arXiv subjects

Gionni Marchetti

Publications and source records attributed to Gionni Marchetti.

17 recordsLinked to original sources

arXiv2026

Beyond Explained Variance: A Cautionary Tale of PCA

We address shortcomings of principal component analysis (PCA) for visualizing high-dimensional data lying on a nonlinear low-dimensional manifold via two-dimensional scatterplots, focusing on a fossil teeth dataset from the early mammalian insectivore Kuehneotherium. While the PCA scatterplot reported by Jolliffe and Cadima (Philosophical Transactions of the Royal Society A, 2016) shows clustering in the region where PC2 < 0, our analysis based on t-SNE and persistent homology (PH) reveals a ring-like structure with no evident clustering and intrinsic dimensionality equal to one. We further propose a generative probabilistic-geometric model in which the data are sampled uniformly from a unit circle. Under this model, pairwise cosine distances follow an arcsine distribution, in qualitative agreement with the observed U-shaped distribution, thereby independently supporting the analysis based on t-SNE and persistent homology.

cond-mat.stat-mech↗

arXiv2026

Learning the Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou Trajectories: A Nonlinear Approach using a Deep Autoencoder Model

We address the intrinsic dimensionality (ID) of high-dimensional trajectories, comprising $n_s = 4\,000\,000$ data points, of the Fermi-Pasta-Ulam-Tsingou (FPUT) $\beta$ model with $N = 32$ oscillators. To this end, a deep autoencoder (DAE) is used to infer the ID in the weakly nonlinear regime where energy recurrences are observed ($\beta \lesssim 1$). We find that the trajectories lie on a nonlinear Riemannian manifold of dimension $m^{\ast} = 2$ embedded in a $64$-dimensional phase space. By contrast, principal component analysis (PCA) together with the Participation Ratio (PR) method provides only a reasonable upper bound on the ID for each value of $\beta$. Our DAE further reveals that the ID increases to $m^{\ast} = 3$ at $\beta = 1.1$, coinciding with a symmetry-breaking (SB) phenomenon characteristic of the $\beta$ model, in which additional energy modes with even wave numbers $k = 2, 4$ become excited. Notably, the SB phenomenon cannot be detected by the linear approach provided by PCA.

cond-mat.stat-mech↗

arXiv2025

Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou High-Dimensional Trajectories Through Manifold Learning: A Linear Approach

A data-driven approach based on unsupervised machine learning is proposed to infer the intrinsic dimension $m^{\ast}$ of the high-dimensional trajectories of the Fermi-Pasta-Ulam-Tsingou (FPUT) model. Principal component analysis (PCA) is applied to trajectory data consisting of $n_s = 4,000,000$ datapoints, of the FPUT $β$ model with $N = 32$ coupled oscillators, revealing a critical relationship between $m^{\ast}$ and the model's nonlinear strength. By estimating the intrinsic dimension $m^{\ast}$ using multiple methods (participation ratio, Kaiser rule, and the Kneedle algorithm), it is found that $m^{\ast}$ increases with the model nonlinearity. Interestingly, in the weakly nonlinear regime, for trajectories initialized by exciting the first mode, the participation ratio estimates $m^{\ast} = 2, 3$, strongly suggesting that quasi-periodic motion on a low-dimensional Riemannian manifold underlies the characteristic energy recurrences observed in the FPUT model.

cs.LG↗

arXiv2025

A Machine Learning Tool to Analyse Spectroscopic Changes in High-Dimensional Data

When nanoparticles (NPs) are introduced into a biological solution, layers of biomolecules form on their surface, creating a corona. Understanding how the structure of the protein evolves into the corona is essential for evaluating the safety and toxicity of nanotechnology. However, the influence of NP properties on protein conformation is not well understood. In this study, we propose a new method that addresses this issue by analyzing multi-component spectral data using Machine Learning (ML). We apply the method to fibrinogen, a crucial protein in human blood plasma, at physiological concentrations while interacting with hydrophobic carbon or hydrophilic silicon dioxide NPs, revealing striking differences in the temperature dependence of the protein structure between the two cases. Our unsupervised ML method a) does not suffer from the challenges associated with the curse of dimensionality, and b) simultaneously handles spectral data from various sources. The method offers a quantitative analysis of protein structural changes upon adsorption and enhances the understanding of the correlation between protein structure and NP interactions, which could support the development of nanomedical tools to treat various conditions.

cond-mat.stat-mech↗

arXiv2025

Metric Similarity and Manifold Learning of Circular Dichroism Spectra of Proteins

