Sistemi dinamici stocastici su network

L'obiettivo della tesi è studiare la dinamica di un random walk su network. Essa è inoltre suddivisa in due parti: la prima è prettamente teorica, mentre la seconda analizza i risultati ottenuti mediante simulazioni. La parte teorica è caratterizzata dall'introduzione di concetti chiave per comprendere i random walk, come i processi di Markov e la Master Equation. Dopo aver fornito un esempio intuitivo di random walk nel caso unidimensionale, tale concetto viene generalizzato. Così può essere introdotta la Master Equation che determina l'evoluzione del sistema. Successivamente si illustrano i concetti di linearità e non linearità, fondamentali per la parte di simulazione. Nella seconda parte si studia il comportamento di un random walk su network nel caso lineare e non lineare, studiando le caratteristiche della soluzione stazionaria. La non linearità introdotta simula un comportamento egoista da parte di popolazioni in interazioni. In particolare si dimostra l'esistenza di una Biforcazione di Hopf.

Proprietà statistiche di network dinamici

L'obbiettivo di questa tesi è quello di studiare alcune proprietà statistiche di un random walk su network. Dopo aver definito il concetto di network e di random walk su network, sono state studiate le caratteristiche dello stato stazionario di questo sistema, la loro dipendenza dalla topologia della rete e l'andamento del sistema verso l'equilibrio, con particolare interesse per la distribuzione delle fluttuazioni delle popolazioni sui differenti nodi, una volta raggiunto lo stato stazionario. In seguito, si è voluto osservare il comportamento del network sottoposto ad una forzatura costante, rappresentata da sorgenti e pozzi applicati in diversi nodi, e quindi la sua suscettività a perturbazioni esterne. Tramite alcune simulazioni al computer, viene provato che una forzatura esterna modifica in modo diverso lo stato del network in base alla topologia di quest'ultimo. Dai risultati si è trovato quali sono i nodi che, una volta perturbati, sono in grado di cambiare ampiamente lo stato generale del sistema e quali lo influenzano in minima parte.

Caratterizzazione di sequenze di DNA mediante catene di Markov

Questa tesi si inserisce nell’ambito di studio dei modelli stocastici applicati alle sequenze di DNA. I random walk e le catene di Markov sono tra i processi aleatori che hanno trovato maggiore diffusione in ambito applicativo grazie alla loro capacità di cogliere le caratteristiche salienti di molti sistemi complessi, pur mantenendo semplice la descrizione di questi. Nello specifico, la trattazione si concentra sull’applicazione di questi nel contesto dell’analisi statistica delle sequenze genomiche. Il DNA può essere rappresentato in prima approssimazione da una sequenza di nucleotidi che risulta ben riprodotta dal modello a catena di Markov; ciò rappresenta il punto di partenza per andare a studiare le proprietà statistiche delle catene di DNA. Si approfondisce questo discorso andando ad analizzare uno studio che si ripropone di caratterizzare le sequenze di DNA tramite le distribuzioni delle distanze inter-dinucleotidiche. Se ne commentano i risultati, al fine di mostrare le potenzialità di questi modelli nel fare emergere caratteristiche rilevanti in altri ambiti, in questo caso quello biologico.

Early bursts of body size and shape evolution are rare in comparative data

George Gaylord Simpson famously postulated that much of life's diversity originated as adaptive radiations-more or less simultaneous divergences of numerous lines from a single ancestral adaptive type. However, identifying adaptive radiations has proven difficult due to a lack of broad-scale comparative datasets. Here, we use phylogenetic comparative data on body size and shape in a diversity of animal clades to test a key model of adaptive radiation, in which initially rapid morphological evolution is followed by relative stasis. We compared the fit of this model to both single selective peak and random walk models. We found little support for the early-burst model of adaptive radiation, whereas both other models, particularly that of selective peaks, were commonly supported. In addition, we found that the net rate of morphological evolution varied inversely with clade age. The youngest clades appear to evolve most rapidly because long-term change typically does not attain the amount of divergence predicted from rates measured over short time scales. Across our entire analysis, the dominant pattern was one of constraints shaping evolution continually through time rather than rapid evolution followed by stasis. We suggest that the classical model of adaptive radiation, where morphological evolution is initially rapid and slows through time, may be rare in comparative data.

