arXiv subjects

Paolo Frasca

Publications and source records attributed to Paolo Frasca.

At least 37 records · Page 2Linked to original sources

arXiv2023

Random Coordinate Descent for Resource Allocation in Open Multi-Agent Systems

We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In particular, we characterize the evolution of the distance to the minimizer in expectation by following a time-varying optimization approach which builds on two components. First, we establish the linear convergence of the algorithm in closed systems, in terms of the estimate towards the minimizer, for general graphs and appropriate step-size. Second, we estimate the change of the optimal solution after a replacement, in order to evaluate its effect on the distance between the current estimate and the minimizer. From these two elements, we derive stability conditions in open systems and establish the linear convergence of the algorithm towards a steady-state expected error. Our results enable to characterize the trade-off between speed of convergence and robustness to agent replacements, under the assumptions that local functions are smooth, strongly convex, and have their minimizers located in a given ball. The approach proposed in this paper can moreover be extended to other algorithms guaranteeing linear convergence in closed system.

cs.MA↗

arXiv2023

On Lyapunov functions for open Hegselmann-Krause dynamics

In this paper, we provide a formulation of an open Hegselmann-Krause (HK) dynamics where agents can join and leave the system during the interactions. We consider a stochastic framework where the time instants corresponding to arrivals and departures are determined by homogeneous Poisson processes. Then, we provide a survey of Lyapunov functions based on global and local disagreement, whose asymptotic behavior can be used to measure the impact of arrivals and departures. After proving analytical results on these Lyapunov functions in the open system, we illustrate them through numerical simulations in two scenarios characterized by a different number of expected agents.

eess.SY↗

arXiv2022

Doing data science with platforms crumbs: an investigation into fakes views on YouTube

This paper contributes to the ongoing discussions on the scholarly access to social media data, discussing a case where this access is barred despite its value for understanding and countering online disinformation and despite the absence of privacy or copyright issues. Our study concerns YouTube's engagement metrics and, more specifically, the way in which the platform removes "fake views" (i.e., views considered as artificial or illegitimate by the platform). Working with one and a half year of data extracted from a thousand French YouTube channels, we show the massive extent of this phenomenon, which concerns the large majority of the channels and more than half the videos in our corpus. Our analysis indicates that most fakes news are corrected relatively late in the life of the videos and that the final view counts of the videos are not independent from the fake views they received. We discuss the potential harm that delays in corrections could produce in content diffusion: by inflating views counts, illegitimate views could make a video appear more popular than it is and unwarrantedly encourage its human and algorithmic recommendation. Unfortunately, we cannot offer a definitive assessment of this phenomenon, because YouTube provides no information on fake views in its API or interface. This paper is, therefore, also a call for greater transparency by YouTube and other online platforms about information that can have crucial implications for the quality of online public debate.

cs.SI↗

arXiv2022

Resource allocation in open multi-agent systems: an online optimization analysis

The resource allocation problem consists of the optimal distribution of a budget between agents in a group. We consider such a problem in the context of open systems, where agents can be replaced at some time instances. These replacements lead to variations in both the budget and the total cost function that hinder the overall network's performance. For a simple setting, we analyze the performance of the Random Coordinate Descent algorithm (RCD) using tools similar to those commonly used in online optimization. In particular, we study the accumulated errors that compare solutions issued from the RCD algorithm and the optimal solution or the non-collaborating selfish strategy and we derive some bounds in expectation for these accumulated errors.

cs.MA↗

arXiv2022

On Online Attention Dynamics

This work aims at emphasizing a number of questions that, although crucial since the early days of media studies, have not yet been the object of the empirical and computational study that they deserve: How does collective attention concentrate and dissipate in modern communication systems? How do subjects and sources rise and fall in public debates? How are these dynamics shaped by media infrastructures? In the perspective of addressing these questions, this chapter provides a review of the literature on the dynamics of online content dissemination: our goal is to prepare the ground for the necessary study, which should comprise empirical investigation, mathematical modeling, numerical simulation, and rigorous system-theoretic analysis.

physics.soc-ph↗

arXiv2021

Random coordinate descent algorithm for open multi-agent systems with complete topology and homogeneous agents

We study the convergence in expectation of the Random Coordinate Descent algorithm (RCD) for solving optimal resource allocations problems in open multi-agent systems, i.e., multi-agent systems that are subject to arrivals and departures of agents. Assuming all local functions are strongly-convex and smooth, and their minimizers lie in a given ball, we analyse the evolution of the distance to the minimizer in expectation when the system is occasionally subject to replacements in addition to the usual iterations of the RCD algorithm. We focus on complete graphs where all agents interact with each other with the same probability, and provide conditions to guarantee convergence in open system. Finally, a discussion around the tightness of our results is provided.

