Idősorok analízise és sztochasztikus fraktál modellek tanulmányozása alkalmazásokkal = Time series analysis and fractal models with applications

Frakcionális Ornstein-Uhlenbeck lepedő tulajdonságait vizsgáltuk abból a szempontból, hogy olyan modellt konstruáljunk, aminek spektruma az origó környezetében nem izotróp módon viselkedik. A Lévy-Flight-ok (közel stabilis Lévy-folyamtok) fontos szerepet játszanak a nem Gauss jelenségek vizsgálatában. Egzakt eredményeket bizonyítottunk a Lévy-Flight-ok aszimptotikus egész és tört rendű momentumaira, ezzel összefüggésben sikerült kimutatni ezek multi-fraktál tulajdonságát. A nemlineáris vektor értékű regresszió problémájával foglalkoztunk, amikor a megfigyelések hibája stacionárius eloszlású. Egzakt formulát adtunk meg a paraméter becslések aszimptotikus szórásmátrixára, és alkalmaztuk eredményünket valódi adatokra is. A magfüggvényes sűrűségfüggvény becslés aszimptotikus normalitását bizonyítottuk úgy, hogy a mezőt egyre nagyobb tartományon figyeljük meg, de közben megfigyelési helyeket is sűrítjük. Kiderül, hogy az aszimptotikus kovariancia függ a sávszélesség és az osztópontok távolságának arányától. | The Fractional Ornstein-Uhlenbeck sheet is investigated, non-isotropic stationary model is constructed and applied for real data. We showed that Lévy-Flights are fractals and proved asymptotical formulae for moments and cumulants.with integer and fractal order. Functional limit theorems are proved for a sequence of Galton-Watson processes with immigration, where the offspring mean tends to its critical value 1 under weak conditions for the variances of offspring and immigration processes. Int he limit theorems the norming factors depend on these variances. We proved the asymptotic normality of the kernel density estimates in 2D. The asymptotic covariance is shown to be dependent of the ratio of the window size and distance between point on the lattice. The nonlinear multiple regression with stationary errors is investigated. A clear formula is given for the asymptotic variance of the parameter estimator and it is applied for the identification of fitting models to real data

Diffusion and Supercritical Spreading Processes on Complex Networks

Die große Menge an Datensätzen, die in den letzten Jahren verfügbar wurden, hat es ermöglicht, sowohl menschlich-getriebene als auch biologische komplexe Systeme in einem beispiellosen Ausmaß empirisch zu untersuchen. Parallel dazu ist die Vorhersage und Kontrolle epidemischer Ausbrüche für Fragen der öffentlichen Gesundheit sehr wichtig geworden. In dieser Arbeit untersuchen wir einige wichtige Aspekte von Diffusionsphänomenen und Ausbreitungsprozeßen auf Netzwerken. Wir untersuchen drei verschiedene Probleme im Zusammenhang mit Ausbreitungsprozeßen im überkritischen Regime. Zunächst untersuchen wir die Reaktionsdiffusion auf Ensembles zufälliger Netzwerke, die durch die beobachteten Levy-Flugeigenschaften der menschlichen Mobilität charakterisiert sind. Das zweite Problem ist die Schätzung der Ankunftszeiten globaler Pandemien. Zu diesem Zweck leiten wir geeignete verborgene Geometrien netzgetriebener Streuprozeße, unter Nutzung der Random-Walk-Theorie, her und identifizieren diese. Durch die Definition von effective distances wird das Problem komplexer raumzeitlicher Muster auf einfache, homogene Wellenausbreitungsmuster reduziert. Drittens führen wir durch die Einbettung von Knoten in den verborgenen Raum, der durch effective distances im Netzwerk definiert ist, eine neuartige Netzwerkzentralität ein, die ViralRank genannt wird und quantifiziert, wie nahe ein Knoten, im Durchschnitt, den anderen Knoten im Netzwerk ist. Diese drei Studien bilden einen einheitlichen Rahmen zur Charakterisierung von Diffusions- und Ausbreitungsprozeßen, die sich auf komplexen Netzwerken allgemein abzeichnen, und bieten neue Ansätze für herausfordernde theoretische Probleme, die für die Bewertung künftiger Modelle verwendet werden können.The large amount of datasets that became available in recent years has made it possible to empirically study humanly-driven, as well as biological complex systems to an unprecedented extent. In parallel, the prediction and control of epidemic outbreaks have become very important for public health issues. In this thesis, we investigate some important aspects of diffusion phenomena and spreading processes unfolding on networks. We study three different problems related to spreading processes in the supercritical regime. First, we study reaction-diffusion on ensembles of random networks characterized by the observed Levy-flight properties of human mobility. The second problem is the estimation of the arrival times of global pandemics. To this end, we derive and identify suitable hidden geometries of network-driven spreading processes, leveraging on random-walk theory. Through the definition of network effective distances, the problem of complex spatiotemporal patterns is reduced to simple, homogeneous wave propagation patterns. Third, by embedding nodes in the hidden space defined by network effective distances, we introduce a novel network centrality, called ViralRank, which quantifies how close a node is, on average, to the other nodes. These three studies constitute a unified framework to characterize diffusion and spreading processes unfolding on complex networks in very general settings, and provide new approaches to challenging theoretical problems that can be used to benchmark future models

