Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

Fate of the herbicide glyphosate and its metabolite AMPA in soils and their transfer to surface waters: A multi-scale approach in the Lavaux vineyards, western Switzerland

The use of herbicides in agriculture may lead to environmental problems, such as surface water pollution, with a potential risk for aquatic organisms. The herbicide glyphosate is the most used active ingredient in the world and in Switzerland. In the Lavaux vineyards it is nearly the only molecule applied. This work aimed at studying its fate in soils and its transfer to surface waters, using a multi-scale approach: from molecular (10-9 m) and microscopic scales (10-6 m), to macroscopic (m) and landscape ones (103 m). First of all, an analytical method was developed for the trace level quantification of this widely used herbicide and its main by-product, aminomethylphosphonic acid (AMPA). Due to their polar nature, their derivatization with 9-fluorenylmethyl chloroformate (FMOC-Cl) was done prior to their concentration and purification by solid phase extraction. They were then analyzed by ultra performance liquid chromatography coupled with tandem mass spectrometry (UPLC-MS/MS). The method was tested in different aqueous matrices with spiking tests and validated for the matrix effect correction in relevant environmental samples. Calibration curves established between 10 and 1000ng/l showed r2 values above 0.989, mean recoveries varied between 86 and 133% and limits of detection and quantification of the method were as low as 5 and 10ng/l respectively. At the parcel scale, two parcels of the Lavaux vineyard area, located near the Lutrive River at 6km to the east of Lausanne, were monitored to assess to which extent glyphosate and AMPA were retained in the soil or exported to surface waters. They were equipped at their bottom with porous ceramic cups and runoff collectors, which allowed retrieving water samples for the growing seasons 2010 and 2011. Results revealed that the mobility of glyphosate and AMPA in the unsaturated zone was likely driven by the precipitation regime and the soil characteristics, such as slope, porosity structure and layer permeability discrepancy. Elevated glyphosate and AMPA concentrations were measured at 60 and 80 cm depth at parcel bottoms, suggesting their infiltration in the upper parts of the parcels and the presence of preferential flow in the studied parcels. Indeed, the succession of rainy days induced the gradual saturation of the soil porosity, leading to rapid infiltration through macropores, as well as surface runoff formation. Furthermore, the presence of more impervious weathered marls at 100 cm depth induced throughflows, the importance of which for the lateral transport of the herbicide molecules was determined by the slope steepness. Important rainfall events (>10 mm/day) were clearly exporting molecules from the soil top layer, as indicated by important concentrations in runoff samples. A mass balance showed that total loss (10-20%) mainly occurred through surface runoff (96%) and, to a minor extent, by throughflows in soils (4%), with subsequent exfiltration to surface waters. Observations made in the Lutrive River revealed interesting details of glyphosate and AMPA dynamics in urbanized landscapes, such as the Lavaux vineyards. Indeed, besides their physical and chemical properties, herbicide dynamics at the catchment level strongly depend on application rates, precipitation regime, land use and also on the presence of drains or constructed channels. Elevated concentrations, up to 4970 ng/l, observed just after the application, confirmed the diffuse export of these compounds from the vineyard area by surface runoff during main rain events. From April to September 2011, a total load of 7.1 kg was calculated, with 85% coming from vineyards and minor urban sources and 15% from arable crops. Small vineyard surfaces could generate high concentrations of herbicides and contribute considerably to the total load calculated at the outlet, due to their steep slopes (~10%). The extrapolated total amount transferred yearly from the Lavaux vineyards to the Lake of Geneva was of 190kg. At the molecular scale, the possible involvement of dissolved organic matter (DOM) in glyphosate and copper transport was studied using UV/Vis fluorescence spectroscopy. Combined with parallel factor (PARAFAC) analysis, this technique allowed characterizing DOM of soil and surface water samples from the studied vineyard area. Glyphosate concentrations were linked to the fulvic-like spectroscopic signature of DOM in soil water samples, as well as to copper, suggesting the formation of ternary complexes. In surface water samples, its concentrations were also correlated to copper ones, but not in a significant way to the fulvic-like signature. Quenching experiments with standards confirmed field tendencies in the laboratory, with a stronger decrease in fluorescence intensity for fulvic-like fluorophore than for more aromatic ones. Lastly, based on maximum concentrations measured in the river, an environmental risk for these compounds was assessed, using laboratory tests and ecotoxicity data from the literature. In our case and with the methodology applied, the risk towards aquatic species was found negligible (RF<1).

