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Miguel A. Muñoz

Publications and source records attributed to Miguel A. Muñoz.

At least 19 recordsLinked to original sources
arXiv2026

Fluctuating Environments Favor Extreme Reproductive Delays and Penalize Intermediate Ones

The timing of reproduction is crucial for biological fitness. Reproductive delays carry an inherent demographic cost: an individual that takes longer to reproduce contributes later to population growth, a priori, without any compensating benefit. However, natural selection favors delayed reproduction under certain environmental conditions, a phenomenon that remains poorly understood. Here, we investigate how the environment can determine the evolution of particular life histories using a parsimonious delayed-logistic model. Individuals become reproductive only after a fixed lag whereas birth rates fluctuate under temporally correlated stochasticity. Numerical integration, analytical calculations and evolutionary simulations reveal that the joint effect of demographic memory and colored multiplicative noise generate a strongly nonmonotonic dependence of fitness on life history, with three distinct regimes of population performance: rapid reproduction maximizes linear growth but amplifies fluctuations and extinction risk; delayed reproduction buffers environmental variability, substantially increasing mean extinction times despite slower growth; strikingly, and central to our results, there is a broad band of maladaptive intermediate life histories that simultaneously reduce both growth and persistence, an effect that arises generically from the mismatch between reproductive timing and environmental autocorrelation. Our results show that reproductive timing is not merely a life-history parameter but an adaptive mechanism tuned to environmental time scales, and that "dangerous middle" maturation times can be inherently disfavored, with implications for understanding reproductive strategies across the tree of life.

q-bio.PE↗
arXiv2026

Driven criticality links universal computation and optimal representations

Near-critical dynamics are often linked to enhanced computation, but the underlying mechanism remains unclear. We address this question in reservoir computing, where a fixed recurrent network maps input sequences into high-dimensional states and only a simple readout is trained. We extend fixed-reservoir universality results to discrete-time input-driven reservoirs and connect their key geometric condition, neighborhood separation, to dynamics. To this end, we introduce a finite-resolution neighborhood separability index and an input-conditioned maximal Lyapunov exponent. We find that neighborhood separability, chaotic time-series prediction, and smooth high-dimensional representation geometry are optimized in the same narrow window of marginal driven stability. In this regime, the covariance spectrum approaches the power-law scaling expected for near-optimal smooth representations. Our results link edge-of-instability computation, universality, readout performance, and optimal representation geometry within a common dynamical framework.

cond-mat.dis-nn↗
arXiv2026

The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes to deliver reliable parameter estimation and model selection from coarsely sampled time series, without requiring analytical solutions. Crucially, we couple mechanistic stochastic models with their inference procedures to quantify how experimental design -specifically, sampling frequency and dataset size- governs estimator precision and model distinguishability. This analysis reveals optimal sampling regimes and sharp, resolution-dependent limits beyond which competing models become empirically indistinguishable. We validate the approach across four disparate systems -trajectories of optically trapped particles, human microbiome dynamics, social-media topic mentions, and forest population time series- recovering parameters and identifying when inference is fundamentally constrained by measurement resolution, thereby clarifying ongoing debates about dominant noise sources in these systems. Together, these results establish path-based Monte Carlo as a practical, general tool for inference and model discrimination in complex systems and provide principled guidelines for designing measurements that maximize information under real-world constraints.

cond-mat.stat-mech↗
arXiv2026

From Chaos to Synchrony in Recurrent Excitatory-Inhibitory Networks with Target-Specific Inhibition

Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers (SCS) showed that random recurrent networks undergo a transition from quiescence to asynchronous chaos, establishing a paradigmatic link between random connectivity, dynamical instability, and internally generated fluctuations in neural circuits. Here, we extend this framework to two-population firing-rate networks with segregated excitatory and inhibitory neurons and target-specific inhibitory couplings that break excitation--inhibition balance. Using dynamical mean-field theory, we derive self-consistent equations for the macroscopic mean activities and autocorrelations, together with stability criteria distinguishing mean-driven and fluctuation-driven instabilities. We show that target-specific inhibition organizes the phase diagram into three qualitative classes: inhibition-dominated or strictly balanced networks display only quiescent activity and asynchronous chaos; excitation-dominated networks display persistent activity together with either synchronous chaos with non-vanishing mean activity or coherent oscillations, depending on the stability-matrix eigenvalues. Crucially, coherent oscillations do not coexist with chaotic fluctuations around the periodic mean trajectory; rather, their onset suppresses the chaotic component, reminiscent of input-induced suppression of chaos. These results generalize SCS theory to recurrent networks with explicit excitatory--inhibitory structure and identify target-specific inhibition as a key control parameter for large-scale neural dynamics.

cond-mat.dis-nn↗
arXiv2026

Non-normal Dynamics on Non-reciprocal Networks: Reactivity and Effective Dimensionality in Neural Circuits

Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple levels: locally, in the dynamics of individual units, and globally, in the topology of their interactions. In this work, we investigate how these two forms of non-reciprocity interact in networks of neuronal populations. At the local level, each population is modeled by a non-reciprocally coupled set of excitatory and inhibitory neural populations exhibiting transient amplification and reactivity. At the network level, these populations are coupled via directed, asymmetric connections that introduce structural non-normality. Since non-reciprocal interactions generically lead to non-normal linear operators, we frame both local and global asymmetries in terms of non-normal dynamics. Using a modified Wilson-Cowan framework, we analyze how the interplay between these two types of non-normality shapes the system's behavior. We show that their combination leads to emergent collective dynamics, including fluctuation-driven transitions, dimensionality reduction, and novel nonequilibrium steady states. Our results provide a minimal yet flexible framework to understand how multi-scale non-reciprocities govern complex dynamics in neural and other interconnected systems.

physics.bio-ph↗
arXiv2026

Microbiome association diversity reflects proximity to the edge of instability

Recent advances in metagenomics have revealed macroecological patterns or "laws" describing robust statistical regularities across microbial communities. Stochastic logistic models (SLMs), which treat species as independent -- akin to ideal gases in physics -- and incorporate environmental noise, reproduce many single-species patterns but cannot account for the pairwise covariation observed in microbiome data. Here we introduce an interacting stochastic logistic model (ISLM) that minimally extends the SLM by sampling an ensemble of random interaction networks chosen to preserve these single-species laws. Using dynamical mean-field theory, we map the model's phase diagram -- stable, chaotic, and unbounded-growth regimes -- where the transition from stable fixed-point to chaos is controlled by network sparsity and interaction heterogeneity via a May-like instability line. Going beyond mean-field theory to account for finite communities, we derive an estimator of an effective stability parameter that quantifies distance to the edge of instability and can be inferred from the width of the distribution of pairwise covariances in empirical species-abundance data. Applying this framework to synthetic data, environmental microbiomes, and human gut cohorts indicates that these communities tend to operate near the edge of instability. Moreover, gut communities from healthy individuals cluster closer to this edge and exhibit broader, more heterogeneous associations, whereas dysbiosis-associated states shift toward more stable regimes -- enabling discrimination across conditions such as Crohn's disease, inflammatory bowel syndrome, and colorectal cancer. Together, our results connect macroecological laws, interaction-network ensembles, and May's stability theory, suggesting that complex communities may benefit from operating near a dynamical phase transition.

