DCP25 – Invited Speakers

Many natural systems are characterized by multiscale variability, emergent dynamics, and signatures of both deterministic chaos and stochastic fluctuations. In such contexts, predictability is inherently scale-dependent, and the structure of the phase-space attractor may vary across temporal and spatial scales, often in a non-stationary way. Understanding how degrees of freedom and predictability horizons evolve with scale is crucial for characterizing the underlying dynamics of complex systems–from fluid turbulence to climate variability. Here, we present a formalism that combines adaptive decomposition techniques with tools from extreme value theory to study the scale-dependent dimensionality and predictability of non- hyperbolic systems. This approach allows for a refined characterization of the invariant set, unveiling how different dynamical components and stochastic fluctuations influence the system’s behavior at different scales. We first apply this framework to a fully developed turbulent flow, showing that the geometrical and topological properties of the attractor are not universal but instead strongly depend on the scale considered. In particular, we identify a breakdown of statistical universality at the onset of the inertial range, where nonlinear interactions responsible for the energy cascade become dominant. The attractor’s structure is shown to change with large-scale forcing, supporting the concept of “chameleon attractors” whose properties evolve across scales and time. As a second application, by analysing benthic foraminiferal δ¹⁸O and δ¹³C records across the Cenozoic we show that the present-day Icehouse climate exhibits unique dynamical characteristics compared to past states such as the Warmhouse, Hothouse, and Coolhouse. Specifically, the Icehouse state is marked by a higher degree of coupling between climate subsystems and a greater number of active feedbacks, particularly at eccentricity and obliquity timescales–suggesting a structurally more interconnected but also potentially more fragile system. In contrast, past warm climates responded differently, with feedbacks operating predominantly at shorter (precessional) timescales and lower inter-component coupling. These findings imply that the mechanisms driving tipping points are not uniform across climate states: the nature, scale, and systemic impact of instabilities are deeply state-dependent, underscoring the distinctiveness and vulnerability of the current climate regime.

The talk investigates how recommender systems (RS) deployed in online retail platforms influence consumer behavior, particularly focusing on consumption volume and diversity. It explores empirical findings and simulation-based approaches to assess whether RS help consumers explore broader products or instead concentrate attention on popular items. Online retail platforms aim to assist consumers in navigating vast product catalogues. RS were introduced to enhance user satisfaction by surfacing relevant products or content. However, there is increasing concern that these systems, while effective in boosting engagement, may also manipulate consumer behavior in many undesirable ways. In order to study such a effects, a significant portion of research is based on controlled experiments using real-world consumer data, offering high reliability but limited generalizability. We will present several studies of this nature in detail, highlighting both the positive and negative factors, as well as the corresponding conclusions. In particular, we will examine a case study in which RSs appear to promote personal diversity while diminishing collective diversity. Conversely, an intriguing study conducted on the Spotify platform suggests the opposite effect. In this case, personal diversity declines significantly, whereas user engagement increases markedly, with users spending more time on the application. We will thus explore the underlying factors that may account for these contrasting outcomes. To overcome limitations of empirical studies, simulation approaches are employed. These enable testing of various recommender architectures and assumptions under controlled conditions. We will examine two simulation studies that explore distinct key systemic factors. The outcomes will be evaluated in relation to the structure of the simulation models, with particular attention to how specific modelling choices influence the final results.

Heart rate variability (HRV) series reflects the dynamical variation of heartbeat-to-heartbeat intervals in time and is one of the outputs of the cardiovascular system. Over the years, this system has been recognized for generating nonlinear and complex heartbeat dynamics, with the latter referring to a high sensitivity to small – theoretically infinitesimal – input changes. While early research associated chaotic behavior with the cardiovascular system, evidence of stochastic inputs to the system, i.e., a physiological noise, invalidated those conclusions. To date, a comprehensive characterization of the cardiovascular system dynamics, accounting for dynamical noise input, has not been undertaken. In this study, we propose a novel methodological framework for evaluating the presence of regular or chaotic dynamics in noisy dynamical systems. The method relies on the estimation of asymptotic growth rate of noisy mean square displacement series in a two-dimensional phase space. We validated the proposed method using synthetic series comprising well-known regular and chaotic maps. We applied the method to real HRV series from healthy subjects, as well as patients with atrial fibrillation and congestive heart failure, during unstructured long-term activity. Results indicate that HRV series are consistently generated by a regular system driven by dynamical noise.

A wealth of evidence shows that real-world networks are endowed with the small-world property, i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultrasmall-world organization, whereby the graph’s diameter is independent of the network size over several orders of magnitude, is still unknown. I will show that the “six degrees of separation” is the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. Moreover, the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.

