arXiv subjects

Dante R. Chialvo

Publications and source records attributed to Dante R. Chialvo.

At least 19 recordsLinked to original sources

arXiv2026

Susceptibility for extremely low external fluctuations and critical behaviour of Greenberg-Hastings neuronal model

We consider the scaling behaviour of the fluctuation susceptibility associated with the average activation in the Greenberg-Hastings neural network model and its relation to microscopic spontaneous activation. We found that, as the spontaneous activation probability tends to zero, a clear finite size scaling behaviour in the susceptibility emerges, characterized by critical exponents which follow already known scaling laws. This shows that the spontaneous activation probability plays the role of an external field conjugated to the order parameter of the dynamical activation transition. The roles of different kinds of activation mechanisms around the different dynamical phase transitions exhibited by the model are characterized numerically and using a mean field approximation.

cond-mat.dis-nn↗

arXiv2026

Data-driven inference of brain dynamical states from the r-spectrum of correlation matrices

We present a data-driven framework to characterize large-scale brain dynamical states directly from correlation matrices at the single-subject level. By treating correlation thresholding as a percolation-like probe of connectivity, the approach tracks multiple cluster- and network-level observables and identifies a characteristic percolation threshold, rc, at which these signatures converge. We use $r_c$ as an operational and physically interpretable descriptor of large-scale brain dynamical state. Applied to resting-state fMRI data from a large cohort of healthy individuals (N = 996), the method yields stable, subject-specific estimates that covary systematically with established dynamical indicators such as temporal autocorrelations. Numerical simulations of a whole-brain model with a known critical regime further show that $r_c$ tracks changes in collective dynamics under controlled variations of excitability. By replacing arbitrary threshold selection with a criterion intrinsic to correlation structure, the r-spectra provides a physically grounded approach for comparing brain dynamical states across individuals.

q-bio.NC↗

arXiv2025

Optimal Griffiths Phase in Heterogeneous Human Brain Networks: Brain Criticality Embracing Stability and Flexibility across Individuals

A prominent hypothesis in neuroscience proposes that brains achieve optimal performance by operating near a critical point. However, this framework, which often assumes a universal critical point, fails to account for the extensive individual variability observed in neural dynamics and cognitive functions. These variabilities are not noise but rather an inherent manifestation of a fundamental systems-biology principle: the necessary trade-off between robustness and flexibility in human populations. Here, we propose that the Griffiths phase (GP), an extended critical regime synergically induced by two kinds of heterogeneities in brain network region and connectivity, offers a unified framework for brain criticality that better reconciles robustness and flexibility and accounts for individual variability. Using Human Connectome Project data and whole-brain modeling, we demonstrated that the synergic interplay between structural network modularity and regional heterogeneity in local excitability yields biologically viable GP featured with widely extended global excitability ranges, with an embedded optimal point that balances global/local information transmission. Crucially, an individua's position within the GP gives rise to unique global network dynamics, which in turn confer a distinctive cognitive profile via flexible configuration of functional connectivity for segregation, integration, and balance between them. These results establish GP as an evolved adaptive mechanism resolving the robustness-flexibility trade-off, fulfilling diverse cognitive demands through individualized criticality landscapes, providing a new framework of brain criticality.

q-bio.NC↗

arXiv2025

Finite-time scaling on low-dimensional map bifurcations

Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in finite systems. In this work, we extend the finite-time scaling approach in several key directions. First, we present numerical results for 1D maps exhibiting period-doubling bifurcations and discontinuous transitions, analyzing selected paradigmatic examples. We then define two observables, the finite-time susceptibility and the finite-time Lyapunov exponent, that also display consistent scaling near bifurcation points. The method is further generalized to special cases of 2D maps including the 2D Chialvo map, capturing its bifurcation between a fixed point and a periodic orbit, while accounting for discontinuities and asymmetric periodic orbits. These results underscore fundamental connections between temporal and spatial observables in complex systems, suggesting new avenues for studying complex dynamical behavior.

