Threshold behaviour and final outcome of an epidemic on a random network with household structure

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.

The Cat Who Walks Through Years: Chris Claremont's X-Men as Kitty Pryde's bildungsroman

This dissertation examines the fictional character Kitty Pryde from the X-Men comic book series during the tenure of writer Chris Claremont. Claremont's work on the character primarily involves the years 1980-1990, though a return to writing the character in the 2000s is also discussed when relevant. The thesis question revolves around the definition of the bildungsroman genre and whether Claremont's narrative arc for Kitty Pryde's character fulfills that definition. Jerome Hamilton Buckley's 1974 book Season of Youth: The Bildungsroman from Dickens to Golding is used as the primary authority for the bildungsroman genre, and more specifically a list of nine criteria that Buckley deems particularly key to the definition of the genre. Each of the nine criteria is looked at in depth, demonstrating where and how they can be found in the narrative, if at all. However, because Buckley's perspective and criteria come from a time of less diversity, examination from a feminist and minority perspective is also added with ideas from Rita Felski and Stella Bolaki. Combining Buckley's initial list of nine criteria with more modern criticism, these ideas are then used to analyze Kitty Pryde's narrative arc and to determine whether it can be seen as a bildungsroman. The findings support reading Claremont's narrative arc of the Kitty Pryde character as a bildungsroman. Three of Buckley's nine key themes are identified as particularly prevalent in the narrative: the search for a vocation, ordeal by love, and the conflict of generations. Three more key themes are found to be less prevalent but still clearly present: the search for a working philosophy, the larger society, and alienation. Because Buckley's definition for the bildungsroman genre requires the presence of six of his nine key themes, the presence of the aforementioned six thus validate the reading of the narrative as a bildungsroman. The text also provides some suggestions for finding the three least applicable key themes within the narrative, but because their presence is not necessary to fulfill the definition of the bildungsroman, they are not rigorously examined. In addition to fulfilling Buckley's key themes, the paper also discusses the more modern minority-oriented views. It is shown how the narrative can be read in terms of a journey to diverge from norms, as per Felski's ideas of the unique qualities of the specifically female bildungsroman. As Kitty Pryde's narrative can be shown to conform to the bildungsroman ideas of both Buckley and Felski, the thesis question is thus answered positively: Chris Claremont's X-Men can indeed be read as Kitty Pryde's bildungsroman.

Testing the random walk hypothesis with variance ratio statistics

Mestrado em Finanças

Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

By Monte Carlo simulations, we study the character of the spinglass (SG) phase in dense disordered packings of magnetic nanoparticles (NPs). We focus on NPs which have large uniaxial anisotropies and can be well represented as Ising dipoles. Dipoles are placed on SC lattices and point along randomly oriented axes. From the behaviour of a SG correlation length we determine the transition temperature Tc between the paramagnetic and a SG phase. For temperatures well below Tc we find distributions of the SG overlap parameter q that are strongly sample-dependent and exhibit several spikes. We find that the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with the system sizes studied. We compare these results with the ones found previously for 3D site-diluted systems of parallel Ising dipoles and with the behaviour of the Sherrington-Kirkpatrick model.

Statistical properties of radiation of multiwavelength random DFB fiber laser

In the presented paper, the temporal and statistical properties of a Lyot filter based multiwavelength random DFB fiber laser with a wide flat spectrum, consisting of individual lines, were investigated. It was shown that separate spectral lines forming the laser spectrum have mostly Gaussian statistics and so represent stochastic radiation, but at the same time the entire radiation is not fully stochastic. A simple model, taking into account phenomenological correlations of the lines' initial phases was established. Radiation structure in the experiment and simulation proved to be different, demanding interactions between different lines to be described via a NLSE-based model.

Disorder-induced light localisation:from random to artificial

Light localisation in one-dimensional (1D) randomly disordered medium is usually characterized by randomly distributed resonances with fluctuating transmission values, instead of selectively distributed resonances with close-to-unity transmission values that are needed in real application fields. By a resonance tuning scheme developed recently, opening of favorable resonances or closing of unfavorable resonances are achieved by disorder micro-modification, both on the layered medium and the fibre Bragg grating (FBG) array. And furthermore, it is shown that those disorder-induced resonances are independently tunable. Therefore, selected resonances and arranged light localisation can be achieved via artificial disorder, and thus meet the demand of various application fields.

