arXiv subjects

Mauricio Girardi-Schappo

Publications and source records attributed to Mauricio Girardi-Schappo.

13 recordsLinked to original sources

arXiv2026

Learning About Learning: A Path from Spin Glasses to Artificial Intelligence

The Hopfield model, originally inspired by spin glasses, occupies a central place at the intersection of statistical mechanics, neural networks, and artificial intelligence. Despite its conceptual simplicity and broad applicability, it is rarely integrated into the undergraduate physics curriculum. We present the Hopfield model as a pedagogically rich framework that naturally unifies core topics from the undergraduate physics curriculum and that provides a concise introduction based on concepts such as a model's energy function, dynamics, and pattern stability. We discuss practical aspects of its simulation and provide simulation codes. We also propose problems designed to mirror research practice, which can be included in undergraduate classes.

cond-mat.dis-nn↗

arXiv2025

Optimal rate-variance coding due to firing threshold adaptation near criticality

Recurrently connected neuron populations play key roles in sensory perception and memory storage across various brain regions. While these populations are often assumed to encode information through firing rates, this method becomes unreliable with weak stimuli. We propose that in such cases, information can be transmitted via spatial spike patterns, employing a sparse or combinatorial coding based on firing rate variance. Around the critical point of a stochastic recurrent excitable network, we uncover a synergistic dual-coding scheme, enabled by single-cell threshold adaptation. This scheme optimizes variance coding for weak signals without compromising rate coding for stronger inputs, thus maximizing input/output mutual information. These optimizations are robust across adaptation rules and coupling strengths through self-suppression of internal noise, particularly around the network's phase transition, and are linked to threshold recovery times observed in hippocampal memory circuits (~$10^2$-$10^3$ms). In contrast, nonadaptive networks perform similarly only at criticality, suggesting that threshold adaptation is essential for reliable encoding of weak signals into diverse spatial patterns. Our results imply a fundamental role for near-critical latent adaptive dynamics enabled by dual coding in biological and artificial neural networks.

q-bio.NC↗

arXiv2025

Devil's staircase inside shrimp-shaped regions reveals periodicity of plateau spikes and bursts

Slow-fast dynamics are intrinsically related to complex phenomena and are responsible for many of the homeostatic dynamics that keep biological systems healthy functioning. We study a discrete-time membrane potential model that can generate a diverse set of spiking behavior depending on the choice of slow-fast time scales, from fast spiking to bursting, or plateau action potentials -- also known as cardiac spikes since they are characteristic in heart myocytes. The plateau of cardiac spikes can lose stability, generating early or delayed afterdepolarizations (EADs and DADs, respectively), both of which are related to cardiac arrhythmia. We show the periodicity changes along the transition from the healthy action potentials to these impaired oscillations. We show that while EADs are mainly periodic attractors, DADs usually come with chaos. EADs are found inside shrimp-shaped regions of the parameter space. However, in our system, multiple periodic attractors live within a shrimp-shaped region, giving it an internal structure made of infinite transitions between periodicities forming a complete devil's staircase. Understanding the periodicity of plateau attractors in slow-fast systems could be useful in unveiling the characteristics of heart myocyte behaviors that are linked to cardiac arrhythmias.

physics.bio-ph↗

arXiv2024

Optimal input reverberation and homeostatic self-organization towards the edge of synchronization

Transient or partial synchronization can be used to do computations, although a fully synchronized network is frequently related to epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization.

nlin.AO↗

arXiv2022

Homeostatic Criticality in Neuronal Networks

In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing external fields $h \to 0$. Considering that this is rarely the case for natural systems, such a restriction poses a challenge to the explanatory power of these models. Besides that, in models of dissipative systems like earthquakes, forest fires, and neuronal networks, there is no true critical behavior, as expressed in clean power laws obeying finite-size scaling, but a scenario called "dirty" criticality or self-organized quasi-criticality (SOqC). Here, we propose simple homeostatic mechanisms which promote self-organization of coupling strengths, gains, and firing thresholds in neuronal networks. We show that with an adequate separation of the timescales for the coupling strength and firing threshold dynamics, near criticality (SOqC) can be reached and sustained even in the presence of significant external input. The firing thresholds adapt to and cancel the inputs ($h$ decreases towards zero). Similar mechanisms can be proposed for the couplings and local thresholds in spin systems and cellular automata, which could lead to applications in earthquake, forest fire, stellar flare, voting, and epidemic modeling.

