Integrating clinical data from cross-sectional and longitudinal studies

Clinical trials are typically conducted over a population in order to illuminate certain characteristics of a health issue or disease process. These cross-sectional studies provide a snapshot of these disease processes over a large population but do not allow us to model the temporal nature of disease. Longitudinal studies on the other hand, are used to explore how these processes develop over time but can be expensive and time-consuming, and only cover a relatively small window within the disease process. This paper explores a technique for integrating cross-sectional and longitudinal studies to build models of disease progression

A Bayesian network approach to explaining time series with changing structure

Many examples exist of multivariate time series where dependencies between variables change over time. If these changing dependencies are not taken into account, any model that is learnt from the data will average over the different dependency structures. Paradigms that try to explain underlying processes and observed events in multivariate time series must explicitly model these changes in order to allow non-experts to analyse and understand such data. In this paper we have developed a method for generating explanations in multivariate time series that takes into account changing dependency structure. We make use of a dynamic Bayesian network model with hidden nodes. We introduce a representa- tion and search technique for learning such models from data and test it on synthetic time series and real-world data from an oil refinery, both of which contain changing underlying structure. We compare our method to an existing EM-based method for learning structure. Results are very promising for our method and we include sample explanations, generated from models learnt from the refinery dataset

The pseudotemporal bootstrap for predicting glaucoma from cross-sectional visual field data

Progressive loss of the field of vision is characteristic of a number of eye diseases such as glaucoma, a leading cause of irreversible blindness in the world. Recently, there has been an explosion in the amount of data being stored on patients who suffer from visual deterioration, including visual field (VF) test, retinal image, and frequent intraocular pressure measurements. Like the progression of many biological and medical processes, VF progression is inherently temporal in nature. However, many datasets associated with the study of such processes are often cross sectional and the time dimension is not measured due to the expensive nature of such studies. In this paper, we address this issue by developing a method to build artificial time series, which we call pseudo time series from cross-sectional data. This involves building trajectories through all of the data that can then, in turn, be used to build temporal models for forecasting (which would otherwise be impossible without longitudinal data). Glaucoma, like many diseases, is a family of conditions and it is, therefore, likely that there will be a number of key trajectories that are important in understanding the disease. In order to deal with such situations, we extend the idea of pseudo time series by using resampling techniques to build multiple sequences prior to model building. This approach naturally handles outliers and multiple possible disease trajectories. We demonstrate some key properties of our approach on synthetic data and present very promising results on VF data for predicting glaucoma

Geometry and dynamics of vortex sheets in 3 dimensions

We consider the properties and dynamics of vortex sheets from a geometrical, coordinate-free, perspective. Distribution-valued forms (de Rham currents) are used to represent the fluid velocity and vorticity due to the vortex sheets. The smooth velocities on either side of the sheets are solved in terms of the sheet strengths using the language of double forms. The classical results regarding the continuity of the sheet normal component of the velocity and the conservation of vorticity are exposed in this setting. The formalism is then applied to the case of the self-induced velocity of an isolated vortex sheet. We develop a simplified expression for the sheet velocity in terms of representative curves. Its relevance to the classical Localized Induction Approximation (LIA) to vortex filament dynamics is discusse

Variable grouping in multivariate time series via correlation

The decomposition of high-dimensional multivariate time series (MTS) into a number of low-dimensional MTS is a useful but challenging task because the number of possible dependencies between variables is likely to be huge. This paper is about a systematic study of the “variable groupings” problem in MTS. In particular, we investigate different methods of utilizing the information regarding correlations among MTS variables. This type of method does not appear to have been studied before. In all, 15 methods are suggested and applied to six datasets where there are identifiable mixed groupings of MTS variables. This paper describes the general methodology, reports extensive experimental results, and concludes with useful insights on the strength and weakness of this type of grouping metho

RGFGA: An efficient representation and crossover for grouping genetic algorithms

There is substantial research into genetic algorithms that are used to group large numbers of objects into mutually exclusive subsets based upon some fitness function. However, nearly all methods involve degeneracy to some degree. We introduce a new representation for grouping genetic algorithms, the restricted growth function genetic algorithm, that effectively removes all degeneracy, resulting in a more efficient search. A new crossover operator is also described that exploits a measure of similarity between chromosomes in a population. Using several synthetic datasets, we compare the performance of our representation and crossover with another well known state-of-the-art GA method, a strawman optimisation method and a well-established statistical clustering algorithm, with encouraging results

An Interview With Albert W. Tucker

The mathematical career of Albert W. Tucker, Professor Emeritus at Princeton University, spans more than 50 years. Best known today for his work in mathematical programming and the theory of games (e.g., the Kuhn-Tucker theorem, Tucker tableaux, and the Prisoner\u27s Dilemma), he was also in his earlier years prominent in topology. Outstanding teacher, administrator and leader, he has been President of the MAA, Chairman of the Princeton Mathematics Department, and course instructor, thesis advisor or general mentor to scores of active mathematicians. He is also known for his views on mathematics education and the proper interplay between teaching and research. Tucker took an active interest in this interview, helping with both the planning and the editing. The interviewer, Professor Maurer, received his Ph.D. under Tucker in 1972 and teaches at Swarthmore College

Differential thermal analysis of lunar soil simulant

Differential thermal analysis of a lunar soil simulant, 'Minnesota Lunar Simulant-1' (MLS-1) was performed. The MLS-1 was tested in as-received form (in glass form) and with another silica. The silica addition was seen to depress nucleation events which lead to a better glass former