Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

Development and evaluation of neural network freeway incident detection models using field data

This paper discusses a multi-layer feedforward (MLF) neural network incident detection model that was developed and evaluated using field data. In contrast to published neural network incident detection models which relied on simulated or limited field data for model development and testing, the model described in this paper was trained and tested on a real-world data set of 100 incidents. The model uses speed, flow and occupancy data measured at dual stations, averaged across all lanes and only from time interval t. The off-line performance of the model is reported under both incident and non-incident conditions. The incident detection performance of the model is reported based on a validation-test data set of 40 incidents that were independent of the 60 incidents used for training. The false alarm rates of the model are evaluated based on non-incident data that were collected from a freeway section which was video-taped for a period of 33 days. A comparative evaluation between the neural network model and the incident detection model in operation on Melbourne's freeways is also presented. The results of the comparative performance evaluation clearly demonstrate the substantial improvement in incident detection performance obtained by the neural network model. The paper also presents additional results that demonstrate how improvements in model performance can be achieved using variable decision thresholds. Finally, the model's fault-tolerance under conditions of corrupt or missing data is investigated and the impact of loop detector failure/malfunction on the performance of the trained model is evaluated and discussed. The results presented in this paper provide a comprehensive evaluation of the developed model and confirm that neural network models can provide fast and reliable incident detection on freeways. (C) 1997 Elsevier Science Ltd. All rights reserved.

Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

Some applications of fractional calculus in engineering

Fractional Calculus FC goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Estimation of infection rate in epidemic models with multiple populations

Dissertação para obtenção do Grau de Mestre em Matemática e Aplicações Especialização em Actuariado, Estatística e Investigação Operacional

Application of Fractional Calculus in Mechatronics

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of mechanical systems.

Stem cell transplantation in brain tumors: a new field for molecular imaging?

Neural stem cells have been proposed as a new and promising treatment modality in various pathologies of the central nervous system, including malignant brain tumors. However, the underlying mechanism by which neural stem cells target tumor areas remains elusive. Monitoring of these cells is currently done by use of various modes of molecular imaging, such as optical imaging, magnetic resonance imaging and positron emission tomography, which is a novel technology for visualizing metabolism and signal transduction to gene expression. In this new context, the microenvironment of (malignant) brain tumors and the blood-brain barrier gains increased interest. The authors of this review give a unique overview of the current molecular-imaging techniques used in different therapeutic experimental brain tumor models in relation to neural stem cells. Such methods for molecular imaging of gene-engineered neural stem/progenitor cells are currently used to trace the location and temporal level of expression of therapeutic and endogenous genes in malignant brain tumors, closing the gap between in vitro and in vivo integrative biology of disease in neural stem cell transplantation.

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

Three essays in financial economics: asset pricing, optimal portfolio selection and financial integration

