From First Lyapunov Coefficients to Maximal Canards

Hopf bifurcations in fast-slow systems of ordinary differential equations can be associated with surprising rapid growth of periodic orbits. This process is referred to as canard explosion. The key step in locating a canard explosion is to calculate the location of a special trajectory, called a maximal canard, in parameter space. A first-order asymptotic expansion of this location was found by Krupa and Szmolyan in the framework of a "canard point"-normal-form for systems with one fast and one slow variable. We show how to compute the coefficient in this expansion using the first Lyapunov coefficient at the Hopf bifurcation thereby avoiding use of this normal form. Our results connect the theory of canard explosions with existing numerical software, enabling easier calculations of where canard explosions occur.Comment: preprint version - for final version see journal referenc

Is your article EV-TRACKed?

The EV-TRACK knowledgebase is developed to cope with the need for transparency and rigour to increase reproducibility and facilitate standardization of extracellular vesicle (EV) research. The knowledgebase includes a checklist for authors and editors intended to improve the transparency of methodological aspects of EV experiments, allows queries and meta-analysis of EV experiments and keeps track of the current state of the art. Widespread implementation by the EV research community is key to its success

Asymptotics of Symmetry in Matroids

We prove that asymptotically almost all matroids have a trivial automorphism group, or an automorphism group generated by a single transposition. Additionally, we show that asymptotically almost all sparse paving matroids have a trivial automorphism group.Comment: 10 page

On the number of matroids compared to the number of sparse paving matroids

It has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enumeration of matroids, i.e. that $\lim_{n\rightarrow\infty} s_n/m_n = 1$, where $m_n$ denotes the number of matroids on $n$ elements, and $s_n$ the number of sparse paving matroids. In this paper, we show that $$\lim_{n\rightarrow \infty}\frac{\log s_n}{\log m_n}=1.$$ We prove this by arguing that each matroid on $n$ elements has a faithful description consisting of a stable set of a Johnson graph together with a (by comparison) vanishing amount of other information, and using that stable sets in these Johnson graphs correspond one-to-one to sparse paving matroids on $n$ elements. As a consequence of our result, we find that for some $\beta > 0$, asymptotically almost all matroids on $n$ elements have rank in the range $n/2 \pm \beta\sqrt{n}$.Comment: 12 pages, 2 figure

Intergenerational transfer of time and risk preferences

Date of Acceptance: 03/06/15 Acknowledgements The Chief Scientist Office of the Scottish Government Health and Social Care Directorates funds HERU. The views expressed in this paper are those of the authors only and not those of the funding body. HB received financial support from the Medical Research Council/Economic and Social Research Council/National Institute of Health Research under grant G0802291. This paper uses unit record data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey. The HILDA Project was initiated and is funded by the Australian Government Department of Families, Housing, Community Services and Indigenous Affairs (FaHCSIA) and is managed by the Melbourne Institute of Applied Economic and Social Research (Melbourne Institute). The findings and views reported in this paper, however, are those of the author and should not be attributed to either FaHCSIA or the Melbourne Institute.Peer reviewedPublisher PD

The Role of Time Preferences in the Intergenerational Transfer of Smoking

Peer reviewedPublisher PD

Intramode and Fermi relaxation in CO2, their influence on multiple-pass, short-pulse energy extraction

Analytical, experimental and numerical results concerning the influence of intramode and Fermi relaxation on multiple-pass, nanosecond-pulse energy extraction are presented. Multiple-pass energy extraction experiments show satisfactory agreement with the analytical and numerical calculations which predict a significant increase in extracted energy. In three passes, an amount of 9.7 J/l was extracted at an efficiency of 4.3%, These values are taken with respect to the volume of the beam inside the amplifier. In a single pass only 3.5 J/l was extracted

Counting matroids in minor-closed classes

A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notion of cover complexity, the minimal size of such a flat cover, as a measure for the complexity of a matroid, and present bounds on the number of matroids on $n$ elements whose cover complexity is bounded. We apply cover complexity to show that the class of matroids without an $N$-minor is asymptotically small in case $N$ is one of the sparse paving matroids $U_{2,k}$, $U_{3,6}$, $P_6$, $Q_6$, or $R_6$, thus confirming a few special cases of a conjecture due to Mayhew, Newman, Welsh, and Whittle. On the other hand, we show a lower bound on the number of matroids without $M(K_4)$-minor which asymptoticaly matches the best known lower bound on the number of all matroids, due to Knuth.Comment: 13 pages, 3 figure

Tetrahydrofuran (co)polymers as potential materials for vascular prostheses

Polyethers were studied as potential materials for vascular prostheses. By crosslinking poly(tetramethylene oxide) (PTMO) with poly(ethylene oxide) (PEO), hydrophilic networks were obtained containing PTMO as well as PEO. Attempts were made to reduce the crystallinity and melting point of PTMO because of the required elastomeric behaviour at body temperature. Compared to non-crosslinked PTMO, crosslinking in the melt resulted in a decrease in the melting point from 43·7 to 38·7°C and a decrease of the crystallinity from 46 to 28%. By copolymerizing tetrahydrofuran with oxetane or dimethyloxetane, melting points below 38°C were obtained, together with crystallinities lower than 20%