Limit cycles of a predator-prey model with intratrophic predation

AbstractWe present some properties of a differential system that can be used to model intratrophic predation in simple predator–prey models. In particular, for the model we determine the maximum number of limit cycles that can exist around the only fine focus in the first quadrant and show that this critical point cannot be a centre

Centres and limit cycles for an extended Kukles system

We present conditions for the origin to be a centre for a class of cubic systems. Some of the centre conditions are determined by finding complicated invariant functions. We also investigate the coexistence of fine foci and the simultaneous bifurcation of limit cycles from them

Integrating biological knowledge into variable selection : an empirical Bayes approach with an application in cancer biology

Background: An important question in the analysis of biochemical data is that of identifying subsets of molecular variables that may jointly influence a biological response. Statistical variable selection methods have been widely used for this purpose. In many settings, it may be important to incorporate ancillary biological information concerning the variables of interest. Pathway and network maps are one example of a source of such information. However, although ancillary information is increasingly available, it is not always clear how it should be used nor how it should be weighted in relation to primary data. Results: We put forward an approach in which biological knowledge is incorporated using informative prior distributions over variable subsets, with prior information selected and weighted in an automated, objective manner using an empirical Bayes formulation. We employ continuous, linear models with interaction terms and exploit biochemically-motivated sparsity constraints to permit exact inference. We show an example of priors for pathway- and network-based information and illustrate our proposed method on both synthetic response data and by an application to cancer drug response data. Comparisons are also made to alternative Bayesian and frequentist penalised-likelihood methods for incorporating network-based information. Conclusions: The empirical Bayes method proposed here can aid prior elicitation for Bayesian variable selection studies and help to guard against mis-specification of priors. Empirical Bayes, together with the proposed pathway-based priors, results in an approach with a competitive variable selection performance. In addition, the overall procedure is fast, deterministic, and has very few user-set parameters, yet is capable of capturing interplay between molecular players. The approach presented is general and readily applicable in any setting with multiple sources of biological prior knowledge

Sustainability of the chemical manufacturing industry - Towards a new paradigm?

This paper describes the current situation of the chemicalmanufacturingindustry, with special reference to Europe and looks to the future sustainability demands on the sector, and the implications of these demands for chemical engineering education. These implications include definitions of sustainability criteria for the sector and the need for transparent reporting under the Triple Bottom Line approach. The response of the education system to the sustainability agenda over the years and a number of strategies to incorporate it into courses are described. The important role of chemical (or more generally, process) engineers in delivering sustainable solutions is emphasised but this also suggests that anew way of thinking about the discipline is required. Indeed, this paper argues that the demand for a sustainable chemicalmanufacturing sector could bring about the next paradigm shift in the discipline which has been predicted for some time

Predictions of mb/mτm_b/m_{\tau} and mtm_t in an Asymptotically Non-Free Theory

We discuss an extention of the Minimal Supersymmetric Standard Model (MSSM) with the 4th and anti-4th generations which have $SU(2)_L\times U(1)_Y$ invariant masses. Due to the the extra generations, all three running gauge couplings become asymptotically non--free while preserving gauge coupling unification at the GUT scale. We show that due to the asymptotically non--free character of the gauge couplings: (1) the top and bottom Yukawa couplings are strongly focused onto infrared fixed points as they are evolved down in scale making their values at \mu=\mz insensitive to their initial values at \mu=\mgut; (2) the model predicts \R(\mz) \equiv Y_b/Y_\tau |_{\mu =\mz}\approx 1.8, which is consistent with the experimental value provided we take the ratio of Yukawa couplings at the GUT scale to be \R(\mgut) = Y_b/Y_\tau |_{\mu = \mgut} = 1/3; (3) the $t$ mass prediction comes out to be \mt\approx 180\,\GeV which is also consistent with experiment.Comment: 20 pgs. 7 figures. Latex2e. othersym.sty, suceqn.sty include