Executive Summary The unifying theme of this thesis is the pursuit of a satisfactory ways to quantify the riskureward trade-off in financial economics. First in the context of a general asset pricing model, then across models and finally across country borders. The guiding principle in that pursuit was to seek innovative solutions by combining ideas from different fields in economics and broad scientific research. For example, in the first part of this thesis we sought a fruitful application of strong existence results in utility theory to topics in asset pricing. In the second part we implement an idea from the field of fuzzy set theory to the optimal portfolio selection problem, while the third part of this thesis is to the best of our knowledge, the first empirical application of some general results in asset pricing in incomplete markets to the important topic of measurement of financial integration. While the first two parts of this thesis effectively combine well-known ways to quantify the risk-reward trade-offs the third one can be viewed as an empirical verification of the usefulness of the so-called "good deal bounds" theory in designing risk-sensitive pricing bounds. Chapter 1 develops a discrete-time asset pricing model, based on a novel ordinally equivalent representation of recursive utility. To the best of our knowledge, we are the first to use a member of a novel class of recursive utility generators to construct a representative agent model to address some long-lasting issues in asset pricing. Applying strong representation results allows us to show that the model features countercyclical risk premia, for both consumption and financial risk, together with low and procyclical risk free rate. As the recursive utility used nests as a special case the well-known time-state separable utility, all results nest the corresponding ones from the standard model and thus shed light on its well-known shortcomings. The empirical investigation to support these theoretical results, however, showed that as long as one resorts to econometric methods based on approximating conditional moments with unconditional ones, it is not possible to distinguish the model we propose from the standard one. Chapter 2 is a join work with Sergei Sontchik. There we provide theoretical and empirical motivation for aggregation of performance measures. The main idea is that as it makes sense to apply several performance measures ex-post, it also makes sense to base optimal portfolio selection on ex-ante maximization of as many possible performance measures as desired. We thus offer a concrete algorithm for optimal portfolio selection via ex-ante optimization over different horizons of several risk-return trade-offs simultaneously. An empirical application of that algorithm, using seven popular performance measures, suggests that realized returns feature better distributional characteristics relative to those of realized returns from portfolio strategies optimal with respect to single performance measures. When comparing the distributions of realized returns we used two partial risk-reward orderings first and second order stochastic dominance. We first used the Kolmogorov Smirnov test to determine if the two distributions are indeed different, which combined with a visual inspection allowed us to demonstrate that the way we propose to aggregate performance measures leads to portfolio realized returns that first order stochastically dominate the ones that result from optimization only with respect to, for example, Treynor ratio and Jensen's alpha. We checked for second order stochastic dominance via point wise comparison of the so-called absolute Lorenz curve, or the sequence of expected shortfalls for a range of quantiles. As soon as the plot of the absolute Lorenz curve for the aggregated performance measures was above the one corresponding to each individual measure, we were tempted to conclude that the algorithm we propose leads to portfolio returns distribution that second order stochastically dominates virtually all performance measures considered. Chapter 3 proposes a measure of financial integration, based on recent advances in asset pricing in incomplete markets. Given a base market (a set of traded assets) and an index of another market, we propose to measure financial integration through time by the size of the spread between the pricing bounds of the market index, relative to the base market. The bigger the spread around country index A, viewed from market B, the less integrated markets A and B are. We investigate the presence of structural breaks in the size of the spread for EMU member country indices before and after the introduction of the Euro. We find evidence that both the level and the volatility of our financial integration measure increased after the introduction of the Euro. That counterintuitive result suggests the presence of an inherent weakness in the attempt to measure financial integration independently of economic fundamentals. Nevertheless, the results about the bounds on the risk free rate appear plausible from the view point of existing economic theory about the impact of integration on interest rates.

Semiclassical equations for weakly inhomogeneous cosmologies

The in-in effective action formalism is used to derive the semiclassical correction to Einsteins equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the back-reaction effect on the gravitational field of the string is discussed.

Quantization of AdS3 black holes in external fields: semiclassical results from pure gravity

(2+1)-dimensional anti-de Sitter (AdS) gravity is quantized in the presence of an external scalar field. We find that the coupling between the scalar field and gravity is equivalently described by a perturbed conformal field theory at the boundary of AdS3. This allows us to perform a microscopic computation of the transition rates between black hole states due to absorption and induced emission of the scalar field. Detailed thermodynamic balance then yields Hawking radiation as spontaneous emission, and we find agreement with the semiclassical result, including greybody factors. This result also has application to four and five-dimensional black holes in supergravity.

Conservation of the Eurasian Lynx (Lynx lynx) in a fragmented landscape - habitat models, dispersal and potential distribution

