arXiv subjects

Daniele De Martino

Publications and source records attributed to Daniele De Martino.

At least 19 recordsLinked to original sources

arXiv2026

Storing Infinite Dynamical Attractors in Nonreciprocal Associative Neural Networks

We develop a dynamical mean-field theory for nonreciprocal associative networks that store an extensive number of dynamical attractors, from limit cycles to strange attractors. Using a path integral calculation under quenched disorder, we derive self-consistent dynamical mean-field equations for pattern overlaps, autocorrelations and response functions. Memory retrieval capacity is governed by the spectral structure of the coupling matrices encoding stored patterns. When their eigenvalues are coherently aligned, retarded self-interactions and quenched noise feed back destructively: at zero eigenphase (fixed point attractors) the classical equilibrium capacity bound is recovered, while for limit cycles retrieval collapses far below it. In contrast, for uniformly distributed eigenphases, retarded self-interactions and much of the quenched noise cancels, reducing the dynamics to an effective single-spin process and amplifying capacity substantially. We validate the theory against microscopic simulations for limit-cycle and chaotic attractors, identifying eigenvalue decoherence as the mechanism enabling enhanced storage of dynamical memories.

cond-mat.dis-nn↗

arXiv2026

Synchronization, Kinematic Waves and Spike-Phase-Separation in Feedback Ising Neural Networks on Heterogeneous Graphs

Structural heterogeneity constrains collective dynamics in complex systems. However, its analytical tractability out of equilibrium remains limited. In this work, we study a class of kinetic Ising neural networks driven out of equilibrium by a homeostatic feedback loop between the neuronal excitability and the population firing rate. Using a Curie-Weiss heterogeneous mean-field approximation validated by Monte Carlo simulations, we provide an analytical characterization of how a macroscopic synchronized limit cycle emerges via an Andronov-Hopf bifurcation on heterogeneous networks. We derive closed-form phase boundaries and show that the onset of oscillations is explicitly controlled by network heterogeneity through the degree moment ratio. Degree heterogeneity decouples the spiking rate per neuron m from the spiking rate per synapse u, generating physical phenomena absent in homogeneous systems. These include (i) kinematic waves of sequential, degree-ordered activations propagating from the network periphery to the hubs, and (ii) a low-temperature phase-separated state emerging via a pitchfork bifurcation. We prove that for highly heterogeneous topologies, this phase-separated fixed point stabilizes and dynamically destroys the synchronized limit cycle. These results provide a mathematical framework for understanding how heterogeneity regulates macroscopic oscillations and out-of-equilibrium transitions in neural networks

cond-mat.stat-mech↗

arXiv2026

Scaling and tuning to criticality in resting-state human magnetoencephalography

From 1/f noise to neuronal avalanches, evidence of scaling in brain activity has been increasingly linked to tuning to or near criticality. The concept of scaling is intimately related to the renormalization group (RG), in essence providing coarse-grained, simplified descriptions that generalize to classes of diverse physical systems. Following the RG idea, scaling laws have been reported in populations of spiking neurons at microscopic scales. Whether similar scaling principles govern large-scale neural activity in the human brain and how they relate to underlying neural physiology remains unresolved. Here, we analyze large-scale electrophysiological recordings (MEG) of human resting-state brain activity and apply a RG-inspired coarse-graining approach to track collective neural dynamics across spatial scales. We find that multiple observables exhibit robust scale-invariant behavior under coarse-graining: activity variance and correlations grow according to power laws, covariance eigenspectra follow a characteristic scaling relation, and neuronal avalanche statistics remain invariant. Using an analytically tractable neural network model, we show that the observed scaling signatures arise when the system operates slightly below criticality, and that the scaling exponents depend on the excitation-inhibition balance. These findings demonstrate that RG-inspired scaling analysis can uncover signatures of critical dynamics in non-invasive human electrophysiology and suggest a principled route toward estimating excitation-inhibition balance from large-scale brain recordings.

