Geometric and topological AI for molecular sciences

Опубликована: Янв. 1, 2023

Ginestra Bianconi (QML, UK).Throughout this Ph.D. journey, I am also grateful for the several seminar and conference opportunities where get to know topology geometry research

Язык: Английский

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Topology and dynamics of higher-order multiplex networks

arXiv (Cornell University), Год журнала: 2023, Номер unknown

Опубликована: Янв. 1, 2023

Higher-order networks are gaining significant scientific attention due to their ability encode the many-body interactions present in complex systems. However, higher-order have limitation that they only capture of same type. To address this limitation, we a mathematical framework determines topology multiplex and illustrates interplay between dynamics. Specifically, examine diffusion topological signals associated not nodes but also links higher-dimensional simplices simplicial complexes. We leverage on ubiquitous presence overlap couple dynamics among layers, introducing definition Hodge Laplacians Dirac operators. show spectral properties these operators determine Betti numbers. Our numerical investigation synthetic real (connectome, microbiome) complexes indicates coupling layers can either speed up or slow down signals. This is very general be applied study generic systems with multiple types. In particular, results might find applications brain which understood both multilayer higher-order.

Язык: Английский

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The mass of simple and higher-order networks

arXiv (Cornell University), Год журнала: 2023, Номер unknown

Опубликована: Янв. 1, 2023

We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology geometry. use discrete topological Dirac operator to define an action for massless self-interacting field inspired by Nambu-Jona Lasinio model. The network is strictly speaking this defined on network; it results chiral symmetry breaking model satisfies self-consistent gap equation. Interestingly, shown depends its spectral properties, topology, Due matter-antimatter observed harmonic modes operator, two possible definitions can be given. For both definitions, comes equation with difference among encoded in value bare mass. Indeed, determined either Betti number $β_0$ or $β_1$ network. provide numerical different networks, including random graphs, scale-free, real weighted collaboration networks. also discuss generalization these defining simplicial complexes. dependence considered geometry could lead interesting physics scenario which coupled dynamical evolution underlying structure.

Язык: Английский

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Complex Quantum Networks: a Topical Review

arXiv (Cornell University), Год журнала: 2023, Номер unknown

Опубликована: Янв. 1, 2023

These are exciting times for quantum physics as new technologies expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving ideal mathematical and computational framework capture the complexity of large interacting systems. Here we provide a comprehensive timely review rising field complex networks. On one side, this subject key harness potential networks in order design principles boost enhance algorithms technologies. other side can generation infer significant properties. The features fundamental research questions diverse designing shape Hamiltonians their corresponding phase diagram, taming many-body systems with theory, revealing how predict novel properties transitions, studying interplay between architecture, topology performance communication Our covers all these multifaceted aspects self-contained presentation aimed both network-curious physicists quantum-curious theorists. We that unifies along four main lines: network-generalized, quantum-applied, quantum-generalized quantum-enhanced. Finally draw attention connections lines, which lead opportunities discoveries interface science.

Язык: Английский

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