Abstract: The expansion of a recovering population - whether re-introduced or spontaneously returning - is shaped by (i) biological (intrinsic) factors such as the land tenure system or dispersal, (ii) the distribution and availability of resources (e.g. prey), (iii) habitat and landscape features, and (iv) human attitudes and activities. In order to develop efficient conservation and recovery strategies, we need to understand all these factors and to predict the potential distribution and explore ways to reach it. An increased number of lynx in the north-western Swiss Alps in the nineties lead to a new controversy about the return of this cat. When the large carnivores were given legal protection in many European countries, most organizations and individuals promoting their protection did not foresee the consequences. Management plans describing how to handle conflicts with large predators are needed to find a balance between "overabundance" and extinction. Wildlife and conservation biologists need to evaluate the various threats confronting populations so that adequate management decisions can be taken. I developed a GIS probability model for the lynx, based on habitat information and radio-telemetry data from the Swiss Jura Mountains, in order to predict the potential distribution of the lynx in this mountain range, which is presently only partly occupied by lynx. Three of the 18 variables tested for each square kilometre describing land use, vegetation, and topography, qualified to predict the probability of lynx presence. The resulting map was evaluated with data from dispersing subadult lynx. Young lynx that were not able to establish home ranges in what was identified as good lynx habitat did not survive their first year of independence, whereas the only one that died in good lynx habitat was illegally killed. Radio-telemetry fixes are often used as input data to calibrate habitat models. Radio-telemetry is the only way to gather accurate and unbiased data on habitat use of elusive larger terrestrial mammals. However, it is time consuming and expensive, and can therefore only be applied in limited areas. Habitat models extrapolated over large areas can in turn be problematic, as habitat characteristics and availability may change from one area to the other. I analysed the predictive power of Ecological Niche Factor Analysis (ENFA) in Switzerland with the lynx as focal species. According to my results, the optimal sampling strategy to predict species distribution in an Alpine area lacking available data would be to pool presence cells from contrasted regions (Jura Mountains, Alps), whereas in regions with a low ecological variance (Jura Mountains), only local presence cells should be used for the calibration of the model. Dispersal influences the dynamics and persistence of populations, the distribution and abundance of species, and gives the communities and ecosystems their characteristic texture in space and time. Between 1988 and 2001, the spatio-temporal behaviour of subadult Eurasian lynx in two re-introduced populations in Switzerland was studied, based on 39 juvenile lynx of which 24 were radio-tagged to understand the factors influencing dispersal. Subadults become independent from their mothers at the age of 8-11 months. No sex bias neither in the dispersal rate nor in the distance moved was detected. Lynx are conservative dispersers, compared to bear and wolf, and settled within or close to known lynx occurrences. Dispersal distances reached in the high lynx density population - shorter than those reported in other Eurasian lynx studies - are limited by habitat restriction hindering connections with neighbouring metapopulations. I postulated that high lynx density would lead to an expansion of the population and validated my predictions with data from the north-western Swiss Alps where about 1995 a strong increase in lynx abundance took place. The general hypothesis that high population density will foster the expansion of the population was not confirmed. This has consequences for the re-introduction and recovery of carnivores in a fragmented landscape. To establish a strong source population in one place might not be an optimal strategy. Rather, population nuclei should be founded in several neighbouring patches. Exchange between established neighbouring subpopulations will later on take place, as adult lynx show a higher propensity to cross barriers than subadults. To estimate the potential population size of the lynx in the Jura Mountains and to assess possible corridors between this population and adjacent areas, I adapted a habitat probability model for lynx distribution in the Jura Mountains with new environmental data and extrapolated it over the entire mountain range. The model predicts a breeding population ranging from 74-101 individuals and from 51-79 individuals when continuous habitat patches < 50 km2 are disregarded. The Jura Mountains could once be part of a metapopulation, as potential corridors exist to