# Mario CasartelliUniversità di Parma | UNIPR · Department of Physics and Earth Sciences

Mario Casartelli

Associate Profssor

## About

56

Publications

2,159

Reads

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571

Citations

## Publications

Publications (56)

We study the dynamics of networks with inhibitory and excitatory
leaky-integrate-and-fire neurons with short-term synaptic plasticity in the
presence of depressive and facilitating mechanisms. The dynamics is analyzed by
a Heterogeneous Mean-Field approximation, that allows to keep track of the
effects of structural disorder in the network. We desc...

We report about the main dynamical features of a model of leaky-integrate-and
fire excitatory neurons with short term plasticity defined on random massive
networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation
of the model, that is able to reproduce dynamical phases characterized by the
presence of quasi-synchronous events....

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal signals are crucial for brain functioning. They strongly depend on the topology of the network and on the fluctua...

The dynamics of neural networks is often characterized by collective behavior and quasi synchronous
events, where a large fraction of neurons fire in short time intervals, separated by
uncorrelated firing activity. These global temporal signals are crucial for brain functioning and
they strongly depend on the topology of the network and on the
flu...

Looking for optimal in clustering for H1N1. Clustering entropy for Rohlin and Hamming at different values for influenza A H1N1. The long plateau, in Rohlin, suggests a stable and well defined value for the optimal . Notice that Hamming is growing.
(TIF)

Reverse analysis for Rohlin clusters. Sequences of minimum distance with the corresponding WHO reference sequences, during years. The great similarity with Fig. 2 shows a strong consistency between Rohlin and HI analysis.
(TIF)

Clustering on random permutations. Effect of random permutation of symbols on the entropy of the clustering, as a function of . R indicates the entropy of clustering with the Rohlin distance and P stands for the entropy of clustering in the sample, obtained under a random permutation of symbols in each sequence.
(TIF)

Looking for optimal in clustering for H3N2 in the restricted time window. Clustering entropy for Rohlin and Hamming at different values for influenza A H3N2, as obtained by considering only the sequences up to the end of the winter season of the year indicated in the plot. In each time window, the long plateau, in Rohlin, suggests a stable and well...

The evolution of the hemagglutinin amino acids sequences of Influenza A virus is studied by a method based on an informational metrics, originally introduced by Rohlin for partitions in abstract probability spaces. This metrics does not require any previous functional or syntactic knowledge about the sequences and it is sensitive to the correlated...

We study the warming process of a semi-infinite cylindrical Ising lattice
initially ordered and coupled at the boundary to a heat reservoir. The adoption
of a proper microcanonical dynamics allows a detailed study of the time
evolution of the system. As expected, thermal propagation displays a diffusive
character and the spatial correlations decay...

An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder, i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, impos...

We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring for cellular automata defined on an arbitrary structure. As a prototype for such systems we focus on the Ising model on a finite Sierpinski gasket, which is known to possess a complex thermodynamic behavior. Our algorithm requires the projectio...

We introduce a new microcanonical dynamics for a large class of Ising systems isolated or maintained out of equilibrium by contact with thermostats at different temperatures. Such a dynamics is very general and can be used in a wide range of situations, including ones with disordered and topologically inhomogeneous systems. Focusing on the two-dime...

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on the particle density. A non-equilibrium stationary flux can be induced by suitable boundary conditions, and we s...

We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we...

Let $\dlap$ be the discrete Laplace operator acting on functions (or rational matrices) $f:\mathbf{Q}_L\to\mathbb{Q}$, where $\mathbf{Q}_L$ is the two dimensional lattice of size $L$ embedded in $\mathbb{Z}_2$. Consider a rational $L\times L$ matrix $\mathcal{H}$, whose inner entries $\mathcal{H}_{ij}$ satisfy $\dlap\mathcal{H}_{ij}=0$. The matrix...

