arXiv subjects

Ginestra Bianconi

Publications and source records attributed to Ginestra Bianconi.

At least 19 recordsLinked to original sources

arXiv2026

Cup and Cap Topological Neural Network

Topological Deep Learning (TDL) is designed to learn features associated with higher-dimensional simplices including not only nodes but also edges, triangles and so on. However, most TDL approaches, being based on boundary operators and Hodge Laplacians, have the limitation that features and signals cannot be lifted or lowered across more than one dimension per layer. To overcome this limitation, in this work, we propose the adoption of the cup and cap products. Specifically, we formulate the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (or 0-cochains) by taking into account their many-body interactions (e.g. triangles) present in the data. We validate CCNN by assessing its performance on the TopoBench datasets, revealing its competitiveness with respect to other simplicial complex neural networks.

cond-mat.dis-nn↗

arXiv2026

$(k,n)$-core percolation on hypergraphs with anchor nodes

Hypergraphs describe higher-order interactions that involve more than a pair of nodes. A characteristic feature of hypergraphs is that their robustness can be strongly affected by the different roles of the nodes. Indeed, some nodes might be essential for a hyperedge's function, while others might not be. The loss of a single essential node completely destroys the hyperedge it belongs to, while the loss of a non-essential node has a buffering effect, inducing the hyperedge to simply reduce its size. In order to capture this phenomenology, we formulate a comprehensive theoretical framework for $(k,n)$-core percolation models on hypergraphs, where each node of a hyperedge is an anchor with probability $θ$, and a hyperedge fails if an anchor node fails. Hypergraph $(k,n)$-core percolation problems can be classified as first-neighbor and second-neighbor problems, indicating that in the pruning process the connectivity is ensured only by the state of the first neighbors or the second neighbors, respectively. We derive self-consistency equations for first-neighbor and second-neighbor (node- and hyperedge-based) pruning processes, and obtain the size of the giant $(k,n)$-core. We obtain the phase diagram, including continuous and discontinuous transitions, and confirm our theory on random hypergraphs using numerical simulations. The results show how the heterogeneity of the nodes' functional roles and the extended range of the interactions affect the robustness of higher-order networks.

physics.soc-ph↗

arXiv2026

Topological Dirac cluster synchronization on directed hypergraphs

Topological higher-order synchronization reveals collective phenomena demonstrating how topology shapes dynamics, yet providing a general theoretical framework for designing and controlling dynamical states on higher-order networks remains a challenge of the field. Here we propose a dynamical systems framework for topological cluster synchronization on directed hypergraphs that can be used to design synchronization patterns on nodes and hyperedges of directed hypergraphs. By encoding oriented hyperedges into the hypergraph topological Dirac Hamiltonian, we obtain a spectrum whose isolated eigenstates correspond to distinct topological synchronization cluster states defined jointly on nodes and hyperedges. By selecting any isolated eigenstate, the system can be driven toward the associated dynamical state reflecting a specific partition of the hypergraph without modifying the underlying hypergraph structure. We numerically demonstrate the ability to design different topological cluster synchronization states on directed-hypergraph block models and empirical systems-including higher-order contact networks and the ABIDE functional brain network. Our results establish a general and interpretable route for controlling collective dynamics in directed higher-order systems.

physics.soc-ph↗

arXiv2026

Thermodynamics of the Gravity from Entropy theory

The Gravity from Entropy (GfE) action posits that gravity that is fundamentally given by the information encoded in the interplay between matter and geometry. The GfE Lagrangian is given by the Geometric Quantum Relative Entropy (GQRE) between the physical metric and the metric induced by matter and curvature, leading to modified gravitational field equations with an emergent dynamical effective dark energy term, which reduce to Einstein's equations in the low energy, small curvature limit. Adopting a thermodynamic viewpoint, we identify the GfE energy density with this emergent effective dark energy term. For homogeneous and isotropic FRW spacetimes, we show that GfE universes admit a thermal description: locally, they are characterized by $k$-temperatures and $k$-pressures satisfying a first law of GfE thermodynamics. In the low energy, small curvature regime with perfect-fluid matter and radiation, GfE solutions are well approximated by Friedmann cosmologies. We show that, while the total GQRE per unit volume does not increase, consistent with its nature as a relative entropy, the total entropy of GfE universes is non-decreasing in time. These results provide a thermodynamic interpretation of GfE cosmologies and of general relativity (GR) itself, recovered in the low energy, small curvature limit of the theory, offering a framework to reconcile local order and complexity with the global increase of entropy in the universe.

