# PIECES

**Physics of Informative, Ecological, Cognitive and Economic Systems**

**National Coordinator (Responsabile Nazionale):**

name: Franco Bagnoli

INFN section: Firenze

e-mail: franco.bagnoli@unifi.it

**Local Coordinators (Responsabili Locali):**

(add as many items as necessary)

● name: Franco Bagnoli

INFN section: Firenze

e-mail: franco.bagnoli@unifi.it

● name: Armando Bazzani

INFN section: Bologna

e-mail: armando.bazzani@bo.infn.it

● name: Alessandro Pluchino

INFN section: Catania

e-mail: alessandro.pluchino@ct.infn.it

● name: Attilio Stella

INFN section: Padova

e-mail: attilio.stella@pd.infn.it

● name: Giuseppe Ali'

INFN section: Rende-Cosenza

e-mail: giuseppe.ali@gmail.com

● name: Marcello Borromeo

INFN section: Perugia

e-mail: marcello.borromeo@pg.infn.it

**Keywords**:

Complex systems, Self-organization, Cooperative effects, Sociophysics, Econophysics

**Abstract:**

This proposal concerns a broad investigation range that have common roots in statistical mechanics, dynamical systems and stochastic processes, and that have applications in physics, biology, cognitive sciences, sociology and economics. The common traits of these application fields are the emerging properties from collective phenomena, cooperative effects and counterintuitive phenomena rising from the interplay of environmental noise with the intrinsic nonlinearity of complex systems.

Examples of such systems range from purely biological one like regolative networks and the neural organization of the brain, to large-scale biological systems like ecosystems, population dynamics, evolutive population theory, to human-related systems. In particular, for what concerns cognitive (human-related) systems, we shall investigate them from the perspective of the single individual (psychological modeling), that of societies (sociophysics), economy and markets (econophysics), mobility systems (pedestrian and automotive) and technological aspects (e.g., Internet). This perspective would allow to explore the possibilities and the limits of a reductionist approach, and put into evidence the universal properties of such systems, as for instance those that lead to the emergence of complex social networks, and the interplay among different levels such as the relations among community structure, infectivity of a disease and its spreading characteristics.

An important application of these studies is in the information and computer technology field, both for what concerns unconventional computation techniques (such as chemical, biological or social computing) and for what concerns the interplay between informative systems and human behavior.

We shall apply techniques derived from theoretical physics, for instance dynamical system theory, bifurcation theory, chaos, synchronization, stochastic equations, stochastic processes, quantum structures, statistical physics methods, phase transitions, criticality, disordered systems theory, small systems, large deviations, long-range coupling, network theory, etc..

We shall also investigate possible applications of these activities to industrial mathematics, especially where complex systems and transport phenomena are involved, susceptible of a network description.

**Composition of the participant Research Units:**

● INFN Section Firenze

● Staff members

● Franco Bagnoli (researcher, Università di Firenze, 80%)

● Roberto Livi (full professor, Università di Firenze, 30%)

● Duccio Fanelli (associate professor, Università di Firenze, 70%)

● Alessandro Torcini (researcher, CNR Firenze, 100% corresponding to 50%)

● Stefano Boccaletti (first researcher, CNR Firenze, 100% corresponding to 50%)

● Cecilia Pennetta (associate professor, Università di Lecce, 100%)

● Post-docs, Ph.D students, Fellows

● Cianci Claudia (PhD student, 100%)

● Lucia Pettinato, (PhD student, 100%)

● Marta Galanti, (PhD student, 100%)

● Stefano Luccioli (post-doc CNR, 100%)

● Simona Olmi (post-doc CNR, 100%)

● Francesca Di Patti (post-doc Università 100%)

● Sandro Sozzo (foreign follow, Università di Lecce, 50%)

● INFN Section Bologna

● Staff members

● Armando Bazzani (associate professor, Università di Bologna, 50%)

● Sandro Rambaldi (associate professor, Università di Bologna, 50%)

● Daniel Remondini (researcher, Università di Bologna, 50%)

● Gastone Castellani (associate professor, Università di Bologna, 50%)

