Seizure semiology: an overview of the 'inverse problem'.

In clinical practice, a classification of seizures based on clinical signs and symptoms leads to an improved understanding of epilepsy-related issues and therefore strongly contributes to a better patient care. The inverse problem involves inferring the anatomical brain localization of a seizure from the scalp surface EEG, a concept we apply here to correlate seizure origin with seizure semiology. The spheres of sensorium, motor features, consciousness changes and autonomic alterations during ictal and postictal manifestations are reviewed, including several subdivisions used to better categorize particular features. Particular attention is given to behavioral features, as well as to features occurring in idiopathic generalized epileptic syndromes and psychogenic nonepileptic spells.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Improving telecommunication security level by integrating quantum key distribution in communication protocols

Résumé La cryptographie classique est basée sur des concepts mathématiques dont la sécurité dépend de la complexité du calcul de l'inverse des fonctions. Ce type de chiffrement est à la merci de la puissance de calcul des ordinateurs ainsi que la découverte d'algorithme permettant le calcul des inverses de certaines fonctions mathématiques en un temps «raisonnable ». L'utilisation d'un procédé dont la sécurité est scientifiquement prouvée s'avère donc indispensable surtout les échanges critiques (systèmes bancaires, gouvernements,...). La cryptographie quantique répond à ce besoin. En effet, sa sécurité est basée sur des lois de la physique quantique lui assurant un fonctionnement inconditionnellement sécurisé. Toutefois, l'application et l'intégration de la cryptographie quantique sont un souci pour les développeurs de ce type de solution. Cette thèse justifie la nécessité de l'utilisation de la cryptographie quantique. Elle montre que le coût engendré par le déploiement de cette solution est justifié. Elle propose un mécanisme simple et réalisable d'intégration de la cryptographie quantique dans des protocoles de communication largement utilisés comme les protocoles PPP, IPSec et le protocole 802.1li. Des scénarios d'application illustrent la faisabilité de ces solutions. Une méthodologie d'évaluation, selon les critères communs, des solutions basées sur la cryptographie quantique est également proposée dans ce document. Abstract Classical cryptography is based on mathematical functions. The robustness of a cryptosystem essentially depends on the difficulty of computing the inverse of its one-way function. There is no mathematical proof that establishes whether it is impossible to find the inverse of a given one-way function. Therefore, it is mandatory to use a cryptosystem whose security is scientifically proven (especially for banking, governments, etc.). On the other hand, the security of quantum cryptography can be formally demonstrated. In fact, its security is based on the laws of physics that assure the unconditional security. How is it possible to use and integrate quantum cryptography into existing solutions? This thesis proposes a method to integrate quantum cryptography into existing communication protocols like PPP, IPSec and the 802.l1i protocol. It sketches out some possible scenarios in order to prove the feasibility and to estimate the cost of such scenarios. Directives and checkpoints are given to help in certifying quantum cryptography solutions according to Common Criteria.

Modelling the influence of change in fire regime on the local distribution of a Mediterranean pyrophytic plant species (Cistus salviifolius) at its northern range limit

Aims: To assess the potential distribution of an obligate seeder and active pyrophyte, Cistus salviifolius, a vulnerable species in the Swiss Red List; to derive scenarios by changing the fire return interval; and to discuss the results from a conservation perspective. A more general aim is to assess the impact of fire as a natural factor influencing the vegetation of the southern slopes of the Alps. Locations: Alps, southern Switzerland. Methods: Presence-absence data to fit the model were obtained from the most recent field mapping of C. salviifolius. The quantitative environmental predictors used in this study include topographic, climatic and disturbance (fire) predictors. Models were fitted by logistic regression and evaluated by jackknife and bootstrap approaches. Changes in fire regime were simulated by increasing the time-return interval of fire (simulating longer periods without fire). Two scenarios were considered: no fire in the past 15 years; or in the past 35 years. Results: Rock cover, slope, topographic position, potential evapotranspiration and time elapsed since the last fire were selected in the final model. The Nagelkerke R-2 of the model for C. salviifolius was 0.57 and the Jackknife area under the curve evaluation was 0.89. The bootstrap evaluation revealed model robustness. By increasing the return interval of fire by either up to 15 years, or 35 years, the modelled C. salviifolius population declined by 30-40%, respectively. Main conclusions: Although fire plays a significant role, topography and rock cover appear to be the most important predictors, suggesting that the distribution of C. salviifolius in the southern Swiss Alps is closely related to the availability of supposedly competition-free sites, such as emerging bedrock, ridge locations or steep slopes. Fire is more likely to play a secondary role in allowing C. salviifolius to extend its occurrence temporarily, by increasing germination rates and reducing the competition from surrounding vegetation. To maintain a viable dormant seed bank for C. salviifolius, conservation managers should consider carrying out vegetation clearing and managing wild fire propagation to reduce competition and ensure sufficient recruitment for this species.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

