arXiv subjects

Lucas Lacasa

Publications and source records attributed to Lucas Lacasa.

At least 37 records · Page 2Linked to original sources

arXiv2023

Irreversibility of symbolic time series: a cautionary tale

Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real-valued, and symbolization is applied subsequently, as in symbolic dynamics of chaotic systems. Among several time series quantifiers, time series irreversibility (the difference between forward and backward statistics in stationary time series) is of great relevance. However, the irreversible character of symbolized time series is not always equivalent to the one of the underlying real-valued signal, leading to some misconceptions and confusion on interpretability. Such confusion is even bigger for binary time series (a classical way to encode chaotic trajectories via symbolic dynamics). In this article we aim to clarify some usual misconceptions and provide theoretical grounding for the practical analysis -- and interpretation -- of time irreversibility in symbolic time series. We outline sources of irreversibility in stationary symbolic sequences coming from frequency asymmetries of non-palindromic pairs which we enumerate, and prove that binary time series cannot show any irreversibility based on words of length m < 4, thus discussing the implications and sources of confusion. We also study irreversibility in the context of symbolic dynamics, and clarify why these can be reversible even when the underlying dynamical system is not, such as the case of the fully chaotic logistic map.

nlin.CD↗

arXiv2023

Higher-order correlations reveal complex memory in temporal hypergraphs

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we use time-varying hypergraphs to describe such systems, and we introduce a framework based on higher-order correlations to characterize their temporal organization. We analyze various social systems, finding that groups of different sizes have typical patterns of long-range temporal correlations. Moreover, our method reveals the presence of non-trivial temporal interdependencies between different group sizes. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the pattern in the data.

physics.soc-ph↗

arXiv2023

Lyapunov Exponents for Temporal Networks

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions, and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low and high dimensional chaos, and finally discuss potential applications.

physics.data-an↗

arXiv2022

Chaotic renormalization group flow and entropy gradients over Haros graphs

Haros graphs have been recently introduced as a set of graphs bijectively related to real numbers in the unit interval. Here we consider the iterated dynamics of a graph operator $\cal R$ over the set of Haros graphs. This operator was previously defined in the realm of graph-theoretical characterisation of low-dimensional nonlinear dynamics, and has a renormalization group (RG) structure. We find that the dynamics of $\cal R$ over Haros graphs is complex and includes unstable periodic orbits or arbitrary period and non-mixing aperiodic orbits, overall portraiting a chaotic RG flow. We identify a single RG stable fixed point whose basin of attraction is the set of rational numbers, associate periodic RG orbits with (pure) quadratic irrationals and aperiodic RG orbits with (non-mixing) families of non-quadratic algebraic irrationals and trascendental numbers. Finally, we show that the entropy gradients inside periodic RG orbits are constant. We discuss the possible physical interpretation of such chaotic RG flow and speculate on the entropy-constant periodic orbits as a possible confirmation of a (quantum field-theoretic) $c$-theorem applied inside the invariant set of a RG flow.

cond-mat.stat-mech↗

arXiv2022

Haros graphs: an exotic representation of real numbers

This paper introduces Haros graphs, a construction which provides a graph-theoretical representation of real numbers in the unit interval reached via paths in the Farey binary tree. We show how the topological structure of Haros graphs yields a natural classification of the reals numbers into a hierarchy of families. To unveil such classification, we introduce an entropic functional on these graphs and show that it can be expressed, thanks to its fractal nature, in terms of a generalised de Rham curve. We show that this entropy reaches a global maximum at the reciprocal of the Golden number and otherwise displays a rich hierarchy of local maxima and minima that relate to specific families of irrationals (noble numbers) and rationals, overall providing an exotic classification and representation of the reals numbers according to entropic principles. We close the paper with a number of conjectures and outline a research programme on Haros graphs.

math.NT↗

arXiv2022

Correlations of network trajectories

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in graph space, following a latent graph dynamical system. Under this paradigm, we propose a way to measure how the network pulsates and collectively fluctuates over time and space. To this aim, we extend the notion of linear correlations function to the case of sequences of network snapshots, i.e. a network trajectory. We construct stochastic and deterministic graph dynamical systems and show that the emergent collective correlations are well captured by simple measures, and illustrate how these patterns are revealed in empirical networks arising in different domains.