● Post-docs, Ph.D students, Fellows

● Enrico Giampieri (post-doc, 100%)

● Riccardo Gallotti (post-doc, 100%)

● Menichetti Giulia (post-doc, 100%)

● INFN Section Rende-Cosenza

● Staff members

● Giuseppe Alì (associate professor, Università della Calabria, 100%)

● Pietro Salvatore Pantano (full professor, Università di Calabria, 100%)

● Roberto Beneduci (researcher, Università di Calabria, 100%)

● Manuela Carini (researcher, Università di Calabria, 100%)

● Giovanni Mascali (researcher, Università di Calabria, 100%)

● Post-docs, Ph.D students, Fellows

● Rosa Claudia Torcasio, (PhD student 100%)

● INFN Section Catania

● Staff members

● Vito Latora (researcher, Università di Catania, 100%)

● Andrea Rapisarda (associate professor, Università di Catania, 50%)

● Alessandro Pluchino (researcher, Università di Catania, 50%)

● INFN Section Padova

● Staff members

● Attilio Stella (full professor, Università di Padova, 100%)

● Amos Maritan (full professor, Università di Padova, 100%)

● Enzo Orlandini (full professor, Università di Padova, 100%)

● Flavio Seno (full professor, Università di Padova, 100%)

● Marco Baiesi (researcher, Università di Padova, 100%)

● Antonio Trovato (researcher, Università di Padova, 100%)

● Fulvio Baldovin (researcher, Università di Padova, 100%)

● Post-docs, Ph.D students, Fellows

● Marco Formentin (Post-Doc, 100%)

● Samir Suweis, (Post-Doc, 100%)

● Claudio Borile, (Post-Doc, 100%)

● Jacopo Grilli, (PhD stident, 100%)

● INFN Section Perugia

● Staff members

● Marcello Borromeo (researcher, Università di Perugia, 100%)

● Umberto Marini Bettolo (associate professor, Università di Camerino, 40%)

● Marconi Stefano Mancini (associate professor, Università di Camerino, 50%)

● Palermo (to be associated to Catania)

● Staff members

● Bernardo Spagnolo (associate professor, Università di Palermo, to be associated 100%)

● Davide Valenti (researcher, Università di Palermo, to be associated 100%)

● Dominique Persano Adorno (researcher, Università di Palermo, to be associated 100%)

● Post-docs, Ph.D students, Fellows

● Claudio Guarcello (PhD student, to be associated 100%)

● Luca Magazzù (PhD student, to be associated 100%)

● Giovanni Denaro (PhD student, to be associated 100%)

● Stefano Spezia (Post-doc, to be associated 100%)

**Status of the relevant research field; scientific context, objectives and envisaged achievements of the proposed network program:**

In recent years the concepts of theoretical physics, in particular that related to statistical physics, dynamical systems and stochastic processes have been successfully applied to many fields, like earth systems, self organization in many fields, network theory, biological and computer viruses, evolutive patterns, cognitive sciences, computational complexity, ecosystems and food webs, pattern formation, etc.

Although these applications look quite scattered, there is a common background in the techniques used, and this is illustrated by the fact that most of proponents of this initiative are working in several different fields. Just as an example, the concept of network structure is central in many fields, as is that of synchronization, self-organization and critical phenomena. In other words, the theoretical background is that of complex systems formed by relatively simple components, where the complexity arises from collective phenomena (induced by criticality, network structure or synchronization), mesoscopic dimensions (intermediate from that typical of dynamical systems and that of statistical physics), non-linear effects and the noisy interaction with the environment.

This initiative aims at investigating the potentialities of application of such complex systems to several interdisciplinary areas, confronting the theoretical or numerical finding with experimental results and, where possible, designing experiments and interacting with them. This initiative complements DYNSYSMATH (ex MI41), which is much more mathematical and theoretical, and TO61, which is devoted to “microscopic” biophysics. We plan to maintain contacts with these initiatives by organizing exchange meetings with them. This initiative is moreover already catalyzing the interest of other participants, like the Palermo elements (not yet associated) that are planning to join the Catania unit in case of approvation. Moreover, some researchers already associated to INFN group V (applied physics) asked to join it.

