InSPIRES: a science shop project Giovanna Pacini, Franco Bagnoli Università di Firenze A science shop is a methodology in which the universities and research centres allow citizens and civil organisations to raising questions, present problems and issues on any topic, according with the available expertise. The answer may require a simple bibliographic consultation or a specific investigation. In any case, the research is assigned to students as part of their work for an exam or as the final dissertation, under the supervision of an experienced researcher. The InSPIRES project aims at favouring the birth of new science shops, especially in the south Europe and related countries, extract the best practices and experimenting with more participative methodologies. We shall illustrate some examples of existing science shops and the planned workflow for the University of Florence.

Accurate quantum chemical protocols for the determination of structural,spectroscopic and energetic properties of small and medium size molecular

systems of biochemical interest

Alice Balbi1, Nicola Tasinato1 and Vincenzo Barone1

1 Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italyalice.balbi@sns.it

Retrieving molecular structures is one of the principal concerns in many areas of chemistry, and the last decades have seen many efforts to determine accurate molecular geometries for systems of increasing sizeand complexity. Nowadays, this represents one of the main approaches to understand the structure of biochemical molecules, because of the close relation between molecular structure and functionality. In this context, rotational spectroscopy provides very accurate experimental information on the geometry of molecules in the gas phase, thus avoiding the complications arising from environmental effects in tuning the overall conformational behavior. Comparing this kind of data with those obtained from the condensed phase allows one to discriminate between the inter- and intra- molecular interactions. However, the interpretation of rotational spectra is often a difficult task, hence laboratory experiments are strongly supported by quantum chemical calculations carried out by using suitable computational protocols to achieve the required accuracy. Theoretical spectroscopic parameters are then employed to assist and guidethe interpretation of the experimental spectra. In order to accurately predict spectroscopic data, the harmonic force field should be computed at a suitable level of theory and then it is necessary to go beyond the harmonic approximation. For the purpose, the coupled cluster theory with singles, doubles excitations and a perturbative estimate of connected triples, CCSD(T), coupled to large basis sets has become the gold standard for the accurate prediction of thermochemical and spectroscopic properties of small molecules. Even more accurate results, rivaling the most refined experimental techniques, can be obtained employing composite schemes [1]. In particular, in the "cheap" computational protocol, developed to handle small bio-molecules, the CCSD(T)/cc-pVTZ level of theory is considered as the starting point, while missing contributions (e.g. basis set extrapolation, higher excitations, core correlationeffects) are recovered by employing second-order Møller–Plesset perturbation theory [2]. Anharmonic effects on structural, rotational and vibrational properties are then evaluated by density functional theory (DFT), specifically at B2PLYP/m-aug-cc-pVTZ-dH and B3LYP/SNSD levels.In this work, quantum chemical calculations exploiting the "cheap" computational protocol and DFT methods are performed for accurately determining the structural and rotational-vibrational spectroscopic properties of L-threonine, creatinine, D-cycloserine and methanimidic acid.

References[1] V. Barone, M. Biczysko, J. Bloino and C. Puzzarini, Phys. Chem. Chem. Phys. 15 (2013) 10094.

[2] C. Puzzarini, Int. J. Quantum. Chem. 116 (2016) 1513.

Small group students activity: a mathematical model forimprove the dynamics

Domenico Brunetto1

1 Department of Mathematics, Politecnico di Milano, Milan, Italybrunetto.domenico@polimi.it

Nowadays active learning have gained more and more attention since such a methodology allows to improve the student learing [1]. In particular, the flipped classroom and the group work activities in classroom are one of the most used form of active learning [2] , because during such activities the students act, interact and communicate much more than in usual frontal lessons settings [3]. In such a context, it is crucial to understand what are the variables which govern the student dynamics and even what is the role of the teacher during a small group activity. Thus, on the path of recent mathematical model of multi-agents dynamics and opinion dynamics [3, 4], Brunetto et al. [5] proposed a mathematical model for smallgroup work activities exploiting the opinion dynamics model [6] and the theoretical framework “I can”-”You can” introduced by Andrà et al. [7], moreover the teacher has a crucial role in group work activities. This work, based on [8], deals with the control problem of multi-agent systems, when the agentsare students who are asked to solve a mathematical task working in small group. The leader of the group is represented by the teacher who is allowed to make mathematical intervention during the students' activity with the purpose of improving students’ performance. Hence, the teacher opinion is the control variable of the dynamics which evolves to achieve some goals abstracted by an object function. To show the reliabilityof the model and the strategy of intervention of the teacher, we provide several numerical results and compare them with realistic scenarios .

