On curves with separated variables

Mathematische Annalen -     

Realizing alternating groups as monodromy groups of genus one covers

We prove that if , a generic Riemann surface of genus 1 admits a meromorphic function (i.e., an analytic branched cover of ) of degree such that every branch point has multiplicity and the monodromy group is the alternating group . To prove this theorem, we construct a Hurwitz space and show that it maps (generically) onto the genus one moduli space.

     

The footprint sorting problem

Phylogenetic footprints are short pieces of noncoding DNA sequence in the vicinity of a gene that are conserved between evolutionary distant species. A seemingly simple problem is to sort footprints in their order along the genomes. It is complicated by the fact that not all footprints are collinear: they may cross each other. The problem thus becomes the identification of the crossing footprints, the sorting of the remaining collinear cliques, and finally the insertion of the noncollinear ones at "reasonable" positions. We show that solving the footprint sorting problem requires the solution of the "Minimum Weight Vertex Feedback Set Problem", which is known to be NP-complete and APX-hard. Nevertheless good approximations can be obtained for data sets of interest. The remaining steps of the sorting process are straightforward: computation of the transitive closure of an acyclic graph, linear extension of the resulting partial order, and finally sorting w.r.t. the linear extension. Alternatively, the footprint sorting problem can be rephrased as a combinatorial optimization problem for which approximate solutions can be obtained by means of general purpose heuristics. Footprint sortings obtained with different methods can be compared using a version of multiple sequence alignment that allows the identification of unambiguously ordered sublists. As an application we show that the rat has a slightly increased insertion/deletion rate in comparison to the mouse genome.     

A Combined Topographical Search Strategy with Ellipsometric Application

A comparison deals with the advantages and disadvantages of the classical random-base, exhaustive and gradient searches and presents a precise local search combined global search control strategy including a new, systematic point selection which makes possible the escape from local minima by time. As a demonstration electrochemically etched porous silicon (PS) samples were investigated by spectroscopic ellipsometry (SE). The evaluation process (a global optimisation task) was made in different ways to see the difficulties and the differences among the evaluating possibilities. The new, topographical search (named Gradient Cube search) was compared with some classical methods (Grid search, Random or Monte-Carlo search, and Levenberg-Marquardt gradient search) and with two more complex algorithms (Genetic Algorithms and Simulated Annealing) by evaluating real measurements. The application results prove that the classical methods have difficulties to give enough reliability and precision at the same time in global optimisation tasks if the error surface is hilly. There is therefore a hard need of escaping from local minima, and a need of a systematic evaluation to avoid the uncertainty of random-base evaluation. The Gradient Cube search is an effective, systematic hill-climbing search with high precision and so it can be useful in ellipsometry.     

Gradient nanoscale polycrystalline elasticity: Intergrain interactions and triple-junction conditions

Using the principle of virtual power, we develop general balance equations, interface conditions, triple-junction conditions, and boundary conditions for second-grade nanocrystalline elastic materials undergoing infinitesimal deformations. We further develop thermodynamically consistent constitutive equations and provide a weak formulation of resulting boundary-value problems that automatically yields internal conditions such those that hold across interfaces and at triple junctions.     

The Effect of Diapause on Neutral Lipids in the Pitcher-Plant Mosquito Wyeomyia smithii as Determined by HPTLC-Densitometry

JPC – Journal of Planar Chromatography – Modern TLC - Diapause in insects typically results in metabolic adjustments that may include the levels of feeding and activity, metabolic rate,...