Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

One billion years of bZIP transcription factor evolution: conservation and change in dimerization and DNA-binding site specificity.

The genomic era has revealed that the large repertoire of observed animal phenotypes is dependent on changes in the expression patterns of a finite number of genes, which are mediated by a plethora of transcription factors (TFs) with distinct specificities. The dimerization of TFs can also increase the complexity of a genetic regulatory network manifold, by combining a small number of monomers into dimers with distinct functions. Therefore, studying the evolution of these dimerizing TFs is vital for understanding how complexity increased during animal evolution. We focus on the second largest family of dimerizing TFs, the basic-region leucine zipper (bZIP), and infer when it expanded and how bZIP DNA-binding and dimerization functions evolved during the major phases of animal evolution. Specifically, we classify the metazoan bZIPs into 19 families and confirm the ancient nature of at least 13 of these families, predating the split of the cnidaria. We observe fixation of a core dimerization network in the last common ancestor of protostomes-deuterostomes. This was followed by an expansion of the number of proteins in the network, but no major dimerization changes in interaction partners, during the emergence of vertebrates. In conclusion, the bZIPs are an excellent model with which to understand how DNA binding and protein interactions of TFs evolved during animal evolution.

KCM, a general framework for codon-based model of evolution

With the advancement of high-throughput sequencing and dramatic increase of available genetic data, statistical modeling has become an essential part in the field of molecular evolution. Statistical modeling results in many interesting discoveries in the field, from detection of highly conserved or diverse regions in a genome to phylogenetic inference of species evolutionary history Among different types of genome sequences, protein coding regions are particularly interesting due to their impact on proteins. The building blocks of proteins, i.e. amino acids, are coded by triples of nucleotides, known as codons. Accordingly, studying the evolution of codons leads to fundamental understanding of how proteins function and evolve. The current codon models can be classified into three principal groups: mechanistic codon models, empirical codon models and hybrid ones. The mechanistic models grasp particular attention due to clarity of their underlying biological assumptions and parameters. However, they suffer from simplified assumptions that are required to overcome the burden of computational complexity. The main assumptions applied to the current mechanistic codon models are (a) double and triple substitutions of nucleotides within codons are negligible, (b) there is no mutation variation among nucleotides of a single codon and (c) assuming HKY nucleotide model is sufficient to capture essence of transition- transversion rates at nucleotide level. In this thesis, I develop a framework of mechanistic codon models, named KCM-based model family framework, based on holding or relaxing the mentioned assumptions. Accordingly, eight different models are proposed from eight combinations of holding or relaxing the assumptions from the simplest one that holds all the assumptions to the most general one that relaxes all of them. The models derived from the proposed framework allow me to investigate the biological plausibility of the three simplified assumptions on real data sets as well as finding the best model that is aligned with the underlying characteristics of the data sets. -- Avec l'avancement de séquençage à haut débit et l'augmentation dramatique des données géné¬tiques disponibles, la modélisation statistique est devenue un élément essentiel dans le domaine dé l'évolution moléculaire. Les résultats de la modélisation statistique dans de nombreuses découvertes intéressantes dans le domaine de la détection, de régions hautement conservées ou diverses dans un génome de l'inférence phylogénétique des espèces histoire évolutive. Parmi les différents types de séquences du génome, les régions codantes de protéines sont particulièrement intéressants en raison de leur impact sur les protéines. Les blocs de construction des protéines, à savoir les acides aminés, sont codés par des triplets de nucléotides, appelés codons. Par conséquent, l'étude de l'évolution des codons mène à la compréhension fondamentale de la façon dont les protéines fonctionnent et évoluent. Les modèles de codons actuels peuvent être classés en trois groupes principaux : les modèles de codons mécanistes, les modèles de codons empiriques et les hybrides. Les modèles mécanistes saisir une attention particulière en raison de la clarté de leurs hypothèses et les paramètres biologiques sous-jacents. Cependant, ils souffrent d'hypothèses simplificatrices qui permettent de surmonter le fardeau de la complexité des calculs. Les principales hypothèses retenues pour les modèles actuels de codons mécanistes sont : a) substitutions doubles et triples de nucleotides dans les codons sont négligeables, b) il n'y a pas de variation de la mutation chez les nucléotides d'un codon unique, et c) en supposant modèle nucléotidique HKY est suffisant pour capturer l'essence de taux de transition transversion au niveau nucléotidique. Dans cette thèse, je poursuis deux objectifs principaux. Le premier objectif est de développer un cadre de modèles de codons mécanistes, nommé cadre KCM-based model family, sur la base de la détention ou de l'assouplissement des hypothèses mentionnées. En conséquence, huit modèles différents sont proposés à partir de huit combinaisons de la détention ou l'assouplissement des hypothèses de la plus simple qui détient toutes les hypothèses à la plus générale qui détend tous. Les modèles dérivés du cadre proposé nous permettent d'enquêter sur la plausibilité biologique des trois hypothèses simplificatrices sur des données réelles ainsi que de trouver le meilleur modèle qui est aligné avec les caractéristiques sous-jacentes des jeux de données. Nos expériences montrent que, dans aucun des jeux de données réelles, tenant les trois hypothèses mentionnées est réaliste. Cela signifie en utilisant des modèles simples qui détiennent ces hypothèses peuvent être trompeuses et les résultats de l'estimation inexacte des paramètres. Le deuxième objectif est de développer un modèle mécaniste de codon généralisée qui détend les trois hypothèses simplificatrices, tandis que d'informatique efficace, en utilisant une opération de matrice appelée produit de Kronecker. Nos expériences montrent que sur un jeux de données choisis au hasard, le modèle proposé de codon mécaniste généralisée surpasse autre modèle de codon par rapport à AICc métrique dans environ la moitié des ensembles de données. En outre, je montre à travers plusieurs expériences que le modèle général proposé est biologiquement plausible.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Nonlinear relaxation time and the detection of weak signals