There are at least two points of view that can be followed to illustrate this initiative: by common elements and by investigation themes.

Common elements are:

**Role of noise: **Stochastic resonance, noise enhanced stability and resonant activation phenomena in complex systems. Dynamics of phase transitions (Firenze, Palermo/Catania) and nonlinear relaxation phenomena in the presence of multiplicative noise. (Palermo/Catania). Fluctuations-induced pattern formation (Firenze, Palermo/Catania). Role of external and internal "environmental noise" in the nervous system (Firenze, Palermo/Catania). Effects of randomicity in human society and random trading (Catania)

**Network concept: **Structure and dynamics of complex networks and synchronization in networks (Catania). Interplay between network structure and spreading properties of diseases (Firenze). Community detection in networks (Firenze, Catania). Mathematical neural networks and networks of more realistic neurons. Neural networks with synaptic plasticity (Firenze, Catania). Social networks and transportations (Bologna, Firenze).

**Self organization:** Quorum sensing in bacteria (Padova) and self-propelling agents (Perugia). Desertification (Lecce/Firenze), landslides (Firenze) and earthquakes (Padova). Evolutionary patterns (Firenze) and structure of ecological networks (Padova, Catania). Emergence of collective behaviours in pulse coupled neuronal networks (Firenze)

We can also identify several overlapping topics, with a deep interplay of the different units, which is a promise of a strong interactions among them.

**Complex biological (eco) systems:**

Desertification processed modeled by stochastic CA (Lecce/Firenze). Diffusion and sensing of signal molecules in bacterial colonies (Padova). Structure of ecological networks (Padova, Catania). Dynamics of self-propelling agents like bacteria (Perugia). Evolutionary patterns: species formation, sexual selections, structure of evolving ecosystems (Firenze). Modeling of ant battles (Firenze). Nonlinear dynamics of interacting populations in ecological systems (plantonic and benthic foraminifera, small pelagics); in biological systems: populations of Nezara Viridula (green bug); in medical physics: viral and bacterial dynamics, models for cancer growth (Palermo/Catania).

**Nervous and cognitive systems: **Emergence of collective behaviours in coupled neuronal networks, response of single neurons to irregular stimuli and modeling of cognitive structures (Firenze). Neural network of C. elegans (Catania). Role of external and internal "environmental noise" in the nervous system, with respect to the sensory phenomena of "recognition" and "permanence of information" contained in complex input signals in the brain (Palermo/Catania)

**Human behavior, organization, mobility, cities (sociophysics):** Human mobility in game players, networks and humans (Catania). Effects of randomicity in human society, random trading (Catania). Traffic patterns and human behavior (Bologna), physics and structure of cities (Bologna, Catania). Dynamics of small groups, community detection, opinion formation and human heuristics (Firenze)

**Economics and finance (econophysics) : **Analysis of data from financial markets for risk management and its dynamical modeling. Stochastic models for the dynamics of financila markets (Palermo/Catania). Water (as equivalent currency) exchange among nations (Padova). Methods of the physics of complex systems applied to quantitative finance (Padova).

**Applied dynamical and stochastic systems: **Anomalous dynamics of polymers, especially translocation (Padova) and models of Langevin dynamics for the translocation of short polymer chains in the presence of external electric fields. (Palermo/Catania). Fluctuations-induced pattern formation (Firenze, Palermo/Catania). Particles in confined systems with massive simulations (Perugia) Transport phenomena in industrial applications, in particular semiconductors (Cosenza, Palermo/Catania). Interconnections among curvature, topology and complexity of motion (Perugia). Earthquakes (Padova), landslides triggered by rain (Firenze).

**Proposed activities and role of the various Research Units**

**Firenze: **Extended the concept of Turing instability to a generalized setting that holds promise to bridge the gap between theory and observation. We shall study pattern formation (e.g. Turing patterns and travelling wave) for reaction diffusion systems defined on a complex network (random/scale free). We will consider both stochastic and deterministic frameworks. We will study the process of diffusion under severe crowding condition for systems defined on both a regular lattice and/or a network.