gr-qc↗

arXiv2026

Learning Dirac Spectral Transforms for Topological Signals

The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain interactions, in contrast to conventional Hodge-Laplacian eigenmodes that operate within a single topological dimension. In this paper, we compare the two alternatives in terms of the distortion/sparsity trade-off and we show how an overcomplete basis built concatenating the two dictionaries can provide better performance with respect to each approach. Then, we propose a parameterized nonredundant transform whose eigenmodes incorporate a mode-specific mass parameter that captures the interplay between node and edge modes. Interestingly, we show that learning the mass parameters from data makes the proposed transform able to achieve the best distortion-sparsity tradeoff with respect to both complete and overcomplete bases.

eess.SP↗

arXiv2026

Directed extended-range percolation

While for standard percolation directionality is known to increase the combinatorial complexity of percolation, here we show that when connectivity is ensured by paths of length $R\geq 2$, network directionality, impeding backtracking, can significantly reduce the complexity of percolation. To illustrate this finding, we introduce Directed Extended-Range Percolation (DERP), defined directed networks with non-reciprocal edges, motivated by applications in quantum communication. In this framework, message transmission is enabled between trusted nodes separated by a directed path of length at most $R$. Using a message-passing approach, we show that directionality enables an exact determination of the percolation threshold and the anomalous critical indices on locally tree-like structures. On random directed networks we find that the critical behavior of DERP depends sensitively on degree correlations. These analytical predictions are corroborated by extensive Monte Carlo simulations, highlighting the profound impact of directionality and correlations on long-range connectivity in complex networks.

cond-mat.dis-nn↗

arXiv2026

Feedback percolation on complex networks

Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified framework that dynamically couples the microscopic activation probability to the macroscopic size of the giant component. We show that this simple feedback mechanism produces a rich variety of behaviors both analytically and numerically. Depending on the feedback functions, the system exhibits explosive discontinuous jumps, hybrid transitions, limit-cycle oscillations, and routes to chaos, absent in classical percolation. Our findings establish that macroscopic feedback provides a unifying physical mechanism for phenomena ranging from self-regulating oscillations to systemic infrastructure collapse.

cond-mat.stat-mech↗

arXiv2026

Topology and higher-order global synchronization on directed and hollow simplicial and cell complexes

Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating higher-order topological dynamics where dynamical variables are not only associated with nodes, but also with edges, triangles, and higher-order simplices and cells. Global Topological Synchronization (GTS) refers to the dynamical state in which identical oscillators associated with higher-dimensional simplices and cells oscillate in unison. On standard unweighted and undirected complexes this dynamical state can be achieved only under strict topological and combinatorial conditions on the underlying discrete support. In this work we consider generalized higher-order network representations including directed and hollow complexes. Based on an in depth investigation of their topology defined by their associated algebraic topology operators and Betti numbers, we determine under which conditions GTS can be observed. We show that directed complexes always admit a global topological synchronization state independently of their topology and structure. However, we demonstrate that for directed complexes this dynamical state cannot be asymptotically stable. While hollow complexes require more stringent topological conditions to sustain global topological synchronization, these topologies can favor both the existence and the stability of global topological synchronization with respect to undirected and unweighted complexes.

physics.soc-ph↗

arXiv2026

Triadic percolation on multilayer networks

Triadic interactions are special types of higher-order interactions that occur when regulator nodes modulate the interactions between other two or more nodes. In presence of triadic interactions, a percolation process occurring on a single-layer network becomes a fully-fledged dynamical system, characterized by period-doubling and a route to chaos. Here, we generalize the model to multilayer networks and name it as the multilayer triadic percolation (MTP) model. We find a much richer dynamical behavior of the MTP model than its single-layer counterpart. MTP displays a Neimark-Sacker bifurcation, leading to oscillations of arbitrarily large period or pseudo-periodic oscillations. Moreover, MTP admits period-two oscillations without negative regulatory interactions, whereas single-layer systems only display discontinuous hybrid transitions. This comprehensive model offers new insights on the importance of regulatory interactions in real-world systems such as brain networks, climate, and ecological systems.