q-bio.NC↗

arXiv2025

Nonequilibrium Thermodynamics of Associative Memory Continuous-Time Recurrent Neural Networks

Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of CTRNNs based on Hopfield-like associative memories with asymmetric couplings. This model combines the expressive power of associative memories with a tractable mathematical formalism to characterize fluctuations in nonequilibrium dynamics. We show that this mathematical description allows us to directly compute the evolution of its macroscopic observables (the encoded features), as well as the instantaneous entropy and entropy dissipation of the system, thereby offering a bridge between dynamical systems descriptions of low-dimensional observables and the statistical mechanics of large nonequilibrium networks. Our results suggest that these nonequilibrium associative CTRNNs can serve as more interpretable models for complex sequence-encoding networks.

cond-mat.dis-nn↗

arXiv2025

Single-cell metabolic flux analysis reveals coexisting optimal sub-groups, cross-feeding, and mixotrophy in a cyanobacterial population

We derive a single-cell level understanding of metabolism in an isogenic cyanobacterial population by integrating secondary ion mass spectrometry (SIMS) derived multi-isotope uptake measurements of Synechocystis sp. PCC6803 with a statistical inference protocol based on Liebig's law of the minimum, the maximum entropy principle, and constraint-based modeling. We find the population is structured in two metabolically distinct clusters: cells optimizing carbon yield while excessively turning over nitrogen, and cells which act reciprocally, optimizing nitrogen yield and excessively turning over carbon. This partition enables partial heterotrophy within the population via metabolic exchange, likely in the form of organic acids. Exchange increases the feasible metabolic space, and mixotrophic cells achieve the fastest growth rates. Metabolic flux analysis at the single-cell level reveals heterogeneity in carbon fixation rates, Rubisco specificity, and nitrogen assimilation. Our results provide a necessary foundation for understanding how population level phenotypes arise from the collective contributions of distinct individuals.

q-bio.PE↗

arXiv2025

Metabolic coordination and phase transitions in spatially distributed multi-cellular systems

During overflow metabolism, cells excrete glycolytic byproducts when growing under aerobic conditions in a seemingly wasteful fashion. While potentially advantageous for microbes with finite oxidative capacity, its role in higher organisms is harder to assess. Recent single-cell experiments suggest overflow metabolism arises due to imbalances in inter-cellular exchange networks. We quantitatively characterize this scenario by integrating spatial metabolic modeling with tools from statistical physics and experimental single-cell flux data. Our results provide a theoretical demonstration of how diffusion-limited exchanges shape the space of accessible multi-cellular metabolic states. Specifically, a phase transition from a balanced network of exchanges to an unbalanced, overflow regime occurs as mean glucose and oxygen uptake rates vary. Heterogeneous single-cell metabolic phenotypes occur near this transition. Time-resolved tumor-stroma co-culture data support the idea that overflow metabolism stems from failure of inter-cellular metabolic coordination. In summary, environmental control is an emergent multi-cellular property, rather than a cell-autonomous effect.

cond-mat.stat-mech↗

arXiv2024

Cross-feeding percolation phase transitions of inter-cellular metabolic networks

Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange fluxes with the medium at single-cell resolution. Here we introduce a tiling-based method to reconstruct the dynamic unfolding of exchange networks from flux data, subsequently applying it to an experimental mammalian co-culture system where lactate exchanges affect the acidification of the environment. We observe that the network, which initially exhibits a dense matrix of exchanges, progressively breaks up into small disconnected clusters of cells. To explain this behaviour, we develop a two-parameter Maximum-Entropy multicellular metabolic model that incorporates diffusion-driven exchanges through a set of global constraints that couple cellular behaviors. The model predicts a transition from a densely interconnected network to a sparse, motif-dominated state as glucose and oxygen consumption levels shift. We characterize such a crossover both numerically, revealing a power-law decay in the cluster-size distribution at the critical transition, and analytically, by computing the critical line through a mean-field approximation based on percolation theory. By comparing empirical data with theoretical predictions, we find that populations evolve towards the sparse phase by remaining near the crossover point between these two regimes. These findings offer new insights into the collective organization driving the adaptive dynamics of cell populations.