the adjoining areas (Alps, Vosges Mountains, and Black Forest). Monitoring of the population size, spatial expansion, and the genetic surveillance in the Jura Mountains must be continued, as the status of the population is still critical. ENFA was used to predict the potential distribution of lynx in the Alps. The resulting model divided the Alps into 37 suitable habitat patches ranging from 50 to 18,711 km2, covering a total area of about 93,600 km2. When using the range of lynx densities found in field studies in Switzerland, the Alps could host a population of 961 to 1,827 residents. The results of the cost-distance analysis revealed that all patches were within the reach of dispersing lynx, as the connection costs were in the range of dispersal cost of radio-tagged subadult lynx moving through unfavorable habitat. Thus, the whole Alps could once be considered as a metapopulation. But experience suggests that only few disperser will cross unsuitable areas and barriers. This low migration rate may seldom allow the spontaneous foundation of new populations in unsettled areas. As an alternative to natural dispersal, artificial transfer of individuals across the barriers should be considered. Wildlife biologists can play a crucial role in developing adaptive management experiments to help managers learning by trial. The case of the lynx in Switzerland is a good example of a fruitful cooperation between wildlife biologists, managers, decision makers and politician in an adaptive management process. This cooperation resulted in a Lynx Management Plan which was implemented in 2000 and updated in 2004 to give the cantons directives on how to handle lynx-related problems. This plan was put into practice e.g. in regard to translocation of lynx into unsettled areas. Résumé: L'expansion d'une population en phase de recolonisation, qu'elle soit issue de réintroductions ou d'un retour naturel dépend 1) de facteurs biologiques tels que le système social et le mode de dispersion, 2) de la distribution et la disponibilité des ressources (proies), 3) de l'habitat et des éléments du paysage, 4) de l'acceptation de l'espèce par la population locale et des activités humaines. Afin de pouvoir développer des stratégies efficaces de conservation et de favoriser la recolonisation, chacun de ces facteurs doit être pris en compte. En plus, la distribution potentielle de l'espèce doit pouvoir être déterminée et enfin, toutes les possibilités pour atteindre les objectifs, examinées. La phase de haute densité que la population de lynx a connue dans les années nonante dans le nord-ouest des Alpes suisses a donné lieu à une controverse assez vive. La protection du lynx dans de nombreux pays européens, promue par différentes organisations, a entraîné des conséquences inattendues; ces dernières montrent que tout plan de gestion doit impérativement indiquer des pistes quant à la manière de gérer les conflits, tout en trouvant un équilibre entre l'extinction et la surabondance de l'espèce. Les biologistes de la conservation et de la faune sauvage doivent pour cela évaluer les différents risques encourus par les populations de lynx, afin de pouvoir rapidement prendre les meilleuresmdécisions de gestion. Un modèle d'habitat pour le lynx, basé sur des caractéristiques de l'habitat et des données radio télémétriques collectées dans la chaîne du Jura, a été élaboré afin de prédire la distribution potentielle dans cette région, qui n'est que partiellement occupée par l'espèce. Trois des 18 variables testées, décrivant pour chaque kilomètre carré l'utilisation du sol, la végétation ainsi que la topographie, ont été retenues pour déterminer la probabilité de présence du lynx. La carte qui en résulte a été comparée aux données télémétriques de lynx subadultes en phase de dispersion. Les jeunes qui n'ont pas pu établir leur domaine vital dans l'habitat favorable prédit par le modèle n'ont pas survécu leur première année d'indépendance alors que le seul individu qui est mort dans l'habitat favorable a été braconné. Les données radio-télémétriques sont souvent utilisées pour l'étalonnage de modèles d'habitat. C'est un des seuls moyens à disposition qui permette de récolter des données non biaisées et précises sur l'occupation de l'habitat par des mammifères terrestres aux moeurs discrètes. Mais ces méthodes de- mandent un important investissement en moyens financiers et en temps et peuvent, de ce fait, n'être appliquées qu'à des zones limitées. Les modèles d'habitat sont ainsi souvent extrapolés à de grandes surfaces malgré le risque d'imprécision, qui résulte des variations des caractéristiques et de la disponibilité de l'habitat d'une zone à l'autre. Le pouvoir de prédiction de l'Analyse Ecologique de la Niche (AEN) dans les zones où les données de présence n'ont pas été prises en compte dans le calibrage du modèle a été analysée dans le cas du lynx en Suisse. D'après les résultats obtenus, la meilleure mé- thode pour prédire la distribution du lynx dans une zone alpine dépourvue