We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a (sub-)linear function of the indegree of the older vertex at that time. We provide a limit theorem with rates of convergence for the distribution of a vertex, chosen uniformly at random, as the number of vertices tends to infinity. To do so, we develop Stein's method for a new class of limting distributions including power-laws. Similar, but slightly weaker results are shown to be deducible using coupling techniques. Concentrating on a specific preferential attachment model we also show that the outdegree distribution asymptotically follows a Poisson law. In addition, we deduce a central limit theorem for the number of isolated vertices. We thereto construct a size-bias coupling which in combination with Stein’s method also yields bounds on the distributional distance.

A partir de l’hémodialyse, nous étudierons certains problèmes plus généralement liés à la maladie chronique mais aussi la fin de vie pour mettre en tension trois dualités : l’exactitude et la vérité, les morales déontologiques et téléologiques, et la logique d’équivalence et de surabondance. Dans la maladie chronique, nous nous intéresserons aux cas où il existe une contradiction entre le devoir thérapeutique du médecin et la volonté de la personne malade. Nous montrerons que ces refus de soin en dialyse sont sous-tendus par une tension entre l’exactitude technique des traitements proposés et la vérité éthique et existentielle de la personne. Dans la fin de vie, nous nous poserons la question de savoir quand commence l’obstination déraisonnable, comment définir sa limite, et comment limiter ou arrêter la dialyse tout en étant certain de ne pas réaliser un homicide ? Nous montrerons également que les normes, les indicateurs et les protocoles prolifèrent pour participer à une standardisation des pratiques de plus en plus hégémonique, où plusieurs moteurs sont à l’œuvre, comme la rationalité néolibérale et la gestion du risque.  Ceci aboutit à un désenchantement des soignants. Un constat apparait : l’exactitude, la technique, les morales déontologiques rabattues sous forme de protocoles et la logique d’équivalence deviennent envahissantes. A l’inverse la vérité du sujet, l’éthique, la responsabilité de l'autre vulnérable, le don d’hospitalité tendent à être précarisés. La riposte à cette dérive pourrait être la réhabilitation de la singularité du sujet et la création de métaphore vive entre exactitude technique et la vérité éthique. Enfin, nous montrerons comment lorsqu’il existe un dilemme lié à une tension entre technique et éthique, la mise en place d’une réunion d’éthique nous a permis d’apporter la réponse la plus humaine possible et de favoriser le développement d’une culture d’équipe. / From hemodialysis, we will study certain problems more generally related to chronic disease but also to the end of life bring out the tension between three dualities: the accuracy and the truth, déontological and teleological ethics, and the logics of equivalence and superabundance. In chronic illness, we will be interested in cases where there is a contradiction between the medical duty of the physician and the will of the sick person. We will show that these refusals of care in dialysis are underpinned by a tension between the technical accuracy of the proposed treatments and the ethical and existential truth of the person. In the end of life, we will ask ourselves the question of when unreasonable obstinacy begins, how to define its limit, and how to limit or stop dialysis while being sure not to perform a homicide? We will also show that norms, standards, indicators and protocols proliferate to participate in a standardization of increasingly hegemonic practices, where several drivers are at work, such as neoliberal rationality and risk management. This leads to a disenchantment of caregivers. One observation emerges: the accuracy, the technique, the déontological ethics folded in the form of protocols and the logic of equivalence become invasive. Conversely, the truth of the subject, ethics, the responsibility of the other vulnerable, the gift of hospitality tend to be precarious. The response to this drift could be the rehabilitation of the singularity of the subject and the creation of a metaphor between technical accuracy and ethical truth. Finally, we will show how, when there is a dilemma linked to a tension between technique and ethics, the setting up of an ethics meeting allowed us to provide the most humane answer possible and to foster the development of a team culture.

