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Claudio GIBERTI

Professore Ordinario presso: Dipartimento di Scienze e Metodi dell'Ingegneria


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Pubblicazioni

2021 - Approximating the Cumulant Generating Function of Triangles in the Erdös–Rényi Random Graph [Articolo su rivista]
Giardina', Cristian; Giberti, Claudio; Magnanini, Elena
abstract

We study the pressure of the “edge-triangle model”, which is equivalent to the cumulant generating function of triangles in the Erdös–Rényi random graph. The investigation involves a population dynamics method on finite graphs of increasing volume, as well as a discretization of the graphon variational problem arising in the infinite volume limit. As a result, we locate a curve in the parameter space where a one-step replica symmetry breaking transition occurs. Sampling a large graph in the broken symmetry phase is well described by a graphon with a structure very close to the one of an equi-bipartite graph.


2021 - Displacement autocorrelation functions for strong anomalous diffusion: A scaling form, universal behavior, and corrections to scaling" [Articolo su rivista]
Vollmer, Jürgen; Rondoni, Lamberto; Tayyab, Muhammad; Giberti, Claudio; Mejía-Monasterio, Carlos
abstract


2020 - Dissipation Function: Nonequilibrium Physics and Dynamical Systems [Articolo su rivista]
Caruso, Salvatore; Giberti, Claudio; Rondoni, Lamberto
abstract


2019 - Emergence of stationary uphill currents in 2D Ising models: the role of reservoirs and boundary conditions [Articolo su rivista]
Colangeli, Matteo; Giberti, Claudio; Vernia, Cecilia; Kröger, Martin
abstract

We investigate the dynamics of a 2D Ising model on a square lattice with conservative Kawasaki dynamics in the bulk, coupled with two external reservoirs that pull the dynamics out of equilibrium. Two different mechanisms for the action of the reservoirs are considered. In the first, called ISF, the condition of local equilibrium between reservoir and the lattice is not satisfied. The second mechanism, called detailed balance (DB), implements a DB condition, thus satisfying the local equilibrium property. We provide numerical evidence that, for a suitable choice of the temperature (i.e. below the critical temperature of the equilibrium 2D Ising model) and the reservoir magnetizations, in the long time limit the ISF model undergoes a ferromagnetic phase transition and gives rise to stationary uphill currents, namely positive spins diffuse from the reservoir with lower magnetization to the reservoir with higher magnetization. The same phenomenon does not occur for DB dynamics with properly chosen boundary conditions. Our analysis extends the results reported in Colangeli et al. [Phys. Rev. E 97, 030103(R) (2018)], shedding also light on the effect of temperature and the role of different boundary conditions for this model. These issues may be relevant in a variety of situations (e.g. mesoscopic systems) in which the violation of the local equilibrium condition produces unexpected phenomena that seem to contradict the standard laws of transport.


2019 - Equivalence of position–position auto-correlations in the Slicer Map and the Lévy–Lorentz gas [Articolo su rivista]
Giberti, C; Rondoni, L; Tayyab, M; Vollmer, J
abstract

The Slicer Map (SM) is a one-dimensional non-chaotic dynamical system that shows sub-, super-, and normal diffusion as a function of its control parameter. In a recent paper (Salari et al 2015 Chaos 25 073113) it was found that the moments of the position distributions as the SM have the same asymptotic behaviour as the Lévy–Lorentz gas (LLg), a random walk on the line in which the scatterers are randomly distributed according to a Lévy-stable probability distribution. Here we derive analytic expressions for the position–position correlations of the SM and, on the ground of this result, we formulate some conjectures about the asymptotic behaviour of position–position correlations of the LLg, for which the information in the literature is minimal. The numerically estimated position–position correlations of the Lévy–Lorentz show a remarkable agreement with the conjectured asymptotic scaling


2019 - O(N) Fluctuations and Lattice Distortions in 1-Dimensional Systems [Articolo su rivista]
Giberti, C.; Rondoni, L.; Vernia, C.
abstract

