Το ριβόσωμα παρέχει την πλατφόρμα πάνω στη οποία το mRNA αναγνωρίζεται και αποκωδικοποιείται από τα μεταφορικά RNAs. Δρα καταλυτικά ως ριβοένζυμο και συνθέτει την αντίστοιχη αλληλουχία αμινοξέων. Σημαντικά λειτουργικό κομμάτι του ριβοσώματος αποτελεί το τούνελ εξόδου, το οποίο βρίσκεται στη μεγάλη υπομονάδα του ριβοσώματος και αποτελεί το κανάλι, μέσω του οποίου οι νεοσυντιθέμενες πεπτιδικές αλυσίδες εξέρχονται στο κυτταροδιάλυμα. Νεότερες ερμηνείες προσδίδουν στο τούνελ εξόδου έναν πιο ενεργό ρόλο, καταδεικνύοντας τη σπουδαιότητά του όχι μόνο ως διάδρομος εξόδου της πεπτιδικής αλυσίδας, αλλά και ως λειτουργική περιοχή του ριβοσώματος με σημαντικό ρόλο στη ρύθμιση της πρωτεϊνικής σύνθεσης. Το δίκτυο επικοινωνίας μεταξύ τούνελ και πεπτιδυλοτρανσφεράσης δεν έχει ακόμα χαρτογραφηθεί και μελετηθεί πλήρως, υπάρχουν όμως μέχρι στιγμής πολυπληθείς αναφορές που επιβεβαιώνουν ότι μέρος του αποτελούν κυρίως βάσεις του 23S rRNA, συστατικά του τοιχώματος της εισόδου στο τούνελ, και βάσεις ευρισκόμενες στο κέντρο της πεπτιδυλοτρανσφεράσης, συντηρημένες εξελεικτικά, γνωστές από την αλληλεπιδρασή τους με αναστολείς της πεπτιδυλοτρανσφεράσης και κυρίως με αναστολείς της οικογένειας των μακρολιδίων. Στην παρούσα διατριβή μελετήσαμε την αλληλεπίδραση των χαρακτηριστικών αυτών βάσεων που συγκροτούν το δίκτυο επικοινωνίας μεταξύ του τούνελ εξόδου και της πεπτιδυλοτρανσφεράσης με τη βοήθεια νέων μακρολιδίων τρίτης γενιάς, των κετολιδίων, που φέρουν επί πλέον και άτομα φθορίου, παρέχοντας έτσι στο μόριο μεγαλύτερη συγγένεια για φορτισμένες ομάδες. Σύμφωνα με τα αποτελέσματά μας, αποτελούν εξαιρετικά υποσχόμενους αντιμικροβιακούς θεραπευτικούς παράγοντες, και αναστέλλουν ισχυρά την μετάφραση. Παράλληλα καταλαμβάνουν αμοιβαία αποκλειόμενες θέσεις στο ριβόσωμα, στην είσοδο του τούνελ, αλληλεπιδρώντας με τις βάσεις Α2058, Α2059, Α2062 και Α752. Επειδή όλες οι παραπάνω βάσεις αποτελούν μέρος του δικτύου επικοινωνίας τούνελ-πεπτιδυλοτρανσφεράσης, θα μπορούσαμε να συμπληρώσουμε τον ήδη υπάρχοντα μηχανισμό δράσης των μακρολιδίων (drop-off, λόγω αύξησης της koff) με την επικοινωνία του τούνελ με την πεπτιδυλοτρανσφεράση, ώστε να απενεργοποιηθεί η τελευταία με τελική κατάληξη τη διακοπή της πρωτεϊνικής σύνθεσης και την επαγωγή του drop-off. Για την περαιτέρω μελέτη της αλληλεπίδρασης του τούνελ με την νεοσυντιθέμενη πεπτιδική αλυσίδα, σχεδιάσθηκαν νέα πεπτιδυλο παράγωγα της χλωραμφανικόλης, τα οποία προσομοιάζουν πεπτιδυλο-tRNAs προσδεδεμένα στην Α-θέση του ριβοσώματος, με την ολιγοπεπτιδική αλληλουχία να εκτείνεται βαθύτερα στο τούνελ, υιοθετώντας μία ανοικτή διαμόρφωση. Όπως διαπιστώσαμε με συναγωνιστικές μελέτες με ραδιενεργό ερυθρομυκίνη, τα συγκεκριμένα ανάλογα καταλαμβάνουν την Α-θέση στο κέντρο της πεπτιδυλοτρανσφεράσης, ενώ η συγγένεια του κάθε αναλόγου ως αναστολέα της λειτουργίας του ριβοσώματος, είναι απόλυτα ιδιοσυγκρατική, καθώς εξαρτάται από την αλληλουχία των αμινοξέων που συγκροτούν το πεπτίδιο. Μελετώντας το αποτύπωμα των ενώσεων αυτών στο ριβόσωμα, διαπιστώσαμε ότι ενώ η βάση της χλωραμφαινικόλης διατηρεί τη θέση της στη περιοχή Α, το πεπτίδιο εισέρχεται βαθειά στην είσοδο του τούνελ, αλληλεπιδρώντας με την βάση Α752. Συνεπώς τα πεπτιδυλο ανάλογα της χλωραμφαινικόλης, τα οποία συμπεριφέρονται ως ισχυροί αναστολείς της μετάφρασης, αποτελούν κατάλληλα εργαλεία μελέτης της αλληλεπίδρασης μεταξύ της νεοσυντιθέμενης πεπτιδικής αλληλουχίας και στοιχείων του τούνελ εξόδου του ριβοσώματος. / Ribosomes translate the genetic code into proteins in all living cells with extremely high efficiency, owing to their inherent flexibility and to their spectacular architecture. These large ribonucleoprotein particles synthesize proteins in all cells, using messenger RNA as the template, confirming that the ribosome is indeed a ribozyme, and aminoacyl-transfer RNAs as substrates. As the nascent polypeptide chain is being synthesized, it passes through a tunnel within the large ribosomal subunit and emerges at the solvent side where protein