Graphs with specified degree distributions, simple epidemics and local vaccination strategies

Consider a random graph, having a pre-specified degree distribution F but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation the paper determines R_0 and tau_0, the basic reproduction number and the asymptotic final size in case of a major outbreak. Further, the paper looks at some different local vaccination strategies where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies the paper determines R_v: the reproduction number, and tau_v: the asymptotic final proportion infected in case of a major outbreak, after vaccinating a fraction v.Comment: 31 pages, 3 figure

The maximum of Brownian motion with parabolic drift

We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.Comment: 37 page

Imaging correlated wave functions of few-electron quantum dots: Theory and scanning tunneling spectroscopy experiments

We show both theoretically and experimentally that scanning tunneling spectroscopy (STS) images of semiconductor quantum dots may display clear signatures of electron-electron correlation. We apply many-body tunneling theory to a realistic model which fully takes into account correlation effects and dot anisotropy. Comparing measured STS images of freestanding InAs quantum dots with those calculated by the full configuration interaction method, we explain the wave function sequence in terms of images of one- and two-electron states. The STS map corresponding to double charging is significantly distorted by electron correlation with respect to the non-interacting case.Comment: RevTeX 4.0, 5 pages, 3 B/W figures, 1 table. This paper is based on an invited talk presented by the authors at the 28th International Conference on the Physics of Semiconductors, which was held 24-28 July 2006, in Vienna, Austri

An exactly solvable self-convolutive recurrence

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the $n$th coefficient is expressed as the $(n-1)$th moment of a measure, and also as the trace of the $(n-1)$th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics

Rates of agonism among female primates: a cross-taxon perspective

Agonism is common in group-living animals, shaping dominance relationships and ultimately impacting individual tness. Rates of agonism vary considerably among taxa, however, and explaining this variation has been central in ecological models of female social relationships in primates. Early iterations of these models posited a link to diet, with more frequent agonism predicted in frugivorous species due to the presumed greater contestability of fruits relative to other food types. Although some more recent studies have suggested that dietary categories may be poor predictors of contest competition among primates, to date there have been no broad, cross-taxa comparisons of rates of female–female agonism in relation to diet. This study tests whether dietary variables do indeed pre- dict rates of female agonism and further investigates the role of group size (i.e., number of competitors) and substrate use (i.e., degree of arboreality) on the frequency of agonism. Data from 44 wild, unprovisioned groups, including 3 strepsirhine species, 3 platyrrhines, 5 colobines, 10 cercopithecines, and 2 hominoids were analyzed using phylogenetically controlled and uncontrolled methods. Results indicate that diet does not predict agonistic rates, with trends actually being in the opposite direction than predicted for all taxa except cercopithecines. In contrast, agonistic rates are positively associated with group size and possibly degree of terrestriality. Competitor density and perhaps the risk of ghting, thus, appear more important than general diet in predicting agonism among female primates. We discuss the implications of these results for socio-ecological hypotheses

Selfish or altruistic? An analysis of alarm call function in wild capuchin monkeys, Cebus apella nigritus

Alarm calls facilitate some antipredatory benefits of group living but may endanger the caller by attracting the predator's attention. A number of hypotheses invoking kin selection and individual selection have been proposed to explain how such behaviour could evolve. This study tests eight hypotheses for alarm call evolution by examining the responses of tufted capuchin monkeys to models of felids, perched raptors and vipers. Specifically, this study examines: (1) differences between individuals in their propensity to call in response to different threat types, (2) whether there is an audience effect for alarm calling and (3) the response of conspecifics to alarms. Results indicate that the benefits likely to be afforded to the caller vary with stimulus type. Alarm calling in response to felids is most likely selfish, with calls apparently directed towards both the predator and potential conspecific mobbers. Alarm calling in response to vipers attracts additional mobbers as well, but also appears to be driven by kin selection in the case of males and parental care benefits in the case of females. Alarm responses to perched raptors are rare, but seem to be selfish, with callers benefiting by recruiting additional mobbers

A Survey for Massive Giant Planets in Debris Disks with Evacuated Inner Cavities

The commonality of collisionally replenished debris around main sequence stars suggests that minor bodies are frequent around Sun-like stars. Whether or not debris disks in general are accompanied by planets is yet unknown, but debris disks with large inner cavities - perhaps dynamically cleared - are considered to be prime candidates for hosting large-separation massive giant planets. We present here a high-contrast VLT/NACO angular differential imaging survey for eight such cold debris disks. We investigated the presence of massive giant planets in the range of orbital radii where the inner edge of the dust debris is expected. Our observations are sensitive to planets and brown dwarfs with masses >3 to 7 Jupiter mass, depending on the age and distance of the target star. Our observations did not identify any planet candidates. We compare the derived planet mass upper limits to the minimum planet mass required to dynamically clear the inner disks. While we cannot exclude that single giant planets are responsible for clearing out the inner debris disks, our observations constrain the parameter space available for such planets. The non-detection of massive planets in these evacuated debris disks further reinforces the notion that the giant planet population is confined to the inner disk (<15 AU).Comment: Accepted for publication in Ap

Active contractility in actomyosin networks

Contractile forces are essential for many developmental processes involving cell shape change and tissue deformation. Recent experiments on reconstituted actomyosin networks, the major component of the contractile machinery, have shown that active contractility occurs above a threshold motor concentration and within a window of crosslink concentration. We present a microscopic dynamic model that incorporates two essential aspects of actomyosin self-organization: the asymmetric load response of individual actin filaments and the correlated motor-driven events mimicking myosin-induced filament sliding. Using computer simulations we examine how the concentration and susceptibility of motors contribute to their collective behavior and interplay with the network connectivity to regulate macroscopic contractility. Our model is shown to capture the formation and dynamics of contractile structures and agree with the observed dependence of active contractility on microscopic parameters including the contractility onset. Cooperative action of load-resisting motors in a force-percolating structure integrates local contraction/buckling events into a global contractile state via an active coarsening process, in contrast to the flow transition driven by uncorrelated kicks of susceptible motors.Comment: 15 pages, 4 main figures, 4 supplementary figure

Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time

We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. The results from numerical simulations are in excellent agreement with our analytical predictions.Comment: 13 pages, 5 figures. Published in Journal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech. (2007) P10008, doi:10.1088/1742-5468/2007/10/P10008

Decrease in alarm call response among tufted capuchins in competitive feeding contexts: possible evidence for counterdeception

Animal signals function to elicit behaviors in receivers that ultimately benefit the signaler, while receivers should respond in a way that maximizes their own fitness. However, the best response may be difficult for receivers to determine when unreliable signaling is common. “Deceptive” alarm calling is common among tufted capuchins (Cebus apella nigritus) in competitive feeding contexts, and responding to these calls is costly. Receivers should thus vary their responses based on whether a call is likely to be reliable. If capuchins are indeed able to assess reliability, I predicted that receivers will be less likely to respond to alarms that are given during competitive feeding contexts than in noncompetitive contexts, and, within feeding contexts, that individuals inside or adjacent to a food patch will be less likely to respond to alarms than those further from the resource. I tested these predictions in a group of wild capuchins by observing the reactions of focal animals to alarm calls in both noncompetitive contexts and experimental feeding contexts. Antipredator escape reactions, but not vigilance reactions, occurred significantly less often in competitive feeding contexts than in noncompetitive contexts and individuals adjacent to food patches were more likely to respond to alarm calls than were those inside or further from food patches. Although not all predictions were fully supported, the findings demonstrate that receivers vary their behavior in a way that minimizes the costs associated with “deceptive” alarms, but further research is needed to determine whether or not this can be attributed to counterdeception