Reducibility of Gene Patterns in Ciliates using the Breakpoint Graph

Gene assembly in ciliates is one of the most involved DNA processings going on in any organism. This process transforms one nucleus (the micronucleus) into another functionally different nucleus (the macronucleus). We continue the development of the theoretical models of gene assembly, and in particular we demonstrate the use of the concept of the breakpoint graph, known from another branch of DNA transformation research. More specifically: (1) we characterize the intermediate gene patterns that can occur during the transformation of a given micronuclear gene pattern to its macronuclear form; (2) we determine the number of applications of the loop recombination operation (the most basic of the three molecular operations that accomplish gene assembly) needed in this transformation; (3) we generalize previous results (and give elegant alternatives for some proofs) concerning characterizations of the micronuclear gene patterns that can be assembled using a specific subset of the three molecular operations.Comment: 30 pages, 13 figure

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

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

Bispecial factors in circular non-pushy D0L languages

We study bispecial factors in fixed points of morphisms. In particular, we propose a simple method of how to find all bispecial words of non-pushy circular D0L-systems. This method can be formulated as an algorithm. Moreover, we prove that non-pushy circular D0L-systems are exactly those with finite critical exponent.Comment: 18 pages, 5 figure

Structure theorem for U5-free tournaments

Let $U_5$ be the tournament with vertices $v_1$, ..., $v_5$ such that $v_2 \rightarrow v_1$, and $v_i \rightarrow v_j$ if $j-i \equiv 1$, $2 \pmod{5}$ and ${i,j} \neq {1,2}$. In this paper we describe the tournaments which do not have $U_5$ as a subtournament. Specifically, we show that if a tournament $G$ is "prime"---that is, if there is no subset $X \subseteq V(G)$, $1 < |X| < |V(G)|$, such that for all $v \in V(G) \backslash X$, either $v \rightarrow x$ for all $x \in X$ or $x \rightarrow v$ for all $x \in X$---then $G$ is $U_5$-free if and only if either $G$ is a specific tournament $T_n$ or $V(G)$ can be partitioned into sets $X$, $Y$, $Z$ such that $X \cup Y$, $Y \cup Z$, and $Z \cup X$ are transitive. From the prime $U_5$-free tournaments we can construct all the $U_5$-free tournaments. We use the theorem to show that every $U_5$-free tournament with $n$ vertices has a transitive subtournament with at least $n^{\log_3 2}$ vertices, and that this bound is tight.Comment: 15 pages, 1 figure. Changes from previous version: Added a section; added the definitions of v, A, and B to the main proof; general edit

Modeling post-depositional changes of delta-D in ice due to sublimation

Ice cores are a valuable component with regards to paleoclimate reconstruction due to the ability to use stable water isotopic concentrations in ice as a proxy for paleo-temperature records. It is therefore important to understand the processes and conditions under which isotopic concentrations can be altered after ice has formed. Historically, sublimation has been considered to only have a trivial impact on the isotopic record in glacial ice due to the low diffusivity of solid ice (~10-15 m2 s-1). Recent publications have shown that diffusion of impurities through ice can occur at much faster rates than the diffusivity of solid ice would imply, and have proposed that networks of unfrozen liquid (premelt) between ice grains may expedite the diffusion process. However, the application of this mode of diffusion to isotopic concentrations in ice under non-equilibrium conditions has been largely unexplored. Here I model changes in isotopic concentrations in ice using a two-dimensional diffusion mechanism, which incorporates premelt, coupled with a sublimation flux at the surface. Model results show an increase in δD at the ice surface and in near-surface ice. Concentrations exponentially decrease from the surface value to the initial concentration at depth. These results are consistent with recent experimental results

Nullity Invariance for Pivot and the Interlace Polynomial

We show that the effect of principal pivot transform on the nullity values of the principal submatrices of a given (square) matrix is described by the symmetric difference operator (for sets). We consider its consequences for graphs, and in particular generalize the recursive relation of the interlace polynomial and simplify its proof.Comment: small revision of Section 8 w.r.t. v2, 14 pages, 6 figure

Reaction Systems: a Formal Framework for Processes Based on Biochemical Interactions

This paper presents a formal framework for investigating processes driven by interactions between biochemical reactions in living cells. These interactions are based on the mechanisms of facilitation and inhibition, which underlie the definition of reaction systems - the central construct of our framework. We discuss in this paper the basic setup for reaction systems, and its motivation. We also present an important extension of reaction systems as well as some research topics and results

Walking in the City

Motivated by traffic congestion, excessive energy use and poor health outcomes, planning and public health researchers have developed an extensive body of research that examines walking and other active transport as well as walking for recreation. In different discussions, walking has become a newly interesting subject and method to understand urban (and non urban) life, and a growing number of researchers have sought to understa nd mobility, the social experience and functions of walking and its cultural meanings. These areas of research rarely overlap. The latter has the potential for enriching the research about active travel and physical activity and, through doing so, suggest more effective pathways to healthier and less energy intensive life patterns. This project first examines these divergent literatures. It then uses New Orleans to discuss both the pedestrian improvements and the vibrant public life that New Orleans sustained without the new pedestrian infrastructure. It concludes with a discussion about pedestrian oriented research agenda