Statistical mechanics harmonizes mechanical and thermodynamical quantities, via the notion of local thermodynamic equilibrium (LTE). In absence of external drivings, LTE becomes equilibrium tout court, and states are characterized by several thermodynamic quantities, each of which is associated with negligibly fluctuating microscopic properties. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the system are represented by the transport coefficients. In 1-dimensional systems, on the other hand, various anomalies are reported, such as the dependence of the heat conductivity on the global state, rather than on the local state. Such deductions, that rely on the existence of thermodynamic quantities like temperature and heat, are here interpreted within the framework of boundary driven 1-dimensional Lennard-Jones chains of N oscillators. It is found that these chains experience non-negligible O(N) lattice distortions, resulting in strongly inhomogeneous systems, and O(N) position fluctuations, that are in contrast with the requirements of LTE.


2019 - Temperature and correlations in 1-dimensional systems [Articolo su rivista]
Giberti, Claudio; Rondoni, Lamberto; Vernia, Cecilia
abstract

Local thermodynamic equilibrium(LTE) plays a crucial role in statistical mechanics and thermodynamics. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the systems at hand are represented by the transport coefficients. The robustness and universality of equilibrium properties is not guaranteed in nonequilibrium states, in which different microscopic quantities may behave differently, even if they coincide at equilibrium. We investigate these issues considering 1-dimensional chains of N oscillators. We observe that non-negligible fluctuations, and persistence of correlations frustrate the onset of LTE, hence the existence of thermodynamic fields, such as temperature.


2018 - Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees [Articolo su rivista]
Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; Hofstad, Remco Van Der
abstract

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertices in the graph and show how it gives rise to interesting correlated random graphs.


2018 - Nonequilibrium two-dimensional Ising model with stationary uphill diffusion [Articolo su rivista]
Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia
abstract

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as “uphill diffusion”) has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from “downhill” to “uphill”. Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.


2016 - A learning model for the allocation of training hours in a multistage setting [Articolo su rivista]
Lolli, Francesco; Gamberini, Rita; Giberti, Claudio; Gamberi, Mauro; Bortolini, Marco; Bruini, Emanuele
abstract

In line with the continuous improvement theory, the learning phenomenon is often incorporated into models for predicting the evolution of the unitary quality costs. In this paper, the quality metric predicted is the rate of supplied non-conforming units through a learning process with autonomous and induced sources of experience. The former is simply learning by doing, i.e. supplying, whilst the latter is driven by the allocation of training hours to suppliers. A revised learning model with time-varying learning rates is proposed for embracing both these effects into a multistage assembly/production setting. A single-period prevention–appraisal–failure cost function is achieved, and the sample inspection rates adopted among suppliers are also considered in order to evaluate their effect. If these sample rates are given, the goal of allocating the training hours among suppliers is pursued by means of integer linear programming. Otherwise, a mixed-integer quadratic problem arises for the concurrent allocation of training hours and inspection sample rates among suppliers. A case study is finally carried out for demonstrating the applicability of the model, as well as for providing managerial insights.


2016 - A simulative approach for evaluating alternative feeding scenarios in a kanban system [Articolo su rivista]
Lolli, Francesco; Gamberini, Rita; Giberti, Claudio; Rimini, Bianca; Bondi, Federica
abstract

In accordance with the lean production philosophy, an assembly line may be supplied by means of a kanban system, which regulates and simplifies the flow of materials between the lines and the warehouses. This paper focuses on evaluation of feeding policies that differ from each other in term of the number of kanbans managed per feeding tour. A pure cost-based approach is thus proposed, which considers both inline inventories along with handling costs proportionate to the number of operators involved in the parts-feeding process. A multi-scenario simulative approach is applied in order to establish the number of operators required to avoid inline shortages. The scenario minimising total cost is then selected. The innovation introduced is a model for describing kanban arrivals and their requests for feeding, improving the potential of the simulation to describe real-life environments. Lastly, a case study from the automotive industry is presented in order to highlight the applicability of the proposed approach as well and the effects of alternative feeding policies on the total cost incurred.


