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>> Publications at DIEP
DIEP aims at performing groundbreaking interdisciplinary research that connects different fields and shines light on aspects of emergence. Below you find a list of publications of some of the researchers associated with DIEP in 2025 and 2026. To access older publications, you can check the publication archives 2020-2023 and the publications archive 2024.
>> Cellular Adaptation to Signal Fluctuations as Learning
by Tuan Minh Pham, David Saad | July 2026
Cells represent one of the most fundamental units of life. Underlying their robust performance against envi- ronmental variability, such as temporal fluctuations of chemical signals, is a dynamical interrelation between the two components of an intracellular pathway: a gene-regulatory network and its upstream signal transducers. To understand how a single cell utilizes this feedback to self-regulate its gene-expressions, we develop a multiscale model of the pathway’s components, in which the adaptive variables responsible for signal interpretation follow a feedback-induced learning process. We then derive a macroscopic theory capturing the covariations between these components – so-called collective modes. Our theory shows how cells can achieve robust output against signal fluctuations via self-regulation rather than a simple noise suppression. Such robustness corresponds to a transition from random- to structured collective modes beyond a critical adaptation rate
>> Symmetric preferences, asymmetric outcomes: Tipping dynamics in an open-city segregation model
by Fabio van Dissel, Tuan Minh Pham, Wout Merbis | June 2026
Schelling's model of segregation demonstrates that even in the absence of social or governmental interventions, individuals with mild in-group preferences can self-organize into strongly segregated neighborhoods. Many variants of this celebrated model have been proposed by assuming agents tend to increase their satisfaction. Complementary to this traditional, utility-based approach, we model residential moves using satisfaction-independent reaction rates in a spatially extended chemical reaction network. The resulting model exhibits an emergent phenomenon: despite symmetric in-group preferences, the system undergoes a tipping transition at a critical preference level, beyond which one agent type dominates. We characterize this asymmetric phase transition in details using mean-field analysis, numerical simulations and finite size scaling methods. We find that while the transition shares key features with the Ising universality class, such as ℤ2 symmetry breaking and similar exponent ratios, the full set of critical exponents does not match any known universality class.
>> A Compositional Calculus for Semantic Synergy in Language Model Embeddings
by Abel Jansma | 2026
We introduce semantic synergy: a training-free measure of non-compositional representation in language models, obtained by taking the discrete derivative of a phrase embedding over its sub-span structure. Formally, semantic synergy is the Möbius inverse of the embedding function on the partial order of contiguous sub-spans. Across two embedding models and 107 pairs of short English idiomatic and literal phrases, semantic synergy strongly separates idiomatic from literal phrases (Cohen's d ≈ 1.80–1.81, p < 10^−28), outperforming alternative residuals. The measure further distinguishes non-compositional proper names in a supporting experiment, and yields steering directions that move phrase embeddings toward idiomatic interpretations. Layer-wise extraction in Qwen3-0.6B and Pythia-1B models shows that the non-compositional structure emerges mainly in middle-to-late layers, and becomes strong only late in training. Span-Möbius residuals therefore provide a lightweight algebraic probe of compositional structure in embedding spaces and a bridge toward hidden-state mechanistic analysis.
>> Polarisation in increasingly connected societies
by Tuan Pham, Sidney Redner, Lourens Waldorp, Jay Armas, Han L. J. van der Maas | May 2026
Explanations of societal polarization often rely on one of three mechanisms: homophily, bounded confidence, and community-based interactions. Opinion dynamics models based on these mechanisms consider the lack of interactions as the main cause of polarization. Given the increasing connectivity in modern society, this explanation of polarization may be insufficient. To understand how society becomes more polarized as its connectedness increases, we propose a voter-type model (called I-voter) that incorporates involvement as a key mechanism in opinion formation and study its dependence on the network connectivity. We describe the steady-state behavior of the model analytically, at the mean-field and the moment-hierarchy levels, and stress the generality of our findings by considering various extensions and different network topologies.
