XVIII CONVEGNO NAZIONALE DI FISICA STATISTICA E DEI SISTEMI COMPLESSI
Lunedì 24 - Mercoledì 26 giugno 2013, Università di Parma

sessione poster
Michele Bellingeri - Università degli Studi di Parma
Robustness of complex ecological networks
Food webs are ecological complex networks describing trophic relationships among species in ecosystems.Notions of system robustness to node loss, and of error and attack sensitivity were first introduced in the physical literature and then successfully applied to the study of food webs. We use simulations to test the robustness of 14 empirical food webs to species loss by varying a parameter I (intentionality) that defines the removal probability (extinction risk) of species with high number of trophic connections. The removal probability of highly connected species (nodes) increases with I. We found that food web robustness decreases slowly when the extinction risk of highly connected species increases (we call this region random removal regime), until a threshold value of I is reached. For greater values of the threshold, we found a dramatic reduction in robustness with increasing intentionality in almost all the food webs (intentional attack regime).The existence of a clear transition in system behaviour has relevant consequences for the interpretation of extinction patterns in ecosystems and prioritizing species for conservation planning.
Luca Caniparoli - SISSA Trieste
Synonymous but not the same: extracting information from codon bias
The genetic code is degenerate since most amino acids are translated by more than one synonymous codon. Although, the codons aren't used randomly and their choice is thought to encode a further layer of information. Here we develop a model which, given the sequences of mRNA as the only data, is able to capture some of this information: we introduce and compute the Codon Information Index (CII) for over 3000 transcripts from S. Cerevisiae, observing a remarkable correlation with the mRNAs and proteins abundance in the cell. Moreover, the CII is consistent with an index previously defined in the literature (the tAI).
Claudia Cianci - Università di Firenze
Turing instabilities in reaction-diffusion systems with cross diffusion
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share the same spatial reservoir and experience a degree of mutual interference due to the competition for the available resources. Turing instability can set in for all ratios of the main diffusivities, also when the (isolated) activator diffuses faster then the (isolated) inhibitor. This conclusion, at odd with the conventional vision, is here exemplified for the Brusselator model and ultimately stems from having assumed a generalized model of multispecies diffusion, fully anchored to first principles, which also holds under crowded conditions.
Francesca Di Patti - Università di Firenze
Stochastic Turing Patterns on Networks
The process of stochastic Turing instability on a network is discussed for a specific case study, the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes, outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically, and eventually traced back to the finite size corrections stemming from the inherent graininess of the scrutinized medium.
Andrea Galluzzi - Università di Roma "La Sapienza"
We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzmann machine and we show its thermodynamical equivalence to an associative working memory able to retrieve several patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky theory. Results obtained through statistical mechanics, the signal-to-noise technique, and Monte Carlo simulations are overall in perfect agreement and carry interesting biological insights. Indeed, these associative networks pave new perspectives in the understanding of multitasking features expressed by complex systems, e.g., neural and immune networks.
Alejandro Lage Castellanos - Politecnico di Torino
Metastable states of Edwards Anderson 2D using GBP