How do indirect measures of evaluation work? Evaluating the inference of prejudice in the Implicit Association Test

There has been significant interest in indirect measures of attitudes like the Implicit Association Test (IAT), presumably because of the possibility of uncovering implicit prejudices. The authors derived a set of qualitative predictions for people's performance in the IAT on the basis of random walk models. These were supported in 3 experiments comparing clearly positive or negative categories to nonwords. They also provided evidence that participants shift their response criterion when doing the IAT. Because of these criterion shifts, a response pattern in the IAT can have multiple causes. Thus, it is not possible to infer a single cause (such as prejudice) from IAT results. A surprising additional result was that nonwords were treated as though they were evaluated more negatively than obviously negative items like insects, suggesting that low familiarity items may generate the pattern of data previously interpreted as evidence for implicit prejudice.

Resolving diffusion in clay minerals at different time scales: Combination of experimental and modeling approaches

Since no single experimental or modeling technique provides data that allow a description of transport processes in clays and clay minerals at all relevant scales, several complementary approaches have to be combined to understand and explain the interplay between transport relevant phenomena. In this paper molecular dynamics simulations (MD) were used to investigate the mobility of water in the interlayer of montmorillonite (Mt), and to estimate the influence of mineral surfaces and interlayer ions on the water diffusion. Random Walk (RW) simulations based on a simplified representation of pore space in Mt were used to estimate and understand the effect of the arrangement of Mt particles on the meso- to macroscopic diffusivity of water. These theoretical calculations were complemented with quasielastic neutron scattering (QENS) measurements of aqueous diffusion in Mt with two pseudo-layers of water performed at four significantly different energy resolutions (i.e. observation times). The size of the interlayer and the size of Mt particles are two characteristic dimensions which determine the time dependent behavior of water diffusion in Mt. MD simulations show that at very short time scales water dynamics has the characteristic features of an oscillatory motion in the cage formed by neighbors in the first coordination shell. At longer time scales, the interaction of water with the surface determines the water dynamics, and the effect of confinement on the overall water mobility within the interlayer becomes evident. At time scales corresponding to an average water displacement equivalent to the average size of Mt particles, the effects of tortuosity are observed in the meso- to macroscopic pore scale simulations. Consistent with the picture obtained in the simulations, the QENS data can be described using a (local) 3D diffusion at short observation times, whereas at sufficiently long observation times a 2D diffusive motion is clearly observed. The effects of tortuosity measured in macroscopic tracer diffusion experiments are in qualitative agreement with RW simulations. By using experimental data to calibrate molecular and mesoscopic theoretical models, a consistent description of water mobility in clay minerals from the molecular to the macroscopic scale can be achieved. In turn, simulations help in choosing optimal conditions for the experimental measurements and the data interpretation. (C) 2014 Elsevier B.V. All rights reserved.

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.

Effectiveness of non-steroidal anti-inflammatory drugs for the treatment of pain in knee and hip osteoarthritis: a network meta-analysis.

BACKGROUND Non-steroidal anti-inflammatory drugs (NSAIDs) are the backbone of osteoarthritis pain management. We aimed to assess the effectiveness of different preparations and doses of NSAIDs on osteoarthritis pain in a network meta-analysis. METHODS For this network meta-analysis, we considered randomised trials comparing any of the following interventions: NSAIDs, paracetamol, or placebo, for the treatment of osteoarthritis pain. We searched the Cochrane Central Register of Controlled Trials (CENTRAL) and the reference lists of relevant articles for trials published between Jan 1, 1980, and Feb 24, 2015, with at least 100 patients per group. The prespecified primary and secondary outcomes were pain and physical function, and were extracted in duplicate for up to seven timepoints after the start of treatment. We used an extension of multivariable Bayesian random effects models for mixed multiple treatment comparisons with a random effect at the level of trials. For the primary analysis, a random walk of first order was used to account for multiple follow-up outcome data within a trial. Preparations that used different total daily dose were considered separately in the analysis. To assess a potential dose-response relation, we used preparation-specific covariates assuming linearity on log relative dose. FINDINGS We identified 8973 manuscripts from our search, of which 74 randomised trials with a total of 58 556 patients were included in this analysis. 23 nodes concerning seven different NSAIDs or paracetamol with specific daily dose of administration or placebo were considered. All preparations, irrespective of dose, improved point estimates of pain symptoms when compared with placebo. For six interventions (diclofenac 150 mg/day, etoricoxib 30 mg/day, 60 mg/day, and 90 mg/day, and rofecoxib 25 mg/day and 50 mg/day), the probability that the difference to placebo is at or below a prespecified minimum clinically important effect for pain reduction (effect size [ES] -0·37) was at least 95%. Among maximally approved daily doses, diclofenac 150 mg/day (ES -0·57, 95% credibility interval [CrI] -0·69 to -0·46) and etoricoxib 60 mg/day (ES -0·58, -0·73 to -0·43) had the highest probability to be the best intervention, both with 100% probability to reach the minimum clinically important difference. Treatment effects increased as drug dose increased, but corresponding tests for a linear dose effect were significant only for celecoxib (p=0·030), diclofenac (p=0·031), and naproxen (p=0·026). We found no evidence that treatment effects varied over the duration of treatment. Model fit was good, and between-trial heterogeneity and inconsistency were low in all analyses. All trials were deemed to have a low risk of bias for blinding of patients. Effect estimates did not change in sensitivity analyses with two additional statistical models and accounting for methodological quality criteria in meta-regression analysis. INTERPRETATION On the basis of the available data, we see no role for single-agent paracetamol for the treatment of patients with osteoarthritis irrespective of dose. We provide sound evidence that diclofenac 150 mg/day is the most effective NSAID available at present, in terms of improving both pain and function. Nevertheless, in view of the safety profile of these drugs, physicians need to consider our results together with all known safety information when selecting the preparation and dose for individual patients. FUNDING Swiss National Science Foundation (grant number 405340-104762) and Arco Foundation, Switzerland.