Neuronal networks with short and long term plasticity: analysis of the response to impulsive stimuli. By following the experimental results by Bonifazi et al (Science 2009) on an network of excitatory neurons we plan to investigate the response of an excitatory plastic network (exhibiting bursting behaviour) with power-law distributed connectivity to impulsive stimuli. In order to understand the mechanisms at the basis of the network silencing induced by impulsive stimuli injected in hub neurons in the experimental work.

Dynamics of evolutive ecosystems: sympatric speciation, sexual selection, small-world effects in evolution. Human evolution and emergence of human huristics. Emergence of cognitive structures beyond the neural network concept (with experiments). Dynamics of small groups (with experiments). Opinion formation and the role of non-conformism. Interplay between risk perception, human heuristics and disease spreading. Applications of human heuristics to computer sciences.

Landslides triggering by rainfall and propagation by means of a model inspired by molecular dynamics. Models of ants battle (with experiments).

**Lecce (associated to Firenze): **Study of the desertification transition in semi-arid ecosystems. Abrupt desertification transitions induced by several kinds of external stresses and identification of early warning signals of desertification.

**Padova**: Diffusion and sensing of signal molecules in bacterial colonies. The theoretical modeling will be developed in close connected with experiments run by Prof. A. Squartini at DAFNAE (Unipd). Emergence of nested structures in ecosystems.

Anomalous dynamics of polymers, especially translocation. Active matter models.

The impact of fragmentation on biodiversity of the environment '(disordered ecosystems).

Models for earthquakes where each event can be seen as a unit that generates

off-springs according to its magnitude and to known correlations between events. Methods of the physics of complex systems applied to quantitative finance. Modeling of asset dynamics inspired by the renormalization group approach to critical phenomena. Option pricing beyond Black-Scholes based on closed formulas.

Network of virtual water flows (any amount 'of food can' be converted into a cost in terms of water needed to produce it).

**Catania: **Randomness in physical, social and economical systems. Effect of a small quantity of noise on the synchronization of a linear chain of coupled logistic maps. “Peter principle”, which induces a spreading of incompetence and inefficiency in hierarchical organizations. Effectiveness of random trading strategies with respect to the standard ones by means of simulations based on real time series of four popular financial all-share indexes. “Brain-drain” phenomenon as function of the agents’ social capital calculated, respectively, at home and abroad.

Remote synchronization in functional brain signals, suggesting that brain dynamics might result from the orchestrated activity of symmetrically-placed cortical

regions.

Network studies: Neural network of the C.elegans and a large urban area located north of Milano, as time-evolving read networks.

Properties of human mobility in a society of individuals, the players of an online-game, which provides complete information on their movements in a network-shaped universe and on their social and economic interactions. We reviewed the advantages of closed and open structures in social systems and we proposed a new measure, the ``Simmelian brokerage'', that captures opportunities of brokerage between otherwise disconnected cohesive groups of contacts.

**Perugia: **Diffusion and mobility of interacting particles moving in confined systems, by means of massively parallel simulations running on graphics cards. Evolution of self-propelling interacting particles. The investigated models are relevant in understanding the behaviour of bacteria colonies and will be studied using graphics card simulations.

Macroscopic description of a system by means of probabilities assigned to macro-variables in order to account for the lack of knowledge about their relations with the microscopic entities. The dynamics of such probabilities should take place according to information constraints. We propose the use of Riemannian geometry applied to probability theory together with inductive statistical inference (Maximum Relative Entropy methods). We will then investigate the interconnections among curvature, topology and complexity of motion (geodesic spread).

**Cosenza: **Mathematical models of semiconductors. Macroscopic models for transportation of charge carriers from the semiclassical Boltzmann equation, coupled with the principle of maximum entropy. Microscopic models for confined electrons in silicon devices, semiclassical in the direction transverse (hydrodynamic system), including quantum effects in the direction of confinement (Schroedinger-Poisson system). Theory of cellular neural networks for complexity, self-organizing systems and artificial life.

