arXiv subjects

Ana P. Millán

Publications and source records attributed to Ana P. Millán.

13 recordsLinked to original sources

arXiv2026

Collective dynamics on higher-order networks

Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here we provide an overview of this rapidly growing field, and of the techniques that can be used to describe and analyze them. We focus in particular on new phenomena and challenges that emerge when nonpairwise interactions are considered. We conclude by discussing open questions and promising future directions on the collective dynamics of higher-order networks.

nlin.AO↗

arXiv2026

Neighbourhood topology unveils pathological hubs in the brain networks of epilepsy-surgery patients

Pathological hubs in the brain networks of epilepsy patients are hypothesized to drive seizure generation and propagation. In epilepsy-surgery patients, these hubs have traditionally been associated with the resection area (RA): the region removed during the surgery with the goal of stopping the seizures, and which is typically used as a proxy for the epileptogenic zone. However, recent studies hypothesize that pathological hubs may extend to the vicinity of the RA, potentially complicating post-surgical seizure control. Here we propose a neighbourhood-based analysis of brain organization to investigate this hypothesis. We exploit a large dataset of pre-surgical magnetoencephalography-derived whole-brain networks from 91 epilepsy-surgery patients. Our neighbourhood focus is 2-fold. Firstly, we propose a partition of the brain regions into three sets, namely resected nodes, their neighbours and the remaining network nodes. Secondly, we introduce generalized centrality metrics that describe the neighbourhood of each node, providing a regional measure of hubness. Our analyses reveal that both the RA and its neighbourhood present large hub status, but with significant variability across patients. For some, hubs appear in the RA; for others, in its neighbourhood. Moreover, this variability does not correlate with surgical outcome. These results highlight the potential of neighbourhood-based analyses to uncover novel insights into brain connectivity in brain pathologies, and the need for individualized studies, with large enough cohorts, that account for patient-specific variability.

physics.data-an↗

arXiv2025

Astrocyte-Mediated Higher-Order Control of Synaptic Plasticity

The dynamics of higher-order topological signals are increasingly recognized as a key aspect of the activity of complex systems. A paradigmatic example are synaptic dynamics: synaptic efficacy changes over time driven by different mechanisms. Beyond traditional node-driven short-term plasticity mechanisms, the role of astrocyte modulation through higher-order interactions, in the so-called tripartite synapse, is increasingly recognized. However, the competition and interplay between node-driven and higher-order mechanisms have yet to be considered. Here, we introduce a simple higher-order model of the tripartite synapse accounting for astrocyte-synapse-neuron interactions in short-term plasticity. In the model, astrocyte gliotransmission and pre-synaptic intrinsic facilitation mechanisms jointly modulate the probability of neurotransmitter release at the synapse, generalizing previous short-term plasticity models. We investigate the implications of such mechanisms in a minimal recurrent motif -- a directed ring of three excitatory leaky integrate-and-fire neurons -- where one neuron receives external stimulation that propagates through the circuit. Due to its strong recurrence, the circuit is highly prone to self-sustained activity, which can make it insensitive to external input. By introducing higher-order interactions among different synapses through astrocyte modulation, we show that higher-order modulation robustly stabilizes circuit dynamics and expands the parameter space that supports stimulus-driven activity. Our findings highlight a plausible mechanism by which astrocytes can reshape effective connectivity and enhance information processing through higher-order structural interactions -- even in the simplest recurrent circuits.

q-bio.NC↗

arXiv2025

On the robustness of exoplanet atmospheric detections: insights from extensive simulations

The classical picture of our Solar System being the archetypal outcome of planet formation has been rendered obsolete by the astonishing diversity of extrasolar-system architectures. From rare hot-Jupiters to abundant super-Earths and sub-Neptunes, most detected exoplanets have no analogs in our system, and their interior and atmospheric compositions remain largely unknown. Fortunately, new methodologies enable us to analyze exoplanet atmospheres, inferring their compositions, temperatures, dynamics, and even formation pathways. Specifically, ground-based high-resolution Doppler spectroscopy (HRDS) can disentangle spectral-line profiles of weak exo-atmospheric signals from the dominating features of Earth's atmosphere in the observed flux. For over a decade, HRDS has focused on hot Jupiters (close-orbiting gas giants) due to their high signal-to-noise ratio, which makes them ideal laboratories for advancing our knowledge. However, there have been concerns regarding potential biases in exo-atmospheric-detection methods, hindering comparative planetology. Here we propose a modeling framework based on extensive simulations of HRDS exo-atmospheric observations to systematically explore in-silico underlying biases in commonly-used pipelines, particularly under the presence of observational noise. Our findings show that exo-atmospheric detection-significances are highly contingent on details of the analysis-pipeline used, with different techniques responding differently to noise: A given technique may fail to recover a true-signal that is detected by another. Noise effects in the computed significances are non-trivial and pipeline-dependent. Statistical analyses provide a complementary tool to contextualize signal-significances, which will gain in relevance as we move towards studying the atmospheres of smaller, potentially habitable exoplanets with even weaker signals.

astro-ph.EP↗

arXiv2024

Spatio-temporal activity patterns induced by triadic interactions in an in silico neural medium

