Hereditarily Optimal Realizations of Consistent Metrics

One of the main problems in phylogenetics is to find good approximations of metrics by weighted trees. As an aid to solving this problem, it could be tempting to consider optimal realizations of metrics—the guiding principle being that, the (necessarily unique) optimal realization of a tree metric is the weighted tree that realizes this metric. And, although optimal realizations of arbitrary metrics are, in general, not trees, but rather weighted networks, one could still hope to obtain a phylogenetically informative representation of a given metric, maybe even more informative than the best approximating tree. However, optimal realizations are not only difficult to compute, they may also be non-unique. Here we focus on one possible way out of this dilemma: hereditarily optimal realizations. These are essentially unique, and can be described in a rather explicit way. In this paper, we recall what a hereditarily optimal realization of a metric is and how it is related to the 1-skeleton of the tight span of that metric, and we investigate under what conditions it coincides with this 1-skeleton. As a consequence, we will show that hereditarily optimal realizations for consistent metrics, a large class of phylogentically relevant metrics, can be computed in a straight-forward fashion. Received August 26, 2004     

Isoconversional kinetic analysis of stoichiometric and off-stoichiometric epoxy-amine cures

The curing reaction of stoichiometric and off-stoichiometric diglycidyl ether of bisphenol A (DGEBA) and 1,3-phenylene diamine (m-PDA) mixtures was studied by differential scanning calorimetry, thermogravimetric analysis and rheological measurements. In order to highlight the side reactions such as etherification and homopolymerization, the neat DGEBA and DGEBA/DMBA (N,N-dimethylbenzylamine) mixture were examined. The classical model-fitting and the advanced isoconversional methods were used to determine the activation energy of the different reactions. The advanced isoconversional method leads to a good agreement between isothermal, nonisothermal and rheological results. The effective activation energies of primary amine epoxy reaction, etherification and homopolymerization were estimated to about 55-60, 104 and 170 kJ mol⁻¹, respectively.     

Deformations in Mathematics and Physics

This text is my introductory talk given at the Workshop “Deformations and Contractions in Mathematics and Physics” in Oberwolfach in January 2006. The author is grateful for the Mathematisches Forschungsinsitut Oberwolfach for being able to organize this Meeting. The work was partially supported bt grants OTKA T043641 and T043034.