Adaptive dynamical networks

Berner, Rico; Gross, Thilo; Kuehn, Christian; Kurths, Jürgen; Yanchuk, Serhiy

doi:10.1016/j.physrep.2023.08.001

Cited by 29 publications

(9 citation statements)

References 465 publications

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“…is put inside an additional saturation function tanh for M > 10, to keep the output bounded between 0 and 1. NARMA tasks with three different memory requirements are considered in this study, M ∈ [5,10,15]. The goal here is to emulate the NARMA output sequence.…”

Section: Methodsmentioning

confidence: 99%

Evolution beats random chance: Performance-dependent network evolution for enhanced computational capacity

Yadav,

Sinha,

Stender

2024

Preprint

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The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we investigate how optimal and specific network structures form to efficiently solve distinct tasks using a novel framework of performance-dependent network evolution, leveraging reservoir computing principles. Our study demonstrates that task-specific minimal network structures obtained through this framework consistently outperform networks generated by alternative growth strategies and Erdős-Rényi random networks. Evolved networks exhibit unexpected sparsity and adhere to scaling laws in node-density space while showcasing a distinctive asymmetry in input and information readout nodes distribution. Consequently, we propose a heuristic for quantifying task complexity from performance-dependently evolved networks, offering valuable insights into the evolutionary dynamics of network structure-function relationship. Our findings not only advance the fundamental understanding of process-specific network evolution but also shed light on the design and optimization of complex information processing mechanisms, notably in machine learning.

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Section: Methodsmentioning

confidence: 99%

Evolution beats random chance: Performance-dependent network evolution for enhanced computational capacity

Yadav,

Sinha,

Stender

2024

Preprint

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“…where in the last inequality we used the bound (9). Hence, by means of the Dominated Convergence Theorem, as we let R → ∞ in (10), we obtain…”

Section: 1mentioning

confidence: 99%

“…Adaptive network models have been used to study a wide range of problems from neuroscience to game theory and economics. We refer the reader to the survey paper [10] for an introduction to the field of adaptive networks and their further potential applications.…”

Section: Introductionmentioning

confidence: 99%

On evolution PDEs on co-evolving graphs

Esposito,

Mikolás

2024

DCDS

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We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the dynamics on the graph. This is relevant in applications to opinion dynamics and transportation networks. Existence and uniqueness of suitably defined solutions is obtained by exploiting the Banach fixed-point theorem. We consider different time scales for the evolution of the weight function: faster and slower than the flow defined on the graph. The former leads to graphs whose weight functions depend nonlocally on the density configuration at the vertices, while the latter induces static graphs. Furthermore, we prove a discrete-to-continuum limit for the PDEs under study as the number of vertices converges to infinity.

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“…A feature of such networks is the change in the strength of connections between nodes depending on their current states. In general, the dynamics of adaptive networks can be represented as a two-level process, consisting of the coevolution of the states of network elements and interelement connections [4,5]. Adaptive network models appear in the description of processes in a wide range of applications, including physics, chemistry, biology, neuroscience, sociology and other fields (see reviews [6,7] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Transient Phase Clusters in a Two-Population Network of Kuramoto Oscillators with Heterogeneous Adaptive Interaction

Кasatkin

Nekorkin

2023

Entropy

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Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character of adaptive couplings influences the emergence of new scenarios in the collective behavior of networks. Within the framework of a two-population network of coupled phase oscillators, we analyze the role of various factors of heterogeneous interaction, such as the rules of coupling adaptation and the rate of their change in the formation of various types of coherent behavior of the network. We show that various schemes of heterogeneous adaptation lead to the formation of transient phase clusters of various types.

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Adaptive dynamical networks

Cited by 29 publications

References 465 publications

Evolution beats random chance: Performance-dependent network evolution for enhanced computational capacity

Evolution beats random chance: Performance-dependent network evolution for enhanced computational capacity

On evolution PDEs on co-evolving graphs

Transient Phase Clusters in a Two-Population Network of Kuramoto Oscillators with Heterogeneous Adaptive Interaction

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