On the Energy Dependence of Galactic Cosmic Ray Anisotropies in the Very Local Interstellar Medium

We report on the energy dependence of galactic cosmic rays (GCRs) in the very local interstellar medium (VLISM) as measured by the Low Energy Charged Particle (LECP) instrument on the Voyager 1 (V1) spacecraft. The LECP instrument includes a dual-ended solid state detector particle telescope mechanically scanning through 360 deg across eight equally-spaced angular sectors. As reported previously, LECP measurements showed a dramatic increase in GCR intensities for all sectors of the >=211 MeV count rate (CH31) at the V1 heliopause (HP) crossing in 2012, however, since then the count rate data have demonstrated systematic episodes of intensity decrease for particles around 90{\deg} pitch angle. To shed light on the energy dependence of these GCR anisotropies over a wide range of energies, we use V1 LECP count rate and pulse height analyzer (PHA) data from >=211 MeV channel together with lower energy LECP channels. Our analysis shows that while GCR anisotropies are present over a wide range of energies, there is a decreasing trend in the amplitude of second-order anisotropy with increasing energy during anisotropy episodes. A stronger pitch-angle scattering at the higher velocities is argued as a potential cause for this energy dependence. A possible cause for this velocity dependence arising from weak rigidity dependence of the scattering mean free path and resulting velocity-dominated scattering rate is discussed. This interpretation is consistent with a recently reported lack of corresponding GCR electron anisotropies

The International Research Society of Spinal Deformities (IRSSD) and its contribution to science

From the time of its initial, informal meetings starting in 1980 to its formal creation in 1990, the IRSSD has met on a bi-annual basis to discuss all aspects of the spine and associated deformities. It has encouraged open discussion on all topics and, in particular, has tried to be the seed-bed for new ideas. The members are spread around the world and include people from all areas of academia as well as the most important people, the patients themselves. Most notably, application of the ideas and results of the research has always been at the forefront of the discussions. This paper was conceived with the idea of evaluating the impact made by the IRSSD over the last 30 years in the various areas and is intended to create discussion for the upcoming meeting in Montreal regarding future focus: "We are lost over the Atlantic Ocean but we are making good time.

The association between air pollution and type 2 diabetes in a large cross-sectional study in Leicester: The CHAMPIONS Study

Background: Observational evidence suggests there is an association between air pollution and type 2 diabetes; however, there is high risk of bias. Objective: To investigate the association between air pollution and type 2 diabetes, while reducing bias due to exposure assessment, outcome assessment, and confounder assessment. Methods: Data were collected from 10,443 participants in three diabetes screening studies in Leicestershire, UK. Exposure assessment included standard, prevailing estimates of outdoor nitrogen dioxide and particulate matter concentrations in a 1 × 1 km area at the participant's home postcode. Three-year exposure was investigated in the primary analysis and one-year exposure in a sensitivity analysis. Outcome assessment included the oral glucose tolerance test for type 2 diabetes. Confounder assessment included demographic factors (age, sex, ethnicity, smoking, area social deprivation, urban or rural location), lifestyle factors (body mass index and physical activity), and neighbourhood green space. Results: Nitrogen dioxide and particulate matter concentrations were associated with type 2 diabetes in unadjusted models. There was no statistically significant association between nitrogen dioxide concentration and type 2 diabetes after adjustment for demographic factors (odds: 1.08; 95% CI: 0.91, 1.29). The odds of type 2 diabetes was 1.10 (95% CI: 0.92, 1.32) after further adjustment for lifestyle factors and 0.91 (95% CI: 0.72, 1.16) after yet further adjustment for neighbourhood green space. The associations between particulate matter concentrations and type 2 diabetes were also explained away by demographic factors. There was no evidence of exposure definition bias. Conclusions: Demographic factors seemed to explain the association between air pollution and type 2 diabetes in this cross-sectional study. High-quality longitudinal studies are needed to improve our understanding of the association