**Bologna**: Application of Statistical Physics methods to socio-economical and biological systems. The main goal is to understand how the macroscopic statistical laws that are suggested by the empirical observations on complex systems can be justified according to the dynamical properties of the heterogeneous elementary components and their interaction network. We propose a mesoscopic approach to study the emergent properties by developing a statistical physic approach to stochastic dynamical systems which interact through a network like structure. We will take advantage from the results of stochastic dynamical systems theory and the network theory. The goal is to characterize the existence of equilibria, stationary and almost stationary states, critical states and phase transitions. We also plan to develop a thermodynamic approach to describe the non-equilibrium states of the system and to study the fluctuation effects.

**Palermo (to be associated to Catania): **Stochastic Resonance, Noise Enhanced Stability and Resonant Activation phenomena in Complex Systems. Nonlinear dynamics of interacting populations in: Ecological Systems: Plantonic and benthic foraminifera, Small Pelagics. Biological Systems: Populations of Nezara Viridula (Green Bug) Medical Physics: Viral and Bacterial Dynamics, models for cancer growth. Role of external and internal noise in the nervous system. Stochastic dynamics of physical, biological and financial complex systems. Dynamics of Phase Transitions and nonlinear relaxation phenomena in the presence of multiplicative noise. Noise effects in spintronics and quantum open systems.

**Most significant publications of the last five years of each Research Unit:**

● **INFN Section Firenze**

1. D. Fanelli, C. Cianci, F. Di Patti Turing instabilities in reaction diffusion systems with cross diffusion, Europ. Phys. J B **86**, 142 (2013)

2. Malbor Asslani, Francesca Di Patti, Duccio Fanelli,Stochastic Turing patterns on a network. Physical Review E **86**, 046105-1- 046105-6, (2012).

3. Duccio Fanelli, Alan McKane, Diffusion in a crowded environment. Physical Review E, **82**, ISSN: 1539-3755 (2010).

4. J. Haas, T. Kreuz, A. Torcini, A. Politi, and HDI Abarbanel, "Rate maintenance and resonance in the entorhinal cortex", European J. Neuroscience **32**, 1930-1939 (2010).

5. K. Mikkelsen, A. Imparato, and A. Torcini, " Emergence of slow collective oscillations in neural networks with spike timing dependent plasticity", Phys. Rev. Lett. **110**, 208101 (2013).

6. S. Luccioli, S. Olmi, A.Politi, and A. Torcini, "Collective dynamics in sparse networks", Phys. Rev. Lett. **109**, 138103 (2012).

7. G Martelloni, F Bagnoli, E Massaro, A computational toy model for shallow landslides: Molecular Dynamics approach, Communications in Nonlinear Science and Numerical Simulation **18**, 2479–2492 (2013).

8. E Massaro, F Bagnoli, A Guazzini, P Lió, Information dynamics algorithm for detecting communities in networks, Communications in Nonlinear Science and Numerical Simulation **17**, 4294-4303 (2012).

9. V Nicosia, F Bagnoli, V Latora, Impact of network structure on a model of diffusion and competitive interaction EPL (Europhysics Letters) **94** (6), 68009 (2011).

10. F Bagnoli, P Lió, How the mutational-selection interplay organizes the fitness landscape, Journal of Nonlinear Mathematical Physics **18** (supp02), 265-286 (2011).

● **INFN Section Catania**

1. V. Nicosia, M. Valencia, M. Chavez, A. Diaz-Guilera, V. Latora, Remote synchronization reveals network symmetries and functional modules,

Phys. Rev. Lett. **110**, 174102 (2013)

2. J. Gomez-Gardenes, V. Nicosia, R. Sinatra, V. Latora, Motion-induced synchronization in metapopulations of mobile agents, Phys. Rev. E **87**, 032814 (2013).

3. V. Nicosia, P. Vertes, W. Schafer, V. Latora, E. Bullmore, Phase transition in the economically modeled growth of a cellular nervous system, Proc. Natl. Acad. Sci. USA, **110**, 7880 (2013).

4. E. Strano, V. Nicosia, S. Porta, V. Latora, M. Barthelemy, Elementary processes governing the evolution of road networks, Scientific Reports **2**, 296 (2012).

5. M. Szell, R. Sinatra, G. Petri, S. Thurner, V. Latora, Understanding mobility in a social petri dish, Scientific Reports **2**, 457 (2012).

