This talk introduces the topic of random walks on a finitely generated group and asks what properties of such a group can be detected through knowledge of such walks.
We apply the novel method of potential analysis to study climatic records. The method comprises (i) derivation of the number of climate states from time series, (ii) derivation of the potential coefficients. Dynamically
monitoring patterns of potential analysis yields indications of possible bifurcations and transitions of the system.
The method is tested on artificial data and then applied to various climatic records [1,2]. It can be applied to a wide range of stochastic systems where time series of sufficient length and temporal resolution are available and transitions or bifurcations are surmised. A recent application of the method in a model of globally coupled bistable systems [3] confirms its general applicability for studying time series in statistical physics.
[1] Livina et al, Climate of the Past, 2010.
[2] Livina et al, Climate Dynamics (submitted)
[3] Vaz Martins et al, Phys. Rev. E, 2010
Following work done by the 'Oxford Spies' we uncover more secrets of 'surface-active Agents'. In modern-day applications we refer to these agents as surfactants, which are now extensively used in industrial, chemical, biological and domestic applications. Our work focuses on the dynamic behaviour of surfactant and polymer-surfactant mixtures.
In this talk we propose a mathematical model that incorporates the effects of diffusion, advection and reactions to describe the dynamic behaviour of such systems and apply the model to the over-flowing-cylinder experiment (OFC). We solve the governing equations of the model numerically and, by exploiting large parameters in the model, obtain analytical asymptotic solutions for the concentrations of the bulk species in the system. Thus, these solutions uncover secrets of the 'surface-active Agents' and provide an important insight into the system behaviour, predicting the regimes under which we observe phase transitions of the species in the system. Finally, we suggest how our models can be extended to uncover the secrets of more complex systems in the field.
This workshop is half-seminar, half-workshop. \\ \\ HSBC have an on-going problem and they submitted a proposal for an MSc in Applied Stats project on this topic. Unfortunately, the project was submitted too late for this cohort of students. Eurico will talk about "the first approach at the problem" but please be aware that it is an open problem which requires further work. Eurico's abstract is as follows. \\ \\
This article examines modelling yield curves through chaotic dynamical systems whose dynamics can be unfolded using non-linear embeddings in higher dimensions. We then refine recent techniques used in the state space reconstruction of spatially extended time series in order to forecast the dynamics of yield curves.
We use daily LIBOR GBP data (January 2007-June 2008) in order to perform forecasts over a 1-month horizon. Our method seems to outperform random walk and other benchmark models on the basis of mean square forecast error criteria.