arXiv subjects

Duccio Fanelli

Publications and source records attributed to Duccio Fanelli.

At least 55 records · Page 3Linked to original sources

arXiv2021

Mobility-based prediction of SARS-CoV-2 spreading

The rapid spreading of SARS-CoV-2 and its dramatic consequences, are forcing policymakers to take strict measures in order to keep the population safe. At the same time, societal and economical interactions are to be safeguarded. A wide spectrum of containment measures have been hence devised and implemented, in different countries and at different stages of the pandemic evolution. Mobility towards workplace or retails, public transit usage and permanence in residential areas constitute reliable tools to indirectly photograph the actual grade of the imposed containment protocols. In this paper, taking Italy as an example, we will develop and test a deep learning model which can forecast various spreading scenarios based on different mobility indices, at a regional level. We will show that containment measures contribute to "flatten the curve" and quantify the minimum time frame necessary for the imposed restrictions to result in a perceptible impact, depending on their associated grade.

cond-mat.dis-nn↗

arXiv2020

Random walks and community detection in hypergraphs

We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process defines its own hypergraph projection on a weighted network. We then explore the differences between them by considering the community structure associated to each random walk process. To do so, we generalise the Markov stability framework to hypergraphs and test it on artificial and real-world hypergraphs.

cond-mat.stat-mech↗

arXiv2020

Machine learning in spectral domain

Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvalues and eigenvectors of transfer operators in direct space. The proposed method is ductile and can be tailored to return either linear or non-linear classifiers. Adjusting the eigenvalues, when freezing the eigenvectors entries, yields performances which are superior to those attained with standard methods {\it restricted} to a operate with an identical number of free parameters. Tuning the eigenvalues correspond in fact to performing a global training of the neural network, a procedure which promotes (resp. inhibits) collective modes on which an effective information processing relies. This is at variance with the usual approach to learning which implements instead a local modulation of the weights associated to pairwise links. Interestingly, spectral learning limited to the eigenvalues returns a distribution of the predicted weights which is close to that obtained when training the neural network in direct space, with no restrictions on the parameters to be tuned. Based on the above, it is surmised that spectral learning bound to the eigenvalues could be also employed for pre-training of deep neural networks, in conjunction with conventional machine-learning schemes. Changing the eigenvectors to a different non-orthogonal basis alters the topology of the network in direct space and thus allows to export the spectral learning strategy to other frameworks, as e.g. reservoir computing.

cs.LG↗

arXiv2020

How to fairly share a watermelon

Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates into the students a loss of interest with a consequent removal of motivation in the study of such topics and more widely in pursuing scientific curricula. With this note we put to the fore a simple example of practical interest where the above concepts prove central; our aim is thus to motivate students and to reverse the dropout trend by proposing an introduction to the theory starting from practical applications. More precisely, we will show how using a mixture of geometry, calculus and integrals one can easily share a watermelon into regular slices with equal volume.

physics.ed-ph↗

arXiv2020

Reconstruction scheme for excitatory and inhibitory dynamics with quenched disorder: application to zebrafish imaging

An inverse procedure is developed and tested to recover functional and structural information from global signals of brains activity. The method assumes a leaky-integrate and fire model with excitatory and inhibitory neurons, coupled via a directed network. Neurons are endowed with a heterogenous current value, which sets their associated dynamical regime. By making use of a heterogenous mean-field approximation, the method seeks to reconstructing from global activity patterns the distribution of in-coming degrees, for both excitatory and inhibitory neurons, as well as the distribution of the assigned currents. The proposed inverse scheme is first validated against synthetic data. Then, time-lapse acquisitions of a zebrafish larva recorded with a two-photon light sheet microscope are used as an input to the reconstruction algorithm. A power law distribution of the in-coming connectivity of the excitatory neurons is found. Local degree distributions are also computed by segmenting the whole brain in sub-regions traced from annotated atlas.