cond-mat.dis-nn↗

arXiv2025

Behavior of the scaling correlation functions under severe subsampling

Scale-invariance is a ubiquitous observation in the dynamics of large distributed complex systems. The computation of its scaling exponents, which provide clues on its origin, is often hampered by the limited available sampling data, making an appropriate mathematical description a challenge. This work investigates the behavior of correlation functions in fractal systems under conditions of severe subsampling. Analytical and numerical results reveal a striking robustness: the correlation functions continue to capture the expected scaling exponents despite substantial data reduction. This behavior is demonstrated numerically for the random 2-D Cantor set and the Sierpinski gasket, both consistent with exact analytical predictions. Similar robustness is observed in 1-D time series both synthetic and experimental, as well as in high-resolution images of a neuronal structure. Overall, these findings are broadly relevant for the structural characterization of biological systems under realistic sampling constraints.

physics.comp-ph↗

arXiv2025

Using Space-Filling Curves and Fractals to Reveal Spatial and Temporal Patterns in Neuroimaging Data

We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis (DFA). The method is suitable for multidimensional geometrically embedded data, especially for neuroimaging data which is highly correlated temporally and spatially. We conduct extensive feasibility studies on diverse, artificially generated data with known fractal characteristics: the fractional Brownian motion, Cantor sets, and Gaussian processes. We compare the suitability of dimensionality reduction via Hilbert SFC and a data-driven alternative. FSCA is then successfully applied to real-world magnetic resonance imaging (MRI) and functional MRI (fMRI) scans. The method utilizing Hilbert curves is optimized for computational efficiency, proven robust against boundary effects typical in experimental data analysis, and resistant to data sub-sampling. It is able to correctly quantify and discern correlations in both stationary and dynamic two-dimensional images. In MRI Alzheimer's dataset, patients reveal a progression of the disease associated with a systematic decrease of the Hurst exponent. In fMRI recording of breath-holding task, the change in the exponent allows distinguishing different experimental phases. This study introduces a robust method for fractal characterization of spatial and temporal correlations in many types of multidimensional neuroimaging data. Very few assumptions allow it to be generalized to more dimensions than typical for neuroimaging and utilized in other scientific fields. The method can be particularly useful in analyzing fMRI experiments to compute markers of pathological conditions resulting from neurodegeneration. We also showcase its potential for providing insights into brain dynamics in task-related experiments.

q-bio.NC↗

arXiv2024

On the linear scaling of entropy vs. energy in human brain activity, the Hagedorn temperature and the Zipf law

It is well established that the brain spontaneously traverses through a very large number of states. Nevertheless, despite its relevance to understanding brain function, a formal description of this phenomenon is still lacking. To this end, we introduce a machine learning based method allowing for the determination of the probabilities of all possible states at a given coarse-graining, from which all the thermodynamics can be derived. This is a challenge not unique to the brain, since similar problems are at the heart of the statistical mechanics of complex systems. This paper uncovers a linear scaling of the entropies and energies of the brain states, a behaviour first conjectured by Hagedorn to be typical at the limiting temperature in which ordinary matter disintegrates into quark matter. Equivalently, this establishes the existence of a Zipf law scaling underlying the appearance of a wide range of brain states. Based on our estimation of the density of states for large scale functional magnetic resonance imaging (fMRI) human brain recordings, we observe that the brain operates asymptotically at the Hagedorn temperature. The presented approach is not only relevant to brain function but should be applicable for a wide variety of complex systems.

q-bio.NC↗

arXiv2024

Uncontrolled learning: co-design of neuromorphic hardware topology for neuromorphic algorithms