Inverse metamorphic zonation in very low-grade Tibetan zone series of SE Zanskar and its tectonic consequences (NW India, Himalaya)

The metamorphism of the carbonate rocks of the SE Zanskar Tibetan zone has been studied by `'illite crystallinity'' and calcite-dolomite thermometry. The epizonal Zangla unit overlies the anchizonal Chumik unit. This discontinuous inverse zonation demonstrates a late to post-metamorphic thrust of the first unit over the second. The studied area underwent a complex tectonic history: - The tectonic units were stacked from the NE to the SW, generating recumbent folds, NE dipping thrusts and the regional metamorphism. The compressive movements were active under lower temperature conditions, resulting in late thrusts that disturbed the metamorphic zonation. The discontinuous inverse metamorphic zonation dates from this phase. - A NE vergent backfolding phase occurred at lower temperature conditions. It caused the uplift of more metamorphic levels. - A late extensional phase is revealed by the presence of NE dipping low angle normal faults, and a major high angle fault, the Sarchu fault. The low angle normal faults locally run along earlier thrusts (composite tectonic contacts). Their throw has been sufficient to reset a normal stratigraphic superposition (young layers overlying old ones), but insufficient to erase the inverse metamorphic relationship. However, the combined action of backfolding and normal faulting can locally lessen, or even cancel, the inverse metamorphic superposition. After deduction of the normal fault translation, the vertical component of the original thrust displacement through stratigraphy is 400 m, which is a value far too low to explain the temperature difference between the two units. The horizontal component of displacement is therefore far more important than the vertical one. The regional distribution of metamorphism within the Zangla unit points out to an anchizonal front and an epizonal inner part. This fact is in agreement with nappe tectonics.

Multifractal portrayal of the distribution of the Swiss population

The present research studies the spatial patterns of the distribution of the Swiss population (DSP). This description is carried out using a wide variety of global spatial structural analysis tools such as topological, statistical and fractal measures, which enable the estimation of the spatial degree of clustering of a point pattern. A particular attention is given to the analysis of the multifractality to characterize the spatial structure of the DSP at different scales. This will be achieved by measuring the generalized q-dimensions and the singularity spectrum. This research is based on high quality data of the Swiss Population Census of the Year 2000 at a hectometric resolution (grid 100 x 100 m) issued by the Swiss Federal Statistical Office (FSO).

Are niche-based species distribution models transferable in space?

Aim To assess the geographical transferability of niche-based species distribution models fitted with two modelling techniques. Location Two distinct geographical study areas in Switzerland and Austria, in the subalpine and alpine belts. Methods Generalized linear and generalized additive models (GLM and GAM) with a binomial probability distribution and a logit link were fitted for 54 plant species, based on topoclimatic predictor variables. These models were then evaluated quantitatively and used for spatially explicit predictions within (internal evaluation and prediction) and between (external evaluation and prediction) the two regions. Comparisons of evaluations and spatial predictions between regions and models were conducted in order to test if species and methods meet the criteria of full transferability. By full transferability, we mean that: (1) the internal evaluation of models fitted in region A and B must be similar; (2) a model fitted in region A must at least retain a comparable external evaluation when projected into region B, and vice-versa; and (3) internal and external spatial predictions have to match within both regions. Results The measures of model fit are, on average, 24% higher for GAMs than for GLMs in both regions. However, the differences between internal and external evaluations (AUC coefficient) are also higher for GAMs than for GLMs (a difference of 30% for models fitted in Switzerland and 54% for models fitted in Austria). Transferability, as measured with the AUC evaluation, fails for 68% of the species in Switzerland and 55% in Austria for GLMs (respectively for 67% and 53% of the species for GAMs). For both GAMs and GLMs, the agreement between internal and external predictions is rather weak on average (Kulczynski's coefficient in the range 0.3-0.4), but varies widely among individual species. The dominant pattern is an asymmetrical transferability between the two study regions (a mean decrease of 20% for the AUC coefficient when the models are transferred from Switzerland and 13% when they are transferred from Austria). Main conclusions The large inter-specific variability observed among the 54 study species underlines the need to consider more than a few species to test properly the transferability of species distribution models. The pronounced asymmetry in transferability between the two study regions may be due to peculiarities of these regions, such as differences in the ranges of environmental predictors or the varied impact of land-use history, or to species-specific reasons like differential phenotypic plasticity, existence of ecotypes or varied dependence on biotic interactions that are not properly incorporated into niche-based models. The lower variation between internal and external evaluation of GLMs compared to GAMs further suggests that overfitting may reduce transferability. Overall, a limited geographical transferability calls for caution when projecting niche-based models for assessing the fate of species in future environments.