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<div>In this thesis we study two different types of self-interacting random walks. First, we study excited random walk in a deterministic, identically-piled cookie environment under the constraint that the total drift contained in the cookies at each site is finite. We show that the walk is recurrent when this parameter is between -1 and 1 and transient when it is less than -1 or greater than 1. In the critical case, we show that the walk is recurrent under a mild assumption on the environment. We also construct an environment where the total drift per site is 1 but in which the walk is transient. This behavior was not present in previously-studied excited random walk models.</div><div><br></div><div>Second, we study the "have your cookie and eat it'' random walk proposed by Pinsky, who already proved criteria for determining when the walk is recurrent or transient and when it is ballistic. We establish limiting distributions for both the hitting times and position of the walk in the transient regime which, depending on the environment, can be either stable or Gaussian.</div>

In the production of biodiesel via the transesterification of vegetable oils, purification to international standards is challenging. A key measure of biodiesel quality is the level of free glycerol in the biodiesel. In order to remove glycerol from fatty acid methyl ester (FAME or biodiesel), a membrane separation setup was tested. The main objective of this thesis was to develop a membrane process for the separation of free glycerol dispersed in FAME after completion of the transesterification reaction and to investigate the effect of different factors on glycerol removal. These factors included membrane pore size, pressure, temperature, and methanol, soap and water content. First, a study of the effect of different materials present in the transesterification reaction, such as water, soap, and methanol, on the final free glycerol separation was performed using a modified polyacrylonitrile (PAN) membrane, with 100 kD (ultrafiltration) molecular weight cut off for all runs at 25°C. Results showed low concentrations of water had a considerable effect in removing glycerol from the FAME. The mechanism of separation of free glycerol from FAME was due to the removal of an ultrafine dispersed glycerol-rich phase present in the untreated (or raw) FAME. The size of the droplets and the free glycerol separation both increased with increasing water content of the FAME. Next, three types of polymeric membranes in the ultrafiltration range with different molecular weight cut off, were tested at three fixed operating pressures and three operating temperatures (0, 5 and 25oC) to remove the free glycerol from a biodiesel reactor effluent. The ASTM standard for free glycerol concentration was met for the experiments performed at 25°C. The results of this study indicate that glycerol could be separated from raw FAME to meet ASTM and EN standards at methanol feed concentrations of up to 3 mass%. The process was demonstrated to rely on the formation of a dynamic polar layer on the membrane surface. Ceramic membranes of different pore sizes (0.05 µm (ultrafiltration (UF) range) and 0.2 µm (microfiltration (MF) range)) were used to treat raw FAME directly using the membrane separation set up at temperatures of 0, 5 and 25°C. The results were encouraging for the 0.05 µm pore size membrane at the highest temperature (25°C). The effect of temperature on glycerol removal was evident from its relation with the concentration factor (CF). Higher temperatures promoted the achievement of the appropriate CF value sooner for faster separation. Membrane pore size was also found to affect separation performance. A subsequent study revealed the effect of different variables on the size of the glycerol droplets using dynamic light scattering (DLS). A key parameter in the use of membrane separation technology is the size of the glycerol droplets and the influence of other components such as water, methanol and soaps on that droplet size. The effect of water, methanol, soap and glycerol on the size of suspended glycerol droplets in FAME was studied using a 3-level Box-Behnken experimental design technique. Standard statistical analysis techniques revealed the significant effect of water and glycerol on increasing droplet size while methanol and soap served to reduce the droplet size. Finally, a study on the effect of trans-membrane pressure (TMP) at different water concentrations in the FAME phase on glycerol removal using UF (0.03 µm pore size, polyethersulfone (PES)) and MF (0.1 and 0.22 µm pore sizes, PES) membranes at 25, 40 and 60°C was performed. Results showed that running at 25°C for the two membrane types produced the best results for glycerol removal and exceeded the ASTM and EN standards. An enhancement of glycerol removal was found by adding small amounts of water up to the maximum solubility limit in biodiesel. An increase in temperature resulted in an increase in the solubility of water in the FAME and less effective glycerol removal. Application of cake filtration theory and a gel layer model showed that the gel layer on the membrane surface is not compressible and the specific cake resistance and gel layer concentration decrease with increasing temperature. An approximate value for the limiting (steady-state) flux was reported and it was found that the highest fluxes were obtained at the lowest initial water concentrations at fixed temperatures. In conclusion, dispersed glycerol can be successfully removed from raw FAME (untreated FAME) using a membrane separation system to meet the ASTM biodiesel fuel standards. The addition of water close to the solubility limit to the FAME mixture enables the formation of larger glycerol droplets and makes the separation of these droplets straightforward.

