Oscar García-Prada - The Mathematics of Kolam

In Tamil Nadu, a state in southern India, it is an old tradition to decorate the entrance to the home with a geometric figure called ``Kolam''. A kolam is a geometrical line drawing composed of curved loops, drawn around a grid pattern of dots. This is typically done by women using white rice flour. Kolams have connections to discrete mathematics, number theory, abstract algebra, sequences, fractals and computer science. After reviewing a bit of its history, Oscar will explore some of these connections. 

Claudia Silva - Kolam: An Ephemeral Women´s art of South India

Kolam is a street drawing, performed by women in south India. This daily ritual of "putting" the kolam on the ground represents a time of intimacy, concentration and creativity. Through some videos, Claudia will explain some basic features of kolam, focusing on anthropological, religious, educational and artistic aspects of this beautiful female art expression.

The lectures are accompanied by a photography exhibition at Wolfson College.

Neural networks underpin both biological intelligence and modern AI systems, yet there is relatively little theory for how the observed behavior of these networks arises. Even the connectivity of neurons within the brain remains largely unknown, and popular deep learning algorithms lack theoretical justification or reliability guarantees.  In this talk, we consider paths towards a more rigorous understanding of neural networks. We characterize and, where possible, prove essential properties of neural algorithms: expressivity, learning, and robustness. We show how observed emergent behavior can arise from network dynamics, and we develop algorithms for learning more about the network structure of the brain.

Fake accounts detection and users’ polarization are two very well known topics concerning the social media sphere, that have been extensively discussed and analyzed, both in the academic literature and in everyday life. Social bots are autonomous accounts that are explicitly created to increase the number of followers of a target user, in order to inflate its visibility and consensus in a social media context. For this reason, a great variety of methods for their detection have been proposed and tested. Polarisation, also known as confirmation bias, is instead the common tendency to look for information that confirms one's preexisting beliefs, while ignoring opposite ones. Within this environment, groups of individuals characterized by the same system of beliefs are very likely to form. In the present talk we will first review part of the literature discussing both these topics. Then we will focus on a new dataset collecting tweets from the last Italian parliament elections in 2018 and some preliminary results will be discussed.

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Cascading phenomena are prevalent in natural and social-technical complex networks. We study the persistent cascade-recovery dynamics on random networks which are robust against small trigger but may collapse for larger one. It is observed that depending on the relative intensity of triggering and recovery, the network belongs one of the two dynamical phases: collapsing or active phase. We devise an analytical framework which characterizes not only the critical behaviour but also the temporal evolution of network activity in both phases. Results from agent-based simulations show good agreement with theoretical calculations. This work is an important attempt in understanding networked systems gradually evolving into a state of critical transition, with many potential applications.