arXiv subjects

Caterina De Bacco

Publications and source records attributed to Caterina De Bacco.

51 records · Page 3Linked to original sources

arXiv2020

Network extraction by routing optimization

Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a dynamical system of equations, which can instead be solved efficiently using numerical methods. This results in enabling the acquisition of optimal network topologies from a variety of routing problems. However, the actual extraction of the solution in terms of a final network topology relies on numerical details which can prevent an accurate investigation of their topological properties. In this context, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. In particular, in this framework, final graph acquisition is a challenging problem in-and-of-itself. Here we introduce a method to extract networks topologies from dynamical equations related to routing optimization under various parameters' settings. Our method is made of three steps: first, it extracts an optimal trajectory by solving a dynamical system, then it pre-extracts a network and finally, it filters out potential redundancies. Remarkably, we propose a principled model to address the filtering in the last step, and give a quantitative interpretation in terms of a transport-related cost function. This principled filtering can be applied to more general problems such as network extraction from images, thus going beyond the scenarios envisioned in the first step. Overall, this novel algorithm allows practitioners to easily extract optimal network topologies by combining basic tools from numerical methods, optimization and network theory. Thus, we provide an alternative to manual graph extraction which allows a grounded extraction from a large variety of optimal topologies.

physics.soc-ph↗

arXiv2020

Sampling on networks: estimating spectral centrality measures and their impact in evaluating other relevant network measures

We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures. In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other topological quantities. Our goal is on one hand to extend the analysis of the behavior of TCEC [Ruggeri2019], a theoretically-grounded sampling method for eigenvector centrality estimation. On the other hand, to demonstrate more broadly how sampling can impact the estimation of relevant network properties like centrality measures different than the one aimed at optimizing, community structure and node attribute distribution. Finally, we adapt the theoretical framework behind TCEC for the case of PageRank centrality and propose a sampling algorithm aimed at optimizing its estimation. We show that, while the theoretical derivation can be suitably adapted to cover this case, the resulting algorithm suffers of a high computational complexity that requires further approximations compared to the eigenvector centrality case.

cs.SI↗

arXiv2019

Sampling on networks: estimating eigenvector centrality on incomplete graphs

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios where data collection is expensive, the network is too big for data storage capacity or only partial information is available. The sampling algorithm is theoretically grounded by results derived from spectral approximation theory. We studied the problem on both synthetic and real data and tested the performance comparing with traditional methods, such as random walk and uniform sampling. We show that approximations obtained from such methods are not always reliable and that our algorithm, while preserving computational scalability, improves performance under different error measures.

cs.SI↗

arXiv2018

Community detection, link prediction, and layer interdependence in multilayer networks

Complex systems are often characterized by distinct types of interactions between the same entities. These can be described as a multilayer network where each layer represents one type of interaction. These layers may be interdependent in complicated ways, revealing different kinds of structure in the network. In this work we present a generative model, and an efficient expectation-maximization algorithm, which allows us to perform inference tasks such as community detection and link prediction in this setting. Our model assumes overlapping communities that are common between the layers, while allowing these communities to affect each layer in a different way, including arbitrary mixtures of assortative, disassortative, or directed structure. It also gives us a mathematically principled way to define the interdependence between layers, by measuring how much information about one layer helps us predict links in another layer. In particular, this allows us to bundle layers together to compress redundant information, and identify small groups of layers which suffice to predict the remaining layers accurately. We illustrate these findings by analyzing synthetic data and two real multilayer networks, one representing social support relationships among villagers in South India and the other representing shared genetic substrings material between genes of the malaria parasite.

cs.SI↗

arXiv2018

A physical model for efficient ranking in networks

We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that interactions are more likely to occur between individuals with similar ranks. It provides a natural statistical significance test for the inferred hierarchy, and it can be used to perform inference tasks such as predicting the existence or direction of edges. The ranking is obtained by solving a linear system of equations, which is sparse if the network is; thus the resulting algorithm is extremely efficient and scalable. We illustrate these findings by analyzing real and synthetic data, including datasets from animal behavior, faculty hiring, social support networks, and sports tournaments. We show that our method often outperforms a variety of others, in both speed and accuracy, in recovering the underlying ranks and predicting edge directions.

physics.soc-ph↗

arXiv2018

Are `Water Smart Landscapes' Contagious? An epidemic approach on networks to study peer effects

We test the existence of a neighborhood based peer effect around participation in an incentive based conservation program called `Water Smart Landscapes' (WSL) in the city of Las Vegas, Nevada. We use 15 years of geo-coded daily records of WSL program applications and approvals compiled by the Southern Nevada Water Authority and Clark County Tax Assessors rolls for home characteristics. We use this data to test whether a spatially mediated peer effect can be observed in WSL participation likelihood at the household level. We show that epidemic spreading models provide more flexibility in modeling assumptions, and also provide one mechanism for addressing problems associated with correlated unobservables than hazards models which can also be applied to address the same questions. We build networks of neighborhood based peers for 16 randomly selected neighborhoods in Las Vegas and test for the existence of a peer based influence on WSL participation by using a Susceptible-Exposed-Infected-Recovered epidemic spreading model (SEIR), in which a home can become infected via autoinfection or through contagion from its infected neighbors. We show that this type of epidemic model can be directly recast to an additive-multiplicative hazard model, but not to purely multiplicative one. Using both inference and prediction approaches we find evidence of peer effects in several Las Vegas neighborhoods.