cs.SI↗

arXiv2022

Visibility graphs of animal foraging trajectories

The study of self-propelled particles is a fast-growing research topic where biologically inspired movement is increasingly becoming of much interest. A relevant example is the collective motion of social insects, whose variety and complexity offer fertile grounds for theoretical abstractions. It has been demonstrated that the collective motion involved in the searching behavior of termites is consistent with self-similarity, anomalous diffusion and Lévy walks. In this work, we use visibility graphs -- a method that maps time series into graphs and quantifies the signal complexity via graph topological metrics -- in the context of social insects foraging trajectories extracted from experiments. Our analysis indicates that the patterns observed for isolated termites change qualitatively when the termite density is increased, and such change cannot be explained by jamming effects only, pointing to collective effects emerging due to non-trivial foraging interactions between insects as the cause. Moreover, we find that such an onset of complexity is maximized for intermediate termite densities.

cond-mat.stat-mech↗

arXiv2020

Beyond pairwise network similarity: exploring Mediation and Suppression between networks

Network similarity measures quantify how and when two networks are symmetrically related, including measures of statistical association such as pairwise distance or other correlation measures between networks or between the layers of a multiplex network, but neither can directly unveil whether there are hidden confounding network factors nor can they estimate when such correlation is underpinned by a causal relation. In this work we extend this pairwise conceptual framework to triplets of networks and quantify how and when a network is related to a second network directly or via the indirect mediation or interaction with a third network. Accordingly, we develop a simple and intuitive set-theoretic approach to quantify mediation and suppression between networks. We validate our theory with synthetic models and further apply it to triplets of real-world networks, unveiling mediation and suppression effects which emerge when considering different modes of interaction in online social networks and different routes of information processing in the brain.

cs.SI↗

arXiv2020

The shape of memory in temporal networks

Temporal networks are widely used models for describing the architecture of complex systems. Network memory -- that is the dependence of a temporal network's structure on its past -- has been shown to play a prominent role in diffusion, epidemics and other processes occurring over the network, and even to alter its community structure. Recent works have proposed to estimate the length of memory in a temporal network by using high-order Markov models. Here we show that network memory is inherently multidimensional and cannot be meaningfully reduced to a single scalar quantity. Accordingly, we introduce a mathematical framework for defining and efficiently estimating the microscopic shape of memory, which fully characterises how the activity of each link intertwines with the activities of all other links. We validate our methodology on a wide range of synthetic models of temporal networks with tuneable memory, and subsequently study the heterogeneous shapes of memory emerging in various real-world networks.

physics.soc-ph↗

arXiv2020

The arrow of time across five centuries of classical music

The concept of time series irreversibility -- the degree by which the statistics of signals are not invariant under time reversal -- naturally appears in non-equilibrium physics in stationary systems which operate away from equilibrium and produce entropy. This concept has not been explored to date in the realm of musical scores as these are typically short sequences whose time reversibility estimation could suffer from strong finite size effects which preclude interpretability. Here we show that the so-called Horizontal Visibility Graph method -- which recently was shown to quantify such statistical property even in non-stationary signals -- is a method that can estimate time reversibility of short symbolic sequences, thus unlocking the possibility of exploring such properties in the context of musical compositions. Accordingly, we analyse over 8000 musical pieces ranging from the Renaissance to the early Modern period and certify that, indeed, most of them display clear signatures of time irreversibility. Since by construction stochastic processes with a linear correlation structure (such as 1/f noise) are time reversible, we conclude that musical compositions have a considerably richer structure, that goes beyond the traditional properties retrieved by the power spectrum or similar approaches. We also show that musical compositions display strong signs of nonlinear correlations, that nonlinearity is correlated to irreversibility, and that these are also related to asymmetries in the abundance of musical intervals, which we associate to the narrative underpinning a musical composition. These findings provide tools for the study of musical periods and composers, as well as criteria related to music appreciation and cognition.