More precisely, let N be the number of students whose opinions are abstracted by variables xi, i=1,…,N, while xN+1 represents the opinion of the teacher and x0 is the correct solution to the assigned math task. The dynamics of the group is described by a set of ordinary differential equations (e.g. see [6]) with suitable non-linear weights depending on the attitude of the students and their mathematical knowledge. In such a context, the teacher is supposed to act a strategy in order to minimize a suitable object function J which is designed to improve the students performance.

References [1] Prince, Michael. "Does active learning work? A review of the research." Journal of engineering education 93.3(2004): 223-231.[2] Jensen, Jamie L., et al. "Improvements from a flipped classroom may simply be the fruits of active learning."CBE-Life Sciences Education 14.1 (2015): ar5.[3] Sfard, Anna. "Learning mathematics as developing a discourse." Proceedings of 21st Conference of PME-NA.Clearing House for Science, Mathematics, and Environmental Education, 2001.[4] Albi, Giacomo, et al. "Recent advances in opinion modeling: control and social influence." Active Particles,Volume 1. Springer International Publishing, 2017. 49-98.[5] Brunetto, Domenico et al. "Student interactions during class activities: a mathematical model". Communicationin Applied and Industrial Mathematics [in press] [6] Hegselmann, Rainer, and Ulrich Krause. "Opinion dynamics and bounded confidence models, analysis, andsimulation." Journal of artificial societies and social simulation 5.3 (2002).[7] Andrà, Chiara, et al. "'I can–you can': Cooperation in group activities." CERME 9-Ninth Congress of theEuropean Society for Research in Mathematics Education. 2015.[8] Wongkaew, Suttida, et al. "On the control through leadership of the Hegselmann–Krause opinion formationmodel." Mathematical Models and Methods in Applied Sciences 25.03 (2015): 565-585.

Learning Dynamics in Complex Systems

Diletta Burini1,2,* and Silvana De Lillo1,2

1 Università degli Studi di Perugia2 INFN, Sezione di Perugia

*dilettaburini@alice.it

This talk proposes a systems approach to the theory of perception and learning in populations composed of many living entities. Starting from a phenomenological description of these processes, a mathematical structure is derived which is deemed to incorporate their complexity feature. The modeling is based on a generalization of kinetic theory methods where interactions are described by theoretical tools of game theory.

References

[1] D. Burini, S. De Lillo and L. Gibelli, Physics of Life Reviews 16 (2016) 123.

[2] D. Burini, S. De Lillo and L. Gibelli, Physics of Life Reviews 16 (2016) 152.

[3] D. Burini,Physics of Life Reviews 18 (2016) 25.

University of Bologna - Physics and Astronomy Department Abstract

Learning by message-passing in networks

of discrete synapses:

the tra�c congestion prediction

A. Bazzani, N. Curti, R. Luzi

inserire data precisa

Abstract

Belief Propagation (BP) is an iterative message passing algorithm that can be used toderive marginal probabilities on a system within the Bethe-Peierls approximation. It isnot well understood how this deep learning method is able to learn and how it doesn'tget trapped in con�gurations with low computational performance. Since we aim toclassify the congestion situations, we analyze the fundamental diagram of tra�c whichgives a relation between the tra�c �ow and the tra�c density. A tra�c congestionoccurs when the density of the road grows up and the �ow decreases. In order to predictcongestion situations, we train the BP neural network using binarized vectors obtainedby the processing of the fundamental diagram. We apply our method to real data whichhave been recorded by tra�c detectors provided by Emilia Romagna region.

