Splitting process of the Bayesian Namig Game's solution due to the symmetry breaking process produced by the learning probabilities modelled as logistic functions. 

It's hard to believe, but speaking Catalan was forbidden during Franco's dictatorship, that is,  until 1976.

10 May 2024.  My paper Generalized naming game and Bayesian naming game as dynamical systems has been accepted for publication by  Physical Review E

16 May 2024.  Today I opened  Naming-Game-Models, a repository on my  my git-hub account  which will  contain the updated scripts in Python 3.8 to simulate the Naming Game (NG) model and its many variants. During the last recent years while I was developing a new variant of NG based upon the Bayesian inference, I wrote many scripts for simulating the dynamics of its variants, including their time-evolution in different types of complex networks such as random graphs, graphs with small-world properties and scale-free networks. However, the scripts were written in Python 2.7 as this version was required for running the scripts in parallel on computer clusters. However, Python 2.7 reached the end of its life on January 1st, 2020, however until one year I had to make scripts in Python 2.7. For this reason, I am rewriting the previous scripts in Python 3.8, adding also some changes/improvement when required.

At the moment, you can find the script  script ng2c.py for simulating the semiotic dynamics of an ensemble of agents in number N restricted to two names A and B corresponding to integers 0 and 1, respectively, starting from an initial configuration chosen by the user. Note that in such a model there will be always consensus at some time (the convergence time), that is, convergence to a state where all the agents have one name, either A or B, in their inventories. For such a simple model, except for the convergence time, there are two only observables: the total number of names and the success rate of the agents' pairwise interaction. The simulation outputs, including the convergence time and the maximum number of names are stored into file results.text.

3 June 2024.  Finally, my article "Generalized naming game and Bayesian naming game as dynamical systems" is published. Among the results, it shows that there exists a nongeneric bifurcation in the generalised naming game, a classical model of semiotic dynamics, and how such a bifurcation modifies the noise of the stochastic sample paths involved. In this regard, it is found that there are two possible stochastic processes: the Brownian motion and the Ornstein-Uhlenbeck process. Finally, it shows that the logistic function, widely used in Deep Learning, can be employed for modeling the word learning processes according to a Bayesian concept learning framework proposed by Josh Tenenbaum. As a result, such an approach introduces a symmetry breaking mechanism, otherwise absent in the Bayesian dynamical system. Please, have a look at https://lnkd.in/dGaDV8Ac

23 June 2024. I’m delighted to share that my little contribution to the Thomas-Fermi theory is now published https://lnkd.in/dhR6D6fQ I proposed a probabilistic method for assessing the validity of the Thomas-Fermi potential in three-dimensional condensed matter systems. However, the method can be also used for two-dimensional systems including graphene as in the latter case it can deal with relativistic (Dirac) particles. Finally, my paper contains a brief review of the analytical potentials derived in random phase approximation (RPA) that to my best knowledge is absent in the corresponding literature. I have to thank  Fabio Caruso  for suggesting the right journal!

04-04-2025 A cautionary tale about the Principal Component Analysis (PCA) in spectroscopy. I applied standard PCA to a data set of high-dimensional spectra of globular proteins (the number of components = 105). The respective results are shown in the scatterplot on the left. There is no structure on the two-dimensional scatterplot for which the explained variance is about 70%. Also, some outliers seem to emerge, e.g., Avidin (PDB entry: 1RAV). However, these are PCA artifacts. On the right, there is a scatterplot of the very same data, using a nonlinear manifold learning algorithm in combination with the generative Gaussian Mixture model. Accordingly, two meaningful clusters are correctly identified. Their corresponding instances have specific protein's secondary structures. These and other ML results will be discussed in a paper of mine very soon.

07-06-2025 (Andrews' Curves)  I found a very simple and useful method to visualize high-dimensional data points by mapping them to Andrews' curves. Below, I plot the Andrews' curves of a dataset consisting of 88 observations in a 9-dimensional Euclidean space.

Notably, the two most dissimilar curves—shown in blue and red—correspond to the data points with the largest Euclidean distance between them, which is approximately 1.7 (see the accompanying histogram of all possible pairwise distances). This correspondence arises because the distance between Andrews' curves is simply the Euclidean distance, rescaled by a constant factor equal to π.

It's important to note that the shape of each curve depends on the order of the variables, so the shape itself is not inherently meaningful. 

15-06-2025. Finally, I have uploaded the data from high-dimensional trajectories, consisting of 4, 000, 000 datapoints, of the Fermi-Pasta-Ulam-Tsingou model to Zenodo.The orbits have been accurately computed using a suitable symplectic integrator, and in some cases, validated through comparison with previous simulations to confirm the accuracy of the data.

This dataset is a bonanza for investigating the connection between ergodicity and the geometry and topology of the manifolds on which the trajectories lie or evolve near. It is particularly valuable for applying state-of-the-art unsupervised machine learning techniques such as manifold learning and topological data analysis.

A particularly intriguing direction is to explore how increasing the model’s nonlinearity leads to symmetry breaking, and how this relates to changes in the underlying Riemannian manifold.

I would like to thank CERN and Google for providing free repository and high-performance computing resources. Link to Zenodo: https://lnkd.in/dy4wcT-p.

31th July 2025. I uploaded on Zenodo several datasets containing 12,000 quantum scattering phase shifts in s-wave, p-wave, d-wave, accurately computed using the Variable Phase Method, for Yukawa (or equivalently Thomas-Fermi), Double Yukawa, and Exponential Cosine Screened Coulomb potentials. These are important potentials in Plasma, Condensed Matter, and Nuclear physics. It has been shown that phase shifts in s-wave can be accurately predicted without solving the radial Schroedinger equation, in a previous work of mine with Alessandro Romualdi, using convolutional neural networks (please see article . In principle, I read, it could be possible to reconstruct the potentials from the phase shifts, but I do not know this theory. The datasets can be found here https://lnkd.in/dDQ_62ra . Thanks to CERN