arXiv subjects

Elkaïoum M. Moutuou

Publications and source records attributed to Elkaïoum M. Moutuou.

5 recordsLinked to original sources

arXiv2026

Graphs as focal interaction systems in higher-order dynamics

Graphs and hypergraphs are commonly distinguished by the order of the relations they represent, with graphs encoding pairwise relations and hypergraphs encoding interactions among arbitrary groups. We show that, for node-update dynamics, a more natural viewpoint is to regard a graph as a collection of focal neighbourhoods, each centered on a vertex and consisting of the vertex and its neighbours. From this perspective, hypergraphs naturally generalise graph neighbourhoods by allowing arbitrary interaction domains without requiring a distinguished focal node. This viewpoint also clarifies the relationship between graph and hypergraph dynamical models. Although sufficiently general graph-based node functions can reproduce the dynamics of higher-order interactions, such dynamical equivalence does not imply equivalence of the underlying interaction structures. Graph representations may encode higher-order organisation implicitly in their functions while losing the explicit grouping, roles, and symmetries carried by hyperedges. We therefore distinguish dynamical expressivity from structural representation and show that hypergraphs provide a generalisation of graph-based interaction domains even when their dynamics can be emulated by graph models.

physics.soc-ph↗

arXiv2026

Weight geometry governs functional memory in complex systems

Complex systems, from gene regulatory networks to neural circuits and ecological food webs, exhibit rich functional behaviour that topology alone does not capture. Yet functional complexity remains difficult to quantify independently of structural organisation. Here we introduce a thermodynamic framework in which functional complexity is characterised through the hierarchical organisation of functional memory, quantifying how the influence of past interactions is distributed and progressively compressed across scales. Across thirty-four empirical networks spanning biological, ecological, social, technological, and biophysical systems and several orders of magnitude in size and density, real interaction strengths organise functional memory at greater hierarchical depth than random weight assignment on the same topology in every domain studied. The framework further reveals that functional memory occupies a remarkably low-dimensional space, collapsing onto four recurrent dynamical organisations. Comparisons with null models that selectively perturb weighted transport geometry, mesoscale wiring, and directionality show that these structural ingredients play distinct roles: weighted transport geometry systematically governs memory depth, whereas mesoscale wiring organises memory across scales and directionality modulates the response of the cascade to structural perturbation. The same comparisons provide an operational criterion for determining whether network weights encode functionally meaningful structure beyond topology. These results establish weighted transport geometry as a primary organiser of functional memory and provide a quantitative framework for studying functional complexity in directed weighted networks.

cond-mat.dis-nn↗

arXiv2026

Thermodynamic connectivity reveals functional specialization and multiplex organization of extrasynaptic signaling

Neural communication operates on both fast synaptic transmission and slower, diffusive extrasynaptic signaling, yet how these two modes jointly organize brain function remains unclear. Here, using the complete synaptic and neuropeptidergic connectomes of \emph{Caenorhabditis elegans}, we develop a unified multiplex framework linking anatomical wiring to functional communication. We infer structure-derived functional connectivity from the synaptic connectome using equilibrium principles from statistical physics, yielding a probabilistic map of information flow across all synaptic pathways, and compare this functional layer directly with the extrasynaptic connectome. This reveals a principled functional specialization across four communication regimes: (i) a topology-dependent layer that reinforces and stabilizes synaptic motor circuits, (ii) a topology-resilient modulatory layer supporting global regulation and behavioral state control, (iii) a purely extrasynaptic network sustaining survival and homeostasis, and (iv) a purely synaptic regime mediating rapid, low-latency sensorimotor processing. Together, these findings reveal that synaptic and extrasynaptic signaling form complementary architectures optimized for speed, modulation, robustness, and survival, and provide a general strategy for integrating structural and modulatory connectomes to understand how distinct communication modes cooperate to sustain coherent brain function.

q-bio.NC↗

arXiv2025

Brain functions emerge as thermal equilibrium states of the connectome

A fundamental idea in neuroscience is that cognitive functions -- such as perception, learning, memory, and locomotion -- are shaped and constrained by the brain's structural organization. Despite significant progress in mapping and analyzing structural connectomes, the principles linking the brain's physical architecture to its functional capabilities remain elusive. Here, we introduce an algebraic quantum model to bridge this theoretical gap, offering new insights into the relationship between the connectome and emergent brain functions, while connecting structural data to functional predictions. Using the well-mapped C. elegans anatomical and extrasynaptic connectomes, we demonstrate that brain functions, defined as functional networks of a neural system, emerge as thermal equilibrium states of an algebraic quantum system derived from the graph algebra of the underlying directed multigraph. Specifically, these equilibrium states, characterized by the Kubo-Martin-Schwinger (KMS) formalism, reveal how individual neurons contribute to functional network formation. Our model illuminates the structure-function relationship in neural circuits through two key features: (1) a functional connectome that delineates topologically driven neuronal interactions and (2) an Integration Capacity (IC) index that quantifies how effectively neurons coordinate and modulate diverse information flows. Together, these features provide a statistical and mechanistic account of information flow and reveal how the network topology of the connectome predicts cognition and complex behaviors.

q-bio.NC↗

arXiv2023

Topology and spectral interconnectivities of higher-order multilayer networks

Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific collaboration. But describing such systems through a purely graph-theoretic formalism presupposes that the interactions that define the underlying infrastructures and support their functions are only pairwise-based; a strong assumption likely leading to oversimplifications. Indeed, most interdependent systems intrinsically involve higher-order intra- and inter-layer interactions. For instance, ecological systems involve interactions among groups within and in-between species, collaborations and citations link teams of coauthors to articles and vice versa, interactions might exist among groups of friends from different social networks, etc. While higher-order interactions have been studied for monolayer systems through the language of simplicial complexes and hypergraphs, a broad and systematic formalism incorporating them into the realm of multilayer systems is still lacking. Here, we introduce the concept of crossimplicial multicomplexes as a general formalism for modelling interdependent systems involving higher-order intra- and inter-layer connections. Subsequently, we introduce cross-homology and its spectral counterpart, the cross-Laplacian operators, to establish a rigorous mathematical framework for quantifying global and local intra- and inter-layer topological structures in such systems. When applied to multilayer networks, these cross-Laplacians provide powerful methods for detecting clusters in one layer that are controlled by hubs in another layer. We call such hubs spectral cross-hubs and define spectral persistence as a way to rank them according to their emergence along the cross-Laplacian spectra.

math.AT↗