Generalized belief propagation gives good estimates of correlations of nearby spins in Edwards-Anderson 2D at high temperatures. However, below a certain temperature, an unphysical transition to a spin glass state is found. We show that in spite of not being correct as an equilibrium description of the state, the local magnetizations found by GBP characterize the metastable states in which a local Monte Carlo dynamics slows down. We show that this relation can be used in both senses, to speed up the Monte Carlo, and to seed the message passing.
Alejandro Lage Castellanos - Politecnico di Torino
Upstream contamination by floating particles
It has been known at least since the studies of Reynolds and Marangoni in the 1880's that floating particulates strongly affect water surface behaviors, and research involving particle-surface effects continues in modern applications ranging from microfluidics and self-cleaning surfaces to colloidal dynamics and self-assembly. Here we analyze the behavior of fine particles on a steady downstream flow. Surprisingly, we find that rapid and robust vortices appear, transporting particulate material upstream at accelerations as much as 20 times gravity. We confirm through experiments and simulations that this upstream contamination is paradoxically driven by downstream flow of clean water which establishes a surface tension gradient that sustains the particulate motion. We briefly outline possible implications of this work.
Gianluca Martelloni - Università di Firenze
3D molecular dynamics scheme for landslide modeling with hydrologically triggering conditions modeled by means of fractional Richards equation
In this work we explore the integration between existing soil infiltration modeling and particle based methods in order to simulate three-dimensional schemes of triggered deep seated landslides. In literature, usually, the infiltration models are based on continuum scheme, i.e., Eulerian approach by means of which it is possible to define the field of the pore pressure within a soil (e.g., Iverson, 2000). Differently the particle based method follow a discrete Lagrangian scheme that allow to identify the trajectory of the particles and its dynamical properties. At present we test the classical and fractional Richards equations that are adapted to the molecular dynamics approach according to the failure criterion of Mohr-Coulomb to simulate the triggering mechanism. In case of analytical infiltration model solution, the latter is discretized, differently a numerical one is achieved and the increasing pore pressure effect is simulated at soil particle level, i.e., we can simulate the rainfall in terms of water mass and then we take into account the water content in time and space at each thickness of our fictitious soil. The inter-particle interactions are through a force that, in the absence of suitable experimental data and due to the arbitrariness of the grain dimension, is modeled by means of a potential similar to the Lennard-Jones one. For the prediction of the particle positions, after and during a rainfall, we use a molecular dynamics approach that results very suitable to simulate this type of systems. The outcome of simulations are quite satisfactory and we can claim that this types of modeling can represent a new method to simulate landslides triggered by rainfall. Particularly, the results are consistent with the behavior of real landslides, e.g., it is possible to apply the method of the inverse surface displacement velocity for predicting the failure time (Fukuzono 1985). An interesting behavior emerges from the dynamic and statistical points of view. In our simulations emerging phenomena such as detachments, fractures and arching are observed. Finally, in our simulated system, we can observed a transition of the mean energy increment distribution from Gaussian to power law varying the value of some parameters (i.e., viscosity coefficient) or, fixed all parameters, the same behavior can be observed in the time, during single simulation, due to the stick and slip phases.
Giulia Menichetti - Università degli Studi di Bologna
Network Entropy measures and their applications to different systemic perturbations of cell basal state

