[34] L. Bartoli, S. Cacace, E. Cristiani, R. Ferretti
A macroscopic pedestrian model with variable maximal density
> arXiv:2406.14649
> code Test 1

[33] E. Cristiani, N. Loy, M. Menci, A. Tosin
Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions
> arXiv:2310.19700

[32] M. Briani, E. Cristiani, E. Onofri
Inverting the fundamental diagram and forecasting boundary conditions: How machine learning can improve macroscopic models for traffic flow
> arXiv:2303.12740

[31] E. Cristiani, M. Menci, A. Malagnino, G. G. Amaro
An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances
Physica A, 616 (2023), 128625
> article (open access)
> code Test 1a
> code Test 3
To use the code please acknowledge the authors of the paper and GAe Engineering srl for funding the research

[30] E. Cristiani, A. De Santo, M. Menci
A generalized mean-field game model for the dynamics of pedestrians with limited predictive abilities
Commun. Math. Sci., 21 (2023), 65-82
> arXiv:2108.00086

[29] G. G. Amaro, E. Cristiani, M. Menci
Preventing congestion in crowd dynamics caused by reversing flow
Math. Model. Computing, 9 (2022), 555-566
> article (open access)

[28] E. Cristiani, M. Menci, M. Papi, L. Brafman
An all-lader agent-based model for turning and flocking birds

J. Math. Biol., 83 (2021), 45
> arXiv:2010.01990

[27] M. Briani, E. Cristiani, P. Ranut
Macroscopic and multi-scale models for multi-class vehicular dynamics with uneven space occupancy: a case study

Axioms, 10 (2021), 102
> article (open access)

[26] P. Centorrino, A. Corbetta, E. Cristiani, E. Onofri
Managing crowded museums: visitors flow measurements, analysis, modeling, and optimization
J. Comput. Sci., 53 (2021), 101357
> article (open access)

[25] G. Albi, E. Cristiani, L. Pareschi, D. Peri
Mathematical models and methods for crowd dynamics control
In: L. Gibelli (ed.) “Crowd Dynamics Vol. 2 - Theory, Models, and Applications”, p. 159-197, Birkhńuser-Springer, 2020
> article

[24] P. Centorrino, A. Corbetta, E. Cristiani, E. Onofri
Measurement and analysis of visitors’ trajectories in crowded museums
2019 IMEKO TC-4 International Conference on Metrology for Archaeology and Cultural Heritage (Florence, December, 4-6, 2019)
> article

[23] A. Alla, C. Balzotti, M. Briani, E. Cristiani
Understanding mass transfer directions via data-driven models with application to mobile phone data
SIAM J. Appl. Dyn. Syst., 19 (2020), 1372-1391
> article

[22] M. Haghani, E. Cristiani, N. W. F. Bode, M. Boltes, A. Corbetta
Panic, irrationality, and herding: Three ambiguous terms in crowd dynamics research
J. Adv. Transport., Vol. 2019, Article ID 9267643.
> article

[21] E. Cristiani, E. Iacomini
An interface-free multi-scale multi-order model for traffic flow
Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 6189-6207

[20] E. Cristiani, D. Peri
Robust design optimization for egressing pedestrians in unkwnown environments
Appl. Math. Model., 72 (2019), 553-568

[19] E. Cristiani, M. C. Saladino
Comparing comparisons between vehicular traffic states in microscopic and macroscopic first-order models
Math. Meth. Appl. Sci., 42 (2019), 918-934

[18] G. Bretti, E. Cristiani, C. Lattanzio, A. Maurizi, B. Piccoli
Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road
Mathematics in Engineering, 1 (2018), 55-83

[17] C. Balzotti, M. Briani, A. Corbetta, E. Cristiani, M. Minozzi, R. Natalini, S. Suriano, F. Toschi
Forecasting visitors’ behaviour in crowded museums. A case study: The 'Galleria Borghese' in Rome
Proceedings of the 9th Conference on Pedestrian and Evacuation Dynamics (PED2018) (Lund, Sweden, August 21-24, 2018)
> article

[16] C. Balzotti, A. Bragagnini, M. Briani, E. Cristiani
Understanding human mobility flows from aggregated mobile phone data
IFAC-PapersOnLine, 51 (2018), 25-30

[15] E. Cristiani, A. Tosin
Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls
Multiscale Model. Simul. 16 (2018), 528-549
> article

[14] M. Briani, E. Cristiani, E. Iacomini
Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance
Commun. Math. Sci. 16 (2018), 123-144

[13] E. Cristiani, D. Peri
Handling obstacles in pedestrian simulations: models and optimization
Appl. Math. Model., 45 (2017), 285-302

[12] E. Cristiani, S. Sahu
On the micro-to-macro limit for first-order traffic flow models on networks
Netw. Heterog. Media, 11 (2016), 395-413

[11] G. Albi, M. Bongini, E. Cristiani, D. Kalise
Invisible control of self-organizing agents leaving unknown environments
SIAM J. Appl. Math., 76 (2016), 1683-1710