Greenhouse gas benefits of fighting obesity

Obesity has become a serious public health problem in both industrialized and rapidly industrializing countries. It increases greenhouse gas emissions through higher fuel needs for transportation of heavier people, lifecycle emissions from additional food production and methane emissions from higher amounts of organic waste. A reduction of average weight by 5 kg could reduce OECD transport CO2 emissions by more than 10 million t, while a reduction of consumption of energy-rich food to 1990 levels would lead to life-cycle emissions savings of more than 100 million t CO2 equivalent and by more than 2 million t through reduction of associated food waste. Due to the intimate behavioural nature of the obesity problem, policies to reduce obesity such as food taxation, subsidization of human-powered transport, incentives to reduce sedentary leisure and regulation of fat in foodstuffs have not yet been implemented to any extent. The emissions benefits of fiscal and regulatory measures to reduce obesity could accelerate the tipping point where a majority of voters feels that the problem warrants policy action. --public health,food production,transport,waste management,greenhouse gas emissions

Desarrollo y evaluación de modelos marginales y de evolución temporal para el tráfico agregado de redes IP

En las redes de comunicaciones actuales existe una gran discrepancia entre las características del tráfico observadas y las predichas por los modelos de tráfico clásicos como el de Poisson, históricamente utilizados. En concreto, se observa un cierto grado de impulsividad tanto en la tasa binaria como en la cantidad de paquetes recibidos por unidad de tiempo, así como ciertas características de autosimilitud en el tráfico de red que estos modelos no son capaces de reflejar. Ante estas evidencias, en los últimos años han surgido multitud de propuestas de modelos de tráfico de red más avanzados que los tradicionales, aunque aún no existe consenso acerca de la superioridad de alguno de ellos. En este Trabajo Fin de Máster se desarrolla y evalúa la validez de un modelo de tráfico basado Vuelos de Lévy Truncados Suavemente (STLF) para el tráfico agregado en redes IP.Teoría de la Señal y Comunicaciones e Ingeniería TelemáticaMáster en Investigación en Tecnologías de la Información y las Comunicacione

From standards and regulations to executable rules: A case study in the Building Accessibility domain

Regulatory compliance check in the building industry is a complex task that involves cross-domain national and international standards and regulations. This paper introduces a refined approach to extract SWRL rules from building accessibility regulatory texts and then to transform them into executable rules for semi-automatic compliance checking of Building Information Models. The domain ontology model is a key input to the approach and is enriched by new knowledge extracted from the regulatory text. This semantic technology enhanced rule extraction approach standardized the rule extraction process by covering the whole lifecycle from regulatory text to executable rules. It is based on the open standards and applies open source tools and thereby portable and extendable. It conforms to the open BIM principle to support knowledge sharing cross domains and disciplines. The approach is also adaptable to other types of regulatory rules in the building industry.publishedVersio

Mandelbrot's stochastic time series models

I survey and illustrate the main time series models that Mandelbrot introduced into time series analysis in the 1960s and 1970s. I focus particularly on the members of the additive fractional stable family including Lévy flights and fractional Brownian motion (fBm), noting some of the less well‐known aspects of this family, such as the cases when the self‐similarity exponent H and the Hurst exponent J differ. I briefly discuss the role of multiplicative models in modeling the physics of cascades. I then recount the still little‐known story of Mandelbrot's work on fractional renewal models in the late 1960s, explaining how these differ from their more familiar fBm counterpart and form a “missing link” between fBm and the problem of random change points. I conclude by highlighting the frontier problem of damped fractional models

An Enhanced Cuckoo Search for Optimization of Bloom Filter in Spam Filtering

Bloom Filter BF is a simple but powerful data structure that can check membership to a static set The tradeoff to use Bloom filter is a certain configurable risk of false positives The odds of a false positive can be made very low if the hash bitmap is sufficiently large Spam is an irrelevant or inappropriate message sent on the internet to a large number of newsgroups or users A spam word is a list of well-known words that often appear in spam mails The proposed system of Bin Bloom Filter BBF groups the words into number of bins with different false positive rates based on the weights of the spam words An Enhanced Cuckoo Search ECS algorithm is employed to minimize the total membership invalidation cost of the BFs by finding the optimal false positive rates and number of elements stored in every bin The experimental results have demonstrated for CS and ECS for various numbers of bin