2016 - Annealed central limit theorems for the Ising model on random graphs [Articolo su rivista]
Giardina', Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa
abstract

The aim of this paper is to prove central limit theorems with respect to the annealed measure for the magnetization rescaled by $sqrt{N}$ of Ising models on random graphs. More precisely, we consider the general rank-1 inhomogeneous random graph (or generalized random graph), the 2-regular configuration model and the configuration model with degrees 1 and 2. For the generalized random graph, we first show the existence of a finite annealed inverse critical temperature $0le eta^{mathrm{an}}_c < infty$ and then prove our results in the uniqueness regime, i.e., the values of inverse temperature $eta$ and external magnetic field $B$ for which either $eta<eta^{mathrm{an}}_c$ and $B=0$, or $eta>0$ and $B eq 0$. In the case of the configuration model, the central limit theorem holds in the whole region of the parameters $eta$ and $B$, because phase transitions do not exist for these systems as they are closely related to one-dimensional Ising models. Our proofs are based on explicit computations that are possible since the Ising model on the generalized random graph in the annealed setting is reduced to an inhomogeneous Curie-Weiss model, while the analysis of the configuration model with degrees only taking values 1 and 2 relies on that of the classical one-dimensional Ising model.


2016 - Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs [Articolo su rivista]
Dommers, Sander; Giardina', Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa
abstract

We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant Jij(β) for the edge ij on the complete graph is given by Jij(β) = βwiwj/ (∑ k∈[N]wk). We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature β replaced by sinh (β) ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights (wi)i∈[N] are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent τ with τ∈ (3 , 5) , then the critical exponents depend sensitively on τ. In addition, at criticality, the total spin SN satisfies that SN/ N(τ-2)/(τ-1) converges in law to some limiting random variable whose distribution we explicitly characterize.


2015 - A simple non-chaotic map generating subdiffusive, diffusive, and superdiffusive dynamics [Articolo su rivista]
Salari, Lucia; Rondoni, Lamberto; Giberti, Claudio; Klages, Rainer
abstract

Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here, we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto the whole real line which preserves distances except at a countable set of points. This property, which leads to vanishing Lyapunov exponents, is designed to mimic diffusion in non-chaotic polygonal billiards that give rise to normal and anomalous diffusion in a fully deterministic setting. As these billiards are typically too complicated to be analyzed from first principles, simplified models are needed to identify the minimal ingredients generating the different transport regimes. For our model, which we call the slicer map, we calculate all its moments in position analytically under variation of a single control parameter. We show that the slicer map exhibits a transition from subdiffusion over normal diffusion to superdiffusion under parameter variation. Our results may help to understand the delicate parameter dependence of the type of diffusion generated by polygonal billiards. We argue that in different parameter regions the transport properties of our simple model match to different classes of known stochastic processes. This may shed light on difficulties to match diffusion in polygonal billiards to a single anomalous stochastic process.


2015 - Dualities in population genetics: A fresh look with new dualities [Articolo su rivista]
Carinci, Gioia; Giardina', Cristian; Giberti, Claudio; Frank, Redig
abstract

We apply our general method of duality, introduced in [15], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman’s type, as well as for models with finite population size. Next, using SU(1, 1) raising and lowering operators, we find new dualities between the Wright-Fisher diffusion with d types and the Moran model, both in presence and absence of mutations. These new dualities relates two forward evolutions. From our general scheme we also identify self-duality of the Moran model.