We present a machine learning analysis of circular dichroism spectra of globular proteins from the SP175 database, using the optimal transport-based $1$-Wasserstein distance $\mathcal{W}_1$ (with order $p=1$) and the manifold learning algorithm $t$-SNE. Our results demonstrate that $\mathcal{W}_1$ is consistent with both Euclidean and Manhattan metrics while exhibiting robustness to noise. On the other hand, $t$-SNE uncovers meaningful structure in the high-dimensional data. The clustering in the $t$-SNE embedding is primarily determined by proteins with distinct secondary structure compositions: one cluster predominantly contains $β$-rich proteins, while the other consists mainly of proteins with mixed $α/β$ and $α$-helical content.

physics.soc-ph↗

arXiv2024

Generalized Naming Game and Bayesian Naming Game as Dynamical Systems

We study the $β$-model ($β$-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the $β$-model, we demonstrate the existence of a non-generic bifurcation with a bifurcation point $β_c = 1/3$. As $β$ passes through $β_c$, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities $p_A$ and $p_B$ as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that $p_A = p_B = p$, where $p$ is a constant.

physics.soc-ph↗

arXiv2024

Revisiting the Thomas-Fermi Potential for Three-Dimensional Condensed Matter Systems

We proposed a formally exact, probabilistic method to assess the validity of the Thomas-Fermi potential for three-dimensional condensed matter systems where electron dynamics is constrained to the Fermi surface. Our method, which relies on accurate solutions of the radial Schrödinger equation, yields the probability density function for momentum transfer. This allows for the computation of its expectation values, which can be compared with unity to confirm the validity of the Thomas-Fermi approximation. We applied this method to three {\it n}-type direct-gap III-V model semiconductors (GaAs, InAs, InSb) and found that the Thomas-Fermi approximation is certainly valid at high electron densities. In these cases, the probability density function exhibits the same profile, irrespective of the material under scrutiny. Furthermore, we show that this approximation can lead to serious errors in the computation of observables when applied to GaAs at zero temperature for most electron densities under scrutiny.

cond-mat.mtrl-sci↗

arXiv2023

The Role of bilinguals in the Bayesian naming game

We study the recently introduced Bayesian naming game model, in which the one-shot learning of the minimal naming game is replaced by a more realistic learning process defined according to Bayesian inference. The results are compared with those obtained from the minimal naming game model. We focus on the dynamics of the bilingual population, providing analytical estimates of the upper bound for the number of bilinguals in both models based on the mean-field equations, and validate them through numerical simulations of the multi-agent models. We show that in the Bayesian model the maximum number of bilinguals is always lower with respect to the minimal naming game and that the two models are characterized by qualitatively different time evolutions.

physics.soc-ph↗

arXiv2023

Electron-electron Scattering in the Diffusive Regime and Dyakonov-Perel Theory: a case study of spin decoherence in n-type GaAs

We argue that in the ensemble Monte Carlo approach, the spin decoherence caused by electron-electron interactions in n-type bulk GaAs at room temperature, according to Dyakonov-Perel theory, is mainly induced by the electron density while electron-electron scattering itself does not directly affect spin lifetime but instead influences it through any energy dependence of other scattering mechanisms as typically expected in the case of the electron mobility. Therefore, our analysis, which is strongly supported by Bayesian Occam's razor, reconciles the semiclassical Monte Carlo approach with the novel computational first-principles tool recently proposed by Xu, Habib, Sundararaman and Ping.

cond-mat.mtrl-sci↗

arXiv2022

Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schrödinger Equation

We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts caused by different three-dimensional spherically symmetric potentials at fixed collision energy thereby bypassing the radial Schrödinger equation. In out work, we discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor. The good performance, even in presence of bound states in the data sets, exhibited by our model that accordingly is trained on the Hamiltonian through each scattering potential, demonstrates the feasibility of this proof of principle.

physics.comp-ph↗

arXiv2020

A Bird's-Eye View of Naming Game Dynamics: From Trait Competition to Bayesian Inference

The present contribution reviews a set of different versions of the basic naming game model, differing in the underlying topology or in the mechanisms regulating the interactions between agents. We include also a Bayesian naming game model recently introduced, which merges the social dynamics of the basic naming game model with the Bayesian learning framework introduced by Tenenbaum and co-workers. The latter model goes beyond the fixed nature of names and concepts of standard semiotic dynamics models and the corresponding one-shot learning process, by describing dynamically how agents can generalize a concept from a few examples, according to principles of Bayesian inference.

physics.soc-ph↗

arXiv2019

A Bayesian Approach to the Naming Game Model

We present a novel Bayesian approach to semiotic dynamics, which is a cognitive analogue of the naming game model restricted to two conventions. The one-shot learning that characterizes the agent dynamics in the basic naming game is replaced by a word-learning process, in which agents learn a new word by generalizing from the evidence garnered through pairwise-interactions with other agents. The principle underlying the model is that agents, like humans, can learn from a few positive examples and that such a process is modeled in a Bayesian probabilistic framework. We show that the model presents some analogies but also crucial differences with respect to the dynamics of the basic two-convention naming game model. The model introduced aims at providing a starting point for the construction of a general framework for studying the combined effects of cognitive and social dynamics.

