arXiv subjects

Jan M. Baetens

Publications and source records attributed to Jan M. Baetens.

At least 19 recordsLinked to original sources

arXiv2026

Social Contagion in COVID-19 Discussions within the Belgian Reddit Community: A Statistical and Modeling Study

Understanding how sentiment toward COVID-19 mitigation measures evolves on social media can inform both epidemiological models and public health policy. We analyzed 655,642 posts by 28,559 users on r/Belgium from January 2020 to June 2022, classifying posts into three mitigation topics (lockdowns, masks, vaccinations) using a BERT-based topic model and scoring sentiment with a RoBERTa-based classifier. Post volume tracked external events such as policy announcements, but we found no evidence of within-Reddit social contagion in topic initiation, suggesting topics are seeded by external information rather than platform-internal spread. Sentiment, however, exhibited significant homophily: comment sentiment correlated with that of the parent post. To capture the underlying dynamics, we developed the Smooth Latent-Expressed Bounded Confidence (SLEBC) model, which distinguishes a latent sentiment trajectory from noisy expressed sentiment and uses bounded confidence rather than linear update rules. Evaluated against two alternatives by WAIC, SLEBC fit best across all three topics. The model indicates that expressed sentiment adapts more strongly to the immediate parent comment than the user's latent state updates from interaction history, suggesting that expressed sentiment is a poor proxy for underlying opinion. These findings imply that infodemic models for Reddit-like platforms should seed topics from external sources and model sentiment spread via bounded confidence mechanisms.

cs.SI↗

arXiv2026

Exact Lyapunov spectra of affine cellular automata and the parity rule on networks

The Lyapunov exponent quantifies the sensitivity of a dynamical system to perturbations, and the full Lyapunov spectrum extends this to every orthogonal direction in tangent space. For cellular automata the spectrum is almost always approximated numerically, and the approximation is delicate. We show that the affine rules, those whose update is a XOR of a subset of the inputs together with a constant, admit an exact Lyapunov spectrum. An affine rule has a configuration-independent Boolean Jacobian, so the spectrum reduces to the logarithms of the singular values of a single constant matrix, with no simulation and no limit involved. Two cases carry a closed form. For an affine cellular automaton on a periodic lattice the Jacobian is a multilevel circulant matrix, and the spectrum is the discrete Fourier transform of the rule's gradient stencil, valid in any spatial dimension. For the parity rule on an arbitrary graph the Jacobian is the adjacency matrix itself, so the Lyapunov spectrum is the logarithm of the absolute adjacency spectrum, and the maximal exponent is the logarithm of the spectral radius. The long-time amplitude of a single-site perturbation then scales with the eigenvector centrality of the seeded node. Reading the periodic lattice as the Cayley graph of an abelian group unifies the two cases. Because they are exact, the affine spectra also serve as benchmarks: they reveal numerical artefacts in previously reported spectra and turn the informal correspondence between spectral radius and dynamical sensitivity into an exact identity.

nlin.CG↗

arXiv2026

Modification speed and radius of higher-order interactions alter the oscillatory dynamics in an agent-based model

Understanding the population dynamics of ecological systems is crucial for predicting shifts in biodiversity and ensuring the protection of these systems. Established models often focus on pairwise species interactions, yet recent studies have highlighted the importance of higher-order interactions (HOIs) in shaping community structure and function. In this study, we investigate the effects of HOIs in an agent-based model with three species engaged in intransitive competition. We introduce an HOI where one species modifies the competition between the other two. We explore the impact of the strength, radius of influence, and speed of this interaction modification on species abundances and oscillations thereof. Our results show that these abundances are not only greatly impacted by the strength, but also by the radius and speed of the interaction modification. A deeper investigation demonstrates that the changes in the oscillations are caused by the interaction modification itself, and not the change in pairwise interaction strength caused by the HOI. These results emphasize the importance of considering the spatio-temporal scales of higher-order interactions when assessing ecosystem stability, highlighting that such interactions can introduce complex dynamical behaviors that go beyond the predictions of traditional pairwise or simpler higher-order models

q-bio.PE↗

arXiv2025

Essential metrics for Life on graphs

We present a strong theoretical foundation that frames a well-defined family of outer-totalistic network automaton models as a topological generalisation of binary outer-totalistic cellular automata, of which the Game of Life is one notable particular case. These "Life-like network automata" are quantitatively described by expressing their genotype (the mean field curve and Derrida curve) and phenotype (the evolution of the state and defect averages). After demonstrating that the genotype and phenotype are correlated, we illustrate the utility of these essential metrics by tackling the firing squad synchronisation problem in a bottom-up fashion, with results that exceed a 90% success rate.

