On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees.Received March 16, 2004     

Sodium trichloro­methane­sulfonate monohydrate

Sodium trichloro­methane­sulfonate monohydrate, Na⁺·CCl₃SO₃⁻·H₂O, crystallizes in P2₁/a with all the atoms located in general positions. The trichloro­methane­sulfonate (trichlate) anion consists of pyramidal SO₃ and CCl₃ groups connected via an S—C bond in a staggered conformation with approximate C_3v symmetry. The water mol­ecule is hydrogen bonded to the sulfonate O atoms, with one water H atom forming weak bifurcated O—H⋯O hydrogen bonds to two different trichlate ions. Two water O atoms and three O atoms from different SO₃ groups form a square‐pyramidal arrangement around the sodium ion.     

Isolation and On‐Line LC/CD Analysis of 3,8″‐Linked Biflavonoids from Gnidia involucrata

Investigation of the methanol extract of the roots of Gnidia involucrata (Thymelaeaceae) led to the isolation and characterization of two new 3,8″‐biflavonoid diastereoisomers, named GB‐4 ( 6a ) and GB‐4a ( 6b ). Their absolute configurations were determined in mixture by on‐line LC/CD measurements, which also allowed the revision of absolute configurations of the biflavanoids GB‐1 and GB‐2, and the configurational assignment of GB‐3.     

Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20     

Structural reliability and stochastic structural optimization

Mathematical Methods of Operations Research -     

Volumetric path following algorithms for linear programming

We consider the construction of small step path following algorithms using volumetric, and mixed volumetric-logarithmic, barriers. We establish quadratic convergence of a volumetric centering measure using pure Newton steps, enabling us to use relatively standard proof techniques for several subsequently needed results. Using a mixed volumetric-logarithmic barrier we obtain an O(n ^1/4 m ^1/4 L) iteration algorithm for linear programs withn variables andm inequality constraints, providing an alternative derivation for results first obtained by Vaidya and Atkinson. In addition, we show that the same iteration complexity can be attained while holding the work per iteration to O(n ² m), as opposed to O(nm ²), operations, by avoiding use of the true Hessian of the volumetric barrier. Our analysis also provides a simplified proof of self-concordancy of the volumetric and mixed volumetric-logarithmic barriers, originally due to Nesterov and Nemirovskii. This paper was first presented at the 1994 Faculty Research Seminar “Optimization in Theory and Practice”, at the University of Iowa Center for Advanced Studies.     

Anionic polymerization of star-shaped nylon 6 with a trifunctional initiator

The anionic polymerization of ?-caprolactam (CLM) has been shown to proceed at high reaction rate when catalyzed by metallic lactamates and initiated by acyllactams. The role of initiator and catalyst concentration on the process of ?-caprolactam anionic polymerization has been explored, with the aim of selecting the most suitable experimental conditions for reaction injection molding (RIM). The overall polymerization rates and physical properties for reaction injection molding of star-shaped nylon 6 homopolymer have been studied by the quasi-adiabatic process. In order to model the actual rapid molding conditions, time vs. temperature reaction profiles were measured, and the relative rates of polymerization subsequently determined from these data.     

Traces on Noncommutative Homogeneous Spaces

We study properties of C*-algebraic deformations of homogeneous spaces G/Γ which are equivariant in the sense that they preserve the natural action of G by left translation. The center is shown to be isomorphic to C(G/G⁰_ρ) for a certain subgroup G⁰_ρ of G, and there is a 1-1 correspondence between normalised traces and probability measures on G/G⁰_ρ. This makes it possible to represent the deformed algebra as operators over L²(G/Γ). Applications to K-theory are also mentioned.