Expansive homeomorphisms of the plane

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques involve topological and metric aspects of the plane. The use of a Lyapunov metric function which defines the same topology as the one induced by the usual metric but that, in general, is not equivalent to it is an example of such techniques. The discovery of a hypothesis about the behavior of Lyapunov functions at infinity allows us to generalize some results that are valid in the compact context. Additional local properties allow us to obtain another classification theorem.Comment: 29 pages, 22 figure

Thermodynamic behaviour and structural properties of an aqueous sodium chloride solution upon supercooling

We present the results of a molecular dynamics simulation study of thermodynamic and structural properties upon supercooling of a low concentration sodium chloride solution in TIP4P water and the comparison with the corresponding bulk quantities. We study the isotherms and the isochores for both the aqueous solution and bulk water. The comparison of the phase diagrams shows that thermodynamic properties of the solution are not merely shifted with respect to the bulk. Moreover, from the analysis of the thermodynamic curves, both the spinodal line and the temperatures of maximum density curve can be calculated. The spinodal line appears not to be influenced by the presence of ions at the chosen concentration, while the temperatures of maximum density curve displays both a mild shift in temperature and a shape modification with respect to bulk. Signatures of the presence of a liquid-liquid critical point are found in the aqueous solution. By analysing the water-ion radial distribution functions of the aqueous solution we observe that upon changing density, structural modifications appear close to the spinodal. For low temperatures additional modifications appear also for densities close to that corresponding to a low density configurational energy minimum.Comment: 10 pages, 13 figures, 2 tables. To be published in J. Chem. Phy

Histories of hating

This roundtable discussion presents a dialogue between digital culture scholars on the seemingly increased presence of hating and hate speech online. Revolving primarily around the recent #GamerGate campaign of intensely misogynistic discourse aimed at women in video games, the discussion suggests that the current moment for hate online needs to be situated historically. From the perspective of intersecting cultural histories of hate speech, discrimination, and networked communication, we interrogate the ontological specificity of online hating before going on to explore potential responses to the harmful consequences of hateful speech. Finally, a research agenda for furthering the historical understandings of contemporary online hating is suggested in order to address the urgent need for scholarly interventions into the exclusionary cultures of networked media

Distinguishing Social from Nonsocial Navigation in Moving Animal Groups

Many animals, such as migrating shoals of fish, navigate in groups. Knowing the mechanisms involved in animal navigation is important when it comes to explaining navigation accuracy, dispersal patterns, population and evolutionary dynamics, and consequently, the design of conservation strategies. When navigating toward a common target, animals could interact socially by sharing available information directly or indirectly, or each individual could navigate by itself and aggregations may not disperse because all animals are moving toward the same target. Here we present an analysis technique that uses individual movement trajectories to determine the extent to which individuals in navigating groups interact socially, given knowledge of their target. The basic idea of our approach is that the movement directions of individuals arise from a combination of responses to the environment and to other individuals. We estimate the relative importance of these responses, distinguishing between social and nonsocial interactions. We develop and test our method, using simulated groups, and we demonstrate its applicability to empirical data in a case study on groups of guppies moving toward shelter in a tank. Our approach is generic and can be extended to different scenarios of animal group movement. © 2012 by The University of Chicago

Ecological Knowledge, Leadership, and the Evolution of Menopause in Killer Whales

SummaryClassic life-history theory predicts that menopause should not occur because there should be no selection for survival after the cessation of reproduction [1]. Yet, human females routinely live 30 years after they have stopped reproducing [2]. Only two other species—killer whales (Orcinus orca) and short-finned pilot whales (Globicephala macrorhynchus) [3, 4]—have comparable postreproductive lifespans. In theory, menopause can evolve via inclusive fitness benefits [5, 6], but the mechanisms by which postreproductive females help their kin remain enigmatic. One hypothesis is that postreproductive females act as repositories of ecological knowledge and thereby buffer kin against environmental hardships [7, 8]. We provide the first test of this hypothesis using a unique long-term dataset on wild resident killer whales. We show three key results. First, postreproductively aged females lead groups during collective movement in salmon foraging grounds. Second, leadership by postreproductively aged females is especially prominent in difficult years when salmon abundance is low. This finding is critical because salmon abundance drives both mortality and reproductive success in resident killer whales [9, 10]. Third, females are more likely to lead their sons than they are to lead their daughters, supporting predictions of recent models [5] of the evolution of menopause based on kinship dynamics. Our results show that postreproductive females may boost the fitness of kin through the transfer of ecological knowledge. The value gained from the wisdom of elders can help explain why female resident killer whales and humans continue to live long after they have stopped reproducing

Galanin neurons unite sleep homeostasis and α2-adrenergic sedation

Our urge to sleep increases with time spent awake, until sleep becomes inescapable. The sleep following sleep deprivation is longer and deeper, with an increased power of delta (0.5 - 4 Hz) oscillations, a phenomenon termed sleep homeostasis [1-4]. Although widely-expressed genes regulate sleep homeostasis [1, 4-10], and the process is tracked by somnogens and phosphorylation [1, 3, 7, 11-14], at the circuit level sleep homeostasis has remained mysterious. Previously we found that sedation induced with 2 adrenergic agonists (e.g. dexmedetomidine) and sleep homeostasis both depend on the preoptic (PO) hypothalamus [15, 16]. Dexmedetomidine, increasingly used for long-term sedation in intensive care units [17], induces a NREM-like sleep but with undesirable hypothermia [18, 19]. Within the PO, various neuronal subtypes (e.g. GABA/galanin and glutamate/NOS1) induce NREM sleep [20-22] and concomitant body cooling [21, 22]. This could be because NREM sleep’s restorative effects depend on lower body temperature [23, 24]. Here, we show that mice with lesioned PO galanin neurons have reduced sleep homeostasis: in the recovery sleep following sleep deprivation, there is a diminished increase in delta power, and the mice catch up little on lost sleep. Furthermore, dexmedetomidine cannot induce high-power delta oscillations or sustained hypothermia. Some hours after dexmedetomidine administration to wild-type mice there is a rebound in delta power when they enter normal NREM sleep, reminiscent of emergence from torpor. This delta rebound is reduced in mice lacking PO galanin neurons. Thus, sleep homeostasis and dexmedetomidine-induced sedation require PO galanin neurons and likely share common mechanisms

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

Development of High Resolution Scintillator Systems Based on Photocell Technology

Inorganic scintillator/photomultiplier-based spectrometers are the systems of choice for a multitude of X-ray and gamma radiation measurement applications. Despite widespread use, they have numerous shortcomings. The most serious shortcoming is the relatively poor energy resolution that makes isotope identification problematic, particularly in the case of trace quantities. Energy resolution in scintillator/photomultiplier tube (PMT) spectrometers is governed by a combination of the crystal intrinsic resolution that includes non-linearity effects, photomultiplier statistics, and the variability in the probability of a scintillation photon generating a photoelectron at the photocathode. It is evident that energy resolution in these systems is linked to both the physics of light generation in the scintillator and the characteristics of the PMT. PMTs also present design problems, especially in the case of handheld and portable instruments, due to their considerable weight and volume. Additionally, PMTs require well-regulated high voltage, and are vulnerable to magnetic fields. The objective of this work is to provide instrument designers of scintillation-based gamma-ray spectrometers with superior energy resolution and greatly reduced weight and volume. It is planned to achieve this advancement by optimizing the performance of a new class of inorganic scintillators by matching their emission spectra with the enhanced quantum efficiency of certain photocells