2015 - Quenched Central Limit Theorems for the Ising Model on Random Graphs [Articolo su rivista]
Giardina', Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa
abstract

Themain goal of the paper is to prove central limit theorems for the magnetization rescaled by the square root of N for the Ising model on random graphs with N vertices.Both random quenched and averaged quenched measures are considered.We work in the uniqueness regime β > βc or β > 0 and B not equal to 0, where β is the inverse temperature, βc is the critical inverse temperature and B is the external magnetic field. In the random quenched setting our results apply to general tree-like random graphs (as introduced by Dembo, Montanari and further studied by Dommers and the first and third author) and our proof follows that of Ellis in Z^d. For the averaged quenched setting, we specialize to two particular random graph models, namely the 2-regular configuration model and the configuration model with degrees 1 and 2. In these cases our proofs are based on explicit computations relying on the solution of the one dimensional Ising models


2013 - Duality for Stochastic Models of Transport [Articolo su rivista]
Carinci, Gioia; Giardina', Cristian; Giberti, Claudio; F., Redig
abstract

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particle densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites. The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Longrange correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.


2013 - Interaction Flip Identities for non Centered Spin Glasses [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio
abstract

We consider spin glass models with non-centered interactions and investigate the effect, on the random free energies, of flipping the interaction in a subregion of the entire volume. A fluctuation bound obtained by martingale methods produces, with the help of integration by parts technique, a family of polynomial identities involving overlaps and magnetizations.


2012 - Structural spin-glass identities from a stability property: an explicit derivation [Relazione in Atti di Convegno]
Contucci, Pierluigi; Giardina', Cristian; Giberti, Claudio
abstract

In this paper a recent extension (P.Contucci, C.Giardina', C.Giberti, EPL.96, 17003 (2011)) of the stochastic stability property ( M.Aizenman, P.Contucci, Journal of Statistical Physics, Vol.92, N. 5/6, 765-783, (1998)) is analyzed and shown to lead to the Ghirlanda Guerra identities for Gaussian spin glass models. The result is explicitly obtained by integration by parts techinque.


2011 - Anomalies and absence of local equilibrium, and universality, in one-dimensional particles systems [Articolo su rivista]
GIBERTI, Claudio; L., Rondoni
abstract

One-dimensional systems are under intense investigation, both from theoretical and experimental points ofview, since they have rather peculiar characteristics which are of both conceptual and technological interest.We analyze the dependence of the behavior of one-dimensional, time-reversal invariant, nonequilibrium systemson the parameters defining their microscopic dynamics. In particular, we consider chains of identical oscillatorsinteracting via hard-core elastic collisions and harmonic potentials, driven by boundary Nos´e-Hoover thermostats.Their behavior mirrors qualitatively that of stochastically driven systems, showing that anomalous properties aretypical of physics in one dimension. Chaos, by itself, does not lead to standard behavior, since it does not guaranteelocal thermodynamic equilibrium.Alinear relation is found between density fluctuations and temperature profiles.This link and the temporal asymmetry of fluctuations of the main observables are robust against modifications ofthermostat parameters and against perturbations of the dynamics.


2011 - Interface Energy in the Edwards-Anderson Model [Articolo su rivista]
Pierluigi, Contucci; Giardina', Cristian; Giberti, Claudio; Giorgio, Parisi; Vernia, Cecilia
abstract

We numerically investigate the spin glass energy interface problem in three dimensions. We analyze the energy cost of changing the overlap from −1 to +1 at one boundary of two coupled systems (in the other boundary the overlap is kept fixed to +1). We implement a parallel tempering algorithm that simulates finite temperature systems and works with both cubic lattices and parallelepiped with fixed aspect ratio. We find results consistent with a lower critical dimension D c =2.5. The results show a good agreement with the mean field theory predictions.


2011 - Stability of the Spin Glass Phase under Perturbations [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio
abstract

We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.


2010 - Modelling Complex Systems with Statistical Mechanics: The Computational Approach [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; Vernia, Cecilia
abstract

Real-world phenomena are often described by complex systems with competitive and cooperative behaviour. Such systems, as much as the described phenomena, are hard to understand in a scientific perspective mainly due to the lack of general exact solutions. For cases like this, the computational sciences provide a very useful virtual laboratory. The case of disordered systems is an example of scientific computing techniques being used to test theoretical predictions and uncover new phenomena that remain unreachable by traditional analytical methods.