nlin.CG↗

arXiv2025

Epidemic risk perception and social interactions lead to awareness cascades on multiplex networks

The course of an epidemic is not only shaped by infection transmission over face-to-face contacts, but also by preventive behaviour caused by risk perception and social interactions. This study explores the dynamics of coupled awareness and biological infection spread within a two-layer multiplex network framework. One layer embodies face-to-face contacts, with a biological infection transmission following a simple contagion model, the SIR process. Awareness, modelled by the linear threshold model, a complex contagion, spreads over a social layer and induces behaviour that lowers the chance of a biological infection occurring. It may be provoked by the presence of either aware or infectious neighbours. We introduce a novel model combining these influences through a convex combination, creating a continuum between pure social contagion and local risk perception. Simulation of the model shows distinct effects arising from the awareness sources. Also, for convex combinations where both input sources are of importance, awareness cascades that are not attributable to only one of these sources, emerge. Under these conditions, the combination of a small-world face-to-face and a scale-free social layer, but not vice versa, make that the extent of the infections decreases with increasing transmission probability.

physics.soc-ph↗

arXiv2024

A Comprehensive Taxonomy of Cellular Automata

Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and abundant computational power, the current lack of a complete survey on the 'taxonomy' of various families of CAs impedes efficient and interdisciplinary progress. This review paper mitigates that deficiency; it provides a methodical overview of five important CA 'families': asynchronous, stochastic, multi-state, extended-neighbourhood, and non-uniform CAs. These five CA families are subsequently presented from four angles. First, a rigorous mathematical definition is given. Second, we map prominent variations within each CA family, as such highlighting mathematical equivalences with types from other families. Third, we discuss the genotype and phenotype of these CA types by means of mathematical tools, indicating when established tools break down. Fourth, we conclude each section with a brief overview of applications related to information theory and mathematical modelling.

nlin.CG↗

arXiv2024

Efficient Simulation of Non-uniform Cellular Automata with a Convolutional Neural Network

Cellular automata (CAs) and convolutional neural networks (CNNs) are closely related due to the local nature of information processing. The connection between these topics is beneficial to both related fields, for conceptual as well as practical reasons. Our contribution solidifies this connection in the case of non-uniform CAs (nuCAs), simulating a global update in the architecture of the Python package TensorFlow. Additionally, we demonstrate how the highly optimised out-of-the-box multiprocessing in TensorFlow offers interesting computational benefits, especially when simulating large numbers of nuCAs with many cells.

nlin.CG↗

arXiv2024

Convolutional Neural Networks for Automated Cellular Automaton Classification

The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally too diverse and numerous to exhaustively classify manually. In this chapter we treat the spacetime diagram as a digital image, and implement simple computer vision techniques to perform an automated classification of elementary cellular automata into the five Li-Packard classes. In particular, we present a supervised learning task to a convolutional neural network, in such a way that it may be generalised to non-elementary CAs. If we want to do so, we must divert the algorithm's focus away from the underlying 'microscopic' local updates. We first show that previously developed deep learning approaches have in fact been trained to identify the local update rule, rather than directly focus on the mesoscopic patterns that are associated with the particular behavioural classes. By means of a well-argued neural network design, as well as a number of data augmentation techniques, we then present a convolutional neural network that performs nearly perfectly at identifying the behavioural class, without necessarily first identifying the underlying microscopic dynamics.

nlin.CG↗

arXiv2024

Modification speed alters stability of ecological higher-order interaction networks

Higher-order interactions (HOIs) have the potential to greatly increase our understanding of ecological interaction networks beyond what is possible with established models that usually consider only pairwise interactions between organisms. While equilibrium values of such HOI-based models have been studied, the dynamics of these models and the stability of their equilibria remain underexplored. Here we present a novel investigation on the effect of the onset speed of a higher-order interaction. In particular, we study the stability of the equilibrium of all configurations of a three-species interaction network, including transitive as well as intransitive ones. We show that the HOI onset speed has a dramatic effect on the evolution and stability of the ecological network, with significant structural changes compared to commonly used HOI extensions or pairwise networks. Changes in the HOI onset speed from fast to slow can reverse the stability of the interaction network. The evolution of the system also affects the equilibrium that will be reached, influenced by the HOI onset speed. This implies that the HOI onset speed is an important determinant in the dynamics of ecological systems, and including it in models of ecological networks can improve our understanding thereof.

