arXiv subjects

Giordano De Marzo

Publications and source records attributed to Giordano De Marzo.

31 records · Page 2Linked to original sources

arXiv2023

The effect of Collaborative-Filtering based Recommendation Algorithms on Opinion Polarization

A central role in shaping the experience of users online is played by recommendation algorithms. On the one hand they help retrieving content that best suits users taste, but on the other hand they may give rise to the so called "filter bubble" effect, favoring the rise of polarization. In the present paper we study how a user-user collaborative-filtering algorithm affects the behavior of a group of agents repeatedly exposed to it. By means of analytical and numerical techniques we show how the system stationary state depends on the strength of the similarity and popularity biases, quantifying respectively the weight given to the most similar users and to the best rated items. In particular, we derive a phase diagram of the model, where we observe three distinct phases: disorder, consensus and polarization. In the latter users spontaneously split into different groups, each focused on a single item. We identify, at the boundary between the disorder and polarization phases, a region where recommendations are nontrivially personalized without leading to filter bubbles. Finally, we show that our model can reproduce the behavior of users in the online music platform last.fm. This analysis paves the way to a systematic analysis of recommendation algorithms by means of statistical physics methods and opens to the possibility of devising less polarizing recommendation algorithms.

physics.soc-ph↗

arXiv2023

The Tully-Fisher relation and the Bosma effect

We show that the rotation curves of 16 nearby disc galaxies in the THINGS sample and the Milky Way can be described by the NFW halo model and by the Bosma effect at approximately the same level of accuracy. The latter effect suggests that the behavior of the rotation curve at large radii is determined by the rescaled gas component and thus that dark matter and gas distributions are tightly correlated. By focusing on galaxies with exponential decay in their gas surface density, we can normalize their rotation curves to match the exponential thin disc model at large enough radii. This normalization assumes that the galaxy mass is estimated consistently within this model, assuming a thin disc structure. We show that this rescaling allows us to derive a new version of the Tully-Fisher (TF) relation, the Bosma TF relation that nicely fit the data. In the framework of this model, the connection between the Bosma Tully-Fisher (TF) relation and the baryonic TF relation can be established by considering an additional empirical relation between the baryonic mass and the total mass of the disc, as measured in the data.

astro-ph.GA↗

arXiv2023

Mapping non-axisymmetric velocity fields of external galaxies

Disk galaxies are typically in a stable configuration where matter moves in almost closed circular orbits. However, non-circular motions caused by distortions, warps, lopsidedness, or satellite interactions are common and leave distinct signatures on galaxy velocity maps. We develop an algorithm that uses an ordinary least square method for fitting a non-axisymmetric model to the observed two-dimensional line-of-sight velocity map of an external galaxy, which allows for anisotropic non-circular motions. The method approximates a galaxy as a flat disk, which is an appropriate assumption for spiral galaxies within the optical radius where warps are rare. In the outer parts of HI distributions, which may extend well into the warp region, we use this method in combination with a standard rotating tilted ring model to constrain the range of radii where the flat disk assumption can be conservatively considered valid. Within this range, the transversal and radial velocity profiles, averaged in rings, can be directly reconstructed from the velocity map. The novelty of the algorithm consists in using arc segments in addition to rings: in this way spatial velocity anisotropies can be measured in both components, allowing for the reconstruction of angularly resolved coarse-grained two-dimensional velocity maps. We applied this algorithm to 25 disk galaxies from the THINGS sample for which we can provide 2D maps of both velocity components.

astro-ph.GA↗

arXiv2023

Mapping job complexity and skills into wages

We use algorithmic and network-based tools to build and analyze the bipartite network connecting jobs with the skills they require. We quantify and represent the relatedness between jobs and skills by using statistically validated networks. Using the fitness and complexity algorithm, we compute a skill-based complexity of jobs. This quantity is positively correlated with the average salary, abstraction, and non-routinarity level of jobs. Furthermore, coherent jobs - defined as the ones requiring closely related skills - have, on average, lower wages. We find that salaries may not always reflect the intrinsic value of a job, but rather other wage-setting dynamics that may not be directly related to its skill composition. Our results provide valuable information for policymakers, employers, and individuals to better understand the dynamics of the labor market and make informed decisions about their careers.