2009 - Interaction-Flip Identities in Spin Glasses [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio
abstract

We study the properties of fluctuation for the free energies and internal energies of two spinglass systems that differ for having some set of interactions flipped. We show that their difference has avariance that grows like the volumeof the flipped region. Using a new interpolation method,which extends to the entire circle the standard interpolation technique, we show by integration by parts that the bound imply new overlap identities for the equilibrium state. As a side result the case of the non-interacting random field is analyzed and the triviality of its overlap distribution proved.


2009 - Structure of correlations in three dimensional spin glasses [Articolo su rivista]
P., Contucci; GIARDINA', Cristian; GIBERTI, Claudio; G., Parisi; VERNIA, Cecilia
abstract

We investigate the low temperature phase of the three dimensional Edward-Anderson model with Bernoulli random couplings. We show that, at a fixed value Q of the overlap, the model fulfills the clustering property: The connected correlation functions between two local overlaps have power law decay. Our findings are in agreement with the replica symmetry breaking theory and show that the overlap is a good order parameter. © 2009 The American Physical Society.


2008 - Answer to Comment on "Ultrametricity in the Edwards-Anderson Model" [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; G., Parisi; Vernia, Cecilia
abstract

In this paper we reply to a critical comment by T. Jorg and F. Krzakala to the Letter "Ultrametricity in the Edwards-Anderson Model" PRL 99, 057206 (2007). We show that the procedure developed in the aforementioned paper to detect ultrametricity is able to discriminate the non-ultrametric behavior of the two-dimensional Edwards-Anderson model from the ultrametric three-dimensional one. Moreover, the interesting finding of Jorg and Krzakala that in the two-dimensional Edwards-Anderson model three random configurations have ordered overlaps fulfilling the ultrametric distribution is discussed and an explanation of this phenomenon is proposed.


2008 - Numerical study of ground state energy fluctuations in spin glasses [Altro]
Giberti, Claudio; Vernia, Cecilia
abstract

Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The algorithm is based on a suitable annealing procedure coupled with a balanced greedy-reluctant strategy that drives the systems towards the deepest minimum of the energy function.


2007 - Temporal asymmetry of fluctuations in the nonequilibrium FPU model [Articolo su rivista]
Giberti, Claudio; L., Rondoni; Vernia, Cecilia
abstract

The large deviation theory recently developed by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim is meant to extend the Onsager–Machlup theory to nonequilibrium phenomena, and predicts that the fluctuations of densities and currents in certain stochastic processes are not symmetric with respect to the time reversal operation. In this paper, several notions of fluctuations are introduced for deterministic systems, and it is observed that temporally asymmetric (not necessarily large) fluctuations are ubiquitous, even in the context of time reversal invariant dynamics of particle systems, in nonequilibrium states. To illustrate these ideas, the nonequilibrium FPU chain devised by Lepri, Livi and Politi is studied in detail.


2007 - Ultrametricity in the Edwards-Anderson model. [Articolo su rivista]
P., Contucci; GIARDINA', Cristian; GIBERTI, Claudio; G., Parisi; VERNIA, Cecilia
abstract

We test the property of ultrametricity for the spin-glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to 203 spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution, our result contradicts the droplet theory. © 2007 The American Physical Society.


2006 - Asymmetric fluctuations-relaxations paths in FPU models [Articolo su rivista]
Giberti, Claudio; L., Rondoni; Vernia, Cecilia
abstract

A recent theory by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim predicts a temporal asymmetry in thefluctuation–relaxation paths of certain observables of nonequilibrium systems in local thermodynamic equilibrium. Wefind temporal asymmetries in the fluctuation–relaxation paths of a form of local heat flow, in the nonequilibrium FPU-bmodel of Lepri, Livi and Politi.