>> Temperature of an active nematic
by Jay Armas, Akash Jain, Ruben Lier | April 2026
We employ a hydrodynamic framework for active matter coupled to an environment to study the local temperature of an active nematic, assuming proximity to thermal equilibrium. We show that, due to the mechanosensitivity of fuel consumption, linearized temperature correlations in a homogeneous active nematic steady state remain unaffected by activity. However, we demonstrate that local shearing and twisting cause a confined active nematic undergoing a spontaneous flow transition to develop a distinctive inhomogeneous temperature profile, serving as a thermal signature of activity.
>> Microscopically reversible kinetic theory of flocking
by Ruben Lier | April 2026
We formulate a kinetic theory of two species of hard spheres undergoing reactive collisions that convert chemical energy into kinetic energy. The model describes an active species interacting with a passive background, labeled as “birds” and “air,” respectively, with the reactive collisions representing self-propulsion. Microscopic reversibility of the reactive dynamics is imposed, and a chemostat is introduced to drive the system out of equilibrium. When the chemostat is sufficiently strong, and one restricts to grazing interspecies collisions, we find that the bird momentum damping coefficient can change sign, giving rise to a flocking transition
>> Entropy Production Rate in Stochastically Time-evolving Asymmetric Networks
by Tuan Pham, Deepak Gupta | March 2026
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to address this problem, we develop a framework in which fluctuating interactions between units of nonlinear network systems are modeled as uncorrelated colored noise (i.e., annealed disorder) with a correlation time. This approach enables us to quantify how the entropy production rate (EPR) depends on both the characteristic time-scale and the strength of the disorder. Using dynamical mean field theory, we derive an exact expression for EPR at any transient time that is validated by simulations of the full non-linear dynamics. At stationarity, a relation between EPR and autocorrelation is established and then used to analytically study the particular case of linear systems.
>> Field theories and quantum methods for stochastic reaction-diffusion systems
by Mauricio J. del Razo, Tommaso Lamma, Wout Merbis | January 2026
Complex systems are composed of many particles or agents that move and interact with one another. In most real-world applications, these systems involve a varying number of particles or agents that change owing to interactions with the environment or their internal dynamics. The underlying mathematical framework to model these systems must incorporate the spatial transport of particles or agents and their interactions, as well as changes to their copy numbers, all of which can be formulated in terms of stochastic reaction-diffusion processes. However, the standard probabilistic representation of these processes can be overly complex because of the combinatorial aspects arising from the nonlinear interactions and varying particle numbers. This review addresses the main field theory representations of stochastic reaction-diffusion systems, which handle these issues “under the hood.” To begin, the focus is on bringing techniques familiar to theoretical physicists—such as second quantization, Fock space, path integrals, and quantum field theory—back into the classical domain of reaction-diffusion systems. It is demonstrated how various field theory representations, which have evolved historically, can be unified under a single basis-independent representation. Existing quantum-based methods and notation are then extended to work directly on the level of the unifying representation, and it is illustrated how they can be used to consistently obtain previous known results in a more straightforward manner, such as through numerical discretizations and relations between model parameters at multiple scales. Throughout, the review contextualizes how these representations mirror well-known models of chemical physics depending on their spatial resolution, as well as the corresponding macroscopic (large copy-number) limits. The framework presented here may find applications in a diverse set of scientific fields, including physical chemistry, theoretical ecology, epidemiology, game theory, and socioeconomic models of complex systems, specifically in the modeling and multiscale simulation of complex systems with varying numbers of particles or agents. The presentation is done in a self-contained educational and unifying manner such that it can be followed by researchers across several fields.
>> Heterophobic interactions hinder consensus formation in sparse random networks
by Alejandro Castro, Tuan Minh Pham, Ernesto Ortega, David Machado | December 2025
Heterophobic interactions, which drive individuals to be repelled from others with opposite opinions, play a role as important as homophilic ones in shaping many dynamical processes on social networks, such as opinion formation, social balance, or epidemic spreading. In this paper, we use belief propagation and Monte Carlo simulations on treelike signed graphs to predict that a sufficient propensity to heterophobia can impede a consensus that would otherwise emerge via a phase transition. As the strength of heterophobic interactions and the rationality of individuals with respect to social stress decrease, this transition changes from continuous to discontinuous, with a strong dependence on the initial conditions. The size of the parameter region where consensus can be reached from any initial condition decays as a power-law function of the number of discussed topics.
