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

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

Periodic orbits of period 3 in the disc

Let f be an orientation preserving homeomorphism of the disc D2 which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi /3 or 4 pi /3, or f has a periodic point of least period n for each n in N*.Comment: 7 page

Molecular modeling of a tandem two pore domain potassium channel reveals a putative binding Site for general anesthetics

[Image: see text] Anesthetics are thought to mediate a portion of their activity via binding to and modulation of potassium channels. In particular, tandem pore potassium channels (K2P) are transmembrane ion channels whose current is modulated by the presence of general anesthetics and whose genetic absence has been shown to confer a level of anesthetic resistance. While the exact molecular structure of all K2P forms remains unknown, significant progress has been made toward understanding their structure and interactions with anesthetics via the methods of molecular modeling, coupled with the recently released higher resolution structures of homologous potassium channels to act as templates. Such models reveal the convergence of amino acid regions that are known to modulate anesthetic activity onto a common three- dimensional cavity that forms a putative anesthetic binding site. The model successfully predicts additional important residues that are also involved in the putative binding site as validated by the results of suggested experimental mutations. Such a model can now be used to further predict other amino acid residues that may be intimately involved in the target-based structure–activity relationships that are necessary for anesthetic binding

Migration control: A distance compensation strategy in ants

©The Author(s) 2016. This article is published with open access at Springerlink.com. Migratory behaviour forms an intrinsic part of the life histories of many organisms but is often a high-risk process. Consequently, varied strategies have evolved to negate such risks, but empirical data relating to their functioning are limited. In this study, we use the model system of the househunting ant Temnothorax albipennis to demonstrate a key strategy that can shorten migration exposure times in a group of social insects. Colonies of these ants frequently migrate to new nest sites, and due to the nature of their habitat, the distances over which they do so are variable, leading to fluctuating potential costs dependent on migration parameters. We show that colonies of this species facultatively alter the dynamics of a migration and so compensate for the distance over which a given migration occurs. Specifically, they achieve this by modulating the rate of ‘tandem running’, in which workers teach each other the route to a new nest site. Using this method, colonies are able to engage a larger number of individuals in the migration process when the distance to be traversed is greater, and furthermore, the system appears to be based on perceived encounter rate at the individual level. This form of decentralised control highlights the adaptive nature of a behaviour of ecological importance, and indicates that the key to its robustness lies in the use of simple rules. Additionally, our results suggest that such coordinated group reactions are central to achieving the high levels of ecological success seen in many eusocial organisms

Relationships between the El-Niño Southern Oscillation and spate flows in southern Africa and Australia

International audienceThe flow records of arid zone rivers are characterised by a high degree of seasonal variability, being dominated by long periods of very low or zero flow. Discrete flow events in these rivers are influenced by aseasonal factors such as global climate forcings. The atmospheric circulations of the El-Niño Southern Oscillation (ENSO) have been shown to influence climate regimes across many parts of the world. Strong teleconnections between changing ENSO regimes and discharges are likely to be observed in highly variable arid zones. In this paper, the influence of ENSO mechanisms on the flow records of two arid zone rivers in each of Australia and Southern Africa are identified. ENSO signals, together with multi-decadal variability in their impact as identified through seasonal values of the Interdecadal Pacific Oscillation (IPO) index, are shown to influence both the rate of occurrence and the size of discrete flow episodes in these rivers. Keywords: arid zones, streamflow, spates, climate variability, ENSO, Interdecadal Pacific Oscillation, IP

Partnership, ownership and control: the impact of corporate governance on employment relations

Prevailing patterns of dispersed share ownership and rules of corporate governance for UK listed companies appear to constrain the ability of managers to make credible, long-term commitments to employees of the kind needed to foster effective labour-management partnerships. We present case study evidence which suggests that such partnerships can nevertheless emerge where product market conditions and the regulatory environment favour a stakeholder orientation. Proactive and mature partnerships may also be sustained where the board takes a strategic approach to mediating between the claims of different stakeholder groups, institutional investors are prepared to take a long-term view of their holdings, and strong and independent trade unions are in a position to facilitate organisational change

Control of CNS midline transcription by asymmetric E-box-like elements: Similarity to xenobiotic responsive regulation

Central nervous system midline cells constitute a discrete group of Drosophila embryonic cells with numerous functional and developmental roles. Corresponding to their separate identity, the midline cells display patterns of gene expression distinct from the lateral central nervous system. A conserved 5 base pair sequence (ACGTG) was identified in central nervous system midline transcriptional enhancers of three genes. Germ-line transformation experiments indicate that this motif forms the core of an element required for central nervous system midline transcription. The central nervous system midline element is related to the mammalian xenobiotic response element, which regulates transcription of genes that metabolize aromatic hydrocarbons. These data suggest a model whereby related basic-helix-loop-helix-PAS proteins interact with asymmetric E-box-like target sequences to control these disparate processes

Risky business for a juvenile marine predator? Testing the influence of foraging strategies on size and growth rate under natural conditions

Mechanisms driving selection of body size and growth rate in wild marine vertebrates are poorly understood, thus limiting knowledge of their fitness costs at ecological, physiological and genetic scales. Here, we indirectly tested whether selection for size-related traits of juvenile sharks that inhabit a nursery hosting two dichotomous habitats, protected mangroves (low predation risk) and exposed seagrass beds (high predation risk), is influenced by their foraging behaviour. Juvenile sharks displayed a continuum of foraging strategies between mangrove and seagrass areas, with some individuals preferentially feeding in one habitat over another. Foraging habitat was correlated with growth rate, whereby slower growing, smaller individuals fed predominantly in sheltered mangroves, whereas larger, faster growing animals fed over exposed seagrass. Concomitantly, tracked juveniles undertook variable movement behaviours across both the low and high predation risk habitat. These data provide supporting evidence for the hypothesis that directional selection favouring smaller size and slower growth rate, both heritable traits in this shark population, may be driven by variability in foraging behaviour and predation risk. Such evolutionary pathways may be critical to adaptation within predator-driven marine ecosystems