folding occurs. New studies indicate that in some cases, the tunnel plays a more active role. Accumulated evidence had definitely concluded that ribosomal tunnel is not only a passive conduit for the nascent chains but a rather functionally important compartment, where specific peptide sequences establish direct interactions with the tunnel, talking back to the ribosome in order to regulate peptide synthesis, leading to translational stalling. In this study, we have investigated functional interactions between distinct locations of the ribosomal tunnel and specific residues of the peptidyltransferase, using new macrolides, known as ketolides, which carry also fluorine attached to the lactone ring either directly or indirectly. According to our results, the new antibiotics exhibited better antimicrobial activity, inhibiting strongly the translational apparatus and could be useful tools in the future for treatment of bacterial infections. Binding studies with radiolabeled erythromycin revealed that these drugs bound competitively with erythromycin at the large ribosomal subunit, with extremely low dissociation constants. In parallel, RNA footprinting indicated that the new ketolides occupy the main macrolide binding site in the ribosome, which is located at the entrance of the exit tunnel adjacent to the peptidyltransferase center. These drugs interact with A2058, A2059 and A2062, as well as their extended heteroaromatic alkyl-aryl side chain penetrates deeper in the tunnel protecting A752 of Helix 35, interacting with basepair A752-U2609. To explore further this interaction, we have synthesized new peptidyl conjugates of chloramphenicol, which resemble nascent peptidyl-tRNA chains bound to the A-site of the ribosome, with their peptide sequence located deeper within tunnel, adopting an extended configuration. According to our data, these compounds did indeed bind to the peptidyl transferase center, competing with radiolabelled- chloramphenicol for binding to the ribosome. The binding of each analog, as well as its inhibitory activity of ribosomal function, is absolutely idiosyncratic, depending on the sequence of amino acid of peptide moiety. Studying the footprinting pattern of these compounds on the ribosome, we confirmed that while the chloramphenicol base maintains its position on the A-site, the peptide moiety penetrates deeper in the entrance of the exit tunnel, interacting with nucleotide A752. Therefore, we believe that these chloramphenicol peptides could be useful tools for probing nascent polypeptide chain interaction with the ribosome.

This paper seeks to understand the role of proximity to Silicon Valley and the Silicon Valley network effect on venture success. Despite the wealth of literature on the role and importance of geographic proximity in the venture capital process, no studies have specifically examined the impact of geographic proximity to Silicon Valley on venture success. I build my study on existing literature but deviate from past research in the following ways: first, I narrow the research question to the relationship between geographic proximity to Silicon Valley and successful exit; second, I consider success from the perspective of the venture rather than the venture-backing firm; third, I employ a logistical model as well as a linear probability model; fourth I control for endogeneity by isolating first rounds; lastly, I exclude syndicated deals, focusing on 1:1 venture-backing firm-to-venture deals. I use VenureXpert data for Silicon Valley-backed firms located both in and outside Silicon Valley to test hypotheses regarding geographic proximity. The results are significant and suggest that venture location in Silicon Valley is associated with greater venture success. Based on the results, it is clear that the impact of the Silicon Valley network effect is statistically meaningful and should encourage ventures to continue to strategically locate themselves in Silicon Valley.

