arXiv subjects

Giulia Bertagnolli

Publications and source records attributed to Giulia Bertagnolli.

9 recordsLinked to original sources

arXiv2026

Estimation of a multivariate von Mises distribution for contaminated torus data

The occurrence of atypical circular observations on the torus can badly affect parameter estimation of the multivariate von Mises distribution. This paper addresses the problem of robust fitting of the multivariate von Mises model using the weighted likelihood methodology. The key ingredients are non-parametric density estimation for multivariate circular data and the definition of appropriate weighted estimating equations. Some theoretical properties are discussed. The finite sample behavior of the proposed weighted likelihood estimator has been investigated by Monte Carlo numerical studies and empirical applications.

stat.ME↗

arXiv2025

A Weighted Likelihood Approach Based on Statistical Data Depths

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical depth of each data point relative to the model, as opposed to the sample. An observation is considered regular when the corresponding difference of these two depths is close to zero. When this difference is large the observation score contribution is downweighted. We study the asymptotic properties of the proposed estimator, including consistency and asymptotic normality, for a broad class of weight functions. In particular, we establish asymptotic normality under the standard regularity conditions typically assumed for the maximum likelihood estimator (MLE). Our weighted likelihood estimator achieves the same asymptotic efficiency as the MLE in the absence of contamination, while maintaining a high degree of robustness in contaminated settings. In stark contrast to the traditional minimum divergence/disparity estimators, our results hold even if the dimension of the data diverges with the sample size, without requiring additional assumptions on the existence or smoothness of the underlying densities. We also derive the finite sample breakdown point of our estimator for both location and scatter matrix in the elliptically symmetric model. Detailed results and examples are presented for robust parameter estimation in the multivariate normal model. Robustness is further illustrated using two real data sets and a Monte Carlo simulation study.

math.ST↗

arXiv2024

Multilayer Network Science: from Cells to Societies

Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple distinct ways, simultaneously -- was demonstrated to be an effective modeling and analytical framework for a wide spectrum of empirical systems, from biopolymer networks (such as interactome and metabolomes) to neuronal networks (such as connectomes), from social networks to urban and transportation networks. In this Element, a decade after the publication of one of the most seminal papers on this topic, we review the most salient features of multilayer network science, covering both theoretical aspects and direct applications to real-world coupled/interdependent systems, from the point of view of multilayer structure, dynamics, and function. We discuss potential frontiers for this topic and the corresponding challenges in the field for the future.

physics.soc-ph↗

arXiv2023

Efficient network exploration by means of resetting self-avoiding random walkers

The self-avoiding random walk (SARW) is a stochastic process whose state variable avoids returning to previously visited states. This non-Markovian feature has turned SARWs a powerful tool for modelling a plethora of relevant aspects in network science, such as network navigability, robustness and resilience. We analytically characterize self-avoiding random walkers that evolve on complex networks and whose memory suffers stochastic resetting, that is, at each step, with a certain probability, they forget their previous trajectory and start free diffusion anew. Several out-of-equilibrium properties are addressed, such as the time-dependent position of the walker, the time-dependent degree distribution of the non-visited network and the first-passage time distribution, and its moments, to target nodes. We examine these metrics for different resetting parameters and network topologies, both synthetic and empirical, and find a good agreement with simulations in all cases. We also explore the role of resetting on network exploration and report a non-monotonic behavior of the cover time: frequent memory resets induce a global minimum in the cover time, significantly outperforming the well-known case of the pure random walk, while reset events that are too spaced apart become detrimental for the network discovery. Our results provide new insights into the profound interplay between topology and dynamics in complex networks, and shed light on the fundamental properties of SARWs in nontrivial environments.

