## Operational Research and Statistics Seminars 2012-2013

### Programme

All seminars will commence at 11:00am in room M/1.25, The Mathematics Institute, Cardiff University, Senghennydd Road (unless otherwise stated).

Please contact Dr Iskander Aliev for more details regarding Operational Research/WIMCS lectures and Dr Jonathan Gillard for more details regarding Statistics lectures.

##### 2 October 2012 at 12:00 in M/1.25

**Speaker: **Dr Konstantin Usevich (University of Southampton)

**Title:** Mosaic Hankel structured low-rank approximation with variable projection.

**Abstract:** Structured low-rank approximation (SLRA) is a problem of approximating a given structured data matrix with a structured matrix of low rank. In this seminar we discuss several examples that can be viewed as special cases of SLRA with mosaic Hankel structure and weighted 2-norm. Variable projection principle is often used to reduce the dimension of the search space in SLRA. We discuss properties of this reduction and show that variable projection leads to efficient local optimization algorithms for mosaic Hankel case.

##### 3 October 2012

**Speaker: ** Dr Coralia Cartis (Edinburgh)

**Title:** A new and improved recovery analysis for iterative hard thresholding algorithms in compressed sensing.

**Abstract:** We present a novel average-case analysis for a standard compressed sensing algorithm, Iterative Hard Thresholding (IHT). For arbitrary measurement matrices, we derive a condition guaranteeing convergence of IHT to a fixedpoint, and a condition ensuring that all fixed points of IHT are `close' to the underlying signal. at most one fixed point, namely the original signal. We also give a weaker requirement guaranteeing the algorithm's convergence to some fixed point. Thus, if both conditions are satisfied, signal recovery is guaranteed. we ensure recovery of the original signal. For the specific case of Gaussian measurement matrices and independent signals, comparison with existing worst-case results by means of the phase transition framework shows a substantial quantitative improvement. Our analysis also applies to IHT variants with variable stepsize, such as normalized IHT, yielding again a significant improvement for the phase transition of Gaussian measurement matrices. This work is joint with Andrew Thompson (Edinburgh, UK and Duke University, USA).

##### 23 October 2012 at 11:00 in Room M/2.06

**Speaker: **Maria Vronskaya (Cardiff)

**Title:** Granger Causality and linearized MSSA.

**Abstract:** The concept of causality is widely studied in econnometrics and statistics since 1969, when C. Granger published his paper "Investigating causual relations by econometric models and cross-spectral methods". The intuitive understanding of causality is that series Y is causing series X if it can be used to improve the forecast of series X.

The talk will outline Granger's definition of causality and then present an alternative approach of defining and measuring causality. This involves a linear approximation of MSSA, which be of interest in its own right.

##### 7 November 2012 at 14:00 in Room M/1.25

**Speaker: **Dr Honora Smith

**Title:** TBC.

**Abstract:** TBC.

##### 14 November 2012

**Speaker: **Rosa M. Espejo (University of Granada, Spain)

**Title:** TBC.

**Abstract:** Time series theory in Hilbert spaces allows to represent the dynamics in
time and space, of curves and surfaces. In the temporal context,
non-parametric estimation of the autocorrelation operator is achieved in
the
ARH(1) case, in combination with the Kalman filtering for prediction. In
the spatial context, an extended non-parametric formulation is
contemplated for estimation of the operators defining the parameters of
the functional state equation associated with SARH(1) models (Spatial
autoregressive models of order one). Several applications in the area of
Geophysics, Finance and Epidemiology are showed to illustrate the
performance of the estimation methodology proposed.

##### 28 November 2012

**Speaker: **Prof Andrew Thomas (University Of Glamorgan)

**Title:** TBC.

**Abstract:** TBC.

##### 30 January 2013 at 11:00 in Room M/1.25

**Speaker: **Dr Mark Kelbert (Swansea)

**Title:** Absence of continuous symmetry breakdown in 2-D quantum

Gibbs states.