HIV/AIDS is already the leading cause of death worldwide (Unicef et al., 2004:10) with more than 5 million people out of a total of 46 million South Africans that were HIV positive in 2004, giving a total population prevalence rate of 11 per cent (Dorrington et al., 2004:1). Many people infected do not have access to even the basic drugs needed to treat HIV-related infections and other conditions (Wikipedia, 2004:3). The relative high price of many of the antiretroviral (ARV) drugs and diagnostics on the other hand are one of the main barriers to their availability in developing countries (Unicef et al., 2004:77). ARV drugs registered in South Africa include the Nucleoside/Nucleotide Reverse Transcriptase Inhibitors (NRTIs), Non-Nucleoside Reverse Transcriptase Inhibitors (NNRTIs) and Protease Inhibitors (PIs) (MCC, 2004:1). The objective of this study was to review, analyse and interpret the prescribing patterns of antiviral drugs, with special reference to antiretroviral drugs, in the private health care sector in South Africa by using a medicine claims database. A quantitative, retrospective drug utilisation review was performed. The data ranging from 1 January 2001 to 31 December 2001, 1 January 2002 to 31 December 2002, and 1 January 2004 to 31 December 2004 were used, dividing each year into three four-month periods, namely January to April, May to August, and September to December. It was found that 0.38 per cent (n=1 475 380) for 2001, 0.72 per cent (n=2 076 236) for 2002, and 1.68 per cent (n=2 595 254) for 2004 of all studied prescriptions for the research periods 2001, 2002, and 2004 respectively, contained ARV drugs. ARV drugs constituted 0.33 per cent (n=2 951 326) for 2001, 0.87 per cent (n=4 042 145) for 2002, and 1.92 per cent (n=5 305 882) for 2004 of the total number of medicine items prescribed for the study years 2001, 2002 and 2004 respectively. The total cost of ARV drugs amounted to R4 990 784.29, thus constituting 1.31 per cent of the total cost (R379 708 489) of all medicine items on the database for 2001, increased to R18 235 075.75, thus constituting 3.03 per cent of the total cost (R601 350 325) of all medicine items on the database for 2002, and increased to R34 714 483.64, thus constituting 5.25 per cent of the total cost (R661 223 146) of all medicine items on the database for 2004. It was found that 35.31 per cent (n=5 599) for 2001, 52.68 per cent (n=15 004) for 2002, and 74.27 per cent (n=43 482) for 2004 of all studied antiviral prescriptions for the research periods 2001, 2002, and 2004 respectively, contained ARV drugs. ARV drugs constituted 46.25 per cent (n=21 183) for 2001, 70.20 per cent (n=50 246) for 2002, and 85.87 per cent (n=118 718) for 2004 of the total number of antiviral medicine items prescribed for the study years 2001, 2002 and 2004 respectively. The total cost of ARV medicine items, represented 67.33 per cent (n=R4 990 784.29) during 2001, 84.72 per cent (n=R18 235 075.75) during 2002, and 91.20 per cent (n=R34 714 483.64) during 2004 of the total cost of all antiviral medicine items claimed through the database (n=R7412577.73 for 2001, n=R21523365.56 for 2002, and n=R38 064 347.38 for 2004). The average cost per ARV medicine items for 2004 increased from R317.93i190.80 for the period January to April to R369.2W219.50 for the period May to August, and decreased to R324.79±212.48 for the period September to December and resulted in a cost saving of R41 044.35 for the period May to August versus September to December for the ARV medicine items. The implementation of the pricing regulations could thus be a possible reason for this cost saving, due to fact that the single exit price only came into effect from May 2004. The weighted average number of ARV medicine items per prescription was 1.75*0.31 for 2001, increased to 2.35±0.03 to 2002 and remained stable on 2.35±0.02 for 2004. It was found that majority of prescriptions contained more combination ARV medicine items than single ARV medicine items, ranging from 6 834 (69.76 per cent; n=9 796) prescriptions containing combination ARV medicine items in 2001 and 32 941 (93.39 per cent; n=35 271) prescriptions containing combination ARV medicine items in 2002 to 98 805 (96.93 per cent; n=101 938) prescriptions containing combination ARV medicine items in 2004. Lastly, it was perceived that didanosine was the active ingredient with the largest prevalence for all three four-month periods of 2001 and also for the periods January to April and May to August of 2002, whilst efavirenz represented the active ingredient with the largest prevalence for the period September to December of 2002, and also for all three four-month periods of 2004. Didanosine represented the active ingredient with the highest total cost for the period January to April of 2001, whilst the combination of lamivudine/zidovudine represented the active ingredient with the highest total cost for the periods May to August and September to December of 2001, and also for all three-four month periods of 2002 and 2004. Nelfinavir has the highest average cost for period January to April of 2001, ritonavir for period May to August of 2001, and saquinavir mesylate for period September to December of 2001. Nelfinavir has the highest average cost for all three-four month periods of 2002, while didanosine has the highest average cost for all three four-month periods of 2004. / Thesis (M.Pharm. (Pharmacy Practice))--North-West University, Potchefstroom Campus, 2006

Four essays, or chapters, model the capital structure, governance, and investment decisions as part of a sequential game. Each chapter is separate in its context, assumptions, and conclusions. The titles of the chapters are below. Abstracts of each essay or chapter can be found at the beginning of each chapter. The titles of the chapters or essays are as follows: I. Managerial Ownership with Rent-Seeking Employees, II. Financing Professional Partnerships, III. Sunk Cost Efficiency with Identical Competitors, and IV. Business Stealing and Bankruptcy. With the exception of Chapter III, which is meant to complement Chapter IV, these essays argue that the structure of financial contracts can affect the real behavior of firms. The first chapter argues that financial governance policies affect the behavior of rank-and-file employees. In Chapter II, the governance and capital structure of professional service firms affects clients’ expectations of the firm’s quality. In Chapter IV, the enforcement of financial contracts by bankruptcy courts affects the number of firms that enter and exit the industry.

Ce mémoire analyse les trajectoires de sortie de communautés juives ultraorthodoxes. Plus précisément, il cherche à mettre en lumière le processus par lequel certains juifs hassidiques parviennent à s’affranchir de leur communauté d’origine. Dans une recherche alliant entrevues, notes de terrain et observation,notre étude montre comment malgré la présence d’un fort contrôle social au sein de ces communautés ultra-religieuses certains de leurs membres le déjouent. Ce mémoire vise à repérer et à analyser les stratégies d’adaptation et les ruses mises en place par les hassidim pour échapper au contrôle et ainsi enclencher le processus de sortie. À la lumière de la théorie goffmanienne nous montrons comment dans un environnement contrôlant,les individus réussissent à s’aménager des marges de manoeuvre. C’est en se créant des espaces de liberté durant le processus de sortie qu’ils parviennent à avoir les coudées franches pour s’en affranchir définitivement. / This master’s thesis analyses the paths taken by individuals who exit ultraorthodox Jewish communities. More precisely, it illuminates the process by which certain Hasidim take it upon themselves to leave behind the lifestyle and the community in which they were born and raised. My research primarily uses interviews and field notes to show how certain individuals manage to exit such ultra-religious communities despite the presence of strong social controls to prevent leaving. This study examines adjustment strategies and ruses used by Hasidim to avoid religious control and prompt their departure process. Drawing from Goffman’s theory, I will show how in a controlled environment individuals are still able to succeed in creating some marges de manoeuvre. These particular spaces of liberty shaped by each individual allow for the ultimate success of completely leaving the community.