>> Interdependent Scaling Exponents in the Human Brain
by Daniel M. Castro, Ernesto P. Raposo, Mauro Copelli, Fernando A. N. Santos | November 2025
We apply the phenomenological renormalization group to resting-state fMRI time series of brain activity in a large population. By recursively coarse graining the data, we compute scaling exponents for the series variance, log probability of silence, and largest covariance eigenvalue. The scaling exponents clearly exhibit linear interdependencies in the form of scaling relations and inherent variability of values closely related to the structure of correlations of brain activity. The scaling relations between the exponents are derived analytically. We find a significant correlation of exponents with clinical (gray matter volume) and behavioral (cognitive performance) traits. Akin to scaling relations near critical points in thermodynamics, our results suggest that this interdependency is intrinsic to brain organization, and may also exist in other complex systems.
>> Blurring the Busse balloon: Patterns in a stochastic Klausmeier model
by Christian Hamster, Peter van Heijster, Eric Siero | November 2025
We investigate the effect of stochastic forcing on spatially periodic patterns in a one-dimensional Klausmeier model for dryland vegetation. Using numerical methods, we can accurately describe the transient dynamics of the stochastic solutions and compare several notions of stability. In particular, we show that the boundary of the Busse balloon — which represents the deterministically stable patterns — becomes blurred under the stochastic perturbations and that the stochastic stability heavily depends on the model parameters, the intensity of the noise and the location of the wave number of the periodic pattern within the deterministic Busse balloon.
>> Hydrodynamics of thermal active matter
by Jay Armas, Akash Jain, Ruben Lier | November 2025
Active matter concerns many-body systems comproed of living or self-driven agents that collectively exhibit macroscopic phenomena distinct from conventional passive matter. Using Schwinger-Keldysh effective field theory, we develop a hydrodynamic framework for thermal active matter that accounts for energy balance, local temperature variations, and the ensuing stochastic effects. By modeling active matter as a driven open system, we show that the source of active contributions to hydrodynamics, violations of fluctuation-dissipation theorems, and detailed balance is rooted in the breaking of time-translation symmetry due to the presence of fuel consumption and an external environmental bath. In addition, our framework allows for nonequilibrium steady states that produce entropy, with a well-defined notion of steady-state temperature. We use our framework of active hydrodynamics to develop effective field theory actions for active superfluids and active nematics that offer a first-principle derivation of various active transport coefficients and feature activity-induced phase transitions. We also show how to incorporate temperature, energy, and noise in fluctuating hydrodynamics for active matter. Our work suggests a broader perspective on active matter that can leave an imprint across scales.
>> Rethinking tipping points in spatial ecosystems
by Swarnendu Banerjee, Mara Baudena, Paul Carter, Robbin Bastiaansen, Arjen Doelman, Max Rietkerk | October 2025
The theory of alternative stable states and tipping points has garnered substantial attention in the last several decades. It predicts potential critical transitions from one ecosystem state to a completely different state under increasing environmental stress. However, typically, ecosystem models that predict tipping do not resolve space explicitly. Ecosystems being inherently spatial, it is important to understand the effects of spatial processes. In fact, it has been argued that spatial dynamics can actually help ecosystems evade tipping. Here, using a dryland and a savanna-forest model as example systems, we provide a synthesis of several mechanisms by which spatial processes can change our predictions of tipping in ecosystems. We show that self-organized Turing patterns can emerge in drylands that help evade tipping, but that (non-Turing) patterns driven by environmental heterogeneity are key to evasion of tipping in humid savannas. Since the ecological interactions driving the dynamics of these ecosystems differ from each other, we suggest that tipping evasion mechanisms in ecosystems may be connected to the key ecological interactions in a system. This highlights the need for further research into the link between the two in order to formulate better strategies to make ecosystems resilient to global change.