cs.MA↗

arXiv2021

Generalized solutions to opinion dynamics models with discontinuities

Social dynamics models may present discontinuities in the right-hand side of the dynamics for multiple reasons, including topology changes and quantization. Several concepts of generalized solutions for discontinuous equations are available in the literature and are useful to analyze these models. In this chapter, we study Caratheodory and Krasovsky generalized solutions for discontinuous models of opinion dynamics with state dependent interactions. We consider two definitions of "bounded confidence" interactions, which we respectively call metric and topological: in the former, individuals interact if their opinions are closer than a threshold; in the latter, individuals interact with a fixed number of nearest neighbors. We compare the dynamics produced by the two kinds of interactions, in terms of existence, uniqueness and asymptotic behavior of different types of solutions.

math.OC↗

arXiv2021

A collaborative path to scientific discovery: Distribution of labor, productivity and innovation in collaborative science

In this work we dig into the process of scientific discovery by looking at a yet unexploited source of information: Polymath projects. Polymath projects are an original attempt to collectively solve mathematical problems in an online collaborative environment. To investigate the Polymath experiment, we analyze all the posts related to the projects that arrived to a peer reviewed publication with a particular attention to the organization of labor and the innovations originating from the author contributions. We observe that a significant presence of sporadic contributor boosts the productivity of the most active users and that productivity, in terms of number of posts, grows super-linearly with the number of contributors. When it comes to innovation in large scale collaborations, there is no exact rule determining, a priori, who the main innovators will be. Sometimes, serendipitous interactions by sporadic contributors can have a large impact on the discovery process and a single post by an occasional participant can steer the work into a new direction.

physics.soc-ph↗

arXiv2021

A Continuation Method for Large-Scale Modeling and Control: from ODEs to PDE, a Round Trip

In this paper we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space- and time-varying systems. When applied to a large-scale network, the continuation provides a PDE describing evolution of continuous state approximation that respects the spatial structure of the original ODE. Our method is illustrated by multiple examples including transport equations, Kuramoto equations and heat diffusion equations. As a main example, we perform the continuation of a Newtonian system of interacting particles and obtain the Euler equations for compressible fluids, thereby providing an original alternative solution to Hilbert's 6th problem. Finally, we leverage our derivation of the Euler equations to control multiagent systems, designing a nonlinear control algorithm for robot formation based on its continuous approximation.

eess.SY↗

arXiv2020

The Laplacian Spectrum of Large Graphs Sampled from Graphons

This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively approximated by using the degree function of the corresponding graphon. More specifically, we show how to approximate the distribution of the Laplacian eigenvalues and the average effective resistance (Kirchhoff index) of the graph. For all cases, we provide explicit bounds on the approximation errors and derive the asymptotic rates at which the errors go to zero when the number of nodes goes to infinity. Our main results are proved under the conditions that the graphon is piecewise Lipschitz and bounded away from zero.

math.PR↗

arXiv2020

The Rhythms of the Night: increase in online night activity and emotional resilience during the Spring 2020 Covid-19 lockdown

Context. The lockdown orders established in multiple countries in response to the Covid-19 pandemics are arguably one of the most widespread and deepest shock experienced by societies in recent years. Studying their impact trough the lens of social media offers an unprecedented opportunity to understand the susceptibility and the resilience of human activity patterns to large-scale exogenous shocks. Firstly, we investigate the changes that this upheaval has caused in online activity in terms of time spent online, themes and emotion shared on the platforms, and rhythms of content consumption. Secondly, we examine the resilience of certain platform characteristics, such as the daily rhythms of emotion expression. Data. Two independent datasets about the French cyberspace: a fine-grained temporal record of almost 100 thousand YouTube videos and a collection of 8 million Tweets between February 17 and April 14, 2020. Findings. In both datasets we observe a reshaping of the circadian rhythms with an increase of night activity during the lockdown. The analysis of the videos and tweets published during lockdown shows a general decrease in emotional contents and a shift from themes like work and money to themes like death and safety. However, the daily patterns of emotions remain mostly unchanged, thereby suggesting that emotional cycles are resilient to exogenous shocks.

physics.soc-ph↗

arXiv2020

Junk News Bubbles: Modelling the Rise and Fall of Attention in Online Arenas

In this paper, we present a type of media disorder which we call "`junk news bubbles" and which derives from the effort invested by online platforms and their users to identify and share contents with rising popularity. Such emphasis on trending matters, we claim, can have two detrimental effects on public debates: first, it shortens the amount of time available to discuss each matter; second it increases the ephemeral concentration of media attention. We provide a formal description of the dynamic of junk news bubbles, through a mathematical exploration the famous "public arenas model" developed by Hilgartner and Bosk in 1988. Our objective is to describe the dynamics of the junk news bubbles as precisely as possible to facilitate its further investigation with empirical data.

cs.SI↗

arXiv2020

Modeling limited attention in opinion dynamics by topological interactions

This work explores models of opinion dynamics with opinion-dependent connectivity. Our starting point is that individuals have limited capabilities to engage in interactions with their peers. Motivated by this observation, we propose a continuous-time opinion dynamics model such that interactions take place with a limited number of peers: we refer to these interactions as topological, as opposed to metric interactions that are postulated in classical bounded-confidence models. We observe that topological interactions produce equilibria that are very robust to perturbations.