Multi-scale systems analysis of plant development : beyond cellular signaling and tissue morphodynamics

Les plantes sont essentielles pour les sociétés humaines. Notre alimentation quotidienne, les matériaux de constructions et les sources énergétiques dérivent de la biomasse végétale. En revanche, la compréhension des multiples aspects développementaux des plantes est encore peu exploitée et représente un sujet de recherche majeur pour la science. L'émergence des technologies à haut débit pour le séquençage de génome à grande échelle ou l'imagerie de haute résolution permet à présent de produire des quantités énormes d'information. L'analyse informatique est une façon d'intégrer ces données et de réduire la complexité apparente vers une échelle d'abstraction appropriée, dont la finalité est de fournir des perspectives de recherches ciblées. Ceci représente la raison première de cette thèse. En d'autres termes, nous appliquons des méthodes descriptives et prédictives combinées à des simulations numériques afin d'apporter des solutions originales à des problèmes relatifs à la morphogénèse à l'échelle de la cellule et de l'organe. Nous nous sommes fixés parmi les objectifs principaux de cette thèse d'élucider de quelle manière l'interaction croisée des phytohormones auxine et brassinosteroïdes (BRs) détermine la croissance de la cellule dans la racine du méristème apical d'Arabidopsis thaliana, l'organisme modèle de référence pour les études moléculaires en plantes. Pour reconstruire le réseau de signalement cellulaire, nous avons extrait de la littérature les informations pertinentes concernant les relations entre les protéines impliquées dans la transduction des signaux hormonaux. Le réseau a ensuite été modélisé en utilisant un formalisme logique et qualitatif pour pallier l'absence de données quantitatives. Tout d'abord, Les résultats ont permis de confirmer que l'auxine et les BRs agissent en synergie pour contrôler la croissance de la cellule, puis, d'expliquer des observations phénotypiques paradoxales et au final, de mettre à jour une interaction clef entre deux protéines dans la maintenance du méristème de la racine. Une étude ultérieure chez la plante modèle Brachypodium dystachion (Brachypo- dium) a révélé l'ajustement du réseau d'interaction croisée entre auxine et éthylène par rapport à Arabidopsis. Chez ce dernier, interférer avec la biosynthèse de l'auxine mène à la formation d'une racine courte. Néanmoins, nous avons isolé chez Brachypodium un mutant hypomorphique dans la biosynthèse de l'auxine qui affiche une racine plus longue. Nous avons alors conduit une analyse morphométrique qui a confirmé que des cellules plus anisotropique (plus fines et longues) sont à l'origine de ce phénotype racinaire. Des analyses plus approfondies ont démontré que la différence phénotypique entre Brachypodium et Arabidopsis s'explique par une inversion de la fonction régulatrice dans la relation entre le réseau de signalisation par l'éthylène et la biosynthèse de l'auxine. L'analyse morphométrique utilisée dans l'étude précédente exploite le pipeline de traitement d'image de notre méthode d'histologie quantitative. Pendant la croissance secondaire, la symétrie bilatérale de l'hypocotyle est remplacée par une symétrie radiale et une organisation concentrique des tissus constitutifs. Ces tissus sont initialement composés d'une douzaine de cellules mais peuvent aisément atteindre des dizaines de milliers dans les derniers stades du développement. Cette échelle dépasse largement le seuil d'investigation par les moyens dits 'traditionnels' comme l'imagerie directe de tissus en profondeur. L'étude de ce système pendant cette phase de développement ne peut se faire qu'en réalisant des coupes fines de l'organe, ce qui empêche une compréhension des phénomènes cellulaires dynamiques sous-jacents. Nous y avons remédié en proposant une stratégie originale nommée, histologie quantitative. De fait, nous avons extrait l'information contenue dans des images de très haute résolution de sections transverses d'hypocotyles en utilisant un pipeline d'analyse et de segmentation d'image à grande échelle. Nous l'avons ensuite combiné avec un algorithme de reconnaissance automatique des cellules. Cet outil nous a permis de réaliser une description quantitative de la progression de la croissance secondaire révélant des schémas développementales non-apparents avec une inspection visuelle classique. La formation de pôle de phloèmes en structure répétée et espacée entre eux d'une longueur constante illustre les bénéfices de notre approche. Par ailleurs, l'exploitation approfondie de ces résultats a montré un changement de croissance anisotropique des cellules du cambium et du phloème qui semble en phase avec l'expansion du xylème. Combinant des outils génétiques et de la modélisation biomécanique, nous avons démontré que seule la croissance plus rapide des tissus internes peut produire une réorientation de l'axe de croissance anisotropique des tissus