math.DS↗

arXiv2024

Assessing the impact of forced and voluntary behavioral changes on economic-epidemiological co-dynamics: A comparative case study between Belgium and Sweden during the 2020 COVID-19 pandemic

During the COVID-19 pandemic, governments faced the challenge of managing population behavior to prevent their healthcare systems from collapsing. Sweden adopted a strategy centered on voluntary sanitary recommendations while Belgium resorted to mandatory measures. Their consequences on pandemic progression and associated economic impacts remain insufficiently understood. This study leverages the divergent policies of Belgium and Sweden during the COVID-19 pandemic to relax the unrealistic -- but persistently used -- assumption that social contacts are not influenced by an epidemic's dynamics. We develop an epidemiological-economic co-simulation model where pandemic-induced behavioral changes are a superposition of voluntary actions driven by fear, prosocial behavior or social pressure, and compulsory compliance with government directives. Our findings emphasize the importance of early responses, which reduce the stringency of measures necessary to safeguard healthcare systems and minimize ensuing economic damage. Voluntary behavioral changes lead to a pattern of recurring epidemics, which should be regarded as the natural long-term course of pandemics. Governments should carefully consider prolonging lockdown longer than necessary because this leads to higher economic damage and a potentially higher second surge when measures are released. Our model can aid policymakers in the selection of an appropriate long-term strategy that minimizes economic damage.

econ.EM↗

arXiv2024

Validating a dynamic input-output model for the propagation of supply and demand shocks during the COVID-19 pandemic in Belgium

This work validates a dynamic production network model, used to quantify the impact of economic shocks caused by COVID-19 in the UK, using data for Belgium. Because the model was published early during the 2020 COVID-19 pandemic, it relied on several assumptions regarding the magnitude of the observed economic shocks, for which more accurate data have become available in the meantime. We refined the propagated shocks to align with observed data collected during the pandemic and calibrated some less well-informed parameters using 115 economic time series. The refined model effectively captures the evolution of GDP, revenue, and employment during the COVID-19 pandemic in Belgium at both individual economic activity and aggregate levels. However, the reduction in business-to-business demand is overestimated, revealing structural shortcomings in accounting for businesses' motivations to sustain trade despite the pandemic's induced shocks. We confirm that the relaxation of the stringent Leontief production function by a survey on the criticality of inputs significantly improved the model's accuracy. However, despite a large dataset, distinguishing between varying degrees of relaxation proved challenging. Overall, this work demonstrates the model's validity in assessing the impact of economic shocks caused by an epidemic in Belgium.

econ.GN↗

arXiv2023

pySODM: Simulating and Optimizing Dynamical Models in Python 3

In this work, we present our generic framework to construct, simulate, and calibrate dynamical systems in Python 3. Its goal is to reduce the time it takes to implement a dynamical system with $n$-dimensional states represented by coupled ordinary differential equations (ODEs), simulate the system deterministically or stochastically, and, calibrate the system using n-dimensional data. We demonstrate our code's capabilities by building three models in the context of two case studies. First, we forecast the yields of the enzymatic esterification reaction of D-glucose and lauric acid, performed in a continuous-flow, packed-bed reactor. The model yields a satisfactory description of the reaction yields under different flow rates and can be applied to design a viable process. Second, we build a stochastic, age-stratified model to make forecasts on the evolution of influenza in Belgium during the 2017-2018 season. Using only limited data, our simple model was able to make a fairly accurate assessment of the future course of the epidemic. By presenting real-world case studies from two scientific disciplines, we demonstrate our code's applicability across domains.

physics.data-an↗

arXiv2023

A Stochastic Mobility-Driven Spatially Explicit SEIQRD COVID-19 Model with VOCs, Seasonality, and Vaccines

In this work, we extend our previously developed compartmental SEIQRD model for SARS-CoV-2 in Belgium. We introduce SARS-CoV-2 variants of concern, vaccines, and seasonality in our model, as their addition has proven necessary for modelling SARS-CoV-2 transmission dynamics during the 2020-2021 COVID-19 pandemic in Belgium. The model is geographically stratified into eleven spatial patches (provinces), and a telecommunication dataset provided by Belgium's biggest operator is used to incorporate interprovincial mobility. We calibrate the model using the daily number of hospitalisations in each province and serological data. We find the model adequately describes these data, but the addition of interprovincial mobility was not necessary to obtain an accurate description of the 2020-2021 SARS-CoV-2 pandemic in Belgium. We further demonstrate how our model can be used to help policymakers decide on the optimal timing of the release of social restrictions. We find that adding spatial heterogeneity by geographically stratifying the model results in more uncertain model projections as compared to an equivalent nation-level model, which has both communicative advantages and disadvantages. We finally discuss the impact of imposing local mobility or social contact restrictions to contain an epidemic in a given province and find that lowering social contact is a more effective strategy than lowering mobility.

