arXiv subjects

Luca Rossi

Publications and source records attributed to Luca Rossi.

At least 73 records · Page 4Linked to original sources

arXiv2016

The Freidlin-Gartner formula for general reaction terms

We devise a new geometric approach to study the propagation of disturbance - compactly supported data - in reaction diffusion equations. The method builds a bridge between the propagation of disturbance and of almost planar solutions. It applies to very general reaction-diffusion equations. The main consequences we derive in this paper are: a new proof of the classical Freidlin-Gartner formula for the asymptotic speed of spreading for periodic Fisher-KPP equations, extension of the formula to the monostable, combustion and bistable cases, existence of the asymptotic speed of spreading for equations with almost periodic temporal dependence, multilevel propagation for multistable equations.

math.AP↗

arXiv2016

Symmetrization and anti-symmetrization in parabolic equations

We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones a quantitative estimate of how far the level sets of solutions are from being spherical. Next, using this property, we derive a criterion providing solutions whose level sets do not converge to spheres for a class of equations including linear equations and Fisher-KPP reaction-diffusion equations.

math.AP↗

arXiv2016

Transition waves for Fisher-KPP equations with general time-heterogeneous and space-periodic coefficients

This paper is devoted to existence and non-existence results for generalized tran-sition waves solutions of space-time heterogeneous Fisher-KPP equations. When the coefficients of the equation are periodic in space but otherwise depend in a fairly gen-eral fashion on time, we prove that such waves exist as soon as their speed is sufficiently large in a sense. When this speed is too small, transition waves do not exist anymore, this result holds without assuming periodicity in space. These necessary and sufficient conditions are proved to be optimal when the coefficients are periodic both in space and time. Our method is quite robust and extends to general non-periodic space-time heterogeneous coefficients, showing that transition waves solutions of the nonlinear equation exist as soon as one can construct appropriate solutions of a given linearized equation.

math.AP↗

arXiv2016

Efficient Computation of Decoherent Quantum Walks through Eigenvalue Perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving a state vector whose size is quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report, we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n^2 x n^2 Lindblad super-operator from the eigendecomposition of the n x n graph Hamiltonian.

quant-ph↗

arXiv2015

On a parabolic Hamilton-Jacobi-Bellman equation degenerating at the boundary

We derive the long time asymptotic of solutions to an evolutive Hamilton-Jacobi-Bellman equation in a bounded smooth domain, in connection with ergodic problems recently studied in \cite{bcr}. Our main assumption is an appropriate degeneracy condition on the operator at the boundary. This condition is related to the characteristic boundary points for linear operators as well as to the irrelevant points for the generalized Dirichlet problem, and implies in particular that no boundary datum has to be imposed. We prove that there exists a constant $c$ such that the solutions of the evolutive problem converge uniformly, in the reference frame moving with constant velocity $c$, to a unique steady state solving a suitable ergodic problem.

math.AP↗

arXiv2015

Spatio-Temporal Techniques for User Identification by means of GPS Mobility Data

One of the greatest concerns related to the popularity of GPS-enabled devices and applications is the increasing availability of the personal location information generated by them and shared with application and service providers. Moreover, people tend to have regular routines and be characterized by a set of "significant places", thus making it possible to identify a user from his/her mobility data. In this paper we present a series of techniques for identifying individuals from their GPS movements. More specifically, we study the uniqueness of GPS information for three popular datasets, and we provide a detailed analysis of the discriminatory power of speed, direction and distance of travel. Most importantly, we present a simple yet effective technique for the identification of users from location information that are not included in the original dataset used for training, thus raising important privacy concerns for the management of location datasets.

cs.CR↗

arXiv2015

The effect of a line with non-local diffusion on Fisher-KPP propagation

We propose here a new model of accelerating fronts, consisting of one equation with non-local diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation in the upper half-plane. The underlying biological question is to understand how transportation networks may enhance biological invasions. We show that the line accelerates the propagation in the direction of the line and enhances the overall propagation in the plane and that the propagation is directed by diffusion on the line, where it is exponentially fast in time. We also describe completely the invasion in the upper half-plane. This work is a non-local version of the model introduced in [Berestycki-Roquejoffre-Rossi 2013], where the line had a strong but local diffusion described by the classical Laplace operator.