nlin.AO↗

arXiv2026

Directionality and node heterogeneity reshape criticality in hypergraph percolation

Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of others only weakens interactions. Metabolic reaction networks offer an intuitive example of such asymmetric dependencies. Here we develop a message-passing and statistical mechanics framework for percolation in directed hypergraphs that explicitly incorporates directionality and node heterogeneity. Remarkably, we show that these hypergraph features have a fundamental effect on the critical properties of hypergraph percolation, reshaping criticality in a way that depends on network structure. Specifically, we derive anomalous critical exponents that depend on whether node or hyperedge percolation is considered in maximally correlated, heavy-tailed regimes. These theoretical predictions are validated on synthetic hypergraph models and on a real directed metabolic network, opening new perspectives for the characterization of the robustness and resilience of real-world directed, heterogeneous higher-order networks.

cond-mat.dis-nn↗

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

Designing topological cluster synchronization patterns with the Dirac operator

Designing stable cluster synchronization patterns is a fundamental challenge in nonlinear dynamics of networks with great relevance to understanding neuronal and brain dynamics. So far, cluster synchronization has been studied exclusively in a node-based dynamical approach, according to which oscillators are associated only with the nodes of the network. Here, we propose a topological synchronization dynamics model based on the use of the Topological Dirac operator, which allows us to design cluster synchronization patterns for topological oscillators associated with both nodes and edges of a network. In particular, by modulating the ground state of the free energy associated with the dynamical model, we construct topological cluster synchronization patterns. These are aligned with the eigenstates of the Topological Dirac Equation that provide a very useful decomposition of the dynamical state of node and edge signals associated with the network. We use linear stability analysis to predict the stability of the topological cluster synchronization patterns and provide numerical evidence of the ability to design several stable topological cluster synchronization states on real connectome data, random graphs, and on stochastic block models.

nlin.AO↗

arXiv2025

Beyond holography: the entropic quantum gravity foundations of image processing

Recently, thanks to the development of artificial intelligence (AI) there is increasing scientific attention in establishing the connections between theoretical physics and AI. Traditionally, these connections have been focusing mostly on the relation between string theory and image processing and involve important theoretical paradigms such as holography. Recently G. Bianconi has formulated the Gravity from Entropy (GfE) approach to quantum gravity in which gravity is derived from the geometric quantum relative entropy (GQRE) between two metrics associated with the Lorentzian spacetime. Here it is demonstrated that the famous Perona-Malik algorithm for image processing is the gradient flow that maximizes the GfE action in its simple warm-up scenario. Specifically, this algorithm is the outcome of the maximization of the GfE action calculated between two Euclidean metrics: the one of the support of the image and the one induced by the image. As the Perona-Malik algorithm is known to preserve sharp contours, this implies that the GfE action, does not in general lead to uniform images upon iteration of the gradient flow dynamics as it would be intuitively expected from entropic actions maximising classical entropies. Rather, the outcome of the maximization of the GfE action is compatible with the preservation of complex structures. These results provide the geometrical and information theory foundations for the Perona-Malik algorithm and might contribute to establish deeper connections between GfE, machine learning and brain research.

cond-mat.dis-nn↗

arXiv2025

Mining higher-order triadic interactions

Complex systems often involve higher-order interactions which require us to go beyond their description in terms of pairwise networks. Triadic interactions are a fundamental type of higher-order interaction that occurs when one node regulates the interaction between two other nodes. Triadic interactions are found in a large variety of biological systems, from neuron-glia interactions to gene-regulation and ecosystems. However, triadic interactions have so far been mostly neglected. In this article, we propose {the Triadic Perceptron Model (TPM)} that demonstrates that triadic interactions can modulate the mutual information between the dynamical state of two linked nodes. Leveraging this result, we formulate the Triadic Interaction Mining (TRIM) algorithm to extract triadic interactions from node metadata, and we apply this framework to gene expression data, finding new candidates for triadic interactions relevant for Acute Myeloid Leukemia. Our work reveals important aspects of higher-order triadic interactions that are often ignored, yet can transform our understanding of complex systems and be applied to a large variety of systems ranging from biology to climate.