2006 - Overlap equivalence in the Edwards-Anderson model [Articolo su rivista]
P., Contucci; GIARDINA', Cristian; GIBERTI, Claudio; VERNIA, Cecilia
abstract

We study the relative fluctuations of the link overlap and the square standard overlap in the three-dimensional Gaussian Edwards-Anderson model with zero external field. We first analyze the correlation coefficient and find that the two quantities are uncorrelated above the critical temperature. Below the critical temperature we find that the link overlap has vanishing fluctuations for fixed values of the square standard overlap and large volumes. Our data show that the conditional variance scales to zero in the thermodynamic limit. This implies that, if one of the two random variables tends to a trivial one (i.e., deltalike distributed), then the other does also, and as a consequence, the "trivial-nontrivial" picture should be dismissed. Our results show that the two overlaps are completely equivalent in the description of the low temperature phase of the Edwards-Anderson model. © 2006 The American Physical Society.


2005 - Bifurcation of Homogeneous Solutions in a Chain of Logistic Maps [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

In this paper we study the bifurcation of the homogeneous fixed point of a lattice of n diffusively coupled logistic maps. An analytical computation of the reduced map on the centermanifold is performed by taking into account the symmetries of the system. If n is even, a subcritical flip bifurcation causes a symmetry breaking of the homogeneous pattern whichproduces a traveling (rotating) wave with velocity 1 and time period 2. For odd n, since the bifurcation has a two dimensional normal form, we limit ourselves to consider only the simplest case (n = 3). In this case, a supercritical flip bifurcation is observed; three less symmetric periodic orbits of time period 2 are generated by the breaking of the homogeneous orbit. However, the bifurcation is rather degenerate and we have numerical hints that a second family of asymmetric periodic points is generated. Some details, pertaining to the dynamicsof the truncated map on the two dimensional center manifold for n = 3, are also presented.


2005 - Finding minima in complex landscapes: Annealed, greedy and reluctant algorithms. [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; Vernia, Cecilia
abstract

We consider optimization problems for complex systems in which the cost function has a multivalleyed landscape. We introduce a new class of dynamical algorithms which, using a suitable annealing procedure coupled with a balanced greedy-reluctant strategy drive the systems towards the deepest minimum of the cost function. Results are presented for the Sherrington-Kirkpatrick model of spin-glasses. © World Scientific Publishing Company.


2005 - Interpolating greedy and reluctant algorithms [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; Unguendoli, Francesco; Vernia, Cecilia
abstract

In a standard NP-complete optimization problem, we introduce an interpolating algorithm between the quick decrease along the steepest descent direction (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that, for a fixed elapsed computer time, the best performance of the optimization is reached at a special value of the interpolation parameter, considerably improving the results of the pure cases of greedy and reluctant. © 2005 Taylor & Francis Group Ltd.


2004 - Coexistence of chaotic and non-chaotic states in the two-dimensional Gauss-Navier-Stokes dynamics [Articolo su rivista]
Giberti, Claudio; L., Rondoni; Vernia, Cecilia
abstract

Recently, Gallavotti proposed an Equivalence Conjecture in hydrodynamics, which states that forced-damped fluids can be equally Well represented by means of the Navier-Stokes equations (NS) and by means of time reversible modifications of NS called Gauss-Navier-Stokes equations (GNS). This Equivalence Conjecture received numerical support in several recent papers concerning two-dimensional fluid mechanics. The corresponding results rely on the fact that the NS and GNS systems only, have one attracting set. Performing similar two-dimensional simulations, we find that there are conditions to be met by the GNS system for this to be the case. In particular, increasing the Reynolds number, while keeping fixed the number of Fourier modes, leads to the coexistence of different attractors. This makes difficult a test of the Equivalence Conjecture, but constitutes a spurious effect due to the insufficient spectral resolution. With sufficiently fine spectral resolution, the steady states are unique and the Equivalence Conjecture can be conveniently established.