References

[1] Jiquan Ngiam, Adam Coates, Ahbik Lahiri, Bobby Prochnow, Quoc V Le, and An-drew Y Ng, On optimization methods for deep learning. In Proceedings of the 28th

International Conference on Machine Learning (ICML-11), pages 265�272, 2011.

[2] N. Brunel, V. Hakim, P. Isope, J.-P. Nadal, B. Barbour, Neuron 43, pages 745-757,2004.

[3] M. Mezard and G. Parisi, The Cavity Method at Zero Temperature Journal of Statis-tical Physics, Vol. 111, Nos. 1/2, April 2003.

[4] D. Achlioptas, F. Ricci-Tersenghi, On the solution-space geometry of random con-

straint satisfaction problems STOC 2006.

[5] A. Braunstein and R. Zecchina, Survey Propagation as local equilibrium equations J.Stat. Mech. Theory Experiment (JSTAT), p06007, 2004.

1

University of Bologna - Physics and Astronomy Department Abstract

[6] A. Braunstein, R. Mulet, A. Pagnani, M. Weigt, and R. Zecchina, Polynomial iterativealgorithms for coloring and analyzing random graphs Phys. Rev. E 68, 036702, 2003.

[7] U. Feige, E. Mossel and D. Vilenchik, Complete convergence of message passing algo-rithms for some satis�ability problems, In Proceedings of Random 2006, LNCS 4110Springer, 339�350,2006.

[8] M. Mezard and R. Zecchina Random K-satis�ability: from an analytic solution to a

new e�cient algorithm Phys.Rev. E E, 66, 056126, 2002.

[9] T. Richardson and R. Urbanke, The Capacity of Low-Density Parity Check Codes

under Message-Passing Decoding, IEEE Trans. Info. Theory, Vol. 47, pp 599-618,2001.

[10] J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible In-

ference, San Francisco, CA: Morgan Kaufmann, 1988.

[11] N. Friedman, Inferring Cellular Networks Using Probabilistic Graphical Models Sci-ence; 303(5659):799-805, Feb 6 2004.

[12] I. Gat-Viks, A. Tanay, D. Raijman and R. Shamir, Factor graph network models for

biological systems Proc. of RECOMB 2005, pp. 31-47, Lecture Notes in Bioinformatics3500, Springer, Berlin, 2005.

[13] C. Yanover and Y. Weiss, Approximate inference and protein folding Advances inNeural Processing Systems, 2002.

[14] M. Tappen and W. Freemand, Graph cuts and belief propagation for stereo, using

identical MRF parameters ICCV, 2003.

[15] B. Frey and D. Dueck, Clustering by Passing Messages Between Data Points Science315, 972, 2007.

[16] C. Baldassi, A. Ingrosso, C. Lucibello, L. Saglietti and R. Zecchina, SubdominantDense Clusters Allow for Simple Learning and High Computational Performance in

Neural Networks with Discrete Synapses Physical Review Letters, 115(12):128101,September 2015.

[17] C. Baldassi, C. Borgs, J. Chayes, A. Ingrosso, C. Lucibello, L. Saglietti and R.Zecchina,Unreasonable E�ectiveness of Learning Neural Networks: From Accessi-

ble States and Robust Ensembles to Basic Algorithmic Schemes arXiv:1605.06444v3,2016.

[18] D.JC MacKay, Information theory, inference and learning algorithms Cambridgeuniversity press, 2003.

[19] J. S. Yedidia, W. T. Freeman and Y. Weiss, Constructing free-energy approximationsand generalized belief propagation algorithms Information Theory, IEEE Transactionson, 51(7):2282�2312, 2005.