Triadic interactions are general mechanisms by which a node or neuron can regulate directly the link or synapse between other two neurons. The regulation takes place in a familiar way by either depressing or facilitating synaptic transmission. Such interactions are ubiquitous in neural systems, accounting for axo-axonic synapses and tripartite synapses mediated by astrocytes, for instance, and have been related to neuronal and synaptic processes at different time-scales, including short and long-term synaptic plasticity. In the field of network science, triadic interactions have been shown to produce complex spatio-temporal patterns of connectivity. Here, we investigate the emergent behavior of an in silico neural medium constituted by a population of leaky integrate-and-fire neurons with triadic interactions. We observe that, depending on relevant parameters defining triadic interactions, different activity patterns emerge. These include i) a silent phase, ii) a low-activity phase in which complex spatio-temporal patterns of low neuronal firing rate emerge that propagate through the medium, iii) a high-activity phase characterized by complex spatio-temporal patterns of high neuronal firing rate that propagate through the neural medium as waves of high firing activity over a bulk of low activity neurons, and iv) a pseudo-blinking phase in which the neural medium switches between high and low activity states, in a similar fashion to up/down state transitions. Here we analyse in depth the features of such patterns and relate our findings to the recently proposed model of triadic percolation.

q-bio.NC↗

arXiv2023

Triadic percolation induces dynamical topological patterns in higher-order networks

Triadic interactions are higher-order interactions that occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axon-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully-fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time-dependent as in neuroscience.

nlin.AO↗

arXiv2021

Complex networks with tuneable dimensions as a universality playground

Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter for universality, the spectral dimension. For this purpose, we construct a complex network model where the probability of a bond between two nodes is proportional to a power law of the nodes' distances. By explicit computation we prove that the spectral dimension for this model can be tuned continuously from $1$ to infinity, and we discuss related network connectivity measures. We propose our model as a tool to probe universal behaviour on inhomogeneous structures and comment on the possibility that the universal behaviour of correlated models on such networks mimics the one of continuous field theories in fractional Euclidean dimensions.

cond-mat.stat-mech↗

arXiv2020

Explosive higher-order Kuramoto dynamics on simplicial complexes

The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Kuramoto model which describes the interactions between oscillators placed not only on nodes but also on links, triangles, and so on. We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.

nlin.AO↗

arXiv2020

The shape of memory in temporal networks

Temporal networks are widely used models for describing the architecture of complex systems. Network memory -- that is the dependence of a temporal network's structure on its past -- has been shown to play a prominent role in diffusion, epidemics and other processes occurring over the network, and even to alter its community structure. Recent works have proposed to estimate the length of memory in a temporal network by using high-order Markov models. Here we show that network memory is inherently multidimensional and cannot be meaningfully reduced to a single scalar quantity. Accordingly, we introduce a mathematical framework for defining and efficiently estimating the microscopic shape of memory, which fully characterises how the activity of each link intertwines with the activities of all other links. We validate our methodology on a wide range of synthetic models of temporal networks with tuneable memory, and subsequently study the heterogeneous shapes of memory emerging in various real-world networks.

physics.soc-ph↗

arXiv2019

Growth strategy determines network performance

The interplay between structure and function is crucial in determining some emerging properties of many natural systems. Here we use an adaptive neural network model inspired in observations of synaptic pruning that couples activity and topological dynamics and reproduces experimental temporal profiles of synaptic density, including an initial transient period of relatively high synaptic connectivity. Using a simplified framework, we prove that the existence of this transient is critical in providing ordered stationary states that have the property of being able to store stable memories. In fact, there is a discontinuous phase transition between the ordered memory phase and a disordered one as a function of the initial transient synaptic density. We also show that intermediate synaptic density values are optimal in order to obtain these stable memory states with a minimum energy consumption, and that ultimately it is the transient heterogeneity in the network what determines the stationary state. Our results here could explain why the pruning curves observed in actual brain areas present their characteristic temporal profiles and, eventually, anomalies such as autism and schizophrenia associated, respectively, with a deficit or an excess of pruning.

physics.soc-ph↗

arXiv2019

Concurrence of form and function in developing networks and its role in synaptic pruning

A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of synapses. A feedback loop then arises leading to two qualitatively different types of behaviour. In one, the network structure becomes heterogeneous and dissasortative, and the system displays good memory performance; furthermore, the structure is optimised for the particular memory patterns stored during the process. In the other, the structure remains homogeneous and incapable of pattern retrieval. These findings provide an inspiring picture of brain structure and dynamics, are compatible with experimental results on early brain development, and may help to explain synaptic pruning. Other evolving networks -- such as those of protein interaction -- might share the basic ingredients for this feedback loop and other questions, and indeed many of their structural features are as predicted by our model.

nlin.AO↗

arXiv2019

Synchronization in Network Geometries with Finite Spectral Dimension

Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model. We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater than two. We numerically test our analytical predictions on the recently introduced model of network geometry called Complex Network Manifolds which displays a tunable spectral dimension.

cond-mat.dis-nn↗

arXiv2018

Complex Network Geometry and Frustrated Synchronization

The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the theoretical point of view. Here we reveal the rich interplay between network geometry and synchronization of coupled oscillators in the context of a simplicial complex model of manifolds called Complex Network Manifold. The networks generated by this model combine small world properties (infinite Hausdorff dimension) and a high modular structure with finite and tunable spectral dimension. We show that the networks display frustrated synchronization for a wide range of the coupling strength of the oscillators, and that the synchronization properties are directly affected by the spectral dimension of the network.

cond-mat.dis-nn↗