Samuel Koovely

The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs. We demonstrate that this entropic measure satisfies the first and second laws of thermodynamics, thereby providing a physical interpretation of diffusion dynamics on networks. We outline a mathematical framework that contextualizes diffusion and conditional entropy within the theories of continuous-time Markov chains and information theory. Furthermore, we obtain explicit results for its evolution on complete, path, and circulant graphs, as well as a mean-field approximation for Erdős-Rényi graphs. We also obtain asymptotic results for general networks. Finally, we experimentally demonstrate several properties of conditional entropy for diffusion over random graphs, such as the Watts-Strogatz model.

T-cells are a core component of the adaptive immune system: they play a major role in mounting an effective and tailored response to foreign pathogens, and they are also relevant in the context of cancer and cer- tain autoimmune diseases. T-cells receptors are protein complexes present on T-cells’ surface that are responsible for identifying foreign and own antigens. Given the complexity of protein-protein interactions, this identification process exhibits a quasi-stochastic behaviour that can be modeled with probabilistic and statistical models. Graphical models can represent a multivariate distribution in a convenient and transparent way as a graph. In this paper we introduce COMIC-Tree, an undirected graphical model for protein-protein interactions, and DrawCOMIC-Tree, a greedy algorithm based on conditional mutual information for learning COMIC-Tree structures. We provide a solid mathematical foundation for them, highlight some theoretical aspects, and test them empirically on a dataset of T-cell receptors.

The output of the original PC-algorithm depends on the order of the evaluated variables, and the separating sets used during its pruning process might be inconsistent with the final result. We give an overview of some variations of this method that address these shortcomings and perform a simulationstudy of these algorithms.