physics.soc-ph↗

arXiv2020

Predicting e-commerce customer conversion from minimal temporal patterns on symbolized clickstream trajectories

Knowing if a user is a buyer or window shopper solely based on clickstream data is of crucial importance for e-commerce platforms seeking to implement real-time accurate NBA (next best action) policies. However, due to the low frequency of conversion events and the noisiness of browsing data, classifying user sessions is very challenging. In this paper, we address the clickstream classification problem in the eCommerce industry and present three major contributions to the burgeoning field of AI-for-retail: first, we collected, normalized and prepared a novel dataset of live shopping sessions from a major European e-commerce website; second, we use the dataset to test in a controlled environment strong baselines and SOTA models from the literature; finally, we propose a new discriminative neural model that outperforms neural architectures recently proposed at Rakuten labs.

cs.LG↗

arXiv2019

Prediction is very hard, especially about conversion. Predicting user purchases from clickstream data in fashion e-commerce

Knowing if a user is a buyer vs window shopper solely based on clickstream data is of crucial importance for ecommerce platforms seeking to implement real-time accurate NBA (next best action) policies. However, due to the low frequency of conversion events and the noisiness of browsing data, classifying user sessions is very challenging. In this paper, we address the clickstream classification problem in the fashion industry and present three major contributions to the burgeoning field of AI in fashion: first, we collected, normalized and prepared a novel dataset of live shopping sessions from a major European e-commerce fashion website; second, we use the dataset to test in a controlled environment strong baselines and SOTA models from the literature; finally, we propose a new discriminative neural model that outperforms neural architectures recently proposed at Rakuten labs.

cs.IR↗

arXiv2019

Predicting success in the worldwide start-up network

By drawing on large-scale online data we construct and analyze the time-varying worldwide network of professional relationships among start-ups. The nodes of this network represent companies, while the links model the flow of employees and the associated transfer of know-how across companies. We use network centrality measures to assess, at an early stage, the likelihood of the long-term positive performance of a start-up, showing that the start-up network has predictive power and provides valuable recommendations doubling the current state of the art performance of venture funds. Our network-based approach not only offers an effective alternative to the labour-intensive screening processes of venture capital firms, but can also enable entrepreneurs and policy-makers to conduct a more objective assessment of the long-term potentials of innovation ecosystems and to target interventions accordingly.

physics.soc-ph↗

arXiv2019

On the spectral properties of Feigenbaum graphs

A Horizontal Visibility Graph (HVG) is a simple graph extracted from an ordered sequence of real values, and this mapping has been used to provide a combinatorial encryption of time series for the task of performing network based time series analysis. While some properties of the spectrum of these graphs --such as the largest eigenvalue of the adjacency matrix-- have been routinely used as measures to characterise time series complexity, a theoretic understanding of such properties is lacking. In this work we explore some algebraic and spectral properties of these graphs associated to periodic and chaotic time series. We focus on the family of Feigenbaum graphs, which are HVGs constructed in correspondence with the trajectories of one-parameter unimodal maps undergoing a period-doubling route to chaos (Feigenbaum scenario). For the set of values of the map's parameter $μ$ for which the orbits are periodic with period $2^n$, Feigenbaum graphs are fully characterised by two integers (n,k) and admit an algebraic structure. We explore the spectral properties of these graphs for finite n and k, and among other interesting patterns we find a scaling relation for the maximal eigenvalue and we prove some bounds explaining it. We also provide numerical and rigorous results on a few other properties including the determinant or the number of spanning trees. In a second step, we explore the set of Feigenbaum graphs obtained for the range of values of the map's parameter $μ$ for which the system displays chaos. We show that in this case, Feigenbaum graphs form an ensemble for each value of $μ$ and the system is typically weakly self-averaging. Unexpectedly, we find that while the largest eigenvalue can distinguish chaos from an iid process, it is not a good measure to quantify the chaoticity of the process, and that the eigenvalue density does a better job.

