A spatial approach to network generation for three properties:Degree distribution, clustering coefficient and degree assortativity

Social networks generally display a positively skewed degree distribution and higher values for clustering coefficient and degree assortativity than would be expected from the degree sequence. For some types of simulation studies, these properties need to be varied in the artificial networks over which simulations are to be conducted. Various algorithms to generate networks have been described in the literature but their ability to control all three of these network properties is limited. We introduce a spatially constructed algorithm that generates networks with constrained but arbitrary degree distribution, clustering coefficient and assortativity. Both a general approach and specific implementation are presented. The specific implementation is validated and used to generate networks with a constrained but broad range of property values. © Copyright JASSS.

Measuring the shape of degree distributions

Degree distribution is a fundamental property of networks. While mean degree provides a standard measure of scale, there are several commonly used shape measures. Widespread use of a single shape measure would enable comparisons between networks and facilitate investigations about the relationship between degree distribution properties and other network features. This paper describes five candidate measures of heterogeneity and recommends the Gini coefficient. It has theoretical advantages over many of the previously proposed measures, is meaningful for the broad range of distribution shapes seen in different types of networks, and has several accessible interpretations. While this paper focusses on degree, the distribution of other node based network properties could also be described with Gini coefficients.

Determination of the degree of dissociation in an inductively coupled hydrogen plasma using optical emission spectroscopy and laser diagnostics

Gas temperature is of major importance in plasma based surface treatment, since the surface processes are strongly temperature sensitive. The spatial distribution of reactive species responsible for surface modification is also influenced by the gas temperature. Industrial applications of RF plasma reactors require a high degree of homogeneity of the plasma in contact with the substrate. Reliable measurements of spatially resolved gas temperatures are, therefore, of great importance. The gas temperature can be obtained, e.g. by optical emission spectroscopy (OES). Common methods of OES to obtain gas temperatures from analysis of rotational distributions in excited states do not include the population dynamics influenced by cascading processes from higher electronic states. A model was developed to evaluate this effect on the apparent rotational temperature that is observed. Phase resolved OES confirmed the validity of this model. It was found that cascading leads to higher apparent temperatures, but the deviation (~25 K) is relatively small and can be ignored in most cases. This analysis is applied to investigate axially and radially resolved temperature profiles in an inductively coupled hydrogen RF discharge.

Factors influencing the distribution of native and introduced Gammarus spp. in Irish river systems

Populations of Gammarus duebeni celticus, previously the only amphipod species resident in the rivers of the Lough Neagh catchment, N. Ireland, have been subjected to invasion by G. pulex from the British mainland. Numerous previous studies have investigated the potential behavioural mechanisms, principally differential mutual predation, underlying the replacement of G. d. celticus by G. pulex in Irish waters, and the mutually exclusive distributions of these species in Britain and mainland Europe. However, the relative degree of influence of abiotic versus biotic factors in structuring these amphipod communities remains unresolved. This study used principal component analysis (PCA) to distinguish physico-chemical parameters that have significant roles in determining the current distribution of G. pulex relative to G. d. celticus in L. Neagh rivers. We show that the original domination of rivers by the native G. d, celticus has changed radically, with many sites in several rivers containing either both species or only G. pulex. G. pulex was more abundant than the G. d. celticus in sites with low dissolved oxygen levels. This was reflected in the macroinvertebrate assemblages associated with G. pulex in these sites, which tended to be those tolerant of low biological water quality. The present study thus emphasizes the importance of the habitat template, particularly water quality, for Gammarus spp. interactions. If rivers become increasingly stressed by organic pollution, it is probable the range expansion of G. pulex will continue. Because these two species are not ecological equivalents, the outcomes of G. pulex incursions into G. d. celticus sites may ultimately depend on the prevailing physico-chemical regimes in each site.

