Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

Exploiting topology-directed nanoparticle disassembly for triggered drug delivery

YesThe physical properties of cyclic and linear polymers are markedly different; however, there are few examples which exploit these differences in clinical applications. In this study, we demonstrate that self-assemblies comprised of cyclic-linear graft copolymers are significantly more stable than the equivalent linear-linear graft copolymer assemblies. This difference in stability can be exploited to allow for triggered disassembly by cleavage of just a single bond within the cyclic polymer backbone, via disulfide reduction, in the presence of intracellular levels of l-glutathione. This topological effect was exploited to demonstrate the first example of topology-controlled particle disassembly for the controlled release of an anti-cancer drug in vitro. This approach represents a markedly different strategy for controlled release from polymer nanoparticles and highlights for the first time that a change in polymer topology can be used as a trigger in the design of delivery vehicles. We propose such constructs, which demonstrate disassembly behavior upon a change in polymer topology, could find application in the targeted delivery of therapeutic agents.ERC are acknowledged for support to M.C.A., A.P.D. (grant number: 681559) and R.O.R. (grant number: 615142)

Rotating black hole orbit functionals in the frequency domain

In many astrophysical problems, it is important to understand the behavior of functions that come from rotating (Kerr) black hole orbits. It can be particularly useful to work with the frequency domain representation of those functions, in order to bring out their harmonic dependence upon the fundamental orbital frequencies of Kerr black holes. Although, as has recently been shown by W. Schmidt, such a frequency domain representation must exist, the coupled nature of a black hole orbit's $r$ and $\theta$ motions makes it difficult to construct such a representation in practice. Combining Schmidt's description with a clever choice of timelike coordinate suggested by Y. Mino, we have developed a simple procedure that sidesteps this difficulty. One first Fourier expands all quantities using Mino's time coordinate $\lambda$. In particular, the observer's time $t$ is decomposed with $\lambda$. The frequency domain description is then built from the $\lambda$-Fourier expansion and the expansion of $t$. We have found this procedure to be quite simple to implement, and to be applicable to a wide class of functionals. We test the procedure using a simple test function, and then apply it in a particularly interesting case, the Weyl curvature scalar $\psi_4$ used in black hole perturbation theory.Comment: 16 pages, 2 figures. Submitted to Phys Rev D. New version gives a vastly improved algorithm due to Drasco for computing the Fourier transforms. Drasco has been added as an author. Also fixed some references and exterminated a small herd of typos; final published versio

Causal mechanisms in the clinical course and treatment of back pain

In recent years, there has been increasing interest in studying causal mechanisms in the development and treatment of back pain. The aim of this article is to provide an overview of our current understanding of causal mechanisms in the field. In the first section, we introduce key concepts and terminology. In the second section, we provide a brief synopsis of systematic reviews of mechanism studies relevant to the clinical course and treatment of back pain. In the third section, we reflect on the findings of our review to explain how understanding causal mechanisms can inform clinical practice and the implementation of best practice. In the final sections, we introduce contemporary methodological advances, highlight the key assumptions of these methods, and discuss future directions to advance the quality of mechanism-related studies in the back pain field

Acceleration Schemes for Ab-Initio Molecular Dynamics and Electronic Structure Calculations

We study the convergence and the stability of fictitious dynamical methods for electrons. First, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground-state than first-order steepest descent algorithms while retaining their numerical cost per time step. Our damped dynamics has efficiency comparable to that of conjugate gradient methods in typical electronic minimization problems. Then, we analyse the factors that limit the size of the integration time step in approaches based on plane-wave expansions. The maximum allowed time step is dictated by the highest frequency components of the fictitious electronic dynamics. These can result either from the large wavevector components of the kinetic energy or from the small wavevector components of the Coulomb potential giving rise to the so called {\it charge sloshing} problem. We show how to eliminate large wavevector instabilities by adopting a preconditioning scheme that is implemented here for the first-time in the context of Car-Parrinello ab-initio molecular dynamics simulations of the ionic motion. We also show how to solve the charge-sloshing problem when this is present. We substantiate our theoretical analysis with numerical tests on a number of different silicon and carbon systems having both insulating and metallic character.Comment: RevTex, 9 figures available upon request, to appear in Phys. Rev.