2003 - Optimization Strategies in Complex Systems [Capitolo/Saggio]
L., Bussolari; P., Contucci; Giardina', Cristian; Giberti, Claudio; Unguendoli, Francesco; Vernia, Cecilia
abstract

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the "greedy'' (quick decrease along the gradient) and the "reluctant'' (slow decrease close to the level curves) as well as those of a "stochastic convex interpolation'' of the two.Concepts like the average relaxation time and the wideness of theattraction basin are analyzed and their system size dependenceillustrated.


2002 - Numerical study of stability of non-chaotic patterns in coupled map lattices [Relazione in Atti di Convegno]
Giberti, Claudio; Vernia, Cecilia
abstract

The stability of non-chaotic structures in lattices ofcoupled logistic maps is analyzed in parameter space. We state theexistence of a few elementary structures the stability of whichdetermines that of almost all non-chaotic patterns of any size.This allows us to propose a technique for predicting whichattractors can exist in a given parameter region.


2002 - On quasiperiodic travelling waves in coupled map lattices [Articolo su rivista]
Franceschini, Valter; Giberti, Claudio; Vernia, Cecilia
abstract

We investigate quasiperiodic travelling waves (QTWs) in lattices of diffusively coupled logistic maps. Starting from the assumption that any spatial structure can be broken down into simpler elementary structures, a classification scheme for QTWs is introduced. Within this framework. the phenomenon of discrete velocities is reviewed and further investigated. In addition, a new technique is proposed for predicting whether QTWs can occur for given parameter values and which they might be.


2002 - Tori breakdown in coupled map lattices [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

In this paper we present a numerical study of invariant tori in a lattice of coupled logistic maps. In particular, we are interested in bifurcations leading to chaos. Here we consider six different examples of tori breakdown: two of them completely confirm the theory of Afraimovich and Shilnikov, while the others appear peculiar to the model.


2001 - Tori Breakdown in coupled map lattice [Abstract in Atti di Convegno]
Giberti, Claudio
abstract

We present a numerical study of the behaviour and breakdown of tori in a lattice of diffusively coupled logistic maps.


1998 - Formation, Stability and Predictability of Structures in Coupled Map Lattices [Articolo su rivista]
Franceschini, Valter; Giberti, Claudio; Vernia, Cecilia
abstract

Some significant non-chaotic behaviors of the lattices ofcoupled logistic maps are analyzed. In particular, the review concerns the organization of cycles for small coupling andthe fundamental role played by heteroclinic cycles and quasiperiodic traveling waves. Moreover, we point to the existence of a few elementary cycles the stability of which determines that of almost all non-chaotic structures of any size, in particular for high nonlinearity and medium and large coupling.This allows an approximate prediction of which attractors can occur for given parameter values.


1998 - Stable state analysis of an immune network model [Articolo su rivista]
G. C., Castellani; Giberti, Claudio; C., Franceschi; F., Bersani
abstract

The paper analyzes a model of immune system developed by different authors (Perelson, De Beer, Weisbuch and others). The model describes interactions among B-lymphocytes. It does not consider antibodies as interaction intermediaries, although it uses a typical activation curve. The relevant parameters are: an influx term, a threshold value, a proliferation rate, and a decay parameter. The study of the n-dimensional extension of the model and a bifurcation analysis of the stationary states with respect to the influx parameter show that the influx value for which biologically acceptable solutions exist decreases as n increases. When the influx term is neglected the stationary states are obtained analytically and their stability is discussed. Moreover, it is discussed how the stable solutions can be considered as selective states, that is, with only one high idiotypic concentration, when we suppose a complete connectivity.


1997 - On stability of structures and patterns in extended systems [Articolo su rivista]
L. A., Bunimovich; Franceschini, Valter; Giberti, Claudio; Vernia, Cecilia
abstract

We study the stability of spatial structures in extended systems. Each spatial structure consists of some simple (undecomposable) structures that we call. patterns. We show numerically for some classes of coupled map lattices that the stability of a spatial structure is determined by the stability of its pattern with the minimal (spatial) scale, i.e. by the most tiny detail of this structure.