**Abstract: **We extend the famous Mermin-Wagner theorem about the preserving of continuous symmetries in 2-D systems of classical statistical mechanics to the models of quantum statistics and quantum gravity. The technique involves some non-trivial probabilistic constructions such as the

system with spins represented by Brownian loops and asymptotics

of critical branching processes emerging in the construction of

Lorentzian triangulations.

##### 24 April 2013 at 15:10 in Room M/0.40

**Speaker: **Prof. Bob John (University of Nottingham)

**Title:** Type-2 Fuzzy Logic for Decision Support.

**Abstract: **Type-2 fuzzy sets are fuzzy-fuzzy sets - that is, where the fuzzy set has membership grades that are themselves fuzzy sets, rather than numbers in [0,1]. Fuzzy sets (type-1) have had significant success in control applications but by their very definition are not particularly 'fuzzy' and struggle in applications that attempt to mimic human reasoning in decision support systems. Firstly, this talk will briefly introduce the audience to type-1 and type-2 fuzzy logic and then Bob will summarise key theoretical developments that allow for novel representations and fast computation in type-2 fuzzy logic systems. He will also describe applications of type-2 fuzzy logic in decision support.

##### 8 May 2013 at 11:00 in Room M/1.25

**Speaker: **Professor Thomas Simon (University of Lille, France)

**Title:** On the self-decomposability of the Fréchet distribution.

**Abstract: **Fréchet distributions, or extreme value distributions of type II, are affine transformations of negative powers of the exponential law. With the help of exponential functionals of Lévy processes, we will show that these distributions are self-decomposable when the power exponent lies in $(-1,0).$ Put together with previous results, this gives a characterization of the infinite divisibility of all extreme value distributions. We shall also give a new proof of the self-decomposability of the Fréchet distribution in the case when the power exponent lies in $(-\infty, -1).$ We will finally discuss several open questions. This is a joint work with Pierre Bosch (Lille 1)..

##### 10 May 2013 at 11:00 in Room M/1.25

**Speaker: **Dr Mark Kelbert (Swansea)

**Title:** An Outbreak Spread and Travelling Waves in Spatially Distributed Populations.

**Abstract: **Mathematical models, based on the SIR (susceptible-infected-removed) process. have long been used to analyze epidemics of infectious disease. We consider spatial aspects of interacting SIR populations by introducing a one-dimensional lattice of SIR nodes. We obtain an accurate approximation for the propagation speed of travelling-wave type solutions. When coupling coefficients are randomly distributed, the average speed of propagation is shown to slow down. The critical reaction time between initial registration of an epidemic and the actual intervention before the number of infected reaches a critical proportion is studied in a stochastic framework. We develop a two-staged model of developed epidemic describing the evolution as a deterministic system with randomized initial conditions linked to the stochastic stage when the number of infected is small and the fluctuations are essential.

##### 10 July 2013 at 11:00 in Room M/1.25

**Speaker: **M.P Frias (University of Jaen, Spain)

**Title:** Parameter estimation of long-range dependence spatial and

spatiotemporal processes.

**Abstract: **Spatiotemporal data displaying long-range dependence are often involved in the statistical analysis of phenomena of interest in many applied fields as Geophysical, Environmental Systems, Economics and Finance. Since the classical pure point spectral projection methods can not be applied in this context, several efforts have been made for the definition of suitable models. Most of these models display global or local self similarity which can be related with fractality. This seminar provides an overview of the parameter estimation algorithms implemented for spatial or spatiotemporal parameter estimation of long-range dependence models in the spectral or wavelet-spectral domain, in terms of log-regression estimators derived in these domains. Consistency of these estimators is investigated in the case of log-periodogram-based and log-wavelet-based methods. Extension of these results to more general contexts like parameter estimation of stationary processes with multiple spectral sigularities will be addressed in subsequent papers.