Persistent Dirac for molecular representation

Wee, JunJie; Bianconi, Ginestra; Xia, Kelin

doi:10.1038/s41598-023-37853-z

Cited by 10 publications

(4 citation statements)

References 68 publications

(59 reference statements)

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“…100 Additionally, a persistent Dirac-based molecular representation proves capable of distinguishing between different material structures. 101 The de Rham-Hodge method may provide a multiscale analysis of homology manifolds, revealing transitions in the number of connected components, tunnels, or cavities. 102 Recurrent neural nets (RNNs) can recognize knot types as described by their homological invariants in polymer conformations.…”

Section: Graph Representationsmentioning

confidence: 99%

“…Persistent homology identifies topological structures that persist across various scales, corresponding to clusters or voids within the material system. , By examining the discrete Ricci curvature, which involves the eigenvalues of the Hodge Laplacian, on a molecular graph geodesic (representing the shortest graph path for information spreading), it is possible to predict protein–ligand binding affinity . Additionally, a persistent Dirac-based molecular representation proves capable of distinguishing between different material structures . The de Rham-Hodge method may provide a multiscale analysis of homology manifolds, revealing transitions in the number of connected components, tunnels, or cavities .…”

Section: Ann For Nanoscale Mixturesmentioning

confidence: 99%

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Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Nicolle,

Deng,

Ihme

et al. 2024

J. Chem. Inf. Model.

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Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the ’recomposition’ of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure–Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

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Section: Graph Representationsmentioning

confidence: 99%

Section: Ann For Nanoscale Mixturesmentioning

confidence: 99%

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Nicolle,

Deng,

Ihme

et al. 2024

J. Chem. Inf. Model.

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“…The proposed quantum algorithm is shown to display an exponential speed-up over the best known classical algorithms for calculating homology. Recently in [392,393] this approach has been extended also to propose a quantum algorithm for the calculation of persistent homology of simplicial complexes.…”

Section: Quantum Higher-order Network and The Topological Dirac Operatormentioning

confidence: 99%

Complex quantum networks: a topical review

Nokkala,

Piilo,

Bianconi

2024

J. Phys. A: Math. Theor.

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

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“…Recently, growing attention is addressed to the discrete topological Dirac operator [1,2], originally introduced in non-commutative geometry [3][4][5][6][7], and then used in quantum graphs [8][9][10][11][12][13][14][15] and in network theory [16][17][18][19][20][21]. On a network, the discrete topological Dirac operator is defined over topological spinors, which are the direct sum of zero-cochain and one-cochains.…”

Section: Introductionmentioning

confidence: 99%

The mass of simple and higher-order networks

Bianconi

2023

J. Phys. A: Math. Theor.

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We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu–Jona-Lasinio model. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry. Due to the breaking of the matter–antimatter symmetry observed for the harmonic modes of the discrete topological Dirac operator, two possible definitions of the network mass can be given. For both possible definitions, the mass of the network comes from a gap equation with the difference among the two definitions encoded in the value of the bare mass. Indeed, the bare mass can be determined either by the Betti number β 0 or by the Betti number β 1 of the network. We provide numerical results on the mass of different networks, including random graphs, scale-free, and real weighted collaboration networks. We also discuss the generalization of these results to higher-order networks, defining the mass of simplicial complexes. The observed dependence of the mass of the considered topological Dirac field with the topology and geometry of the network could lead to interesting physics in the scenario in which the considered Dirac field is coupled with a dynamical evolution of the underlying network structure.

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Persistent Dirac for molecular representation

Cited by 10 publications

References 68 publications

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Complex quantum networks: a topical review

The mass of simple and higher-order networks

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