Seed coat mediated resistance against Aspergillus flavus infection in peanut

Toxic metabolites known as aflatoxins are produced via certain species of the Aspergillus genus, specifically A. flavus, A. parasiticus, A. nomius, and A. tamarie. Although various pre- and post-harvest strategies have been employed, aflatoxin contamination remains a major problem within peanut crop, especially in subtropical environments. Aflatoxins are the most well-known and researched mycotoxins produced within the Aspergillus genus (namely Aspergillus flavus) and are classified as group 1 carcinogens. Their effects and etiology have been extensively researched and aflatoxins are commonly linked to growth defects and liver diseases in humans and livestock. Despite the known importance of seed coats in plant defense against pathogens, peanut seed coat mediated defenses against Aspergillus flavus resistance, have not received considerable attention. The peanut seed coat (testa) is primarily composed of a complex cell wall matrix consisting of cellulose, lignin, hemicellulose, phenolic compounds, and structural proteins. Due to cell wall desiccation during seed coat maturation, postharvest A. flavus infection occurs without the pathogen encountering any active genetic resistance from the live cell(s) and the testa acts as a physical and biochemical barrier only against infection. The structure of peanut seed coat cell walls and the presence of polyphenolic compounds have been reported to inhibit the growth of A. flavus and aflatoxin contamination; however, there is no comprehensive information available on peanut seed coat mediated resistance. We have recently reviewed various plant breeding, genomic, and molecular mechanisms, and management practices for reducing A. flavus infection and aflatoxin contamination. Further, we have also proved that seed coat acts as a physical and biochemical barrier against A. flavus infection. The current review focuses specifically on the peanut seed coat cell wall-mediated disease resistance, which will enable researchers to understand the mechanism and design efficient strategies for seed coat cell wall-mediated resistance against A. flavus infection and aflatoxin contamination

Kaon-Nucleon Scattering Amplitudes and Z∗^*-Enhancements from Quark Born Diagrams

We derive closed form kaon-nucleon scattering amplitudes using the ``quark Born diagram" formalism, which describes the scattering as a single interaction (here the OGE spin-spin term) followed by quark line rearrangement. The low energy I=0 and I=1 S-wave KN phase shifts are in reasonably good agreement with experiment given conventional quark model parameters. For $k_{lab}> 0.7$ Gev however the I=1 elastic phase shift is larger than predicted by Gaussian wavefunctions, and we suggest possible reasons for this discrepancy. Equivalent low energy KN potentials for S-wave scattering are also derived. Finally we consider OGE forces in the related channels K$\Delta$, K$^*$N and K$^*\Delta$, and determine which have attractive interactions and might therefore exhibit strong threshold enhancements or ``Z$^*$-molecule" meson-baryon bound states. We find that the minimum-spin, minimum-isospin channels and two additional K$^*\Delta$ channels are most conducive to the formation of bound states. Related interesting topics for future experimental and theoretical studies of KN interactions are also discussed.Comment: 34 pages, figures available from the authors, revte

Manageable creativity

This article notes a perception in mainstream management theory and practice that creativity has shifted from being disruptive or destructive to 'manageable'. This concept of manageable creativity in business is reflected in a similar rhetoric in cultural policy, especially towards the creative industries. The article argues that the idea of 'manageable creativity' can be traced back to a 'heroic' and a 'structural' model of creativity. It is argued that the 'heroic' model of creativity is being subsumed within a 'structural' model which emphasises the systems and infrastructure around individual creativity rather than focusing on raw talent and pure content. Yet this structured approach carries problems of its own, in particular a tendency to overlook the unpredictability of creative processes, people and products. Ironically, it may be that some confusion in our policies towards creativity is inevitable, reflecting the paradoxes and transitions which characterise the creative process

Isospin-Violating Meson-Nucleon Vertices as an Alternate Mechanism of Charge-Symmetry Breaking

We compute isospin-violating meson-nucleon coupling constants and their consequent charge-symmetry-breaking nucleon-nucleon potentials. The couplings result from evaluating matrix elements of quark currents between nucleon states in a nonrelativistic constituent quark model; the isospin violations arise from the difference in the up and down constituent quark masses. We find, in particular, that isospin violation in the omega-meson--nucleon vertex dominates the class IV CSB potential obtained from these considerations. We evaluate the resulting spin-singlet--triplet mixing angles, the quantities germane to the difference of neutron and proton analyzing powers measured in elastic $\vec{n}-\vec{p}$ scattering, and find them commensurate to those computed originally using the on-shell value of the $\rho$-$\omega$ mixing amplitude. The use of the on-shell $\rho$-$\omega$ mixing amplitude at $q^2=0$ has been called into question; rather, the amplitude is zero in a wide class of models. Our model possesses no contribution from $\rho$-$\omega$ mixing at $q^2=0$, and we find that omega-meson exchange suffices to explain the measured $n-p$ analyzing power difference~at~183 MeV.Comment: 20 pages, revtex, 3 uuencoded PostScript figure