arXiv subjects
Publications and source records attributed to Riccardo Balzan.
We perform a numerical study of a new microcanonical polymer model on the three dimensional cubic lattice, consisting of ideal chains whose range and number of nearest-neighbor contacts are fixed to given values. Our simulations suggest an interesting exact relation concerning the internal energy per monomer of the Interacting Self-Avoiding Walk at the $θ-$point.
An influential theory of increasing returns has been proposed by the economist W. B. Arthur in the '80s to explain the lock-in phenomenon between two competing commercial products. In the most simplified situation there are two competing products that gain customers according to a majority mechanism: each new customer arrives and asks which product they bought to a certain odd number of previous customers, and then buy the most shared product within this sample. It is known that one of these two companies reaches monopoly almost surely in the limit of infinite customers. Here we consider a generalization [G. Dosi, Y. Ermoliev, Y. Kaniovsky, J. Math. Econom. 23, 1-19 (1994)] where the new customer follows the indication of the sample with some probability, and buy the other product otherwise. Other than economy, this model can be reduced to the urn of Hill, Lane and Sudderth, and includes several models of physical interest as special cases, like the Elephant Random Walk, the Friedman's urn and other generalized urn models. We provide a large deviation analysis of this model at the sample-path level, and give a formula that allows to find the most likely trajectories followed by the market share variable. Interestingly, in the parameter range where the lock-in phase is expected, we observe a whole region of convergence where the entropy cost is sub-linear. We also find a non-linear differential equation for the cumulant generating function of the market share variable, that can be studied with a suitable perturbations theory.
We describe a microcanonical approach for polymer models that combines atmospheric methods with urn theory. We show that Large Deviation Properties of urn models can provide quite deep mathematical insight by analyzing the Random Walk Range problem in $\mathbb{Z}^{d}$. We also provide a new mean field theory for the Range Problem that is exactly solvable by analogy with the Bagchi-Pal urn model.
Brain-computer interfaces surged extraordinary developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro- and meso-scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neurons activity, and generalize the maximum entropy model for neural networks so that also the time evolution of the system is taken into account. This is obtained by bridging particle physics and neuroscience, paving the way to particle physics-inspired models of neocortex.
In this work we experimentally study the behavior of a freely-rotating asymmetric probe immersed in a vibrated granular medium. For a wide variety of vibration conditions the probe exhibits a steady rotation whose direction is constant with respect to the asymmetry. By changing the vibration amplitude and by filtering the noise in different frequency bands we show that the velocity of rotation does not depend only on the RMS acceleration $Γ$, but also on the amount of energy provided to two separate frequency bands which are revealed to be important for the dynamics of the granular medium: the first band governs the transfer of energy from the grains to the probe, and the second affects the dynamics by altering the viscosity of the vibro-fluidized material.