Monday 21^{st} November 2016
University of Southampton
Ketley Room, Mathematics (Building 54)
10:00 – 11:00 
Coffee 
11:0011:45 
Paweł Dłotko
(INRIA Orsay) Title:
Topological data analysis  from diagrams to information, from
information to knowledge. (slides) Abstract: In this talk I will discuss various techniques in topological data analysis which are based on persistent homology. After a mild introduction to persistence, by using simple examples we will show various ways to turn persistence diagrams into a useful tool in statistics and machine learning. During this part of the talk, I will give a demonstration of a recently developed software package for topological statistics. At the end, I will show a few examples where the presented techniques are used in practice: we will discuss biological analysis of various types of embedded trees, and a couple of problems from material sciences. 
12:00 – 12:30 
Francisco “Kiko” Belchí Guillamón (University of
Southampton) Title: Understanding respiratory diseases
through the use of persistent homology. (slides) Abstract: In a work in collaboration with the
Southampton Respiratory Biomedical Research Unit we aim at better diagnosing and
treating pulmonary diseases. In this talk I will explain how, as a
preliminary step, we are using topological tools to figure out the relation
between some respiratory diseases and how the bronchi bend and occupy space
in our lungs. 
12:30 – 14:15 
Break for Lunch and Discussions 
14:15 – 15:00 
Matteo Rucco
(CNR/IMATI, Genova) Title: Topological data
analysis and formal methods in computer science for modeling complex systems. Abstract: In this talk I report on a
new methodology for modelling complex systems. The methodology can be
considered the first characterization of the S[B]
paradigm and it is based on the following pillars: formal methods in computer
science, computational topology, information theory, and automata theory. The
S[B] paradigm represents a complex system by two
entangled levels: the structural S level and the behavioural B level. In
terms of data volume a complex system can be associated to a big
heterogeneous dataset, and in order to extract from it useful information new
techniques have been recently introduced, most of them in the area of
Topological Data Analysis (TDA). TDA is a subarea of computational topology
that develops and applies topological based techniques for achieving robust
analysis of scientific data. TDA basically performs the construction and the
analysis of a topological space from data. TDA geometrically represents a
dataset D with a family of simplicial complexes C, that are obtained from D
by completion, namely constructs the simplicial complex C which has D as
1skeleton (scaffold). The features of this new topological space are
extracted by computing persistent homology. We used jHoles,
a java high performance tool, that implements the Clique Weight Rank
Persistent Homology algorithm for computing persistent homology. The dynamics
of a complex system can be modelled by using measures that are formally
defined in information theory, e.g. entropy, etc…
.We defined a new entropy, the socalled persistent entropy, that is based on
the persistent barcode. The newly defined Persistent Entropy Automaton is
the formal model used for representing the dynamics of a complex systems
within the S level of the S[B] paradigm. Complex systems have the attitude to
execute simultaneously two or more actions against same resources. This
feature is known in computer science as concurrency. A new runtime
verification is defined for dealing with the formal verification of S[B]
concurrent models. We successfully applied the methodology to a real case
study: a networkbased model of the Immune System, the socalled Idiotypic Network. The methodology is able to identify
when the system performs the immunization against antigens and which are the
optimal executions for reaching the immune memory. 
15:15 – 16:00 
Conrad D’Souza (University of Southampton) Title: Applying HodgeRank to Predict the Outcome of Competitive Events  A Case Study of Horse Racing (slides) Abstract: In this talk, we will explore how topology can be applied to past performance data of horse races to make profitable predictions. We employ HodgeRank, a topologicallyinspired ranking algorithm for pairwise comparison data between alternatives which is particularly useful for incomplete and inconsistent data, to measure the underlying quality of horses. We can construct a simplicial complex which represents the relative performances of pairs of horses. By applying a discrete version of the Hodge Decomposition Theorem to our complex, we can separate the dataset into consistent and inconsistent data (in other words cycles). From the consistent data, we can measure the underlying quality of horses with the induced pairwise comparisons minimising the weighted square error with respect to the observed comparisons. These measures of quality are
fed into a conditional logit model to calculate the probability of each horse
winning a race. We show that these measurements improve the accuracy and
profitability of the predictions made by the betting market. 

List of participants:
Will appear here. 