1994 - Normally attracting manifolds and periodic behavior in one-dimensional and two-dimensional coupled map lattices [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable.


1993 - Behavior of a Three-Torus in Truncated Navier-Stokes Equations [Articolo su rivista]
Giberti, Claudio; R., Zanasi
abstract

The presence of a three-torus in a seven-mode truncation of the three-dimensional Navier-Stokes equations is investigated numerically by means of cross-section and power spectra. Furthermore, by taking advantage of particular features of the model, rotation vectors, circle maps and torus maps can be computed with high accuracy and used to study the dynamics. In particular, some interesting phenomena of partial phase-locking are described in deep detail. The three-torus, which arises via a Hopf bifurcation and persists in a wide parameter range, is found to break and originate a strange attractor. The onset of chaos and the associated bifurcation point can be defined quite precisely.


1993 - Characterization of the Lorenz Attractor by Unstable Periodic Orbits [Articolo su rivista]
Franceschini, Valter; Giberti, Claudio; Zheng, Zm
abstract

We characterize the chaotic attractors of the Lorenz system associated with R = 28 and R = 60 in terms of the unstable periodic orbits and their eigenvalues. While the Hausdorff dimension is approximated with very good accuracy in both cases, the topological entropy is computed, in an exact sense, only for R = 28.


1993 - On the presence of Normally Atracting Manifolds Containing Periodic or Quasiperiodic Orbits in Coupled Map Lattices [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

The significant presence of normally attracting invariant manifolds, formed by closed curves or two-tori, is investigated in two-dimensional lattices of coupled chaotic maps. In the case of a manifold formed by closed curves, it contains symmetrically placed periodic orbits, with the property of a very weak hyperbolicity along the manifold itself. The resulting dynamics is an extremely slow relaxation to periodic behavior. Analogously, a manifold consisting of two-tori includes very weakly hyperbolic periodic (or quasiperiodic) orbits, which in this case also implies quite a long time before any solution approaches periodicity or quasiperiodicity.The normally attracting manifolds and the contained weak attractors can undergo several global bifurcations. Some of them, including saddle-node bifurcation, period-doubling and Hopf bifurcation, are illustrated.Almost all the asymptotic solutions that we discuss have flat rows or flat columns, which means that they can occur also in one-dimensional lattices.


1991 - Qualitative and Quantitative Stabilized Behavior of Truncated Two-Dimensional Navier-Stokes Equations [Articolo su rivista]
Franceschini, Valter; Giberti, Claudio
abstract

N-mode truncations of the Navier-Stokes equations on a two-dimensional torus are investigated for increasing N, up to a maximum of N=1000. A parameter range is considered in which the behavior is first quasi-periodic and then chaotic. A Poincaré map analysis shows features which clearly stabilize as N increases, from both a qualitative and quantitative point of view. Concerning the onset of chaos, it is found that the appearance of bumps and foldings in the section curve is the cause of the breaking of the torus. A detailed description of the transition is given for N=502.


1989 - Parallelism in a Highly Accurate Algorithm for Turbulence Simulation [Abstract in Atti di Convegno]
Canuto, C; Giberti, Claudio
abstract

A parallel version of a spectral algorithm for the direct simulation of homogeneous, fully developed turbulence has been developed for the four-processor CRAY X-MP/48. We report a detailed performance analysis which enlights the various factors affecting parallel performance.


1988 - Common Periodic Behavior in Larger and Larger Truncations of the Navier-Stokes Equations [Articolo su rivista]
Franceschini, Valter; Giberti, Claudio; M., Nicolini
abstract

The periodic behavior of N-mode truncations of the Navier-Stokes equations on a two-dimensional torus is studied forN=44, 60, 80, and 98. Significant common features are found, particularly for not too high Reynolds numbers. In all models periodicity ends, giving rise, though at quite different parameter values, to quasiperiodicity.