This thesis evaluates the viability of a data cube as a basis for visualization of unbounded data. A cube designed for use with visualization of static data was adapted to allow for point-by-point insertions. The new cube was evaluated by measuring the time it took to insert different numbers of data points. The results indicate that the cube can keep up with data streams with a velocity of up to approximately 100 000 data points per second. The conclusion is that the cube is useful if the velocity of the data stream is within this bound, and if the granularity of the represented dimensions is sufficiently low. / Det här exjobbet utvärderar dugligheten av en datakub som bas för visualisering av obegränsad data. En kub designad för användning till visualisering av statisk data anpassades till att medge insättning punkt för punkt. Den nya kuben evaluerades genom att mäta tiden det tog att sätta in olika antal datapunkter. Resultaten indikerade att kuben kan hantera dataströmmar med en hastighet på upp till 100 000 punkter per sekund. Slutsatsen är att kuben är användbar om hastigheten av dataströmmen är inom denna gräns, och om grovheten av de representerade dimensionerna är tillräckligt hög.

Nous nous intéressons dans ce mémoire à des équations d'évolution associées aux fonctionnelles de Ginzburg-Landau, de nature parabolique. Notre but est de décrire le comportement temporel de la limite des solutions quand un petit paramètre de pénalisation tend vers 0.Dans le premier chapitre, nous retraçons de manière synthétique l'étude remarquable due à Bethuel, Orlandi et Smets sur l'équation de Ginzburg-Landau parabolique en dimension 2 : l'évolution des points vortex est gouvernée par le flot gradient de la fonctionnelle de Kirchoff-Onsager modifié par un terme de drift; elle est régulière hors des temps de collision ou de séparation de vortex ;ces phénomènes sont soumis à la conservation du degré local et à la dissipation d'énergie.Dans le second chapitre, nous considérons le problème de Cauchy pour des systèmes d'équations paraboliques semi-linéaires. Motivés par l'exemple des vortex, nous construisons, pour des nonlinéarités défocalisantes, des solutions globales de l'équation intégrale associée ayant des données initiales non bornées en espace (croissant comme exp(x^2)). Dans le cas de nonlinéarités focalisantes, nous montrons un phénomène d'explosion instantanée.Dans le troisième chapitre, nous revenons à l'équation de Ginzburg-Landau parabolique en dimension quelconque. Nous remplaçons la borne sur l'énergie de Bethuel, Orlandi et Smets, par une borne locale en espace, qui permet de traiter des configurations générales de vortex sans avoir recours aux « vortex évanescents ». Nous étendons leur analyse, et montrons des résultats de décomposition de l'énergie renormalisée, et du mouvement par courbure moyenne de la mesure d'énergie concentrée. / We are interested in this thesis in evolution equations related to the Ginzburg-Landau functionals, of parabolic nature. Our goal is to describe the temporal behavior of limiting solutions as a small penalisation parameter tends to 0.In the first chapter, we retrace in a synthetic way the remarkable study by Bethuel, Orlandi and Smets on the parabolic Ginzburg-Landau equation in dimension 2 : the evolution of point vortices is governed by the gradient flow of the Kirchoff-Onsager functionnal modified by a drift term ; it is smooth away from the merging and splitting times ; these phenomenon are subject to conservation of the local degree and energy dissipation.In the second chapter, we consider the Cauchy problem for systems of semi-linear parabolic equations. Motivated by the example of the vortices, we construct, for defocusing nonlinearities, global solutions to the associated integral equation with intial data unbounded in space (allowed to grow like exp(x^2)). In the case of focusing nonlinearities, we show a phenomenon of instantaneous blow-up.In the third chapter, we go back to the parabolic Ginzburg-Landau equation. We replace the energy bound of Bethuel, Orlandi et Smets by a local-in-space bound on the energy. This allows to consider general configurations of vortices without the help of « vanishing vortices ». We extend their analysis, and show various results of decomposition of the renormalized energy, and that the concentrated energy moves according to the mean curvature flow.

Accelerated advancements in technology, the Internet of Things, and cloud computing have spurred an emergence of unstructured data that is contributing to rapid growth in data volumes. No human can manage to keep up with monitoring and analyzing these unbounded data streams and thus predictive and analytic tools are needed. By leveraging machine learning this data can be converted into insights which are enabling datadriven decisions that can drastically accelerate innovation, improve user experience, and drive operational efficiency. The purpose of this thesis is to design and implement a system for real-time outlier detection using unbounded data streams and machine learning. Traditionally, this is accomplished by using alarm-thresholds on important system metrics. Yet, a static threshold cannot account for changes in trends and seasonality, changes in the system, or an increased system load. Thus, the intention is to leverage machine learning to instead look for deviations in the behavior of the data not caused by natural changes but by malfunctions. The use-case driving the thesis forward is real-time outlier detection in a Content Delivery Network (CDN). The input data includes Http-error messages received by clients, and contextual information like region, cache domains, and error codes, to provide tailormade predictions accounting for the trends in the data. The outlier detection system consists of a data collection pipeline leveraging the technique of stream processing, a MiniBatchKMeans clustering model that provides online clustering of incoming data according to their similar characteristics, and an LSTM AutoEncoder that accounts for temporal nature of the data and detects outlier data points in the clusters. An important finding is that an outlier is defined as an abnormal amount of outlier data points all originating from the same cluster, not a single outlier data point. Thus, the alerting system will be implementing an outlier percentage threshold. The experimental results show that an outlier is detected within one minute from a cache break-down. This triggers an alert to the system owners, containing graphs of the clustered data to narrow down the search area of the cause to enable preventive action towards the prominent incident. Further results show that within 2 minutes from fixing the cause the system will provide feedback that the actions taken were successful. Considering the real-time requirements of the CDN environment, it is concluded that the short delay for detection is indeed real-time. Proving that machine learning is indeed able to detect outliers in unbounded data streams in a real-time manner. Further analysis shows that the system is more accurate during peakhours when more data is in circulation than during none peak-hours, despite the temporal LSTM layers. Presumably, an effect from the model needing to train on more data to better account for seasonality and trends. Future work necessary to put the outlier detection system in production thus includes more training to improve accuracy and correctness. Furthermore, one could consider implementing necessary functionality for a production environment and possibly adding enhancing features that can automatically avert incidents detected and handle the causes of them.