An improved approach for predicting the distribution of rare and endangered species from occurrence and pseudo-absence data

1. Few examples of habitat-modelling studies of rare and endangered species exist in the literature, although from a conservation perspective predicting their distribution would prove particularly useful. Paucity of data and lack of valid absences are the probable reasons for this shortcoming. Analytic solutions to accommodate the lack of absence include the ecological niche factor analysis (ENFA) and the use of generalized linear models (GLM) with simulated pseudo-absences. 2. In this study we tested a new approach to generating pseudo-absences, based on a preliminary ENFA habitat suitability (HS) map, for the endangered species Eryngium alpinum. This method of generating pseudo-absences was compared with two others: (i) use of a GLM with pseudo-absences generated totally at random, and (ii) use of an ENFA only. 3. The influence of two different spatial resolutions (i.e. grain) was also assessed for tackling the dilemma of quality (grain) vs. quantity (number of occurrences). Each combination of the three above-mentioned methods with the two grains generated a distinct HS map. 4. Four evaluation measures were used for comparing these HS maps: total deviance explained, best kappa, Gini coefficient and minimal predicted area (MPA). The last is a new evaluation criterion proposed in this study. 5. Results showed that (i) GLM models using ENFA-weighted pseudo-absence provide better results, except for the MPA value, and that (ii) quality (spatial resolution and locational accuracy) of the data appears to be more important than quantity (number of occurrences). Furthermore, the proposed MPA value is suggested as a useful measure of model evaluation when used to complement classical statistical measures. 6. Synthesis and applications. We suggest that the use of ENFA-weighted pseudo-absence is a possible way to enhance the quality of GLM-based potential distribution maps and that data quality (i.e. spatial resolution) prevails over quantity (i.e. number of data). Increased accuracy of potential distribution maps could help to define better suitable areas for species protection and reintroduction.

Le pergélisol dans les terrains sédimentaires à forte déclivité: distribution, régime thermique et instabilités