Hardware-based neuromorphic computing remains an elusive goal with the potential to profoundly impact future technologies and deepen our understanding of emergent intelligence. The learning-from-mistakes algorithm is one of the few training algorithms inspired by the brain's simple learning rules, utilizing inhibition and pruning to demonstrate self-organized learning. Here we implement this algorithm in purely neuromorphic memristive hardware through a co-design process. This implementation requires evaluating hardware trade-offs and constraints. It has been shown that learning-from-mistakes successfully trains small networks to function as binary classifiers and perceptrons. However, without tailoring the hardware to the algorithm, performance decreases exponentially as the network size increases. When implementing neuromorphic algorithms on neuromorphic hardware, we investigate the trade-offs between depth, controllability, and capacity, the latter being the number of learnable patterns. We emphasize the significance of topology and the use of governing equations, demonstrating theoretical tools to aid in the co-design of neuromorphic hardware and algorithms. We provide quantitative techniques to evaluate the computational capacity of a neuromorphic device based on the measurements performed and the underlying circuit structure. This approach shows that breaking the symmetry of a neural network can increase both the controllability and average network capacity. By pruning the circuit, neuromorphic algorithms in all-memristive device circuits leverage stochastic resources to drive local contrast in network weights. Our combined experimental and simulation efforts explore the parameters that make a network suited for displaying emergent intelligence from simple rules.

cond-mat.dis-nn↗

arXiv2023

Mean-field solution of the neural dynamics in a Greenberg-Hastings model with excitatory and inhibitory units

We present a mean field solution of the dynamics of a Greenberg-Hastings neural network with both excitatory and inhibitory units. We analyse the dynamical phase transitions that appear in the stationary state as the model parameters are varied. Analytical solutions are compared with numerical simulations of the microscopic model defined on a fully connected network. We found that the stationary state of this system exhibits a first order dynamical phase transition (with the associated hysteresis) when the fraction of inhibitory units $f< f_t \leq 1/2$, even for a finite system. In finite systems, when $f > f_t$ the first order transition is replaced by a pseudo critical one, namely a continuous crossover between regions of low and high activity that resembles the finite size behaviour of a continuous phase transition order parameter. However, in the thermodynamic limit, we found that $f_t\to 1/2$ and the activity for $f\geq f_t$ becomes negligible for any value of $T>0$, while the first order transition for $f<f_t$ remains.

cond-mat.dis-nn↗

arXiv2023

Beehive scale-free emergent dynamics

It has been repeatedly reported that the collective dynamics of social insects exhibit universal emergent properties similar to other complex systems. In this note, we study a previously published data set in which the positions of thousands of honeybees in a hive are individually tracked over multiple days. The results show that the hive dynamics exhibit long-range spatial and temporal correlations in the occupancy density fluctuations, despite the characteristic short-range bees' mutual interactions. The variations in the occupancy unveil a non-monotonic function between density and bees' flow, reminiscent of the car traffic dynamic near a jamming transition at which the system performance is optimized to achieve the highest possible throughput. Overall, these results suggest that the beehive collective dynamics are self-adjusted towards a point near its optimal density.

q-bio.QM↗

arXiv2023

Scale-free correlations in the dynamics of a small (N ~ 10000) cortical network

The advent of novel opto-genetics technology allows the recording of brain activity with a resolution never seen before. The characterisation of these very large data sets offers new challenges as well as unique theory-testing opportunities. Here we discuss whether the spatial and temporal correlation of the collective activity of thousands of neurons are tangled as predicted by the theory of critical phenomena. The analysis shows that both, the correlation length $ξ$ and the correlation time $τ$ scale as predicted as a function of the system size. With some peculiarities that we discuss, the analysis uncovers new evidence consistent with the view that the large scale brain cortical dynamics corresponds to critical phenomena.