2

Nonlinear diffusion in material tissues:

a free boundary problem

Diletta Burini1,2 and Silvana De Lillo1,2,*

1 Università degli Studi di Perugia2 INFN, Sezione di Perugia*silvana.delillo@pg.infn.it

A free boundary problem on a nite interval is formulated and solved for a nonlinear diusion-convection equation. The model is suitable to describe drug diusion in arterial tissues after the drug is released by an arterial stent. The problem is reduced to a system of nonlinear integral equations, admitting a unique solution for small time. The existence of an exact solution corresponding to a moving front is also shown.

References

[1] D. Burini and S. De Lillo, J. Phys. A: Math. Theor. 45 (2012) 405201.

[2] S. McGinty and G. Pontrelli, J. Control. Release 217 (2015) 327.

[3] S. De Lillo and A.S. Fokas, Physica Scripta 89 (2014) 1.

Effects of backbone protonation on Tyrosine UV-VIS absorption spectrum

Sara Del Galdo1, Oliver Carrillo-Parramon1, Massimiliano Aschi2, Giordano Mancini1,4,Andrea Amadei3 and Vincenzo Barone1,4

1 Scuola Normale Superiore di Pisa, Pisa, 56126, Italia. 2 Università di L’Aquila, L’Aquila, 67100, Italia.

3 Università di Roma Tor Vergata, Roma, 00100, Italia.4Istituto Nazionale di Fisica Nucleare (INFN) sezione di Pisa, Pisa, 56127, Italia.

e-mail: sara.delgaldo@sns.it

The UV-Vis spectral properties of aromatic amino acids can be exploited to probe protein structure,dynamics and interactions. In particular, Tyrosine (Tyr) spectroscopy is routinely used for studying proteinsresponse to environmental changes. Tyrosine’s phenolic side chain (the p-Cresol) is highly sensitive to itsmolecular environment thus making Tyr spectroscopy an appropriate choice for such a purpose. In thisregard, a detailed understanding of the environmental effects on the chromophore electronic properties ishighly important [1].

In this study, we theoretically reproduce the UV-Vis absorption spectrum of aqueous solutions of p-Cresol, and zwitterionic, cationic and anionic Tyrosines, pinpointing the effects of the backboneprotonation on the electronic absorption properties of the chromophore. To this purpose, we apply thePerturbed Matrix Method (PMM). The PMM is a method based on the first principles of QuantumMechanics which permits to include the effects of the environment in the evaluation of the quantumproperties of a quantum center (i.e. the system subpart to be treated at quantum mechanical level). Themethod was developed by Amadei et al. [2] and recently implemented in the Gaussian package withseveral improvements [3]. Molecular Dynamics (MD) simulations provided the statistical-mechanicalensemble for the study. To achieve a better accuracy in the MD sampling, the Force Field (FF) wasparameterized ad hoc for each solute of interest, deriving all the FF parameters according to the procedureimplemented in JOYCE software [4].

References [1] J. M. Antosiewicz and D. Shugar, Biophys. Rev. (2016) 163.

[2] M. Aschi, R. Spezia, A. Di Nola and A. Amadei, Chem. Phys. Lett. (2001) 374.

[3] O. Carrillo et al. J. Chem. Theory Compu. (under revision).

[4] V. Barone et al., Phys. Chem. Chem. Phys. (2013) 3736.

Force Field Parametrization of Metal Ions From Statistical Learning Techniques.

Francesco Fracchia1, Gianluca Del Frate1, Giordano Mancini1, Vincenzo Barone1 1 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

francesco.fracchia@sns.it

A novel statistical procedure has been developed to optimize the parameters of a theoretical model through a supervised training process. The method exploits the combination of the linear ridge regression and the cross-validation techniques [1] with the differential evolution algorithm [2]. Both linear and non-linear parameters can be optimized, allowing the optimization of a wide variety of functional forms of the model. The procedure has been applied to the parametrization of non-bonded force fields of metal ions in soft matter, using as output references ab initio forces and energies calculated for model systems. The methodology has been tested by generating the force fields of five metal ions (Zn2+, Ni2+ Mg2+, Ca2+, and Na+) in water. The estimates of the thermodynamic and structural properties calculated from molecular dynamics simulations using our force fields are on average of better quality of the state of art level [3]. References [1] J. Friedman, T. Hastie, R. Tibshirani, The Elements of Statistical Learning, (Springer, Berlin, 2001).

