# Spikning of PhD Theses

**2018-09-05**

### On Tuesday 4th of September 2018 Fioralba Ajazi has nailed her PhD Theses titled "Random geometric graphs and their applications in neuronal modelling"

**Abstract **

Random graph theory is an important tool to study different problems arising from real world.

In this thesis we study how to model connections between neurons (nodes) and synaptic con-

nections (edges) in the brain using inhomogeneous random distance graph models. We present

four models which have in common the characteristic of having a probability of connections

between the nodes dependent on the distance between the nodes. In Paper I it is described a

one-dimensional inhomogeneous random graph which introduce this connectivity dependence

on the distance, then the degree distribution and some clustering properties are studied. Paper

II extend the model in the two-dimensional case scaling the probability of the connection both

with the distance and the dimension of the network. The threshold of the giant component

is analysed. In Paper III and Paper IV the model describes in simplified way the growth of

potential synapses between the nodes and describe the probability of connection with respect

to distance and time of growth. Many observations on the behaviour of the brain connectivity

and functionality indicate that the brain network has the capacity of being both functional

segregated and functional integrated. This means that the structure has both densely inter-

connected clusters of neurons and robust number of intermediate links which connect those

clusters. The models presented in the thesis are meant to be a tool where the parameters

involved can be chosen in order to mimic biological characteristics.