We investigate the qualitative behavior of a wind-driven double-gyre system using a reduced gravity 1.5-layer quasi-geostrophic model, analyzed through a novel topological framework known as Templex. This approach allows us to characterize and classify the system’s attractors in phase space across a range of dynamical regimes—from low-energy, smooth temporal behavior to highly energetic, chaotic states. Our focus is on the case of stationary wind stress forcing, which serves as a simplified yet insightful scenario to probe the core physical processes and guide further exploration within the model hierarchy. The governing partial differential equations are discretized using finite-difference methods, yielding a system of ordinary differential equations. The model is implemented in the Julia programming language, enabling the application of continuation techniques and the performance of stability analyses along bifurcation branches. These branches are computed under pseudo-adiabatic changes in wind forcing. Our results demonstrate the value of topological methods in uncovering the structural features of bifurcations and suggest promising avenues for applying such tools to the study of nonlinear dynamics in more complex geophysical fluid systems. This work aims to encourage dialogue on the role of topology-based techniques in advancing our understanding of dynamics in the geosciences.

As AI systems become increasingly distributed, decentralized learning is emerging as a compelling alternative to traditional centralized approaches. By keeping data local and exchanging only high-level knowledge, this paradigm supports collaborative model training while preserving privacy, data ownership, and low-latency requirements. It is especially well-suited to settings where data cannot be moved or where real-time inference demands proximity to the data source. However, this shift introduces new research challenges—chief among them, understanding how the structure of the communication network impacts learning. In this talk, we explore how network topology influences model convergence, particularly in the early phases, and how it affects final performance and system robustness in the presence of node or data disruptions.

We study the problem of the extension of the classical thermodynamic formalism of dynamical systems to the case of differentiable intermittent maps of the interval. An interesting application is the study of the asymptotic behaviour of the moments of the Birkhoff sums for these systems.

A simple yet extremely valuable approach to the study of the climate system comes from the use of Energy Balance Models (EBMs). Such models describe the key features of the zonally averaged temperature on the Earth’s surface. The classical EBM can be improved by increasing the vertical resolution. This talk presents a two-layer energy balance model that allows for vertical exchanges between a surface layer and the atmosphere. Considering random perturbations of the model will allow to better study its long-time average behaviour. Thanks to the weak Harris’ theorem we will establish exponential ergodicity. This is a first step to study the model dependence on different forcing scenarios via response theory.

Time irreversibility, a hallmark of non-equilibrium behavior, is a key feature for studying dissipative systems from theoretical and experimental perspectives. Given knowledge of a system, methods from stochastic thermodynamics can be used to quantify the irreversibility via entropy production, but for many data-driven applications only a finite time seriesrepresenting the system dynamics is available. Despite advancements in both theory and computation, optimized measures of irreversibility that effectively bridge the gap between theoretical concepts and their application to real-world data are still needed. Here we introduce a data-driven approach to identifying efficient statistical indicators of temporal asymmetry in short, noisy univariate time series, that involves comparing across a comprehensive algorithmic library of over 7000 time-series statistics in the hctsa software tool. We compare the performance of these methods by simulating a set of nonlinear dynamical systems, generating forward and time-reversed stationary time series with known reversibility properties. Our findings reveal promising methodical approaches to inferring time-reversibility from data, including metrics based on time-series symbolization and those capturing higher-order correlations and nonlinearity. When applied to neural dynamics, our approach reveals that metrics that most sensitively detect time-asymmetry are also effective at distinguishing between seizure and non-seizure activity from short electroencephalogram (EEG) recordings, demonstrating the potential real-world applicability of statistical tools derived from the theory of time reversibility. Our analysis improves the ability to quantify and interpret temporal asymmetries in non-equilibrium systems, establishing important connections between the theory of time reversibility of equilibrium and non-equilibrium systems, and its practical impact on data-driven applications.

First-passage time, the moment a process first satisfies a condition (e.g., reaching a specific spatial point for the first time), is a fundamental concept in stochastic dynamics. In this seminar, we explore recent tools for analyzing first-passage statistics in both continuous and discrete space-time. We use Montroll’s defect technique to tackle the first-passage problems in discrete space-time. On the other hand, in the continuous space-time setting, we show how Martingales can be employed with remarkable efficiency in obtaining first-passage statistics. Using these approaches, we analyze first-passage problems in various Markovian and non-Markovian processes, including biased diffusion, its area functional, and run-and-tumble walks with applications in movement ecology.

Biophotons are ultra-weak emissions of photons in the visible range, spontaneously produced by living matter without external stimulation. These emissions are increasingly investigated as potential indicators of metabolic activity and intercellular communication. In this talk, we present a detailed analysis of biophoton emission during the germination of plant seeds, using a highly sensitive detection setup capable of measuring extremely low-intensity light. We monitored the biophotonic activity of lentil seeds and a single bean throughout the entire germination process. The analysis focused both on the spectral composition of the emitted photons—investigated using a series of low-pass optical filters—and on the statistical distribution of photon counts across different germination stages. Despite the overall similarity in the spectral profiles observed in both seed types, our study reveals distinct emission characteristics that correlate with the developmental progression of each specimen. These differences suggest that the dynamics of biophoton emission are not only species-specific but also linked to the physiological state of the organism. The experimental approach and findings outlined in this work lay the groundwork for further investigations into biophoton emission as a functional signature of biological activity. In particular, future applications may include time-resolved studies on cell cultures, where controlled environments could allow for the exploration of biophotons as potential markers of cell differentiation, stress responses, or communication mechanisms.