eess.SY↗

arXiv2020

On the Influence of Noise in Randomized Consensus Algorithms

In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower bounds that are simpler to evaluate. Motivated by the study of Open Multi-Agent Systems, we concentrate on Randomly Induced Discretized Laplacians, a family of update matrices that are generated by sampling subgraphs of a large undirected graph. For these matrices, we express the bounds by using the eigenvalues of the Laplacian matrix of the underlying graph or the graph's average effective resistance, thereby proving their tightness. Finally, we derive expressions for the bounds on some examples of graphs and numerically evaluate them.

eess.SY↗

arXiv2020

Graphon-based sensitivity analysis of SIS epidemics

In this work, we use the spectral properties of graphons to study stability and sensitivity to noise of deterministic SIS epidemics over large networks. We consider the presence of additive noise in a linearized SIS model and we derive a noise index to quantify the deviation from the disease-free state due to noise. For finite networks, we show that the index depends on the adjacency eigenvalues of its graph. We then assume that the graph is a random sample from a piecewise Lipschitz graphon with finite rank and, using the eigenvalues of the associated graphon operator, we find an approximation of the index that is tight when the network size goes to infinity. A numerical example is included to illustrate the results.

eess.SY↗

arXiv2019

The closed loop between opinion formation and personalised recommendations

In online platforms, recommender systems are responsible for directing users to relevant contents. In order to enhance the users' engagement, recommender systems adapt their output to the reactions of the users, who are in turn affected by the recommended contents. In this work, we study a tractable analytical model of a user that interacts with an online news aggregator, with the purpose of making explicit the feedback loop between the evolution of the user's opinion and the personalised recommendation of contents. More specifically, we assume that the user is endowed with a scalar opinion about a certain issue and seeks news about it on a news aggregator: this opinion is influenced by all received news, which are characterized by a binary position on the issue at hand. The user is affected by a confirmation bias, that is, a preference for news that confirm her current opinion. The news aggregator recommends items with the goal of maximizing the number of user's clicks (as a measure of her engagement): in order to fulfil its goal, the recommender has to compromise between exploring the user's preferences and exploiting what it has learned so far. After defining suitable metrics for the effectiveness of the recommender systems (such as the click-through rate) and for its impact on the opinion, we perform both extensive numerical simulations and a mathematical analysis of the model. We find that personalised recommendations markedly affect the evolution of opinions and favor the emergence of more extreme ones: the intensity of these effects is inherently related to the effectiveness of the recommender. We also show that by tuning the amount of randomness in the recommendation algorithm, one can seek a balance between the effectiveness of the recommendation system and its impact on the opinions.

cs.SI↗

arXiv2019

Functional target controllability of networks: structural properties and efficient algorithms

In this paper we consider the problem of controlling a limited number of target nodes of a network. Equivalently, we can see this problem as controlling the target variables of a structured system, where the state variables of the system are associated to the nodes of the network. We deal with this problem from a different point of view as compared to most recent literature. Indeed, instead of considering controllability in the Kalman sense, that is, as the ability to drive the target states to a desired value, we consider the stronger requirement of driving the target variables as time functions. The latter notion is called functional target controllability. We think that restricting the controllability requirement to a limited set of important variables justifies using a more accurate notion of controllability for these variables. Remarkably, the notion of functional controllability allows formulating very simple graphical conditions for target controllability in the spirit of the structural approach to controllability. The functional approach enables us, moreover, to determine the smallest set of steering nodes that need to be actuated to ensure target controllability, where these steering nodes are constrained to belong to a given set. We show that such a smallest set can be found in polynomial time. We are also able to classify the possible actuated variables in terms of their importance with respect to the functional target controllability problem.

eess.SY↗

arXiv2019

Protecting shared information in networks: a network security game with strategic attacks

A digital security breach, by which confidential information is leaked, does not only affect the agent whose system is infiltrated, but is also detrimental to other agents socially connected to the infiltrated system. Although it has been argued that these externalities create incentives to under-invest in security, this presumption is challenged by the possibility of strategic adversaries that attack the least protected agents. In this paper we study a new model of security games in which agents share tokens of sensitive information in a network of contacts. The agents have the opportunity to invest in security to protect against an attack that can be either strategically or randomly targeted. We show that, in the presence of random attack, under-investments always prevail at the Nash equilibrium in comparison with the social optimum. Instead, when the attack is strategic, either under-investments or over-investments are possible, depending on the network topology and on the characteristics of the process of the spreading of information. Actually, agents invest more in security than socially optimal when dependencies among agents are low (which can happen because the information network is sparsely connected or because the probability that information tokens are shared is small). These over-investments pass on to under-investments when information sharing is more likely (and therefore, when the risk brought by the attack is higher).

cs.SI↗