physics.data-an↗

arXiv2019

Quantifying and predicting success in show business

Recent studies in the science of success have shown that the highest-impact works of scientists or artists happen randomly and uniformly over the individual's career. Yet in certain artistic endeavours, such as acting in films and TV, having a job is perhaps the most important achievement: success is simply making a living. By analysing a large online database of information related to films and television we are able to study the success of those working in the entertainment industry. We first support our initial claim, finding that two in three actors are "one-hit wonders". In addition we find that, in agreement with previous works, activity is clustered in hot streaks, and the percentage of careers where individuals are active is unpredictable. However, we also discover that productivity in show business has a range of distinctive features, which are predictable. We unveil the presence of a rich-get-richer mechanism underlying the assignment of jobs, with a Zipf law emerging for total productivity. We find that productivity tends to be highest at the beginning of a career and that the location of the "annus mirabilis" -- the most productive year of an actor -- can indeed be predicted. Based on these stylized signatures we then develop a machine learning method which predicts, with up to 85% accuracy, whether the annus mirabilis of an actor has yet passed or if better days are still to come. Finally, our analysis is performed on both actors and actresses separately, and we reveal measurable and statistically significant differences between these two groups across different metrics, thereby providing compelling evidence of gender bias in show business.

physics.soc-ph↗

arXiv2018

Election Forensics: quantitative methods for electoral fraud detection

The last decade has witnessed an explosion on the computational power and a parallel increase of the access to large sets of data (the so called Big Data paradigm) which is enabling to develop brand new quantitative strategies underpinning description, understanding and control of complex scenarios. One interesting area of application concerns fraud detection from online data, and more particularly extracting meaningful information from massive digital fingerprints of electoral activity to detect, a posteriori, evidence of fraudulent behavior. In this short article we discuss a few quantitative methodologies that have emerged in recent years on this respect, which altogether form the nascent interdisciplinary field of election forensics.

physics.soc-ph↗

arXiv2018

The Dynamics of Norm Change in the Cultural Evolution of Language

What happens when a new social convention replaces an old one? While the possible forces favoring norm change - such as institutions or committed activists - have been identified since a long time, little is known about how a population adopts a new convention, due to the difficulties of finding representative data. Here we address this issue by looking at changes occurred to 2,541 orthographic and lexical norms in English and Spanish through the analysis of a large corpora of books published between the years 1800 and 2008. We detect three markedly distinct patterns in the data, depending on whether the behavioral change results from the action of a formal institution, an informal authority or a spontaneous process of unregulated evolution. We propose a simple evolutionary model able to capture all the observed behaviors and we show that it reproduces quantitatively the empirical data. This work identifies general mechanisms of norm change and we anticipate that it will be of interest to researchers investigating the cultural evolution of language and, more broadly, human collective behavior.

physics.soc-ph↗

arXiv2018

Effect of antipsychotics on community structure in functional brain networks

Schizophrenia, a mental disorder that is characterized by abnormal social behavior and failure to distinguish one's own thoughts and ideas from reality, has been associated with structural abnormalities in the architecture of functional brain networks. Using various methods from network analysis, we examine the effect of two classical therapeutic antipsychotics --- Aripiprazole and Sulpiride --- on the structure of functional brain networks of healthy controls and patients who have been diagnosed with schizophrenia. We compare the community structures of functional brain networks of different individuals using mesoscopic response functions, which measure how community structure changes across different scales of a network. We are able to do a reasonably good job of distinguishing patients from controls, and we are most successful at this task on people who have been treated with Aripiprazole. We demonstrate that this increased separation between patients and controls is related only to a change in the control group, as the functional brain networks of the patient group appear to be predominantly unaffected by this drug. This suggests that Aripiprazole has a significant and measurable effect on community structure in healthy individuals but not in individuals who are diagnosed with schizophrenia. In contrast, we find for individuals are given the drug Sulpiride that it is more difficult to separate the networks of patients from those of controls. Overall, we observe differences in the effects of the drugs (and a placebo) on community structure in patients and controls and also that this effect differs across groups. We thereby demonstrate that different types of antipsychotic drugs selectively affect mesoscale structures of brain networks, providing support that mesoscale structures such as communities are meaningful functional units in the brain.

physics.med-ph↗