chloroform) is 0.22 L/mol s at 25°C, 0.72 at 35°C, and 2.0 at 45°C, corresponding to an activation energy of 87 kJ/mol. Comparison is made with literature data, and effects of mass transfer on the apparent rate constant are discussed.     

Dual characterization of properties of risk measures on Orlicz hearts

We extend earlier representation results for monetary risk measures on Orlicz hearts. Then we give general conditions for such risk measures to be Gateaux-differentiable, strictly monotone with respect to almost sure inequality, strictly convex modulo translation, strictly convex modulo comonotonicity, or monotone with respect to different stochastic orders. The theoretical results are used to analyze various specific examples of risk measures. We thank Andreas Hamel and Michael Kupper for fruitful discussions and helpful comments. P. Cheridito has been supported by NSF Grant DMS-0642361, a Rheinstein Award and a Peek Fellowship. T. Li has been supported by a Marshall Scholarship and a Merage Fellowship.     

Synthesis and axial chirality of an enantiopure aminodibenzazepinone

A route for the synthesis of (S,S)-7-amino-5-methyl-5H-dibenzo[b,d]azepin-6(7H)-one hydrochloride is disclosed. The synthesis includes a Friedel–Crafts alkylation to form the seven-membered ring and a highly efficient classical resolution. Additional studies on the enantiopure material showed the amine to be highly resistant to racemization, which led us to investigate the unexpected stability. We propose that the inherent axial chirality contained in the dibenzazepinone works to produce an interesting chirality transfer mechanism, which accounts for the observed robustness of the stereocenter. This previously unrecognized stereochemical element exists within this specific class of molecules, and they should be drawn in a manner which displays the axial chirality.     

1/f-Like Scaling in Normal Neutrophil Dynamics: Implications for Hematologic Monitoring

Daily neutrophil counts show considerable variability in normal subjects. The dynamics of these apparently erratic fluctuations have not been characterized. We hypothesized that this variability might reflect the kind of 1/f-like (inverse power-law) spectrum seen in other physiologic processes. Fast Fourier transform analysis of neutrophil count data over 64 consecutive days from four previously reported normal volunteers showed a good fit (r = 0.84; p 0.001) to the predicted power-law regression line (y = ?1.14x ?1.05). Further characterization of normal and pathologic neutrophil spectra may have diagnostic value.