Caterpillar compaction NA compaction, say Ryan Case, YunPei Chang, Nicholas Cozzarelli, Carlos Bustamante, and colleagues (University of California, Berkeley, CA), may work via a cooperative caterpillar-like mechanism. The caterpillar is formed by multiple copies of condensin protein—in this case MukBEF—with each V-shaped condensin contributing two legs. Compaction occurs when the caterpillar’s...

The bandwidth problem has a long history and a number of important applications. It is the problem of enumerating the vertices of a given graph G such that the maximum difference between the numbers of adjacent vertices is minimal. We will show for any constant k 2 IN that there is no polynomial time approximation algorithm with an approximation factor of k. Furthermore, we will show that this ...

In this paper, we propose an efficient implicit representation of caterpillar and bounded degree trees of n vertices. Our scheme, called Traversal & Jumping, assigns to the n vertices of any bounded degree tree distinct binary labels of log2 n+O(1) bits in O(n) time such that we can compute adjacency between two vertices only from their labels. We use our result to improve previous known upper ...

Rapidly increasing levels of light pollution subject nocturnal organisms to major alterations of their habitat, the ecological consequences of which are largely unknown. Moths are well-known to be attracted to light at night, but effects of light on other aspects of moth ecology, such as larval development and life-history, remain unknown. Such effects may have important consequences for fitnes...

In this paper we obtain the necessary and sufficient condition for balanced-caterpillar factorization of crowns and that for directed caterpillar factorization of symmetric crowns.

Forest fragmentation can disrupt important ecological processes both within and among species. Of particular interest is the extent to which fragmentation decouples economically important pest species from their parasites. In an influential paper, Roland and Taylor (1997) advanced the hypothesis that forest fragmentation at a relatively fine spatial scale would disrupt the ability of parasitoid...

Suppose G is a tree. Graham’s “Tree Reconstruction Conjecture” states that G is uniquely determined by the integer sequence |G|, |L(G)|, |L(L(G))|, |L(L(L(G)))|, . . ., where L(H) denotes the line graph of the graph H . Little is known about this question apart from a few simple observations. We show that the number of trees on n vertices which can be distinguished by their associated integer s...

Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies that differ from that of the species tree can be most probable under the standard multispecies coalescent model, making species tree inference more difficult. ...

When we consider an embedding of graphs into a plane, it would be nice if it does not intersect internally since the embedding simply shows us the structure of graphs. It is easy to embed a tree into a plane with non-self-intersections. If we embed two or more trees into a plane with non-self-intersections, what occurs? In this paper, we consider embeddings of two trees into a plane with using ...

We introduce and study the 1-planar packing problem: Given k graphs with n vertices \(G_1, \dots , G_k\), find a graph that contains given as edge-disjoint spanning subgraphs. mainly focus on case when each \(G_i\) is tree \(k=3\). prove triple consisting of three caterpillars or two path may not admit packing, while paths special type caterpillar always have one. then packings few crossings (r...