The entropy of network ensembles SNE is related to the number of possible networks that satisfy some chosen constraints. Once given a real network, its main important features are encoded as constraints upon network ensembles. A high value of SNE means that a large number of networks satisfy the given constraints, thus the set of features associated to the observed network is not very particular (i.e. informative from an information theory point of view). On the contrary, for low entropy values, only few configurations can satisfy the given constraints, and there are less degrees of freedom.

We applied this measure to different biological designs (case-control and time series studies) where the parameter space represents the cell states. A high value SNE becomes usually associated to a high degree of plasticity for the system in this case, since a wide range of parameter values (e.g. gene expression profiles) are allowed to the cell. On the other hand, a low value of SNE can be interpreted as 1) the system has been more finely tuned or 2) the system has a smaller range available to its parameters

In collaboration with: G. Bianconi, E. Giampieri, G. Castellani and D. Remondini

Thomas C.T. Michaels - University of Oxford
Nucleated polymerisation with association
The formation of protein filaments is a phenomenon that underlies a range of functional and pathological processes in nature, including the generation of functional scaffolds but also the development of pathological aggregates in the context of Alzheimer's disease and related disorders. Kinetic studies have proved to be a particularly powerful tool to elucidate the mechanisms and rates underlying this important biological selfassembly process. The master equation describing filamentous growth has been known since the pioneering work by Oosawa in the 1960 and this framework and its extensions to secondary nucleation processes have been shown to describe the kinetics of protein filament growth accurately under a wide variety of different conditions and for very different protein systems. The study of the equilibrium behaviour of such systems has, however been complicated by the fact that the long time limit of the kinetic equations typically does not describe thermodynamic equilibrium as the master equation does not satisfy detailed balance. We have addressed this problem by combining nucleated polymerisation with living polymerisation to generate a master equation that satisfies detailed balance in the steady state. In our kinetic model for nucleated growth filamentous structures can undergo association, in addition to elongation and fragmentation or other secondary processes. Within our approach we take into account all possible association and fragmentation processes between clusters of any size. We explore the physical features of the model and give self-consistent analytical solutions to the growth kinetics and length distribution and identify the key time scales that describe relaxation to equilibrium. We test the validity of our analytical results against numerical solutions of the corresponding equations.

In collaboration with T.P.J. Knowles.
Amandine Miksic - ISC-CNR Roma
Acoustic emission characterization in a sheared granular medium
We realize spring-driven shear tests on a 3-D granular sample and record the acoustic emission (AE) from the frictional sliding. The transition from a stick-slip response to a liquid-like behavior of the granular sample is observed when we increase the applied shear rate. The AE signals are clearly different for the two regimes, but the AE intensity seems related to the shear rate in both cases. In addition, the acoustic emission presents different signatures for each regime: in the frequency domain, as well as in the distribution of AE intensities.
Rachele Nerattini - Università degli Studi di Firenze
Energy landscapes of classical spin models

Energy landscape methods make use of the stationary points of the energy function of a system to infer some of its collective properties. Recently this approach has been applied to equilibrium phase transitions, showing that a connection between some properties of the energy landscape and the occurrence of a phase transition exists at least for certain classes of models [1,2,3,4]. To better understand this connection we have studied the energy landscapes of classical $$O(n)$$ models defined on regular lattices and with ferromagnetic interactions. Although a complete enumeration of all the stationary points is practically unfeasible when the number of degrees of freedom increases, we have been able to find at least one class of stationary configurations with interesting properties. In particular we found that a one-to-one relation between a class of stationary points of the energy landscape of O(n) models on a lattice and the configurations of an Ising model ($$n=1$$) defined on the same lattice and with the same interactions exists. This suggested an approximate expression for the microcanonical density of states of the $$O(n)$$ models in terms of the microcanonical density of states of the Ising model [5]. If correct this would implies the equivalence of the critical values of the energy densities of a $$O(n)$$ model with ferromagnetic interactions defined on a lattice and the $$n=1$$ case, i.e., a system of Ising spins with the same interactions [5,6]. Both numerical analysis carried on the Ising model ($$n=1$$), the XY model ($$n=2$$), the Heisenberg model ($$n=3$$) and the $$O(4)$$ model ($$n=4$$) in three dimensions and analytical calculations carried on the mean field XY model and on the one dimensional XY model with nearest neighbors interactions [6] showed the reasonableness of this approximation and gave us an empirical test of its range of validity. Generalizations to more general cases are still under investigations.