6. V. Latora, V. Nicosia, P. Panzarasa Social cohesion, structural holes, and a tale of two measures, J. Stat. Phys. **151** (3-4), 745 (2013).

7. A.Pluchino, A.Rapisarda, C.Garofalo, “Efficient Promotion Strategies in Hierarchical Organizations”, Physica A **390** (2011) 3496–3511

8. A.Pluchino, C.Garofalo, A.Rapisarda, S.Spagano, M.Caserta, “Accidental Politicians: How Randomly Selected Legislators Can Improve Parliament Efficiency”, Physica A **390**, 3944–3954 (2011)

9. A.E.Biondo, A.Pluchino, A.Rapisarda, “The beneficial role of random strategies in social and financial systems”, Journal of Statistical Physics **151,** 607-622 (2013).

10. A.E.Biondo, A.Pluchino, A.Rapisarda, “Return Migration after Brain Drain: a Simulation Approach”, Journal of Artificial Societies and Social Simulation, **16** 11 (2013).

● **INFN Section Perugia**

1. Marconi, UMB; Melchionna, S "Dynamics of fluid mixtures in nanospaces”, Journal of Chemical Physics **134** (2011)

2. Melchionna, S.; Marconi, U. Marini Bettolo, "Electro-osmotic flows under nanoconfinement: A self-consistent approach" Epl **95** (2011)

3. Marconi, UMB; Melchionna, S"Dynamic density functional theory versus kinetic theory of simple fluids" Journal of Physics-Condensed Matter Volume: 22 Issue: 36 (2010) DOI: 10.1088/0953-8984/22/36/364110

4. Marconi, UMB; Puglisi, A; Rondoni, L; et al. "Fluctuation-dissipation: Response theory in statistical physics" Physics Reports-Review Section of Physics Letters **461**,111-195 (2008).

5. Ammenti, A; Cecconi, F; Marconi, UMB; et al. "A Statistical Model for Translocation of Structured Polypeptide Chains through Nanopores" Journal of Physical Chemistry B **113**,10348-10356 (2009)

● **INFN Section Padova**

1. S. Suweis, A. Rinaldo, A. Maritan , P. D'Odorico, Proc. Natl. Acad. Sci. (USA), **10**, 92-95 (2013).

2. F Simini, A Maritan, Z Néda, Human Mobility in a Continuum Approach PloS one **8**, e60069 (2013).

3. T Anfodillo, M Carrer, F Simini, I Popa, JR Banavar, A Maritan, An allometry-based approach for understanding forest structure, predicting tree-size distribution and assessing the degree of disturbance, Proceedings of the Royal Society B: Biological Sciences **280**, 1751 (2013).

4. J Grilli, S Azaele, JR Banavar, A Maritan, Absence of detailed balance in ecology, EPL (Europhysics Letters) **100**, 38002 (2012).

5. C Borile, MA Muñoz, S Azaele, JR Banavar, A Maritan, Spontaneously Broken Neutral Symmetry in an Ecological System, Physical Review Letters **109**, 038102 (2012).

6. GK Iliev, E Orlandini, SG Whittington, Pulling polymers adsorbed on a striped surface, Journal of Physics A: Mathematical and Theoretical **46**, 055001 (2013).

7. GP Saracco, G Gonnella, D Marenduzzo, E Orlandini, Equilibrium and dynamical behavior in the Vicsek model for self-propelled particles under shear, Central European Journal of Physics **10**, 1109-1115 (2012)

8. F. Baldovin, A. L. Stella, Scaling and efficiency determine the irreversible evolution of a market, PNAS **104**, 19741 (2007)

● **INFN section Bologna**

1. Elisa Omodei, Armando Bazzani, Sandro Rambaldi, Paolo Michieletto, Bruno Giorgini, “The physics of the city: pedestrians dynamics and crowding panic equation in Venezia”, Quality & Quantity (7 October 2012), pp. 1-27 (2012)

2. Armando Bazzani, Bruno Giorgini, Sandro Rambaldi, Riccardo Gallotti, Luca Giovannini, “Statistical laws in urban mobility from microscopic GPS data in the area of Florence”, *J. Stat. Mech.*, **2010**, P05001, (2010).