cond-mat.stat-mech↗

arXiv2022

Dismantling the information flow in complex interconnected systems

Microscopic structural damage, such as lesions in neural systems or disruptions in urban transportation networks, can impair the dynamics crucial for systems' functionality, such as electrochemical signals or human flows, or any other type of information exchange, respectively, at larger topological scales. Damage is usually modeled by progressive removal of components or connections and, consequently, systems' robustness is assessed in terms of how fast their structure fragments into disconnected sub-systems. Yet, this approach fails to capture how damage hinders the propagation of information across scales, since system function can be degraded even in absence of fragmentation -- e.g., pathological yet structurally integrated human brain. Here, we probe the response to damage of dynamical processes on the top of complex networks, to study how such an information flow is affected. We find that removal of nodes central for network connectivity might have insignificant effects, challenging the traditional assumption that structural metrics alone are sufficient to gain insights about how complex systems operate. Using a damaging protocol explicitly accounting for flow dynamics, we analyze synthetic and empirical systems, from biological to infrastructural ones, and show that it is possible to drive the system towards functional fragmentation before full structural disintegration.

physics.soc-ph↗

arXiv2021

Diffusion geometry of multiplex and interdependent systems

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by adequate metrics. Random walks, a proxy for a broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used in [Phys. Rev. Lett. 118, 168301 (2017)] to define the class of diffusion geometry and pinpoint the functional mesoscale organization of complex networks from a genuine geometric perspective. Here, we firstly extend this class to families of distinct random walk dynamics -- including local and nonlocal information -- on multilayer networks -- a paradigm for biological, neural, social, transportation, biological and financial systems -- overcoming limitations such as the presence of isolated nodes and disconnected components, typical of real-world networks. Secondly, we characterize the multilayer diffusion geometry of synthetic and empirical systems, highlighting the role played by different random search dynamics in shaping the geometric features of the corresponding diffusion manifolds.

physics.soc-ph↗

arXiv2021

Unraveling the hidden organisation of urban systems and their mobility flows

Increasing evidence suggests that cities are complex systems, with structural and dynamical features responsible for a broad spectrum of emerging phenomena. Here we use a unique data set of human flows and couple it with information on the underlying street network to study, simultaneously, the structural and functional organisation of 10 world megacities. We quantify the efficiency of flow exchange between areas of a city in terms of integration and segregation using well defined measures. Results reveal unexpected complex patterns that shed new light on urban organisation. Large cities tend to be more segregated and less integrated, while their overall topological organisation resembles that of small world networks. At the same time, the heterogeneity of flows distribution might act as a catalyst for further integrating a city. Our analysis unravels how human behaviour influences, and is influenced by, the urban environment, suggesting quantitative indicators to control integration and segregation of human flows that can be used, among others, for restriction policies to adopt during emergencies and, as an interesting byproduct, allows us to characterise functional (dis)similarities of different metropolitan areas, countries, and cultures.

physics.soc-ph↗

arXiv2020

Quantifying efficient information exchange in real network flows

Network science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and interconnections strength. It is well-known that the topology of a network affects its resilience to failures or attacks, as well as its functions. Exchanging information is crucial for many real systems: the internet, transportation networks and the brain are key examples. Despite the introduction of measures of efficiency to analyze network flows, i.e. topologies characterized by weighted connectivity, here we show that they fail to capture combined information of link existence and link weight. In this letter we propose a physically-grounded estimator of flow efficiency which can be computed for every weighted network, regardless from the scale and nature of weights and from any (missing) metadata. Remarkably, results show that our estimator captures the heterogeneity of flows along with topological differences and its complement information obtained from percolation analysis of several empirical systems, including transportation, trade, migrations, and brain networks. We show that cutting the heaviest connections may increase the average communication efficiency of the system and hence, counterintuively, a sparser network is not necessarily less efficient. Remarkably, our estimator enables the comparison of communication efficiency of networks arising from different fields, without the possible pitfalls deriving from the scale of flow.

physics.soc-ph↗

arXiv2019

Network depth: identifying median and contours in complex networks

Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be considered as the `centre' of a complex network. In fact, this problem corresponds to finding the median of a complex network. The median is a non-parametric and robust estimator of the location parameter of a probability distribution. In this work, we present the most natural generalisation of the concept of median to the realm of complex networks, discussing its advantages for defining the centre of the system and percentiles around that centre. To this aim, we introduce a new statistical data depth and we apply it to networks embedded in a geometric space induced by different metrics. The application of our framework to empirical networks allows us to identify median nodes which are socially or biologically relevant.

stat.ME↗