Precise regulation of cell cycle events by the Cdk-control network is essential for cell proliferation and the perpetuation of life. The unidirectionality of cell cycle progression is governed by several critical irreversible transitions: the G1-to-S transition, the G2-to-M transition, and the M-to-G1 transition. Recent experimental and theoretical evidence has pulled into question the consensus view that irreversible protein degradation causes the irreversibility of those transitions. A new view has started to emerge, which explains the irreversibility of cell cycle transitions as a consequence of systems-level feedback rather than of proteolysis. This thesis applies mathematical modelling approaches to test this proposal for the Mto- G1 transition, which consists of two consecutive irreversible substeps: the metaphase-to-anaphase transition, and mitotic exit. The main objectives of the present work were: (i) to develop deterministic models to identify the essential molecular feedback loops and to examine their roles in the irreversibility of the M-to-G1 transition; (ii) to present a straightforward and reliable workflow to translate deterministic models of reaction networks into stochastic models; (iii) to explore the effects of noise on the cell cycle transitions using stochastic models, and to compare the deterministic and the stochastic approaches. In the first part of this thesis, I constructed a simplified deterministic model of the metaphase-to-anaphase transition, which is mainly regulated by the spindle assembly checkpoint (the SAC). Based on the essential feedback loops causing the bistability of the transition, this deterministic model provides explanations for three open questions regarding the SAC: Why is the SAC not reactivated when the kinetochore tension decreases to zero at anaphase onset? How can a single unattached kinetochore keep the SAC active? How is the synchronized and abrupt destruction of cohesin triggered? This deterministic model was then translated into a stochastic model of the SAC by treating the kinetochore microtubule attachment at prometaphase as a noisy process. The stochastic model was analyzed and simulation results were compared to the experimental data, with the aim of explaining the mitotic timing regulation by the SAC. Our model works remarkably well in qualitatively explaining experimental key findings and also makes testable predictions for different cell lines with very different number of chromosomes. The noise generated from the chemical interactions was found to only perturb the transit timing of the mitotic events, but not their ultimate outcomes: all cells eventually undergo anaphase, however, the time required to satisfy the SAC differs between cells due to stochastic effects. In the second part of the thesis, stochastic models of mitotic exit were created for two model organisms, budding yeast and mammalian cells. I analyzed the role of noise in mitotic exit at both the single-cell and the population level. Stochastic time series simulations of the models are able to explain the phenomenon of reversible mitotic exit, which is observed under specific experimental conditions in both model organisms. In spite of the fact that the detailed molecular networks of mitotic exit are very different in budding yeast and mammalian cells, their dynamic properties are similar. Importantly, bistability of the transitions is successfully captured also in the stochastic models. This work strongly supports the hypothesis that uni-directional cell cycle progression is a consequence of systems-level feedback in the cell cycle control system. Systems-level feedback creates alternative steady states, which allows cells to accomplish irreversible transitions, such as the M-to-G1 transition studied here. We demonstrate that stochastic models can serve as powerful tools to capture and study the heterogeneity of dynamical features among individual cells. In this way, stochastic simulations not only complement the deterministic approach, but also help to obtain a better understanding of mechanistic aspects. We argue that the effects of noise and the potential needs for stochastic simulations should not be overlooked in studying dynamic features of biological systems.

Dans cette thèse, nous étudions le comportement asymptotique précis à basse température de l’événement de sortie d'un domaine métastable $Omegasubset mathbb R^d$ (point de sortie et temps de sortie) pour le processus de Langevin sur amorti. En pratique, le processus de Langevin sur amorti peut par exemple simuler l'évolution des positions des atomes d'une molécule ou la diffusion d'impuretés interstitielles dans un cristal. Nos résultats principaux concernent le comportement asymptotique précis de la distribution de la loi du point de sortie de $Omega$. Dans la limite d'une petite température, ces résultats permettent de justifier l'utilisation de la formule d'Eyring-Kramers pour modéliser les événements de sortie de $Omega$. La loi d'Eyring-Kramers est par exemple utilisée pour calculer les taux de transition entre les états d'un système dans un algorithme de Monte-Carlo cinétique afin de simuler efficacement les différents états visités par le système. L'analyse repose de manière essentielle sur la distribution quasi stationnaire associée au processus de Langevin sur amorti dans $Omega$. Nos preuves utilisent des outils d'analyse semi-classique. La