arXiv subjects

Davide Cassi

Publications and source records attributed to Davide Cassi.

At least 19 recordsLinked to original sources

arXiv2025

Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures

"Every object that biology studies is a system of systems." (Fran\c{c}ois Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but reshaped. Linking the properties of primitive components to the emergent behavior of composite networks remains a key open challenge. Here, we show that modular compositions generically decouple the spectral and Fiedler dimensions, so that networks with identical thermodynamic exponents can exhibit parametrically different equilibration dynamics.

cond-mat.stat-mech↗

arXiv2022

Quantum Coherence in Loopless Superconductive Networks

Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gap over specific branches of the networks and sharp increases of pair currents are the main signatures of the coherent states and, in order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent, but isolated, counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases of the Josephson currents, along the above mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks and in both cases the observed effects provide positive quantitative evidence of the predictions of existing theoretical models.

cond-mat.supr-con↗

arXiv2020

Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

In this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi-Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that higher level of modularity decreases the model network robustness under both attack strategies, i.e. model network with higher community structure showed faster LCC disruption when subjected to node removal. Very interesting, we find that when model networks showed non-modular structure or low modularity, the degree-based (ID) is more effective than the betweenness-based node attack strategy (IB). Conversely, in the case the model network present higher modularity, the IB strategies becomes clearly the most effective to fragment the LCC. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the robustness and the efficacy of the attack strategies in 12 real-world social networks. We found that the modularity Q is negatively correlated with the robustness of the real-world social networks under IB node attack strategy (p-value< 0.001). This result indicates how real-world networks with higher modularity (i.e. with higher community structure) may be more fragile to betwenness-based node attack. The results presented in this paper unveil the role of modularity and community structure for the robustness of networks and may be useful to select the best node attack strategies in network.

physics.soc-ph↗

arXiv2020

New nodes attack strategies for real complex weighted networks

In this work we introduce a new nodes attack strategy removing nodes with highest conditional weighted betweenness centrality (CondWBet). We compare its efficacy with well-known attack strategies from literature over five real-world complex weighted networks. We use the network weighted efficiency (WEFF) like a measure encompassing the weighted structure of the network in addition to the commonly used binary-topological measure, the largest connected cluster (LCC). We find that the recently proposed conditional betweenness strategy (CondBet) (Nguyen et al. 2019) is the best to fragment the LCC in all cases. Further, we find that the introduced CondWBet strategy is the best to decrease the network efficiency (WEFF) in 3 out of 5 cases. Last, CondWBet is be the most effective strategy to reduce WEFF at the beginning of the removal process whereas the Strength that removes nodes with highest link weights first, shows the highest efficacy in the final phase of the removal process when the network is broken in many small clusters. These last outcomes would suggest that a better attacking strategy could be a combination of the CondWBet and Strength strategies

physics.soc-ph↗

arXiv2019

Abrupt efficiency collapse in real-world complex weighted networks: robustness decrease with link weights heterogeneity

Here we report a comprehensive analysis of the robustness of five high-quality real-world complex weighted networks to errors and attacks of nodes and links. We analyze C. Elegans, Cargo ship, E. Coli, Us Airports and Human brain real-world complex weighted networks. We use measures of the network damage conceived for a binary (e.g. largest connected cluster LCC, and binary efficiency Effbin) or a weighted network structure (e.g. the efficiency Eff, and the total energy-information En). We find that removing a very small fraction of nodes and links with respectively higher strength and weight triggers an abrupt collapse of the weighted functioning measures while measures that evaluate the binary-topological connectedness are almost unaffected. These findings unveil a problematic response-state of the real-world complex networks where the attack of a small fraction of nodes-links returns these systems in a connected but highly inefficient state. Our findings unveil how the robustness may be heavily overestimated focusing on the connectedness of the components only. Last, to understand how the networks robustness is generally affected by link weights heterogeneity, we randomly assign link weights over the topological structure of the real-world networks. We find that highly heterogeneous networks experienced a faster efficiency decrease under nodes-links removal: i.e. the robustness of the real-world complex networks against both random than attack is negatively correlated with links weight heterogeneity.

physics.soc-ph↗

arXiv2018

An energy window study of light transmission-disorder relationship in 1D photonic structures

While the light transmission of photonic crystals is characterized by the photonic band gap, the one of disordered photonic structures is typified by a multiplicity of transmission depths. The total transmission over a range of wavelengths is related to the width of such range, but also to the type of disorder. Less homogeneous disordered structures transmit more light than the ordered counterpart regardless of the wavelengths range width. More homogeneous disordered structures transmit more light than the ordered counterpart only above a certain value of the width. We studied this behaviour with a statistical analysis over 5000 permutations of structures for each wavelength width and for each homogeneity degree (Shannon-Wiener index).

