arXiv subjects

Tommaso Gili

Publications and source records attributed to Tommaso Gili.

At least 19 recordsLinked to original sources

arXiv2026

Assessing imbalance in signed brain networks

Many complex systems - be they financial, natural, or social - are composed of units - such as stocks, neurons, or agents - whose joint activity can be represented as a multivariate time series. An issue of both practical and theoretical importance concerns the possibility of inferring the presence of a static relationship between any two units solely from their dynamic behaviour. The present contribution aims at tackling such an issue within the framework of traditional hypothesis testing: briefly speaking, our suggestion is that of linking any two units if behaving in a sufficiently similar way. To achieve such a goal, we project a multivariate time series onto a signed graph by (1) comparing the empirical properties of the former with those expected under a suitable benchmark and (2) linking any two units with a positive (negative) edge in case the corresponding series shares a significantly large number of concordant (discordant) values. To define our benchmarks, we adopt an information-theoretic approach that is rooted into the constrained maximisation of Shannon entropy, a procedure inducing an ensemble of multivariate time series that preserves some of the empirical properties on average, while randomising everything else. We showcase the possible applications of our method by addressing one of the most timely issues in the domain of neurosciences, i.e. that of determining if brain networks are frustrated or not, and, if so, to what extent. As our results suggest, this is indeed the case, with the major contribution to the underlying negative subgraph coming from the subcortical regions (and, to a lesser extent, from the limbic ones). At the mesoscopic level, the minimisation of the Bayesian information criterion, instantiated with the signed stochastic block model, reveals that brain regions gather into modules aligning with the statistical variant of the relaxed balance theory.

physics.soc-ph↗

arXiv2026

Network-based drug repurposing for MYH9-related nephritis

Using tools from network theory, we analyze the organization of a MYH9-oriented drug-like library in chemical space using a multi-descriptor framework. The dataset is drawn from ZINC, a publicly available database of commercially accessible compounds curated for virtual screening and drug discovery. Starting from 6004 molecules, preprocessing yields 5000 structurally valid and descriptor-complete compounds. Similarity is defined via Tanimoto distance on Morgan fingerprints and single-descriptor distances for xLogP, HBD, HBA, molecular weight, and rotatable bonds. For each representation, we construct k-nearest-neighbor networks and identify communities using the Louvain-Leiden algorithm. All networks exhibit highly significant modularity (Q=0.91-0.99) relative to degree-preserving null models, demonstrating pronounced nonrandom chemical organization across descriptors. Cross-descriptor robustness is quantified through a co-clustering matrix over 1.25 X 10^7 molecular pairs, measuring how consistently compound pairs co-occur within the same community across descriptor-specific networks. Although most pairs show limited agreement, a sparse high-consensus core emerges, highlighting the complementarity of the descriptors. Minimum spanning trees derived from structural and consensus similarities reveal distinct backbone topologies: a scaffold-driven, sparse structure versus a compact, hub-rich consensus network. Betweenness centrality on these backbones identifies compounds that are both structurally central and descriptor-balanced. These results provide a statistically validated network representation of chemical space and a principled strategy to extract consensus-stable compounds for downstream screening.

physics.bio-ph↗

arXiv2026

Topological Symmetry Breaking in Antagonistic Dynamics

A dynamic concordia discors, a finely tuned equilibrium between opposing forces, is hypothesized to drive historical transformations. Similarly, a precise interplay of excitation and inhibition, often approximated by an 80:20 ratio, underlies the normal functionality of neural systems. In artificial neural networks, reinforcement learning enables the fine-tuning of internal signed connections, optimizing adaptive responses to complex stimuli and ensuring robust performance. Engineered systems with antagonistic interactions remain comparatively unexplored, particularly because their emergent phases are closely linked to frustration mechanisms in the underlying network. In this context, spin-glass theory has shown how apparently uncontrollable non-ergodic and chaotic behavior can arise from the complex interplay of competing interactions and frustration among units, leading to multiple metastable states that prevent the system from exploring all accessible configurations over time. Here, we show how topology constrains dynamics in systems with antagonistic interactions. We use the signed Laplacian operator to demonstrate how fundamental topological defects in lattices and networks percolate, shaping the geometrical structure and the complex energy landscape of the system. This reveals novel and highly robust multistable phases and establishes deep connections with spin glasses when thermal noise is considered, providing a natural topological and algebraic description of emergent multistability and non-ergodicity in frustrated systems.