>> Resistive relativistic magnetohydrodynamics without Ampère’s law
by Ruben Lier, Akash Jain, Jay Armas, Oliver Porth | October 2025
Resistive magnetohydrodynamics is thought to play a key role in transient high-energy astrophysical phenomena such as flares from black hole and neutron star magnetospheres. When performing numerical simulations of resistive magnetohydrodynamics, one is faced with the issue that Ampère’s law becomes stiff in the high conductivity limit which poses challenges to the numerical evolution. We show that using a description of resistive magnetohydrodynamics based on higher-form symmetry, one can perform simulations with a generalized dual Faraday tensor without having to use Ampère’s law, thereby avoiding the stiffness problem. We also explain the relation of this dual model to a traditional description of resistive magnetohydrodynamics and how causality is guaranteed by introducing second order corrections.
>> Möbius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs
by Patrick Forré, Abel Jansma | October 2025
We generalize the concept of Möbius inversion and Shapley values to directed acyclic multigraphs and weighted versions thereof. We further allow value functions (games) and thus their Möbius transforms (synergy function) and Shapley values to have values in any abelian group that is a module over a ring that contains the graph weights, e.g. vector-valued functions. To achieve this and overcome the obstruction that the classical axioms (linearity, efficiency, null player, symmetry) are not strong enough to uniquely determine Shapley values in this more general setting, we analyze Shapley values from two novel points of view: 1) We introduce projection operators that allow us to interpret Shapley values as the recursive projection and re-attribution of higher-order synergies to lower-order ones; 2) we propose a strengthening of the null player axiom and a localized symmetry axiom, namely the weak elements and flat hierarchy axioms. The former allows us to remove coalitions with vanishing synergy while preserving the rest of the hierarchical structure. The latter treats player-coalition bonds uniformly in the corner case of hierarchically flat graphs. Together with linearity these axioms already imply a unique explicit formula for the Shapley values, as well as classical properties like efficiency, null player, symmetry, and novel ones like the projection property. This whole framework then specializes to finite inclusion algebras, lattices, partial orders and mereologies, and also recovers certain previously known cases as corner cases, and presents others from a new perspective. The admission of general weighted directed acyclic multigraph structured hierarchies and vector-valued functions and Shapley values opens up the possibility for new analytic tools and application areas, like machine learning, language processing, explainable artificial intelligence, and many more.
>> Engineering Emergence
by Abel Jansma, Erik Hoel | October 2025
A defining property of complex systems is that they have multiscale structure. How does this multiscale structure come about? We argue that within systems there emerges a hierarchy of scales that contribute to a system's causal workings. An intuitive example is how a computer can be described at the level of its hardware circuitry (its microscale) but also its machine code (a mesoscale) and all the way up at its operating system (its macroscale). Here we show that even simple systems possess this kind of emergent hierarchy, which usually forms over only a small subset of the super-exponentially many possible scales of description. To capture this formally, we extend the theory of causal emergence (version 2.0) so as to analyze how causal contributions span the full multiscale structure of a system. Our analysis reveals that systems can be classified along a taxonomy of emergence, such as being either top-heavy or bottom-heavy in their causal workings. From this new taxonomy of emergence, we derive a measure of complexity based on a literal notion of scale-freeness (here, when causation is spread equally across the scales of a system) and compare this to the standard network science definition of scale-freeness based on degree distribution, showing the two are closely related. Finally, we demonstrate the ability to engineer not just the degree of emergence in a system, but to control it with pinpoint precision.
>> Corruption and extremism
by Attila Gáspár, Tommaso Giommoni, Massimo Morelli, Antonio Nicolò | October 2025
This paper shows that corruption generates extremism, but mainly on the opposition side. While corruption hurts all citizens, only voters on the minority side may desire to switch to a more extreme representative when they perceive a more corrupt political system. In our model, campaigning on a corruption scandal against the incumbent gives a higher winning probability for the opposition politician but simultaneously reduces expected future rents from office. As extremist politicians normally are less likely to win against a moderate opponent, they have a stronger incentive to take a stand against corruption. Given that the side of the political minority has a lower chance of having their representative elected to office, they face a smaller opportunity cost of voting for extremists. Our main result is that minorities are more likely to react to corruption with more extremism. We provide causal evidence for this novel asymmetric prediction from Indonesia and Brazil.