physics.soc-ph↗

arXiv2023

Mobility and the spatial spread of SARS-CoV-2 in Belgium

We analyse and mutually compare time series of COVID-19-related data and mobility data across Belgium's 43 arrondissements (NUTS 3). In this way, we reach three conclusions. First, we could detect a decrease in mobility during high-incidence stages of the pandemic. This is expressed as a significant change in the average amount of time spent outside one's home arrondissement, investigated over five distinct periods, and in more detail using an inter-arrondissement ``connectivity index'' (CI). Second, we analyse spatio-temporal COVID-19-related hospitalisation time series, after smoothing them using a generalise additive mixed model (GAMM). We confirm that some arrondissements are ahead of others and morphologically dissimilar to others, in terms of epidemiological progression. The tools used to quantify this are time-lagged cross-correlation (TLCC) and dynamic time warping (DTW), respectively. Third, we demonstrate that an arrondissement's CI with one of the three identified first-outbreak arrondissements is correlated to a significant local excess mortality some five to six weeks after the first outbreak. More generally, we couple results leading to the first and second conclusion, in order to demonstrate an overall correlation between CI values on the one hand, and TLCC and DTW values on the other. We conclude that there is a strong correlation between physical movement of people and viral spread in the early stage of the SARS-CoV-2 epidemic in Belgium, though its strength weakens as the virus spreads

physics.soc-ph↗

arXiv2019

A split-and-perturb decomposition of number-conserving cellular automata

This paper concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of particular interest to mathematicians, computer scientists and physicists, as they can serve as models of physical phenomena obeying some conservation law. We propose a new approach to study such cellular automata that works in any dimension $d$ and for any set of states $Q$. Essentially, the local rule of a cellular automaton is decomposed into two parts: a split function and a perturbation. This decomposition is unique and, moreover, the set of all possible split functions has a very simple structure, while the set of all perturbations forms a linear space and is therefore very easy to describe in terms of its basis. We show how this approach allows to find all number-conserving cellular automata in many cases of $d$ and $Q$. In particular, we find all three-dimensional number-conserving CAs with three states, which until now was beyond the capabilities of computers.

math-ph↗

arXiv2019

The Impact of Hurricanes on the Oceanographic Conditions in the Exclusive Economic Zone of Cuba

In this work, we analysed the satellite-based responses of sea surface temperature (SST) and chlorophyll-a (chl-a) concentration in the waters of the Exclusive Economic Zone (EEZ) of Cuba to hurricanes that crossed the EEZ between 1998 and 2016. We considered two spatial scales to capture the spatially heterogeneous nature of the effects of hurricanes. A first more fine-grained one where we considered 120 km radius disks centered at every consecutive hurricane position within the EEZ (scale 1) and a second more coarse grained one enclosing the entire EEZ (scale 2). We conclude that the hurricanes induced a weak cooling since 75 and 85% of the SST anomalies at scale 1 and 2, respectively, were smaller than -1°C. The cooling was mainly caused by the wind, inducing mixing and/or upwelling of subsurface cool waters. The maximum chl-a responses were recorded in the first and second post-storm weeks, with 60% ranging between -0.01 and 0.04 mg m$^{-3}$ at scale 1, and between -0.07 and 0.02 mg m$^{-3}$ at scale 2. During those post-storm weeks SST and chl-a anomalies were 18 and 44% higher at scale 1 than at scale 2, respectively. We argue that the transport of chl-a from the deep chlorophyll maximum and/or the rich coastal waters are the dominant mechanisms determining the post-storm chl-a response in the EEZ. We also found that the magnitude of the Island Mass Effect in the EEZ after the passage of the hurricanes was 89% higher than before its passage.

physics.ao-ph↗

arXiv2017

Number-conserving cellular automata with a von Neumann neighborhood of range one

We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use of the geometric structure of the von Neumann neighborhood allows for computationally tractable conditions even in higher dimensions.

math.DS↗

arXiv2016

Stability of cellular automata trajectories revisited: branching walks and Lyapunov profiles

We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analogue of Floquet theory for cellular automata.

math.PR↗