[2] R. Storn, K. Price, J. Glob. Optim 11. (1997). 341.

[3] P. Li, B. P. Roberts, D. K. Chakravorty, K. M. Merz, J. Chem. Theory Comput. 9. (2013). 2733.

Statistical models for (financial) networks Fabrizio Lillo Università di Bologna In this talk I will survey some recent advances in the statistical modelling of networks and I will discuss their application in the financial domain. I will consider the interbank market and I show how a suitable Stochastic Block Model can be used to identify the large scale (for example core-periphery) structure of the network. I then consider the dynamics of a network, proposing a statistical time series model able to capture the interplay between link temporal persistence and the memory properties of the nodes fitness. Finally, by using the Maximum Entropy principle, I will propose a method for reconstructing a bipartite network from partial information, showing that this method is very effective in estimating the systemic risk due to fire sale spillovers and portfolio overlaps among banks.

Force Fields development: case studies and applications examples. Marina Macchiagodena1, Giordano Mancini1, Marco Pagliai2, Gianluca Del Frate1,

Vincenzo Barone1 1 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

2 Dipartimento di Chimica “Ugo Schiff”, Università degli Studi di Firenze, Via della Lastruccia

3, 50019 Sesto Fiorentino, Italy.

marina.macchiagodena@sns.it

Computational methods such as Molecular Dynamics (MD) are powerful tools to estimate macroscopic

properties from microscopic models [1]. These methodologies have shown to be especially useful to

investigate the structure of organic liquids that are used as solvents in chemical, biological, and

technological sectors. In classical MD, electronic degrees of freedom are replaced by a simplified set of

functions called Force Field (FF) in order to make atomistic simulations computationally feasible. FFs are

usually trained on the basis of higher level (quantum mechanical) calculations and/or experimental data.

The selection and the availability of the most appropriate FF for the system to be investigated is crucial for

the reliability of the simulation results. Another critical aspect in FFs is the electrostatic interactions based

on the generation of partial charges. Several strategies have been followed to determine appropriate partial

atomic charges, one of them is to optimize their values to reproduce the QM derived electrostatic potential

surrounding a molecule [2]. The atomic charges values depend strongly on the level of theory used in QM

calculation and the description of solvation effects.

Here, we present a FFs development method for different classes of molecules with minimal use of

empiric parameters and able to reproduce experimental values of target properties and to explain

accurately their microscopic liquid structure.

One studied molecular class is formed by flexible molecules which requires dihedral angles

parameterization, essential to describe conformational equilibrium [3]. Another class consists of aromatic

molecules, for which a new protocol for point charges fitting has been developed [4].

The new FFs has been applied to perform MD simulations of pure liquids as well solutions. Bulk

properties and an accurate nanoscopic description have been derived and compared with experimental

data.

References

[1] D. C. Rapaport, The art of molecular dynamics simulation, edited by Cambridge university Press, 2007.

[2] A. V. Marenich, S. Jerome, C. J. Cramer, D. Truhlar, J. Chem. Theory Comput., 2012, 8, 527.

[3] M. Macchiagodena, G. Mancini, M. Pagliai, V. Barone, Phys. Chem. Chem. Phys., 2016, 18, 25342.

[4] M. Macchiagodena, G. Mancini, M. Pagliai, G. Del Frate, V. Barone, Chemical Physics Letters, 2017, 677, 120.

Franco Bagnoli, Gianmario Marelli Università di Firenze Recent results about the Mercedes-Benz water model The Mercedes-Benz model of water is a simple two-dimensional model that can reproduce some of the anomalies of water, in particular the decrease of density of ice with respect to liquid water. We describe the lattice version of the model and discuss its phase diagram with respect to the variation of some parameters. We also show how to reproduce the phenomenon of supercooled water and the eutectic effect of salt and ice mixtures.

