Statistical Properties of Avalanches on Complex Networks

We characterize the distribution of sizes and durations of avalanches propagating in complex networks. We find that the statistics of avalanches can be characterized in terms of the Perron-Frobenius eigenvalue and eigenvectors of an appropriate adjacency matrix which encodes the structure of the network. By using mean-field analyses, previous studies of avalanches in networks have not considered the effect of network structure on the distribution of size and duration of avalanches in all cases. Our results are specific to individual networks and allow us to find expressions for the distribution of size and duration of avalanches starting at particular nodes. These findings apply more broadly to branching processes in networks such as cascading power grid failures and critical brain dynamics. In particular, our results show that some experimental signatures of critical brain dynamics (i.e., power-law distributions of neuronal avalanches sizes and durations), are robust to complex underlying network topologies. We model avalanches in complex networks by considering a collection of connected nodes where the connection strength between two nodes determines the probability that an excitation is passed from one node to the next. Networks of size $N$ can be identified with a N x N adjacency matrix where the ijth entry represents the connection strength from node i to node j. Networks are separated into three classes: subcritical, critical, and supercritical based on the largest eigenvalue of the adjacency matrix. We are able to determine the distribution for avalanche size and duration for each type of network

Statistical Properties of Avalanches in Networks

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some probability, then stimulate subsequent firings of the nodes to which it is connected, resulting in a cascade of firings. This type of process is relevant to a wide variety of situations, including neuroscience, cascading failures on electrical power grids, and epidemology. We find that the statistics of avalanches can be characterized in terms of the largest eigenvalue and corresponding eigenvector of an appropriate adjacency matrix which encodes the structure of the network. By using mean-field analyses, previous studies of avalanches in networks have not considered the effect of network structure on the distribution of size and duration of avalanches. Our results apply to individual networks (rather than network ensembles) and provide expressions for the distributions of size and duration of avalanches starting at particular nodes in the network. These findings might find application in the analysis of branching processes in networks, such as cascading power grid failures and critical brain dynamics. In particular, our results show that some experimental signatures of critical brain dynamics (i.e., power-law distributions of size and duration of neuronal avalanches), are robust to complex underlying network topologies.Comment: 11 pages, 7 figure

Low genetic variability, female-biased dispersal and high movement rates in an urban population of Eurasian badgersMeles meles

1. Urban and rural populations of animals can differ in their behaviour, both in order to meet their ecological requirements and due to the constraints imposed by different environments. The study of urban populations can therefore offer useful insights into the behavioural flexibility of a species as a whole, as well as indicating how the species in question adapts to a specifically urban environment. 2. The genetic structure of a population can provide information about social structure and movement patterns that is difficult to obtain by other means. Using non-invasively collected hair samples, we estimated the population size of Eurasian badgers Meles meles in the city of Brighton, England, and calculated population-specific parameters of genetic variability and sex-specific rates of outbreeding and dispersal. 3. Population density was high in the context of badger densities reported throughout their range. This was due to a high density of social groups rather than large numbers of individuals per group. 4. The allelic richness of the population was low compared with other British populations. However, the rate of extra-group paternity and the relatively frequent (mainly temporary) intergroup movements suggest that, on a local scale, the population was outbred. Although members of both sexes visited other groups, there was a trend for more females to make intergroup movements. 5. The results reveal that urban badgers can achieve high densities and suggest that while some population parameters are similar between urban and rural populations, the frequency of intergroup movements is higher among urban badgers. In a wider context, these results demonstrate the ability of non-invasive genetic sampling to provide information about the population density, social structure and behaviour of urban wildlife

Evidence of Zavora Bay as a critical site for reef manta rays, Mobula alfredi, in southern Mozambique