physics.optics↗

arXiv2018

One-dimensional disordered photonic structures with two or more materials

Here we would like to discuss the light transmission modulation by periodic and disordered one dimensional (1D) photonic structures. In particular, we will present some theoretical and experimental findings highlighting the peculiar optical properties of: i) 1D periodic and disordered photonic structures made with two or more materials; ii) 1D photonic structures in which the homogeneity or the aggregation of the high refractive index layers is controlled. We will focus also on the fabrication aspects of these structures.

physics.optics↗

arXiv2016

The two-particle problem in comb-like structures

Encounters between walkers performing a random motion on an appropriate structure can describe a wide variety of natural phenomena ranging from pharmacokinetics to foraging. On homogeneous structures the asymptotic encounter probability between two walkers is (qualitatively) independent of whether both walkers are moving or one is kept fixed. On infinite comb-like structures this is no longer the case and here we deepen the mechanisms underlying the emergence of a finite probability that two random walkers will never meet, while one single random walker is certain to visit any site. In particular, we introduce an analytical approach to address this problem and even more general problems such as the case of two walkers with different diffusivity, particles walking on a finite comb and on arbitrary bundled structures, possibly in the presence of loops. Our investigations are both analytical and numerical and highlight that, in general, the outcome of a reaction involving two reactants on a comb-like architecture can be strongly different according to whether both reactants are moving (no matter their relative diffusivities) or only one, and according to the density of short-cuts among the branches.

cond-mat.stat-mech↗

arXiv2015

Lévy flights with power-law absorption

We consider a particle performing a stochastic motion on a one-dimensional lattice with jump widths distributed according to a power-law with exponent $μ+ 1$. Assuming that the walker moves in the presence of a distribution $a(x)$ of targets (traps) depending on the spatial coordinate $x$, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions $a(x) \sim x^{-α}$ and we find that as long as $μ< α$ there is a finite probability that the walker will never be trapped, no matter how long the process is. This analytical result, valid on infinite chains, is corroborated by numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.

cond-mat.stat-mech↗

arXiv2015

Hitting and Trapping Times on Branched Structures

In this work we consider a simple random walk embedded in a generic branched structure and we find a close-form formula to calculate the hitting time $H\left(i,f\right)$ between two arbitrary nodes $i$ and $j$. We then use this formula to obtain the set of hitting times $\left\{ H\left(i,f\right)\right\} $ for combs and their expectation values, namely the mean-first passage time $\left( \mbox{MFPT}_{f} \right)$, where the average is performed over the initial node while the final node $f$ is given, and the global mean-first passage time $\left( \mbox{GMFPT} \right)$, where the average is performed over both the initial and the final node. Finally, we discuss applications in the context of reaction-diffusion problems.

cond-mat.stat-mech↗

arXiv2014

Slow Encounters of Particle Pairs in Branched Structures

On infinite homogeneous structures, two random walkers meet with certainty if and only if the structure is recurrent, i.e., a single random walker returns to its starting point with probability 1. However, on general inhomogeneous structures this property does not hold and, although a single random walker will certainly return to its starting point, two moving particles may never meet. This striking property has been shown to hold, for instance, on infinite combs. Due to the huge variety of natural phenomena which can be modeled in terms of encounters between two (or more) particles diffusing in comb-like structures, it is fundamental to investigate if and, if so, to what extent similar effects may take place in finite structures. By means of numerical simulations we evidence that, indeed, even on finite structures, the topological inhomogeneity can qualitatively affect the two-particle problem. In particular, the mean encounter time can be polynomially larger than the time expected from the related one particle problem.

cond-mat.stat-mech↗

arXiv2013

Efficiency of attack strategies on complex model and real-world networks

We investigated the efficiency of attack strategies to network nodes when targeting several complex model and real-world networks. We tested 5 attack strategies, 3 of which were introduced in this work for the first time, to attack 3 model (Erdos and Renyi, Barabasi and Albert preferential attachment network, and scale-free network configuration models) and 3 real networks (Gnutella peer-to-peer network, email network of the University of Rovira i Virgili, and immunoglobulin interaction network). Nodes were removed sequentially according to the importance criterion defined by the attack strategy. We used the size of the largest connected component (LCC) as a measure of network damage. We found that the efficiency of attack strategies (fraction of nodes to be deleted for a given reduction of LCC size) depends on the topology of the network, although attacks based on the number of connections of a node and betweenness centrality were often the most efficient strategies. Sequential deletion of nodes in decreasing order of betweenness centrality was the most efficient attack strategy when targeting real-world networks. In particular for networks with power-law degree distribution, we observed that most efficient strategy change during the sequential removal of nodes.

