"Bridging the Gap Between Real-world Decision Making and Mathematics: Multiobjective Optimisation in Action"

This talk presents several studies that illustrate the power of multiobjective optimisation in supporting decision makers facing conflicting goals. These studies are drawn from the fields of transportation (airline operations, traffic modelling), health (radiation therapy treatment), and manufacturing (composite materials). I will illustrate the widely differing mathematical methods used in these applications, but emphasise the common benefits of the multiobejctive optimisation approach: The improved understanding of the problem achieved through additional insight into the problem structure; the improved support for decision makers through the ability to properly account for trade-offs between conflicting goals; and last but not least, the considerable benefits that result in terms of quality of decisions and/or improved decision making processes.

"Rationality and The Bayesian Paradigm"

It is claimed that rationality does not imply Bayesianism. We first define what is meant by the two terms, so that the statement is not tautologically false. Two notions of rationality are discussed, and related to two main approaches to statistical inference. It is followed by a brief survey of the arguments against the definition of rationality by Savage's axioms, as well as some alternative approaches to decision making.

"Can we win the clone war?"

Suppose that we have a family of linear orders on a finite set C. A subset of C which is ranked consecutively (though possibly in different order) in all linear orders is called a clone set. All clone sets for a given family of linear orders form a clone structure. In this paper we formalise and study properties of clone structures. In particular, we give an axiomatic characterisation of clone structures, relate them to PQ-trees, define the composition of those, classify irreducible ones, and show that it is sufficient to have only three linear orders to realise any clone structure. We also discuss clone structures implementable by single-peaked and single-crossing profiles.
In applications, a set of linear orders is normally interpreted as opinions of voters about candidates in a set C. Cloning candidates (products) is one of the most sophisticated tools of manipulation of elections (consumer surveys). Unfortunately most common voting rules are vulnerable to this method of manipulation. So clones do matter.
This is a joint work with Piotr Faliszewski (Krakow) and Edith Elkind (Oxford).

"The Challenge of Constrained Markov Chains: toward the next generation of authoring tools in music and text"

Markov chains are routinely used in many fields of analysis. They are increasingly used also for generation of content such as music or text, because they faithfully represent local properties of the style of a given corpus. However, in practice, many types of constraints are needed to enforce structural properties of sequences. These properties cannot be learned by Markov processes, by definition of the the Markov hypothesis. In this talk I introduce Markov Constraints, a reformulation of Markov sequence generation in the framework of constraint satisfaction that makes it possible to generate Markov sequences enforcing various strutural properties. I present ssome results concerning unary and binary constraints, as well as meter, and describe current challenges concerning, e.g. the distribution of sequences. I illustrate these issues with applications in music and text generation.