Social networks: evolving graphs with memory dependent edges

The plethora, and mass take up, of digital communication tech- nologies has resulted in a wealth of interest in social network data collection and analysis in recent years. Within many such networks the interactions are transient: thus those networks evolve over time. In this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges, which may appear and disappear according to their recent history. We consider time discrete and time continuous variants of the model. We consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence. In particular we show that such networks may continue evolving forever, or else may quench and become static (containing immortal and/or extinct edges). This depends on the ex- istence or otherwise of certain infinite products and series involving age dependent model parameters. To test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data, and we apply these concepts to three real networks: summary data on mobile phone use from a developing region; online social-business network data from China; and disaggregated mobile phone communications data from a reality mining experiment in the US. In each case we show that there is evidence for memory dependent dynamics, such as that embodied within the class of models proposed here.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memory

Automatic near real-time selection of flood water levels from high resolution Synthetic Aperture Radar images for assimilation into hydraulic models: a case study

Flood extents caused by fluvial floods in urban and rural areas may be predicted by hydraulic models. Assimilation may be used to correct the model state and improve the estimates of the model parameters or external forcing. One common observation assimilated is the water level at various points along the modelled reach. Distributed water levels may be estimated indirectly along the flood extents in Synthetic Aperture Radar (SAR) images by intersecting the extents with the floodplain topography. It is necessary to select a subset of levels for assimilation because adjacent levels along the flood extent will be strongly correlated. A method for selecting such a subset automatically and in near real-time is described, which would allow the SAR water levels to be used in a forecasting model. The method first selects candidate waterline points in flooded rural areas having low slope. The waterline levels and positions are corrected for the effects of double reflections between the water surface and emergent vegetation at the flood edge. Waterline points are also selected in flooded urban areas away from radar shadow and layover caused by buildings, with levels similar to those in adjacent rural areas. The resulting points are thinned to reduce spatial autocorrelation using a top-down clustering approach. The method was developed using a TerraSAR-X image from a particular case study involving urban and rural flooding. The waterline points extracted proved to be spatially uncorrelated, with levels reasonably similar to those determined manually from aerial photographs, and in good agreement with those of nearby gauges.

Landscape, regional and global estimates of nitrogen flux from land to sea: errors and uncertainties

Regional to global scale modelling of N flux from land to ocean has progressed to date through the development of simple empirical models representing bulk N flux rates from large watersheds, regions, or continents on the basis of a limited selection of model parameters. Watershed scale N flux modelling has developed a range of physically-based approaches ranging from models where N flux rates are predicted through a physical representation of the processes involved, through to catchment scale models which provide a simplified representation of true systems behaviour. Generally, these watershed scale models describe within their structure the dominant process controls on N flux at the catchment or watershed scale, and take into account variations in the extent to which these processes control N flux rates as a function of landscape sensitivity to N cycling and export. This paper addresses the nature of the errors and uncertainties inherent in existing regional to global scale models, and the nature of error propagation associated with upscaling from small catchment to regional scale through a suite of spatial aggregation and conceptual lumping experiments conducted on a validated watershed scale model, the export coefficient model. Results from the analysis support the findings of other researchers developing macroscale models in allied research fields. Conclusions from the study confirm that reliable and accurate regional scale N flux modelling needs to take account of the heterogeneity of landscapes and the impact that this has on N cycling processes within homogenous landscape units.

Realistic mean field forward predictions for the integration of co-registered EEG/fMRI

Brain activity can be measured non-invasively with functional imaging techniques. Each pixel in such an image represents a neural mass of about 105 to 107 neurons. Mean field models (MFMs) approximate their activity by averaging out neural variability while retaining salient underlying features, like neurotransmitter kinetics. However, MFMs incorporating the regional variability, realistic geometry and connectivity of cortex have so far appeared intractable. This lack of biological realism has led to a focus on gross temporal features of the EEG. We address these impediments and showcase a "proof of principle" forward prediction of co-registered EEG/fMRI for a full-size human cortex in a realistic head model with anatomical connectivity, see figure 1. MFMs usually assume homogeneous neural masses, isotropic long-range connectivity and simplistic signal expression to allow rapid computation with partial differential equations. But these approximations are insufficient in particular for the high spatial resolution obtained with fMRI, since different cortical areas vary in their architectonic and dynamical properties, have complex connectivity, and can contribute non-trivially to the measured signal. Our code instead supports the local variation of model parameters and freely chosen connectivity for many thousand triangulation nodes spanning a cortical surface extracted from structural MRI. This allows the introduction of realistic anatomical and physiological parameters for cortical areas and their connectivity, including both intra- and inter-area connections. Proper cortical folding and conduction through a realistic head model is then added to obtain accurate signal expression for a comparison to experimental data. To showcase the synergy of these computational developments, we predict simultaneously EEG and fMRI BOLD responses by adding an established model for neurovascular coupling and convolving "Balloon-Windkessel" hemodynamics. We also incorporate regional connectivity extracted from the CoCoMac database [1]. Importantly, these extensions can be easily adapted according to future insights and data. Furthermore, while our own simulation is based on one specific MFM [2], the computational framework is general and can be applied to models favored by the user. Finally, we provide a brief outlook on improving the integration of multi-modal imaging data through iterative fits of a single underlying MFM in this realistic simulation framework.

