6797458
Graphs without K4 and well-quasi-ordering
Abstract It is proved that given an infinite sequence G 1 , G 2 , G 3 ,…, of series-parallel graphs there are indices i j such that G j contains an induced subgraph contractable onto G i . An example is given showing that for planar graphs the preceding theorem fails.
206570580
Sachs' Linkless Embedding Conjecture
Abstract We prove Sachs′ conjecture that a graph can be embedded in 3-space so that it contains no non-trivial link (in the sense of knot theory) if and only if it contains as a minor none of the seven graphs obtainable from K 6 by Y − Δ and Δ − Y exchanges. We also show the following: (i) A graph admits such a "linkless" embedding if and only if it admits a "panelled" embedding, one such that every circuit of the graph bounds a disc disjoint from the remainder of the graph. This was a conjecture of Bohme. (ii) An embedding is panelled if and only if for every subgraph, its complement in 3-space has free fundamental group. This extends a theorem of Scharlemann and Thompson, who proved it for planar graphs. (iii) If two panelled embeddings of the same graph are "different," that is, are not related by an orientation-preserving homeomorphism of the 3-space, then there is a subgraph which is a subdivision of K 5 or K 3, 3 such that the two induced embeddings of this subgraph are still different.
18561897
Excluding infinite minors
Let ? be an infinite cardinal, and let H be either a complete graph with ? vertices, or a tree in which every vertex has valency ?. What can we say about graphs G which (i) have no minor isomorphic to H, or (ii) contain no subgraph which is a subdivision of H?These four questions are answered for each infinite cardinal ?. In each case we find that there corresponds a necessary and sufficient structural condition (or, in some cases, several equivalent conditions) for G not to contain H in the appropriate way. We survey these results and a number of related theorems.
33726107
A menger-like property of tree-width: The finite case
The notion of tree-width was introduced by Robertson and Symour. A graph has tree-width ≦ w if it admits a tree-decomposition of tree-width ≦ w. We prove here that if G is finite and has tree-width ≦ w then it admits a tree-decomposition of tree-width ≦ w which satisfies a certain Menger-like condition. This result will be used in a future paper on well-quasi-ordering infinite graphs of bounded tree-width.
10511288
Clique Minors in Graphs and Their Complements
A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t?1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c=c(t) independent of G such that the complement of G has a minor isomorphic to Ks, where s=?12(1+1/t)n?c?. We prove that Kostochka's conjecture is equivalent to the conjecture of Duchet and Meyniel that every graph with no minor isomorphic to Kt+1 has an independent set of size at least n/t. We deduce that Kostochka's conjecture holds for all integers t?5, and that a weaker form with s replaced by s?=?12(1+1/(2t))n?c? holds for all integers t?1.
2783736
List Edge-Colorings of Series-Parallel Graphs
It is proved that for every integer $k\ge3$, for every (simple) series-parallel graph $G$ with maximum degree at most $k$, and for every collection $(L(e):e\in E(G))$ of sets, each of size at least $k$, there exists a proper edge-coloring of $G$ such that for every edge $e\in E(G)$, the color of $e$ belongs to $L(e)$.
31409070
Hermite interpolation with a pair of spirals
Abstract The Hermite interpolation problem in the plane considered here is to join two points and to match given unit tangent vectors and signed curvatures at the two points with various G 2 curves consisting of a pair of spirals. The rotation of the tangent vector of the interpolating curve from one point to the other is restricted to being less than π. The necessary and sufficient conditions for the existence of each of the various curves are given.
18563409
A conditional density error model for the statistical analysis of microarray data
MOTIVATION
In many microarray experiments, relatively few intra- and inter-array replicate measurements are made due to significant cost limitations and sample availability. Compounding this problem is a lack of robust statistical methods for analyzing gene expression data with limited experimental replicates. As a result, the interpretation of the results of these experiments are difficult with little understanding of the probability of type I and type II errors.


RESULTS
The variability in a series of replicate microarray measurements was modelled using a combination of parametric and non-parametric methods. A 3-dimensional surface was created for the conditional distribution of the variability given the mean signal intensity in both the Cy3 and Cy5 channels. The results were used as the basis for developing statistical methods for analyzing gene expression data with limited experimental replicates.


AVAILABILITY
The statistical analysis scripts are available upon request.
3050709
Quality assurance in a student-based agile software engineering process
Agile methodologies have proven to be a popular addition to the software engineering toolbox, promising significant advances in quality for small teams, with developers no longer weighed under by the documentation said to characterise traditional approaches. Yet, in spite of these claims, quality assurance remains a question to which agile methodologies have given only a partially satisfactory answer. This work examines quality assurance practices among student developers working within a lightweight iterative development process. Our focus is upon the linkages between their reported practices and the quality levels observed in the systems delivered. The study has identified a range of approaches to improving quality for small, inexperienced teams, with applications to both the educational and SME environments.
37344904
Power System Bidding Tournaments for a Deregulated Environment
In this paper we describe certain tools for understanding and operating power systems in a deregulated environment. Many of the current models for this competitive market that employ an independent system operator (ISO) for controlling transmission, ensuring fair access and security, and providing a spot market for power will be studied. This centrally-dispatched power pool also ensures that generation meets demand based on bids submitted daily from independent generators (and from customers offering interruptible loads). Currently, most I S 0 bidding models allow only a single bid per day. In this paper, we present an asynchronous bidding scheme as a possible alternative. In particular, we examine the effects of including a feedback mechanism such that upon receiving generation levels from the ISO, independent generators (IGs) be allowed to modify their bid if they so desire. This competitive or ‘sequential’ bidding process should be allowed to take place each day for a predetermined period of time; in this way, IGs will have a chance to compete and hopefully optimize their profit margins. This paper also discusses the development tools necessary for examining the effects of different bidding processes on the I S 0 model and evaluating their capability of driving the market to an efJicient state of operation.
1283266
A guided clothoid spline
Abstract A method is described whereby a G 2 planar curve consisting of clothoid (Cornu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically, and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restricted somewhat so that a unique clothoid exists between each pair of points.