econ.GN↗

arXiv2022

Quantifying the complexity and similarity of chess openings using online chess community data

Hundreds of years after its creation, the game of chess is still widely played worldwide. Opening Theory is one of the pillars of chess and requires years of study to be mastered. Here we exploit the "wisdom of the crowd" in an online chess platform to answer questions that, traditionally, only chess experts could tackle. We first define the relatedness network of chess openings that quantifies how similar two openings are to play. In this network, we spot communities of nodes corresponding to the most common opening choices and their mutual relationships, information which is hard to obtain from the existing classification of openings. Moreover, we use the relatedness network to forecast the future openings players will start to play and we back-test these predictions, obtaining performances considerably higher than those of a random predictor. Finally, we use the Economic Fitness and Complexity algorithm to measure how difficult to play openings are and how skilled in openings players are. This study not only gives a new perspective on chess analysis but also opens the possibility of suggesting personalized opening recommendations using complex network theory.

physics.soc-ph↗

arXiv2022

Effect of spatial correlations on Hopfield Neural Network and Dense Associative Memories

Hopfield model is one of the few neural networks for which analytical results can be obtained. However, most of them are derived under the assumption of random uncorrelated patterns, while in real life applications data to be stored show non-trivial correlations. In the present paper we study how the retrieval capability of the Hopfield network at null temperature is affected by spatial correlations in the data we feed to it. In particular, we use as patterns to be stored the configurations of a linear Ising model at inverse temperature $β$. Exploiting the signal to noise technique we obtain a phase diagram in the load of the Hopfield network and the Ising temperature where a fuzzy phase and a retrieval region can be observed. Remarkably, as the spatial correlation inside patterns is increased, the critical load of the Hopfield network diminishes, a result also confirmed by numerical simulations. The analysis is then generalized to Dense Associative Memories with arbitrary odd-body interactions, for which we obtain analogous results.

cond-mat.stat-mech↗

arXiv2022

Filter Bubble effect in the multistate voter model

Social media influence online activity by recommending to users content strongly correlated with what they have preferred in the past. In this way they constrain users within filter bubbles that strongly limit their exposure to new or alternative content. We investigate this type of dynamics by considering a multistate voter model where, with a given probability $λ$, a user interacts with a "personalized information" suggesting the opinion most frequently held in the past. By means of theoretical arguments and numerical simulations, we show the existence of a nontrivial transition between a region (for small $λ$) where consensus is reached and a region (above a threshold $λ_c$) where the system gets polarized and clusters of users with different opinions persist indefinitely. The threshold always vanishes for large system size $N$, showing that consensus becomes impossible for a large number of users. This finding opens new questions about the side effects of the widespread use of personalized recommendation algorithms.

physics.soc-ph↗

arXiv2022

Quantifying the Unexpected: a scientific approach to Black Swans

Many natural and socio-economic systems are characterized by power-law distributions that make the occurrence of extreme events not negligible. Such events are sometimes referred to as Black Swans, but a quantitative definition of a Black Swan is still lacking. Here, by leveraging on the properties of Zipf-Mandelbrot law, we investigate the relations between such extreme events and the dynamics of the upper cutoff of the inherent distribution. This approach permits a quantification of extreme events and allows to classify them as White, Grey, or Black Swans. Our criterion is in accordance with some previous findings, but also allows us to spot new examples of Black Swans, such as Lionel Messi and the Turkish Airline Flight 981 disaster. The systematic and quantitative methodology we developed allows a scientific and immediate categorization of rare events, providing also new insight into the generative mechanism behind Black Swans.

