Peeling phylogenetic ‘oranges’

We investigate the combinatorics of a topological space that is generated by the set of edge-weighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial order on semilabelled forests. We then describe some combinatorial properties of this poset, showing that, for example, it is pure, thin and contractible.     

On the Curvature of the Central Path of Linear Programming Theory

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms of the number of independent variables of the primal problem, and independent of the number of constraints.     

Flips and the Hilbert scheme over an exterior algebra

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.     

Fire containment in grids of dimension three and higher

We consider a deterministic discrete-time model of fire spread introduced by Hartnell [Firefighter! an application of domination, Presentation, in: 20th Conference on Numerical Mathematics and Computing, University of Manitoba in Winnipeg, Canada, September 1995] and the problem of minimizing the number of burnt vertices when a fixed number of vertices can be defended by firefighters per time step. While only two firefighters per time step are needed in the two-dimensional lattice to contain any outbreak, we prove a conjecture of Wang and Moeller [Fire control on graphs, J. Combin. Math. Combin. Comput. 41 (2002) 19-34] that 2d-1 firefighters per time step are needed to contain a fire outbreak starting at a single vertex in the d-dimensional square lattice for d?3; we also prove that in the d-dimensional lattice, d?3, for each positive integer f there is some outbreak of fire such that f firefighters per time step are insufficient to contain the outbreak. We prove another conjecture of Wang and Moeller that the proportion of elements in the three-dimensional grid P_n×P_n×P_n which can be saved with one firefighter per time step when an outbreak starts at one vertex goes to 0 as n gets large. Finally, we use integer programming to prove results about the minimum number of time steps needed and minimum number of burnt vertices when containing a fire outbreak in the two-dimensional square lattice with two firefighters per time step.     

Timetabling County Cricket Fixtures Using a Form of Tabu Search

This paper concerns a computer system which has been devised to timetable the county cricket matches in England. The context of the work is discussed and the many constraints and objectives described. Details of the solution method are given; it involves tabu search with a form of diversification dependent on the solution subcosts as well as the overall cost. Experiments are described which suggest that this type of diversification may have wide applicability to large, complex, multi-objective combinatorial problems.     

Efficient synthesis of an imidazole-substituted delta-amino acid by the integration of chiral technologies

Two methods to produce (2S)-5-amino-2-(1-n-propyl-1H-imidazol-4-ylmethyl)-pentanoic acid were investigated. Diastereoisomeric salt resolution, using the quinidine salt, gave the desired intermediate in 98% ee and 33% yield. Asymmetric hydrogenation of various substrates gave high conversions, with up to 83% ee. Integration of these two approaches via asymmetric hydrogenation of a quinidine salt substrate followed by crystallization provided the desired intermediate in 94% ee and 76% yield.     

Introduction to session 2

Applied Biochemistry and Biotechnology -     

High-throughput purification of combinatorial libraries I: a high-throughput purification system using an accelerated retention window approach

We have developed a high-throughput purification system to purify combinatorial libraries at a 50-100-mg scale with a throughput of 250 samples/instrument/day. We applied an accelerated retention window method to shorten the purification time and targeted one fraction per injection to simplify data tracking, lower QC workload, and simplify the postpurification processing. First, we determined the accurate retention time and peak height for all compounds using an eight-channel parallel LC/UV/MS system, and calculated the specific preparative HPLC conditions for individual compounds. The preparative HPLC conditions include the compound-specific gradient segment for individual compounds with a fixed gradient slope and the compound-specific UV or ELSD threshold for triggering a fraction collection device. A unique solvent composition or solvent strength was programmed for each compound in the preparative HPLC in order to elute all compounds at the same target time. Considering the possible deviation of the predicted retention time, a 1-min window around the target time was set to collect peaks above a threshold based on UV or ELSD detection. Dual column preparative instruments were used to maximize throughput. We have purified more than 500 000 druglike compounds using this system in the past 3 years. We report various components of this high-throughput purification system and some of our purification results.     

Determination of (R)- and (S)-phenprocoumon in human plasma by enantioselective liquid chromatography/electrospray ionisation tandem mass spectrometry

Phenprocoumon is a commonly used oral anticoagulant of the coumarin type, and has found extensive clinical use in the treatment of thrombophlebitis, pulmonary embolism and atrial fibrillation. In the course of a clinical study to investigate the influence of genetic polymorphisms of the CYP2C9 enzyme on phenprocoumon metabolism, we developed a new enantioselective liquid chromatography/electrospray ionisation tandem mass spectrometry (LC/MS/MS) method to quantify (R)- and (S)-phenprocoumon in human plasma. HPLC separation of the enantiomers was achieved on a Chira-Grom-2 column under isocratic conditions using a water/acetonitrile/formic acid eluent. For detection and quantification a triple-quadrupole MS system was used in the selected reaction monitoring (SRM) mode. As an internal standard the structurally homologous compound warfarin was chosen. The detector response was linear with a correlation coefficient of 0.988-0.999 for (R)-phenprocoumon and 0.989-0.999 for (S)-phenprocoumon in the investigated concentration range between 62.5 and 1000 ng/mL (per enantiomer). The limit of detection (LOD) was 12.5 ng/mL.