thèse se décompose en trois chapitres indépendants. Le premier chapitre (rédigé en français) est une introduction aux résultats obtenus. Les deux autres chapitres (rédigées en anglais) sont consacrés aux énoncés mathématiques / This thesis is dedicated to the study of the sharp asymptotic behaviour in the low temperature regime of the exit event from a metastable domain $Omegasubset mathbb R^d$ (exit point and exit time) for the overdamped Langevin process. In practice, the overdamped Langevin dynamics can be used to describe for example the motion of the atoms of a molecule or the diffusion of interstitial impurities in a crystal. The obtention of sharp asymptotic approximations of the first exit point density in the small temperature regime is the main result of this thesis. These results justify the use of the Eyring-Kramers law to model the exit event. The Eyring-Kramers law is used for example to compute the transition rates between the states of a system in a kinetic Monte-Carlo algorithm in order to sample efficiently the state-to-state dynamics. The cornerstone of our analysis is the quasi stationary distribution associated with the overdamped Langevin dynamics in $Omega$. The proofs are based on tools from semi-classical analysis. This thesis is divided into three independent chapters. The first chapter (in French) is dedicated to an introduction to the mathematical results. The other two chapters (in English) are devoted to the precise statements and proofs

Diese Arbeit behandelt die Asymptotik von Austritts- und Übergangszeiten für gewisse schwach zeitinhomogene Diffusionsprozesse. Darauf basierend wird ein probabilistischer Begriff der stochastischen Resonanz (SR) studiert. Techniken der großen Abweichungen spielen eine zentrale Rolle. Im ersten Teil der Arbeit (Kapitel 1-3) werden Resultate aus der Theorie der großen Abweichungen für zeithomogene Diffusionen rekapituliert. Es werden die klassischen Resultate von Freidlin und Wentzell und Erweiterungen dieser Theorie präsentiert, und es wird an das Kramers''sche Austrittszeitengesetz erinnert. Teil II befasst sich mit dem Phänomen der SR, d.h. mit Periodizitätseigenschaften von Diffusionen. In Kapitel 4 werden physikalische Maße zur Messung der Periodizität diskutiert. Deren Nachteile legen es nahe, einem alternativen, probabilistischen Ansatz zu folgen, der hier behandelt wird. Das 5. Kapitel dient der Herleitung eines gleichmäßigen Prinzips der großen Abweichungen für Diffusionen mit schwach zeitabhängigem, periodischem Drift. Die Gleichmäßigkeit des Prinzips ermöglicht die exakte Bestimmung exponentieller Übergangsraten in Kapitel 6, das die zentralen Ergebnisse des 2. Teils beinhaltet. Hierdurch wird die Maximierung gewisser Übergangswahrscheinlichkeiten ermöglicht, was zum in Kapitel 7 studierten Resonanzbegriff führt. Teil III der Arbeit setzt sich mit der Asymptotik von Austrittszeiten sogenannter selbststabilisierender Diffusionen auseinander. In Kapitel 8 wird der Zusammenhang zwischen interagierenden Teilchensystemen und selbststabilisierenden Diffusionen erläutert und die Existenz- und Eindeutigkeitsfrage behandelt. Das 9. Kapitel dient dem Studium der großen Abweichungen dieser Klasse von Diffusionen. In Kapitel 10 wird das Kramers''sche Austrittszeitengesetz auf selbststabilisierende Diffusionen übertragen, und in Kapitel 11 wird der Einfluß der selbststabilisierenden Komponente auf das Austrittszeitengesetz illustriert. / In this thesis, we study the asymptotic behavior of exit and transition times of certain weakly time inhomogeneous diffusion processes. Based on these asymptotics, a probabilistic notion of stochastic resonance (SR) is investigated. Large deviations techniques play the key role throughout this work. In the first part (Chapters 1-3) we recall the large deviations theory for time homogeneous diffusions. We present the classical results due to Freidlin and Wentzell and extensions thereof, and we remind of Kramers'' exit time law. Part II deals with the phenomenon of stochastic resonance. That is, we study periodicity properties of diffusion processes. In Chapter 4 we explain the paradigm of stochastic resonance and discuss physical notions of measuring periodicity of diffusions. Their drawbacks suggest to follow an alternative probabilistic approach, which is treated in this work. In Chapter 5 we derive a large deviations principle for diffusions subject to a weakly time dependent periodic drift term. The uniformity of the obtained large deviations bounds w.r.t. the system''s parameters plays a key role for the treatment of transition time asymptotics in Chapter 6, which contains the main result of the second part. The exact exponential transition rates obtained here allow for maximizing transition probabilities, which finally leads to the announced probabilistic notion of resonance studied in Chapter 7. In the third part we investigate the exit time asymptotics of a certain class of so-called self-stabilizing diffusions. In Chapter 8 we explain the connection between interacting particle systems and self-stabilizing diffusions, and we address the question of existence. The following Chapter 9 is devoted to the study of the large deviations behavior of these diffusions. In Chapter 10 Kramers'' exit law is carried over to our class of self-stabilizing diffusions. Finally, the influence of self-stabilization is illustrated in Chapter 11.