Laser systems can be used to detect very weak optical signals. The physical mechanism is the dynamical process of the relaxation of a laser from an unstable state to a steady stable state. We present an analysis of this process based on the study of the nonlinear relaxation time. Our analytical results are compared with numerical integration of the stochastic differential equations that model this process.

Carbon dioxide evolution from snow-covered agricultural ecosystems in Finland

Selostus: Hiilidioksidin kulku lumipeitteisessä ja paljaassa maassa

Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. All cases are simulated and experimentally implemented by a compact joint transform correlator.

Design of surface forces apparatus for tribology studies combined with nonlinear optical spectroscopy

We describe the design, calibration, and performance of surface forces apparatus with the capability of illumination of the contact interface for spectroscopic investigation using optical techniques. The apparatus can be placed in the path of a Nd-YAG laser for studies of the linear response or the second harmonic and sum-frequency generation from a material confined between the two surfaces. In addition to the standard fringes of equal chromatic order technique, which we have digitized for accurate and fast analysis, the distance of separation can be measured with a fiber-optic interferometer during spectroscopic measurements (2 Å resolution and 10 ms response time). The sample approach is accomplished through application of a motor drive, piezoelectric actuator, or electromagnetic lever deflection for variable degrees of range, sensitivity, and response time. To demonstrate the operation of the instrument, the stepwise expulsion of discrete layers of octamethylcyclotetrasiloxane from the contact is shown. Lateral forces may also be studied by using piezoelectric bimorphs to induce and direct the motion of one surface.

