Random path sampling applied to vector models of magnetism

The recently reported Monte Carlo Random Path Sampling method (RPS) is here improved and its application is expanded to the study of the 2D and 3D Ising and discrete Heisenberg models. The methodology was implemented to allow use in both CPU-based high-performance computing infrastructures (C/MPI) and GPU-based (CUDA) parallel computation, with significant computational performance gains. Convergence is discussed, both in terms of free energy and magnetization dependence on field/temperature. From the calculated magnetization-energy joint density of states, fast calculations of field and temperature dependent thermodynamic properties are performed, including the effects of anisotropy on coercivity, and the magnetocaloric effect. The emergence of first-order magneto-volume transitions in the compressible Ising model is interpreted using the Landau theory of phase transitions. Using metallic Gadolinium as a real-world example, the possibility of using RPS as a tool for computational magnetic materials design is discussed. Experimental magnetic and structural properties of a Gadolinium single crystal are compared to RPS-based calculations using microscopic parameters obtained from Density Functional Theory.

Existence and wandering of bumps in a spiking neural network model

We study spatially localized states of a spiking neuronal network populated by a pulse coupled phase oscillator known as the lighthouse model. We show that in the limit of slow synaptic interactions in the continuum limit the dynamics reduce to those of the standard Amari model. For non-slow synaptic connections we are able to go beyond the standard firing rate analysis of localized solutions allowing us to explicitly construct a family of co-existing one-bump solutions, and then track bump width and firing pattern as a function of system parameters. We also present an analysis of the model on a discrete lattice. We show that multiple width bump states can co-exist and uncover a mechanism for bump wandering linked to the speed of synaptic processing. Moreover, beyond a wandering transition point we show that the bump undergoes an effective random walk with a diffusion coefficient that scales exponentially with the rate of synaptic processing and linearly with the lattice spacing.

A comprehensive study of multiplicative attribute graph model

Graphs are powerful tools to describe social, technological and biological networks, with nodes representing agents (people, websites, gene, etc.) and edges (or links) representing relations (or interactions) between agents. Examples of real-world networks include social networks, the World Wide Web, collaboration networks, protein networks, etc. Researchers often model these networks as random graphs. In this dissertation, we study a recently introduced social network model, named the Multiplicative Attribute Graph model (MAG), which takes into account the randomness of nodal attributes in the process of link formation (i.e., the probability of a link existing between two nodes depends on their attributes). Kim and Lesckovec, who defined the model, have claimed that this model exhibit some of the properties a real world social network is expected to have. Focusing on a homogeneous version of this model, we investigate the existence of zero-one laws for graph properties, e.g., the absence of isolated nodes, graph connectivity and the emergence of triangles. We obtain conditions on the parameters of the model, so that these properties occur with high or vanishingly probability as the number of nodes becomes unboundedly large. In that regime, we also investigate the property of triadic closure and the nodal degree distribution.

A Random Walk down Main Street

US suburbs have often been characterized by their relatively low walk accessibility compared to more urban environments, and US urban environments have been characterized by low walk accessibility compared to cities in other countries. Lower overall density in the suburbs implies that activities, if spread out, would have a greater distance between them. But why should activities be spread out instead of developed contiguously? This brief research note builds a positive model for the emergence of contiguous development along “Main Street” to illustrate the trade-offs that result in the built environment we observe. It then suggests some policy interventions to place a “thumb on the scale” to choose which parcels will develop in which sequence to achieve socially preferred outcomes.

Protecting databases from schema disclosure: a CRUD-based protection model

Database schemas, in many organizations, are considered one of the critical assets to be protected. From database schemas, it is not only possible to infer the information being collected but also the way organizations manage their businesses and/or activities. One of the ways to disclose database schemas is through the Create, Read, Update and Delete (CRUD) expressions. In fact, their use can follow strict security rules or be unregulated by malicious users. In the first case, users are required to master database schemas. This can be critical when applications that access the database directly, which we call database interface applications (DIA), are developed by third party organizations via outsourcing. In the second case, users can disclose partially or totally database schemas following malicious algorithms based on CRUD expressions. To overcome this vulnerability, we propose a new technique where CRUD expressions cannot be directly manipulated by DIAs any more. Whenever a DIA starts-up, the associated database server generates a random codified token for each CRUD expression and sends it to the DIA that the database servers can use to execute the correspondent CRUD expression. In order to validate our proposal, we present a conceptual architectural model and a proof of concept.

Optimisation of a crossdocking distribution centre simulation model

This paper reports on continuing research into the modelling of an order picking process within a Crossdocking distribution centre using Simulation Optimisation. The aim of this project is to optimise a discrete event simulation model and to understand factors that affect finding its optimal performance. Our initial investigation revealed that the precision of the selected simulation output performance measure and the number of replications required for the evaluation of the optimisation objective function through simulation influences the ability of the optimisation technique. We experimented with Common Random Numbers, in order to improve the precision of our simulation output performance measure, and intended to use the number of replications utilised for this purpose as the initial number of replications for the optimisation of our Crossdocking distribution centre simulation model. Our results demonstrate that we can improve the precision of our selected simulation output performance measure value using Common Random Numbers at various levels of replications. Furthermore, after optimising our Crossdocking distribution centre simulation model, we are able to achieve optimal performance using fewer simulations runs for the simulation model which uses Common Random Numbers as compared to the simulation model which does not use Common Random Numbers.

A risk model with an observer in a Markov environment

We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.

Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.

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.

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.

Generating Effective Test Suites for Model Transformations Using Classifying Terms

Generating sample models for testing a model transformation is no easy task. This paper explores the use of classifying terms and stratified sampling for developing richer test cases for model transformations. Classifying terms are used to define the equivalence classes that characterize the relevant subgroups for the test cases. From each equivalence class of object models, several representative models are chosen depending on the required sample size. We compare our results with test suites developed using random sampling, and conclude that by using an ordered and stratified approach the coverage and effectiveness of the test suite can be significantly improved.

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.

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.