cond-mat.stat-mech↗

arXiv2023

Emergence of collective self-oscillations in minimal lattice models with feedback

The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase transitions. Here we consider classical lattice models, namely the Ising, the Blume-Capel and the Potts models, with a feedback among the order and control parameters. With linear response theory we derive low-dimensional dynamical systems for mean field cases that quantitatively reproduce many-body stochastic simulations. In general, we find that the usual equilibrium phase transitions are taken over by complex bifurcations where self-oscillations emerge, a behavior that we illustrate by the feedback Landau theory. For the case of the Ising model, we obtain that the bifurcation that takes over the critical point is non-trivial in finite dimensions. We provide numerical evidence that in 2D the most probable value of the amplitude follows the Onsager law. We illustrate multi-stability for the case of discontinuously emerging oscillations in the Blume-Capel model, whose tricritical point is substituted by the Bautin bifurcation. For the Potts model with q = 3 colors we highlight the appearance of two mirror stable limit cycles at a bifurcation line and characterize the onset of chaotic oscillations that emerge at low temperature through either the Feigenbaum cascade of period doubling or the Aifraimovich-Shilnikov scenario of a torus destruction. We show that entropy production singularities as a function of the temperature correspond to change in the spectrum of Lyapunov exponents. Our results show that mean-field behaviour can be described by the bifurcation theory of low-dimensional dynamical systems, which paves the way for the definition of universality classes of collective oscillations.

cond-mat.stat-mech↗

arXiv2023

Modelling spatial constraints and scaling effects of catalyst phase separation on linear pathway kinetics

Chemical reactions are usually studied under the assumption that both substrates and catalysts are well mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in cellular environments, where biomolecules can undergo liquid-liquid phase separation (LLPS) and form condensates, leading to important functional outcomes, including the modulation of catalytic action. Similar processes may also play a role in protocellular systems, like primitive coacervates, or in membrane-assisted prebiotic pathways. Here we explore whether the de-mixing of catalysts could lead to the formation of micro-environments that influence the kinetics of a linear (multi-step) reaction pathway, as compared to a WM system. We implemented a general lattice model to simulate LLPS of an ensemble of different catalysts and extended it to include diffusion and a sequence of reactions of small substrates. We carried out a quantitative analysis of how the phase separation of the catalysts affects reaction times depending on the affinity between substrates and catalysts, the length of the reaction pathway, the system size, and the degree of homogeneity of the condensate. A key aspect underlying the differences reported between the two scenarios is that the scale invariance observed in the WM system is broken by condensation processes. The main theoretical implications of our results for mean-field chemistry are drawn, extending the mass action kinetics scheme to include substrate initial hitting times to reach the catalysts condensate. We finally test this approach by considering open non-linear conditions, where we successfully predict, through microscopic simulations, that phase separation inhibits chemical oscillatory behaviour, providing a possible explanation for the marginal role that this complex dynamic behaviour plays in real metabolisms.

cond-mat.stat-mech↗

arXiv2022

Statistical modeling of adaptive neural networks explains coexistence of avalanches and oscillations in resting human brain

Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equilibrium feedback-driven Ising like class of neural networks that simultaneously and quantitatively captures scale-free avalanches and scale-specific oscillations. In the most simple yet fully microscopic model version we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations and collective behaviors of nearly-synchronous extreme events on multiple sensors, to neuronal avalanches unfolding over multiple sensors across multiple time bins. Importantly, the inferred parameters correlate with model-independent signatures of "closeness to criticality", indicating that the coexistence of scale-specific (neural oscillations) and scale-free (neuronal avalanches) dynamics in brain activity occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations.

q-bio.NC↗

arXiv2022

Relationship between fitness and heterogeneity in exponentially growing microbial populations

