The aim of this thesis is to inform our understanding of the exquisite relationship between function and structure of complex systems with a particular focus on the inverse problem of inferring structure from collective expression. There exists a rich body of work explaining complex collective behaviour through its interdependence on structure and this forms the core subject matter of the field complex networks. However, in many cases of interest, the underlying structure of the observed system is often unknown and can only be studied through limited measurements. The first chapters of this thesis develop and refine a method of inferring the structure of a priori unknown networks by leveraging the celebrated Heterogeneous mean-field approximations. The inverse protocol is first formulated for and rigorously challenged against synthetic simulations of reactive-random-walkers to successfully recover the degree distributions from partial observations of the system. The reconstruction framework developed is powerful enough to be applicable to many real-world systems of great interest. This is demonstrated by the extension of the method to a nonlinear Leaky-Integrate and Fire (LIF) excitatory neuronal model evolving on a directed network support to recover both the in-degree distribution and the distribution of associated current in Chapter 5. In this chapter, this method is also applied to wide-field calcium imaging data from the brains of mice undergoing stroke and rehabilitation, which is presented as a spatiotemporal analysis in Chapter 4. The findings of Chapters 4 and 5 complement each other to showcase two potential non-invasive ways of tracking the post-stroke recovery of these animals. One analysis focuses on the subtle changes in propagation patterns quantified through three novel biomarkers, while the other shifts the attention to the changes in structure and inherent dynamics as seen through the inverse protocol. This reconstruction recipe has also been extended to a more general two species LIF model accounting for both inhibitory and excitatory neurons. in Chapter 6. This was applied to two-photon light-sheet microscopy data from zebrafish brains upon successful validation in silico. Lastly, Chapter 7 studies a particular phenomenon of interest where structure and inherent dynamics affect the function in a different but popular class of networks. A zero-mean noise-like prestrain is used to induce contractions in 1D Elastic Network Models. The analysis shows that the exact solution is difficult to probe analytically, while the mean behaviours of the networks are predictable and controllable by tuning the magnitude of the applied prestrain.

Structure and collective behaviour: a focus on the inverse problem / Ihusan Adam. - (2021).

Structure and collective behaviour: a focus on the inverse problem

Ihusan Adam
2021

Abstract

The aim of this thesis is to inform our understanding of the exquisite relationship between function and structure of complex systems with a particular focus on the inverse problem of inferring structure from collective expression. There exists a rich body of work explaining complex collective behaviour through its interdependence on structure and this forms the core subject matter of the field complex networks. However, in many cases of interest, the underlying structure of the observed system is often unknown and can only be studied through limited measurements. The first chapters of this thesis develop and refine a method of inferring the structure of a priori unknown networks by leveraging the celebrated Heterogeneous mean-field approximations. The inverse protocol is first formulated for and rigorously challenged against synthetic simulations of reactive-random-walkers to successfully recover the degree distributions from partial observations of the system. The reconstruction framework developed is powerful enough to be applicable to many real-world systems of great interest. This is demonstrated by the extension of the method to a nonlinear Leaky-Integrate and Fire (LIF) excitatory neuronal model evolving on a directed network support to recover both the in-degree distribution and the distribution of associated current in Chapter 5. In this chapter, this method is also applied to wide-field calcium imaging data from the brains of mice undergoing stroke and rehabilitation, which is presented as a spatiotemporal analysis in Chapter 4. The findings of Chapters 4 and 5 complement each other to showcase two potential non-invasive ways of tracking the post-stroke recovery of these animals. One analysis focuses on the subtle changes in propagation patterns quantified through three novel biomarkers, while the other shifts the attention to the changes in structure and inherent dynamics as seen through the inverse protocol. This reconstruction recipe has also been extended to a more general two species LIF model accounting for both inhibitory and excitatory neurons. in Chapter 6. This was applied to two-photon light-sheet microscopy data from zebrafish brains upon successful validation in silico. Lastly, Chapter 7 studies a particular phenomenon of interest where structure and inherent dynamics affect the function in a different but popular class of networks. A zero-mean noise-like prestrain is used to induce contractions in 1D Elastic Network Models. The analysis shows that the exact solution is difficult to probe analytically, while the mean behaviours of the networks are predictable and controllable by tuning the magnitude of the applied prestrain.
2021
Duccio Fanelli, Giacomo Innocenti
MALDIVE
Goal 9: Industry, Innovation, and Infrastructure
Ihusan Adam
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Descrizione: Final PhD Thesis
Tipologia: Tesi di dottorato
Licenza: Open Access
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1230776
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