The Fibers and Range of Reduction Graphs in Ciliates

The biological process of gene assembly has been modeled based on three types of string rewriting rules, called string pointer rules, defined on so-called legal strings. It has been shown that reduction graphs, graphs that are based on the notion of breakpoint graph in the theory of sorting by reversal, for legal strings provide valuable insights into the gene assembly process. We characterize which legal strings obtain the same reduction graph (up to isomorphism), and moreover we characterize which graphs are (isomorphic to) reduction graphs.Comment: 24 pages, 13 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

Computational Complexity of Atomic Chemical Reaction Networks

Informally, a chemical reaction network is "atomic" if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational complexity of deciding whether a given network is atomic according to each of these definitions. Our first definition, primitive atomic, which requires each reaction to preserve the total number of atoms, is to shown to be equivalent to mass conservation. Since it is known that it can be decided in polynomial time whether a given chemical reaction network is mass-conserving, the equivalence gives an efficient algorithm to decide primitive atomicity. Another definition, subset atomic, further requires that all atoms are species. We show that deciding whether a given network is subset atomic is in $\textsf{NP}$, and the problem "is a network subset atomic with respect to a given atom set" is strongly $\textsf{NP}$-$\textsf{Complete}$. A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et al., further requires that each species has a sequence of reactions splitting it into its constituent atoms. We show that there is a $\textbf{polynomial-time algorithm}$ to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is $\textbf{decidable}$. We show that the reachability problem for reachably atomic networks is $\textsf{Pspace}$-$\textsf{Complete}$. Finally, we demonstrate equivalence relationships between our definitions and some special cases of another existing definition of atomicity due to Gnacadja

An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

Membrane systems with external control

We consider the idea of controlling the evolution of a membrane system. In particular, we investigate a model of membrane systems using promoted rules, where a string of promoters (called the control string) "travels" through the regions, activating the rules of the system. This control string is present in the skin region at the beginning of the computation - one can interpret that it has been inserted in the system before starting the computation - and it is "consumed", symbol by symbol, while traveling through the system. In this way, the inserted string drives the computation of the membrane system by controlling the activation of evolution rules. When the control string is entirely consumed and no rule can be applied anymore, then the system halts - this corresponds to a successful computation. The number of objects present in the output region is the result of such a computation. In this way, using a set of control strings (a control program), one generates a set of numbers. We also consider a more restrictive definition of a successful computation, and then study the corresponding model. In this paper we investigate the influence of the structure of control programs on the generative power. We demonstrate that different structures yield generative powers ranging from finite to recursively enumerable number sets. In determining the way that the control string moves through the regions, we consider two possible "strategies of traveling", and prove that they are similar as far as the generative power is concerned. © Springer-Verlag Berlin Heidelberg 2006