Pivots, Determinants, and Perfect Matchings of Graphs

We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the same set S of vertices (modulo two). Moreover, given a set of vertices S, we characterize whether or not such a sequence using precisely the vertices of S exists. We also relate pivots to perfect matchings to obtain a graph-theoretical characterization. Finally, we consider graphs with self-loops to carry over the results to sequences containing both pivots and local complementation operations.Comment: 16 page

Strategies of Loop Recombination in Ciliates

Gene assembly in ciliates is an extremely involved DNA transformation process, which transforms a nucleus, the micronucleus, to another functionally different nucleus, the macronucleus. In this paper we characterize which loop recombination operations (one of the three types of molecular operations that accomplish gene assembly) can possibly be applied in the transformation of a given gene from its micronuclear form to its macronuclear form. We also characterize in which order these loop recombination operations are applicable. This is done in the abstract and more general setting of so-called legal strings.Comment: 22 pages, 14 figure

Models of natural computation : gene assembly and membrane systems

This thesis is concerned with two research areas in natural computing: the computational nature of gene assembly and membrane computing. Gene assembly is a process occurring in unicellular organisms called ciliates. During this process genes are transformed through cut-and-paste operations. We study this process from a theoretical point of view. More specifically, we relate the theory of gene assembly to sorting by reversal, which is another well-known theory of DNA transformation. In this way we obtain a novel graph-theoretical representation that provides new insights into the nature of gene assembly. Membrane computing is a computational model inspired by the functioning of membranes in cells. Membrane systems compute in a parallel fashion by moving objects, through membranes, between compartments. We study the computational power of various classes of membrane systems, and also relate them to other well-known models of computation.Netherlands Organisation for Scientific Research (NWO), Institute for Programming research and Algorithmics (IPA)UBL - phd migration 201

Parallelism in gene assembly

The process of gene assembly in ciliates, an ancient group of organisms, is one of the most complex instances of DNA manipulation known in any organisms. This process is fascinating from the computational point of view, with ciliates even using the linked lists data structure. Three molecular operations (ld, hi, and dlad) have been postulated for the gene assembly process. We initiate here the study of parallelism in this process, raising several natural questions, such as: when can a number of operations be applied in parallel to a gene pattern; or how many steps are needed to assemble (in parallel) a micronuclear gene. In particular, this gives rise to a new measure of complexity for the process of gene assembly in ciliates