Hydrogen Bond Dynamics of Imidazole in Water

Giada Funghi1, Marco Pagliai1, Piero Procacci1, Gianni Cardini1 1Dipartimento di Chimica “Ugo Schiff”, Università degli Studi di Firenze, via della Lastruccia 3,

Sesto Fiorentino (FI), 50019, Italy.

marco.pagliai@unifi.it

Imidazole is an aromatic heterocycle with a 5-membered ring, as shown in Figure 1. The imidazole ring

occurs, as molecule or building block, in systems with important biological, pharmacological and chemical

applications [1,2]. In water, at physiological pH, imidazole is present both as neutral and protonated

species and interacts with this solvent forming hydrogen bonds [2]. To characterize the structural and

dynamic properties of imidazole in water, ab initio molecular dynamics simulations have been performed

with the Car-Parrinello method (CPMD) [3]. During these simulations, the potential is determined within

the framework of density functional theory, whereas the van der Waals interactions have been properly

considered with the Grimme method [4].

Since CPMD simulations provide a description of the hydrogen bond interactions in agreement with

experimental findings [2], selected results have been adopted to validate a series of force fields for classical

molecular dynamics simulations. Accurate force fields are needed to determine structural and dynamic

properties of imidazole in aqueous solution for a correct interpretation of the experimental measurements.

Figure 1. Molecular structure of imidazole. Atom colors: carbon, grey; nitrogen, blue; hydrogen, white.

References

[1] M. S. Shaik, S. Y. Liem, Y. Yuan and P. L. A. Popelier, Phys. Chem. Chem. Phys. 12 (2010) 15040.

[2] E. Duboué-Dijon, P. E. Mason, H. E. Fischer and P. Jungwirth, J. Chem. Phys. 146 (2017) 185102.

[3] R. Car and M. Parrinello, Phys. Rev. Lett. 55 (1985) 2471.

[4] S. Grimme, J. Comput. Chem. 27 (2006) 1787.

A Rare Mutation Model in a Spatial Heterogeneous Environment Anna Lisa Amadori1,2, Roberto Natalini2 and Davide Palmigiani2,3

1 Dipartimento di Scienze Applicate, Università di Napoli “Parthenope”, Napoli, Italy. 2 Istituto per le Applicazioni del Calcolo “M.Picone” (C.N.R.), Roma, Italy.

3 Dipartimento di Matematica, Università di Roma “La Sapienza”, Roma, Italy.

e-mail address of corresponding author: davide@palmigiani.it

We propose a stochastic model in evolutionary game theory where individuals (or subpopulations) can

mutate changing their strategies randomly (but rarely) and explore the external environment. This

environment affects the selective pressure by modifying the payoff arising from the interactions between

strategies. We derive a Fokker-Plank integro-differential equation and provide Monte Carlo simulations

for the Hawks vs Doves game. In particular we show that, in some cases, taking into account the external

environment favors the persistence of the low-fitness strategy.

Evolutionary Dynamics describes biological systems subject to Darwinian Evolution by taking into

account the main mechanisms and phenomena of Evolution itself. In [2], Maynard Smith and Price

propose an instance of this approach by considering a population modified according to the replicator

dynamics, a system of diffential equations describing the selection and adaptation mechanism.

The rate of increment of a type is given by its absolute fitness, balanced with the average fitness of the

population. In evolutionary matrix game theory the vector of absolute fitness is defined by means of a

matrix of payoff that rules the interplay between different strategists.

However, it is clear that the basic element for the generation of evolutionary novelties are mutations. The

quasispecies equation, dating back to the 1970s, modifies the growth rate of each species by considering

the dispersion due to the birth of mutated offspring. However, an important aspect of mutations stands in

their randomness, which is quite underrated in the quasispecies equation. Since then many more refined

models have been proposed to put into the right light randomness; we refer at [1], where it has been

proposed a macroscopic stochastic model where mutations occur at a different time scale than selection.

Within the framework of social dilemma, where the types are read as strategies, a "mutation" happens

when a player changes his strategy. The model in [1] assumes that such events happen on rare and

random occasions, even more than once before the system reaches its stable state.