Nowadays, Decentralized Exchanges are a significant component of the financial world. Billions of dollars are traded daily on these venues, and the exchanged volume seems meant to increase further. A milestone in such growth is Uniswap v3. Its main feature, Concentrated Liquidity, and the peculiar organization of the trading flow via memory-pools have revolutionized the liquidity provision and how we think about it, posing new challenges and reward opportunities for Liquidity Providers and Maximal Extractable Value searchers. As a result, it has shortly become the most traded decentralized exchange. The industry mainly drives this innovation, and the academic research follows with several contributions mainly oriented toward optimizing profit opportunities. Nonetheless, little attention has been paid to analyzing the statistical properties of such markets and highlighting common patterns that are frequently noticed. Thus, our work aims to fill this gap. Specifically, we examine the price and liquidity time series from a microstructural point of view, starting from event-time frequency. Our study is carried out on the twenty-four most active pools in Uniswap v3. The analysis is focused on understanding how the new trading mechanisms introduced in Decentralized Exchanges impact their microstructural properties, giving rise to peculiar patterns in the autocorrelation, long-memory, and dependencies between the market variables, which deviate from what is observed in traditional markets. To this end, we investigate the main clusters of agents entering the market and their impact. Our ultimate aim is twofold. On one side, we review the essential features of Uniswap v3 and provide a guideline to researchers working in this field. On the other side, we collect some directions for future studies that could enhance the theoretical insight into Decentralized Exchanges.

Triadic motifs are the smallest building blocks of higher-order interactions in complex networks and can be detected as over-occurrences with respect to null models with only pair-wise interactions. Recently, the motif structure of production networks has attracted attention in light of its possible role in the propagation of economic shocks. However, its characterization at the level of individual commodities is still poorly understood. Here we analyze both binary and weighted triadic motifs in the Dutch inter-industry production network disaggregated at the level of 187 commodity groups, which Statistics Netherlands reconstructed from National Accounts registers, surveys and known empirical data. We introduce appropriate null models that filter out node heterogeneity and the strong effects of link reciprocity and find that, while the aggregate network that overlays all products is characterized by a multitude of triadic motifs, most single-product layers feature no significant motif, and roughly 85% of the layers feature only two motifs or less. This result paves the way for identifying a simple ‘triadic fingerprint’ of each commodity and for reconstructing most product-specific networks from partial information in a pairwise fashion by controlling for their reciprocity structure. We discuss how these results can help statistical bureaus identify fine-grained information in structural analyses of interest for policymakers.

The common observation of power laws in nature and society, that is, that quantities or probabilities follow 1/xα distributions, has for long intrigued scientists. In the brain, power laws in the power spectral density (PSD) have been observed in electrophysiological recordings, both at the microscopic (single-neuron recordings) and macroscopic (EEG) levels. While complex network behavior and criticality have been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. By a combination of numerical simulations of biophysically detailed neuron models and analytical investigations of the so called ball-and-stick neuron model, we demonstrate that high-frequency power laws in key experimental neural measures will arise naturally when the noise sources are evenly distributed across the neuronal membrane. Comparison with available data further suggests that the apparent power laws observed in experiments may stem from uncorrelated current sources, presumably intrinsic potassium ion channels, which are homogeneously distributed across the neural membranes and themselves exhibit pink (1/f) noise distributions. The significance of this finding goes beyond neuroscience as it demonstrates how 1/fα power laws with a wide range of possible power-law exponents α may arise from a simple, linear physics equation. References: Halnes et at, “Electric Brain Signals”, Cambridge University Press, 2024; Pettersen et al, “Power laws from linear cable theory”, PLoS Comp Biol, 2014

Before game theory was established as it is today, we find mathematically interesting approaches about. Although the birth of modern game theory can be coincided with the publication of the article ‘On the Theory of Games of Strategy’ by John von Neumann in 1928, we later find significant contributions, including the one from 1934 by R.A. Fisher. The title of the article is ‘ Randomisation and an Old Enigma of Card Play’. This game is precisely ‘Le Her’. In 1713, in a letter attributed to Charles Waldegrave, a card game called ‘Le Her’ is analyzed. In this letter, Waldegrave provides a minimax solution in mixed strategies for a two-player version of this game. In addition to an interesting historical significance, this article by Fisher can give some suggestions for current research.