périphériques. Cette prédiction a été confirmée par le calcul du ratio des taux de croissance du xylème et du phloème au cours de développement secondaire ; des ratios élevés sont effectivement observés et concomitant à l'établissement progressif et tangentiel du cambium. Ces résultats suggèrent un mécanisme d'auto-organisation établi par un gradient de division méristématique qui génèrent une distribution de contraintes mécaniques. Ceci réoriente la croissance anisotropique des tissus périphériques pour supporter la croissance secondaire. - Plants are essential for human society, because our daily food, construction materials and sustainable energy are derived from plant biomass. Yet, despite this importance, the multiple developmental aspects of plants are still poorly understood and represent a major challenge for science. With the emergence of high throughput devices for genome sequencing and high-resolution imaging, data has never been so easy to collect, generating huge amounts of information. Computational analysis is one way to integrate those data and to decrease the apparent complexity towards an appropriate scale of abstraction with the aim to eventually provide new answers and direct further research perspectives. This is the motivation behind this thesis work, i.e. the application of descriptive and predictive analytics combined with computational modeling to answer problems that revolve around morphogenesis at the subcellular and organ scale. One of the goals of this thesis is to elucidate how the auxin-brassinosteroid phytohormone interaction determines the cell growth in the root apical meristem of Arabidopsis thaliana (Arabidopsis), the plant model of reference for molecular studies. The pertinent information about signaling protein relationships was obtained through the literature to reconstruct the entire hormonal crosstalk. Due to a lack of quantitative information, we employed a qualitative modeling formalism. This work permitted to confirm the synergistic effect of the hormonal crosstalk on cell elongation, to explain some of our paradoxical mutant phenotypes and to predict a novel interaction between the BREVIS RADIX (BRX) protein and the transcription factor MONOPTEROS (MP),which turned out to be critical for the maintenance of the root meristem. On the same subcellular scale, another study in the monocot model Brachypodium dystachion (Brachypodium) revealed an alternative wiring of auxin-ethylene crosstalk as compared to Arabidopsis. In the latter, increasing interference with auxin biosynthesis results in progressively shorter roots. By contrast, a hypomorphic Brachypodium mutant isolated in this study in an enzyme of the auxin biosynthesis pathway displayed a dramatically longer seminal root. Our morphometric analysis confirmed that more anisotropic cells (thinner and longer) are principally responsible for the mutant root phenotype. Further characterization pointed towards an inverted regulatory logic in the relation between ethylene signaling and auxin biosynthesis in Brachypodium as compared to Arabidopsis, which explains the phenotypic discrepancy. Finally, the morphometric analysis of hypocotyl secondary growth that we applied in this study was performed with the image-processing pipeline of our quantitative histology method. During its secondary growth, the hypocotyl reorganizes its primary bilateral symmetry to a radial symmetry of highly specialized tissues comprising several thousand cells, starting with a few dozens. However, such a scale only permits observations in thin cross-sections, severely hampering a comprehensive analysis of the morphodynamics involved. Our quantitative histology strategy overcomes this limitation. We acquired hypocotyl cross-sections from tiled high-resolution images and extracted their information content using custom high-throughput image processing and segmentation. Coupled with an automated cell type recognition algorithm, it allows precise quantitative characterization of vascular development and reveals developmental patterns that were not evident from visual inspection, for example the steady interspace distance of the phloem poles. Further analyses indicated a change in growth anisotropy of cambial and phloem cells, which appeared in phase with the expansion of xylem. Combining genetic tools and computational modeling, we showed that the reorientation of growth anisotropy axis of peripheral tissue layers only occurs when the growth rate of central tissue is higher than the peripheral one. This was confirmed by the calculation of the ratio of the growth rate xylem to phloem throughout secondary growth. High ratios are indeed observed and concomitant with the homogenization of cambium anisotropy. These results suggest a self-organization mechanism, promoted by a gradient of division in the cambium that generates a pattern of mechanical constraints. This, in turn, reorients the growth anisotropy of peripheral tissues to sustain the secondary growth.