math.AP↗

arXiv2015

Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control

For a class of Bellman equations in bounded domains we prove that sub- and supersolutions whose growth at the boundary is suitably controlled must be constant. The ellipticity of the operator is assumed to degenerate at the boundary and a condition involving also the drift is further imposed. We apply this result to stochastic control problems, in particular to an exit problem and to the small discount limit related with ergodic control with state constraints. In this context, our condition on the behavior of the operator near the boundary ensures some invariance property of the domain for the associated controlled diffusion process.

math.AP↗

arXiv2015

The effect on Fisher-KPP propagation in a cylinder with fast diffusion on the boundary

In this paper we consider a reaction-diffusion equation of Fisher-KPP type inside an infinite cylindrical domain in $\mathbb{R}^{N+1}$, coupled with a reaction-diffusion equation on the boundary of the domain, where potentially fast diffusion is allowed. We will study the existence of an asymptotic speed of propagation for solutions of the Cauchy problem associated with such system, as well as the dependence of this speed on the diffusivity at the boundary and the amplitude of the cylinder. When $N=1$ the domain reduces to a strip between two straight lines. This models the effect of two roads with fast diffusion on a strip-shaped field bounded by them.

math.AP↗

arXiv2015

Progmosis: Evaluating Risky Individual Behavior During Epidemics Using Mobile Network Data

The possibility to analyze, quantify and forecast epidemic outbreaks is fundamental when devising effective disease containment strategies. Policy makers are faced with the intricate task of drafting realistically implementable policies that strike a balance between risk management and cost. Two major techniques policy makers have at their disposal are: epidemic modeling and contact tracing. Models are used to forecast the evolution of the epidemic both globally and regionally, while contact tracing is used to reconstruct the chain of people who have been potentially infected, so that they can be tested, isolated and treated immediately. However, both techniques might provide limited information, especially during an already advanced crisis when the need for action is urgent. In this paper we propose an alternative approach that goes beyond epidemic modeling and contact tracing, and leverages behavioral data generated by mobile carrier networks to evaluate contagion risk on a per-user basis. The individual risk represents the loss incurred by not isolating or treating a specific person, both in terms of how likely it is for this person to spread the disease as well as how many secondary infections it will cause. To this aim, we develop a model, named Progmosis, which quantifies this risk based on movement and regional aggregated statistics about infection rates. We develop and release an open-source tool that calculates this risk based on cellular network events. We simulate a realistic epidemic scenarios, based on an Ebola virus outbreak; we find that gradually restricting the mobility of a subset of individuals reduces the number of infected people after 30 days by 24%.

cs.SI↗

arXiv2015

On the k-Anonymization of Time-varying and Multi-layer Social Graphs

The popularity of online social media platforms provides an unprecedented opportunity to study real-world complex networks of interactions. However, releasing this data to researchers and the public comes at the cost of potentially exposing private and sensitive user information. It has been shown that a naive anonymization of a network by removing the identity of the nodes is not sufficient to preserve users' privacy. In order to deal with malicious attacks, k-anonymity solutions have been proposed to partially obfuscate topological information that can be used to infer nodes' identity. In this paper, we study the problem of ensuring k-anonymity in time-varying graphs, i.e., graphs with a structure that changes over time, and multi-layer graphs, i.e., graphs with multiple types of links. More specifically, we examine the case in which the attacker has access to the degree of the nodes. The goal is to generate a new graph where, given the degree of a node in each (temporal) layer of the graph, such a node remains indistinguishable from other k-1 nodes in the graph. In order to achieve this, we find the optimal partitioning of the graph nodes such that the cost of anonymizing the degree information within each group is minimum. We show that this reduces to a special case of a Generalized Assignment Problem, and we propose a simple yet effective algorithm to solve it. Finally, we introduce an iterated linear programming approach to enforce the realizability of the anonymized degree sequences. The efficacy of the method is assessed through an extensive set of experiments on synthetic and real-world graphs.

cs.CR↗

arXiv2015

Privacy and the City: User Identification and Location Semantics in Location-Based Social Networks