Despite major environmental and genetic differences, microbial metabolic networks are known to generate consistent physiological outcomes across vastly different organisms. This remarkable robustness suggests that, at least in bacteria, metabolic activity may be guided by universal principles. The constrained optimization of evolutionarily-motivated objective functions like the growth rate has emerged as the key theoretical assumption for the study of bacterial metabolism. While conceptually and practically useful in many situations, the idea that certain functions are optimized is hard to validate in data. Moreover, it is not always clear how optimality can be reconciled with the high degree of single-cell variability observed in experiments within microbial populations. To shed light on these issues, we develop an inverse modeling framework that connects the fitness of a population of cells (represented by the mean single-cell growth rate) to the underlying metabolic variability through the Maximum-Entropy inference of the distribution of metabolic phenotypes from data. While no clear objective function emerges, we find that, as the medium gets richer, the fitness and inferred variability for Escherichia coli populations follow and slowly approach the theoretically optimal bound defined by minimal reduction of variability at given fitness. These results suggest that bacterial metabolism may be crucially shaped by a population-level trade-off between growth and heterogeneity.

q-bio.MN↗

arXiv2020

Epidemic oscillations induced by social network control: the discontinuous case

Epidemic spreading can be suppressed by the introduction of containment measures such as social distancing and lock downs. Yet, when such measures are relaxed, new epidemic waves and infection cycles may occur. Here we explore this issue in compartmentalized epidemic models on graphs in presence of a feedback between the infection state of the population and the structure of its social network for the case of discontinuous control. We show that in random graphs the effect of containment measures is simply captured by a renormalization of the effective infection rate that accounts for the change in the branching ratio of the network. In our simple setting, a piece-wise mean-field approximations can be used to derive analytical formulae for the number of epidemic waves and their length. A variant of the model with imperfect information is used to model data of the recent covid-19 epidemics in the Basque Country and Lombardy, where we estimate the extent of social network disruption during lock downs and characterize the dynamical attractors.

physics.soc-ph↗

arXiv2019

Oscillations in feedback driven systems: thermodynamics and noise

Oscillations in nonequilibrium noisy systems are important physical phenomena. These oscillations can happen in autonomous biochemical oscillators such as circadian clocks. They can also manifest as subharmonic oscillations in periodically driven systems such as time-crystals. Oscillations in autonomous systems and, to a lesser degree, subharmonic oscillations in periodically driven systems have been both thoroughly investigated, including their relation with thermodynamic cost and noise. We perform a systematic study of oscillations in a third class of nonequilibrium systems: feedback driven systems. In particular, we use the apparatus of stochastic thermodynamics to investigate the role of noise and thermodynamic cost in feedback driven oscillations. For a simple two-state model that displays oscillations, we analyze the relation between precision and dissipation, revealing that oscillations can remain coherent for an indefinite time in a finite system with thermal fluctuations in a limit of diverging thermodynamic cost. We consider oscillations in a more complex system with several degrees of freedom, an Ising model driven by feedback between the magnetization and the external field. This feedback driven system can display subharmonic oscillations similar to the ones observed in time-crystals. We illustrate the second law for feedback driven systems that display oscillations. For the Ising model, the oscillating dissipated heat can be negative. However, when we consider the total entropy that also includes an informational term related to measurements, the oscillating total entropy change is always positive. We also study the finite-size scaling of the dissipated heat, providing evidence for the existence of a first-order phase transition for certain parameter regimes.

cond-mat.stat-mech↗

arXiv2018

On the origin of self-oscillations in large systems

In this article is shown that large systems endowing phase coexistence display self-oscillations in presence of linear feedback between the control and order parameters, where an Andronov-Hopf bifurcation takes over the phase transition. This is simply illustrated through the mean field Landau theory whose feedback dynamics turns out to be described by the Van der Pol equation and it is then validated for the fully connected Ising model following heat bath dynamics. Despite its simplicity, this theory accounts potentially for a rich range of phenomena: here it is applied to describe in a stylized way i) excess demand-price cycles due to strong herding in a simple agent-based market model; ii) congestion waves in queueing networks triggered by users feedback to delays in overloaded conditions; iii) metabolic network oscillations resulting from cell growth control in a bistable phenotypic landscape.