q-bio.NC↗

arXiv2020

Generalized patterns from local and non local reactions

A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are treated in a mean-field setting which enables the system to reach a homogeneous consensus state, either constant or time dependent. We provide analytical evidence that such homogeneous solution can turn unstable under externally imposed disturbances, following a symmetry breaking mechanism which anticipates the subsequent outbreak of the patterns. The onset of the instability can be traced back, via a linear stability analysis, to a dispersion relation that is shaped by the spectrum of an unconventional reactive Laplacian. The proposed mechanism prescinds from the classical Local Activation and Lateral Inhibition scheme, which sits at the core of the Turing recipe for diffusion driven instabilities. Examples of systems displaying a fixed-point or a limit cycle, in their uncoupled versions, are discussed. Taken together, our results pave the way for alternative mechanisms of pattern formation, opening new possibilities for modeling ecological, chemical and physical interacting systems.

nlin.PS↗

arXiv2020

Nonlinear walkers and efficient exploration of congested networks

Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the modules of a given network, its most central nodes and paths, or to determine the typical times to reach a target. Although various types of random walks whose motion is node biased have been proposed, which are still amenable to analytical solution, most if not all of them rely on the assumption of linearity and independence of the walkers. We introduce a novel class of nonlinear stochastic processes describing a system of interacting random walkers moving over networks with finite node capacities. The transition probabilities are modulated by nonlinear functions of the available space at the destination node, with a bias parameter that allows to tune the tendency of the walkers to avoid nodes occupied by other walkers. Firstly, we derive the master equation governing the dynamics of the system, and we determine an analytical expression for the occupation probability of the walkers at equilibrium in the most general case, and under different level of network congestions. Then, we study different type of synthetic and real-world networks, presenting numerical and analytical results for the entropy rate, a proxy for the network exploration capacities of the walkers.We find that, for each level of the nonlinear bias, there is an optimal crowding that maximises the entropy rate in a given network topology. The analysis suggests that a large fraction of real-world networks are organised in such a way as to favour exploration under congested conditions. Our work provides a general and versatile framework to model nonlinear stochastic processes whose transition probabilities vary in time depending on the current state of the system.

cond-mat.stat-mech↗

arXiv2020

Dynamical systems on Hypergraphs

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider a general class of dynamical systems anchored on hypergraphs. Hyperedges of arbitrary size ideally encircle individual units so as to account for multiple, simultaneous interactions. These latter are mediated by a combinatorial Laplacian, that is here introduced and characterised. The formalism of the Master Stability Function is adapted to the present setting. Turing patterns and the synchronisation of non linear (regular and chaotic) oscillators are studied, for a general class of systems evolving on hypergraphs. The response to externally imposed perturbations bears the imprint of the higher order nature of the interactions.

nlin.AO↗

arXiv2020

COVID-19: The unreasonable effectiveness of simple models

When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by national authorities all over the world. However, despite the diversity of novel theoretical approaches and the comprehensiveness of many widely established models, the official figures that recount the course of the outbreak still sketch a largely elusive and intimidating picture. Here we show unambiguously that the dynamics of the COVID-19 outbreak belongs to the simple universality class of the SIR model and extensions thereof. Our analysis naturally leads us to establish that there exists a fundamental limitation to any theoretical approach, namely the unpredictable non-stationarity of the testing frames behind the reported figures. However, we show how such bias can be quantified self-consistently and employed to mine useful and accurate information from the data. In particular, we describe how the time evolution of the reporting rates controls the occurrence of the apparent epidemic peak, which typically follows the true one in countries that were not vigorous enough in their testing at the onset of the outbreak. The importance of testing early and resolutely appears as a natural corollary of our analysis, as countries that tested massively at the start clearly had their true peak earlier and less deaths overall.

