Survey of the storage behaviour of uranium dioxide.

The storage behaviour of uranium dioxide powder is reviewed. Topics covered include the amount of oxygen taken up under storage conditions, the basic oxidation processes, the effects of extra oxygen on the fabrication and irradiation behaviour of uranium dioxide, the pyrophoric reaction of uranium dioxide powders in air, the stabilization of uranium dioxide against oxidation, and the effectiveness of sealed containers. The pyrophoric process in air at room temperature is shown to be the result of rapid chemisorption of oxygen, and a theory explaining this effect is developed. Equations are also derived to describe the overall oxidation behaviour in air at room temperature, and they are found to agree with what few experimental data are available

A Universal Point Set for 2-Outerplanar Graphs

A point set $S \subseteq \mathbb{R}^2$ is universal for a class $\cal G$ if every graph of ${\cal G}$ has a planar straight-line embedding on $S$. It is well-known that the integer grid is a quadratic-size universal point set for planar graphs, while the existence of a sub-quadratic universal point set for them is one of the most fascinating open problems in Graph Drawing. Motivated by the fact that outerplanarity is a key property for the existence of small universal point sets, we study 2-outerplanar graphs and provide for them a universal point set of size $O(n \log n)$.Comment: 23 pages, 11 figures, conference version at GD 201

Beyond Outerplanarity

We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer $k$-planar graphs, where each edge is crossed by at most $k$ other edges; and, outer $k$-quasi-planar graphs where no $k$ edges can mutually cross. We show that the outer $k$-planar graphs are $(\lfloor\sqrt{4k+1}\rfloor+1)$-degenerate, and consequently that every outer $k$-planar graph can be $(\lfloor\sqrt{4k+1}\rfloor+2)$-colored, and this bound is tight. We further show that every outer $k$-planar graph has a balanced separator of size $O(k)$. This implies that every outer $k$-planar graph has treewidth $O(k)$. For fixed $k$, these small balanced separators allow us to obtain a simple quasi-polynomial time algorithm to test whether a given graph is outer $k$-planar, i.e., none of these recognition problems are NP-complete unless ETH fails. For the outer $k$-quasi-planar graphs we prove that, unlike other beyond-planar graph classes, every edge-maximal $n$-vertex outer $k$-quasi planar graph has the same number of edges, namely $2(k-1)n - \binom{2k-1}{2}$. We also construct planar 3-trees that are not outer $3$-quasi-planar. Finally, we restrict outer $k$-planar and outer $k$-quasi-planar drawings to \emph{closed} drawings, where the vertex sequence on the boundary is a cycle in the graph. For each $k$, we express closed outer $k$-planarity and \emph{closed outer $k$-quasi-planarity} in extended monadic second-order logic. Thus, closed outer $k$-planarity is linear-time testable by Courcelle's Theorem.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Bundled Crossings Revisited

An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into \emph{bundles}. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between two bundles, i.e., as a \emph{bundled crossing}. We consider the problem of bundled crossing minimization: A graph is given and the goal is to find a bundled drawing with at most $k$ bundled crossings. We show that the problem is NP-hard when we require a simple drawing. Our main result is an FPT algorithm (in $k$) when we require a simple circular layout. These results make use of the connection between bundled crossings and graph genus.Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019

Estradiol and testosterone levels in patients undergoing partial hepatectomy - A possible signal for hepatic regeneration?

In five adult male patients undergoing a 40-60% partial hepatectomy, serum sex hormone levels before and after hepatic resection were determined. Blood was drawn immediately prior to each surgical procedure and at specified time points postoperatively. Compared to hormone levels found prior to surgery, following major hepatic resection, estradiol levels increase at 24 and 48 hr, while testosterone levels decline, being significantly reduced at 96 and 144 hr. These data demonstrate that adult males who undergo a 40-60% partial hepatectomy experience alterations in their sex hormone levels similar to those observed in male rats following a 70% hepatectomy. These changes in sex hormone levels have been associated in animals with an alteration of the sex hormone receptor status of the liver that is thought to participate in the initiation of the regenerative response. These studies suggest, but do not prove, that in man, as in the case of the rat, sex hormones may participate in the initiation of or at least modulate in part the regenerative response that occurs following a major hepatic resection. © 1989 Plenum Publishing Corporation

Universal Geometric Graphs

We introduce and study the problem of constructing geometric graphs that have few vertices and edges and that are universal for planar graphs or for some sub-class of planar graphs; a geometric graph is \emph{universal} for a class $\mathcal H$ of planar graphs if it contains an embedding, i.e., a crossing-free drawing, of every graph in $\mathcal H$. Our main result is that there exists a geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex forests; this extends to the geometric setting a well-known graph-theoretic result by Chung and Graham, which states that there exists an $n$-vertex graph with $O(n \log n)$ edges that contains every $n$-vertex forest as a subgraph. Our $O(n \log n)$ bound on the number of edges cannot be improved, even if more than $n$ vertices are allowed. We also prove that, for every positive integer $h$, every $n$-vertex convex geometric graph that is universal for $n$-vertex outerplanar graphs has a near-quadratic number of edges, namely $\Omega_h(n^{2-1/h})$; this almost matches the trivial $O(n^2)$ upper bound given by the $n$-vertex complete convex geometric graph. Finally, we prove that there exists an $n$-vertex convex geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex caterpillars.Comment: 20 pages, 8 figures; a 12-page extended abstracts of this paper will appear in the Proceedings of the 46th Workshop on Graph-Theoretic Concepts in Computer Science (WG 2020