[10] E. Cristiani, F. S. Priuli
A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks
Netw. Heterog. Media, 10 (2015), 857-876

[9] E. Cristiani, F. S. Priuli, A. Tosin
Modeling rationality to control self-organization of crowds: an environmental approach
SIAM J. Appl. Math., 75 (2015), 605-629
> article

[8] E. Cristiani, B. Piccoli, A. Tosin
Multiscale modeling of pedestrian dynamics
Springer, 2014
Supplementary material

[7] M. Briani, E. Cristiani
An easy-to-use algorithm for simulating traffic flow on networks: theoretical study
Netw. Heterog. Media, 9 (2014), 519-552

[6] G. Bretti, M. Briani, E. Cristiani
An easy-to-use algorithm for simulating traffic flow on networks: numerical experiments
Discrete Contin. Dyn. Syst. Ser. S, 7 (2014), 379-394

[5] E. Cristiani, B. Piccoli, A. Tosin
How can macroscopic models reveal self-organization in traffic flow?
Proceedings of 51st IEEE CDC (Maui, Hawaii, USA, 10-13 dicembre 2012), 6989-6994

[4] E. Cristiani, B. Piccoli, A. Tosin
Multiscale modeling of granular flows with application to crowd dynamics
Multiscale Model. Simul., 9 (2011), 155-182
> article

[3] E. Cristiani, P. Frasca, B. Piccoli
Effects of anisotropic interactions on the structure of animal groups
J. Math. Biol., 62 (2011), 569-588

[2] E. Cristiani, B. Piccoli, A. Tosin
Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints
In: G. Naldi, L. Pareschi, G. Toscani (Eds.), “Mathematical modeling of collective behavior in socio-economic and life sciences”, 337-364, Birkhńuser Boston, Cambridge, MA, 2010

[1] E. Cristiani, C. de Fabritiis, B. Piccoli
A fluid dynamic approach for traffic forecast from mobile sensor data
Commun. Appl. Ind. Math., 1 (2010), 54-71
> article

[17] E. Cristiani
Hamilton-Jacobi equations
In: B. Engquist (ed.), Encyclopedia of Applied and Computational Mathematics, 625-627, Springer-Verlag, Berlin Heidelberg, 2015.

[16] S. Cacace, E. Cristiani, M. Falcone
Two semi-Lagrangian fast methods for Hamilton-Jacobi-Bellman equations
In: C. P÷tzsche et al. (Eds.), System Modeling and Optimization, Vol. 443, 74-84, Springer, 2014

[15] S. Cacace, E. Cristiani, M. Falcone
Can local single-pass methods solve any stationary Hamilton-Jacobi-Bellman equation?
SIAM J. Sci. Comput., 36 (2014), A570-A587 

[14] S. Cacace, E. Cristiani, M. Falcone
Numerical approximation of Nash equilibria for a class of non-cooperative differential games
In: L. Petrosjan and V. Mazalov (Eds.), Game Theory and Applications, Vol. 16, Ch. 4, Nova Publishers, New York, 2013

[13] S. Cacace, E. Cristiani, M. Falcone, A. Picarelli
A patchy dynamic programming scheme for a class of Hamilton-Jacobi-Bellman equations
SIAM J. Sci. Comput., 34 (2012), A2625-A2649
> article

[12] O. Bokanowski, E. Cristiani, J. Laurent-Varin, H. Zidani
Hamilton-Jacobi-Bellman approach for the climbing problem for multi-stage launchers
20th International Symposium on Mathematical Theory of Networks and Systems (Melbourne, Australia, July 9-13, 2012)
> article

[11] M. Breuss, E. Cristiani, P. Gwosdek, O. Vogel
An adaptive domain-decomposition technique for parallelization of the Fast Marching method
Appl. Math. Comput., 218 (2011), 32-44
> preprint, journal

[10] S. Cacace, E. Cristiani, M. Falcone
A local ordered upwind method for Hamilton-Jacobi and Isaacs equations
Proceedings of the 18th IFAC World Congress 2011
> article

[9] E. Cristiani, P. Martinon
Initialization of the shooting method via the Hamilton-Jacobi-Bellman approach
J. Optim. Theory Appl., 146 (2010), 321-346

[8] O. Bokanowski, E. Cristiani, H. Zidani
An efficient data structure and accurate scheme to solve front propagation problems
J. Sci. Comput., 42 (2010), 251-273

[7] E. Cristiani
A fast marching method for Hamilton-Jacobi equations modeling monotone front propagations
J. Sci. Comput., 39 (2009), 189-205
> preprint

[6] E. Cristiani, M. Falcone
Fully-discrete schemes for the value function of Pursuit-Evasion games with state constraints
Ann. Intl. Soc. Dyn. Games, 10 (2009), 178-205

[5] E. Cristiani, M. Falcone
A characteristics driven Fast Marching method for the eikonal equation
In: K. Kunisch, G. Of, O. Steinbach (eds.), Proceedings of ENUMATH 2007 (Graz, Austria, September 10-14, 2007), 695-702, Springer, 2008
> article