physics.soc-ph↗

arXiv2021

The emergence of a concept in shallow neural networks

We consider restricted Boltzmann machine (RBMs) trained over an unstructured dataset made of blurred copies of definite but unavailable ``archetypes'' and we show that there exists a critical sample size beyond which the RBM can learn archetypes, namely the machine can successfully play as a generative model or as a classifier, according to the operational routine. In general, assessing a critical sample size (possibly in relation to the quality of the dataset) is still an open problem in machine learning. Here, restricting to the random theory, where shallow networks suffice and the grand-mother cell scenario is correct, we leverage the formal equivalence between RBMs and Hopfield networks, to obtain a phase diagram for both the neural architectures which highlights regions, in the space of the control parameters (i.e., number of archetypes, number of neurons, size and quality of the training set), where learning can be accomplished. Our investigations are led by analytical methods based on the statistical-mechanics of disordered systems and results are further corroborated by extensive Monte Carlo simulations.

cond-mat.dis-nn↗

arXiv2021

Zipf's law for cosmic structures: how large are the greatest structures in the universe?

The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greatest structures in the universe. This point is closely related to whether or not such a distribution can be approximated as being homogeneous on large enough scales. Here we assess this problem by considering the size distribution of superclusters of galaxies and by leveraging on the properties of Zipf-Mandelbrot law, providing a novel approach which complements standard analysis based on the correlation functions. We find that galaxy superclusters are well described by a pure Zipf's law with no deviations and this implies that all the catalogs currently available are not sufficiently large to spot a truncation in the power-law behavior. This finding provides evidence that structures larger than the greatest superclusters already observed are expected to be found when deeper redshift surveys will be completed. As a consequence the scale beyond which galaxy distribution crossovers toward homogeneity, if any, should increase accordingly

astro-ph.CO↗

arXiv2020

Emergence of polarization in a voter model with personalized information

The flourishing of fake news is favored by recommendation algorithms of online social networks which, based on previous users activity, provide content adapted to their preferences and so create filter bubbles. We introduce an analytically tractable voter model with personalized information, in which an external field tends to align the agent opinion with the one she held more frequently in the past. Our model shows a surprisingly rich dynamics despite its simplicity. An analytical mean-field approach, confirmed by numerical simulations, allows us to build a phase diagram and to predict if and how consensus is reached. Remarkably, polarization can be avoided only for weak interaction with the personalized information and if the number of agents is below a threshold. We analytically compute this critical size, which depends on the interaction probability in a strongly non linear way.

physics.soc-ph↗

arXiv2020

Dynamical approach to Zipf's law

The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a dynamical approach is crucial: during their evolution, some systems are attracted towards Zipf's law, while others presents Zipf's law only temporarily and, therefore, spuriously. A truly Zipfian dynamics is characterized by a dynamical constraint, or coherence, among the parameters of the generating PDF, and the number of elements in the system. A clear-cut example of such coherence is natural language. Our framework allows us to derive some quantitative results that go well beyond the usual Zipf's law: i) earthquakes can evolve only incoherently and thus show Zipf's law spuriously; this allows an assessment of the largest possible magnitude of an earthquake occurring in a geographical region. ii) We prove that Zipfian dynamics are not additive, explaining analytically why US cities evolve coherently, while world cities do not. iii) Our concept of coherence can be used for model selection, for example, the Yule-Simon process can describe the dynamics of world countries' GDP. iv) World cities present spurious Zipf's law and we use this property for estimating the maximal population of an urban agglomeration.

physics.soc-ph↗

arXiv2020

Tolerance versus synaptic noise in dense associative memories

The retrieval capabilities of associative neural networks can be impaired by different kinds of noise: the fast noise (which makes neurons more prone to failure), the slow noise (stemming from interference among stored memories), and synaptic noise (due to possible flaws during the learning or the storing stage). In this work we consider dense associative neural networks, where neurons can interact in $p$-plets, in the absence of fast noise, and we investigate the interplay of slow and synaptic noise. In particular, leveraging on the duality between associative neural networks and restricted Boltzmann machines, we analyze the effect of corrupted information, imperfect learning and storing errors. For $p=2$ (corresponding to the Hopfield model) any source of synaptic noise breaks-down retrieval if the number of memories $K$ scales as the network size. For $p>2$, in the relatively low-load regime $K \sim N$, synaptic noise is tolerated up to a certain bound, depending on the density of the structure.

cond-mat.dis-nn↗