>> Mean-field theory of the general-spin Ising model
by Lourens Waldorp, Tuan Pham, Han L. J. van der Maas | October 2025
Motivated by modelling in physics and other disciplines, such as sociology and psychology, we derive the mean field of the general-spin Ising model from the variational principle of the Gibbs free energy. The general-spin Ising model has 2k+1 spin values, generated by −(k−j)/k, with j=0,1,2…,2k, such that for k=1 we obtain −1,0,1, for example; the Hamiltonian is identical to that of the standard Ising model. The general-spin Ising model exhibits spontaneous magnetisation, similar to the standard Ising model, but with the location translated by a factor depending on the number of categories 2k+1. We also show how the accuracy of the mean field depends on both the number of nodes and node degree, and that the hysteresis effect decreases and saturates with the number of categories 2k+1. Monte Carlo simulations confirm the theoretical results.
>> Coupling plankton and cholera dynamics: insights into outbreak prediction and practical disease management
by Biplab Maity, Swarnendu Banerjee, Abhishek Senapati, Jon Pitchford, Joydev Chattopadhyay | September 2025
Despite extensive control efforts over the centuries, cholera remains a globally significant health issue. Seasonal emergence of cholera cases has been reported, particularly in the Bengal delta region, which is often synchronized with plankton blooms. This phenomenon has been widely attributed to the commensal interaction between Vibrio cholerae and zooplankton in aquatic environments. Understanding the role of plankton dynamics in cholera epidemiology is therefore crucial for effective policy-making. To this end, we propose and analyze a novel compartment-based transmission model that integrates phytoplankton-zooplankton interactions into a human-bacteria cholera model. We show that zooplankton-mediated transmission can lead to counterintuitive outcomes, such as an outbreak with a delayed and lower peak still resulting in a larger overall outbreak size. Such outbreaks are prolonged by maintaining infections at lower levels during the post-peak phase, thereby intensifying epidemic overshoot and promoting the inter-epidemic persistence of pathogens. Furthermore, our analysis reveals that the timing of filtration-like interventions can be strategically guided by ecological indicators, such as phytoplankton blooms. Our study underscores the importance of incorporating ecological aspects in epidemiological research to gain a deeper understanding of disease dynamics.
>> Fast Möbius transform: An algebraic approach to information decomposition
by Abel Jansma, Pedro A.M. Mediano, Fernando E. Rosas | July 2025
The partial information decomposition (PID) and its extension integrated information decomposition (ΦID) are promising frameworks to investigate information phenomena involving multiple variables. An important limitation of these approaches is the high computational cost involved in their calculation. Here we leverage fundamental algebraic properties of these decompositions to enable a computationally-efficient method to estimate them, which we call the fast Möbius transform. Our approach is based on a formula for estimating the Möbius function that circumvents important computational bottlenecks and can in some cases offer a double-exponential speedup. We showcase the capabilities of this approach by presenting two analyses that would be unfeasible without this method: decomposing the information that neural activity at different frequency bands yields about the brain's macroscopic functional organization and identifying distinctive dynamical properties of the interactions between multiple voices in baroque music. Overall, our proposed approach illuminates the value of algebraic facets of information decomposition and opens the way to a wide range of future analyses.
>> Fiscal Rules, Corruption, and Electoral Accountability
by Gianmarco Daniele, Tommaso Giommoni | July 2025
As corruption mostly takes place through the misuse of public spending, it is crucial to understand how policies limiting the spending capacity of local governments may affect corruption. We study the extension of fiscal rules to small Italian municipalities. First, we find a decrease in both corruption charges and corruption charges per euro spent. This effect emerges only in areas in which fiscal rules put a binding cap on municipal capital expenditures. Second, the reduction in corruption is linked to accountability incentives, as it emerges mostly in preelectoral years and for reeligible mayors. Third, we do not find any meaningful impact on local public goods or living standards. Overall, our findings suggest that fiscal rules together with electoral incentives might reduce rent-seeking through lower public spending without depressing local welfare.