Evolution of a Ladinian (Middle Triassic) intraplatform basin : stratigraphy, microfacies and palaeoecology of the Meride Limestone (Monte San Giorgio, Canton Ticino, Southern Switzerland)

The Monte San Giorgio (Southern Alps, Ticino, Switzerland) is the most important locality in the world for vertebrates dating back to the Middle Triassic. For this reason it was registered in 2003 as a UNESCO World Heritage Site. One of the objectives of this doctoral thesis was to fill some of the cognitive gaps regarding the Ladinian succession, including in particular the San Giorgio Dolomite and the Meride Limestone. In order to achieve this, the entire succession, more than 600 metres thick, was measured and sampled. Biostratigraphic research based on new finds of fossil invertebrates and microfossils and on the palynological analysis of the entire section was integrated with single-zircon U-Pb dating of volcanic ash layers intercalated in the carbonate succession. This enabled a redefinition of the bio-chronostratigraphic and geochronologic framework of the succession, which encompasses a significantly shorter time interval than previously held. The Ladinian section extends from the E. curionii Ammonoid Zone (Early Fassanian) to the P. archelaus Ammonoid Zone (Early Longobardian). The age of the classic fossiliferous levels of the Meride Limestone, rich in organic matter and containing vertebrate fossils which are known all over the world, was defined in both biostratigraphic and geochronologic terms. The presumed stratigraphie significance of the pachypleurosaurid reptiles found in such levels is called into question by new finds. These fossiliferous horizons were found to correspond to the main volcanoclastic intervals of the Buchenstein Formation (Middle and Upper Pietra Verde). Thus, a correlation with the Bagolino Section (Italy) containing the GSSP for the base of the Ladinian was proposed. Bulk sedimentation rates in the studied succession average 200 m/Myr and therefore prove to be 20 times higher than those of the South-Alpine pelagic basins. These values express high carbonate productivity from the surrounding platforms on one hand, and on the other a marked subsidence of the basin. Only in the intervals consisting of laminated limestones did the sedimentation rates drop to average values of around 30 m/Myr. The distribution of organic and inorganic facies appears to be the consequence of relative variations in sea-level. The laminated and organic-matter- rich intervals of the Meride Limestone are linked to a relative sea-level drop which favoured dysoxic to anoxic bottom-water conditions, coupled with an increase in runoff, perhaps due to recurrent explosive volcanic activity. The transient development under dysoxic conditions of monospecific benthic meio-/macrofaunas was documented. Organic matter suggests a predominant origin due to benthic bacterial activity, as can be witnessed in alveolar structures typical of exopolymeric substances secreted by bacteria within microbial mats. A microbial contribution to the carbonate (peloidal) precipitation was documented. The protective effect exerted by these microbial mats is also indicated as the main taphonomic factor contributing to the excellent preservation of vertebrate fossils. A radiolarian assemblage discovered in the lower part of the section (earliest Ladinian, E. curionii Zone) suggests the transient existence of open-marine but not deep-water connections with the tethyan pelagic basins. It shows marked similarities to the faunas typical of the late Anisian, suggesting therefore a low resolution power provided by radiolarian biostratigraphy in recognizing the Anisian/Ladinian boundary. The present thesis describes a new species of conifer (Elatocladus cassinae), a new species of insect (Dasyleptus triassicus) and seven new species of radiolarians (Eptingium danieli, Eptingium neriae, Parentactinosphaera eoladinica, Sepsagon ticinensis, Sepsagon? valporinae, Novamuria wirzi and Pessagnollum? hexaspinosum). In addition, following revision of the type material of already existent taxa, four new genera of radiolarians are introduced: Bernoulliella, Eohexastylus, Ticinosphaera and Lahmosphaera.

Fuzzy logic applied to the modeling of water dynamics in an Oxisol in northeastern Brazil

Modeling of water movement in non-saturated soil usually requires a large number of parameters and variables, such as initial soil water content, saturated water content and saturated hydraulic conductivity, which can be assessed relatively easily. Dimensional flow of water in the soil is usually modeled by a nonlinear partial differential equation, known as the Richards equation. Since this equation cannot be solved analytically in certain cases, one way to approach its solution is by numerical algorithms. The success of numerical models in describing the dynamics of water in the soil is closely related to the accuracy with which the water-physical parameters are determined. That has been a big challenge in the use of numerical models because these parameters are generally difficult to determine since they present great spatial variability in the soil. Therefore, it is necessary to develop and use methods that properly incorporate the uncertainties inherent to water displacement in soils. In this paper, a model based on fuzzy logic is used as an alternative to describe water flow in the vadose zone. This fuzzy model was developed to simulate the displacement of water in a non-vegetated crop soil during the period called the emergency phase. The principle of this model consists of a Mamdani fuzzy rule-based system in which the rules are based on the moisture content of adjacent soil layers. The performances of the results modeled by the fuzzy system were evaluated by the evolution of moisture profiles over time as compared to those obtained in the field. The results obtained through use of the fuzzy model provided satisfactory reproduction of soil moisture profiles.