An empirical analysis on the efficiency of the microfinance investment market

This paper empirically analyzes the market efficiency of microfinance investment funds. For the empirical analysis, we use an index of the microfinance investment funds and apply two kinds of variance ratio tests to examine whether or not this index follows a random walk. We use the entire sample period from December 2003 to June 2010 as well as two sub-samples which divide the entire period before and after January 2007. The empirical evidence demonstrates that the index does not follow a random walk, suggesting that the market of the microfinance investment funds is not efficient. This result is not affected by changes in either empirical techniques or sample periods.

Percolation in soils at Different Bulk Densities: Porosity, Connectivity and Grey Threshold.

To improve percolation modelling on soils the geometrical properties of the pore space must be understood; this includes porosity, particle and pore size distribution and connectivity of the pores. A study was conducted with a soil at different bulk densities based on 3D grey images acquired by X-ray computed tomography. The objective was to analyze the effect in percolation of aspects of pore network geometry and discuss the influence of the grey threshold applied to the images. A model based on random walk algorithms was applied to the images, combining five bulk densities with up to six threshold values per density. This allowed for a dynamical perspective of soil structure in relation to water transport through the inclusion of percolation speed in the analyses. To evaluate separately connectivity and isolate the effect of the grey threshold, a critical value of 35% of porosity was selected for every density. This value was the smallest at which total-percolation walks appeared for the all images of the same porosity and may represent a situation of percolation comparable among bulks densities. This criterion avoided an arbitrary decision in grey thresholds. Besides, a random matrix simulation at 35% of porosity with real images was used to test the existence of pore connectivity as a consequence of a non-random soil structure.

Topology of a percolating soil pore network.

A connectivity function defined by the 3D-Euler number, is a topological indicator and can be related to hydraulic properties (Vogel and Roth, 2001). This study aims to develop connectivity Euler indexes as indicators of the ability of soils for fluid percolation. The starting point was a 3D grey image acquired by X-ray computed tomography of a soil at bulk density of 1.2 mg cm-3. This image was used in the simulation of 40000 particles following a directed random walk algorithms with 7 binarization thresholds. These data consisted of 7 files containing the simulated end points of the 40000 random walks, obtained in Ruiz-Ramos et al. (2010). MATLAB software was used for computing the frequency matrix of the number of particles arriving at every end point of the random walks and their 3D representation.

Systematic analysis of direct-drive baseline designs for shock ignition with the Laser MégaJoule

We present direct-drive target design studies for the laser mégajoule using two distinct initial aspect ratios (A = 34 and A = 5). Laser pulse shapes are optimized by a random walk method and drive power variations are used to cover a wide variety of implosion velocities between 260 km/s and 365 km/s. For selected implosion velocities and for each initial aspect ratio, scaled-target families are built in order to find self-ignition threshold. High-gain shock ignition is also investigated in the context of Laser MégaJoule for marginally igniting targets below their own self-ignition threshold.

