General Adiabatic Evolution with a Gap Condition

We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity, away from the rest of the spectrum. The restriction of the generator to the spectral subspace corresponding to the distinguished eigenvalues is not assumed to be diagonalizable. The presence of eigenilpotents in the spectral decomposition of the generator forbids the evolution to follow the instantaneous eigenprojectors of the generator in the adiabatic limit. Making use of superadiabatic renormalization, we construct a different set of time-dependent projectors, close to the instantaneous eigeprojectors of the generator in the adiabatic limit, and an approximation of the evolution semigroup which intertwines exactly between the values of these projectors at the initial and final times. Hence, the evolution semigroup follows the constructed set of projectors in the adiabatic regime, modulo error terms we control

Polydomy enhances foraging performance in ant colonies.

Collective foraging confers benefits in terms of reduced predation risk and access to social information, but it heightens local competition when resources are limited. In social insects, resource limitation has been suggested as a possible cause for the typical decrease in per capita productivity observed with increasing colony size, a phenomenon known as Michener's paradox. Polydomy (distribution of a colony's brood and workers across multiple nests) is believed to help circumvent this paradox through its positive effect on foraging efficiency, but there is still little supporting evidence for this hypothesis. Here, we show experimentally that polydomy enhances the foraging performance of food-deprived Temnothorax nylanderi ant colonies via several mechanisms. First, polydomy influences task allocation within colonies, resulting in faster retrieval of protein resources. Second, communication between sister nests reduces search times for far away resources. Third, colonies move queens, brood and workers across available nest sites in response to spatial heterogeneities in protein and carbohydrate resources. This suggests that polydomy represents a flexible mechanism for space occupancy, helping ant colonies adjust to the environment

Close to Uniform Prime Number Generation With Fewer Random Bits

In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$, the basic idea is to fix a constant $q\propto x^{1-\varepsilon}$, pick a uniformly random $a<q$ coprime to $q$, and choose $p$ of the form $a+t\cdot q$, where only $t$ is updated if the primality test fails. We prove that variants of this approach provide prime generation algorithms requiring few random bits and whose output distribution is close to uniform, under less and less expensive assumptions: first a relatively strong conjecture by H.L. Montgomery, made precise by Friedlander and Granville; then the Extended Riemann Hypothesis; and finally fully unconditionally using the Barban-Davenport-Halberstam theorem. We argue that this approach has a number of desirable properties compared to previous algorithms.Comment: Full version of ICALP 2014 paper. Alternate version of IACR ePrint Report 2011/48

Edge currents in the absence of edges

We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely degenerate eigenvalues, between them the system has bands of absolutely continuous spectrum and exhibits thus a transport along the array. We also compute the band functions and the corresponding probability current.Comment: Final version, to appear in Phys. Lett. A; 10 LaTeX pages with 3 eps figure

Antero-medial approach to the wrist: anatomic basis and new application in cases of fracture of the lunate facet

The Henry approach is the classical anterolateral surgical exposure of the volar aspect of the distal radius. This approach does not allow good access to the medial side of the volar distal radius (lunate facet) and the distal radio-ulnar joint, unless it is extended proximally, retracting the tendons and the median nerve medially, which can cause some trauma. The purpose of our study was to investigate the anatomic basis and to outline the advantages of the unusual anteromedial approach, reporting our experience in the treatment of 4 distal radius fractures, with a 90° or 180° twist of the lunate facet, and 10 wrist dissections on cadavers. The average follow-up was 68.8 months (range 18 to 115 months). In our series, this approach did not cause any nerve injuries or any sensory loss of the distal forearm and the palm. All the fractures of the lunate facet and of the radial styloid process healed. One patient with an ulnar styloid process fracture associated showed pseudarthrosis, but with no instability of the distal radio-ulnar joint or pain on the ulnar side. Using the criteria of Green and O&#8217;Brien, modified by Cooney, the results were: excellent in two cases, good in one case, and average in another. The evaluation of arthritis according to Knirk and Jupiter&#8217;s classification showed grade 0 in three cases and grade 3 in one case with osteochondral sclerosis. We showed that the anteromedial approach is reliable and convenient in the case of fractures situated in the antero-medial portion of the radius, for the double objective of reducing the fracture under direct control and checking the congruence of the distal radio-ulnar joint. (Folia Morphol 2011; 70, 3: 204&#8211;210

