Natural and artificial complex systems, composed of numerous interacting components like neurons in the brain or individuals in societies, exhibit intricate structures with varying degrees of complexity. Understanding the principles governing these networks is a fundamental question in physics, as it enables the identification of networks shaped by similar underlying rules. Recent studies on mammalian connectomes' topological features, such as average shortest path length and clustering coefficient, reveal notable intra-order similarities with the phylogenetic tree taxonomy. However, a comprehensive understanding of brain functionality across different species requires examination not only of structural pathways but also of the flow of information—i.e., electrochemical signals—through them. Utilizing recent advances in statistical physics, this research employs network density matrices to characterize and compare the short- to long-range information flow in mammalian connectomes. Our findings confirm high intra-order similarity along six orders of mammalians. By employing an unsupervised learning pipeline, we cluster mammalian connectomes based on their density matrix proximity, and entropy-free energy profile across various scales, uncovering some similarities to phylogenetic relationships. Furthermore, the results from the functional analysis are consistent with those from the topological analysis, reinforcing the dependency of connectome taxonomy on phylogenetic trees and highlighting the mutual information embedded in density matrices across different scales. To gain deeper insights into real networks, we optimize procedures for aligning theoretical models with real-world biological networks, particularly the mammalian connectome. We quantify network distances using entropy profiles derived from the density matrix formalism and apply optimization algorithms such as Simulated Annealing and Particle Swarm Optimization. These methods minimize the distance between synthetic and empirical networks, effectively capturing information pathways across various scales. By exploring different parameters of generative models, we generate networks that closely resemble the target network. We conducted a series of experiments on synthetic networks to compare different generative models. These experiments focused on evaluating and analyzing the performance of each model in replicating the functional properties of the networks. The comparison was carried out using metrics like Jensen-Shannon Divergence (JSD) to assess how well each model captured the characteristics of the target network. Finally, we validate our approach by fitting synthetic networks to a real mammalian connectome from the MAMI dataset, demonstrating the effectiveness of our optimized generative models in capturing the intricate details of biological networks. This work advances the understanding of connectome structures and information flow while providing robust optimization techniques for modeling complex biological systems.
Generalized Thermodynamics in Complex Information Dynamics: Optimization Techniques and Applications to Mammalian Connectomes
ROSHANA, MOJTABA
2023/2024
Abstract
Natural and artificial complex systems, composed of numerous interacting components like neurons in the brain or individuals in societies, exhibit intricate structures with varying degrees of complexity. Understanding the principles governing these networks is a fundamental question in physics, as it enables the identification of networks shaped by similar underlying rules. Recent studies on mammalian connectomes' topological features, such as average shortest path length and clustering coefficient, reveal notable intra-order similarities with the phylogenetic tree taxonomy. However, a comprehensive understanding of brain functionality across different species requires examination not only of structural pathways but also of the flow of information—i.e., electrochemical signals—through them. Utilizing recent advances in statistical physics, this research employs network density matrices to characterize and compare the short- to long-range information flow in mammalian connectomes. Our findings confirm high intra-order similarity along six orders of mammalians. By employing an unsupervised learning pipeline, we cluster mammalian connectomes based on their density matrix proximity, and entropy-free energy profile across various scales, uncovering some similarities to phylogenetic relationships. Furthermore, the results from the functional analysis are consistent with those from the topological analysis, reinforcing the dependency of connectome taxonomy on phylogenetic trees and highlighting the mutual information embedded in density matrices across different scales. To gain deeper insights into real networks, we optimize procedures for aligning theoretical models with real-world biological networks, particularly the mammalian connectome. We quantify network distances using entropy profiles derived from the density matrix formalism and apply optimization algorithms such as Simulated Annealing and Particle Swarm Optimization. These methods minimize the distance between synthetic and empirical networks, effectively capturing information pathways across various scales. By exploring different parameters of generative models, we generate networks that closely resemble the target network. We conducted a series of experiments on synthetic networks to compare different generative models. These experiments focused on evaluating and analyzing the performance of each model in replicating the functional properties of the networks. The comparison was carried out using metrics like Jensen-Shannon Divergence (JSD) to assess how well each model captured the characteristics of the target network. Finally, we validate our approach by fitting synthetic networks to a real mammalian connectome from the MAMI dataset, demonstrating the effectiveness of our optimized generative models in capturing the intricate details of biological networks. This work advances the understanding of connectome structures and information flow while providing robust optimization techniques for modeling complex biological systems.File | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/70808