cond-mat.dis-nn↗

arXiv2026

Fibration Symmetries and Cluster Synchronization in Multi-Body Systems

Based on recent advances in fibration symmetry theory, we investigate how structural symmetries influence synchronization in systems with higher-order interactions (HOI). Using bipartite graph representations, we identify a node partition in fibres, based on equivalent incidence relations in hypergraphs. We study how identical nodes with an isomorphic input set can synchronize due to structural properties under our specific model assumptions, examining the dynamical model of Kuramoto with higher-order interactions and frustration parameters. Recent works established for directed hypergraphs that balanced partitions characterize robust synchrony, invariant under all admissible dynamics, whereas our contribution isolates the case of Kuramoto dynamics and shows that synchrony under homogeneous initial conditions and natural frequencies necessarily coincides with the fibration partition. As a conclusion, let us examine situations that require adjustments to the hypergraph topology to handle redundancy or to align with a target cluster configuration, especially in the presence of noise or incomplete information. These considerations open up new questions for future investigations. Our methodology combines theoretical modeling and simulations with applications to real-world data topologies, highlighting how representational choices and local input equivalence influence synchronization behavior.

math.DS↗

arXiv2025

Topological protection breakdown: a route to frustrated ferroelectricity

Phases manifesting topological patterns in functional systems, like ferroelectric and ferromagnetic vortex superlattices, can manifest intricate and apparently ungovernable behavior, typical of frustrated non-ergodic states with high-dimensional energy landscapes. This is also the case for potassium-tantalate-niobate (KTN) crystals. These transparent ferroelectrics manifest remarkable but little-understood metastable domain patterns at optical (micrometer and above) scales near the cubic-to-tetragonal structural phase transition. Here, we formulate the Topological Breakdown Model based on the competition between intrinsic scales of domain-domain collinear and non-collinear interactions associated with polarization-charge screening. The model is able to explain observed KTN mesoscopic domain patterns and phase diagram as a function of temperature and external electric field. Findings include a precise set of sharp and broad percolative transitions that are experimentally verified, validating our model. Our study identifies the central role played by competing topologically protected states, identifying a fundamental link between topological protection and frustration that supports a hitherto unexplored functional non-ergodic arena.

cond-mat.stat-mech↗

arXiv2024

Multi-scale Laplacian community detection in heterogeneous networks

Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem of complex network theory. By taking advantage of the recent Laplacian Renormalization Group, we scrutinize information diffusion pathways throughout networks to shed further light on this issue. Based on inter-node communicability, our definition provides a clear-cut framework for resolving the multi-scale mesh of structures in complex networks, disentangling their intrinsic arboreal architecture. As it does not consider any topological null-model assumption, the LRG naturally permits the introduction of scale-dependent optimal partitions. Moreover, we demonstrate the existence of a particular class of nodes, called 'metastable' nodes, that switching regions to which they belong at different scales, likely playing a pivotal role in cross-regional communication and, therefore, in managing macroscopic effects of the whole network.

physics.soc-ph↗

arXiv2024

Fibration symmetry-breaking supports functional transitions in a brain network engaged in language

In his book 'A Beautiful Question', physicist Frank Wilczek argues that symmetry is 'nature's deep design,' governing the behavior of the universe, from the smallest particles to the largest structures. While symmetry is a cornerstone of physics, it has not yet been found widespread applicability to describe biological systems, particularly the human brain. In this context, we study the human brain network engaged in language and explore the relationship between the structural connectivity (connectome or structural network) and the emergent synchronization of the mesoscopic regions of interest (functional network). We explain this relationship through a different kind of symmetry than physical symmetry, derived from the categorical notion of Grothendieck fibrations. This introduces a new understanding of the human brain by proposing a local symmetry theory of the connectome, which accounts for how the structure of the brain's network determines its coherent activity. Among the allowed patterns of structural connectivity, synchronization elicits different symmetry subsets according to the functional engagement of the brain. We show that the resting state is a particular realization of the cerebral synchronization pattern characterized by a fibration symmetry that is broken in the transition from rest to language. Our findings suggest that the brain's network symmetry at the local level determines its coherent function, and we can understand this relationship from theoretical principles.

q-bio.NC↗

arXiv2024

Symmetries and synchronization from whole-neural activity in {\it C. elegans} connectome: Integration of functional and structural networks

