Prevalent Behavior of Strongly Order Preserving Semiflows

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence. For monotone reaction-diffusion systems with Neumann boundary conditions on convex domains, we show that the set of continuous initial data corresponding to solutions that converge to a spatially homogeneous equilibrium is prevalent. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is given to the measurability of the various sets involved.Comment: 18 page

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Unravelling the size distribution of social groups with information theory on complex networks

The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [arXiv:0908.0504]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place in a network's competitive cluster growth process. We find a scaling rule that allows to classify the final cluster-size distributions using only one parameter that we call the competitiveness. Empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness, which also allows to correctly predict well-established assessments such as the "six-degrees of separation", which is shown here to be a direct consequence of the maximum number of stable social relationships that one person can maintain, known as Dunbar's number. Finally, we show that scaled city-size distributions of large countries follow the same universal distribution

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship

Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship

Anomaly analysis of Hawking radiation from Kaluza-Klein black hole with squashed horizon

Considering gravitational and gauge anomalies at the horizon, a new method that to derive Hawking radiations from black holes has been developed by Wilczek et al. In this paper, we apply this method to non-rotating and rotating Kaluza-Klein black holes with squashed horizon, respectively. For the rotating case, we found that, after the dimensional reduction, an effective U(1) gauge field is generated by an angular isometry. The results show that the gauge current and energy-momentum tensor fluxes are exactly equivalent to Hawking radiation from the event horizon.Comment: 15 pages, no figures, the improved version, accepted by Eur. Phys. J.

A Pre-Landing Assessment of Regolith Properties at the InSight Landing Site

This article discusses relevant physical properties of the regolith at the Mars InSight landing site as understood prior to landing of the spacecraft. InSight will land in the northern lowland plains of Mars, close to the equator, where the regolith is estimated to be ≥3--5 m thick. These investigations of physical properties have relied on data collected from Mars orbital measurements, previously collected lander and rover data, results of studies of data and samples from Apollo lunar missions, laboratory measurements on regolith simulants, and theoretical studies. The investigations include changes in properties with depth and temperature. Mechanical properties investigated include density, grain-size distribution, cohesion, and angle of internal friction. Thermophysical properties include thermal inertia, surface emissivity and albedo, thermal conductivity and diffusivity, and specific heat. Regolith elastic properties not only include parameters that control seismic wave velocities in the immediate vicinity of the Insight lander but also coupling of the lander and other potential noise sources to the InSight broadband seismometer. The related properties include Poisson’s ratio, P- and S-wave velocities, Young’s modulus, and seismic attenuation. Finally, mass diffusivity was investigated to estimate gas movements in the regolith driven by atmospheric pressure changes. Physical properties presented here are all to some degree speculative. However, they form a basis for interpretation of the early data to be returned from the InSight mission.Additional co-authors: Nick Teanby and Sharon Keda

Macrophyte abundance in Waquoit Bay : effects of land-derived nitrogen loads on seasonal and multi-year biomass patterns

Author Posting. © The Author(s), 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Estuaries and Coasts 31 (2008): 532-541, doi:10.1007/s12237-008-9039-6.Anthropogenic inputs of nutrients to coastal waters have rapidly restructured coastal ecosystems. To examine the response of macrophyte communities to land-derived nitrogen loading, we measured macrophyte biomass monthly for six years in three estuaries subject to different nitrogen loads owing to different land uses on the watersheds. The set of estuaries sampled had nitrogen loads over the broad range of 12 to 601 kg N ha-1 y-1. Macrophyte biomass increased as nitrogen loads increased, but the response of individual taxa varied. Specifically, biomass of Cladophora vagabunda and Gracilaria tikvahiae increased significantly as nitrogen loads increased. The biomass of other macroalgal taxa tended to decrease with increasing load, and the relative proportion of these taxa to total macrophyte biomass also decreased. The seagrass, Zostera marina, disappeared from the higher loaded estuaries, but remained abundant in the estuary with the lowest load. Seasonal changes in macroalgal standing stock were also affected by nitrogen load, with larger fluctuations in biomass across the year and higher minimum biomass of macroalgae in the higher loaded estuaries. There were no significant changes in macrophyte biomass over the six years of this study, but there was a slight trend of increasing macroalgal biomass in the latter years. Macroalgal biomass was not related to irradiance or temperature, but Z. marina biomass was highest during the summer months when light and temperatures peak. Irradiance might, however, be a secondary limiting factor controlling macroalgal biomass in the higher loaded estuaries by restricting the depth of the macroalgal canopy. The relationship between the bloom-forming macroalgal species, C. vagabunda and G. tikvahiae, and nitrogen loads suggested a strong connection between development on watersheds and macroalgal blooms and loss of seagrasses. The influence of watershed land uses largely overwhelmed seasonal and inter-annual differences in standing stock of macrophytes in these temperate estuaries.This research was supported by the National Oceanic and Atmospheric Administration (NOAA), Cooperative Institute for Coastal and Estuarine Environmental Technologies (CICEET-UNH#99-304, NOAA NA87OR512), NOAA National Estuarine Research Reserve Graduate Research Fellowship NERRS GRF, #NA77OR0228), and an Environmental Protection Agency (EPA) STAR Fellowship for Graduate Environmental Study (U-915335-01-0) awarded to J. Hauxwell. S. Fox was supported by a NOAA NERRS GRF (#NA03NOS4200132) and an EPA STAR Graduate Research Fellowship. We also thank the Quebec-Labrador Foundation Atlantic Center for the Environment's Sounds Conservancy Program and the Boston University Ablon/Bay Committee for their awarding research funds

Many analysts, one data set: making transparent how variations in analytic choices affect results

Twenty-nine teams involving 61 analysts used the same data set to address the same research question: whether soccer referees are more likely to give red cards to dark-skin-toned players than to light-skin-toned players. Analytic approaches varied widely across the teams, and the estimated effect sizes ranged from 0.89 to 2.93 (Mdn = 1.31) in odds-ratio units. Twenty teams (69%) found a statistically significant positive effect, and 9 teams (31%) did not observe a significant relationship. Overall, the 29 different analyses used 21 unique combinations of covariates. Neither analysts’ prior beliefs about the effect of interest nor their level of expertise readily explained the variation in the outcomes of the analyses. Peer ratings of the quality of the analyses also did not account for the variability. These findings suggest that significant variation in the results of analyses of complex data may be difficult to avoid, even by experts with honest intentions. Crowdsourcing data analysis, a strategy in which numerous research teams are recruited to simultaneously investigate the same research question, makes transparent how defensible, yet subjective, analytic choices influence research results