Evolution of mRNA expression levels of autosomal and sex-linked genes in amniotes

In addition to differences in protein-coding gene sequences, changes in expression resulting from mutations in regulatory sequences have long been hypothesized to be responsible for phenotypic differences between species. However, unlike comparison of genome sequences, few studies, generally restricted to pairwise comparisons of closely related mammalian species, have assessed between-species differences at the transcriptome level. They reported that gene expression evolves at different rates in various organs and in a pattern that is overall consistent with neutral models of evolution. In the first part of my thesis, I investigated the evolution of gene expression in therian mammals (i.e.7 placental and marsupials), based on microarray data from human, mouse and the gray short-tailed opossum (Monodelphis domestica). In addition to autosomal genes, a special focus was given to the evolution of X-linked genes. The therian X chromosome was recently shown to be younger than previously thought and to harbor a specific gene content (e.g., genes involved in brain or reproductive functions) that is thought to have been shaped by specific sex-related evolutionary forces. Sex chromosomes derive from ordinary autosomes and their differentiation led to the degeneration of the Y chromosome (in mammals) or W chromosome (in birds). Consequently, X- or Z-linked genes differ in gene dose between males and females such that the heterogametic sex has half the X/Z gene dose compared to the ancestral state. To cope with this dosage imbalance, mammals have been reported to have evolved mechanisms of dosage compensation.¦In the first project, I could first show that transcriptomes evolve at different rates in different organs. Out of the five tissues I investigated, the testis is the most rapidly evolving organ at the gene expression level while the brain has the most conserved transcriptome. Second, my analyses revealed that mammalian gene expression evolution is compatible with a neutral model, where the rates of change in gene expression levels is linked to the efficiency of purifying selection in a given lineage, which, in turn, is determined by the long-term effective population size in that lineage. Thus, the rate of DNA sequence evolution, which could be expected to determine the rate of regulatory sequence change, does not seem to be a major determinant of the rate of gene expression evolution. Thus, most gene expression changes seem to be (slightly) deleterious. Finally, X-linked genes seem to have experienced elevated rates of gene expression change during the early stage of X evolution. To further investigate the evolution of mammalian gene expression, we generated an extensive RNA-Seq gene expression dataset for nine mammalian species and a bird. The analyses of this dataset confirmed the patterns previously observed with microarrays and helped to significantly deepen our view on gene expression evolution.¦In a specific project based on these data, I sought to assess in detail patterns of evolution of dosage compensation in amniotes. My analyses revealed the absence of male to female dosage compensation in monotremes and its presence in marsupials and, in addition, confirmed patterns previously described for placental mammals and birds. I then assessed the global level of expression of X/Z chromosomes and contrasted this with its ancestral gene expression levels estimated from orthologous autosomal genes in species with non-homologous sex chromosomes. This analysis revealed a lack of up-regulation for placental mammals, the level of expression of X-linked genes being proportional to gene dose. Interestingly, the ancestral gene expression level was at least partially restored in marsupials as well as in the heterogametic sex of monotremes and birds. Finally, I investigated alternative mechanisms of dosage compensation and found that gene duplication did not seem to be a widespread mechanism to restore the ancestral gene dose. However, I could show that placental mammals have preferentially down-regulated autosomal genes interacting with X-linked genes which underwent gene expression decrease, and thus identified a novel alternative mechanism of dosage compensation.