Raul De Maio

Raul De Maio

Ph.D. Candidate in Mathematical Modeling for Engineering, Electromagnetism and Nanosciences

La Sapienza S.B.A.I. Dep. - La Sapienza

Curriculum Vitae

About Me

From November 2015, I'm a PhD. student at La Sapienza - S.B.A.I. Department. At the moment, my research involves mathematical models about: transport-diffusion equations on networks, traffic management and optimization problems and fractional calculus. My aim is to use my research to make a contribution to our society through the use of Big Data and smart technologies.

I am also an avid traveler, always looking for something to know and learn. Some hobbies: photography, hiking, cooking.

Supervisors: Prof. Fabio Camilli (La Sapienza), Prof. Andrea Tosin (Politecnico di Torino).

Publications on "Fractional derivatives and Applications"

Memory effects in measure transport equations

F. Camilli, R. De Maio, 27th June 2018, submitted

We provide a well-posedness theory for weak measure solutions of the problem and an integral formula which generalizes the classical push-forward representation formula to this setting.

A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time derivative

F. Camilli, R. De Maio and E. Iacomini, 25th March 2018, submitted

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 trapping effects.

A time-fractional mean field game

F. Camilli and R. De Maio, 30th January 2018, accepted by Adv. in Diff. Eq.

We consider a Mean Field Games model where the dynamics of the agents is subdiffusive.

Publications on "Multiscale models for Vehicular Traffic on Networks"

A measure theoretic approach to traffic flow optimization on networks

S. Cacace, F. Camilli, R. De Maio and A. Tosin, 5th September 2018, accepted by European Journal of Applied Mathematics

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average speed,controlling few agents, for example smart traffic lights and automated cars. The measuretheoretic approach allows to study in a same setting local and nonlocal drivers interactionsand to consider the control variables as additional measures interacting with the driversdistribution. We also propose a gradient descent adjoint-based optimization method, ob-tained by deriving first-order optimality conditions for the control problem, and we providesome numerical experiments in the case of smart traffic lights for a 2-1 junction.

Measure-valued solutions to transport equations on networks with nonlocal velocity

F. Camilli, R. De Maio and A. Tosin, Journal of Diff. Eq., Vol. 254, Iss. 12, pg. 7213 - 7241, 15th June 2018

Transport of measures on networks

F. Camilli, R. De Maio and A. Tosin, Networks and Heterogeneous Media, Vol. 12, No. 2, June 2017


Notes


Teaching

Analysis II - Ingegneria Gestionale - La Sapienza A.A. 2016/2017

Lecturer and examiner for a 2nd year class in Analysis II. Subject: ordinary differential equations and differential forms.

Exam results of the winter session

Exercises and syllabus

Tutor - preparatory class in Mathematics - La Sapienza A.A. 2016/2017 and 2017/2018.

Lecturer and tutor for a class 100 new student in Engineering.

Experiences, projects and awards

Participant Mars42: Innovation School @ SISSA & TheDoers SISSA - Trieste, Italy, May/June 2018

Visiting researcher, with PhD Mobility Scholarship - Instituit Francais INRIA - Sophia Antipolis (NI), France, late September - December 2017

Research period abroad for a project about Big Data, IoT, smart cities and smart communities.

Consultant - FindYourDoc (July - October 2016)

Occasional experience as a consultant for a PMI of Nothern Italy, in Lecco area, to to process an algorithm able to estimate time, waste material and more from the data supplied by the company.

This experience has played a very important role in my training and it allowed me to understand how a doctorate can have a precious value within private industry.

Participant - 124th Worhskop ESGI, August 2016, Rome

During the 124th European Study Group with Industry, partecipation and collaboration in an international team to help SAG Italia in soles production process.

Participant (2nd Place) - 25X25 Talenti September - November 2015

In occasion of "25x25 Talenti", a project by Fondazione IBM:Italia, I had a short introduction to IoT, Cloud and Big Data. This experience ended with the team-project GrowNet (2nd place).