>> The Economic Costs of Ambiguous Laws
by Massimo Morelli, Luigi Guiso, Claudio Michelacci, Tommaso Giommoni | June 2025
We develop a strategy to measure the economic costs of poorly written laws, a potential threat to the rule of law. Using the full corpus of Italian legislation, we show that legal uncertainty-measured by the probability of disagreement between the Supreme Court of Cassation and lower courts-is higher for cases involving poorly written laws and varies systematically across courts. To identify the economic impacts, we exploit a reform that reassigned firms to courts. We estimate that GDP would be 5 percent higher if laws had been written as clearly as the Constitution, with two-thirds of the loss accruing over the past 20 years.
>> A Machine Learning Approach to Analyze and Support Anticorruption Policy
by Elliott Ash, Sergio Galetta, Tommaso Giommoni | May 2025
Can machine learning support better governance? This study uses a tree-based, gradient-boosted classifier to predict corruption in Brazilian municipalities using budget data as predictors. The trained model offers a predictive measure of corruption, which we validate through replication and extension of previous corruption studies. Our policy simulations show that machine learning can significantly enhance corruption detection: Compared to random audits, a machine-guided targeted policy could detect almost twice as many corrupt municipalities for the same audit rate.
>> Random evolutionary dynamics in predator–prey systems yields large, clustered ecosystems
by Christian Hamster, Jorik Schaap, Peter van Heijster, Joshua Dijksman | May 2025
We study the effect of introducing new species through evolution into communities. We use the setting of predator–prey systems. Predator–prey dynamics is classically well modeled by Lotka–Volterra (LV) equations, also when multiple predator and prey species co-exist. We use a stochastic method to introduce new species in a two-trophic LV system. We find that introducing random evolving species leads to robust ecosystems in which large numbers of species coexist. Crucially, in these large ecosystems an emergent clustering of species is observed, tying functional differences to phylogenetic history.
>> Effective dimensional reduction of complex systems based on tensor networks
by Wout Merbis, Madelon Geurts, Clélia de Mulatier, Philippe Corboz | April 2025
The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components n. Mean-field approximations provide an effective reduction in complexity of the models, requiring only a number of phase space variables polynomial in system size. However, this comes at the cost of losing accuracy close to critical points in the systems dynamics and an inability to capture correlations in the system. In this work, we introduce a tunable approximation scheme for Markovian spreading models on networks based on matrix product states (MPSs). By controlling the bond dimensions of the MPS, we can investigate the effective dimensionality needed to accurately represent the exact 2n dimensional steady-state distribution. We introduce the entanglement entropy as a measure of the compressibility of the system and find that it peaks just after the phase transition on the disordered side, in line with the intuition that more complex states are at the 'edge of chaos'. We compare the accuracy of the MPS with exact methods on different types of small random networks and with Markov chain Monte Carlo methods for a simplified version of the railway network of the Netherlands with 55 nodes. The MPS provides a systematic way to tune the accuracy of the approximation by reducing the dimensionality of the systems state vector, leading to an improvement over second-order mean-field approximations for sufficiently large bond dimensions.
>> Mereological approach to higher-order structure in complex systems: From macro to micro with Möbius
by Abel Jansma | April 2025
Relating macroscopic observables to microscopic interactions is a central challenge in the study of complex systems. While current approaches often focus on pairwise interactions, a complete understanding requires going beyond these to capture the full range of possible interactions. We present a unified mathematical formalism, based on the Möbius inversion theorem, that reveals how different decompositions of a system into parts lead to different, but equally valid, microscopic theories. By providing an exact bridge between microscopic and macroscopic descriptions, this framework demonstrates that many existing notions of interaction, from epistasis in genetics and many-body couplings in physics, to synergy in game theory and artificial intelligence, naturally and uniquely arise from particular choices of system decomposition, or mereology. By revealing the common mathematical structure underlying seemingly disparate phenomena, our paper highlights how the choice of decomposition fundamentally determines the nature of the resulting interactions. We discuss how this unifying perspective can facilitate the transfer of insights across domains, guide the selection of appropriate system decompositions, and enable the search for new notions of interaction. To illustrate the latter in practice, we decompose the Kullback-Leibler divergence, and show that our method correctly identifies which variables are responsible for the divergence. In addition, we use Rota's Galois connection theorem to describe coarse grainings of mereologies, and efficiently derive the renormalized couplings of a 1D Ising model. Our results suggest that the Möbius inversion theorem provides a powerful and practical lens for understanding the emergence of complex behavior from the interplay of microscopic parts, with applications across a wide range of disciplines.