A cylindrical Ising model between thermostats is used to explore the heat conduction for any temperature
interval. The standard Q2R and Creutz dynamics, previously used by Saito, Takesue and Miyashita, fail below the critical temperature,
limiting the analysis to high temperatures intervals. We introduce improved dynamics by removing limitations du...

The non-ergodic behavior of the deterministic Fixed Energy Sandpile (DFES), with Bak-Tang-Wiesenfeld (BTW) rule, is explained by the complete characterization of a class of dynamical invariants (or toppling invariants). The link between such constants of motion and the discrete Laplacian's properties on graphs is algebraically and numerically clari...

The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon entropy, Hamming and Rohlin distances. Previous results based on the two peaks shape of the specific heat, suggest...

In anharmonic chains with even potentials, including classical Fermi-Pasta-Ulam model, we show how ordered structures can coexist with high degree stochasticity.

We introduce a new type of discrete map on positive reals, showing peculiar kinds of complexity. They combine a large-scale component (Collatz's itineraries on integers) with a small-scale component (standard chaotic systems, such as logistic maps, or random noise). Usual characterizations, for example by Lyapunov exponents, prove senseless or dece...

We study a class of non-integrable systems, linear chains with homogeneous attractive potentials and periodic boundary conditions, which are not perturbations of the harmonic chain. In particular, we deal with the system H4 with a purely quartic potential, which may be shown to be stochastic without any transition. For this model we prove the follo...

We evaluate the power spectra of the time series for the following simple observables in the Fermi-Pasta-Ulam model: harmonic energy, kinetic energy, microcanonical density, Frenet-Serret curvature and the Lyapunov variable. For some of these observables, also in the stochastic regime, the spectra show a well defined quasi-harmonic structure, with...

A new characterization of self-organized criticality (SOC) states is developed by using metric features of the configuration's space. Quantities mainly referring to the partition formalism, as mutual factorization, Shannon entropy and Rohlin distances with their distributions and power spectra, are considered. Time series for these observables give...

Key words in my talk will be “way of representation”, “way of notation”, “symbolical formalization”, and similar ones. These concepts, deserving many distinctions in principle, are grouped here on the basis of an elementary observation: experience and common sense testify indeed that, in all scientific disciplines, the perspective on certain proble...

Connected partitions in two-dimensional lattices naturally arise in studying the cluster configurations of a large class of dynamical systems. We introduce a factorization into dichotomic factors allowing a meaningful implementation of the partition algebra. This factorization proves useful, in particular, in the reduction process between couples o...

We consider curvatures of all orders, as defined by the generalized Frenet - Serret formulae, along the trajectories of a classical Hamiltonian system with N degrees of freedom. In the spirit of previous experiments on the first two of them, time averages are numerically computed for the curvatures up to fifth order and for the microcanonical densi...

We introduce geometrical indicators (Frenet - Serret curvature and torsion) together with microcanonical density to give evidence to the stochastic transition of classical Hamiltonian models (Fermi - Pasta - Ulam and Lennard - Jones systems) when the specific energy grows. The transition is clearly detected through the breakdown of the harmonic-lik...

We introduce a large class of transformations allowing rearrangements of the fullerene surface. We call this set of rearrangements generalized Stone-Wales transformations (gSW) because the well-known Stone-Wales (or pyracylene) flip may be seen as the simplest representative of the novel gSW family. The interconversion between the two C28 fullerene...

For the periodic Fermi-Pasta-Ulam chain with quartic potential we prove the relation p
k
2
T
(1+)
k
2
q
k
2
, i.e., the proportionality, already at early timesT, between averaged kinetic and harmonic energies of each mode. The factor depends on the parameters of the model, but not on the mode and the number of degrees of freedom. It grows...

We present numerical experiments on Hamiltonian nonlinear chains at fixed specific energy in the stochastic domain with a growing number of degrees of freedom, up to N = 2048. Previous results on the rates of changes of action variables, with reference to translational invariance, are confirmed and specified. Furthermore, for models with other cons...