The introduction of active elements in optical networks may lead to lasing action. The resulting emission is based on the modes of the network itself and can be very complicated, reflecting the topology of the connections. This system, named LANER (i.e., lasing network), can be easily implemented in a laboratory and represents a powerful scheme for various investigations.. We discuss the main features of the concept and report on some experimental implementations and results.

We investigate the distribution and clustering of extreme events of stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on R^n. We do so by studying the action of an annealed transfer operators on a suitable spaces of densities. The spectral properties of such operators are obtained by employing a mixture of techniques coming from SDE theory and a functional analytic approach to dynamical systems.

The neural representation of information that is shared across brains is encoded in fine-scale functional topographies that vary from brain to brain. Hyperalignment models this shared information in a common information space. Hyperalignment transformations project idiosyncratic individual topographies into the common model information space. These transformations contain topographic basis functions, affording estimates of how shared information in the common model space is instantiated in the idiosyncratic functional topographies of individual brains. This new model of the functional organization of cortex – as multiplexed, overlapping basis functions – captures the idiosyncratic conformations of both coarse-scale topographies, such as retinotopy and category-selectivity in the visual cortices, and fine-scale topographies. Hyperalignment also makes it possible to investigate how information that is encoded in fine-scale topographies differs across brains. These individual differences in cortical function were not accessible with previous methods. We are developing a normative dataset to produce a standardized template for hyperalignment that will provide a new functional atlas for fMRI research, HyperBrain, that captures shared fine-scale functional topography as a basis for data sharing and investigation of individual and group differences.

Glioblastoma (GBM) is the most aggressive form of primary brain tumors, strongly spreading in and infiltrating the adjacent healthy brain tissue. Infiltration in general occurs by single cells but also involves collective migration, and its extent correlates with the grading of gliomas. In recent years, biomechanical approaches provided valuable insights into the process of tumor infiltration and migration in multiple tumor types, showing even prognostic capabilities. Here, we analyzed how different biophysical properties, including cell-cell-adhesion, tension, cell density and associated signs of self-organization affect the migratory properties of GBM cells. In contrast to healthy, immobile glial cells GBM cells were found generally in a mobile, fluid like state. GBM cells showed signs of a phase transition like process, reminiscent of a jamming transition, resulting in a non-migratory state if the equilibrium of adhesion and tension was tuned in favor of tension. Interestingly, another route to induce migratory arrest was by increasing cell density, but only in cell types showing no signs of self-organization in aster- or stream-like patterns. Thereby, GBM cells showed organized patterns of several millimeters in diameter, where cells were aligned similar to liquid crystals, including topological defects. Interestingly, inside aligned streams of cells the movement was not organized in streams of parallel moving cells, but rather small anti-parallel moving cell streams. In conclusion, the equilibrium of cell-adhesion and tension, as well as total cell density seem to play important roles in determining migratory potential of GBM. Furthermore, it can be speculated about a role of self-organization in the maintenance of collective migration of GBM cells for high cell densities. These results might open new routes into identifying new and evaluating the effect of potential therapeutics.

We investigate a population of coupled oscillators characterized by both spatial and phase dynamics, exploring their collective behavior. Specifically, we focus on how “dynamic” oscillators influence the system’s coherence. When spatial and phase dynamics are completely decoupled, dynamic oscillators, operating at their intrinsic frequencies, have no effect on the system’s ordering behavior. However, when these dynamics are coupled, both static and dynamic oscillators contribute to the ordering process, resulting in enhanced coherence. This coherence enhancement is driven by the breaking of π-reflection symmetry, a phenomenon absent in the classic Kuramoto model, where decoupled dynamics preserve π-reflection symmetry and do not influence synchronization. To illustrate this, we propose a minimal model and demonstrate how π-reflection symmetry breaking, driven by dynamic oscillators, enhances coherence within the system.

We aim to obtain a model to describe the evolution of the leverages of a system of multiple banks of different sizes investing in an asset and to analyze it mathematically. Under certain assumptions, this system can be described by a discrete-time dynamical system defined by a set of coupled unimodal maps, which reduces to a deterministic skew product system in the limit in which a bank is much bigger than the other. Among other results, one gets for instance that the choice of the value of even a single parameter made by even a single larger bank crucially determines whether the system as a whole will be chaotic or not. Moreover, interestingly a Hénon-like attractor is observed when looking at the long-term behavior of the system. This is joint work with Matteo Tanzi, King’s College London.

Globally coupled phase oscillators with inertia, as described by the second-order Kuramoto model (2nd KM), pose fundamental challenges in understanding synchronization dynamics beyond the mean-field description scope governed by a giant synchronized cluster. Here, due to the inertia effect, we find that the 2nd KM exhibits distinct synchronization patterns, including discontinuous transitions, multi-cluster synchronization, and Devil’s Staircases. The microscopic mechanisms underlying these features are uncovered by setting corase-grained 2nd KM. We show that a primary cluster (PC) initially forms, exerting an attractive force on other oscillators and temporarily inhibiting further clustering. Once stabilized, oscillators that orbit near its aphelion merge into secondary (SC) and higher-order clusters, where their frequencies synchronize at rational number ratios, revealing a Devil’s Staircase pattern. Moreover, when the inertia is large, the initially formed PC shatters into individuals; they either merge into the two SCs or oscillate between them. We derive analytical expressions for the PC and SC frequency ranges, providing methods to control the synchronized cluster size and deeply understand the underdamped dynamics of coupled oscillators in a different aspect.