cond-mat.stat-mech↗

arXiv2017

A Van-Der-Waals picture for metabolic networks from MaxEnt modeling: inherent bistability and elusive coexistence

In this work maximum entropy distributions in the space of steady states of metabolic networks are defined upon constraining the first and second moment of the growth rate. Inherent bistability of fast and slow phenotypes, akin to a Van-Der Waals picture, emerges upon considering control on the average growth (optimization/repression) and its fluctuations (heterogeneity). This is applied to the carbon catabolic core of E.coli where it agrees with some stylized facts on the persisters phenotype and it provides a quantitative map with metabolic fluxes, opening for the possibility to detect coexistence from flux data. Preliminary analysis on data for E.Coli cultures in standard conditions shows, on the other hand, degeneracy for the inferred parameters that extend in the coexistence region.

q-bio.MN↗

arXiv2017

Constraint-based inverse modeling of metabolic networks: a proof of concept

We consider the problem of inferring the probability distribution of flux configurations in metabolic network models from empirical flux data. For the simple case in which experimental averages are to be retrieved, data are described by a Boltzmann-like distribution ($\propto e^{F/T}$) where $F$ is a linear combination of fluxes and the `temperature' parameter $T\geq 0$ allows for fluctuations. The zero-temperature limit corresponds to a Flux Balance Analysis scenario, where an objective function ($F$) is maximized. As a test, we have inverse modeled, by means of Boltzmann learning, the catabolic core of Escherichia coli in glucose-limited aerobic stationary growth conditions. Empirical means are best reproduced when $F$ is a simple combination of biomass production and glucose uptake and the temperature is finite, implying the presence of fluctuations. The scheme presented here has the potential to deliver new quantitative insight on cellular metabolism. Our implementation is however computationally intensive, and highlights the major role that effective algorithms to sample the high-dimensional solution space of metabolic networks can play in this field.

q-bio.MN↗

arXiv2017

Statistical mechanics for metabolic networks during steady-state growth

Which properties of metabolic networks can be derived solely from stoichiometric information about the network's constituent reactions? Predictive results have been obtained by Flux Balance Analysis (FBA), by postulating that cells set metabolic fluxes within the allowed stoichiometry so as to maximize their growth. Here, we generalize this framework to single cell level using maximum entropy models from statistical physics. We define and compute, for the core metabolism of Escherichia coli, a joint distribution over all fluxes that yields the experimentally observed growth rate. This solution, containing FBA as a limiting case, provides a better match to the measured fluxes in the wild type and several mutants. We find that E. coli metabolism is close to, but not at, the optimality assumed by FBA. Moreover, our model makes a wide range of predictions: (i) on flux variability, its regulation, and flux correlations across individual cells; (ii) on the relative importance of stoichiometric constraints vs. growth rate optimization; (iii) on quantitative scaling relations for singe-cell growth rate distributions. We validate these scaling predictions using data from individual bacterial cells grown in a microfluidic device at different sub-inhibitory antibiotic concentrations. Under mild dynamical assumptions, fluctuation-response relations further predict the autocorrelation timescale in growth data and growth rate adaptation times following an environmental perturbation.

q-bio.MN↗

arXiv2017

The free lunch of a scale-free metabolism

In this work it is shown that scale free tails in metabolic flux distributions inferred from realistic large scale models can be simply an artefact due to reactions involved in thermodynamically unfeasible cycles, that are unbounded by physical constraints and would be able to perform work without expenditure of free energy. After correcting for thermodynamics, the metabolic space scales meaningfully with the physical limiting factors, acquiring in turn a richer multimodal structure potentially leading to symmetry breaking while optimizing for objective functions.

q-bio.MN↗