In this paper we take a step further and address our attention to the environment, seen as a place where

individuals can evolve but also as a factor that can influence the dynamics of interaction between

strategists. The model takes into account how the natural environment can modify the interactions

between individuals, changing selective pressures; we add a new variable that stands for the position of

the population or, more widely, for an external parameter that affects the results of the interplay between

strategies. It changes according to a velocity, partly deterministic, partly stochastic, and influences the

selection mechanism because the payoff matrix depends on y. In some particular cases, the environment

itself allows for the survival of the low fitness species.

References

[1] A.L. Amadori, A. Calzolari, R. Natalini, and B. Torti. (2015) Rare mutations in evolutionary dynamics. Journal

of Differential Equations, 259 (11): 6191-6214.

[2] J. Maynard Smith and G. R. Price. (1973) The logic of animal conflict. Nature, 246:15-18.

Mean field coarse-graining of confined fluidsGiovanni Pireddu1, Federico G. Pazzona1, Giuseppe B. Suffritti1 and Pierfranco Demontis1

1University of Sassari, Sassari, 07100, Italy. gpireddu@uniss.it

Nowadays, multiscale modelling techniques hold great promise for the representation of physical systemsin relatively broad spatial and temporal scales. Such procedures involve the combination of differentcomputational tools describing the same system at different resolutions. Reaching larger scales oftenrequires performing a coarse-graining procedure in order to obtain a simpler but more computationallyefficient model. At a coarse-grained level, stochastic models are very often used to address the problem of modelling ofadsorption and diffusion of fluids in microporous materials. In order to represent accuratelythermodynamic properties, such as the average local density as a function of the fugacity, it is crucial toestimate correctly the amount of free energy associated with each local configuration of the coarse-graineddegrees of freedom. For this purpose, Tunca and Ford proposed a Monte Carlo approach based on theExpanded Ensemble Method to calculate the partition function of an isolated pair of connected pores [1].In this work, we introduce a new protocol to obtain a coarse-grained model by employing a mean fieldapproximation of the pore lattice. In this procedure, instead of considering isolated pores and isolated pairof connected pores, the first neighborhood is included as a set of fictitious, mean field, pores, whichimitates the same topology of the reference system. This method allows including first neighborscontributions to single-cell and pair partition functions estimates.For the sake of comparison between the two approaches, we chosen to use a simple lattice gas model as acommon reference system. Such models are commonly used to simulate fluid adsorption and diffusion in acertain environment, from a molecular point of view [2]. Due to the discrete nature of lattice models, localpartition functions can be calculated exactly, producing a flawless reference for the comparison purpose.The reference lattice is a grid of sites, each able to host one molecule at most, and its global state is definedby the set of occupancies of all the sites. In the coarse-grained version of such system, the lattice isuniformly partitioned into non-overlapping cells, each containing the same number of sites, and the state ofthe coarse-grained system is defined as the set of cell (rather than site) occupancies.The effective occupancy dependent free energy of single cells and cell pairs are estimated throughrecurrence relations, implying precise mean field models of the cell lattice. Local free energies aresupposed to depend on temperature but not on the fugacity (or chemical potential). Finally, the system issimulated via a Metropolis-Hastings scheme. This model is capable of accurately reproduce referencesystem static properties such as the average occupancy and local density fluctuations.

References [1] C. Tunca and D. M. Ford, J. Phys. Chem. B. 106 (2002) 10982.

[2] F. G. Pazzona, P. Demontis and G. B. Suffritti, J. Chem. Phys. 131 (2009). 234703.

Exploiting network knowledge for biomedical application Daniel Remondini Università di Bologna Network are ubiquitous in nature, and particularly in biology, due to the strong interacting nature of its elements (cells, genes, proteins, metabolites). In this presentation we will give an overview of which biological data can be used for this approaches, and which biological datasets can be exploited which already show a network structure. A case study on real data will be shown, that combines multiple biological and clinical data from public databases for developing new multidrug treatments or perform trans-tumour drug translation in oncology.