q-bio.PE↗
arXiv2025

Ergodicity Breaking and High-Dimensional Chaos in Random Recurrent Networks

The neural model introduced by Sompolinsky, Crisanti, and Sommers (SCS) nearly four decades ago has become a paradigmatic framework for studying complex dynamics in random recurrent networks. In its original formulation, with balanced positive and negative couplings, the model exhibits two phases: a quiescent regime, where all activity ceases, and a regime of ongoing irregular collective activity, termed asynchronous chaos (AC), in which state variables fluctuate strongly in time and across units but average to zero across the network. Building on recent work, we analyze an extension of the SCS model that breaks this coupling balance, yielding a richer phase diagram. In addition to the classical quiescent and AC phases, two additional regimes emerge, marked by spontaneous symmetry breaking. In the persistent-activity (PA) phase, each unit settles into a distinct, stable activation state. In the synchronous-chaotic (SC) phase, dynamics remain irregular and chaotic but fluctuate around a nonzero mean, generating sustained long-time autocorrelations. Using analytical techniques based on dynamical mean-field theory, complemented by extensive numerical simulations, we show how structural disorder gives rise to symmetry and ergodicity breaking. Remarkably, the resulting phase diagram closely parallels that of the Sherrington-Kirkpatrick spin-glass model, with the onset of the SC phase coinciding with the transition associated with replica-symmetry breaking. All key features of spin glasses, including ergodicity breaking, have clear counterparts in this recurrent network context, albeit with crucial idiosyncratic differences, highlighting a unified perspective on complexity in disordered systems.

cond-mat.dis-nn↗
arXiv2025

Robust Scaling in Human Brain Dynamics Despite Latent Variables and Limited Sampling Distortions

The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is intrinsic or input-driven. We show that autocorrelated inputs and temporal resolution influence observed scaling exponents in simple neural models. We also demonstrate analytically that under subsampling, non-critical systems driven by independent autocorrelated signals can exhibit strong signatures of apparent criticality. To address these pitfalls, we develop a robust framework and apply it to pooled neural data, revealing resting-state brain activity at the population level is slightly sub-critical yet near-critical. Notably, the extracted critical exponents closely match predictions from a simple recurrent firing-rate model, supporting the emergence of near-critical dynamics from reverberant network activity, with potential implications for information processing and artificial intelligence.

q-bio.NC↗
arXiv2024

Representational Drift and Learning-Induced Stabilization in the Olfactory Cortex

The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Recent experiments show that neural representations for a given stimulus change over time. However, the mechanistic origin for the observed "representational drift" (RD) remains unclear. Here, we propose a biologically-realistic computational model of the piriform cortex to study RD in the mammalian olfactory system by combining two mechanisms for the dynamics of synaptic weights at two separate timescales: spontaneous fluctuations on a scale of days and spike-time dependent plasticity (STDP) on a scale of seconds. Our study shows that, while spontaneous fluctuations in synaptic weights induce RD, STDP-based learning during repeated stimulus presentations can reduce it. Our model quantitatively explains recent experiments on RD in the olfactory system and offers a mechanistic explanation for the emergence of drift and its relation to learning, which may be useful to study RD in other brain regions.

q-bio.NC↗
arXiv2024

Networks with many structural scales: a Renormalization Group perspective

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a constant entropy-loss rate across scales in a renormalization-group coarse-graining setting. This framework enables us to differentiate between scale-free and scale-invariant networks, revealing distinct characteristics within each class. Furthermore, we offer a comprehensive inventory of genuinely scale-invariant networks, both natural and artificially constructed, demonstrating, e.g., that the human connectome exhibits notable features of scale invariance. Our findings open new avenues for exploring the scale-invariant structural properties crucial in biological and socio-technological systems.

cond-mat.stat-mech↗
arXiv2024

Stochastic trade-offs and the emergence of diversification in E. coli evolution experiments

Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such ''evolutionary branching'' occurs stochastically, even under fixed and stable conditions. This stochastic nature is characterized by: (i) occurrence in a significant fraction, but not all, of experimental settings, (ii) emergence at widely varying times, and (iii) variable relative abundances of the resulting subpopulations across experiments. Theoretical approaches to understanding evolutionary branching under these conditions have been previously developed within the (deterministic) framework of ''adaptive dynamics''. Here, we advance the understanding of the stochastic nature of evolutionary outcomes by introducing the concept of ''stochastic trade-offs'' as opposed to ''hard'' ones. The key idea is that the stochasticity of mutations occurs in a high-dimensional trait space and this translates into variability that is constrained to a flexible tradeoff curve. By incorporating this additional source of stochasticity, we are able to account for the observed empirical variability and make predictions regarding the likelihood of evolutionary branching under different conditions. This approach effectively bridges the gap between theoretical predictions and experimental observations, providing insights into when and how evolutionary branching is more likely to occur in laboratory experiments.