Understanding the dynamical behavior of complex systems from their underlying network architectures is a long-standing question in complexity theory. Therefore, many metrics have been devised to extract network features like motifs, centrality, and modularity measures. It has previously been proposed that network symmetries are of particular importance since they are expected to underly the synchronization of a system's units, which is ubiquitously observed in nervous system activity patterns. However, perfectly symmetrical structures are difficult to assess in noisy measurements of biological systems, like neuronal connectomes. Here, we devise a principled method to infer network symmetries from combined connectome and neuronal activity data. Using nervous system-wide population activity recordings of the \textit{C.elegans} backward locomotor system, we infer structures in the connectome called fibration symmetries, which can explain which group of neurons synchronize their activity. Our analysis suggests functional building blocks in the animal's motor periphery, providing new testable hypotheses on how descending interneuron circuits communicate with the motor periphery to control behavior. Our approach opens a new door to exploring the structure-function relations in other complex systems, like the nervous systems of larger animals.

q-bio.NC↗

arXiv2024

Laplacian Renormalization Group: An introduction to heterogeneous coarse-graining

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

cond-mat.stat-mech↗

arXiv2024

Evidence of scale-free clusters of vegetation in tropical rainforests

Tropical rainforests exhibit a rich repertoire of spatial patterns emerging from the intricate relationship between the microscopic interaction between species. In particular, the distribution of vegetation clusters can shed much light on the underlying process regulating the ecosystem. Analyzing the distribution of vegetation clusters at different resolution scales, we show the first robust evidence of scale-invariant clusters of vegetation, suggesting the coexistence of multiple intertwined scales in the collective dynamics of tropical rainforests. We use field data and computational simulations to confirm our hypothesis, proposing a predictor that could be particularly interesting to monitor the ecological resilience of the world's 'green lungs'.

cond-mat.stat-mech↗

arXiv2024

Network topology mapping of Chemical Compounds Space

We define bipartite and monopartite relational networks of chemical elements and compounds using two different datasets of inorganic chemical and material compounds, as well as study their topology. We discover that the connectivity between elements and compounds is distributed exponentially for materials, and with a fat tail for chemicals. Compounds networks show similar distribution of degrees, and feature a highly-connected club due to oxygen. Chemical compounds networks appear more modular than material ones, while the communities detected reveal different dominant elements specific to the topology. We successfully reproduce the connectivity of the empirical chemicals and materials networks by using a family of fitness models, where the fitness values are derived from the abundances of the elements in the aggregate compound data. Our results pave the way towards a relational network-based understanding of the inherent complexity of the vast chemical knowledge atlas, and our methodology can be applied to other systems with the ingredient-composite structure.

cond-mat.stat-mech↗

arXiv2024

Higher-order Laplacian Renormalization

We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based on diffusion dynamics was recently introduced for complex networks with dyadic interactions. Despite mounting evidence of the importance of polyadic interactions, we still lack a general RG scheme for higher-order networks. Our approach uses a diffusion process to group nodes or simplices, where information can flow between nodes and between simplices (higher-order interactions). This approach allows us (i) to probe higher-order structures, defining scale-invariance at various orders, and (ii) to propose a coarse-graining scheme. We demonstrate our approach on controlled synthetic higher-order systems and then use it to detect the presence of order-specific scale-invariant profiles of real-world complex systems from multiple domains.

cond-mat.stat-mech↗

arXiv2024

Influence of scanning plane on Human Spinal Cord functional Magnetic Resonance echo planar imaging

BACKGROUND: Functional Magnetic Resonance Imaging (fMRI) is based on the Blood Oxygenation Level Dependent contrast and has been exploited for the indirect study of the neuronal activity within both the brain and the spinal cord. However, the interpretation of spinal cord fMRI (scfMRI) is still controversial and its diffusion is rather limited because of technical limitations. Overcoming these limitations would have a beneficial effect for the assessment and follow-up of spinal injuries and neurodegenerative diseases. PURPOSE: This study was aimed at systematically verify whether sagittal scanning in scfMRI using EPI readout is a viable alternative to the more common axial scanning, and at optimizing a pipeline for EPI-based scfMRI data analysis, based on Spinal Cord Toolbox (SCT). METHODS: Forty-five healthy subjects underwent MRI acquisition in a Philips Achieva 3T MRI scanner. T2*-weighted fMRI data were acquired using a GE-EPI sequence along sagittal and axial planes during an isometric motor task. Differences on benchmarks were assessed via paired two-sample t-test at p=0.05. RESULTS: We investigated the impact of the acquisition strategy by means of various metrics such as Temporal Signal to Noise Ratio (tSNR), Dice Coefficient to assess geometric distortions, Reproducibility and Sensitivity. tSNR was higher in axial than in sagittal scans, as well as reproducibility within the whole cord mask (t=7.4, p<0.01) and within the GM mask (t=4.2, p<0.01). The other benchmarks, associated with distortion and functional response, showed no difference between images obtained along the axial and sagittal planes. CONCLUSIONS: Quantitative metrics of data quality suggest that axial scanning would be the optimal choice. We conclude that axial acquisition is advantageous specially to mitigate the effects of physiological noise and to minimize inter-subject variance.