Multi-scale effects of nestling diet on breeding performance in a terrestrial top predator inferred from stable isotope analysis

Inter-individual diet variation within populations is likely to have important ecological and evolutionary implications. The diet-fitness relationships at the individual level and the emerging population processes are, however, poorly understood for most avian predators inhabiting complex terrestrial ecosystems. In this study, we use an isotopic approach to assess the trophic ecology of nestlings in a long-lived raptor, the Bonelli"s eagle Aquila fasciata, and investigate whether nestling dietary breath and main prey consumption can affect the species" reproductive performance at two spatial scales: territories within populations and populations over a large geographic area. At the territory level, those breeding pairs whose nestlings consumed similar diets to the overall population (i.e. moderate consumption of preferred prey, but complemented by alternative prey categories) or those disproportionally consuming preferred prey were more likely to fledge two chicks. An increase in the diet diversity, however, related negatively with productivity. The age and replacements of breeding pair members had also an influence on productivity, with more fledglings associated to adult pairs with few replacements, as expected in long-lived species. At the population level, mean productivity was higher in those population-years with lower dietary breadth and higher diet similarity among territories, which was related to an overall higher consumption of preferred prey. Thus, we revealed a correspondence in diet-fitness relationships at two spatial scales: territories and populations. We suggest that stable isotope analyses may be a powerful tool to monitor the diet of terrestrial avian predators on large spatio-temporal scales, which could serve to detect potential changes in the availability of those prey on which predators depend for breeding. We encourage ecologists and evolutionary and conservation biologists concerned with the multi-scale fitness consequences of inter-individual variation in resource use to employ similar stable isotope-based approaches, which can be successfully applied to complex ecosystems such as the Mediterranean.

Very high-resolution digital elevation models: are multi-scale-derived variables ecologically relevant?

1. Digital elevation models (DEMs) are often used in landscape ecology to retrieve elevation or first derivative terrain attributes such as slope or aspect in the context of species distribution modelling. However, DEM-derived variables are scale-dependent and, given the increasing availability of very high-resolution (VHR) DEMs, their ecological relevancemust be assessed for different spatial resolutions. 2. In a study area located in the Swiss Western Alps, we computed VHR DEMs-derived variables related to morphometry, hydrology and solar radiation. Based on an original spatial resolution of 0.5 m, we generated DEM-derived variables at 1, 2 and 4 mspatial resolutions, applying a Gaussian Pyramid. Their associations with local climatic factors, measured by sensors (direct and ambient air temperature, air humidity and soil moisture) as well as ecological indicators derived fromspecies composition, were assessed with multivariate generalized linearmodels (GLM) andmixed models (GLMM). 3. Specific VHR DEM-derived variables showed significant associations with climatic factors. In addition to slope, aspect and curvature, the underused wetness and ruggedness indices modelledmeasured ambient humidity and soilmoisture, respectively. Remarkably, spatial resolution of VHR DEM-derived variables had a significant influence on models' strength, with coefficients of determination decreasing with coarser resolutions or showing a local optimumwith a 2 mresolution, depending on the variable considered. 4. These results support the relevance of using multi-scale DEM variables to provide surrogates for important climatic variables such as humidity, moisture and temperature, offering suitable alternatives to direct measurements for evolutionary ecology studies at a local scale.

Can the fractal dimension be applied for the early diagnosis of non-proliferative diabetic retinopathy?

The fractal dimension has been employed as a useful parameter in the diagnosis of retinal disease. Avakian et al. (Curr Eye Res 2002; 24: 274-280), comparing the vascular pattern of normal patients with mild to moderate non-proliferative diabetic retinopathy (NPDR), found a significant difference between them only in the macular region. This significant difference in the box-counting fractal dimension of the macular region between normal and mild NPDR patients has been proposed as a method of precocious diagnosis of NPDR. The aim of the present study was to determine if fractal dimensions can really be used as a parameter for the early diagnosis of NPDR. Box-counting and information fractal dimensions were used to parameterize the vascular pattern of the human retina. The two methods were applied to the whole retina and to nine anatomical regions of the retina in 5 individuals with mild NPDR and in 28 diabetic but opthalmically normal individuals (controls), with age between 31 and 86 years. All images of retina were obtained from the Digital Retinal Images for Vessel Extraction (DRIVE) database. The results showed that the fractal dimension parameter was not sensitive enough to be of use for an early diagnosis of NPDR.

