Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree 'shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each possible binary phylogenetic tree has exactly the same distribution for its parsimony score. Despite this pleasing and slightly surprising symmetry, some bi...

We study upward planar straight-line embeddings (UPSE) of directed trees on given point sets. The set S has size at least the number vertices in tree. For special case where tree is a path P we show that: (a) If one-sided convex, UPSE s equals maximal monotone paths P. (b) general position and composed by three paths, middle longer than other two, then it always admits an S. that decision probl...

Caterpillars are soft-bodied animals. They have a relatively simple nervous system, and yet are capable of exhibiting complex movement. This paper presents a 2D caterpillar simulation which mimics caterpillar locomotion using Assur tensegrity structures. Tensegrity structures are structures composed of a set of elements always under compression and a set of elements always under tension. Assur ...

Plants frequently respond to herbivorous insect attack by synthesizing defense proteins that deter insect feeding and prevent additional herbivory. Maize (Zea mays L.) lines, resistant to feeding by a number of lepidopteran species, rapidly mobilize a unique 33-kDa cysteine protease in response to caterpillar feeding. The accumulation of the 33-kDa cysteine protease in the maize mid-whorl was c...

In closed-canopy forests, gap formation and closure are thought to be major drivers of forest dynamics. Crown defoliation by insects, however, may also influence understory resource levels and thus forest dynamics. We evaluate the effect of a forest tent caterpillar outbreak on understory light availability, soil nutrient levels and tree seedling height growth in six sites with contrasting leve...

A rollercoaster is a sequence of real numbers for which every maximal contiguous subsequence, that is increasing or decreasing, has length at least three. By translating this sequence to a set of points in the plane, a rollercoaster can be defined as a polygonal path for which every maximal sub-path, with positiveor negative-slope edges, has at least three points. Given a sequence of distinct r...

Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and have to find a planar graph on n vertices that is the edge-disjoint union of T1 and T2. A clear exception that must be made is the star which cannot be packe...

Let~$G$ be a simple undirected graph. A broadcast on~$G$ is a function $f : V(G)\rightarrow\NNNNN$ such that $f(v)\le e_G(v)$ holds for every vertex~$v$ of~$G$, where $e_G(v)$ denotes the eccentricity of~$v$ in~$G$, is, maximum distance from~$v$ to any other vertex of~$G$. The cost of~$f$ is value $\cost(f)=\sum_{v\in V(G)}f(v)$. A broadcast~$f$ independent if two distinct vertices $u$ an...

As part of its growth strategy, Caterpillar Inc. plans to launch a new P2000 product line of \compact" construction equipment and work tools. In anticipation of this, they asked the authors to construct and analyze potential P2000 supply chain con gurations. Through the use of decomposition, and results from network ow theory, inventory theory, and simulation theory, we were able to provide a s...