[1] R. Franzosi and M. Pettini, Phys. Rev. Lett., 92, 060601 (2004);
[2] M. Kastner, O. Schnetz and S. Schreiber, J.Stat.Mech, P04025 (2008);
[3] L. Casetti, M. Pettini and E. G. D. Cohen, J. Stat. Phys. 111, 1091-1123 (2003);
[4] M. Kastner and D. Mehta, Annals Phys.326, 1425-1440 (2011);
[5] L. Casetti, C. Nardini and R. Nerattini, Phys. Rev. Lett., 106, 057208 (2011);
[6] C. Nardini, R. Nerattini, and L. Casetti, J. Stat. Mech: Theory Exp. 2012, P02007 (2012);
Luca Orefice - Università di Bologna e QSTAR
Analytical phase diagram for the current-carrying states of the quantum phase model
We address the stability of superfluid currents in a system of interacting lattice bosons. We consider various Gutzwiller trial states for the quantum phase model which provides a good approx- imation for the Bose-Hubbard model in the limit of large interactions and boson populations. We thoroughly analyze the current-carrying stationary states of the dynamics ensuing from a Gaussian ansatz, and derive analytical results for the critical lines signaling their modulational and ener- getic instability, as well as the maximum of the carried current. We show that these analytical results are in good qualitative agreement with those obtained numerically in previous works on the Bose-Hubbard model, and in the present work for the quantum phase model.
Giovanna Pacini - Università di Firenze
Science Café 2.0: Telematics and participation in science communication
This poster presents the possibility of application of telematics technology, with particular reference to web 2.0, to a "classical" method of science communication: the Science Café.
The Science Café are meetings of active participation between experts and the public on issues of science and technology: their characterizing aspect is the role of parity between the public and experts.
We have applied telematics in three stages of the Science Café

1) for support the event

2) for streaming via web the debate

3) for the follows up.

We illustrate what has been developed, the ratings for the channels used and future prospects.

In collaboration with F. Bagnoli

Lucia Pettinato - INFN Firenze
Statistical analysis of promoter sequences

Promoters are DNA sequences located upstream of each gene. Through various biochemical mechanisms, they regulate the transcription rate of the corresponding gene, directing when and in which tissues the information stored in the gene must (or must not) be used.

In this work, I analyze a sample of promoters of Homo sapiens, to search for statistically significant properties of promoter sequences. A clustering algorithm, specifically developed, identifies classes of promoters with similar statistical base composition properties. The classes obtained are further characterized developing an algorithm to detect regular regions (i.e. periodic or homogeneous in composition): such regions are known to have an important role in determining the promoter functions.

The combination of these methods allows to identify and characterize three classes of promoters in Homo sapiens; it also gives crucial clues to grasp the pervasive presence of transposons (DNA sequences capable to move from one location on the genome to another) in one of these classes. This analysis, repeated for other species, allows a comparison to search for evolutionary trends in promoter structure.

Vladislav Popkov - Università degli Studi di Firenze
Exact matrix product solution for the boundary-driven Lindblad XXZ-chain

The non-equilibrium dynamics of an open quantum systems is often described in terms of a quantum Master equation in the Lindblad form. We consider an anisotropic Heisenberg XXZ spin chain coupled at the edges with baths of a fixed, and different polarizations. Such a coupling introduces a dissipation which brings the quantum system with time in a non-equilibrium steady state with gradients and currents. We demonstrate that the exact non-equilibrium steady state of the XXZ spin chain driven by boundary Lindblad operators targeting two different completely polarized boundary states, can be constructed explicitly with a matrix product ansatz for the non-equilibrium density matrix where the matrices satisfy a quadratic algebra, related to the quantum algebra $$U_{q}$$[SU(2)] [1]. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms. The method allows to investigate analytically quantum systems of large sizes and in the thermodynamic limit. Our Matrix Product ansatz solution generalizes and simplifies the results of an earlier remarkable paper of T. Prosen [2].

[1] D. Karevski, V. Popkov, and G. M. Schütz, Phys. Rev. Lett. 110, 047201 (2013)

[2] T. Prosen, Phys. Rev. Lett. 107, 137201 (2011).

Marco Pretti - Politecnico di Torino
Belief Propagation approach for multicast scheduling

In the last few years, great interest has been attracted by the relationship between certain approximate free energy functionals (Bethe free energies), developed in the framework of equilibrium statistical mechanics, and Belief Propagation (BP), which is, a class of approximate algorithms for statistical inference and combinatorial optimization, developed independently in the computer science community. Such a relationship has opened new interesting fields of interdisciplinary application of statistical mechanics.

