In this paper, we study the essential dimension of classes of central simple algebras with involutions of index less or equal to 4. Using structural theorems for simple algebras with involutions, we obtain the essential dimension of projective and symplectic groups of small degree.

One of the most important goals in molecular biology is to elucidate the relationship among sequence, structure, function and properties of biomolecules. Such knowledge would enable us to design the modifications of biomolecules for particular functions, and drugs to modify the function and property of biomolecules. Now, the number of entries in the Protein Data Bank (PDB) is over 10,000. These...

Copyright © This paper investigates whether a designer can improve both the incentive provision and the selection performance of a promotion contest by making the competition more (or less) dynamic. A comparison of static (one-stage) and dynamic (two-stage) contests reveals that this is not the case. A structural change that improves the performance in one dimension leads to a deterioration in ...

MOTIVATION So far various bioinformatics and machine learning techniques applied for identification of sequence and functionally conserved residues in proteins. Although few computational methods are available for the prediction of structurally conserved residues from protein structure, almost all methods require homologous structural information and structure-based alignments, which still prov...

Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.

Background The theoretical requirements for a genetic code were well defined and modeled by George Gamow and Francis Crick in the 50-es. Their models failed. However the valid Genetic Code, provided by Nirenberg and Matthaei in 1961, ignores many theoretical requirements for a perfect Code. Something is simply missing from the canonical Code. Results The 3x redundancy of the Genetic code is usu...