Distribution of the common lizard (Zootoca vivipara) and landscape favourability for the species in Northern Ireland

The common lizard (Zootoca vivipara) is Ireland’s only native reptile, forming a key part of the island’s biodiversity. However, there is a general paucity of distributional and abundance data for the species. In this study, we collated incidental records for common lizard sightings to define the distribution of the species in Northern Ireland. Maximum entropy modelling was employed to describe species-habitat associations. The resulting predicted landscape favourability was used to evaluate the current status of the species based on the distribution of its maximum potential range in relation to the degree of fragmentation of remaining suitable habitat. In common with previous studies in the Republic of Ireland, sightings were highly clustered indicating under-recording, observer bias, and fragmentation of suitable habitat. A total of 98 records were collated from 1905 to 2009. The species was recorded in 63 (ca. 34%) of 186 × 10 km Northern Irish grid squares. Lizard occurrence was strongly and positively associated with landscapes dominated by heathland, bog and coastal habitats. The single best approximating model correctly classified the presence of lizards in 84.2% of cases. Upland heath, lowland raised bog and sand dune systems are all subject to Habitat Action Plans in Northern Ireland and are threatened by conversion to agriculture, afforestation, invasive species encroachment and infrastructural development. Consequently, remaining common lizard populations are likely to be small, isolated and highly fragmented. Establishment of an ecological network to preserve connectivity of remaining heath and bog will not only benefit remaining common lizard populations but biodiversity in general.

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Response characteristics of optical sensors for oxygen: models based on a distribution in tau(o) or kappa(q)

The features of two popular models used to describe the observed response characteristics of typical oxygen optical sensors based on luminescence quenching are examined critically. The models are the 'two-site' and 'Gaussian distribution in natural lifetime, tau(o),' models. These models are used to characterise the response features of typical optical oxygen sensors; features which include: downward curving Stern-Volmer plots and increasingly non-first order luminescence decay kinetics with increasing partial pressures of oxygen, pO(2). Neither model appears able to unite these latter features, let alone the observed disparate array of response features exhibited by the myriad optical oxygen sensors reported in the literature, and still maintain any level of physical plausibility. A model based on a Gaussian distribution in quenching rate constant, k(q), is developed and, although flawed by a limited breadth in distribution, rho, does produce Stern-Volmer plots which would cover the range in curvature seen with real optical oxygen sensors. A new 'log-Gaussian distribution in tau(o) or k(q)' model is introduced which has the advantage over a Gaussian distribution model of placing no limitation on the value of rho. Work on a 'log-Gaussian distribution in tau(o)' model reveals that the Stern-Volmer quenching plots would show little degree in curvature, even at large rho values and the luminescence decays would become increasingly first order with increasing pO(2). In fact, with real optical oxygen sensors, the opposite is observed and thus the model appears of little value. In contrast, a 'log-Gaussian distribution in k(o)' model does produce the trends observed with real optical oxygen sensors; although it is technically restricted in use to those in which the kinetics of luminescence decay are good first order in the absence of oxygen. The latter model gives a good fit to the major response features of sensors which show the latter feature, most notably the [Ru(dpp)(3)(2+)(Ph4B-)(2)] in cellulose optical oxygen sensors. The scope of a log-Gaussian model for further expansion and, therefore, application to optical oxygen sensors, by combining both a log-Gaussian distribution in k(o) with one in tau(o) is briefly discussed.

Incorporating uncertainty in predictive species distribution modelling

Motivated by the need to solve ecological problems (climate change, habitat fragmentation and biological invasions), there has been increasing interest in species distribution models (SDMs). Predictions from these models inform conservation policy, invasive species management and disease-control measures. However, predictions are subject to uncertainty, the degree and source of which is often unrecognized. Here, we review the SDM literature in the context of uncertainty, focusing on three main classes of SDM: niche-based models, demographic models and process-based models. We identify sources of uncertainty for each class and discuss how uncertainty can be minimized or included in the modelling process to give realistic measures of confidence around predictions. Because this has typically not been performed, we conclude that uncertainty in SDMs has often been underestimated and a false precision assigned to predictions of geographical distribution. We identify areas where development of new statistical tools will improve predictions from distribution models, notably the development of hierarchical models that link different types of distribution model and their attendant uncertainties across spatial scales. Finally, we discuss the need to develop more defensible methods for assessing predictive performance, quantifying model goodness-of-fit and for assessing the significance of model covariates.