Algorithms and Bounds for Drawing Directed Graphs

In this paper we present a new approach to visualize directed graphs and their hierarchies that completely departs from the classical four-phase framework of Sugiyama and computes readable hierarchical visualizations that contain the complete reachability information of a graph. Additionally, our approach has the advantage that only the necessary edges are drawn in the drawing, thus reducing the visual complexity of the resulting drawing. Furthermore, most problems involved in our framework require only polynomial time. Our framework offers a suite of solutions depending upon the requirements, and it consists of only two steps: (a) the cycle removal step (if the graph contains cycles) and (b) the channel decomposition and hierarchical drawing step. Our framework does not introduce any dummy vertices and it keeps the vertices of a channel vertically aligned. The time complexity of the main drawing algorithms of our framework is $O(kn)$, where $k$ is the number of channels, typically much smaller than $n$ (the number of vertices).Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Calcium Homeostasis in Myogenic Differentiation Factor 1 (MyoD)-Transformed, Virally-Transduced, Skin-Derived Equine Myotubes

Dysfunctional skeletal muscle calcium homeostasis plays a central role in the pathophysiology of several human and animal skeletal muscle disorders, in particular, genetic disorders associated with ryanodine receptor 1 (RYR1) mutations, such as malignant hyperthermia, central core disease, multiminicore disease and certain centronuclear myopathies. In addition, aberrant skeletal muscle calcium handling is believed to play a pivotal role in the highly prevalent disorder of Thoroughbred racehorses, known as Recurrent Exertional Rhabdomyolysis. Traditionally, such defects were studied in human and equine subjects by examining the contractile responses of biopsied muscle strips exposed to caffeine, a potent RYR1 agonist. However, this test is not widely available and, due to its invasive nature, is potentially less suitable for valuable animals in training or in the human paediatric setting. Furthermore, increasingly, RYR1 gene polymorphisms (of unknown pathogenicity and significance) are being identified through next generation sequencing projects. Consequently, we have investigated a less invasive test that can be used to study calcium homeostasis in cultured, skin-derived fibroblasts that are converted to the muscle lineage by viral transduction with a MyoD (myogenic differentiation 1) transgene. Similar models have been utilised to examine calcium homeostasis in human patient cells, however, to date, there has been no detailed assessment of the cells’ calcium homeostasis, and in particular, the responses to agonists and antagonists of RYR1. Here we describe experiments conducted to assess calcium handling of the cells and examine responses to treatment with dantrolene, a drug commonly used for prophylaxis of recurrent exertional rhabdomyolysis in horses and malignant hyperthermia in humans

A Fixed-Parameter Algorithm for the Max-Cut Problem on Embedded 1-Planar Graphs

We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most $3^k$ planar graphs, using edge removal and node contraction. The \textsc{Max-Cut} problem is then solved on the planar graphs using established polynomial-time algorithms. We show that a maximum cut in the given 1-planar graph can be derived from the solutions for the planar graphs. Our algorithm computes a maximum cut in an embedded 1-planar graph with $n$ nodes and $k$ edge crossings in time $\mathcal{O}(3^k \cdot n^{3/2} \log n)$.Comment: conference version from IWOCA 201

Biogenesis of the inner membrane complex is dependent on vesicular transport by the alveolate specific GTPase Rab11B

Apicomplexan parasites belong to a recently recognised group of protozoa referred to as Alveolata. These protists contain membranous sacs (alveoli) beneath the plasma membrane, termed the Inner Membrane Complex (IMC) in the case of Apicomplexa. During parasite replication the IMC is formed de novo within the mother cell in a process described as internal budding. We hypothesized that an alveolate specific factor is involved in the specific transport of vesicles from the Golgi to the IMC and identified the small GTPase Rab11B as an alveolate specific Rab-GTPase that localises to the growing end of the IMC during replication of Toxoplasma gondii. Conditional interference with Rab11B function leads to a profound defect in IMC biogenesis, indicating that Rab11B is required for the transport of Golgi derived vesicles to the nascent IMC of the daughter cell. Curiously, a block in IMC biogenesis did not affect formation of sub-pellicular microtubules, indicating that IMC biogenesis and formation of sub-pellicular microtubules is not mechanistically linked. We propose a model where Rab11B specifically transports vesicles derived from the Golgi to the immature IMC of the growing daughter parasites