L4

On the railway network, for example, there is a large base of installed equipment with a useful life of many years.  This equipment has condition monitoring that can flag a fault when a measured parameter goes outside the permitted range.  If we can use existing measurements to predict when this would occur, preventative maintenance could be targeted more effectively and faults reduced.  As an example, we will consider the current supplied to a points motor as a function of time in each operational cycle.

“Market-Basket (MB) and Household (HH) data provide a fertile substrate for the inference of association between marketing activity (e.g.: prices, promotions, advertisement, etc.) and customer behaviour (e.g.: customers driven to a store, specific product purchases, joint product purchases, etc.). The main aspect of MB and HH data which makes them suitable for this type of inference is the large number of variables of interest they contain at a granularity that is fit for purpose (e.g.: which items are bought together, at what frequency are items bought by a specific household, etc.).

A large number of methods are available to researchers and practitioners to infer meaningful networks of associations between variables of interest (e.g.: Bayesian networks, association rules, etc.). Inferred associations arise from applying statistical inference to the data. In order to use statistical association (correlation) to support an inference of causal association (“which is driving which”), an explicit theory of causality is needed.

Such a theory of causality can be used to design experiments and analyse the resultant data; in such a context certain statistical associations can be interpreted as evidence of causal associations.

On observational data (as opposed to experimental), the link between statistical and causal associations is less straightforward and it requires a theory of causality which is formal enough to support an appropriate calculus (e.g.: do-calculus) of counterfactuals and networks of causation.

My talk will be focused on providing retail analytic problems which may motivate an interest in exploring causal calculi’s potential benefits and challenges.”

In the same way that the classical Torelli theorem determines a curve from its polarized Jacobian we show that moduli spaces of parabolic bundles and parabolic Higgs bundles over a compact Riemann surface X  also determine X. We make use of a theorem of Hurtubise on the geometry of algebraic completely integrable systems in the course of the proof. This is a joint work with I. Biswas and T. Gómez 

Amplitudes in quantum field theory have discontinuities when regarded as
functions of
the scattering kinematics. Such discontinuities can be determined from
Cutkosky rules.
We present a structural analysis of such rules for massive quantum field
theory which combines
algebraic geometry with the combinatorics of Karen Vogtmann's Outer Space.
This is joint work with Spencer Bloch (arXiv:1512.01705).

Multidimensional single molecule microscopy (MSMM) generates image time series of biomolecules in a cellular environment that have been tagged with fluorescent labels. Initial analysis steps of such images consist of image registration of multiple channels, feature detection and single particle tracking. Further analysis may involve the estimation of diffusion rates, the measurement of separations between molecules that are not optically resolved and more. The analysis is done under the condition of poor signal to noise ratios, high density of features and other adverse conditions. Pushing the boundary of what is measurable, we are facing among others the following challenges. Firstly the correct assessment of the uncertainties and the significance of the results, secondly the fast and reliable identification of those features and tracks that fulfil the assumptions of the models used. Simpler models require more rigid preconditions and therefore limiting the usable data, complexer models are theoretically and especially computationally challenging.