A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.

A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.

A multi-scale framework for strategic management of diffuse pollution

A multi-scale framework for decision support is presented that uses a combination of experiments, models, communication, education and decision support tools to arrive at a realistic strategy to minimise diffuse pollution. Effective partnerships between researchers and stakeholders play a key part in successful implementation of this strategy. The Decision Support Matrix (DSM) is introduced as a set of visualisations that can be used at all scales, both to inform decision making and as a communication tool in stakeholder workshops. A demonstration farm is presented and one of its fields is taken as a case study. Hydrological and nutrient flow path models are used for event based simulation (TOPCAT), catchment scale modelling (INCA) and field scale flow visualisation (TopManage). One of the DSMs; The Phosphorus Export Risk Matrix (PERM) is discussed in detail. The PERM was developed iteratively as a point of discussion in stakeholder workshops, as a decision support and education tool. The resulting interactive PERM contains a set of questions and proposed remediation measures that reflect both expert and local knowledge. Education and visualisation tools such as GIS, risk indicators, TopManage and the PERM are found to be invaluable in communicating improved farming practice to stakeholders. (C) 2008 Elsevier Ltd. All rights reserved.

Application of Gaussian multi-scale representation to feature tracking in meteorological satellite imagery

Gaussian multi-scale representation is a mathematical framework that allows to analyse images at different scales in a consistent manner, and to handle derivatives in a way deeply connected to scale. This paper uses Gaussian multi-scale representation to investigate several aspects of the derivation of atmospheric motion vectors (AMVs) from water vapour imagery. The contribution of different spatial frequencies to the tracking is studied, for a range of tracer sizes, and a number of tracer selection methods are presented and compared, using WV 6.2 images from the geostationary satellite MSG-2.

MEGAPOLI: concept of multi-scale modelling of megacity impact on air quality and climate

The EU FP7 Project MEGAPOLI: "Megacities: Emissions, urban, regional and Global Atmospheric POLlution and climate effects, and Integrated tools for assessment and mitigation" (http://megapoli.info) brings together leading European research groups, state-of-the-art scientific tools and key players from non-European countries to investigate the interactions among megacities, air quality and climate. MEGAPOLI bridges the spatial and temporal scales that connect local emissions, air quality and weather with global atmospheric chemistry and climate. The suggested concept of multi-scale integrated modelling of megacity impact on air quality and climate and vice versa is discussed in the paper. It requires considering different spatial and temporal dimensions: time scales from seconds and hours (to understand the interaction mechanisms) up to years and decades (to consider the climate effects); spatial resolutions: with model down- and up-scaling from street- to global-scale; and two-way interactions between meteorological and chemical processes.

Multi-scale sensible heat fluxes in the urban environment from large aperture scintillometry and eddy covariance

Sensible heat fluxes (QH) are determined using scintillometry and eddy covariance over a suburban area. Two large aperture scintillometers provide spatially integrated fluxes across path lengths of 2.8 km and 5.5 km over Swindon, UK. The shorter scintillometer path spans newly built residential areas and has an approximate source area of 2-4 km2, whilst the long path extends from the rural outskirts to the town centre and has a source area of around 5-10 km2. These large-scale heat fluxes are compared with local-scale eddy covariance measurements. Clear seasonal trends are revealed by the long duration of this dataset and variability in monthly QH is related to the meteorological conditions. At shorter time scales the response of QH to solar radiation often gives rise to close agreement between the measurements, but during times of rapidly changing cloud cover spatial differences in the net radiation (Q*) coincide with greater differences between heat fluxes. For clear days QH lags Q*, thus the ratio of QH to Q* increases throughout the day. In summer the observed energy partitioning is related to the vegetation fraction through use of a footprint model. The results demonstrate the value of scintillometry for integrating surface heterogeneity and offer improved understanding of the influence of anthropogenic materials on surface-atmosphere interactions.