[4] E. Cristiani, M. Falcone
Numerical solution of the Isaacs equation for differential games with state constraints
Proceedings of 17th IFAC World Congress (Seoul, Korea, July 6-11, 2008)
> preprint

[3] E. Cristiani, M. Falcone
Fast semi-Lagrangian schemes for the Eikonal equation and applications
SIAM J. Numer. Anal., 45 (2007), 1979-2011

[2] E. Cristiani, M. Falcone
A Fast Marching method for pursuit-evasion games
In: Communications to SIMAI Congress, SIMAI 2006 (Baia Samuele, Ragusa, Italy, May 22-26, 2006), Vol. 1, 2006
> article

[1] E. Carlini, E. Cristiani, N. Forcadel
A non-monotone Fast Marching scheme for a Hamilton-Jacobi equation modelling dislocation dynamics
In: A. Berm˙dez de Castro, D. Gˇmez, P. Quintela, P. Salgado (eds.), Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2005 (Santiago de Compostela, Spain, July 2005), 723-731, Springer, Berlin, 2006
> article

[7] E. Cristiani, M. Falcone, S. Tozza
An overview of some mathematical techniques and problems linking 3D vision to 3D printing
In: E. Cristiani et al. (eds.), Mathematical Methods for Objects Reconstruction. INdAM 2021. Springer INdAM Series, Volume 54. Springer, Singapore, 2023

[6] S. Cacace, E. Cristiani, L. Rocchi
A level set based method for fixing overhangs in 3D printing
Appl. Math. Model., 44 (2017), 446-455
arXiv:1409.1714 (download Lena3D.stl)

[5] M. Breuss, E. Cristiani, J.-D. Durou, M. Falcone, O. Vogel
Perspective Shape from Shading: ambiguity analysis and numerical approximations
SIAM J. Imaging Sciences, 5 (2012), 311-342
> article

[4] O. Vogel, E. Cristiani
Numerical schemes for advanced reflectance models for Shape from Shading
Proceedings of the 18th IEEE ICIP 2011 (Bruxelles, Belgium, September 11-14, 2011)
> article

[3] M. Breuss, E. Cristiani, J.-D. Durou, M. Falcone, O. Vogel
Numerical algorithms for perspective shape from shading
Kybernetika, 46 (2010), 207-225
> article

[2] E. Cristiani, M. Falcone, A. Seghini
Some remarks on Perspective Shape-from-Shading models
In: F. Sgallari, A. Murli, N. Paragios (eds.), SSVM 2007 (Ischia, Italy, May 30 - June 2, 2007), LNCS 4485, 276-287, Springer-Verlag, Berlin Heidelberg, 2007
> article

[1] E. Cristiani, M. Falcone, A. Seghini
Numerical Solution of the Perspective Shape-from-Shading Problem
Proceedings of "Control Systems: Theory, Numerics and Applications" (Rome, Italy, March 30 - April 1, 2005).PoS (CSTNA2005) 008
> article

[4] E. Cristiani, M. Grassi, F. L. Ignoto, G. Pontrelli
Dissolution of variable-in-shape drug particles via the Level-Set method
> arXiv:2407.08350

[3] A. Cerasa, E. Cristiani, B. De Luca, M. L. Denarda, M. C. Cund˛, S. C. Bottani, I. Martino, A. Sarica, D. De Canditiis
May personality influence the selection of life-long mate?
Current Psychology, 2020
> article page

[2] S. Cacace, E. Cristiani, R. Ferretti
Blended numerical schemes for the advection equation and conservation laws
ESAIM: Math. Model. Numer. Anal., 51 (2017), 997-1019

[1] E. Cristiani
Blending Brownian motion and heat equation
J. Coupled Syst. Multiscale Dyn., 3 (2015), 351-356

PhD thesis
"Fast Marching and semi-Lagrangian methods for Hamilton-Jacobi equations with applications"  (download)
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, SAPIENZA - UniversitÓ di Roma
Supervisor: Prof. M. Falcone
Referee: Prof. J. A. Sethian (Berkeley, USA)
Ph.D. thesis was awarded the prize by INdAM-SIMAI as one of the three best Italian Ph.D. thesis in Applied Mathematics in the years 2006-8.

Master thesis (Tesi di Laurea)
"Algoritmi veloci per l'evoluzione dei fronti"  (download)
Dipartimento di Matematica, SAPIENZA - UniversitÓ di Roma
Supervisor: Prof. M. Falcone

[3] S. Cacace, E. Cristiani, D. D'Eustacchio
Myrmedrome: simulating the life of an ant colony
In: M. Emmer (Ed.), Imaging Math. 2. Between Culture and Mathematics
Springer, 2013

[2] E. Cristiani
Chiamalo x!, ovvero, Cosa fanno i matematici?
Springer, 2009

[1] E. Cristiani
Il caos nella scuola
Archimede, 4/2004, 171-177