Empirical analysis of traffic volume for the application of the options theory to highway concessions

*************************************************************************************** EL WCTR es un Congreso de reconocido prestigio internacional en el ámbito de la investigación del transporte que hasta el 2010 publicaba sus libros de abstracts con ISBN. Por ello consideramos que debería seguir teníendose en cuenta para los indicadores de calidad ******************************************************************************************* Investment projects in the field of transportation infrastructures have a high degree of uncertainty and require an important amount of resources. In highway concessions in particular, the calculation of the Net Present Value (NPV) of the project by means of the discount of cash flows, may lead to erroneous results when the project incorporates certain flexibility. In these cases, the theory of real options is an alternative tool for the valuation of concessions. When the variable that generates uncertainty (in our case, the traffic) follows a random walk (or Geometric Brownian Motion), we can calculate the value of the options embedded in the contract starting directly from the process followed by that variable. This procedure notably simplifies the calculation method. In order to test the hypothesis of the evolution of traffic as a Geometric Brownian Motion, we have used the available series of traffic in Spanish highways, and we have applied the Augmented Dickey-Fuller approach, which is the most widely used test for this kind of study. The main result of the analysis is that we cannot reject the hypothesis that traffic follows a Geometric Brownian Motion in the majority of both toll highways and free highways in Spain.

Modelos para el análisis dinámico y la predicción a corto plazo de los precios de la electricidad en mercados liberalizados

En esta tesis se va a describir y aplicar de forma novedosa la técnica del alisado exponencial multivariante a la predicción a corto plazo, a un día vista, de los precios horarios de la electricidad, un problema que se está estudiando intensivamente en la literatura estadística y económica reciente. Se van a demostrar ciertas propiedades interesantes del alisado exponencial multivariante que permiten reducir el número de parámetros para caracterizar la serie temporal y que al mismo tiempo permiten realizar un análisis dinámico factorial de la serie de precios horarios de la electricidad. En particular, este proceso multivariante de elevada dimensión se estimará descomponiéndolo en un número reducido de procesos univariantes independientes de alisado exponencial caracterizado cada uno por un solo parámetro de suavizado que variará entre cero (proceso de ruido blanco) y uno (paseo aleatorio). Para ello, se utilizará la formulación en el espacio de los estados para la estimación del modelo, ya que ello permite conectar esa secuencia de modelos univariantes más eficientes con el modelo multivariante. De manera novedosa, las relaciones entre los dos modelos se obtienen a partir de un simple tratamiento algebraico sin requerir la aplicación del filtro de Kalman. De este modo, se podrán analizar y poner al descubierto las razones últimas de la dinámica de precios de la electricidad. Por otra parte, la vertiente práctica de esta metodología se pondrá de manifiesto con su aplicación práctica a ciertos mercados eléctricos spot, tales como Omel, Powernext y Nord Pool. En los citados mercados se caracterizará la evolución de los precios horarios y se establecerán sus predicciones comparándolas con las de otras técnicas de predicción. ABSTRACT This thesis describes and applies the multivariate exponential smoothing technique to the day-ahead forecast of the hourly prices of electricity in a whole new way. This problem is being studied intensively in recent statistics and economics literature. It will start by demonstrating some interesting properties of the multivariate exponential smoothing that reduce drastically the number of parameters to characterize the time series and that at the same time allow a dynamic factor analysis of the hourly prices of electricity series. In particular this very complex multivariate process of dimension 24 will be estimated by decomposing a very reduced number of univariate independent of exponentially smoothing processes each characterized by a single smoothing parameter that varies between zero (white noise process) and one (random walk). To this end, the formulation is used in the state space model for the estimation, since this connects the sequence of efficient univariate models to the multivariate model. Through a novel way, relations between the two models are obtained from a simple algebraic treatment without applying the Kalman filter. Thus, we will analyze and expose the ultimate reasons for the dynamics of the electricity price. Moreover, the practical aspect of this methodology will be shown by applying this new technique to certain electricity spot markets such as Omel, Powernext and Nord Pool. In those markets the behavior of prices will be characterized, their predictions will be formulated and the results will be compared with those of other forecasting techniques.

Orthogonal MCMC algorithms

Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information using another MCMC technique working on the entire population of current states. These parallel ?vertical? chains are led by random-walk proposals, whereas the ?horizontal? MCMC uses a independent proposal, which can be easily adapted by making use of all the generated samples. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error, as well as robustness w.r.t. to initial values and parameter choice.