In order to understand the weather on longer times scales, like for example, on low frequency variability on annual and decadal scales, but also on climatic and paleoclimatic scales, it is inevitable to incorporate ocean atmosphere coupling and thermodynamical effects into the modelling. We establish the well-posedness of a model consisting of a system of PDEs describing an atmosphere via two quasi-geostrophic layers coupled to a further quasi-geostrophic layer modelling a deep ocean. Furthermore, there are two transport reaction-diffusion PDEs describing the development of the atmosphere and ocean temperature. More specifically, we consider the model which Vannitsem et al. in [1] used (not linearising the infrared radiation terms), which is based on a series of previous models, to mention a few Charney and Strauss ’80, Reinhold and Pierrehumbert ’82; Pierini ’11. A lot of work has been done about this model by meteorologist using physical and numerical considerations. We consider these model from a mathematical analytical angle proving well-posedness, finite dimensionality of the attractor, and we will study determining functionals in order to prove that the thermodynamics of the ocean is governed for large times by the dynamics of the rest of the system. In the last part of the talk we will derive conditions under which the ocean and atmosphere’s temperature (as absolute temperatures in Kelvin) stay positive under the time evolution. An interesting aspect of the model is the asymmetry in the unknowns with respect to regularity, which leads to a not straight forward application of classical techniques for 2D-Navier-Stokes and reaction diffusion equations. This is a joint work with Federico Fornasaro (La Sapienza) and Giulia Carigi (Indiana). [1] Lesley De Cruz, Jonathan Demaeyer, Stephane Vannitsem, The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0, Geoscientific Model Development, 2016.

Non-autonomous systems influenced by noise are prevalent across numerous applications. Of particular interest are tipping points arising from time-dependent parameter variations, where uncertainties play a crucial role in delineating safe operating regimes. Our focus lies on the case of bounded noise, which often constitutes a more realistic modelling assumption, as physical quantities typically fluctuate within finite limits. Under such assumptions, qualitative dynamical transitions become detectable through interactions between localised structures—an analysis that is frequently unattainable in the presence of unbounded noise. Furthermore, the dynamics of a random dynamical system subjected to bounded noise can be effectively characterised at a topological level by a deterministic set-valued dynamical system. This framework encapsulates the aggregate behaviour of the underlying stochastic system by evolving initial conditions across all admissible noise realisations, focusing purely on the topological dynamics rather than stochastic detail. However, set-valued dynamical systems present substantial analytical challenges, as they operate on the space of all compact subsets, which does not constitute a Banach space. This structural limitation poses a well-known barrier to both theoretical investigations and numerical computations, making bifurcation analysis of attractors especially difficult. In this talk, we introduce a non-autonomous generalisation of the so-called boundary map to describe the evolution of non-autonomous invariant sets in set-valued dynamical systems, by tracing the dynamics of their boundaries over time.

Response theory provides a pathway for understanding the sensitivity of a system and, more in general, to predict how its statistical properties change as a possibly time-dependent perturbation is applied. Recently discovered general forms of the celebrated Fluctuation-Dissipation Theorem allow for expressing response operators as correlation functions of suitably defined observables in the unperturbed state, also when such a state is far from equilibrium. In the case of complex and multiscale systems, to achieved enhanced practical applicability, response theory must be interpretable, capable of focusing of relevant timescales, and amenable to implemented by data-driven approaches that are potentially equation-agnostic. Complex systems typically exhibit a hierarchy of temporal behaviors, and unresolved or undesired timescales can obscure the dominant mechanisms driving macroscopic responses. As an element of this desired framework, in the spirit of Markov state modelling, we propose here a comprehensive analysis of the linear and nonlinear response of Markov chains to general time-dependent perturbations. We obtain simple and easily implementable formulas that can be used to predict the response of observables as well as higher-order correlations of the system. The methodology proposed here can be implemented in a purely data-driven setting and even if we do not know the underlying evolution equations. The use of algebraic expansions inspired by Koopmanism allow to elucidate the role of different time scales and find explicit and interpretable expressions for the Green’s functions at all orders. This is a major advantage of the framework proposed here. We illustrate our methodology in a very simple yet instructive metastable system. Finally, our results provide a dynamical foundation for the Prony method, which is commonly used for the statistical analysis of discrete time signals.