3. Luciano Milanesi, Paolo Romano, Gastone Castellani, Daniel Remondini, Pietro Lio, “Trends in modeling Biomedical Complex Systems”, BMC Bioinformatics **10**, No. Suppl 12. (2009), I1.

4. Daniel Remondini, Enrico Giampieri, Armando Bazzani, Gastone Castellani, Amos Maritan, “Analysis of noise-induced bimodality in a Michaelis–Menten single-step enzymatic cycle”, Physica A: Statistical Mechanics and its Applications **392**, 336-342, (2013).

5. Animesh Agarwal, Rhys Adams, Gastone C. Castellani, Harel Z. Shouval, “On the precision of quasi steady state assumptions in stochastic dynamics”, The Journal of Chemical Physics, **137**, 044105, (2012).

6. Francesco Sassi, Cinzia Benazzi, Gastone Castellani, Giuseppe Sarli , “Molecular-based tumour subtypes of canine mammary carcinomas assessed by immunohistochemistry”, BMC Veterinary Research **6** 5, (2010).

7. Castellani, Gastone C., Armando Bazzani, and Leon N. Cooper. "Toward a microscopic model of bidirectional synaptic plasticity." Proceedings of the National Academy of Sciences **106**, 14091-14095 (2009).

8. Bazzani, Armando, et al. "Bistability in the chemical master equation for dual phosphorylation cycles." *The Journal of Chemical Physics* **136** 235102 (2012).

● **INFN section Cosenza**

1. G. Ali, G. Mascali, V. Romano, R.C. Torcasio, A Hydrodynamic Model for Covalent Semiconductors with Applications to GaN and SiC, Acta Appl. Math. 122(1) (2012) pp. 335-348.

2. G. Mascali, V. Romano, A hydrodynamical model for holes in silicon semiconductors: The case of parabolic warped bands, COMPEL **31** (2012) pp. 552-582.

3. G. Mascali, V. Romano, A non parabolic hydrodynamical subband model for semiconductors based on the maximum entropy principle, Mathematical and Computer Modelling **55** (2012) pp. 1003-1020.

4. G. Ali, M. Bisi, G. Spiga, I. Torcicollo, Kinetic approach to sulphite chemical aggression in porous media, Int. J. Nonlin. Mech. **47** (2012) pp. 769-776.

5. G. Mascali, V. Romano, D.V. Camiola, Numerical simulation of a double-gate MOSFET with a subband model for semiconductors based on the maximum entropy principle, Continuum Mech. Therm. **24** (2012) pp. 417-436.

6. G. Ali, N. Rotundo, On the Tractability Index of a Class of Partial Differential-Algebraic Equations, Acta Appl. Math. **122** (2012) pp. 3-17.

7. G. Mascali, V. Romano, A hydrodynamical model for holes in silicon semiconductors: The case of non-parabolic warped bands, Mathematical and Computer Modelling **53** (2011) pp. 213-229.

8. R. Beneduci, J. Brooke, R. Curran, F.E. Schroeck Jr., Classical Mechanics in Hilbert Space, Part 1, Int. J. Theor. Phys. **50** (2011) pp. 3682-3696.

9. R. Beneduci, J. Brooke, R. Curran, F.E. Schroeck Jr., Classical Mechanics in Hilbert Space, Part 2, Int. J. Theor. Phys. **50** (2011) pp. 3697-3723.

10. R. Beneduci, On the Relationships Between the Moments of a POVM and the Generator of the von Neumann Algebra It Generates, Int. J. Theor. Phys. **50** (2011) pp. 3724–3736.

● **Palermo (to be associated to Catania)**

1. Nicola Pizzolato, Alessandro Fiasconaro, Dominique Persano Adorno, and Bernardo Spagnolo, “Translocation dynamics of a short polymer driven by an oscillating force”, Journal of Chemical Physics **138**, 054902 (2013).

2. G. Denaro, A. La Cognata, D. Valenti, B. Spagnolo, A. Bonanno, W. Basilone, S. Mazzola, S. Zgozi, S. Aronica, “Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics”, Ecological Complexity **13** , 21-34 (2013).