physics.soc-ph↗

arXiv2019

Single-particle Relaxation Time in Doped Semiconductors beyond the Born Approximation

We compare the magnitudes of the single-particle relaxation time accurately computed by the variable phase approach are with those computed in the first Born approximation for doped semiconductors such as Si and GaAs, assuming that the Coulomb impurities are randomly distributed centers. We find that for typical dopant concentrations in Si the Born approximation can overestimate the single-particle relaxation time by roughly 40\% and underestimate it by roughly 30\%. It is shown that in the case of GaAs the discrepancies are typically less severe. Our analysis shows that in general these large discrepancies in Si arise from strong violations of the Friedel sum rule. This breakdown occurs in a range of doping densities for which the random phase approximation starts to break down. Moreover, our results suggest that a multi-ion correction to the electron-impurity scattering is needed for high dopant concentrations.

cond-mat.mtrl-sci↗

arXiv2018

Inconsistency between Linearized Thomas-Fermi Approximation and Electron-Ionized Impurity Scattering Rate in the first Born Approximation

We show that by computing the electron-impurity scattering rate at the first order via Fermi's golden rule, and assuming that the localized impurity potential is of Yukawa form, one obtains a wave vector transfer distribution which is inconsistent with the finite temperature linearized Thomas-Fermi approximation for {\it n}-type semiconductors. Our previous findings show that this is not the case for the carrier nondegenerate dynamics, because the average wave vector transferred being in general negligible in this regime. Moreover, we examine the behavior of the electron-impurity differential cross-sections in the first Born approximation for relevant values of the wave vector transfer. We find that in the majority of collisions, the scattering probabilities differ at the most by $1$ \% from the estimates computed by means of the impurity potential at random phase approximation level.

cond-mat.mes-hall↗

arXiv2016

Spin Relaxation in GaAs: Importance of Electron-Electron Interactions

We study spin relaxation in n-type bulk GaAs, due to the Dyakonov--Perel mechanism, using ensemble Monte Carlo methods. Our results confirm that spin relaxation time increases with the electronic density in the regime of moderate electronic concentrations and high temperature. We show that the electron-electron scattering in the non-degenerate regime significantly slows down spin relaxation. This result supports predictions by Glazov and Ivchenko. Most importantly, our findings highlight the importance of many-body interactions for spin dynamics: we show that only by properly taking into account electron-electron interactions within the simulations, results for the spin relaxation time---with respect to both electron density and temperature---will reach good {\it quantitative} agreement with corresponding experimental data. Our calculations contain no fitting parameters.

cond-mat.mtrl-sci↗

arXiv2016

Effect of Ionized Impurity Screening on Spin Decoherence at Low and Intermediate Temperatures in GaAs

We study the effect of charged impurity screening on spin decoherence in bulk {\it n}-type GaAs, and analyse in details the effect of the use of different Born approximations applied to a linearized Thomas-Fermi screening theory. The spin relaxation times are calculated by ensemble Monte Carlo techniques, including electron-electron, electron-impurities, and electron-phonons scattering. We carefully choose a parameter region so that all the physical approximations hold, and, in particular, a Yukawa-type potential can be used to describe the screened Coulomb interaction and the Born series converges. Our results show that including the second order Born approximation yields much shorter spin relaxation times compared to the commonly implemented first Born approximation: spin relaxation times may be reduced by hundreds of picoseconds, with the first Born approximation overestimating results by 30% or more for a large region of parameters. Though our ensemble Monte Carlo simulations include electron-electron and electron-phonon interactions, when considering low to intermediate carrier densities and $T > 50 $ $\mathrm{K}$, but $T$ smaller than the Fermi temperature, our results are in good agreement with Dyakonov-Perel theory when this includes electron-impurity interactions only, which supports this to be the most relevant scattering mechanism for bulk GaAs in this low-intermediate temperature regime.

cond-mat.mtrl-sci↗

arXiv2014

Spin decoherence in n-type GaAs: the effectiveness of the third-body rejection method for electron-electron scattering

We study the spin decoherence in n-type bulk GaAs for moderate electronic densities at room temperature using Ensemble Monte Carlo method. We demonstrate that the third-body rejection method devised by Ridley can be successfully adapted to Ensemble Monte Carlo algorithm, and used to tackle the problem of the electron-electron contribution to spin decoherence.

cond-mat.mtrl-sci↗