physics.soc-ph↗

arXiv2010

Generalization of the Peierls-Griffiths Theorem for the Ising Model on Graphs

We present a sufficient condition for the presence of spontaneous magnetization for the Ising model on a general graph, related to its long-range topology. Applying this condition we are able to prove the existence of a phase transition at temperature T > 0 on a wide class of general networks. The possibility of further extensions of our results is discussed.

cond-mat.stat-mech↗

arXiv2009

Target annihilation by diffusing particles in inhomogeneous geometries

The survival probability of immobile targets, annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks and gels, is analytically investigated. It is shown that, while it cannot in general be related to the number of distinct visited points, as in the case of homogeneous lattices, in the case of bounded coordination numbers its asymptotic behaviour at large times can still be expressed in terms of the spectral dimension $\widetilde {d}$, and its exact analytical expression is given. The results show that the asymptotic survival probability is site independent on recurrent structures ($\widetilde{d}\leq2$), while on transient structures ($\widetilde{d}>2$) it can strongly depend on the target position, and such a dependence is explicitly calculated.

cond-mat.stat-mech↗

arXiv2009

Word-of-mouth and dynamical inhomogeneous markets: Efficiency measure and optimal sampling policies for the pre-launch stage

An important assumption lying behind innovation diffusion models and word-of-mouth processes is that of homogeneous mixing: at any time, the individuals making up the market are uniformly distributed in space. When the geographical parameters of the market, such as its area extension, become important, the movement of individuals must be explicitly taken into account. The authors introduce a model for a "micro-level" process for the diffusion of an innovative product, based on a word-of-mouth mechanism, and they explicitly consider the inhomogeneity of markets and the spatial extent of the geographical region where the process takes place. This results in an unexpected behaviour of macro (aggregate) level measurable quantities. The authors study the particular case of the pre-launch stage, where a product is first presented to the market through free sample distribution. The first triers of the samples then inform the other potential customers via word-of-mouth; additional advertising is absent. The authors find an unexpected general failure of the word-of-mouth mechanism for high market densities and they obtain quantitative results for the optimal sampling policy. By introducing a threshold to discriminate between individuals who will purchase and those who will not purchase according to their individual goodwill, they calculate the length of the pre-launch campaign and the final goodwill as a function of the firm's expenditure. These results are applied to a set of major US urban areas.

physics.soc-ph↗

arXiv2005

Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks

Topological inhomogeneity gives rise to spectral anomalies that can induce Bose-Einstein Condensation (BEC) in low dimensional systems. These anomalies consist in energy regions composed of an infinite number of states with vanishing weight in the thermodynamic limit (hidden states). Here we present a rigorous result giving the most general conditions for BEC on complex networks. We prove that the presence of hidden states in the lowest region of the spectrum is the necessary and sufficient condition for condensation in low dimension (spectral dimension $\bar{d}\leq 2$), while it is shown that BEC always occurs for $\bar{d}>2$.

cond-mat.stat-mech↗

arXiv1998

The $n\to\infty$ limit of O(n) model on graphs

Thirty years ago, Stanley showed that an O(n) spin model on a lattice tends to a spherical model as $n\to\infty$. This means that at any temperature the corresponding free energies coincide. This fundamental result, providing the basis for more detailed studies of continuous symmetry spin models, is no longer valid on more general discrete structures lacking of translation invariance, i.e. on graphs. However only the singular parts of the free energies determine the critical behavior of the two statistical models. Here we show that such singular parts still coincide even on general graphs in the thermodynamic limit. This implies that the critical exponents of O(n) models on graphs for $n\to\infty$ tend to the spherical ones and therefore they only depend on the graph spectral dimension.

cond-mat↗

arXiv1998

Magnetization bound for classical spin models on graphs

In this paper we prove the existence of phase transitions at finite temperature for O(n) classical ferromagnetic spin models on infrared finite graphs. Infrared finite graphs are infinite graphs with $\lim {m\to 0^+} {\bar Tr (L+m)^{-1} < \infty$, where $L$ is the Laplacian operator of the graph. The ferromagnetic couplings are only requested to be bounded by two positive constants. The proof, inspired by the classical result of Fröhlich, Simon and Spencer on lattices, is given through a rigorous bound on the average magnetization. The result holds for $n\ge 1$ and it includes as a particular case the Ising model.

cond-mat.stat-mech↗