Uma parcela significativa dos acidentes de trânsito nas rodovias ocorre devido à saída de veículos da pista, o que pode resultar em choques com obstáculos fixos, quedas em espaços vazios, tombamento, capotagem, etc. Esse tipo de acidente é, em geral, grave, em razão das altas velocidades desenvolvidas nas rodovias. Cerca de 1/3 dos acidentes rodoviários com vítimas fatais nos Estados Unidos resultam de saída de pista. No Brasil, estima-se que 30% dos acidentes rodoviários estão relacionados com saída da pista, sendo esse valor da ordem de 25% nos casos dos acidentes com vítimas fatais. Neste trabalho é apresentado o Modelo QRSP (formado pelas letras iniciais das palavras: Quantificação - Risco - Saída - Pista) em rodovias. O modelo permite quantificar o nível de proteção existente em cada segmento particular da rodovia (análise microscópica) e, a partir dessa informação, quantificar o nível de proteção considerando trechos longos (análise macroscópica). No modelo desenvolvido, a avaliação é feita considerando separadamente os dois lados da pista (direito e esquerdo), podendo os resultados serem compostos no caso da quantificação de trechos longos. O modelo foi desenvolvido para o caso de rodovias de múltiplas faixas por sentido (denominadas comumente de pista dupla), podendo, no entanto, também ser empregado no caso das rodovias de duas faixas e duplo sentido (rodovias de pista simples). O modelo QRSP permite determinar parâmetros não fornecidos pelos métodos ABNT (2007) - norma brasileira - e AASHTO (2002) - norma americana, proporcionando, dessa forma, uma melhor quantificação do risco na saída de veículos da pista. A análise dos resultados fornecidos pelo modelo QRSP mostra que o mesmo representa a realidade de maneira satisfatória. As informações quantitativas fornecidas pelo modelo são de grande utilidade na elaboração de projetos de melhoria das características das laterais de rodovias existentes, bem como na preparação de projetos de novas rodovias. / A significant portion of road traffic accidents on highways occurs because of the exit of vehicles from the runway, which may result in collisions with fixed obstacles, falls in empty spaces, overturning, roll over, etc. This kind of accident is in general quite severe, due to the high speeds on highways. Approximately one third of road accidents with fatalities in the United States result from the runway exit. In Brazil, it is estimated that 30% of road accidents are also related to the runway exit, bringing this value at 25% in the cases of accidents with fatal victims. The QRRE that stands for Quantification the Risk in the Runway Exit of vehicles on highways is presented in this research. The model allows to quantify the level of protection in each particular segment of the highway (microscopic analysis) and from this information, it permits to quantify the level of protection considering long segments (macroscopic analysis). In the developed model, the assessment is done considering separately the left and right sides of the runway, and the results can be compounded in the case of long segments quantification. The model was developed for the case of multilanes highways in each direction, however, this model can also be used in the case of two lanes highways with two-ways direction. The QRRE model allows to determine parameters that are not provided by the methods ABNT (2007) - Brazilian standard, - and AASHTO (2002) - American standard, which provides a better measurement of risk in the exit of vehicles from the runway. The results obtained by QRRE model show that it clearly represents the reality. The quantitative information provided by the model are useful for the development of projects in order to improve the characteristics of the roadside highways available, and the development of projects for new highways.

Les p21-activated kinases (PAK) du sous-groupe I sont impliquées dans de nombreux processus cellulaires tels la prolifération, les mouvements cellulaires, l’adhérence et l’apoptose. Ces kinases sont des effecteurs des Rho-GTPases Rac1 et Cdc42 et participent à la régulation du cytosquelette d’actine. Les deux kinases neuronales PAK1 et PAK3, qui présentent de fortes identités de séquence, régulent le cytosquelette d’actine, contrôlant ainsi la dynamique des épines dendritiques, et la plasticité synaptique.Les mutations du gène pak3, localisé sur le chromosome X, sont responsables de déficience intellectuelle chez l’homme, et les mécanismes moléculaires et cellulaires associés aux défauts cognitifs sont mal connus. Il a été montré que PAK3 participe à la voie proneurale au cours de l’embryogénèse précoce du xénope en favorisant la sortie du cycle cellulaire et la différenciation neuronale. Cependant, le rôle de PAK3 dans la neurogenèse adulte n’a pas été étudié. Or depuis maintenant une quinzaine d’années, il est admis que la neurogenèse perdure à l’âge adulte et participe aux processus de mémorisation et d’apprentissage. Nous nous sommes donc intéressés à l’implication de PAK3 dans la régulation de la