Geophysical and geochemical signatures of Gulf of Mexico seafloor brines

International audienceGeophysical, temperature, and discrete depth-stratified geochemical data illustrate differences between an actively venting mud volcano and a relatively quiescent brine pool in the Gulf of Mexico along the continental slope. Geophysical data, including laser-line scan mosaics and sub-bottom profiles, document the dynamic nature of both environments. Temperature profiles, obtained by lowering a CTD into the brine fluid, show that the venting brine was at least 10°C warmer than the bottom water. At the brine pool, thermal stratification was observed and only small differences in stratification were documented between three sampling times (1991, 1997 and 1998). In contrast, at the mud volcano, substantial temperature variability was observed, with the core brine temperature being slightly higher than bottom water (by 2°C) in 1997 but substantially higher than bottom water (by 19°C) in 1998. Detailed geochemical samples were obtained in 2002 using a device called the "brine trapper" and concentrations of dissolved gases, major ions and nutrients were determined. Both brines contained about four times as much salt as seawater and steep concentration gradients of dissolved ions and nutrients versus brine depth were apparent. Differences in the concentrations of calcium, magnesium and potassium between the two brine fluids suggest that the fluids are derived from different sources, have different dilution/mixing histories, or that brine-sediment reactions are more important at the mud volcano. Substantial concentrations of methane, ammonium, and silicate were observed in both brines, suggesting that fluids expelled from deep ocean brines are important sources of these constituents to the surrounding environment

Sexual selection favours good or bad genes for pathogen resistance depending on males' pathogen exposure.

Resistance to pathogens is often invoked as an indirect benefit of female choice, but experimental evidence for links between father's sexual success and offspring resistance is scarce and equivocal. Two proposed mechanisms might generate such links. Under the first, heritable resistance to diverse pathogens depends on general immunocompetence; owing to shared condition dependence, male sexual traits indicate immunocompetence independently of the male's pathogen exposure. By contrast, other hypotheses (e.g. Hamilton-Zuk) assume that sexual traits only reveal heritable resistance if the males have been exposed to the pathogen. The distinction between the two mechanisms has been neglected by experimental studies. We show that Drosophila melanogaster males that are successful in mating contests (one female with two males) sire sons that are substantially more resistant to the intestinal pathogen Pseudomonas entomophila-but only if the males have themselves been exposed to the pathogen before the mating contest. By contrast, sons of males sexually successful in the absence of pathogen exposure are less resistant than sons of unsuccessful males. We detected no differences in daughters' resistance. Thus, while sexual selection may have considerable consequences for offspring resistance, these consequences may be sex-specific. Furthermore, contrary to the 'general immunocompetence' hypothesis, these consequences can be positive or negative depending on the epidemiological context under which sexual selection operates

Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationnary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman-Kac formula to express the characteristic function of the averaged distribution over the randomness at time $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, we show that this distribution posesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviations principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. We complete the picture by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with arXiv:1010.400

Carbon isotopic evidence for microbial control of carbon supply to Orca Basin at the seawater–brine interface

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 3175-3183, doi:10.5194/bg-10-3175-2013.Orca Basin, an intraslope basin on the Texas-Louisiana continental slope, hosts a hypersaline, anoxic brine in its lowermost 200 m in which limited microbial activity has been reported. This brine contains a large reservoir of reduced and aged carbon, and appears to be stable at decadal time scales: concentrations and isotopic composition of dissolved inorganic (DIC) and organic carbon (DOC) are similar to measurements made in the 1970s. Both DIC and DOC are more "aged" within the brine pool than in overlying water, and the isotopic contrast between brine carbon and seawater carbon is much greater for DIC than DOC. While the stable carbon isotopic composition of brine DIC points towards a combination of methane and organic carbon remineralization as its source, radiocarbon and box model results point to the brine interface as the major source region for DIC, allowing for only limited oxidation of methane diffusing upwards from sediments. This conclusion is consistent with previous studies that identify the seawater–brine interface as the focus of microbial activity associated with Orca Basin brine. Isotopic similarities between DIC and DOC suggest a different relationship between these two carbon reservoirs than is typically observed in deep ocean basins. Radiocarbon values implicate the seawater–brine interface region as the likely source region for DOC to the brine as well as DIC.This work was funded by the WHOI Postdoctoral Scholar program, NSF Cooperative Agreement for the Operation of a National Ocean Sciences Accelerator Mass Spectrometry Facility (OCE-0753487), and the US National Science Foundation’s Emerging Frontiers program (award 0801741 to SBJ)