econ.EM↗

arXiv2018

A matrix product algorithm for stochastic dynamics on networks, applied to non-equilibrium Glauber dynamics

We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, the new approach is based on a matrix product approximation of the so-called edge messages -- conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both, single instances as well as the thermodynamic limit. We employ it to examine prototypical non-equilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

cond-mat.stat-mech↗

arXiv2017

Dynamics of beneficial epidemics

Pathogens can spread epidemically through populations. Beneficial contagions, such as viruses that enhance host survival or technological innovations that improve quality of life, also have the potential to spread epidemically. How do the dynamics of beneficial biological and social epidemics differ from those of detrimental epidemics? We investigate this question using three theoretical approaches. First, in the context of population genetics, we show that a horizontally-transmissible element that increases fitness, such as viral DNA, spreads superexponentially through a population, more quickly than a beneficial mutation. Second, in the context of behavioral epidemiology, we show that infections that cause increased connectivity lead to superexponential fixation in the population. Third, in the context of dynamic social networks, we find that preferences for increased global infection accelerate spread and produce superexponential fixation, but preferences for local assortativity halt epidemics by disconnecting the infected from the susceptible. We conclude that the dynamics of beneficial biological and social epidemics are characterized by the rapid spread of beneficial elements, which is facilitated in biological systems by horizontal transmission and in social systems by active spreading behavior of infected individuals.

physics.soc-ph↗

arXiv2016

Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $α= m/n$ stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of $α$ and the distance between the clusters at which it becomes information-theoretically possible to reconstruct the membership into clusters better than chance. We also determine the accuracy achievable by the Bayes-optimal estimation algorithm. In particular, we find that when the number of clusters is sufficiently large, $r > 4 + 2 \sqrtα$, there is a gap between the threshold for information-theoretically optimal performance and the threshold at which known algorithms succeed.

stat.ML↗

arXiv2016

Stochastic Search with Poisson and Deterministic Resetting

We investigate a stochastic search process in one, two, and three dimensions in which $N$ diffusing searchers that all start at $x_0$ seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate $r$, or deterministically, with a reset time $T$. In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large $N$, resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for $N$ searchers, including the search time being independent of $T$ for $1/T\to 0$ and the search cost being independent of $N$ over a suitable range of $N$. Moreover, deterministic resetting typically leads to a lower search cost than in stochastic resetting.

cond-mat.stat-mech↗

arXiv2015

Rare events statistics of random walks on networks: localization and other dynamical phase transitions

Rare event statistics for random walks on complex networks are investigated using the large deviations formalism. Within this formalism, rare events are realized as typical events in a suitably deformed path-ensemble, and their statistics can be studied in terms of spectral properties of a deformed Markov transition matrix. We observe two different types of phase transition in such systems: (i) rare events which are singled out for sufficiently large values of the deformation parameter may correspond to {\em localized\/} modes of the deformed transition matrix, (ii) "mode-switching transitions" may occur as the deformation parameter is varied. Details depend on the nature of the observable for which the rare event statistics is studied, as well as on the underlying graph ensemble. In the present letter we report on the statistics of the average degree of the nodes visited along a random walk trajectory in Erdős-Rényi networks. Large deviations rate functions and localization properties are studied numerically. For observables of the type considered here, we also derive an analytical approximation for the Legendre transform of the large-deviations rate function, which is valid in the large connectivity limit. It is found to agree well with simulations.

cond-mat.stat-mech↗

arXiv2015

The average number of distinct sites visited by a random walker on random graphs

We study the linear large $n$ behavior of the average number of distinct sites $S(n)$ visited by a random walker after $n$ steps on a large random graph. An expression for the graph topology dependent prefactor $B$ in $S(n) = Bn$ is proposed. We use generating function techniques to relate this prefactor to the graph adjacency matrix and then devise message-passing equations to calculate its value. Numerical simulations are performed to evaluate the agreement between the message passing predictions and random walk simulations on random graphs. Scaling with system size and average graph connectivity are also analysed.

cond-mat.stat-mech↗

arXiv2015

The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.

cond-mat.dis-nn↗

arXiv2014

Shortest node-disjoint paths on random graphs

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length and the transition to the frustrated regime are analysed. The performance of the suggested algorithm is evaluated through a comparison against a greedy algorithm.

cond-mat.dis-nn↗

arXiv2014

Non-equilibrium statistical mechanics of the heat bath for two Brownian particles

We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a `system' is both perturbed and sensed by the Brownian particles. Non-local thermal fluctuation give rise to bath-mediated static forces between the particles. Based on the general sum-rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles' dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment as a part of the whole system is important for micron- or nano-scale physics.

cond-mat.stat-mech↗