q-bio.PE↗
arXiv2024

Frequency-dependent covariance reveals critical spatio-temporal patterns of synchronized activity in the human brain

Recent analyses combining advanced theoretical techniques and high-quality data from thousands of simultaneously recorded neurons provide strong support for the hypothesis that neural dynamics operate near the edge of instability across regions in the brain. However, these analyses, as well as related studies, often fail to capture the intricate temporal structure of brain activity as they primarily rely on time-integrated measurements across neurons. In this study, we present a novel framework designed to explore signatures of criticality across diverse frequency bands and construct a much more comprehensive description of brain activity. Additionally, we introduce a method for projecting brain activity onto a basis of spatio-temporal patterns, facilitating time-dependent dimensionality reduction. Applying this framework to a magnetoencephalography dataset, we observe significant differences in both criticality signatures and spatio-temporal activity patterns between healthy subjects and individuals with Parkinson's disease.

q-bio.NC↗
arXiv2024

From asynchronous states to Griffiths phases and back: structural heterogeneity and homeostasis in excitatory-inhibitory networks

Balanced neural networks -- in which excitatory and inhibitory inputs compensate each other on average -- give rise to a dynamical phase dominated by fluctuations called asynchronous state, crucial for brain functioning. However, structural disorder -- which is inherent to random networks -- can hinder such an excitation-inhibition balance. Indeed, structural and synaptic heterogeneities can generate extended regions in phase space akin to critical points, called Griffiths phases, with dynamical features very different from those of asynchronous states. Here, we study a simple neural-network model with tunable levels of heterogeneity able to display these two types of dynamical regimes -- i.e., asynchronous states and Griffiths phases -- putting them together within a single phase diagram. Using this simple model, we are able to emphasize the crucial role played by synaptic plasticity and homeostasis to re-establish balance in intrinsically heterogeneous networks. Overall, we shed light onto how diverse dynamical regimes, each with different functional advantages, can emerge from a given network as a result of self-organizing homeostatic mechanisms.

cond-mat.stat-mech↗
arXiv2023

Dynamically selected steady states and criticality in non-reciprocal networks

Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand, systems with non-reciprocal (or asymmetric) interactions are inherently out of equilibrium, and exhibit a rich variety of steady states, including fixed points, limit cycles and chaotic trajectories. How are steady states dynamically selected away from equilibrium? We address this question in a simple neural network model, with a tunable level of non-reciprocity. Our study reveals different types of ordered phases and it shows how non-equilibrium steady states are selected in each phase. In the spin-glass region, the system exhibits marginally stable behaviour for reciprocal (or symmetric) interactions and it smoothly transitions to chaotic dynamics, as the non-reciprocity (or asymmetry) in the couplings increases. Such region, on the other hand, shrinks and eventually disappears when couplings become anti-symmetric. Our results are relevant to advance the knowledge of disordered systems beyond the paradigm of reciprocal couplings, and to develop an interface between statistical physics of equilibrium spin-glasses and dynamical systems theory.

cond-mat.dis-nn↗
arXiv2023

Unveiling the intrinsic dynamics of biological and artificial neural networks: from criticality to optimal representations

Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics should operate at the brink of a phase transition, i.e., at the edge between different collective phases, to entail a rich dynamical repertoire and optimize functional capabilities. In recent years, research guided by the advent of high-throughput data and new theoretical developments has contributed to making a quantitative validation of such a hypothesis. Here we review recent advances in this field, stressing our contributions. In particular, we use data from thousands of individually recorded neurons in the mouse brain and tools such as a phenomenological renormalization group analysis, theory of disordered systems, and random matrix theory. These combined approaches provide novel evidence of quasi-universal scaling and near-critical behavior emerging in different brain regions. Moreover, we design artificial neural networks under the reservoir-computing paradigm and show that their internal dynamical states become near critical when we tune the networks for optimal performance. These results not only open new perspectives for understanding the ultimate principles guiding brain function but also towards the development of brain-inspired, neuromorphic computation.