With the advent of GPS enabled smartphones, an increasing number of users is actively sharing their location through a variety of applications and services. Along with the continuing growth of Location-Based Social Networks (LBSNs), security experts have increasingly warned the public of the dangers of exposing sensitive information such as personal location data. Most importantly, in addition to the geographical coordinates of the user's location, LBSNs allow easy access to an additional set of characteristics of that location, such as the venue type or popularity. In this paper, we investigate the role of location semantics in the identification of LBSN users. We simulate a scenario in which the attacker's goal is to reveal the identity of a set of LBSN users by observing their check-in activity. We then propose to answer the following question: what are the types of venues that a malicious user has to monitor to maximize the probability of success? Conversely, when should a user decide whether to make his/her check-in to a location public or not? We perform our study on more than 1 million check-ins distributed over 17 urban regions of the United States. Our analysis shows that different types of venues display different discriminative power in terms of user identity, with most of the venues in the "Residence" category providing the highest re-identification success across the urban regions. Interestingly, we also find that users with a high entropy of their check-ins distribution are not necessarily the hardest to identify, suggesting that it is the collective behaviour of the users' population that determines the complexity of the identification task, rather than the individual behaviour.

cs.CR↗

arXiv2015

The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations

We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given by this cone, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity.

math.AP↗

arXiv2015

Towards effective visual analytics on multiplex and multilayer networks

In this article we discuss visualisation strategies for multiplex networks. Since Moreno's early works on network analysis, visualisation has been one of the main ways to understand networks thanks to its ability to summarise a complex structure into a single representation highlighting multiple properties of the data. However, despite the large renewed interest in the analysis of multiplex networks, no study has proposed specialised visualisation approaches for this context and traditional methods are typically applied instead. In this paper we initiate a critical and structured discussion of this topic, and claim that the development of specific visualisation methods for multiplex networks will be one of the main drivers pushing current research results into daily practice.

cs.SI↗

arXiv2014

Admissible speeds of transition fronts for non-autonomous monostable equations

We consider a reaction-diffusion equation with a nonlinear term of the Fisher-KPP type, depending on time $t$ and admitting two limits as $t\to\pm\infty$. We derive the set of admissible asymptotic past and future speeds of transition fronts for such equation. We further show that any transition front which is non-critical as $t\to-\infty$ always admits two asymptotic past and future speeds. We finally describe the asymptotic profiles of the non-critical fronts as $t\to\pm\infty$.

math.AP↗

arXiv2014

Coding Together at Scale: GitHub as a Collaborative Social Network

GitHub is the most popular repository for open source code. It has more than 3.5 million users, as the company declared in April 2013, and more than 10 million repositories, as of December 2013. It has a publicly accessible API and, since March 2012, it also publishes a stream of all the events occurring on public projects. Interactions among GitHub users are of a complex nature and take place in different forms. Developers create and fork repositories, push code, approve code pushed by others, bookmark their favorite projects and follow other developers to keep track of their activities. In this paper we present a characterization of GitHub, as both a social network and a collaborative platform. To the best of our knowledge, this is the first quantitative study about the interactions happening on GitHub. We analyze the logs from the service over 18 months (between March 11, 2012 and September 11, 2013), describing 183.54 million events and we obtain information about 2.19 million users and 5.68 million repositories, both growing linearly in time. We show that the distributions of the number of contributors per project, watchers per project and followers per user show a power-law-like shape. We analyze social ties and repository-mediated collaboration patterns, and we observe a remarkably low level of reciprocity of the social connections. We also measure the activity of each user in terms of authored events and we observe that very active users do not necessarily have a large number of followers. Finally, we provide a geographic characterization of the centers of activity and we investigate how distance influences collaboration.

cs.SI↗

arXiv2014

Transition fronts for the Fisher-KPP equation

This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the class of transition fronts is much larger and the dynamics of the solutions of such equations is very rich. In the paper, we describe the class of transition fronts and we study their qualitative dynamical properties. In particular, we characterize the set of their admissible asymptotic past and future speeds and their asymptotic profiles and we show that the transition fronts can only accelerate. We also classify the transition fronts in the class of measurable superpositions of standard traveling fronts.

math.AP↗

arXiv2014

Collective attention in the age of (mis)information

In this work we study, on a sample of 2.3 million individuals, how Facebook users consumed different information at the edge of political discussion and news during the last Italian electoral competition. Pages are categorized, according to their topics and the communities of interests they pertain to, in a) alternative information sources (diffusing topics that are neglected by science and main stream media); b) online political activism; and c) main stream media. We show that attention patterns are similar despite the different qualitative nature of the information, meaning that unsubstantiated claims (mainly conspiracy theories) reverberate for as long as other information. Finally, we categorize users according to their interaction patterns among the different topics and measure how a sample of this social ecosystem (1279 users) responded to the injection of 2788 false information posts. Our analysis reveals that users which are prominently interacting with alternative information sources (i.e. more exposed to unsubstantiated claims) are more prone to interact with false claims.

cs.SI↗