## About

17

Publications

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86

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Introduction

Raul De Maio has been a PhD student at the Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome. Raul does research in Applied Mathematics and Analysis. Their current project is 'TraForSafe - Vehicular and pedestrian traffic models: from flow forecast to safety management.'

Additional affiliations

November 2018 - present

**ICONSULTING**

Position

- Consultant

Education

November 2015 - February 2019

## Publications

Publications (17)

Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the Expectation-Maximization algorithm. We propose an alternative approach based on the theory of Mean Field Games, a class of...

Measure Differential Equations (MDE) describe the evolution of probability measures driven by probability velocity fields, i.e. probability measures on the tangent bundle. They are, on one side, a measure-theoretic generalization of ordinary differential equations; on the other side, they allow to describe concentration and diffusion phenomena typi...

In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an agent of one of the populations represented by the components of the mixture model, and we introduce a correspo...

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective is to minimise/maximise macroscopic quantities, such as traffic volume or average speed, controlling few agents, for example smart traffic lights and automated cars. The measure theoretic appro...

In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an agent of one of the populations represented by the components of the mixture model, and we introduce a correspo...

We prove a representation formula of Hopf-Lax type for the solution of a Hamilton-Jacobi equation involving Caputo time-fractional derivative. Equations of these type are associated with optimal control problems where the controlled dynamics is replaced by a time-changed stochastic process describing the trajectory of a particle subject to random t...

Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the time-derivative with power-law kernels, are typical for memory effects in complex systems. In this paper we consid...

Presentation of PhD Defense on multiscale models for vehicular traffic on networks, held at La Sapienza (SBAI Department) 12th February 2019

These are some notes written almost one year ago. I have tried to "use" the frameworks studied during my PhD to interpret and understand the well known supervised task into the Machine Learning Field. Even if the subject is extremely interesting, I had some problems continuing this project because some aspects were still not clear to me.
Some rec...

Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the time-derivative with power-law kernels, are typical for memory effects in complex systems. In this paper we consid...

We study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable, but also on the solution itself. We prove existence, uniqueness and continuous dependence results for the solution of the problem intended in a suitable measure-theoretic sense. We also provide a representation for...

We propose a class of optimal control problems for measure-valued nonlinear transport equations introduced in [2,3] to deal with many problems concerning vehicular traffic on networks. The objective is to minimise/maximise macroscopic quantities controlling few agents, for example smart traffic lights and automated cars. The measure theoretic appro...

We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and the Fokker-Planck equations. We discuss separately the well-posedness for each of the two equations and then...

In this paper we formulate a theory of measure-valued linear transport equations on networks. The building block of our approach is the initial/boundary-value problem for the measure-valued linear transport equation on a bounded interval, which is the prototype of an arc of the network. For this problem we give an explicit representation formula of...

## Projects

Projects (2)

This project is concerned with modelling, control and simulation of vehicle and pedestrian traffic and of the related collective safety issues. One of the main goals is the mathematical description of driver-assist/autonomous vehicles in interaction with the flow of standard human-manned vehicles.
The mathematical methodology is based on:
- Boltzmann-type and Fokker-Planck kinetic equations;
- hydrodynamic limits;
- multiscale conservation laws;
- uncertainty quantification tools.
Extended description available here: http://staff.polito.it/andrea.tosin/pdf/TraForSafe.pdf