d'indices de présence est de combiner des données provenant de régions contrastées (Alpes, Jura). Par contre, seules les données sur la présence locale de l'espèce doivent être utilisées pour les zones présentant une faible variance écologique tel que le Jura. La dispersion influence la dynamique et la stabilité des populations, la distribution et l'abondance des espèces et détermine les caractéristiques spatiales et temporelles des communautés vivantes et des écosystèmes. Entre 1988 et 2001, le comportement spatio-temporel de lynx eurasiens subadultes de deux populations réintroduites en Suisse a été étudié, basé sur le suivi de 39 individus juvéniles dont 24 étaient munis d'un collier émetteur, afin de déterminer les facteurs qui influencent la dispersion. Les subadultes se sont séparés de leur mère à l'âge de 8 à 11 mois. Le sexe n'a pas eu d'influence sur le nombre d'individus ayant dispersés et la distance parcourue au cours de la dispersion. Comparé à l'ours et au loup, le lynx reste très modéré dans ses mouvements de dispersion. Tous les individus ayant dispersés se sont établis à proximité ou dans des zones déjà occupées par des lynx. Les distances parcourues lors de la dispersion ont été plus courtes pour la population en phase de haute densité que celles relevées par les autres études de dispersion du lynx eurasien. Les zones d'habitat peu favorables et les barrières qui interrompent la connectivité entre les populations sont les principales entraves aux déplacements, lors de la dispersion. Dans un premier temps, nous avons fait l'hypothèse que les phases de haute densité favorisaient l'expansion des populations. Mais cette hypothèse a été infirmée par les résultats issus du suivi des lynx réalisé dans le nord-ouest des Alpes, où la population connaissait une phase de haute densité depuis 1995. Ce constat est important pour la conservation d'une population de carnivores dans un habitat fragmenté. Ainsi, instaurer une forte population source à un seul endroit n'est pas forcément la stratégie la plus judicieuse. Il est préférable d'établir des noyaux de populations dans des régions voisines où l'habitat est favorable. Des échanges entre des populations avoisinantes pourront avoir lieu par la suite car les lynx adultes sont plus enclins à franchir les barrières qui entravent leurs déplacements que les individus subadultes. Afin d'estimer la taille de la population de lynx dans le Jura et de déterminer les corridors potentiels entre cette région et les zones avoisinantes, un modèle d'habitat a été utilisé, basé sur un nouveau jeu de variables environnementales et extrapolé à l'ensemble du Jura. Le modèle prédit une population reproductrice de 74 à 101 individus et de 51 à 79 individus lorsque les surfaces d'habitat d'un seul tenant de moins de 50 km2 sont soustraites. Comme des corridors potentiels existent effectivement entre le Jura et les régions avoisinantes (Alpes, Vosges, et Forêt Noire), le Jura pourrait faire partie à l'avenir d'une métapopulation, lorsque les zones avoisinantes seront colonisées par l'espèce. La surveillance de la taille de la population, de son expansion spatiale et de sa structure génétique doit être maintenue car le statut de cette population est encore critique. L'AEN a également été utilisée pour prédire l'habitat favorable du lynx dans les Alpes. Le modèle qui en résulte divise les Alpes en 37 sous-unités d'habitat favorable dont la surface varie de 50 à 18'711 km2, pour une superficie totale de 93'600 km2. En utilisant le spectre des densités observées dans les études radio-télémétriques effectuées en Suisse, les Alpes pourraient accueillir une population de lynx résidents variant de 961 à 1'827 individus. Les résultats des analyses de connectivité montrent que les sous-unités d'habitat favorable se situent à des distances telles que le coût de la dispersion pour l'espèce est admissible. L'ensemble des Alpes pourrait donc un jour former une métapopulation. Mais l'expérience montre que très peu d'individus traverseront des habitats peu favorables et des barrières au cours de leur dispersion. Ce faible taux de migration rendra difficile toute nouvelle implantation de populations dans des zones inoccupées. Une solution alternative existe cependant : transférer artificiellement des individus d'une zone à l'autre. Les biologistes spécialistes de la faune sauvage peuvent jouer un rôle important et complémentaire pour les gestionnaires de la faune, en les aidant à mener des expériences de gestion par essai. Le cas du lynx en Suisse est un bel exemple d'une collaboration fructueuse entre biologistes de la faune sauvage, gestionnaires, organes décisionnaires et politiciens. Cette coopération a permis l'élaboration du Concept Lynx Suisse qui est entré en vigueur en 2000 et remis à jour en 2004. Ce plan donne des directives aux cantons pour appréhender la problématique du lynx. Il y a déjà eu des applications concrètes sur le terrain, notamment par des translocations d'individus dans des zones encore inoccupées.

