Low-dimensional controllability of brain networks

PLoS Computational Biology, Год журнала: 2025, Номер 21(1), С. e1012691 - e1012691

Опубликована: Янв. 7, 2025

Identifying the driver nodes of a network has crucial implications in biological systems from unveiling causal interactions to informing effective intervention strategies. Despite recent advances control theory, results remain inaccurate as number drivers becomes too small compared size, thus limiting concrete usability many real-life applications. To overcome this issue, we introduced framework that integrates principles spectral graph theory and output controllability project state into smaller topological space formed by Laplacian structure. Through extensive simulations on synthetic real networks, showed relatively low projected components can significantly improve accuracy. By introducing new low-dimensional metric experimentally validated our method N = 6134 human connectomes obtained UK-biobank cohort. Results revealed previously unappreciated influential brain regions, enabled draw directed maps between differently specialized cerebral systems, yielded insights hemispheric lateralization. Taken together, offered theoretically grounded solution deal with provided brain.

Язык: Английский

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Higher-order Laplacian renormalization

Nature Physics, Год журнала: 2025, Номер unknown

Опубликована: Фев. 24, 2025

Язык: Английский

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Generalized network density matrices for analysis of multiscale functional diversity

Physical review. E, Год журнала: 2023, Номер 107(4)

Опубликована: Апрель 20, 2023

The network density matrix formalism allows for describing the dynamics of information on top complex structures and it has been successfully used to analyze, e.g., a system's robustness, perturbations, coarse-graining multilayer networks, characterization emergent states, performing multiscale analysis. However, this framework is usually limited diffusion undirected networks. Here, overcome some limitations, we propose an approach derive matrices based dynamical systems theory, which encapsulating much wider range linear nonlinear richer classes structure, such as directed signed ones. We use our study response local stochastic perturbations synthetic empirical including neural consisting excitatory inhibitory links gene-regulatory interactions. Our findings demonstrate that topological complexity does not necessarily lead functional diversity, i.e., heterogeneous stimuli or perturbations. Instead, diversity genuine property cannot be deduced from knowledge features heterogeneity, modularity, presence asymmetries, properties system.

Язык: Английский

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An integrative dynamical perspective for graph theory and the analysis of complex networks

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2024, Номер 34(4)

Опубликована: Апрель 1, 2024

Built upon the shoulders of graph theory, field complex networks has become a central tool for studying real systems across various fields research. Represented as graphs, different can be studied using same analysis methods, which allows their comparison. Here, we challenge widespread idea that theory is universal tool, uniformly applicable to any kind network data. Instead, show many classical metrics-including degree, clustering coefficient, and geodesic distance-arise from common hidden propagation model: discrete cascade. From this perspective, metrics are no longer regarded combinatorial measures but spatiotemporal properties dynamics unfolded at temporal scales. Once seen model-based (and not purely data-driven) freely or intentionally replace cascade by other canonical models define new metrics. This opens opportunity design-explicitly transparently-dedicated analyses types choosing model matches individual constraints. In way, take stand topology cannot always abstracted independently shall jointly studied, key interpretability analyses. The perspective here proposed serves integrate into context both more recent defined in literature were, directly indirectly, inspired phenomena on networks.

Язык: Английский

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Diffusion capacity of single and interconnected networks

Nature Communications, Год журнала: 2023, Номер 14(1)

Опубликована: Апрель 18, 2023

Improving the understanding of diffusive processes in networks with complex topologies is one main challenges today's complexity science. Each network possesses an intrinsic potential that depends on its structural connectivity. However, diffusion a process not only this topological but also dynamical itself. Quantifying will allow design more efficient systems which it necessary either to weaken or enhance diffusion. Here we introduce measure, {\em capacity}, quantifies, through concept paths, element system, and also, system itself, propagate information. Among other examples, study heat model SIR demonstrate value proposed measure. We found, last case, capacity can be used as predictor evolution spreading process. In general, show provides tool evaluate performance systems, identify quantify modifications could improve mechanisms.

