Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

A priori parameterisation of the CERES soil-crop models and tests against several European data sets

Mechanistic soil-crop models have become indispensable tools to investigate the effect of management practices on the productivity or environmental impacts of arable crops. Ideally these models may claim to be universally applicable because they simulate the major processes governing the fate of inputs such as fertiliser nitrogen or pesticides. However, because they deal with complex systems and uncertain phenomena, site-specific calibration is usually a prerequisite to ensure their predictions are realistic. This statement implies that some experimental knowledge on the system to be simulated should be available prior to any modelling attempt, and raises a tremendous limitation to practical applications of models. Because the demand for more general simulation results is high, modellers have nevertheless taken the bold step of extrapolating a model tested within a limited sample of real conditions to a much larger domain. While methodological questions are often disregarded in this extrapolation process, they are specifically addressed in this paper, and in particular the issue of models a priori parameterisation. We thus implemented and tested a standard procedure to parameterize the soil components of a modified version of the CERES models. The procedure converts routinely-available soil properties into functional characteristics by means of pedo-transfer functions. The resulting predictions of soil water and nitrogen dynamics, as well as crop biomass, nitrogen content and leaf area index were compared to observations from trials conducted in five locations across Europe (southern Italy, northern Spain, northern France and northern Germany). In three cases, the model’s performance was judged acceptable when compared to experimental errors on the measurements, based on a test of the model’s root mean squared error (RMSE). Significant deviations between observations and model outputs were however noted in all sites, and could be ascribed to various model routines. In decreasing importance, these were: water balance, the turnover of soil organic matter, and crop N uptake. A better match to field observations could therefore be achieved by visually adjusting related parameters, such as field-capacity water content or the size of soil microbial biomass. As a result, model predictions fell within the measurement errors in all sites for most variables, and the model’s RMSE was within the range of published values for similar tests. We conclude that the proposed a priori method yields acceptable simulations with only a 50% probability, a figure which may be greatly increased through a posteriori calibration. Modellers should thus exercise caution when extrapolating their models to a large sample of pedo-climatic conditions for which they have only limited information.

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential $Q=|Z|^2$ we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials.

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Splat-based surface reconstruction from defect-laden point sets

We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splat-based representation is computed from the point set. A robust local 3D RANSAC-based procedure is used to filter the point set for outliers, then a local jet surface - a low-degree surface approximation - is fitted to the inliers. Second, we extract the reconstructed surface in the form of a surface triangle mesh through Delaunay refinement. The Delaunay refinement meshing approach requires computing intersections between line segment queries and the surface to be meshed. In the present case, intersection queries are solved from the set of splats through a 1D RANSAC procedure

A Comparative Study of Desktop, Fishtank, and Cave Systems for the Exploration of Volume Rendered Confocal Data Sets

We present a participant study that compares biological data exploration tasks using volume renderings of laser confocal microscopy data across three environments that vary in level of immersion: a desktop, fishtank, and cave system. For the tasks, data, and visualization approach used in our study, we found that subjects qualitatively preferred and quantitatively performed better in the cave compared with the fishtank and desktop. Subjects performed real-world biological data analysis tasks that emphasized understanding spatial relationships including characterizing the general features in a volume, identifying colocated features, and reporting geometric relationships such as whether clusters of cells were coplanar. After analyzing data in each environment, subjects were asked to choose which environment they wanted to analyze additional data sets in - subjects uniformly selected the cave environment.