We show that extensive exchange economies fit into the axiomatic approach of Lieb & Yngvason to thermodynamics. As consequences, we deduce: (i) the existence of an entropy function for each economy with the property that it is possible to move a collection of economies from one state to another if and only if the total entropy does not decrease; (ii) the existence of a temperature function such that on financial contact between two economies, money flows from hotter to cooler; (iii) the existence of marginal value functions for each type of good, and hence market prices, such that an economy buys or sells a good if offered a lower or higher price, respectively; (iv) the possibility of making money out of temperature differences; (v) symmetry and negative semi-definiteness of the partial derivatives of values with respect to amounts of goods, and similar for compensated derivatives; (vi) further inequalities between partial derivatives; (vii) positive semi-definiteness of the Onsager matrix relating fluxes to value differences. We illustrate the results by simulations of various Markovian models of extensive exchange economy. Joint work with Nick Chater and Yihang Luo.

The aim of this communication is to describe the ongoing research about ecological webs through the theory of dynamical systems at the local section of the Institute of Complex Systems of CNR in Florence. Ecological webs are networks of dynamical variables that interact in pairs through rules that are mainly empirical, yet they are constrained to satisfy some sensible conditions, e.g. on their asymptotic behaviour. If the pair interaction describes the transfer of biomass from one species to another one, for example in the case of prey-predator relationships, the interaction must show some symmetry properties, taking into account the metabolism of the species involved. Moreover, pair interactions may be influenced by the state of dynamical variables other than the two ones directly involved, giving rise to 3-, 4-, …, n-variable interactions, namely higher order interactions. This is a short review sketching the systems of this type studied in Florence in the local section of the Institute for Complex Systems of the National Research Council of Italy (CNR-ISC). In particular, reference is made to a rich prey-predator system encoding the phenomenon of klepto-parasitism of a scavenger (wild boar) at the expenses of a top predator (wolf) on the predators’ catch, in which the trophic level organization is complicated by this relationship; another example illustrated is that of competition between two algal population on the sea floor, in which topological considerations (borrowed from the so called pack or herd behaviour in animal ecology) allow to treat local interactions in a space-implicit form. Finally, research collaborations already established with the colleagues of the Institute of Biophysics of CNR in Pisa are presented.

Next-venue recommender systems are increasingly embedded in location-based services, shaping individual mobility decisions in urban environments. While their predictive accuracy has been extensively studied, less attention has been paid to their systemic impact on urban dynamics. In this work, we introduce a simulation framework to model the human–AI feedback loop underpinning next-venue recommendation, capturing how algorithmic suggestions influence individual behavior, which in turn reshapes the data used to retrain the models. Our simulations, grounded in real-world mobility data, systematically explore the effects of algorithmic adoption across a range of recommendation strategies. We find that while recommender systems consistently increase individual-level diversity in visited venues, they may simultaneously amplify collective inequality by concentrating visits on a limited subset of popular places. This divergence extends to the structure of social co-location networks, revealing broader implications for urban accessibility and spatial segregation. Our framework operationalizes the feedback loop in next-venue recommendation and offers a novel lens through which to assess the societal impact of AI-assisted mobility—providing a computational tool to anticipate future risks, evaluate regulatory interventions, and inform the design of ethic algorithmic systems.

The Kelly criterion provides a general mathematical framework for optimizing the growth rate of an investment portfolio over time by maximizing the expected logarithmic utility of wealth. While the optimal solution guarantees an asymptotic exponential growth rate, the short-term risk is typically very large compared to other investment strategies. However, market risk is just one factor to consider and is not necessarily the most significant. The optimality condition of the Kelly criterion is highly sensitive to accurate estimates of the probabilities and investment payoffs. Uncertainty in the distribution and misspecification of the model parameters – key aspects of what is known as estimation risk – can significantly affect outcomes, leading to greatly suboptimal portfolio dynamics. In a complete market consisting of a risk-free asset, a risky asset modeled with a binomial tree, and European options, we demonstrate how options can be used to construct a class of Kelly portfolios that are robust to estimation risk. We address the portfolio optimization problem for general hedging strategies, demonstrating that an appropriate convex combination of Kelly portfolios is dominating all alternatives and achieves asymptotic exponential growth under any model misspecification. Furthermore, we establish that asymmetries in the growth rate of the optimal Kelly strategy across varying levels of estimation risk indicate the presence of dynamic arbitrage in the sense of Gatheral (2010).

Simulations of large-scale neural activity are increasingly used to explore the biophysical origins of brain signals. However, estimating measurable signals like the local field potential (LFP) often requires detailed multicompartmental models, which can be computationally demanding. In this talk, I will present a kernel-based method that enables efficient and accurate LFP estimation from a biologically realistic large-scale model of mouse primary visual cortex (V1). This method not only reduces computational cost but also improves LFP interpretability by separating the contributions of specific neuronal populations. Applied to the V1 model, it reveals that LFP signals are primarily shaped by external synaptic inputs originating outside the cortex, while local V1 activity plays only a marginal role. These findings highlight the kernel method as a robust tool for large-scale simulations, with strong potential for uncovering the circuit mechanisms underlying population signals.

Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various vector-based downstream tasks such as network modelling, visualization, data compression, node classification, link prediction, and community detection. Two apparently unrelated limitations affect these algorithms. On one hand, it is not clear what the basic operation defining vector spaces, i.e. the vector sum, corresponds to in terms of the original nodes in the network. On the other hand, while the same input network can be represented at multiple levels of resolution by coarse-graining the constituent nodes into arbitrary block-nodes, the relationship between node embeddings obtained at different hierarchical levels is not understood. Here, building on recent results in network renormalization theory, we address these two limitations at once and define a multiscale node embedding method that, upon arbitrary coarse-grainings, ensures statistical consistency of the embedding vector of a block-node with the sum of the embedding vectors of its constituent nodes. We illustrate the power of this approach on two economic networks that can be naturally represented at multiple resolution levels: namely, international trade between (sets of) countries and input-output flows among (sets of) industries in the Netherlands. We confirm the statistical consistency between networks retrieved from coarse-grained node vectors and networks retrieved

In this talk we discuss the issue of planning individual mobility routes that consider both travel efficiency and the exposure of people (more specifically, pedestrians) to the emissions generated by circulating vehicles. We start from a one-way perspective, where pedestrians try to adapt their routes to existing emission distributions in the city, trading time for exposure. Then, we consider a two-way view, where both vehicles’ trips and pedestrians’ walks collaborate to find the best overall tradeoff. How much can we reduce exposure through small routing adjustments?

We introduce an order parameter for measuring mutual synchrony of angular velocity, analogously to how Kuramoto’s celebrated order parameter measures mutual alignment of phases. The need for such a new metric of synchronisation is reflected in the fact that frequency-synchronisation of oscillators does not necessarily imply that the phases themselves are closely aligned. We illustrate the utility of the new order parameter for autonomous and non-autonomous Kuramoto networks, both with attractive coupling and with mixed attractive-repulsive coupling, where the new order parameter is particularly effective at quantifying synchronisation phenomena not easily detectable by the classical Kuramoto order parameter.

We formally derive the path-kernel formula for the linear response, or the parameter-derivative of averaged statistics, of SDEs. The parameter controls the diffusion coefficients. Our formula combines the path-perturbation and the kernel method (also called likelihood ratio or Cameron-Martin-Girsanov) by extending Bismut-Elworthy-Li’s compensation idea to perturbation on dynamics. It tempers the unstableness by gradually moving the path-perturbation to hit the probability kernel. It does not assume hyperbolicity. We prove by direct comparison of bundles of paths across different parameters. Based on the new formula, we derive a pathwise sampling algorithm for linear responses and demonstrate it on the 40-dimensional Lorenz 96 system with noise; this numerical example is difficult for all other algorithms.

Many dynamical systems operate in a fluctuating environment. However, even in low-dimensional setups, transitions and bifurcations have not yet been fully understood. In this Letter we focus on crises, a sudden flooding of the phase space due to the crossing of the boundary of the basin of attraction. We find that crises occur also in nonautonomous systems although the underlying mechanism is more complex. We show that in the vicinity of the transition, the escape probability scales as exp⁡[−𝛼⁢(ln⁡𝛿)2], where 𝛿 is the distance from the critical point, while 𝛼 is a model-dependent parameter. This prediction is tested and verified in a few different systems, including the Kuramoto model with inertia, where the crisis controls the loss of stability of a chimera state

The talk presents the cryptocurrency network of the FTX exchange during the collapse of its native token, FTT, to understand how network structures adapt to significant financial disruptions, by exploiting vertex centrality measures. We construct the filtered correlation matrix to identify the most significant relations in the FTX and Binance markets. By using suitable centrality measures – closeness and information centrality – we assess network stability during FTX’s bankruptcy. By tracking the changes in centrality values before and during the FTX crisis, we provide useful insights into the structural dynamics of the cryptocurrency market. Results reveal how different cryptocurrencies experienced shifts in their network roles due to the crisis.

Understanding how opinions evolve is crucial for addressing issues such as polarization, radicalization and consensus in social systems. While much research has focused on identifying factors influencing opinion change, the role of language and argumentative fallacies remains underexplored. In this presentation we discuss a research aiming to fill this gap by investigating how language — along with social dynamics — influences opinion evolution. To such an extent, we introduce LODAS, a Language-Driven Opinion Dynamics Model for Agent-Based Simulations. LODAS simulates debates around the Ship of Theseus paradox, in which agents with discrete opinions interact with each other and evolve their opinions by accepting, rejecting, or ignoring the arguments presented. We study three different scenarios: balanced, polarized, and unbalanced opinion distributions. Agreeableness and sycophancy emerge as two main characteristics of LODAS agents, and consensus around the presented statement emerges almost in any setting. Moreover, such AI agents are often producers of fallacious arguments in the attempt of persuading their peers and — for their complacency — they are also highly influenced by arguments built on logical fallacies. These results highlight the potential of this framework not only for simulating social dynamics but also for exploring from another perspective biases and shortcomings of LLMs, which may impact their interactions with humans.