Kinetic and Multiscale Models of Traffic FlowsAndrea Tosin1

1 Politecnico di Torino, Torino, 10129, Italyandrea.tosin@polito.it

In this talk we present a modelling approach to multi­agent systems, with special reference to vehicular andpedestrian traffic, based on Boltzmann­type kinetic equations and measure­valued conservation laws. Wediscuss how to pass from microscopic binary interactions to the description of emerging collective trendsby means of probabilistic and multiscale representations of the particle system. In particular, we show thathyperbolic equations with non­local flux accounting for interactive dynamics arise as a natural modellingparadigm in such a context under a suitable scaling of the kinetic equations.

References[1] F. Camilli, R. De Maio, A. Tosin, Transport of measures on networks, Netw. Heterog. Media, 12(2):191­215,

2017

[2] A. Corbetta, A. Tosin, Comparing first order microscopic and macroscopic crowd models for an increasingnumber of massive agents, Adv. Math. Phys., 2016:6902086/1­17, 2016

[3] E. Cristiani, B. Piccoli, A. Tosin, Multiscale modeling of granular flows with application to crowd dynamics,Multiscale Model. Simul., 9(1):155­182, 2011

[4] E.   Cristiani,   B.   Piccoli,   A.   Tosin,  Multiscale   Modeling   of   Pedestrian   Dynamics,   Springer   InternationalPublishing, 2014

[5] E. Cristiani, A. Tosin, Reducing complexity of multiagent systems with symmetry breaking: an application toopinion dynamics with polls, arXiv:1706.03115 (preprint), 2017

[6] L. Fermo, A. Tosin, A fully­discrete­state kinetic theory approach to modeling vehicular traffic, SIAM J. Appl.Math., 73(4):1533­1556, 2013

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Opinion dynamics over kinetic networks Mattia Zanella1

1 Politecnico di Torino, Torino, 10129, Italy.mattia.zanella@polito.it

In recent years the importance of large scale social networks has grown enormously due to the rapidproliferation of novel communication platforms. The need to handle with millions, and often billions, ofvertices implies a considerable shift of interest to large-scale statistical properties of networks which maybe described through the methods of the kinetic theory. In this talk we propose a kinetic description of theagents' distribution over the evolving network which combines an opinion update based on binaryinteractions between agents with a dynamic creation and removal process of new connections [1,2,3]. Thenumber of connections of each agent influences the spreading of opinions in the network, further the wayconnections are created is influenced by the agents' opinion. We will study the evolution of the network ofconnections by showing that its asymptotic behavior is consistent both with Poisson distributions andtruncated power-laws. In order to study the large time behavior of the opinion dynamics we derive amean-field description which allows to compute exact stationary solutions in some simplified situations.Structure preserving numerical methods are hence employed to describe correctly the large time behaviorof the system, see [4,5].

References[1] G. Albi, L. Pareschi, G. Toscani, M. Zanella. Recent advance in opinion modeling: control and social influence.

In Active Particles Volume 1, Advances in Theory, Models and Applications, Eds. N. Bellomo, P. Degond, E.Tadmor,, Birkhäuser-Springer, 2017.

[2] G. Albi, L. Pareschi, M. Zanella. Opinion dynamics over complex networks: kinetic modelling and numericalmethods. Kinetic and Related Models, 10(1): 1-32, 2017.

[3] L. Pareschi, P. Vellucci, M. Zanella. Kinetic models of collective decision-making in the presence of equalitybias. Physica A: Statistical Mechanics and its Application, 467: 201-217, 2017.

[4] G. Dimarco, L. Pareschi, M. Zanella. Uncertainty quantification for kinetic models in socio-economic and lifesciences. In Uncertainty Quantification for Hyperbolic and Kinetic Equations, Eds. S. Jin, L. Pareschi, SEMASIMAI Springer Series, to appear.

[5] L. Pareschi, M. Zanella. Structure preserving schemes for nonlinear Fokker-Planck equations and applications.Journal of Scientific Computing, to appear.