On the complexity of computing the temporal hybridization number for two phylogenies

Phylogenetic networks are now frequently used to explain the evolutionary history of a set of species for which a collection of gene trees, reconstructed from genetic material of different parts of the species’ genomes, reveal inconsistencies. However, in the context of hybridization, the reconstructed networks are often not temporal. If a hybridization network is temporal, then it satisfies the time constraint of instantaneously occurring hybridization events; i.e. all species that are involved in such an event coexist in time. Furthermore, although a collection of phylogenetic trees can often be merged into a hybridization network that is temporal, many algorithms do not necessarily find such a network since their primary optimization objective is to minimize the number of hybridization events. In this paper, we present a characterization for when two rooted binary phylogenetic trees admit a temporal hybridization network. Furthermore, we show that the underlying optimization problem is APX-hard and, therefore, NP-hard. Thus, unless P=NP, it is unlikely that there are efficient algorithms for either computing an exact solution or approximating it within a ratio arbitrarily close to one.     

Infrared multiphoton dissociation of unsubstituted metal carbonyls at 5 μm

A frequency-doubled carbon dioxide laser of modest output energy (1 mJ) has been used to study, for the first time, the infrared multiphoton absorption by, and dissociation of, the unsubstituted carbonyls of vanadium, chromium, iron, nickel, molybdenum, and tungsten. The multiphoton absorption cross-sections measured for Ni(CO)₄, Fe(CO)₅, Cr(CO)₆, Mo(CO)₆, and V(CO)₆ are high (2×10^–17) and ensure facile multiphoton dissociation. In focussed beams a pressure independent reaction yield proportional to the 1.5 power of the beam energy is observed for Fe(CO)₅, Cr(CO)₆, and Mo(CO)₆ implying threshold fluences of only 32, 25, and 26 mJ cm^–2, respectively. The stoichiometry of the reaction, observed by a pressure measurement technique, is consistent with production of metal atoms and carbon monoxide as final products for Ni(CO)₄, Fe(CO)₅, Cr(CO)₆, and Mo(CO)₆. This extensive decarbonylation along the ground state surface is consistent with recent studies of the photochemistry of these molecules from excited electronic states.NRC/Heriot-Watt Summer Student 1982On sabbatical leave from the Department of Chemistry, Heriot-Watt University, Edinburgh, United Kingdom     

An investigation of the diethyldithio-carbamates of palladium, including the determination of their stability constants

The reaction of palladium with copper diethyldithio-carbamate has been studied and two complexes isolated: palladium diethyldithiocarbamate and palladium chloride diethyldithiocarbamate. The spectra of both complexes have been examined. The extraction constants and partition coefficients between chloroform and water have been determined, the former by the use of other strong complexing reagents as masking agents for palladium. The stability constants and the exchange constant for the two complexes have been calculated.     

Centrifugal separation and equilibration dynamics in an electron-antiproton plasma

Charges in cold, multiple-species, non-neutral plasmas separate radially by mass, forming centrifugally separated states. Here, we report the first detailed measurements of such states in an electron-antiproton plasma, and the first observations of the separation dynamics in any centrifugally separated system. While the observed equilibrium states are expected and in agreement with theory, the equilibration time is approximately constant over a wide range of parameters, a surprising and as yet unexplained result. Electron-antiproton plasmas play a crucial role in antihydrogen trapping experiments.