q-bio.NC↗

arXiv2023

Dynamically altered conductance in an Organic Thin Film Memristive Device

The memristive device is one of the basic elements of novel, brain-inspired, fast, and energy-efficient information processing systems in which there is no separation between memorization and information analysis functions. Since the first demonstration of the resistive switching effect, several types of memristive devices have been developed. In most of them, the memristive effect originates from direct modification of the conducting area, e.g. conducting filament formation/disintegration, or semiconductor doping/dedoping. Here, we report a solution-processed lateral memristive device based on a new conductivity modulation mechanism. The device architecture resembles that of an organic field-effect transistor in which the top gate electrode is replaced with an additional insulator layer containing mobile ions. Alteration of the ion distribution under the influence of applied potential changes the electric field, modifying the conductivity of the semiconductor channel. The devices exhibit highly stable current-voltage hysteresis loops and Short-Term Plasticity (STP). We also demonstrate short-term synaptic plasticity with tunable time constants.

cond-mat.mtrl-sci↗

arXiv2023

Self Tuned Criticality: Controlling a neuron near its bifurcation point via temporal correlations

Previous work showed that the collective activity of large neuronal networks can be tamed to remain near its critical point by a feedback control that maximizes the temporal correlations of the mean-field fluctuations. Since such correlations behave similarly near instabilities across nonlinear dynamical systems, it is expected that the principle should control also low dimensional dynamical systems exhibiting continuous or discontinuous bifurcations from fixed points to limit cycles. Here we present numerical evidence that the dynamics of a single neuron can be controlled in the vicinity of its bifurcation point. The approach is tested in two models: a 2D generic excitable map and the paradigmatic FitzHugh-Nagumo neuron model. The results show that in both cases, the system can be self-tuned to its bifurcation point by modifying the control parameter according to the first coefficient of the autocorrelation function.

q-bio.NC↗

arXiv2023

Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network

In this article, a correlation metric $κ_C$ is proposed for the inference of the dynamical state of neuronal networks. $κ_C$ is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

cond-mat.dis-nn↗

arXiv2022

Tricritical behavior in a neural model with excitatory and inhibitory units

While the support for the relevance of critical dynamics to brain function is increasing, there is much less agreement on the exact nature of the advocated critical point. Thus, a considerable number of theoretical efforts are currently concentrated on which mechanisms and what type/s of transition can be exhibited by neuronal networks models. In that direction, the present work describes the effect of incorporating a fraction of inhibitory neurons on the collective dynamics. As we show, this results in the appearence of a tricritical point for highly connected networks and non-zero fraction of inhibitory neurons. We discuss the relation of the present results with relevant experimental evidence.

cond-mat.dis-nn↗

arXiv2022

Scale free density and correlations fluctuations in the dynamics of large microbial ecosystems

Microorganisms self-organize in very large communities exhibiting complex fluctuations. Despite recent advances, still the mechanism by which these systems are able to exhibit large variability at the one hand and dynamical robustness on the other, is not fully explained. With that motivation, here we analyze three aspects of the dynamics of the microbiota and plankton: the density fluctuations, the correlation structure and the avalanching dynamics. In all communities under study we find that the results exhibits scale-free density fluctuations, anomalous variance' scaling, scale-free abundance correlations and stationary scale-free avalanching dynamics. These behaviors, typical in systems exhibiting critical dynamics, suggest criticality as a potential mechanism to explain both the robustness and (paradoxical) high irregularity of processes observed in very large microbial communities.

q-bio.PE↗

arXiv2021

Untangling the brain web: from the early days of complex functional networks to the non-linear dynamical directed functional connectivity measures

Already two decades passed since the first applications of graph theory to brain neuroimaging. Since that early description, the characterization of the brain as a very large interacting complex network has evolved in several directions. In this brief review we discuss our contributions to this topic and discuss some perspective for future work.

q-bio.NC↗

arXiv2021

Apparently similar neuronal dynamics may lead to different collective repertoire

This report is concerned with the relevance of the microscopic rules, that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large scale neuronal networks. One model, due to Greenberg \& Hastings, (GH) can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi \& Copelli, (KC) represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed "activity" branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the inter-neuronal interactions in large scale numerical simulations, in particular when the network topology is far from a mean field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.

cond-mat.dis-nn↗