Bounds on the diameter of Cayley graphs of the symmetric group

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.Comment: 17 pages, 6 table

Carbonate Deposits in Marine Fish Intestines: A New Source of Biomineralization

Marine teleostean fish are hypo-osmotic to seawater. As part of a multiorgan osmoregulatory strategy they drink seawater and selectively absorb water and minerals across the intestinal epithelium. Notably, divalent cations (Ca2+ and Mg2-) are left behind. We report here that in the gulf toadfish, Opsanus beta, the ionic by-products of osmoregulation in the intestine contribute to de novo formation of a carbonate mineral, tentatively identified as calcian kutnohorite. Our data suggest that intestinal mineralization is a general feature of osmoregulation in marine teleosts and that this process is an unrecognized and possibly substantial source of marine carbonate sediments

In-vivo glenohumeral translation and ligament elongation during abduction and abduction with internal and external rotation

Study Design: Basic Science. To investigate humeral head translations and glenohumeral ligament elongation with a dual fluoroscopic imaging system. Background: The glenohumeral ligaments are partially responsible for restraining the humeral head during the extremes of shoulder motion. However, in-vivo glenohumeral ligaments elongation patterns have yet to be determined. Therefore, the objectives of this study were to 1) quantify the in-vivo humeral head translations and glenohumeral ligament elongations during functional shoulder positions, 2) compare the inferred glenohumeral ligament functions with previous literature and 3) create a baseline data of healthy adult shoulder glenohumeral ligament lengths as controls for future studies. Methods: Five healthy adult shoulders were studied with a validated dual fluoroscopic imaging system (DFIS) and MR imaging technique. Humeral head translations and the superior, middle and inferior glenohumeral ligaments (SGHL, MGHL, IGHL) elongations were determined. Results: The humeral head center on average translated in a range of 6.0mm in the anterior-posterior direction and 2.5mm in the superior-inferior direction. The MGHL showed greater elongation over a broader range of shoulder motion than the SGHL. The anterior-band (AB)-IGHL showed maximum elongation at 90° abduction with maximum external rotation. The posterior-band (PB)-IGHL showed maximum elongation at 90° abduction with maximum internal rotation. Discussion: The results demonstrated that the humeral head translated statistically more in the anterior-posterior direction than the superior-inferior direction (p = 0.01), which supports the concept that glenohumeral kinematics are not ball-in-socket mechanics. The AB-IGHL elongation pattern makes it an important static structure to restrain anterior subluxation of the humeral head during the externally rotated cocking phase of throwing motion. These data suggest that in healthy adult shoulders the ligamentous structures of the glenohumeral joint are not fully elongated in many shoulder positions, but function as restraints at the extremes of glenohumeral motion. Clinically, these results may be helpful in restoring ligament anatomy during the treatment of anterior instability of the shoulder

The evolution of substructure II: linking dynamics to environment

We present results from a series of high-resolution N-body simulations that focus on the formation and evolution of eight dark matter halos, each of order a million particles within the virial radius. We follow the time evolution of hundreds of satellite galaxies with unprecedented time resolution, relating their physical properties to the differing halo environmental conditions. The self-consistent cosmological framework in which our analysis was undertaken allows us to explore satellite disruption within live host potentials, a natural complement to earlier work conducted within static potentials. Our host halos were chosen to sample a variety of formation histories, ages, and triaxialities; despite their obvious differences, we find striking similarities within the associated substructure populations. Namely, all satellite orbits follow nearly the same eccentricity distribution with a correlation between eccentricity and pericentre. We also find that the destruction rate of the substructure population is nearly independent of the mass, age, and triaxiality of the host halo. There are, however, subtle differences in the velocity anisotropy of the satellite distribution. We find that the local velocity bias at all radii is greater than unity for all halos and this increases as we move closer to the halo centre, where it varies from 1.1 to 1.4. For the global velocity bias we find a small but slightly positive bias, although when we restrict the global velocity bias calculation to satellites that have had at least one orbit, the bias is essentially removed.Comment: 14 pages, 14 figures, MNRAS in pres

Evolutionary biology for the 21st century

New theoretical and conceptual frameworks are required for evolutionary biology to capitalize on the wealth of data now becoming available from the study of genomes, phenotypes, and organisms - including humans - in their natural environments.Molecular and Cellular BiologyOrganismic and Evolutionary Biolog

Upper ocean manifestations of a reducing meridional overturning circulation

Most climate models predict a slowing down of the Atlantic Meridional Overturning Circulation during the 21st century. Using a 100year climate change integration of a high resolution coupled climate model, we show that a 5.3Sv reduction in the deep southward transport in the subtropical North Atlantic is balanced solely by a weakening of the northward surface western boundary current, and not by an increase in the southward transport integrated across the interior ocean away from the western boundary. This is consistent with Sverdrup balance holding to a good approximation outside of the western boundary region on decadal time scales, and may help to spatially constrain past and future change in the overturning circulation. The subtropical gyre weakens by 3.4Sv over the same period due to a weakened wind stress curl. These changes combine to give a net 8.7Sv reduction in upper western boundary transport. © 2012. American Geophysical Union. All Rights Reserved

Dust emission from crusted surfaces: Insights from field measurements and modelling

Crusted surfaces can be major sources of mineral dust emission. Quantitative understanding of dust emission from crusted surfaces is limited, because (1) theories on dust emission are not well tested for such surfaces; and (2) modelling is hampered by a lack of input data sufficient to describe the surface conditions. Combining detailed field measurements with physics-based numerical modelling, we present new insights into dust emission from crusted surfaces. Our measurements confirm that crust erodibility and dust-emission intensity can increase or decrease after previous erosion events. To support interpretation of the measurements and to test the applicability of a state-of-the-art parameterisation to simulate dust emission from crusted surfaces, we apply the dust emission scheme of Shao (2004). Saltation flux, which is input to the scheme, is approximated using the parameterisation of Kawamura (1964) and a scaling factor obtained from observations. Limitations of this approach are discussed. Our results show that the dust emission scheme is suitable to estimate dust emission from crusted surfaces if accurate input data and parameters describing the soil-surface condition are provided. The parameters were optimized for each dust event to achieve a best estimate. The variation of the resulting parameter values confirms the observed variability of dust-emission efficiency between the events and provides further evidence that it was caused by variations in crust erodibility. Our study demonstrates that available physics-based dust-emission parameterisations are able to simulate dust emissions under complicated conditions, but also that refined information on the soil-surface conditions are needed as input to the schemes.This study was funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) grant KL 2932/1-1 awarded as a postdoctoral research fellowship to MK. TEG and RSVP acknowledge support from NASA grant NNX16AH13G. 15 NPW acknowledges support through funding from the Department of Interior, Bureau of Land Management. We thank Ralph Lorenz for providing pressure loggers and the Davis anemometer used on Site F. We also thank Sharalyn Peterson, Justin Van Zee, and Bradley Cooper for field and lab assistance. LPI point data were recorded using DIMA (https://jornada.nmsu.edu/monit-assess/dima). Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government. The USDA is an equal opportunity provider and employer. We thank two anonymous reviewers for their positive and helpful comments.Peer ReviewedPostprint (author's final draft

Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.Comment: 8 pages, 2 figures, 5 table