The distribution of arsenic in the body tissues of wood mice and bank voles

Arsenic is accumulated by free-living small mammals, but there is little information on the resultant concentrations in different tissues other than liver and kidney. Such information is important because the severity of toxicological effects may be related to the amount of arsenic accumulated in specific organs, and the availability of arsenic to predators is, in part, dependent on which tissues accumulate arsenic. The objective of this study was to quantify the arsenic concentrations and the percentage of the total body burden (%TBB) accumulated in different body tissues of free-living small mammals and to determine how these factors varied with severity of habitat contamination. Arsenic concentrations were measured in various tissues of wood mice (Apodemus sylvaticus) and bank voles (Clethrionomys glareolus) from a range of arsenic-contaminated sites in southwest Britain. Arsenic concentrations in the gastrointestinal (GI) tract (including contents), liver, kidneys, spleen, lung, femur, and fur of both species varied significantly between sites and were higher in mice and voles from heavily contaminated areas. Heart and brain arsenic concentrations did not vary with degree of environmental contamination. The GI tract and excised carcass contained roughly equal amounts of arsenic and, in sum, comprised 75-85% of the TBB on uncontaminated sites and 90-99% on contaminated sites. Although the excised carcass contains about half of the TBB, its importance in food-chain transfer of arsenic to predators may depend on the bioavailability of arsenic sequestered in fur. In contrast, the GI tract and its contents, provided that it is consumed, will always be a major transfer pathway for arsenic to predators, regardless of the severity of habitat contamination.

Driven optomechanical systems for mechanical entanglement distribution

We consider the distribution of entanglement from a multimode optical driving source to a network of remote and independent optomechanical systems. By focusing on the tripartite case, we analyse the effects that the features of the optical input states have on the degree and sharing structure of the distributed, fully mechanical, entanglement. This study, which is conducted looking at the mechanical steady state, highlights the structure of the entanglement distributed among the nodes and determines the relative efficiency between bipartite and tripartite entanglement transfer. We discuss a few open points, some of which are directed towards the bypassing of such limitations.

The Great Recession and the changing distribution of economic vulnerability by social class:The Irish case

Ireland provides an interesting case study of the distributional consequences of the Great Recession. To explore such effects we develop a measure of economic vulnerability based on a multidimensional risk profile for income poverty, material deprivation and economic stress. In the context of conflicting expectations of trends in social class differentials, we provide a comparison of pre and post-recession periods. Our analysis reveals a doubling of levels of economic vulnerability and a significant change in multidimensional profiles. Income poverty became less closely associated with material deprivation and economic stress and the degree of polarization between vulnerable and non-vulnerable classes was significantly reduced. Economic vulnerability is highly stratified by social class for both pre and post-recession periods. Focusing on absolute change, the main contrast is between the salariat and the non-agricultural self-employed and the remaining classes; providing some support for notions of polarization. In terms of relative change the higher salariat, the non-agricultural self-employed, the semi-unskilled manual and those who never worked gained relative to the remaining classes. This provides support the notion of ‘middle class squeeze’. The changing relationship between social class and household work intensity reflected a similar pattern. The impact of the latter on economic vulnerability declined sharply, while it came to play an increasing role in mediating the impact of membership of the non-agricultural middle classes. Responding to the political pressures likely to be associated with ‘middle class squeeze’ while sustaining the social welfare arrangements that have traditionally protected the economically vulnerable presents formidable challenges in terms of maintaining social cohesion and political legitimacy.

Coherence and discontinuity in the scaling of species' distribution patterns

The spatial distribution of a species can be characterized at many different spatial scales, from fine-scale measures of local population density to coarse-scale geographical-range structure. Previous studies have shown a degree of correlation in species' distribution patterns across narrow ranges of scales, making it possible to predict fine-scale properties from coarser-scale distributions. To test the limits of such extrapolation, we have compiled distributional information on 16 species of British plants, at scales ranging across six orders of magnitude in linear resolution (1 in to 100 km). As expected, the correlation between patterns at different spatial scales tends to degrade as the scales become more widely separated. There is, however, an abrupt breakdown in cross-scale correlations across intermediate (ca. 0.5 km) scales, suggesting that local and regional patterns are influenced by essentially non-overlapping sets of processes. The scaling discontinuity may also reflect characteristic scales of human land use in Britain, suggesting a novel method for analysing the 'footprint' of humanity on a landscape.