We study the performance of Markov chains for the q-state ferromagnetic Potts model on random regular graphs. While the cases of the grid and the complete graph are by now well-understood, the case of random regular graphs has resisted a detailed analysis ...
Graph Neural Networks (GNNs) have emerged as a powerful tool for learning on graphs, demonstrating exceptional performance in various domains. However, as GNNs become increasingly popular, new challenges arise. One of the most pressing is the need to ensur ...
In the beginning was the metabolism. The biochemical processes that make life possible transformed the soup of chemicals into the life on Earth we know today. Since then, living organisms have evolved, and life on Earth has become more complex. Living orga ...
In this work, we develop a new framework for dynamic network flow pro-blems based on optimal transport theory. We show that the dynamic multicommodity minimum-cost network flow problem can be formulated as a multimarginal optimal transport problem, where t ...
In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...
Humans and animals constantly adapt to their environment over the course of their life. This thesis seeks to integrate various timescales of adaptation, ranging from the adaptation of synaptic connections between spiking neurons (milliseconds), rapid behav ...
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently symmetric structures, ev ...
Time-sensitive networks, as in the context of IEEE Time-Sensitive Networking (TSN) and IETF Deterministic Networking (DetNet), offer deterministic services with guaranteed bounded latency in order to support safety-critical applications. In this thesis, we ...
Natural language processing has experienced significant improvements with the development of Transformer-based models, which employ self-attention mechanism and pre-training strategies. However, these models still present several obstacles. A notable issue ...
Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...