Résumé: Dans le contexte d'un climat de plus en plus chaud, la localisation du pergélisol dans les terrains sédimentaires à forte déclivité et l'évaluation des mouvements de terrain qui y ont cours s'avèrent primordiales. S'insérant dans cette problématique, ce travail de thèse s'articule autour de deux axes de recherche différents. D'un point de vue statique, cette recherche propose une étude de la distribution et des caractéristiques du pergélisol dans les éboulis de la zone périglaciaire alpine. D'un point de vue dynamique, une analyse de l'influence des caractéristiques du pergélisol (teneur en glace, température du pergélisol, etc.) et des variations des températures de l'air et du sol sur les vitesses de fluage des corps sédimentaires gelés est effectuée. Afin de répondre à ce double objectif, l'approche "terrain" a été privilégiée. Pour déterminer la répartition et les caractéristiques du pergélisol, les méthodes traditionnelles de prospection du pergélisol ont été utilisées, à savoir la mesure de la température du sol à la base du manteau neigeux (BTS), la mesure de la température du sol en continu ainsi que la méthode géoélectrique. Les mouvements de terrain ont pour leur part été mesurés à l'aide d'un GPS différentiel. L'étude de la distribution du pergélisol a été effectuée dans une quinzaine d'éboulis situés dans les régions du Mont Gelé (Verbier-Nendaz) et d'Arolla principalement. Dans la plupart des cas, un pergélisol a pu être mis en évidence dans la partie inférieure des accumulations sédimentaires, alors que la partie médiane des éboulis n'est, le plus souvent, pas gelée. Si cette absence de pergélisol se prolonge parfois dans les portions sommitales des pentes, les mesures réalisées montrent que dans d'autres cas des sédiments gelés y sont à nouveau présents. Les résistivités électriques mesurées dans les portions gelées des éboulis étudiés sont dans la plupart des cas nettement inférieures à celles mesurées sur les glaciers rocheux. Des études préalables ont montré que des circulations d'air internes sont responsables de l'anomalie thermique négative et, lorsqu'il existe, du pergélisol que l'on trouve dans la partie inférieure d'éboulis situés plus de 1000 m plus bas que la limite inférieure régionale du pergélisol discontinu. L'étude de quatre sites de basse altitude (1400-1900 m), et notamment l'équipement du site de Dreveneuse (Préalpes Valaisannes) avec deux forages, des capteurs de température de surface et un anémomètre a permis de vérifier et de préciser le mécanisme de ventilation actif au sein des éboulis froids de basse altitude. Ce mécanisme fonctionne de la manière suivante: en hiver, l'air contenu dans l'éboulis, plus chaud et plus léger que l'air extérieur, monte à l'intérieur de l'accumulation sédimentaire et est expulsé dans ses parties sommitales. Cet effet de cheminée provoque une aspiration d'air froid à l'intérieur de la partie inférieure de l'éboulis, causant ainsi un sur-refroidissement marqué du terrain. En été, le mécanisme s'inverse, l'éboulis étant plus froid que l'air environnant. De l'air froid est alors expulsé au bas de la pente. Une ventilation ascendante hivernale a pu être mise en évidence dans certains des éboulis de haute altitude étudiés. Elle est probablement en grande partie responsable de la configuration particulière des zones gelées observées. Même si l'existence d'un effet de cheminée n'a pu être démontrée dans tous les cas, du fait notamment de la glace interstitielle qui entrave le cheminement de l'air, des indices laissant présager son possible fonctionnement existent dans la quasi totalité des éboulis étudiés. L'absence de pergélisol à des altitudes qui lui sont favorables pourrait en tous les cas s'expliquer par un réchauffement du terrain lié à des expulsions d'air relativement chaud. L'étude des mouvements de terrain a été effectuée sur une dizaine de sites, principalement sur des glaciers rocheux, mais également sur une moraine de poussée et - II - Résumé ? abstract quelques éboulis. Plusieurs glaciers rocheux présentent des formes de déstabilisation récente (niches d'arrachement, blocs basculés, apparition de la matrice fine à la surface, etc.), ce qui témoigne d'une récente accélération des vitesses de déplacement. Ce phénomène, qui semble général à l'échelle alpine, est probablement à mettre sur le compte du réchauffement du pergélisol depuis une vingtaine d'années. Les vitesses mesurées sur ces formations sont souvent plus élevées que les valeurs habituellement proposées dans la littérature. On note par ailleurs une forte variabilité inter-annuelle des vitesses, qui semblent dépendre de la variation de la température moyenne annuelle de surface. Abstract: In the context of a warmer climate, the localisation of permafrost in steep sedimentary terrain and the measurement of terrain movements that occur in these areas is of great importance. With respect to these problems, this PhD thesis follows two different research axes. From a static point of view, the research presents a study of the permafrost distribution and characteristics in the talus slopes of the alpine periglacial belt. From a dynamic point of view, an analysis of the influence of the permafrost characteristics (ice content, permafrost temperature, etc.) and air and soil temperature variations on the creep velocities of frozen sedimentary bodies is carried out. In order to attain this double objective, the "field" approach was favoured. To determine the distribution and the characteristics of permafrost, the traditional methods of permafrost prospecting were used, i.e. ground surface temperature measurements at the base of the snow cover (BTS), year-round ground temperature measurements and DC-resistivity prospecting. The terrain movements were measured using a differential GPS. The permafrost distribution study was carried out on 15 talus slopes located mainly in the Mont Gelé (Verbier-Nendaz) and Arolla areas (Swiss Alps). In most cases, permafrost was found in the lower part of the talus slope, whereas the medium part was free of ice. In some cases, the upper part of the talus is also free of permafrost, whereas in other cases permafrost is present. Electrical resistivities measured in the frozen parts of the studied talus are in most cases clearly lower than those measured on rock glaciers. Former studies have shown that internal air circulation is responsible for the negative thermal anomaly and, when it exists, the permafrost present in the lower part of talus slopes located more than 1000 m below the regional lower limit of discontinuous permafrost. The study of four low-altitude talus slopes (1400-1900 m), and notably the equipment of Dreveneuse field site (Valais Prealps) with two boreholes, surface temperature sensors and an anemometer permitted to verify and to detail the ventilation mechanism active in low altitude talus slopes. This mechanism works in the following way: in winter, the air contained in the block accumulation is warmer and lighter than the surrounding air and therefore moves upward in the talus and is expelled in its upper part. This chimney effect induces an aspiration of cold air in the interior of the lower part of talus, that causes a strong overcooling of the ground. In summer, the mechanism is reversed because the talus slope is colder than the surrounding air. Cold air is then expelled in the lower part of the slope. Evidence of ascending ventilation in wintertime could also be found in some of the studied high-altitude talus slopes. It is probably mainly responsible for the particular configuration of the observed frozen areas. Even if the existence of a chimney effect could not be demonstrated in all cases, notably because of interstitial ice that obstructs Résumé ? abstract - III - the air circulation, indices of its presence exist in nearly all the studied talus. The absence of permafrost at altitudes favourable to its presence could be explained, for example, by the terrain warming caused by expulsion of relatively warm air. Terrain movements were measured at about ten sites, mainly on rock glaciers, but also on a push moraine and some talus slopes. Field observations reveal that many rock glaciers display recent destabilization features (landslide scars, tilted blocks, presence of fine grained sediments at the surface, etc.) that indicate a probable recent acceleration of the creep velocities. This phenomenon, which seems to be widespread at the alpine scale, is probably linked to the permafrost warming during the last decades. The measured velocities are often higher than values usually proposed in the literature. In addition, strong inter-annual variations of the velocities were observed, which seems to depend on the mean annual ground temperature variations.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Spectral energy distribution of the gamma-ray microquasar LS 5039

