Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Axial Multicentric Osteosarcoma in an English Cocker Spaniel

No abstract available

Intelligent sampling for the measurement of structured surfaces

Uniform sampling in metrology has known drawbacks such as coherent spectral aliasing and a lack of efficiency in terms of measuring time and data storage. The requirement for intelligent sampling strategies has been outlined over recent years, particularly where the measurement of structured surfaces is concerned. Most of the present research on intelligent sampling has focused on dimensional metrology using coordinate-measuring machines with little reported on the area of surface metrology. In the research reported here, potential intelligent sampling strategies for surface topography measurement of structured surfaces are investigated by using numerical simulation and experimental verification. The methods include the jittered uniform method, low-discrepancy pattern sampling and several adaptive methods which originate from computer graphics, coordinate metrology and previous research by the authors. By combining the use of advanced reconstruction methods and feature-based characterization techniques, the measurement performance of the sampling methods is studied using case studies. The advantages, stability and feasibility of these techniques for practical measurements are discussed

Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered

An RNA-Seq bioinformatics pipeline for data processing of Arabidopsis thaliana datasets

Floral transition is a crucial event in the reproductive cycle of a flowering plant during which many genes are expressed that govern the transition phase and regulate the expression and functions of several other genes involved in the process. Identification of additional genes connected to flowering genes is vital since they may regulate flowering genes and vice versa. Through our study, expression values of these additional genes has been found similar to flowering genes FLC and LFY in the transition phase. The presented approach plays a crucial role in this discovery. An RNA-Seq computational pipeline was developed for identification of novel genes involved in floral transition from A. thaliana apical shoot meristem time-series data. By intersecting differentially expressed genes from Cuffdiff, DESeq and edgeR methods, 690 genes were identified. Using FDR cutoff of 0.05, we identified 30 genes involved in glucosinolate and glycosinolate biosynthetic processes as principle regulators in the transition phase which provide protection to plants from herbivores and pathogens during flowering. Additionally, expression profiles of highly connected genes in protein-protein interaction network analysis revealed 76 genes with non-functional association and high correlation to flowering genes FLC and LFY which suggests their potential and principal role in floral regulation not identified previously in any studies

Supersonic optical tunnels for Bose-Einstein condensates

We propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a hollow laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilise up to 9 vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of the optical vortex can be made supersonic by inserting a laser-generated hump potential. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons. Finally, we discuss prospects of using these solitons for analogue gravity experiments.Comment: 14 pages, 3 figures, published versio

Radar-aeolian roughness project

The objective is to establish an empirical relationship between measurements of radar, aeolian, and surface roughness on a variety of natural surfaces and to understand the underlying physical causes. This relationship will form the basis for developing a predictive equation to derive aeolian roughness from radar backscatter. Results are given from investigations carried out in 1989 on the principal elements of the project, with separate sections on field studies, radar data analysis, laboratory simulations, and development of theory for planetary applications

Nanopercolation

We investigate through direct molecular mechanics calculations the geometrical properties of hydrocarbon mantles subjected to percolation disorder. We show that the structures of mantles generated at the critical percolation point have a fractal dimension $d_{f} \approx 2.5$. In addition, the solvent access surface $A_{s}$ and volume $V_{s}$ of these molecules follow power-law behavior, $A_{s} \sim L^{\alpha_A}$ and $V_{s} \sim L^{\alpha_V}$, where $L$ is the system size, and with both critical exponents $\alpha_A$ and $\alpha_V$ being significantly dependent on the radius of the accessing probing molecule, $r_{p}$. Our results from extensive simulations with two distinct microscopic topologies (i.e., square and honeycomb) indicate the consistency of the statistical analysis and confirm the self-similar characteristic of the percolating hydrocarbons. Due to their highly branched topology, some of the potential applications for this new class of disordered molecules include drug delivery, catalysis, and supramolecular structures.Comment: 4 pages, 5 figure

Spin-orbit hybrid entanglement of photons and quantum contextuality

We demonstrate electromagnetic quantum states of single photons and of correlated photon pairs exhibiting "hybrid" entanglement between spin and orbital angular momentum. These states are obtained from entangled photon pairs emitted by spontaneous parametric down conversion, by employing a $q$-plate for coupling the spin and orbital degrees of freedom of a photon. Entanglement and contextual quantum behavior (that is also non-local, in the case of photon pairs) is demonstrated by the reported violation of the Clauser-Horne-Shimony-Holt inequality. In addition a classical analog of the hybrid spin-orbit photonic entanglement is reported and discussed.Comment: 5 pages, 3 figure