physics.med-ph↗

arXiv2023

Noise-cleaning the precision matrix of fMRI time series

We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic Resonance Imaging (fMRI). Assuming a Gaussian model underlying the neural activity, the problem consists in denoising the empirically observed matrices in order to obtain a better estimator of the true precision and covariance matrices. We consider several standard noise-cleaning algorithms and compare them on two types of datasets. The first type are time series of fMRI brain activity of human subjects at rest. The second type are synthetic time series sampled from a generative Gaussian model of which we can vary the fraction of dimensions per sample q = N/T and the strength of off-diagonal correlations. The reliability of each algorithm is assessed in terms of test-set likelihood and, in the case of synthetic data, of the distance from the true precision matrix. We observe that the so called Optimal Rotationally Invariant Estimator, based on Random Matrix Theory, leads to a significantly lower distance from the true precision matrix in synthetic data, and higher test likelihood in natural fMRI data. We propose a variant of the Optimal Rotationally Invariant Estimator in which one of its parameters is optimised by cross-validation. In the severe undersampling regime (large q) typical of fMRI series, it outperforms all the other estimators. We furthermore propose a simple algorithm based on an iterative likelihood gradient ascent, providing an accurate estimation for weakly correlated datasets.

cond-mat.stat-mech↗

arXiv2022

Network analysis of a complex disease: the gut microbiota in the inflammatory bowel disease case

Inflammatory bowel diseases (IBD) are complex diseases in which the gut microbiota is attacked by the immune system of genetically predisposed subjects when they are exposed to yet unclear environmental factors. The complexity of this class of diseases makes them suitable to be represented and studied with network science. In the project, the metagenomic data of the gut microbiota of control, Crohn's disease, and ulcerative colitis subjects were divided in three ranges (prevalent, common, uncommon). Then, correlation networks and co-expression networks were used to represent this data. The former networks involved the calculation of the Pearson's correlation and the use of the percolation threshold to binarize the adjacency matrix, whereas the latter involved the construction of the bipartite networks and the monopartite projection after binarization of the biadjacency matrix. Then, centrality measures and community detection were used on the so-built networks. The main results obtained were about the modules of "Bacteroides", which were connected in control subjects' correlation network, "Faecalibacterium prausnitzii", where co-enzyme A became central in IBD correlation networks and "Escherichia coli", which module has different position in the different diagnoses networks.

q-bio.QM↗

arXiv2022

Laplacian paths in complex networks: information core emerges from entropic transitions

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues. We employ a variety of brand-new theoretical techniques allowing for: (i) bring the theoretical framework to quantify the probability of information diffusion among nodes, (ii) identify critical scales and structures of complex networks regardless of their intrinsic properties, and (iii) demonstrate their dynamical relevance in synchronization phenomena. By combining these ideas, we evidence how the information flow on complex networks unravels different resolution scales. Using computational techniques, we focus on entropic transitions, uncovering a generic mesoscale object, the information core, and controlling information processing in complex networks. Altogether, this study sheds much light on allowing new theoretical techniques paving the way to introduce future renormalization group approaches based on diffusion distances.

physics.soc-ph↗

arXiv2022

Characterizing spatial point processes by percolation transitions

A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical ecology to analyze, e.g., the spatial percolation of a tree species in a tropical forest or a savanna. Here, we revisit the problem of aggregating random points in continuum systems (from $2$ to $6-$dimensional Euclidean spaces) to analyze the nature of the corresponding percolation transition in spatial point processes. This problem finds a natural description in terms of the canonical ensemble but not in the usual grand-canonical one, customarily employed to describe percolation transitions. This leads us to analyze the question of ensemble equivalence and study whether the resulting canonical continuum percolation transition shares its universal properties with standard percolation transitions, analyzing diverse homogeneous and heterogeneous spatial point processes. We, therefore, provide a powerful tool to characterize and classify a vast class of natural point patterns, revealing their fundamental properties based on percolation phase transitions.

cond-mat.stat-mech↗

arXiv2022

Laplacian Renormalization Group for heterogeneous networks

The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is particularly challenging due to correlations between intertwined scales. To date, the explorations are based on hidden geometries hypotheses. Here, we propose a Laplacian RG diffusion-based picture in complex networks, defining both the Kadanoff supernodes' concept, the momentum space procedure, \emph{á la Wilson}, and applying this RG scheme to real networks in a natural and parsimonious way.

cond-mat.stat-mech↗