Large scale internet services are increasingly implemented as distributed systems to achieve availability, fault tolerance and scalability. To achieve fault tolerance, microservices need to employ different resilience mechanisms such as automatic retries, rate limiting, circuit breaking amongst others to make the services handle failures gracefully and cause minimum damage to the performance of the overall system. These features are provided by service proxies such as Envoy which is deployed as a sidecar (sidecar proxy is an application design pattern which abstracts certain features, such as inter-service communications, monitoring and security, away from the main architecture to ease the tracking and maintenance of the application as a whole), the service proxies are very new developments and are constantly evolving. Evaluating their presence in a system to see if they add latency to the system and understand the advantages provided is crucial in determining their fit in a large scale system.Using an experimental approach, the services are load tested with and without the sidecar proxies in different configurations to determine if the usage of Envoy added latency and if its advantages overshadow its disadvantages. The Envoy sidecar proxy adds latency to the system; however, the benefits it brings in terms of resilience, make the services perform better when there is a high number of failures in the system. / Storskaliga internettjänster implementeras alltmer som distribuerade system för att uppnå tillgänglighet, feltolerans och skalbarhet. För att uppnå feltolerans måste microservices använda olika typer av resiliens mekanismer som automatisk återförsök, hastighetsbegränsning, kretsbrytning bland annat som tillåter tjänsterna att hantera misslyckanden graciöst och orsaka minimala skador på prestandan hos det övergripande systemet. Dessa funktioner tillhandahålls av service proxies som Envoy. Dessa proxies används som sidovagn (sidvagnproxy är ett applikationsdesignmönster som abstraherar vissa funktioner, såsom kommunikation mellan kommunikationstjänster, övervakning och säkerhet, bort från huvudarkitekturen för att underlätta spårningen och underhåll av ansökan som helhet). Dessa tjänster är väldigt nya och utvecklas ständigt. Att utvärdera deras närvaro i ett system för att se om de lägger till latens för systemet och förstå fördelarna som tillhandahålls är avgörande för att bestämma hur väl de skulle passa i ett storskaligt system. Med hjälp av ett experimentellt tillvägagångssätt testas tjänsterna med och utan sidospårproxys i olika konfigurationer för att avgöra om användningen av Envoy lägger till latens och om dess fördelar överskuggar dess nackdelar. Envoy sidecar proxy ökar latensen i systemet; De fördelar som det ger med avseende på resiliens gör tjänsterna bättre när det finns ett stort antal misslyckanden i systemet.

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In this research study, a strategy was used for assigning stiffness values to various layers of the pavement system so that there are negligible tensile stresses in the subgrade and base layers. The stiffnesses of the aggregate base layers were assigned double the values of the corresponding subgrade materials. The layer thicknesses were designed to achieve surface deflection values within the acceptable limit. An innovative design procedure was developed for designing pavement sections covering various layer thicknesses, material and environmental variables. The designed sections were compared with the American Association of State Highway and Transportation Officials (AASHTO) procedure and the differences were critiqued. Porous asphalt layer was used as the surface course for all pavement sections. The calculations validated the general principle of pavement design, as the subgrade stiffness decreased the base thickness increased for the same surface course thickness and traffic. Structural design of 63 pavements sections was accomplished representing various temperature and materials including additives. Low Density Polyethylene, performance graded asphalt, different soils, aggregates, lime and cement were the component materials utilized in this research study. An explanation on the mechanics of the mixtures is given in the results and discussion section. / Civil Engineering