The largest known reef manta ray (Mobula alfredi) population in Africa has been monitored for more than 20 years at several locations on the coast of the Inhambane Province in southern Mozambique. Nonetheless, before this study, little had been reported on the population dynamics of M. alfredi from Zavora, a remote bay in the region. Photographic mark-recapture was used to investigate the size and structure of M. alfredi that aggregate at "Red Sands," a reef cleaning station in Zavora Bay. An 11 year photographic data set was used to identify 583 M. alfredi individuals between 2010 and 2021. More than half of M. alfredi individuals were resighted at least once, with most encounters (up to 18 for one individual) occurring during the peak sighting period in July-November each year. An even sex ratio was observed, 44% females and 50% males, with no significant difference in resightings between the sexes. Pollock's robust design population models were used to estimate annual abundance, emigration, annual apparent survival and capture probability at Red Sands from July to November over a 6 year period (2016-2021). Abundance estimates varied year to year, ranging from 35 (95% c.i. [30, 45]) up to 233 (95% c.i. [224, 249]) M. alfredi individuals. Given the seasonal affinity of M. alfredi observed at Red Sands, this study highlights the importance of understanding fine-scale site use within the larger home range of this population to develop local management strategies

Long period variables in 47 Tuc: direct evidence for lost mass

We have identified 22 new variable red giants in 47 Tuc and determined periods for another 8 previously known variables. All red giants redder than V-I_c=1.8 are variable at the limits of our detection threshold, which corresponds to delta V ~ 0.1 mag. This colour limit corresponds to a luminosity log L/L_sun=3.15 and it is considerably below the tip of the RGB at log L/L_sun=3.35. Linear non-adiabatic models without mass loss on the giant branch can not reproduce the observed PL laws for the low amplitude pulsators. Models that have undergone mass loss do reproduce the observed PL relations and they show that mass loss of the order of 0.3 M_sun occurs along the RGB and AGB. The linear pulsation periods do not agree well with the observed periods of the large amplitude Mira variables, which pulsate in the fundamental mode. The solution to this problem appears to be that the nonlinear pulsation periods in these low mass stars are considerably shorter than the linear pulsation periods due to a rearrangement of stellar structure caused by the pulsation. Both observations and theory show that stars evolve up the RGB and first part of the AGB pulsating in low order overtone modes, then switch to fundamental mode at high luminosities.Comment: 11 pages, accepted for publication in A&

Missing data in trial-based cost-effectiveness analysis: An incomplete journey.

Cost-effectiveness analyses (CEA) conducted alongside randomised trials provide key evidence for informing healthcare decision making, but missing data pose substantive challenges. Recently, there have been a number of developments in methods and guidelines addressing missing data in trials. However, it is unclear whether these developments have permeated CEA practice. This paper critically reviews the extent of and methods used to address missing data in recently published trial-based CEA. Issues of the Health Technology Assessment journal from 2013 to 2015 were searched. Fifty-two eligible studies were identified. Missing data were very common; the median proportion of trial participants with complete cost-effectiveness data was 63% (interquartile range: 47%-81%). The most common approach for the primary analysis was to restrict analysis to those with complete data (43%), followed by multiple imputation (30%). Half of the studies conducted some sort of sensitivity analyses, but only 2 (4%) considered possible departures from the missing-at-random assumption. Further improvements are needed to address missing data in cost-effectiveness analyses conducted alongside randomised trials. These should focus on limiting the extent of missing data, choosing an appropriate method for the primary analysis that is valid under contextually plausible assumptions, and conducting sensitivity analyses to departures from the missing-at-random assumption

Atmospheric phase correction using CARMA-PACS: high angular resolution observations of the FU Orionis star PP 13S*

We present 0".15 resolution observations of the 227 GHz continuum emission from the circumstellar disk around the FU Orionis star PP 13S*. The data were obtained with the Combined Array for Research in Millimeter-wave Astronomy (CARMA) Paired Antenna Calibration System (C-PACS), which measures and corrects the atmospheric delay fluctuations on the longest baselines of the array in order to improve the sensitivity and angular resolution of the observations. A description of the C-PACS technique and the data reduction procedures are presented. C-PACS was applied to CARMA observations of PP 13S*, which led to a factor of 1.6 increase in the observed peak flux of the source, a 36% reduction in the noise of the image, and a 52% decrease in the measured size of the source major axis. The calibrated complex visibilities were fitted with a theoretical disk model to constrain the disk surface density. The total disk mass from the best-fit model corresponds to 0.06 M_⊙, which is larger than the median mass of a disk around a classical T Tauri star. The disk is optically thick at a wavelength of 1.3 mm for orbital radii less than 48 AU. At larger radii, the inferred surface density of the PP 13S* disk is an order of magnitude lower than that needed to develop a gravitational instability