Textural controls on induced polarization and permeability in granular media

The spatial resolution visualized with hydrological models and the conceptualized images of subsurface hydrological processes often exceed resolution of the data collected with classical instrumentation at the field scale. In recent years it was possible to increasingly diminish the inherent gap to information from point like field data through the application of hydrogeophysical methods at field-scale. With regards to all common geophysical exploration techniques, electric and electromagnetic methods have arguably to greatest sensitivity to hydrologically relevant parameters. Of particular interest in this context are induced polarisation (IP) measurements, which essentially constrain the capacity of a probed subsurface region to store an electrical charge. In the absence of metallic conductors the IP- response is largely driven by current conduction along the grain surfaces. This offers the perspective to link such measurements to the characteristics of the solid-fluid-interface and thus, at least in unconsolidated sediments, should allow for first-order estimates of the permeability structure.¦While the IP-effect is well explored through laboratory experiments and in part verified through field data for clay-rich environments, the applicability of IP-based characterizations to clay-poor aquifers is not clear. For example, polarization mechanisms like membrane polarization are not applicable in the rather wide pore-systems of clay free sands, and the direct transposition of Schwarz' theory relating polarization of spheres to the relaxation mechanism of polarized cells to complex natural sediments yields ambiguous results.¦In order to improve our understanding of the structural origins of IP-signals in such environments as well as their correlation with pertinent hydrological parameters, various laboratory measurements have been conducted. We consider saturated quartz samples with a grain size spectrum varying from fine sand to fine gravel, that is grain diameters between 0,09 and 5,6 mm, as well as corresponding pertinent mixtures which can be regarded as proxies for widespread alluvial deposits. The pore space characteristics are altered by changing (i) the grain size spectra, (ii) the degree of compaction, and (iii) the level of sorting. We then examined how these changes affect the SIP response, the hydraulic conductivity, and the specific surface area of the considered samples, while keeping any electrochemical variability during the measurements as small as possible. The results do not follow simple assumptions on relationships to single parameters such as grain size. It was found that the complexity of natural occurring media is not yet sufficiently represented when modelling IP. At the same time simple correlation to permeability was found to be strong and consistent. Hence, adaptations with the aim of better representing the geo-structure of natural porous media were applied to the simplified model space used in Schwarz' IP-effect-theory. The resulting semi- empiric relationship was found to more accurately predict the IP-effect and its relation to the parameters grain size and permeability. If combined with recent findings about the effect of pore fluid electrochemistry together with advanced complex resistivity tomography, these results will allow us to picture diverse aspects of the subsurface with relative certainty. Within the framework of single measurement campaigns, hydrologiste can than collect data with information about the geo-structure and geo-chemistry of the subsurface. However, additional research efforts will be necessary to further improve the understanding of the physical origins of IP-effect and minimize the potential for false interpretations.¦-¦Dans l'étude des processus et caractéristiques hydrologiques des subsurfaces, la résolution spatiale donnée par les modèles hydrologiques dépasse souvent la résolution des données du terrain récoltées avec des méthodes classiques d'hydrologie. Récemment il est possible de réduire de plus en plus cet divergence spatiale entre modèles numériques et données du terrain par l'utilisation de méthodes géophysiques, notamment celles géoélectriques. Parmi les méthodes électriques, la polarisation provoquée (PP) permet de représenter la capacité des roches poreuses et des sols à stocker une charge électrique. En l'absence des métaux dans le sous-sol, cet effet est largement influencé par des caractéristiques de surface des matériaux. En conséquence les mesures PP offrent une information des interfaces entre solides et fluides dans les matériaux poreux que nous pouvons lier à la perméabilité également dirigée par ces mêmes paramètres. L'effet de la polarisation provoquée à été étudié dans différentes études de laboratoire, ainsi que sur le terrain. A cause d'une faible capacité de polarisation des matériaux sableux, comparé aux argiles, leur caractérisation par l'effet-PP reste difficile a interpréter d'une manière cohérente pour les environnements hétérogènes.¦Pour améliorer les connaissances sur l'importance de la structure du sous-sol sableux envers l'effet PP et des paramètres hydrologiques, nous avons fait des mesures de laboratoire variées. En détail, nous avons considéré des échantillons sableux de quartz avec des distributions de taille de grain entre sables fins et graviers fins, en diamètre cela fait entre 0,09 et 5,6 mm. Les caractéristiques de l'espace poreux sont changées en modifiant (i) la distribution de taille des grains, (ii) le degré de compaction, et (iii) le niveau d'hétérogénéité dans la distribution de taille de grains. En suite nous étudions comment ces changements influencent l'effet-PP, la perméabilité et la surface spécifique des échantillons. Les paramètres électrochimiques sont gardés à un minimum pendant les mesures. Les résultats ne montrent pas de relation simple entre les paramètres pétro-physiques comme par exemples la taille des grains. La complexité des media naturels n'est pas encore suffisamment représenté par les modèles des processus PP. Néanmoins, la simple corrélation entre effet PP et perméabilité est fort et consistant. En conséquence la théorie de Schwarz sur l'effet-PP a été adapté de manière semi-empirique pour mieux pouvoir estimer la relation entre les résultats de l'effet-PP et les paramètres taille de graines et perméabilité. Nos résultats concernant l'influence de la texture des matériaux et celles de l'effet de l'électrochimie des fluides dans les pores, permettront de visualiser des divers aspects du sous-sol. Avec des telles mesures géo-électriques, les hydrologues peuvent collectionner des données contenant des informations sur la structure et la chimie des fluides des sous-sols. Néanmoins, plus de recherches sur les origines physiques de l'effet-PP sont nécessaires afin de minimiser le risque potentiel d'une mauvaise interprétation des données.

Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.