A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Goodbye to Projects? Briefing Paper 1: An Overview: Projects and Principles.

YesThis briefing paper reports on research exploring ten detailed case studies of livelihoods-oriented interventions operating in Tanzania, Lesotho, South Africa and Uganda. Analysing these interventions through an audit of sustainable livelihood `principles¿ (as a proxy for best practice) revealed general lessons both about the practical opportunities and challenges for employing sustainable livelihoods approaches to the design, implementation, monitoring and evaluation of development interventions and also about the changing format of development interventions.Department for International Developmen

Goodbye to Projects? - Briefing Paper 3: The changing format of development interventions.

yesThis briefing paper reports on research exploring ten detailed case studies of livelihoods-oriented interventions operating in Tanzania, South Africa, Uganda and Lesotho. As a proxy for best practice, these interventions were analysed through an audit of sustainable livelihood `principles¿. This revealed general lessons about both the practical opportunities and challenges for employing sustainable livelihoods approaches to the design, implementation, monitoring and evaluation of development interventions and also about the changing format of development interventions.Department for International Development

Goodbye to Projects? Briefing Paper 2: The Application of the SL Principles.

YesThis briefing paper reports on research exploring ten detailed case studies of livelihoods-oriented interventions operating in Tanzania, South Africa, Uganda and Lesotho. As a proxy for best practice, these interventions were analysed through an audit of sustainable livelihood `principles¿. This revealed general lessons about both the practical opportunities and challenges for employing sustainable livelihoods approaches to the design, implementation, monitoring and evaluation of development interventions and also about the changing format of development interventions.Department for International Development

Goodbye to Projects? - Briefing Paper 4: Lessons for the community-based planning interventions.

YesThis briefing paper compares two approaches to community-based planning in Tanzania, South Africa and Uganda. Analysing these interventions through an audit of sustainable livelihood `principles¿ (as a proxy for best practice) reveals general lessons about both the practical opportunities and challenges for employing sustainable livelihoods approaches to the design, implementation, monitoring and evaluation of development interventions and also about the changing format of development interventions.Department for International Developmen

The effect of sex hormones on the growth of HeLa tumour nodules in male and female mice.

The effect of exogenous sex hormones on the cell mediated response in male and female mice has been studied by measuring the subcutaneous growth of HeLa tumour nodules and the variation in the total lymphocyte count. It was found that oestrogen treated male and female mice experienced a profound lymphopenia which was vary rapid in onset. Concurrent with the lymphopenia there was prolongation of HeLa tumour nodule growth in female mice, but not in males. A lymphopenia occurred in androgen treated male mice with subsequent prolongation of HeLa tumour nodule growth, and a lymphocytosis in female mice, with reduction of HeLa tumour nodule growth

Timing is everything: Drivers of interannual variability in blue whale migration.

Blue whales need to time their migration from their breeding grounds to their feeding grounds to avoid missing peak prey abundances, but the cues they use for this are unknown. We examine migration timing (inferred from the local onset and cessation of blue whale calls recorded on seafloor-mounted hydrophones), environmental conditions (e.g., sea surface temperature anomalies and chlorophyll a), and prey (spring krill biomass from annual net tow surveys) during a 10 year period (2008-2017) in waters of the Southern California Region where blue whales feed in the summer. Colder sea surface temperature anomalies the previous season were correlated with greater krill biomass the following year, and earlier arrival by blue whales. Our results demonstrate a plastic response of blue whales to interannual variability and the importance of krill as a driving force behind migration timing. A decadal-scale increase in temperature due to climate change has led to blue whales extending their overall time in Southern California. By the end of our 10-year study, whales were arriving at the feeding grounds more than one month earlier, while their departure date did not change. Conservation strategies will need to account for increased anthropogenic threats resulting from longer times at the feeding grounds

Why do house-hunting ants recruit in both directions?

To perform tasks, organisms often use multiple procedures. Explaining the breadth of such behavioural repertoires is not always straightforward. During house hunting, colonies of Temnothorax albipennis ants use a range of behaviours to organise their emigrations. In particular, the ants use tandem running to recruit naïve ants to potential nest sites. Initially, they use forward tandem runs (FTRs) in which one leader takes a single follower along the route from the old nest to the new one. Later, they use reverse tandem runs (RTRs) in the opposite direction. Tandem runs are used to teach active ants the route between the nests, so that they can be involved quickly in nest evaluation and subsequent recruitment. When a quorum of decision-makers at the new nest is reached, they switch to carrying nestmates. This is three times faster than tandem running. As a rule, having more FTRs early should thus mean faster emigrations, thereby reducing the colony’s vulnerability. So why do ants use RTRs, which are both slow and late? It would seem quicker and simpler for the ants to use more FTRs (and higher quorums) to have enough knowledgeable ants to do all the carrying. In this study, we present the first testable theoretical explanation for the role of RTRs. We set out to find the theoretically fastest emigration strategy for a set of emigration conditions. We conclude that RTRs can have a positive effect on emigration speed if FTRs are limited. In these cases, low quorums together with lots of reverse tandem running give the fastest emigration

Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat