Covering R-trees, R-free groups, and dendrites

We prove that every length space X is the orbit space (with the quotient metric) of an R-tree T via a free action of a locally free subgroup G(X) of isometries of X. The mapping f:T->X is a kind of generalized covering map called a URL-map and is universal among URL-maps onto X. T is the unique R-tree admitting a URL-map onto X. When X is a complete Riemannian manifold M of dimension n>1, the Menger sponge, the Sierpin'ski carpet or gasket, T is isometric to the so-called "universal" R-tree A_{c}, which has valency equal to the cardinality of the continuum at each point. In these cases, and when X is the Hawaiian earring H, the action of G(X) on T gives examples in addition to those of Dunwoody and Zastrow that negatively answer a question of J. W. Morgan about group actions on R-trees. Indeed, for one length metric on H, we obtain precisely Zastrow's example.Comment: This paper is the result of splitting off some of the results in the preprint "Covering R-trees" and adding additional applications to R-free group

Tuning gaps and phases of a two-subband system in a quantizing magnetic field

In this work we study the properties of a two-subband quasi-two-dimensional electron system in a strong magnetic field when the electron filling factor is equal to four. When the cyclotron energy is close to the intersubband splitting the system can be mapped onto a four-level electron system with an effective filling factor of two. The ground state is either a ferromagnetic state or a spin-singlet state, depending on the values of the inter-level splitting and Zeeman energy. The boundaries between these phases are strongly influenced by the inter-electron interaction. A significant exchange-mediated enhancement of the excitation gap results in the suppression of the electron-phonon interaction. The rate of absorption of non-equilibrium phonons is calculated as a function of Zeeman energy and inter-subband splitting. The phonon absorption rate has two peaks as a function of intersubband splitting and has a step-like structure as a function of Zeeman energy

Universal critical temperature for Kosterlitz-Thouless transitions in bilayer quantum magnets

Recent experiments show that double layer quantum Hall systems may have a ground state with canted antiferromagnetic order. In the experimentally accessible vicinity of a quantum critical point, the order vanishes at a temperature T_{KT} = \kappa H, where H is the magnetic field and \kappa is a universal number determined by the interactions and Berry phases of the thermal excitations. We present quantum Monte Carlo simulations on a model spin system which support the universality of \kappa and determine its numerical value. This allows experimental tests of an intrinsically quantum-mechanical universal quantity, which is not also a property of a higher dimensional classical critical point.Comment: 5 pages, 4 figure

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes ($\approx$ hydrodynamic modes) of the underlying physical system, much more than quasi one- and two-dimensional patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the patten dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for three-dimensional pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a two-dimensional one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given.Comment: 29 pages, 2 figure

Orientation and symmetries of Alexandrov spaces with applications in positive curvature

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice Theorem, correcting omissions in the previous versio

Population health and the economy: Mortality and the Great Recession in Europe

We analyze the evolution of mortality‐based health indicators in 27 European countries before and after the start of the Great Recession. We find that in the countries where the crisis has been particularly severe, mortality reductions in 2007–2010 were considerably bigger than in 2004–2007. Panel models adjusted for space‐invariant and time‐invariant factors show that an increase of 1 percentage point in the national unemployment rate is associated with a reduction of 0.5% (p < .001) in the rate of age‐adjusted mortality. The pattern of mortality oscillating procyclically is found for total and sex‐specific mortality, cause‐specific mortality due to major causes of death, and mortality for ages 30–44 and 75 and over, but not for ages 0–14. Suicides appear increasing when the economy decelerates—countercyclically—but the evidence is weak. Results are robust to using different weights in the regression, applying nonlinear methods for detrending, expanding the sample, and using as business cycle indicator gross domestic product per capita or employment‐to‐population ratios rather than the unemployment rate. We conclude that in the European experience of the past 20 years, recessions, on average, have beneficial short‐term effects on mortality of the adult population.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142224/1/hec3495_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142224/2/hec3495.pd

Deposit Insurance in General Equilibrium

We study the consequences and optimal design of bank deposit insurance in a general equilibrium model. The model involves two production sectors. One sector is financed by issuing bonds to risk-averse households. Firms in the other sector are monitored and financed by banks. Households fund banks through deposits and equity. Deposits are explicitly insured by a de- posit insurance fund. Any remaining shortfall is implicitly guaranteed by the government. The deposit insurance fund charges banks a premium per unit of deposits whereas the government finances any necessary bail-outs by lump-sum taxation of households. When the deposit insurance premium is actuarially fair or higher than actuarially fair, two types of equilibria emerge: One type of equilibria supports the socially optimal (Arrow-Debreu) allo- cation, and the other type does not. In the latter case, bank lending is too large relative to equity and the probability that the banking system collapses is positive. Next, we show that a judicious combination of deposit insurance and reinsurance eliminates all non-optimal equilibrium allocations

Synergy of extreme drought and shrub invasion reduce ecosystem functioning and resilience in water-limited climates

Extreme drought events and plant invasions are major drivers of global change that can critically affect ecosystem functioning and alter ecosystem-atmosphere exchange. Invaders are expanding worldwide and extreme drought events are projected to increase in frequency and intensity. However, very little is known on how these drivers may interact to affect the functioning and resilience of ecosystems to extreme events. Using a manipulative shrub removal experiment and the co-occurrence of an extreme drought event (2011/2012) in a Mediterranean woodland, we show that native shrub invasion and extreme drought synergistically reduced ecosystem transpiration and the resilience of key-stone oak tree species. Ecosystem transpiration was dominated by the water use of the invasive shrub Cistus ladanifer, which further increased after the extreme drought event. Meanwhile, the transpiration of key-stone tree species decreased, indicating a competitive advantage in favour of the invader. Our results suggest that in Mediterranean-type climates the invasion of water spending species and projected recurrent extreme drought events may synergistically cause critical drought tolerance thresholds of key-stone tree species to be surpassed, corroborating observed higher tree mortality in the invaded ecosystems. Ultimately, this may shift seasonally water limited ecosystems into less desirable alternative states dominated by water spending invasive shrubs