The microquasar LS 5039 has recently been detected as a source of very high energy (VHE) $\gamma$-rays. This detection, that confirms the previously proposed association of LS 5039 with the EGRET source 3EG~J1824$-$1514, makes of LS 5039 a special system with observational data covering nearly all the electromagnetic spectrum. In order to reproduce the observed spectrum of LS 5039, from radio to VHE $\gamma$-rays, we have applied a cold matter dominated jet model that takes into account accretion variability, the jet magnetic field, particle acceleration, adiabatic and radiative losses, microscopic energy conservation in the jet, and pair creation and absorption due to the external photon fields, as well as the emission from the first generation of secondaries. The radiative processes taken into account are synchrotron, relativistic Bremsstrahlung and inverse Compton (IC). The model is based on a scenario that has been characterized with recent observational results, concerning the orbital parameters, the orbital variability at X-rays and the nature of the compact object. The computed spectral energy distribution (SED) shows a good agreement with the available observational data.

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.

Statistical Inversion Theory in X-ray Tomography

In this thesis the X-ray tomography is discussed from the Bayesian statistical viewpoint. The unknown parameters are assumed random variables and as opposite to traditional methods the solution is obtained as a large sample of the distribution of all possible solutions. As an introduction to tomography an inversion formula for Radon transform is presented on a plane. The vastly used filtered backprojection algorithm is derived. The traditional regularization methods are presented sufficiently to ground the Bayesian approach. The measurements are foton counts at the detector pixels. Thus the assumption of a Poisson distributed measurement error is justified. Often the error is assumed Gaussian, altough the electronic noise caused by the measurement device can change the error structure. The assumption of Gaussian measurement error is discussed. In the thesis the use of different prior distributions in X-ray tomography is discussed. Especially in severely ill-posed problems the use of a suitable prior is the main part of the whole solution process. In the empirical part the presented prior distributions are tested using simulated measurements. The effect of different prior distributions produce are shown in the empirical part of the thesis. The use of prior is shown obligatory in case of severely ill-posed problem.