q-bio.PE↗

arXiv2020

Generating directed networks with prescribed Laplacian spectra

Complex real-world phenomena are often modeled as dynamical systems on networks. In many cases of interest, the spectrum of the underlying graph Laplacian sets the system stability and ultimately shapes the matter or information flow. This motivates devising suitable strategies, with rigorous mathematical foundation, to generate Laplacian that possess prescribed spectra. In this paper, we show that a weighted Laplacians can be constructed so as to exactly realize a desired complex spectrum. The method configures as a non trivial generalization of existing recipes which assume the spectra to be real. Applications of the proposed technique to (i) a network of Stuart-Landau oscillators and (ii) to the Kuramoto model are discussed. Synchronization can be enforced by assuming a properly engineered, signed and weighted, adjacency matrix to rule the pattern of pairing interactions.

cond-mat.stat-mech↗

arXiv2020

Analysis and forecast of COVID-19 spreading in China, Italy and France

In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-09/03/2020$. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-(confirmed) infected-recovered-deaths model indicates that the kinetic parameter that describes the rate of recovery seems to be the same, irrespective of the country, while the infection and death rates appear to be more variable. The model places the peak in Italy around March 20$^{\rm th}$ 2020, with a maximum number of confirmed infected individuals of about 16,000.

q-bio.PE↗

arXiv2019

Random walks on hypergraphs

In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but involve larger sets of nodes, at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multi-body interactions. We hereby propose a new class of random walks defined on such higher-order structures, and grounded on a microscopic physical model where multi-body proximity is associated to highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterisation of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalised random walk Laplace operator that reduces to the standard random walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have a full control of the high-order structures, and real-world networks where higher-order interactions are at play. As a first application of the method, we compare the behaviour of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As a second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unveiling the effect of higher-order interactions on diffusive processes in higher-order networks, shading light on mechanisms at the hearth of biased information spreading in complex networked systems.

physics.soc-ph↗

arXiv2019

Stabilizing Stuart-Landau oscillators via time-varying networks

A procedure is developed and tested to enforce synchronicity in a family of Stuart-Landau oscillators, coupled through a symmetric network. The proposed method exploits network plasticity, as an inherent non autonomous drive. More specifically, we assume that the system is initially confined on a network which turns the underlying homogeneous synchronous state unstable. A properly engineered network can be always generated, which links the same set of nodes, and allows for synchronicity to be eventually restored, upon performing continuously swappings, at a sufficient rate, between the two aforementioned networks. The result is cast in rigorous terms, as follows an application of the average theorem and the critical swapping rate determined analytically.

nlin.AO↗

arXiv2019

Inferring network structure and local dynamics from neuronal patterns with quenched disorder

An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model with short term plasticity neurons, coupled via a directed network. Neurons are assigned a specific current value, which is heterogenous across the sample, and sets the firing regime in which the neuron is operating in. The aim of the method is to recover the distribution of incoming network degrees, as well as the distribution of the assigned currents, from global field measurements. The proposed approach to the inverse problem implements the reductionist Heterogenous Mean-Field approximation. This amounts in turn to organizing the neurons in different classes, depending on their associated degree and current. When tested again synthetic data, the method returns accurate estimates of the sought distributions, while managing to reproduce and interpolate almost exactly the time series of the supplied global field. Finally, we also applied the proposed technique to longitudinal wide-field fluorescence microscopy data of cortical functionality in groups of awake Thy1-GCaMP6f mice. Mice are induced a photothrombotic stroke in the primary motor cortex and their recovery monitored in time. An all-to-all LIF model which accommodates for currents heterogeneity allows to adequately explain the recorded patterns of activation. Altered distributions in neuron excitability are in particular detected, compatible with the phenomenon of hyperexcitability in the penumbra region after stroke.