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

Random walk with restart over dynamic graphs

Random Walk with Restart (RWR) is an appealing measure of proximity between nodes based on graph structures. Since real graphs are often large and subject to minor changes, it is prohibitively expensive to recompute proximities from scratch. Previous methods use LU decomposition and degree reordering heuristics, entailing O(|V|^3) time and O(|V|^2) memory to compute all (|V|^2) pairs of node proximities in a static graph. In this paper, a dynamic scheme to assess RWR proximities is proposed: (1) For unit update, we characterize the changes to all-pairs proximities as the outer product of two vectors. We notice that the multiplication of an RWR matrix and its transition matrix, unlike traditional matrix multiplications, is commutative. This can greatly reduce the computation of all-pairs proximities from O(|V|^3) to O(|delta|) time for each update without loss of accuracy, where |delta| (<<|V|^2) is the number of affected proximities. (2) To avoid O(|V|^2) memory for all pairs of outputs, we also devise efficient partitioning techniques for our dynamic model, which can compute all pairs of proximities segment-wisely within O(l|V|) memory and O(|V|/l) I/O costs, where 1<=l<=|V| is a user-controlled trade-off between memory and I/O costs. (3) For bulk updates, we also devise aggregation and hashing methods, which can discard many unnecessary updates further and handle chunks of unit updates simultaneously. Our experimental results on various datasets demonstrate that our methods can be 1–2 orders of magnitude faster than other competitors while securing scalability and exactness.

Machine learning per l'idrologia: applicazione del metodo random forests per la previsione degli eventi di piena fluviale con un approccio probabilistico

Le tecniche di Machine Learning sono molto utili in quanto consento di massimizzare l’utilizzo delle informazioni in tempo reale. Il metodo Random Forests può essere annoverato tra le tecniche di Machine Learning più recenti e performanti. Sfruttando le caratteristiche e le potenzialità di questo metodo, la presente tesi di dottorato affronta due casi di studio differenti; grazie ai quali è stato possibile elaborare due differenti modelli previsionali. Il primo caso di studio si è incentrato sui principali fiumi della regione Emilia-Romagna, caratterizzati da tempi di risposta molto brevi. La scelta di questi fiumi non è stata casuale: negli ultimi anni, infatti, in detti bacini si sono verificati diversi eventi di piena, in gran parte di tipo “flash flood”. Il secondo caso di studio riguarda le sezioni principali del fiume Po, dove il tempo di propagazione dell’onda di piena è maggiore rispetto ai corsi d’acqua del primo caso di studio analizzato. Partendo da una grande quantità di dati, il primo passo è stato selezionare e definire i dati in ingresso in funzione degli obiettivi da raggiungere, per entrambi i casi studio. Per l’elaborazione del modello relativo ai fiumi dell’Emilia-Romagna, sono stati presi in considerazione esclusivamente i dati osservati; a differenza del bacino del fiume Po in cui ai dati osservati sono stati affiancati anche i dati di previsione provenienti dalla catena modellistica Mike11 NAM/HD. Sfruttando una delle principali caratteristiche del metodo Random Forests, è stata stimata una probabilità di accadimento: questo aspetto è fondamentale sia nella fase tecnica che in fase decisionale per qualsiasi attività di intervento di protezione civile. L'elaborazione dei dati e i dati sviluppati sono stati effettuati in ambiente R. Al termine della fase di validazione, gli incoraggianti risultati ottenuti hanno permesso di inserire il modello sviluppato nel primo caso studio all’interno dell’architettura operativa di FEWS.

Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle.

A novel approach to Non-Orthogonal Random Access with application to NB-IoT NTN systems

In the Massive IoT vision, millions of devices need to be connected to the Internet through a wireless access technology. However, current IoT-focused standards are not fully prepared for this future. In this thesis, a novel approach to Non-Orthogonal techniques for Random Access, which is the main bottleneck in high density systems, is proposed. First, the most popular wireless access standards are presented, with a focus on Narrowband-IoT. Then, the Random Access procedure as implemented in NB-IoT is analyzed. The Non-Orthogonal Random Access technique is presented next, along with two potential algorithms for the detection of non-orthogonal preambles. Finally, the performance of the proposed solutions are obtained through numerical simulations.