3. Yu.V. Ushakov, A.A. Dubkov and B. Spagnolo, “Regularity of spike trains and harmony perception in a model of the auditory system”, Physical Review Letters **107**, 108103 (2011).

4. Nicola Pizzolato, Dominique Persano Adorno, Davide Valenti, Bernardo Spagnolo, “Stochastic dynamics of leukemic cells under an intermittent targeted therapy”, Theory in Biosciences, **130** 203-210 (2011).

5. Olga A. Chichigina, Alexander A. Dubkov, Davide Valenti, and Bernardo Spagnolo, “Stability in a system subject to noise with regulated periodicity”, Phys. Rev. E **84**, 021134 (2011). Selected for Focus PRL.

6. N. Pizzolato, A. Fiasconaro, D. Persano Adorno, B. Spagnolo, “Resonant activation in polymer translocation: new insights into the escape dynamics of molecules driven by an oscillating field”, Physical Biology **7**, 034001 (2010).

7. A. La Cognata, D. Valenti, A. A. Dubkov, and B. Spagnolo, “Dynamics of two competing species in the presence of Lévy noise sources”, Phys. Rev. E **82**, 011121 (2010). Selected for the July 15, 2010 issue of Virtual Journal of Biological Physics Research http://www.vjbio.org.

8. Yu. V. Ushakov, A. A. Dubkov, and B. Spagnolo, “Spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model”, Phys. Rev. E **81**, 041911 (2010).

9. Alessandro Fiasconaro and Bernardo Spagnolo, “Stability measures in metastable states with Gaussian colored noise”, Phys. Rev. E **80**, 041110 (2009).

10. B. Spagnolo, S. Spezia, L. Curcio, N. Pizzolato, A. Fiasconaro, D. Valenti, P. Lo Bue, E. Peri, S. Colazza, “Noise Effects in two different Biological Systems”, Eur. Phys. J. B **69**, 133 -146 (2009).

**List of the main international collaborations related to the proposal:**

1. Francesco Piazza, University of Orleans (France);

2. Alan McKane, University of Manchester (UK);

3. Timoteo Carletti, University of Namur (Belgium)

4. Raul Rechtman, Instituto de Energia Renovables, UNAM, Cuernavaca, Mexico.

5. Antonio Politi, Aberdeen University UK

6. Alberto Imparato e Kaare Mikkelsens, Aarhus University Denmark

7. Markus Baer, Physikalisch-Technische Bundesanstalt (PTB) Germany

8. Eshel Ben Jacob e Paolo Bonifazi, Tel Aviv University, Israel

9. Stephen Coombes e Noah Russel, Nottingham University, UK

10. Jorge Hidalgo e Miguel A. Munoz: Departamento de Electromagnetismo y Fsica de la Materia and Instituto Carlos I de Fsica Teorica y Computacional, Universidad de Granada. E-18071, Granada, Spain

11. J.R. Banavar: Department of Physics, University of Maryland, College Park, MD 20742, USA

12. A. Rinaldo, EPFL, Lausanne, Switzerland

13. S. Azaele, Department of mathematics, Leeds, UK.

14. F. Simini, Center for Complex Network Research and Department of Physics, Biology and Compute Science, Northeastern University, Boston, Massachusetts 02115, USA.

15. Sandro Vaienti CTP Luminy (Marsiglia) France

16. Leon Cooper Brown University Providence USA,

17. Dirk Helbing ETH Zurigo, Michael Batty UCL London

18. Alexander A. Dubkov, Radiophysics Department, Lobachevski State University, Nishny Novgorod, Russia

19. Lutz Schimansky-Geier, Department of Physics, Humboldt University, Berlin, Germany

20. Olga A. Chichigina, Physics Department, Lomonosov State University, Moscow, Russia.

21. Ewa Gudovska-Nowak, Marian Smoluchowski Institut of Physics, Jagellonian University, Max Kak Institute for Complex Systems, Jagellonian University of Krakow, Krakow, Poland.

22. Pietro Liò. Computer Laboratory, University of Cambridge, UK.