cond-mat.dis-nn↗

arXiv2019

A universal route to pattern formation

Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications, encompassing different fields and scales. Examples of emerging patterns are the spots and stripes on the coat or skin of animals, the spatial distribution of vegetation in arid areas, the organization of the colonies of insects in host-parasitoid systems and the architecture of large complex ecosystems. Spatial self-organization can be described following the visionary intuition of Alan Turing, who showed how non-linear interactions between slow diffusing activators and fast diffusing inhibitors could induce patterns. The Turing instability, as the mechanism described is universally referred to, was raised to paradigm status in those realms of investigations where microscopic entities are subject to diffusion, from small biological systems to large ecosystems. Requiring a significant ratio of the assigned diffusion constants however is a stringent constraint, which limited the applicability of the theory. Building on the observation that spatial interactions are usually direction biased, and often strongly asymmetric, we here propose a novel framework for the generation of short wavelength patterns which overcomes the limitation inherent in the Turing formulation. In particular, we will prove that patterns can always set in when the system is composed by sufficiently many cells - the units of spatial patchiness - and for virtually any ratio of the diffusivities involved. Macroscopic patterns that follow the onset of the instability are robust and show oscillatory or steady-state behavior.

nlin.PS↗

arXiv2019

Resilience for stochastic systems interacting via a quasi-degenerate network

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear lattice, noise gets amplified via a self-consistent process which we trace back to the degenerate spectrum of the embedding support. The same phenomenon holds when the system is bound to explore a quasi degenerate network. In this case, the eigenvalues of the Laplacian operator, which governs species diffusion, accumulate over a limited portion of the complex plane. The larger the network, the more pronounced the amplification. Beyond a critical network size, a system deemed deterministically stable, hence resilient, may turn unstable, yielding seemingly regular patterns in the concentration amount. Non-normality and quasi-degenerate networks may therefore amplify the inherent stochasticity, and so contribute to altering the perception of resilience, as quantified via conventional deterministic methods.

cond-mat.dis-nn↗

arXiv2018

Pattern invariance for reaction-diffusion systems on complex networks

Given a reaction-diffusion system interacting via a complex network, we propose two different techniques to modify the network topology while preserving its dynamical behaviour. In the region of parameters where the homogeneous solution gets spontaneously destabilized, perturbations grow along the unstable directions made available across the networks of connections, yielding irregular spatio-temporal patterns. We exploit the spectral properties of the Laplacian operator associated to the graph in order to modify its topology, while preserving the unstable manifold of the underlying equilibrium. The new network is isodynamic to the former, meaning that it reproduces the dynamical response (pattern) to a perturbation, as displayed by the original system. The first method acts directly on the eigenmodes, thus resulting in a general redistribution of link weights which, in some cases, can completely change the structure of the original network. The second method uses localization properties of the eigenvectors to identify and randomize a subnetwork that is mostly embedded only into the stable manifold. We test both techniques on different network topologies using the Ginzburg-Landau system as a reference model. Whereas the correlation between patterns on isodynamic networks generated via the first recipe is larger, the second method allows for a finer control at the level of single nodes. This work opens up a new perspective on the multiple possibilities for identifying the family of discrete supports that instigate equivalent dynamical responses on a multispecies reaction-diffusion system.

physics.soc-ph↗

arXiv2018

Patterns of non-normality in networked systems

Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the system under scrutiny displays a homogeneous equilibrium, which is destabilized via a symmetry breaking instability which reflects the specificity of the problem being inspected. The Turing instability is among the most celebrated paradigms for pattern formation. In its original form, the diffusion constants of the two mobile species need to be quite different from each other for the instability to develop. Unfortunately, this condition limits the applicability of the theory. To overcome this impediment, and with the ambitious long term goal to eventually reconcile theory and experiments, we here propose an alternative mechanism for promoting the onset of patterns. To this end a multi-species reaction-diffusion system is studied on a discrete, network-like support: the instability is triggered by the non-normality of the embedding network. The non-normal character of the dynamics instigates a short time amplification of the imposed perturbation, thus making the system unstable for a choice of parameters that would yield stability under the conventional scenario. Importantly, non-normal networks are pervasively found, as we shall here briefly review.

nlin.PS↗