Hamilton Institute Seminars (HD / large)

Speaker:

Martin Charlton

Abstract:

Geographically Weighted Regression is a technique for exploratory spatial data analysis. In "normal" regression with data for spatial objects we assume that the relationship we are modelling is uniform across the study area - that is, the estimated regression parameters are "whole-map" statistics. In many situations this is not necessarily the case, as mapping the residuals (the differences between the observed and predicted data) may reveal. Many different solutions have been proposed for dealing with spatial variation in these relationships. GWR provides means of modelling such relationships.

This seminar outlines the characteristics of spatial data and the challenges its use poses for analysis, the ideas underpinning geographically weighted regression and details the process of estimating and interpreting the outputs from GWR models. We finish with a brief survey of current issues in GWR and potential future developments.

Speaker:

Dr. A. Hackett

Abstract:

A cascade or avalanche is observed when interactions between the components of a system allow an initially localized effect to propagate globally. For example, the malfunction of technological systems like email networks or electrical power grids is often attributable to a cascade of failures triggered by some isolated event. Similarly, the transmission of infectious diseases and the adoption of innovations or cultural fads may induce cascades among people in society. It has been extensively demonstrated that such dynamics depend sensitively on the patterns of interaction laid out in the underlying network of the system. One of the primary goals of the study of complex networks is to provide a sound theoretical basis for this dependence.

In this seminar we discuss some recent progress in modelling the interaction between network structure and dynamics. Focusing on the phenomenon of high clustering, we present two recently proposed classes of random graphs that achieve non­ zero clustering coefficients. We provide an analytically tractable framework for modeling cascades in both of these classes. This framework is then used to calculate the mean cascade size and the cascade threshold for a broad class of binary­state dynamics.

Speaker:

Dr. X. Li

Abstract:

Node mobility is often a hindering factor of the networking process in wireless ad hoc networks. In this talk, we will introduce our two recent works that address this problem through a prediction approach.

The first work proposes an AutoRegressive Hello protocol (ARH) for mobile ad hoc networks. A hello protocol is a basic tool for neighborhood discovery. It requires nodes to claim their existence/aliveness by periodic ‘hello’ messages. ARH evolves along with network dynamics by predicting node mobility, and seamlessly tunes itself to obtain ‘hello’ frequency using local knowledge only.

The second work proposes a distributed Prediction-based Secure and Reliable routing framework (PSR) for wireless body area networks. In this protocol, each node predicts the quality of every incidental link and any change in the neighbor set too, based on an autoregressive model. According to the prediction result, it selects routing next hope and decides whether to enables/disables source authentication.

Speaker:

Prof. L. Leskelä

Abstract:

Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. I will model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles perform jumps according to an entropy-maximizing fashion, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential. Time permitting, I will also discuss a recent result which sharply characterizes uniform integrability using the theory of stochastic orders, and allows to interpret the dominating function in Lebesgue's dominated convergence theorem in a natural probabilistic way.

This talk is based on joint work with Harri Varpanen (Aalto University, Finland) and Matti Vihola (University of Jyväskylä, Finland).

Speaker:

Dr. A. Pozdnoukhov

Abstract:

Communication technologies with their very high penetration into society can serve as particularly rich source of information to explore and model evolution of complex social systems.

This talk presents a framework of methods useful for exploratory analysis, modelling and visualization of data streams available from Twitter, instant messenger services and mobile phone communication logs. We apply probabilistic topic models to uncover the temporal evolution and spatial variability of population’s response to various stimuli such as large scale sportive, political or cultural events. We demonstrate how untypical activity levels can be identified by fitting a non-homogeneous Markov-modulated Poisson processes and exploring spatial variability of the component corresponding to unusual bursts/lulls of human activities.

Finally, we present initial ideas on the combined use of available data sources and models within a joint large-scale geocomputation framework to uncover a complex interplay of mobility and communication patterns.

Speaker:

Prof. A. Berman

Abstract:

In this paper a general notion of common diagonal Lyapunov matrix is formulated for a collection of n×n matrices A_1,...,A_s and polyhedral cones k_1,...,k_s in R^n. Necessary and sufficient conditions are derived for the existence of a common diagonal Lyapunov matrix in this setting.

This talk is based on joint work with Christopher King & Robert Shorten.

Speaker:

Prof. S. Kirkland

Abstract:

A square matrix T is called stochastic if its entries are nonnegative and its row sums are all equal to one. Stochastic matrices are the centrepiece of the theory of discrete-time, time homogenous Markov chains on a finite state space. If some power of the stochastic matrix T has all positive entries, then there is a unique left eigenvector for T, known as the stationary distribution, to which the iterates of the Markov chain converge, regardless of what the initial distribution for the chain is. Thus, in this setting, the stationary distribution can be thought of as giving the probability that the chain is in a particular state over the long run.

In many applications, the stochastic matrix under consideration is equipped with an underlying combinatorial structure, which can be recorded in a directed graph. Given a stochastic matrix T, how are the entries in the stationary distribution influenced by the structure of the directed graph associated with T? In this talk we investigate a question of that type by finding the minimum value of the maximum entry in the stationary distribution for T, as T ranges over the set of stochastic matrices with a given directed graph. The solution involves techniques from matrix theory, graph theory, and nonlinear programming.

Speaker:

Dr. H. Šmigoc

Abstract:

The question of which lists of complex numbers are the spectra of nonnegative matrices, is known as the nonnegative inverse eigenvalue problem, and the same question posed for symmetric nonnegative matrices is called the symmetric nonnegative inverse eigenvalue problem. In the talk we will present an overview of some recent results on the symmetric nonnegative inverse eigenvalue problem.

Joint work with T. J. Laffey.

Speaker:

Prof. K.-H. Förster

Abstract:

In this talk following topics will be discussed:

- The Numerical Range of Operators in Banach Spaces.

- The Block Numerical Range of Operators.

- The Block Numerical Range of Operator Functions.

- The Block Numerical Range of m-monic Perron-Frobenius-Matrix-Polynomials.

Speaker:

Prof. P. Colaneri

Abstract:

In this paper the discretisation of switched and non-switched linear positive systems using Padé approximations is considered. Padé approximations to the matrix exponential are sometimes used by control engineers for discretising continuous time systems and for control system design. We observe that this method of approximation is not suited for the discretisation of positive dynamic systems, for two key reasons. First, certain types of Lyapunov stability are not, in general, preserved. Secondly, and more seriously, positivity need not be preserved, even when stability is. Finally we present an alternative approximation to the matrix exponential which preserves positivity, and linear and quadratic stability.

This talk is based on joint work with Steve Kirkland, Annalisa Zappavigna & Robert Shorten