**MATLIS (Mathematics in Life
and Social Sciences)**

1. Introduction
2. Programme.

**Introduction**

The scientific Programme to be
described below intends to explore a number of
relevant problems in Biology, Medicine and Sociology
where the use of advanced mathematical methods is
expected to provide significant help to solve the
issues therein addressed . On the other hand, the
precise formulation of the questions to be
considered is likely to be a source of new and
challenging mathematical problems . It is therefore
expected that a successful completion of the studies
described below will translate into significant
advances in all fields involved.

**Research topics**

We next proceed to describe the basic research units which
will constitute the core of this Programme.

**Vasculogenesis.**

The term vasculogenesis is used to denote the formation of
blood vessels starting from their cell precursors (angioblasts) to produce
vascular nets with
characteristic geometrical forms. These include
vessels with different sizes, ranging from
capillaries to arteries and veins. This process is
characteristic of the embryonic state in vertebrates, while angiogenesis (the formation of vessels
from a preexisting vasculature) always leads to the
formation of small vessels, and continues to happen
during adulthood. We are
interested in deriving models for the formation of
early vasculature that could be checked against
experimental data obtained from chick embryos.
Such models should in particular include aspects as
signalling from the endoderm, angioblasts
differentiation and the onset of the first vascular
networks. We are also interested in the formulation
and subsequent analysis of mathematical models
for advanced stages of vascular networking. In
particular, such models should account for existing
data on characteristic sizes and critical cell
densities corresponding to a stable vasculature

**Modelling and Simulation of Blood Coagulation.**

Blood
coagulation is a robust security mechanism of human
organisms, which prevents bleeding from minor
injuries to occur . Any disruption in such a system
may have significant consequences. For instance, an
impaired ability of blood to coagulate is cause of
haemophilia, a serious hereditary disorder. On the
other hand, an inordinate increase in the activation
of the blood coagulation system may lead to abnormal
thrombi formation, and consequently to a number of thrombotic pathologies .The process of blood
coagulation makes use of a complex array of
interdependent, and finely tuned , biochemical
reactions (the so-called biochemical cascade, BC),
of which many details are known by now . However,
much remains to be done in terms of ascertaining
which points in such cascade are more suitable as
targets for external control , and how such
control has to be implemented, in order to obtain
significant therapeutic improvements with respect
to current protocols.

**Optimization in Radiotherapy.**

Radiotherapy
consists in the delivery of ionizing radiation with
curative goals. It represents a major tool for
treating solid tumours in any anatomical site .
While the first cures of cancer by radiation were
reported in 1899, shortly after the discovery of the
X-rays, it was soon learnt that radiotherapy
requires of precise dosimetry and delivery to hit at
the lesion while sparing surrounding normal
tissue. Nowadays, radiotherapy is a fully
interdisciplinary technique which provides major
challenges in Biology, Engineering, Medicine and
Physics, and where Mathematics has already gained
solid ground. Indeed , mathematical methods are
paramount in Image Treatment, a key aspect in the
choice of the so-called Planned Target Volume (PTV), the region that has to be irradiated . Moreover,
Mathematics has also shown its strength to develop a
quantitative radiobiology, that is , a detailed
description of the interaction between radiation and
living matter . In particular, the question of
predicting the biological response to incoming
radiation has become a central issue in the field
during the last thirty years, once the first
mathematical models for that purpose were derived.

In this
Programme we plan to tackle the question of deriving
an integrated model for optimal radiation delivery,
starting from a sharp identification of the PTV by
means of Imaging Techniques , to the design of an
optimal irradiation strategy based on the study of
suitable variational problems . These will often
involve non-standard constraints or penalty terms,
which will require of advanced variational methods
to identify the corresponding minimizers, as well as
to implement efficient numerical approximations
thereof.

**Mathematical Models of Criminality and Emergent Social Behaviours.**

Crime, and
in general unacceptable social behaviour, has always
been a serious concern in human societies. It is to
be noted that the concept of criminal behaviour
includes, together with some widely accepted facts
(e.g. murder), others which largely differ among
various cultures and historical periods. From a
modelling point of view, a given society can be
considered as a playground for a number of
interacting populations , whose joint evolution
leads to emergent behaviours (sometimes termed as
social phase transitions) while at the same time
has to cope with one or several subpopulations which
refuse to play by the rules - the criminals . In
recent years, mathematical methods have proved their
strength in dealing with the dynamical aspects of
such process, a step forward with respect to the
classical, static picture provide by statistical
techniques.

In this
Programme, we aim at deriving and analysing
agent-based models of social behaviour based on
population dynamics methods on the one hand, as well
as on game theory on the other . Such techniques
will be instrumental to gain insight into the
evolution of complex populations subject to resource
competition and under the action of global
constraints. Among these, we should mention the
total wealth variation , this last been influenced
by aspects as changes in environment and main
resources.