Язык: Английский

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A simplex path integral and a simplex renormalization group for high-order interactions ^*

Reports on Progress in Physics, Год журнала: 2024, Номер 87(8), С. 087601 - 087601

Опубликована: Июль 30, 2024

Modern theories of phase transitions and scale invariance are rooted in path integral formulation renormalization groups (RGs). Despite the applicability these approaches simple systems with only pairwise interactions, they less effective complex undecomposable high-order interactions (i.e. among arbitrary sets units). To precisely characterize universality interacting systems, we propose a simplex RG (SRG) as generalizations classic to heterogeneous interactions. We first formalize trajectories units governed by define integrals on corresponding simplices based propagator. Then, develop method integrate out short-range momentum space, accompanied coarse graining procedure functioning structure generated The proposed SRG, equipped divide-and-conquer framework, can deal absence ergodicity arising from sparse distribution renormalize system intertwined at

Язык: Английский

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Laplacian renormalization group: an introduction to heterogeneous coarse-graining

Journal of Statistical Mechanics Theory and Experiment, Год журнала: 2024, Номер 2024(8), С. 084002 - 084002

Опубликована: Авг. 2, 2024

Abstract The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification into relatively small set universality classes. RG is most powerful tool for investigating organizational scales within dynamic systems. However, application techniques to complex networks has presented significant challenges, primarily due intricate interplay on multiple scales. Existing approaches have relied hypotheses involving hidden geometries based embedding metric spaces. Here, we present practical overview recently introduced Laplacian (LRG) heterogeneous networks. First, brief that justifies use as natural extension well-known field theories analyze spatial disorder. We then draw an analogy traditional real-space procedures, explaining how LRG generalizes concept ‘Kadanoff supernodes’ block nodes span These supernodes help mitigate effects cross-scale small-world properties. Additionally, rigorously define procedure momentum space spirit Wilson RG. Finally, show different analyses evolution network properties along flow following structural changes when properly reduced.

Язык: Английский

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Measuring Entanglement in Physical Networks

Physical Review Letters, Год журнала: 2024, Номер 133(7)

Опубликована: Авг. 13, 2024

The links of a physical network cannot cross, which often forces the layout into nonoptimal entangled states. Here we define fabric as two-dimensional projection and propose average crossing number measure entanglement. We analytically derive dependence on density, link length, degree heterogeneity, community structure show that predictions accurately estimate entanglement both models real networks.

Язык: Английский

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Lattice physics approaches for neural networks

iScience, Год журнала: 2024, Номер 27(12), С. 111390 - 111390

Опубликована: Ноя. 15, 2024

Modern neuroscience has evolved into a frontier field that draws on numerous disciplines, resulting in the flourishing of novel conceptual frames primarily inspired by physics and complex systems science. Contributing this direction, we recently introduced mathematical framework to describe spatiotemporal interactions neurons using lattice theory, reference paradigm for theoretical particle physics. In note, provide concise summary basics aiming be intuitive interdisciplinary community. We contextualize our methods, illustrating how readily connect parameters formulation experimental variables well-known renormalization procedures. This synopsis yields key concepts needed neural networks Such classes methods are attention-worthy an era blistering improvements numerical computations, as they can facilitate relating observation activity generative models underpinned physical principles.

Язык: Английский

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Quantum entropy couples matter with geometry

Journal of Physics A Mathematical and Theoretical, Год журнала: 2024, Номер 57(36), С. 365002 - 365002

Опубликована: Авг. 14, 2024

Abstract We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate network quantum entropy its metric. Specifically we an action having two contributions. first contribution proportional logarithm volume associated by In vacuum this determines geometry. second relative between metric and induced gauge fields. defined in terms topological spinors Dirac operators. spinors, nodes, edges higher-dimensional cells, encode operators act depend as well via version minimal substitution. derive coupled dynamical equations metric, fields, providing information principle obtain field curved space.

Язык: Английский

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