Contrasting probabilistic scoring rules

There are several scoring rules that one can choose from in order to score probabilistic forecasting models or estimate model parameters. Whilst it is generally agreed that proper scoring rules are preferable, there is no clear criterion for preferring one proper scoring rule above another. This manuscript compares and contrasts some commonly used proper scoring rules and provides guidance on scoring rule selection. In particular, it is shown that the logarithmic scoring rule prefers erring with more uncertainty, the spherical scoring rule prefers erring with lower uncertainty, whereas the other scoring rules are indifferent to either option.

Climate impacts on river flow: projections for the Medway catchment UK with UKCP09 and CATCHMOD

The potential impact of climate change on areas of strategic importance for water resources remains a concern. Here, river flow projections for the River Medway, above Teston in southeast England are presented, which is just such an area of strategic importance. The river flow projections use climate inputs from the Hadley Centre Regional Climate Model (HadRM3) for the time period 1960–2080 (a subset of the early release UKCP09 projections). River flow predictions are calculated using CATCHMOD, the main river flow prediction tool of the Environment Agency (EA) of England and Wales. In order to use this tool in the best way for climate change predictions, model setup and performance are analysed using sensitivity and uncertainty analysis. The model's representation of hydrological processes is discussed and the direct percolation and first linear storage constant parameters are found to strongly affect model results in a complex way, with the former more important for low flows and the latter for high flows. The uncertainty in predictions resulting from the hydrological model parameters is demonstrated and the projections of river flow under future climate are analysed. A clear climate change impact signal is evident in the results with a persistent lowering of mean daily river flows for all months and for all projection time slices. Results indicate that a projection of lower flows under future climate is valid even taking into account the uncertainties considered in this modelling chain exercise. The model parameter uncertainty becomes more significant under future climate as the river flows become lower. This has significant implications for those making policy decisions based on such modelling results. Copyright © 2010 John Wiley & Sons, Ltd.

Development of the Surface Urban Energy and Water balance Scheme (SUEWS) for cold climate cities

The Surface Urban Energy and Water Balance Scheme (SUEWS) is developed to include snow. The processes addressed include accumulation of snow on the different urban surface types: snow albedo and density aging, snow melting and re-freezing of meltwater. Individual model parameters are assessed and independently evaluated using long-term observations in the two cold climate cities of Helsinki and Montreal. Eddy covariance sensible and latent heat fluxes and snow depth observations are available for two sites in Montreal and one in Helsinki. Surface runoff from two catchments (24 and 45 ha) in Helsinki and snow properties (albedo and density) from two sites in Montreal are also analysed. As multiple observation sites with different land-cover characteristics are available in both cities, model development is conducted independent of evaluation. The developed model simulates snowmelt related runoff well (within 19% and 3% for the two catchments in Helsinki when there is snow on the ground), with the springtime peak estimated correctly. However, the observed runoff peaks tend to be smoother than the simulated ones, likely due to the water holding capacity of the catchments and the missing time lag between the catchment and the observation point in the model. For all three sites the model simulates the timing of the snow accumulation and melt events well, but underestimates the total snow depth by 18–20% in Helsinki and 29–33% in Montreal. The model is able to reproduce the diurnal pattern of net radiation and turbulent fluxes of sensible and latent heat during cold snow, melting snow and snow-free periods. The largest model uncertainties are related to the timing of the melting period and the parameterization of the snowmelt. The results show that the enhanced model can simulate correctly the exchange of energy and water in cold climate cities at sites with varying surface cover.

Multi‐method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes

When studying hydrological processes with a numerical model, global sensitivity analysis (GSA) is essential if one is to understand the impact of model parameters and model formulation on results. However, different definitions of sensitivity can lead to a difference in the ranking of importance of the different model factors. Here we combine a fuzzy performance function with different methods of calculating global sensitivity to perform a multi-method global sensitivity analysis (MMGSA). We use an application of a finite element subsurface flow model (ESTEL-2D) on a flood inundation event on a floodplain of the River Severn to illustrate this new methodology. We demonstrate the utility of the method for model understanding and show how the prediction of state variables, such as Darcian velocity vectors, can be affected by such a MMGSA. This paper is a first attempt to use GSA with a numerically intensive hydrological model.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

Multi-method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes

When studying hydrological processes with a numerical model, global sensitivity analysis (GSA) is essential if one is to understand the impact of model parameters and model formulation on results. However, different definitions of sensitivity can lead to a difference in the ranking of importance of the different model factors. Here we combine a fuzzy performance function with different methods of calculating global sensitivity to perform a multi-method global sensitivity analysis (MMGSA). We use an application of a finite element subsurface flow model (ESTEL-2D) on a flood inundation event on a floodplain of the River Severn to illustrate this new methodology. We demonstrate the utility of the method for model understanding and show how the prediction of state variables, such as Darcian velocity vectors, can be affected by such a MMGSA. This paper is a first attempt to use GSA with a numerically intensive hydrological model