nlin.AO↗

arXiv2025

Topological network analysis using a programmable photonic quantum processor

Understanding topological features in networks is crucial for unravelling complex phenomena across fields such as neuroscience, condensed matter, and high-energy physics. However, identifying higher-order topological structures -- such as $k$-cliques, fundamental building blocks of complex networks -- remains a significant challenge. Here we develop a universal programmable photonic quantum processor that enables the encoding of arbitrary complex-weight networks, providing a direct pathway to uncovering their topological structures. We demonstrate how this quantum approach can identify weighted $k$-cliques and estimate Betti numbers by leveraging the Gaussian boson sampling algorithm's ability to preferentially select high-weight, dense subgraphs. The unique capabilities of our programmable quantum processor allow us to observe topological phase transitions and identify clique percolation phenomena directly from the entropy of the sampling results. These findings showcase how photonic quantum computing can be applied to analyse the topological characteristics of real-world complex networks, opening new possibilities for quantum-enhanced data analysis.

quant-ph↗

arXiv2025

The quantum relative entropy of the Schwarzschild black-hole and the area law

The area law obeyed by the thermodynamic entropy of black holes is one of the fundamental results relating gravity to statistical mechanics. In this work we provide a derivation of the area law for the quantum relative entropy of the Schwarzschild black-hole for arbitrary Schwarzschild radius. The quantum relative entropy between the metric of the manifold and the metric induced by the geometry and the matter field has been proposed in G. Bianconi "Gravity from entropy", Phys. Rev. D (2025) as the action for entropic quantum gravity leading to modified Einstein equations. The quantum relative entropy generalizes Araki entropy and treats the metrics between zero-forms, one-forms, and two-forms as quantum operators. Although the Schwarzschild metric is not an exact solution of the modified Einstein equations of the entropic quantum gravity, it is an approximate solution valid in the low coupling, small curvature limit. Here we show that the quantum relative entropy associated to the Schwarzschild metric obeys the area law for large Schwarzschild radius. We provide a full statistical mechanics interpretation of the results.

gr-qc↗

arXiv2025

Global Topological Dirac Synchronization

Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network display the same dynamics as received great attention in network theory. Here we propose and investigate Global Topological Dirac Synchronization on higher-order networks such as cell and simplicial complexes. This is a state where oscillators associated to simplices and cells of arbitrary dimension, coupled by the Topological Dirac operator, operate at unison. By combining algebraic topology with non-linear dynamics and machine learning, we derive the topological conditions under which this state exists and the dynamical conditions under which it is stable. We provide evidence of 1-dimensional simplicial complexes (networks) and 2-dimensional simplicial and cell complexes where Global Topological Dirac Synchronization can be observed. Our results point out that Global Topological Dirac Synchronization is a possible dynamical state of simplicial and cell complexes that occur only in some specific network topologies and geometries, the latter ones being determined by the weights of the higher-order networks

cond-mat.stat-mech↗

arXiv2025

Gravity from entropy

Gravity is derived from an entropic action coupling matter fields with geometry. The fundamental idea is to relate the metric of Lorentzian spacetime to a quantum operator, playing the role of an renormalizable effective density matrix and to describe the matter fields topologically, according to a Dirac-Kähler formalism, as the direct sum of a zero-form, a one-form and a two-form. While the geometry of spacetime is defined by its metric, the matter fields can be used to define an alternative metric, the metric induced by the matter fields, which geometrically describes the interplay between spacetime and matter. The proposed entropic action is the quantum relative entropy between the metric of spacetime and the metric induced by the matter fields. The modified Einstein equations obtained from this action reduce to the Einstein equations with zero cosmological constant in the regime of low coupling. By introducing the G-field, which acts as a set of Lagrangian multipliers, the proposed entropic action reduces to a dressed Einstein-Hilbert action with an emergent small and positive cosmological constant only dependent on the G-field. The obtained equations of modified gravity remain second order in the metric and in the G-field. A canonical quantization of this field theory could bring new insights into quantum gravity while further research might clarify the role that the G-field could have for dark matter.

gr-qc↗