>> Extractive Taxation and the French Revolution
by Tommaso Giommoni, Marco Tabellini, Gabriel Loumeau | April 2025
We study the fiscal determinants of the French Revolution, exploiting plausibly exogenous variation in the salt tax - a large source of royal revenues and one of the most extractive forms of taxation of the Ancien Régime. Implementing a Regression Discontinuity design (RDD), we find that parts of France subject to a higher salt tax experienced more revolts against the monarchy between 1750 and 1789. These effects already appear in the 1760s, but become stronger over time and peak in the 1780s. Combining the RD model with variation in local weather conditions during the 1780s, we document that droughts amplify the effects of the salt tax on revolts by increasing wheat prices and activating latent discontent. Then, we connect the discontent generated by the salt tax to the French Revolution. First, we provide evidence that riots spread more quickly in high tax areas. Second, we show that areas burdened by a higher salt tax report more complaints against the salt tax in the list of grievances collected by the king in the spring of 1789. Third, we document that legislators representing areas with a higher salt tax are more likely to demand the end of the monarchy and to support the death penalty for the king.
>> Irreversibility in non-reciprocal chaotic systems
by Tuan Minh Pham, Albert Alonso, Karel Proesmans | February 2025
How is the irreversibility of a high-dimensional chaotic system related to its dynamical behavior? In this paper, we address this question by developing a stochastic-thermodynamics treatment of complex networks that exhibit chaos. Specifically, we establish an exact relation between the averaged entropy production rate—a measure of irreversibility—and the autocorrelation function for an infinite system of neurons coupled via random non-reciprocal interactions. We show how, under given noise strength, the entropy production rate can signal the onset of a transition occurring as the coupling heterogeneity increases beyond a critical value via a change in its functional form upon crossing this point. Furthermore, this transition happens at a fixed, noise-independent entropy production rate, elucidating how robust energetic cost is possibly responsible for optimal information processing at criticality.
>> Decomposing Interventional Causality into Synergistic, Redundant, and Unique Components
by Abel Jansma | January 2025
We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of Möbius inversion. While recent work has explored a similar decomposition of an observational measure, we argue that a proper causal decomposition must be interventional in nature. We develop a mathematical approach that systematically quantifies how causal power is distributed among variables in a system, using a recently derived closed-form expression for the Möbius function of the redundancy lattice. The formalism is then illustrated by decomposing the causal power in logic gates, cellular automata, and chemical reaction networks. Our results reveal how the distribution of causal power can be context- and parameter-dependent. This decomposition provides new insights into complex systems by revealing how causal influences are shared and combined among multiple variables, with potential applications ranging from attribution of responsibility in legal or AI systems, to the analysis of biological networks or climate models.
>> Experimental evidence confirms that triadic social balance can be achieved through dyadic interactions
by Mirta Galesic, Henrik Olsson, Tuan Minh Pham, Johannes Sorger, Stefan Thurner | January 2025
Balanced triadic relationships in social groups, such that friends of friends are considered friends, are at the heart of stable human societies. Computational models of the origins of social balance typically assume that people attend to the indirect relationships between their direct social contacts. This assumption may be of limited plausability but there have been no experimental comparisons of models using different assumptions. We compare one model that assumes that people pay attention only to their direct social relationships1, and another that assumes they try to minimize imbalance in their triadic relationships2. In a longitudinal group experiment with 480 interacting participants, we find that triadic social balance can be achieved even if people pay attention only to their dyadic relationships. Such empirical studies are essential for discerning between the many existing models of social dynamics and identifying the most promising pathways for further theoretical development.
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