Joint data assimilation of satellite reflectance and net ecosystem exchange data constrains ecosystem carbon fluxes at a high-elevation subalpine forest

We utilized an ecosystem process model (SIPNET, simplified photosynthesis and evapotranspiration model) to estimate carbon fluxes of gross primary productivity and total ecosystem respiration of a high-elevation coniferous forest. The data assimilation routine incorporated aggregated twice-daily measurements of the net ecosystem exchange of CO2 (NEE) and satellite-based reflectance measurements of the fraction of absorbed photosynthetically active radiation (fAPAR) on an eight-day timescale. From these data we conducted a data assimilation experiment with fifteen different combinations of available data using twice-daily NEE, aggregated annual NEE, eight-day f AP AR, and average annual fAPAR. Model parameters were conditioned on three years of NEE and fAPAR data and results were evaluated to determine the information content from the different combinations of data streams. Across the data assimilation experiments conducted, model selection metrics such as the Bayesian Information Criterion and Deviance Information Criterion obtained minimum values when assimilating average annual fAPAR and twice-daily NEE data. Application of wavelet coherence analyses showed higher correlations between measured and modeled fAPAR on longer timescales ranging from 9 to 12 months. There were strong correlations between measured and modeled NEE (R2, coefficient of determination, 0.86), but correlations between measured and modeled eight-day fAPAR were quite poor (R2 = −0.94). We conclude that this inability to determine fAPAR on eight-day timescale would improve with the considerations of the radiative transfer through the plant canopy. Modeled fluxes when assimilating average annual fAPAR and annual NEE were comparable to corresponding results when assimilating twice-daily NEE, albeit at a greater uncertainty. Our results support the conclusion that for this coniferous forest twice-daily NEE data are a critical measurement stream for the data assimilation. The results from this modeling exercise indicate that for this coniferous forest, average annuals for satellite-based fAPAR measurements paired with annual NEE estimates may provide spatial detail to components of ecosystem carbon fluxes in proximity of eddy covariance towers. Inclusion of other independent data streams in the assimilation will also reduce uncertainty on modeled values.

Spatial evaluation of volcanic ash forecasts using satellite observations

The decision to close airspace in the event of a volcanic eruption is based on hazard maps of predicted ash extent. These are produced using output from volcanic ash transport and dispersion (VATD)models. In this paper an objectivemetric to evaluate the spatial accuracy of VATD simulations relative to satellite retrievals of volcanic ash is presented. The 5 metric is based on the fractions skill score (FSS). Thismeasure of skill provides more information than traditional point-bypoint metrics, such as success index and Pearson correlation coefficient, as it takes into the account spatial scale overwhich skill is being assessed. The FSS determines the scale overwhich a simulation has skill and can differentiate between a "near miss" and a forecast that is badly misplaced. The 10 idealised scenarios presented show that even simulations with considerable displacement errors have useful skill when evaluated over neighbourhood scales of 200–700km2. This method could be used to compare forecasts produced by different VATDs or using different model parameters, assess the impact of assimilating satellite retrieved ash data and evaluate VATD forecasts over a long time period.

Predicting how many animals will be where: how to build, calibrate and evaluate individual-based models

Individual-based models (IBMs) can simulate the actions of individual animals as they interact with one another and the landscape in which they live. When used in spatially-explicit landscapes IBMs can show how populations change over time in response to management actions. For instance, IBMs are being used to design strategies of conservation and of the exploitation of fisheries, and for assessing the effects on populations of major construction projects and of novel agricultural chemicals. In such real world contexts, it becomes especially important to build IBMs in a principled fashion, and to approach calibration and evaluation systematically. We argue that insights from physiological and behavioural ecology offer a recipe for building realistic models, and that Approximate Bayesian Computation (ABC) is a promising technique for the calibration and evaluation of IBMs. IBMs are constructed primarily from knowledge about individuals. In ecological applications the relevant knowledge is found in physiological and behavioural ecology, and we approach these from an evolutionary perspective by taking into account how physiological and behavioural processes contribute to life histories, and how those life histories evolve. Evolutionary life history theory shows that, other things being equal, organisms should grow to sexual maturity as fast as possible, and then reproduce as fast as possible, while minimising per capita death rate. Physiological and behavioural ecology are largely built on these principles together with the laws of conservation of matter and energy. To complete construction of an IBM information is also needed on the effects of competitors, conspecifics and food scarcity; the maximum rates of ingestion, growth and reproduction, and life-history parameters. Using this knowledge about physiological and behavioural processes provides a principled way to build IBMs, but model parameters vary between species and are often difficult to measure. A common solution is to manually compare model outputs with observations from real landscapes and so to obtain parameters which produce acceptable fits of model to data. However, this procedure can be convoluted and lead to over-calibrated and thus inflexible models. Many formal statistical techniques are unsuitable for use with IBMs, but we argue that ABC offers a potential way forward. It can be used to calibrate and compare complex stochastic models and to assess the uncertainty in their predictions. We describe methods used to implement ABC in an accessible way and illustrate them with examples and discussion of recent studies. Although much progress has been made, theoretical issues remain, and some of these are outlined and discussed.