Computational Topology Techniques for Characterizing Time-Series Data

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and holes - could be useful for real-world data, TDA lets us compare different systems, and even do membership testing or change-point detection. However, TDA is computationally expensive and involves a number of free parameters. This complexity can be obviated by coarse-graining, using a construct called the witness complex. The parametric dependence gives rise to the concept of persistent homology: how shape changes with scale. Its results allow us to distinguish time-series data from different systems - e.g., the same note played on different musical instruments.Comment: 12 pages, 6 Figures, 1 Table, The Sixteenth International Symposium on Intelligent Data Analysis (IDA 2017

Supersonic wings with significant leading-edge thrust at cruise

Experimental/theoretical correlations are presented which show that significant levels of leading edge thrust are possible at supersonic speeds for certain planforms which match the theoretical thrust distribution potential with the supporting airfoil geometry. The analytical process employed spanwise distribution of both it and/or that component of full theoretical thrust which acts as vortex lift. Significantly improved aerodynamic performance in the moderate supersonic speed regime is indicated

Have Welfare-To-Work Programs Improved Over Time In Putting Welfare Recipients To Work?

Data from 76 experimental welfare-to-work programs conducted in the United States between 1983 and 1998 are used to investigate whether the impacts of such programs on employment had been improving over time and whether specific program features influencing such changes can be identified. Over the period, an increasing percentage of control group members received services similar to those offered to program group members. As a result, differential participation in program service activities between program and control group members decreased steadily over time. This reduction in the net receipt of program services tended to reduce the impact of these programs on employment. However, the negative influence of the reduced incremental services was offset by other factors that resulted in program impacts remaining essentially constant from 1983 to 1998. Suggestions are made for possibly improving program impacts in future experiments.Welfare Programs; Program Evaluation; Employment Behavior of Low-Income Families; Meta Analysis

Supersonic aircraft Patent

Design of supersonic aircraft with novel fixed, swept wing planfor

Remote Detection of Saline Intrusion in a Coastal Aquifer Using Borehole Measurements of Self-Potential

Funded by NERC CASE studentship . Grant Number: NE/I018417/1Peer reviewedPublisher PD

Sparse Nerves in Practice

Topological data analysis combines machine learning with methods from algebraic topology. Persistent homology, a method to characterize topological features occurring in data at multiple scales is of particular interest. A major obstacle to the wide-spread use of persistent homology is its computational complexity. In order to be able to calculate persistent homology of large datasets, a number of approximations can be applied in order to reduce its complexity. We propose algorithms for calculation of approximate sparse nerves for classes of Dowker dissimilarities including all finite Dowker dissimilarities and Dowker dissimilarities whose homology is Cech persistent homology. All other sparsification methods and software packages that we are aware of calculate persistent homology with either an additive or a multiplicative interleaving. In dowker_homology, we allow for any non-decreasing interleaving function $\alpha$. We analyze the computational complexity of the algorithms and present some benchmarks. For Euclidean data in dimensions larger than three, the sizes of simplicial complexes we create are in general smaller than the ones created by SimBa. Especially when calculating persistent homology in higher homology dimensions, the differences can become substantial