Detection e Classificazione di Jammer in Protocolli Random Access

Con il crescente utilizzo delle reti wireless la sicurezza e l'affidabilità del servizio stanno diventando requisiti fondamentali da garantire. Questo studio ha come obiettivi il rilevamento di un attacco jammer e la classificazione della tipologia dell'attacco (reattivo, random e periodico) in una rete wireless in cui gli utenti comunicano con un access point tramite il protocollo random access slotted Aloha. La classificazione degli attacchi è infatti fondamentale per attuare le dovute contromisure ed evitare cali di performance nella rete. Le metriche estratte, fra cui la packet delivery ratio (PDR) e la rispettiva analisi spettrale, il rapporto segnale rumore medio e la varianza dell'rapporto segnale rumore, sono risultate essere efficaci nella classificazione dei jammers. In questo elaborato è stato implementato un sistema di detection e classificazione di jammer basato su machine learning, che ha permesso di ottenere una accuratezza complessiva del 92.5% nella classificazione ed una probabilità di detection superiore al 95% per valori di PDR inferiori o uguali al 70%.

Neural Network based Non Orthogonal Random Access for 6G NTN-IoT

Pervasive and distributed Internet of Things (IoT) devices demand ubiquitous coverage beyond No-man’s land. To satisfy plethora of IoT devices with resilient connectivity, Non-Terrestrial Networks (NTN) will be pivotal to assist and complement terrestrial systems. In a massiveMTC scenario over NTN, characterized by sporadic uplink data reports, all the terminals within a satellite beam shall be served during the short visibility window of the flying platform, thus generating congestion due to simultaneous access attempts of IoT devices on the same radio resource. The more terminals collide, the more average-time it takes to complete an access which is due to the decreased number of successful attempts caused by Back-off commands of legacy methods. A possible countermeasure is represented by Non-Orthogonal Multiple Access scheme, which requires the knowledge of the number of superimposed NPRACH preambles. This work addresses this problem by proposing a Neural Network (NN) algorithm to cope with the uncoordinated random access performed by a prodigious number of Narrowband-IoT devices. Our proposed method classifies the number of colliding users, and for each estimates the Time of Arrival (ToA). The performance assessment, under Line of Sight (LoS) and Non-LoS conditions in sub-urban environments with two different satellite configurations, shows significant benefits of the proposed NN algorithm with respect to traditional methods for the ToA estimation.

Random Access Procedures in 5G IoT via NTN: System level performances

The Internet of Things (IoT) is a critical pillar in the digital transformation because it enables interaction with the physical world through remote sensing and actuation. Owing to the advancements in wireless technology, we now have the opportunity of using their features to the best of our abilities and improve over the current situation. Indeed, the Internet of Things market is expanding at an exponential rate, with devices such as alarms and detectors, smart metres, trackers, and wearables being used on a global scale for automotive and agriculture, environment monitoring, infrastructure surveillance and management, healthcare, energy and utilities, logistics, good tracking, and so on. The Third Generation Partnership Project (3GPP) acknowledged the importance of IoT by introducing new features to support it. In particular, in Rel.13, the 3GPP introduced the so-called IoT to support Low Power Wide Area Networks (LPWAN).As these devices will be distributed in areas where terrestrial networks are not feasible or commercially viable, satellite networks will play a complementary role due to their ability to provide global connectivity via their large footprint size and short service deployment time. In this context, the goal of this thesis is to investigate the viability of integrating IoT technology with satellite communication (SatCom) systems, with a focus on the Random Access(RA) Procedure. Indeed, the RA is the most critical procedure because it allows the UE to achieve uplink synchronisation, obtain the permanent ID, and obtain uplink transmission resources. The goal of this thesis is to evaluate preamble detection in the SatCom environment.

Anomaly Detection in Random Graph

La presenti tesi ha come obiettivo lo studio di due algoritmi per il rilevamento di anomalie all' interno di grafi random. Per entrambi gli algoritmi sono stati creati dei modelli generativi di grafi dinamici in modo da eseguire dei test sintetici. La tesi si compone in una parte iniziale teorica e di una seconda parte sperimentale. Il secondo capitolo introduce la teoria dei grafi. Il terzo capitolo presenta il problema del rilevamento di comunità. Il quarto capitolo introduce possibili definizioni del concetto di anomalie dinamiche e il problema del loro rilevamento. Il quinto capitolo propone l' introduzione di un punteggio di outlierness associato ad ogni nodo sulla base del confronto tra la sua dinamica e quella della comunità a cui appartiene. L' ultimo capitolo si incentra sul problema della ricerca di una descrizione della rete in termini di gruppi o ruoli sulla base della quale incentrare la ricerca delle anomalie dinamiche.