We study the relevance of several physical parameters in regulating the rate of energy exchanges for nonlinear systems in the stochastic domain. In particular, exploring the structural features which differentiate models of radiant cavities from nonlinear chains, we prove that the ``superfreezing'', i.e. the quasi harmonical behaviour of the action...

The behavior of basins of periodic orbits, for families of elliptic maps in the 2D torus depending on a parameter, is studied. We give an explicit formula for periodic orbits (i.e., central points of basins), considering also the occurrence of singular situations. Such a formula describes the evolution of basins, showing that onset and disappearanc...

A model of nonlinear oscillators related to classical electrodynamics is studied. Using an indicator based on the energy exchange of harmonic modes, it is possible to establish that equipartition of energy and equipartitions of exchanges go hand inhand: this entails a phenomenon of quasi-harmonic behavior of high modes which we call ``superfreezing...

Results of calculations on a model of a radiant cavity, performed in order to explore the relation between stochasticity and geometrical structure of phase space, are presented. The rate of energy exchanges, as indicator of stochasticity, is found to be quite effective. Furthermore, a trend to equipartition for such a quantity is observed at increa...

The complexity of trajectories in the phase space of anharmonic crystals (mostly a Lennard-Jones chain) is analysed by the
variance of microcanonical density and by new parametersP and ϰ defined, respectively, as the mean value of the time averages and the relative variance of the absolute exchange rate
of energies among the normal modes. Evidence...

By numerical computations of two new parameters related to the curvature and to the phase space velocity in the Hénon-Heiles model, evidence is given to the influence of local geometric structure on relaxation in the low stochastic regime of motion.

We study the stochastic transition of a family of dissipative mappings of the two-dimensional torus, having a pure rotation
and an Anosov hyperbolic automorphism as limit cases. Numerical experiments show that the onset of chaos is characterized
by a sudden destruction of basins of previously conserved invariant sets and by the appearance of a stra...

The stochastic region in the phase space of a classical nonlinear system, a Lennard-Jones chain, is proven to be nonuniform
with respect to a random access, through the sensitivity of the relaxation time to initial conditions. The dependence on various
parameters is analysed and the results are interpreted geometrically as the effect of residual in...

It is shown that the considered singular integral operator Ksigma has a simple discrete spectrum with asymptotic behaviour.

In the numerical study of classical dynamical systems presenting stochastic behaviour one frequently makes use, in an explicit
or an implicit way, of the Birkhoff ergodic theorem. The correct interpretation of the obtained results presents some delicate
problems related to the coexistence of many mutually singular invariant measures. In this paper...

Statistical consequences of the subdivision of the phase space of a classical nonlinear system (a Lennard-Jones chain) into regions of ordered and stochastic motions are investigated by numerical computations on two parameters, which are related to the average fluctuations and to the equipartition of the kinetic energy. While the former parameter b...

The stochastic properties of classical dynamical systems are often studied by means of numerical computations of orbits up
to very large times, so that the accumulation of numerical errors would appear to destroy the reliability of the computations.
We discuss this problem on the basis of a theorem of Anosov and Bowen which implies that, if the err...

In the context of quantum measurements which are of limited accuracy or incomplete, the maximisation of the Segal entropy with respect to a reference state is proven to be a suitable method to recover the Wigner's principle of least interference.

A stochastic parameter which appears to be related to the Kolmogorov entropy is computed for a system of N particles in a line with the nearest-neighbor Lennard-Jones interaction. It is found that the parameter depends on the initial conditions, and is equal to zero or to a positive value which depends on the specific energy u. A limit seems to exi...

Examples are shown to exist in which the Schroedinger and the Born interpretations are compatible. To this end use is made of the Fényes-Weizel-Nelson theorem and of known results of classical ergodic theory.

We present here the results of numerical experiments on the connections between the local complexity of the phase space of Hamiltonian systems and dynamical properties such as relaxation approach to equilibrium, sensitiveness to initial conditions during finite observations, etc. Before going into the more recent studies regarding a model of radian...