Spatial information is encoded by location-dependent hippocampal place cell firing rates and sub-second, rhythmic entrainment of spike times. These rate and temporal codes have primarily been characterized in low-dimensional environments under limited cognitive demands; but how is coding configured in complex environments when individual place cells signal several locations, individual locations contribute to multiple routes and functional demands vary? Quantifying CA1 population dynamics of male rats during a decision-making task, we show that the phase of individual place cells’ spikes relative to the local theta rhythm shifts to differentiate activity in different place fields. Theta phase coding also disambiguates repeated visits to the same location during different routes, particularly preceding spatial decisions. Using unsupervised detection of cell assemblies alongside theoretical simulations, we show that integrating rate and phase coding mechanisms dynamically recruits units to different assemblies, generating spiking sequences that disambiguate episodes of experience and multiplexing spatial information with cognitive context.

Feature selectivity, the ability of neurons to respond preferentially to specific stimulus configurations, is a fundamental building block of cortical functions. Various mechanisms have been proposed to explain its origins, differing primarily in their assumptions about the connectivity between neurons. Some models attribute selectivity to structured, tuning-dependent feedforward or recurrent connections, whereas others suggest it can emerge within randomly connected networks when interactions are sufficiently strong. This range of plausible explanations makes it challenging to identify the core mechanisms of feature selectivity in the cortex. We developed a novel, data-driven approach to construct mechanistic models by utilizing connectomic data-synaptic wiring diagrams obtained through electron microscopy to minimize preconceived assumptions about the underlying connectivity. With this approach, leveraging the MICrONS dataset, we investigate the mechanisms governing selectivity to oriented visual stimuli in layer 2/3 of mouse primary visual cortex. We show that connectome-constrained network models replicate experimental neural responses and point to connectivity heterogeneity as the dominant factor shaping selectivity, with structured recurrent and feedforward connections having a noticeable but secondary effect in its amplification. These findings provide novel insights on the mechanisms underlying feature selectivity in cortex and highlight the potential of connectome-based models for exploring the mechanistic basis of cortical functions.

The ability to simultaneously record the activity from tens to hundreds to thousands of neurons has allowed us to analyze the computational role of population activity as opposed to single neuron activity.  Recent work on a variety of cortical areas suggests that neural function may be built on the activation of population-wide activity patterns, the neural modes, rather than on the independent modulation of individual neural activity. These neural modes, the dominant covariation patterns within the neural population, define a low dimensional neural manifold that captures most of the variance in the recorded neural activity. We refer to the time-dependent activation of the neural modes as their latent dynamics and argue that latent cortical dynamics within the manifold are the fundamental and stable building blocks of neural population activity.

Schizophrenia (SZ) affects ~1% of the global population. While cortical and subcortical alterations are well documented, the cerebellum’s role in cognitive dysfunction remains underexplored [1]. In SZ, cerebellar degeneration involves neuronal loss, dendritic simplification, and weakened connectivity. An emerging hypothesis suggests SZ as a glutamatergic synaptopathy [2] that extends to cerebellar circuits, eventually contributing to “cognitive dysmetria” effects [3], which are ultimately interacting with cerebellar reserve [4]. To explore this framework, we modeled SZ synaptic, cellular, and network-level alterations and resilience. Under baseline conditions, SZ degeneration caused progressive hypoactivity in Purkinje cells (PC), more pronounced in low-resilience networks, which abruptly upregulated thalamic-projecting deep nuclei, suggesting potential overdrive of mesolimbic circuits. To probe dysmetria, we applied saccade-like bursts on mossy fibers (MF) and quantified MF–PC gating. In low-resilience networks, cosine similarity between MF and PC responses dropped markedly (ρ = –0.90, p = 0.002), accompanied by increased lag (+10 ms, ρ = 0.80, p = 0.017), reduced transfer entropy (–179.7 bit, ρ = –0.88, p = 0.004) and phase locking (–0.18, ρ = –0.95, p < 0.001). Impairments were attenuated in high-resilience conditions, suggesting that cerebellar reserve mitigates SZ induced stimulus-driven dysmetric dynamics. These findings highlight brain resilience as a key modulator of cerebellar dysfunction in schizophrenia, opening new avenues for targeted interventions, such as neuromodulation and brain stimulation, to enhance neural protective capacities across the schizophrenia continuum. [1] DOI: 10.3389/fncel.2024.1386583 [2] DOI: 10.1126/science.1179685 [3] DOI: 10.1016/j.neulet.2018.07.005 [4] DOI: 10.1007/s12311-019-01091-9