cond-mat.stat-mech↗
arXiv2023

Depinning in the quenched Kardar-Parisi-Zhang class I: Mappings, simulations and algorithm

Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential energy may generate a different scaling behavior at depinning. The most experimentally relevant is the Kardar-Parisi-Zhang (KPZ) term, proportional to the square of the slope at each site, which drives the critical behavior into the so-called quenched KPZ (qKPZ) universality class. We study this universality class both numerically and analytically: by using exact mappings we show that at least for $d=1,2$ this class encompasses not only the qKPZ equation itself, but also anharmonic depinning and a well-known class of cellular automata introduced by Tang and Leschhorn. We develop scaling arguments for all critical exponents, including size and duration of avalanches. The scale is set by the confining potential strength $m^2$. This allows us to estimate numerically these exponents as well as the $m$-dependent effective force correlator $Δ(w)$, and its correlation length $ρ:= Δ(0)/|Δ'(0^+)|$. Finally we present a new algorithm to numerically estimate the effective ($m$-dependent) elasticity $c$, and the effective KPZ non-linearity $λ$. This allows us to define a dimensionless universal KPZ amplitude ${\cal A}:=ρλ/c$, which takes the value ${\cal A}=1.10(2)$ in all systems considered in $d=1$. This proves that qKPZ is the effective field theory for all these models. Our work paves the way for a deeper understanding of depinning in the qKPZ class, and in particular, for the construction of a field theory that we describe in a companion paper.

cond-mat.dis-nn↗
arXiv2023

Unconventional criticality, scaling breakdown, and diverse universality classes in the Wilson-Cowan model of neural dynamics

The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural networks at a mean-field level, e.g., assuming large fully-connected networks. Moreover, its stochastic counterpart allows one to study fluctuation-induced phenomena, such as avalanches. Here, we revisit the stochastic Wilson-Cowan model paying special attention to the possible phase transitions between quiescent and active phases. We unveil eight possible types of phase transitions, including continuous ones with scaling behavior belonging to known universality classes -- such as directed percolation and tricritical directed percolation -- as well as novel ones. In particular, we show that under some special circumstances, at a so-called Hopf tricritical directed percolation transition, rather unconventional behavior including an anomalous breakdown of scaling emerges. These results broaden our knowledge of the possible types of critical behavior in networks of excitatory and inhibitory units and are of relevance to understanding avalanche dynamics in actual neuronal recordings. From a more general perspective, these results help extend the theory of non-equilibrium phase transitions into quiescent or absorbing states.

cond-mat.stat-mech↗
arXiv2023

Anomalous finite-size scaling in higher-order processes with absorbing states

We study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory (also referred to as Wentzel-Kramers-Brillouin (WKB) method in some contexts). We obtain a general expression for the leading and next-to-leading terms of the stationary probability distribution of the fraction of "active" sites, as a function of parameters and network size $N$. We reproduce several results from the literature and, in particular, we derive all the moments of the stationary distribution for the $q$-susceptible-infected-susceptible ($q-SIS$) model, i.e., a high-order epidemic model requiring of $q$ active ("infected") sites to activate an additional one. We uncover a very rich scenario for the fluctuations of the fraction of active sites, with non-trivial finite-size-scaling properties. In particular, we show that the variance-to-mean ratio diverges at criticality for $[1 \leq q\leq 3]$, with a maximal variability at $q=2$, confirming that complex-contagion processes can exhibit peculiar scaling features including wild variability and that the leading-order in a large-deviation approach does not suffice to describe them: next-to-leading terms are essential to capture the intrinsic singularity at the origin of systems with absorbing states.

cond-mat.stat-mech↗