neurogenèse adulte, posant l’hypothèse qu’un défaut de neurogenèse serait responsable, au moins en partie, des défauts cognitifs chez les patients. Nous avons montré que PAK3 n’est pas exprimée dans les cellules souches neurales/progéniteurs prolifératifs mais son expression augmente fortement dès le retrait des facteurs de croissance, ex vivo, suggérant un rôle dans la neurogenèse adulte. Nous avons montré que l’invalidation de pak3 provoque une augmentation de la fréquence de neurosphères primaires formées ainsi qu’un accroissement de leur taille, ceci sans affecter la taille du réservoir de cellules souches ni les propriétés cardinales de celles-ci (multipotence, auto-renouvellement et prolifération). Toutefois, les cellules progénitrices pak3- poursuivent leur prolifération dans des conditions de culture induisant normalement la différenciation, suggérant un défaut de sortie du cycle cellulaire.Nous nous sommes ensuite demandé si les mutations de déficience intellectuelle du gène pak3 altèrent la neurogenèse adulte. Nous avons créé pour cela un modèle murin portant la mutation R67C, responsable chez l’homme de la forme la plus sévère de déficience intellectuelle associée aux mutations de ce gène. Nous mettons en évidence, dans cette souris knock-in, une forte diminution du nombre de cellules nouveau-nées dans les deux zones neurogéniques du cerveau (la zone sous-ventriculaire et le gyrus denté de l’hippocampe) et une augmentation de la proportion de neurones nouveau-nés immatures. Ces données suggèrent que la mutation R67C n’induit pas une perte de fonction de la kinase mais un changement de fonction dépendante d’une activation préférentielle par la GTPase Rac1.En conclusion, ce travail de thèse montre que PAK3 participe à la régulation de la neurogenèse adulte chez les mammifères, contrôle la sortie du cycle cellulaire des progéniteurs neuraux et que la mutation R67C impacte la maturation des neurones nouveau-nés. L’ensemble de ces données suggère que les défauts de neurogenèse adulte dus aux mutations de déficience intellectuelle du gène pak3 sont à l’origine de certains dysfonctionnements cognitifs. / The group I p21-activated kinases (PAK) are involved in many cellular processes such as proliferation, cell movement, adhesion and apoptosis. These kinases are effectors of Rho GTPases Rac1 and Cdc42, and participate in the regulation of the actin cytoskeleton. Both neuronal kinase PAK1 and PAK3, which exhibit high sequence identities, regulate the actin cytoskeleton, thereby controlling the dynamics of dendritic spines and synaptic plasticity. Mutations of the X-linked pak3 are responsible for intellectual disability (ID) in humans, and the molecular and cellular mechanisms associated with cognitive defects are poorly described. It was shown that PAK3 participates in the proneural pathway during early Xenopus embryogenic development, by promoting cell cycle exit and neuronal differentiation of neural precursors. However, the role of PAK3 in the adult neurogenesis has not been studied in mammals. It is now generally accepted that neurogenesis persists during human adulthood and is involved in learning and memory. We are therefore interested in the involvement of PAK3 in the regulation of adult neurogenesis, on the assumption that defects in neurogenesis may be responsible, at least in part, for cognitive defects in ID patients.We showed that PAK3 is not expressed in proliferative neural stem/progenitor cells but its expression increased significantly upon growth factor removal, suggesting a role in adult neurogenesis. We showed that the invalidation of pak3 gene causes an increase in the frequency and in size of primary neurospheres. However Pak3 invalidation does not affect the size of the stem cell reservoir nor the NCS cardinal properties (pluripotency, self-renewal and proliferation). However, the pak3- progenitor cells continue their proliferation in culture conditions normally inducing differentiation, suggesting a defect in cell cycle exit. We then asked whether pak3 ID mutations affect adult neurogenesis. We created a knock-in model expressing the pak3-R67C mutation responsible in humans for a severe form of intellectual impairment. We observed in the knock-in mice, a significant decrease in the number of newborn cells in both neurogenic areas of the brain (the subventricular zone inforebrain, and the dentate gyrus of the hippocampus) and an increase in the proportion of immature newborn neurons. These data suggest that the R67C mutation does not induce a loss of function of the kinase but a change of a function dependent on preferential activation by the Rac1 GTPase.In conclusion, we show that PAK3 play an important role in the regulation of adult neurogenesis in mammals by controlling the cell cycle exit of neural progenitors. The R67C ID mutation impacts both newborn cell proliferation and their maturation. Taken together, these data suggest that defects in adult neurogenesis caused by ID mutations in the pak3 gene may be involved in some cognitive dysfunctions.