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

Dinoflagellate blooms and physical systems in the Gulf of Maine

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution May 1990Numerous studies have shown dinoflagellate blooms to be closely related to density discontinuities and fronts in the ocean. The spatial and temporal patterns of the dinoflagellate population depend on the predominant mode of physical forcing, and its scales of variability. The present study combined field sampling of hydrographic and biological variables to examine the relationship of dinoflagellate population distributions to physical factors along the southwestern cost of the Gulf of Maine. A bloom of Ceratium longipes occurred along this coast during the month of June, 1987. A simple model which coupled along-isopycnal diffusion with the logistic growth equation suggested that the cells had a growth rate of about 0.1 d-1 , and had reached a steady horizontal across-shelf distribution within about 10 d. Fur~her variations in population density appeared to be related to fluctuations of light with periods of -10 d. To our knowledge, this was the first use of this simple diffusion model as a diagnostic tool for quantifying parameters describing the growth and movement of a specific phytoplankton population. Blooms of the toxic dinoflagellate, Alexandrium tamarense have been nearly annual features along the coasts of southern Maine, New Hampshire and Massachusetts since 1972; however the mechanisms controlling the distribution of cells and concomitant shellfish toxicity are relatively poorly understood. Analysis of field data gathered from April to September, 1987-1989, showed that in two years when toxicity was detected in the southern part of this region, A. tamarense cells were apparently transported into the study area between Portsmouth and Cape Ann, Massachusetts, in a coastally trapped buoyant plume. This plume appears to have been formed off Maine by the outflow from the Androscoggin and Kennebec Rivers. Flow rates of these rivers, hydrographic sections, and satellite images suggest that the plume had a duration of about a month, and extended alongshore for several hundred kilometers. The distribution of cells followed the position of the plume as it was influenced by wind and topography. Thus when winds were downwelling-favourable, cells were moved alongshore to the south, and were held to the coast; when winds were upwelling-favourable, the plume sometimes separated from the coast, advecting the cells offshore. The alongshore advection of toxic cells within a coastally trapped buoyant plume can explain the temporal and spatial patterns of shellfish toxicity along the coast. The general observation of a north-to-south temporal trend of toxicity is consistent with the southward advection of the plume. In 1987 when no plume was present, Alexandrium tamarense cells were scarce, and no toxicity was recorded at the southern stations. A hypothesis was formulated explaining the development and spread of toxic dinoflagellate blooms in this region. This plume-advection hypothesis included: source A. tamarense populations in the north, possibly associated with the Androscoggin and Kennebec estuaries; a relationship between toxicity patterns and river flow volume and timing of flow peaks; and a relationship between wind stresses and the distribution of low salinity water and cells. Predictions of the plume-advection hypothesis were tested with historical records of shellfish toxicity, wind speed and direction, and river flow. The predictions tested included the north-south progression of toxic outbreaks, the occurrence of a peak in river flow prior to the PSP events, the relationship of transit time of PSP toxicity along the coast with river flow volume, and the influence of surface wind stress on the timing and location of shellfish toxicity. All the predictions tested were supported by the historical records. In addition it was found that the plume-advection hypothesis explains many details of the timing and spread of shellfish toxicity, including the sporadic nature of toxic outbreaks south of Massachusetts Bay, and the apparently rare occurrence of toxicity well offshore on Nantucket Shoals and Georges Bank.This research was supported by ONR contract N00014-87-K-0007 and ONR grant N00014-89-J-111 to Donald M. Anderson, and NOAA Office of Sea Grant contract NA86AA-D-SG090

Cooperative Origin of Low-Density Domains in Liquid Water

We study the size of clusters formed by water molecules possessing large enough tetrahedrality with respect to their nearest neighbors. Using Monte Carlo simulation of the SPC/E model of water, together with a geometric analysis based on Voronoi tessellation, we find that regions of lower density than the bulk are formed by accretion of molecules into clusters exceeding a minimum size. Clusters are predominantly linear objects and become less compact as they grow until they reach a size beyond which further accretion is not accompanied by a density decrease. The results suggest that the formation of "ice-like" regions in liquid water is cooperative.Comment: 16 pages, 6 figure

A statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2 table

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

Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

Walking for our health: couple-focused interventions to promote physical activity in older adults

More than 50% of U.S. adults do not engage in sufficient physical activity to meet current recommendations, making physical activity change and maintenance a priority for health promotion throughout adulthood. Among married partners, change in physical activity of one partner often is concordant with change of activity of the other. The primary purpose of this study was to examine two couple-focused interventions that capitalize on the co-occurrence of health behavior change within couples to promote physical activity in older adults. In this study, partners (N = 31 couples) participated together in assessment and intervention activities, and were randomized together into one of two couple-focused conditions. In one condition (concurrent), standard goal-setting techniques were extended to a couple-focused design with each partner setting daily step goals and monitoring her or his own progress. In the other condition (combined), partners collaborated to set and monitor shared daily step goals. Physical activity was assessed with accelerometers pre- and post-intervention. Post-intervention, average weekly physical activity increased by 58 min (p \u3c 0.001), and average body mass index (BMI) decreased by 0.50 kg/m2 (p = 0.001), from pre-intervention measures. Similar levels of change in weekly physical activity and in BMI were detected in both intervention groups. Furthermore, participants demonstrated high adherence to the intervention protocol. Results suggest that couple-focused physical activity interventions can be effective in eliciting increases in physical activity among older adults. Further research is needed to uncover interpersonal mechanisms that maximize physical activity promotion and maintenance within couples over time

Site-site memory equation approach in study of density/pressure dependence of translational diffusion coefficient and rotational relaxation time of polar molecular solutions: acetonitrile in water, methanol in water, and methanol in acetonitrile

We present results of theoretical study and numerical calculation of the dynamics of molecular liquids based on combination of the memory equation formalism and the reference interaction site model - RISM. Memory equations for the site-site intermediate scattering functions are studied in the mode-coupling approximation for the first order memory kernels, while equilibrium properties such as site-site static structure factors are deduced from RISM. The results include the temperature-density(pressure) dependence of translational diffusion coefficients D and orientational relaxation times t for acetonitrile in water, methanol in water and methanol in acetonitrile, all in the limit of infinite dilution. Calculations are performed over the range of temperatures and densities employing the SPC/E model for water and optimized site-site potentials for acetonitrile and methanol. The theory is able to reproduce qualitatively all main features of temperature and density dependences of D and t observed in real and computer experiments. In particular, anomalous behavior, i.e. the increase in mobility with density, is observed for D and t of methanol in water, while acetonitrile in water and methanol in acetonitrile do not show deviations from the ordinary behavior. The variety exhibited by the different solute-solvent systems in the density dependence of the mobility is interpreted in terms of the two competing origins of friction, which interplay with each other as density increases: the collisional and dielectric frictions which, respectively, increase and decrease with increasing density.Comment: 13 pages, 8 eps-figures, 3 tables, RevTeX4-forma

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

Multi-Scale Simulation Modeling for Prevention and Public Health Management of Diabetes in Pregnancy and Sequelae

Diabetes in pregnancy (DIP) is an increasing public health priority in the Australian Capital Territory, particularly due to its impact on risk for developing Type 2 diabetes. While earlier diagnostic screening results in greater capacity for early detection and treatment, such benefits must be balanced with the greater demands this imposes on public health services. To address such planning challenges, a multi-scale hybrid simulation model of DIP was built to explore the interaction of risk factors and capture the dynamics underlying the development of DIP. The impact of interventions on health outcomes at the physiological, health service and population level is measured. Of particular central significance in the model is a compartmental model representing the underlying physiological regulation of glycemic status based on beta-cell dynamics and insulin resistance. The model also simulated the dynamics of continuous BMI evolution, glycemic status change during pregnancy and diabetes classification driven by the individual-level physiological model. We further modeled public health service pathways providing diagnosis and care for DIP to explore the optimization of resource use during service delivery. The model was extensively calibrated against empirical data.Comment: 10 pages, SBP-BRiMS 201