Boltzmann-type equations for multi-agent systems with label switching

Loy, Nadia; Tosin, Andrea

doi:10.3934/krm.2021027

Cited by 16 publications

(13 citation statements)

References 34 publications

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“…(i) microscopic models based on tracking the time evolution of the state of every node of the network (with the identification 'node = agent' or node = metapopulation) [11][12][13]; (ii) mesoscopic models which incorporate a statistical description of the connectivity of the individuals to describe the time evolution of the distribution function of the social traits of interest [9,10]; (iii) mesoscopic models, and corresponding macroscopic limits, in which the individuals are labelled by a variable discriminating their mutual interactions, which reproduces a (weighted) graph [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Opinion polarization in social networks

Loy

Raviola

Tosin

2022

Phil. Trans. R. Soc. A.

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In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a polarization switch of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarization switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.

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Section: Introductionmentioning

confidence: 99%

Opinion polarization in social networks

Loy

Raviola

Tosin

2022

Phil. Trans. R. Soc. A.

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“…Aggregate description: from kinetic to macroscopic equations. The kinetic equations describing the evolution of f i (t, v), i ∈ X , can be derived in the same way as in [24]. Namely, the system of the weak equations for the f i 's is the following:…”

Section: 3mentioning

confidence: 99%

“…Note that in (24) and ( 25) the product λ β ν β has been chosen as bifurcation parameter, λ β ν β is the critical value of λ β ν β , x = (ρ S , ρ I1 , ρ I2 , n I1 , n I2 ) is the state variables vector, F is the right-hand side of system (19), and z and w denote, respectively, the left and right eigenvectors corresponding to the null eigenvalue of the Jacobian matrix evaluated at criticality (i.e. at DFE and λ β ν β = λ β ν β ).…”

Section: Central Manifold Analysismentioning

confidence: 99%

An SIR–like kinetic model tracking individuals' viral load

Marca¹,

Loy

Tosin

2022

NHM

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<p style='text-indent:20px;'>In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load of each infected individual. Here, we investigate the interplay between the evolution of individuals' viral load and the epidemic dynamics from a theoretical point of view. We propose a stochastic particle model describing the infection transmission and the individual physiological course of the disease. Agents have a double microscopic state: a discrete label, that denotes the epidemiological compartment to which they belong and switches in consequence of a Markovian process, and a microscopic trait, measuring their viral load, that changes in consequence of binary interactions or interactions with a background. Specifically, we consider Susceptible–Infected–Removed–like dynamics where infectious individuals may be isolated and the isolation rate may depend on the viral load–sensitivity and frequency of tests. We derive kinetic evolution equations for the distribution functions of the viral load of the individuals in each compartment, whence, via upscaling procedures, we obtain macroscopic equations for the densities and viral load momentum. We perform then a qualitative analysis of the ensuing macroscopic model. Finally, we present numerical tests in the case of both constant and viral load–dependent isolation control.</p>

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“…e.g. [9]), which describe the density ρ of a population, split into different categories I = {1, . .…”

Section: Introductionmentioning

confidence: 99%

Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent

Burger¹,

Rossi²

2022

Preprint

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In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes. Besides problems in biology and physics, we also demonstrate that stochastic gradient descent, the most popular technique in machine learning, can be understood in this setting, when considering a time-continuous variant.Our analysis is focusing on the case of evolution in a collection of external potentials, for which we provide analytical and numerical results about the evolution as well as the stationary problem.

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Boltzmann-type equations for multi-agent systems with label switching

Cited by 16 publications

References 34 publications

Opinion polarization in social networks

Opinion polarization in social networks

An SIR–like kinetic model tracking individuals' viral load

Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent

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