In this work, we consider the application of a BP algorithm to the problem of optimal scheduling for so-called multicast packets in the switching devices of a computer network. Multicast packets differ from ordinary (unicast) packets in that they may have an arbitrary number of destinations. The complexity of the corresponding optimization problem changes from polynomial to NP hard. Belief propagation turns out to provide a good heuristic method for practically solving this problem.

Alisa Santarlasci - Università degli Studi di Firenze
"Chemical" Modelling ants battles from experimental data, by means of a modified Gillespie algorithm
The aim of our study is to describe the dynamics of ant battles, with reference to laboratory experiments, by means of a chemical stochastic model. We focus on ant behavior as an interesting topic for the aptitude to propagate easily to new habitats. In order to predict the ecological evolution of invasive species and their relative fast spreading, a description of their successful strategies, also considering their competition with other ant species is necessary. In our work we want to describe the interactions between two groups of different ant species, with different war strategies, as observed in our experiments. The proposed chemical model considers the single ant individuals and fighting groups in a way similar to atoms and molecules, respectively, considering that ant fighting groups remain stable for a relative long time. Starting from a system of differential non-linear equations (DE), derived from the chemical reactions, we obtain a mean field description of the system. This deterministic approach is valid when the number of individuals of each species is large in the considered unit, while in our experiments we consider battles of at most 10 vs. 10 individuals, due to the difficulties in following the individual behavior in a large assembly. Therefore, we also adapt a Gillespie algorithm to reproduce the fluctuations around the mean field description. The DE schematization is exploited to characterize the stochastic model. The set of reaction constants of chemical equations, obtained by means of a minimization algorithm between the DE and the experimental data, are used by the Gillespie algorithm to generate the stochastic trajectories. We then fit the stochastic paths with the DE, in order to analyze the variability of the parameters and therefore their variance. Finally, we estimate the goodness of the applied methodology and we confirm that the stochastic approach must be considered for a correct description of the observed ant fighting dynamics. With respect to other war models (e.g., Lanchester's ones), our chemical model considers all phases of the battle and not only casualties. Therefore, we can count on more experimental data, but we also have more parameters to fit. In any case, our model allows a much more detailed description of the fights.
Filippo Tramonto - Università degli Studi di Milano
Quantum Monte Carlo study of dynamic properties of ultracold gases
We obtain ab-initio estimations of the dynamic structure factor, S(q,w), of ultracold Bose gases at zero temperature. More precisely, we use the Genetic Inversion via Falsification of Theories (GIFT) algorithm [1], which uses genetic algorithms to perform accurate analytic continuations of imaginary time correlation functions under ill-posed conditions. The imaginary time correlation functions have been computed with an exact projector method, the path integral ground state (PIGS) method [2]. Using the hard-sphere potential to model the two-body interactions between the atoms, we compute S(q,w) changing the gas parameter from the diluteregime up to densities above the freezing point of the hard-spheres system. With increasing density, we observe the emergence of a broad multiphonon contribution accompanying the quasi-particle peak and a crossover of the dispersion of elementary excitations from a Bogoliubov-like spectrum to a phonon-maxon-roton curve.

In collaboration with: R. Rota, D. E. Galli, S. Giorgini

References:
[1] E. Vitali, M. Rossi, L. Reatto and D.E. Galli, Phys. Rev. B 82, 174510,(2010).
[2] A. Sarsa, K. E. Schmidt, and W. R. Magro, J. Chem. Phys. 113, 1366 (2000).
Guido Uguzzoni - Università degli Studi di Parma
An inverse model approach to antibodies affinity maturation
Affinity maturation is a process occurring in the immune system where the antibodies enhances the affinities and the neutralization of specific target potentially harmful. This task is achieved by the mutation and the selection against the antigen. This evolutionary process produce a repertoire that is suitable of being investigated with statistical mechanics tools. We present some preliminary results of an approach that use inverse model to infer structural features of antibodies after the maturation and information of their interactions with the antigen.