nlin.AO↗

arXiv2021

Building a model of the brain: from detailed connectivity maps to network organization

The field of computational modeling of the brain is advancing so rapidly that now it is possible to model large scale networks representing different brain regions with a high level of biological detail in terms of numbers and synapses. For a theoretician approaching a neurobiological question, it is important to analyze the pros and cons of each of the models available. Here, we provide a tutorial review on recent models for different brain circuits, which are based on experimentally obtained connectivity maps. We discuss particularities that may be relevant to the modeler when choosing one of the reviewed models. The objective of this review is to give the reader a fair notion of the computational models covered, with emphasis on the corresponding connectivity maps, and how to use them.

physics.bio-ph↗

arXiv2021

Granger causality in the frequency domain: derivation and applications

Physicists are starting to work in areas where noisy signal analysis is required. In these fields, such as Economics, Neuroscience, and Physics, the notion of causality should be interpreted as a statistical measure. We introduce to the lay reader the Granger causality between two time series and illustrate ways of calculating it: a signal $X$ ``Granger-causes'' a signal $Y$ if the observation of the past of $X$ increases the predictability of the future of $Y$ when compared to the same prediction done with the past of $Y$ alone. In other words, for Granger causality between two quantities it suffices that information extracted from the past of one of them improves the forecast of the future of the other, even in the absence of any physical mechanism of interaction. We present derivations of the Granger causality measure in the time and frequency domains and give numerical examples using a non-parametric estimation method in the frequency domain. Parametric methods are addressed in the Appendix. We discuss the limitations and applications of this method and other alternatives to measure causality.

physics.data-an↗

arXiv2020

Subsampled directed-percolation models explain scaling relations experimentally observed in the brain

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.

q-bio.NC↗

arXiv2019

Comment on "Convergence towards asymptotic state in 1-D mappings: A scaling investigation"

Nonequilibrium phase transitions are characterized by the so-called critical exponents, each of which is related to a different observable. Systems that share the same set of values for these exponents also share the same universality class. Thus, it is important that the exponents are named and treated in a standardized framework. In this comment, we reinterpret the exponents obtained in [Phys Lett A 379:1246-12 (2015)] for the logistic and cubic maps in order to correctly state the universality class of their bifurcations, since these maps may describe the mean-field solution of stochastic spreading processes.

nlin.AO↗

arXiv2019

Self-organized critical balanced networks: a unified framework

Asynchronous irregular (AI) and critical states are two competing frameworks proposed to explain spontaneous neuronal activity. Here, we propose a mean-field model with simple stochastic neurons that generalizes the integrate-and-fire network of Brunel (2000). We show that the point with balanced inhibitory/excitatory synaptic weight ratio $g_c \approx 4$ corresponds to a second order absorbing phase transition usual in self-organized critical (SOC) models. At the synaptic balance point $g_c$, the network exhibits power-law neuronal avalanches with the usual exponents, whereas for nonzero external field the system displays the four usual synchronicity states of balanced networks. We add homeostatic inhibition and firing rate adaption and obtain a self-organized quasi-critical balanced state with avalanches and AI-like activity. Our model might explain why different inhibition levels are obtained in different experimental conditions and for different regions of the brain, since at least two dynamical mechanisms are necessary to obtain a truly balanced state, without which the network may hover in different regions of the presented theoretical phase diagram.

nlin.AO↗

arXiv2018

Measuring neuronal avalanches in disordered systems with absorbing states

Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.

physics.bio-ph↗

arXiv2016

Griffiths phase and long-range correlations in a biologically motivated V1 model

Activity in the brain propagates as waves of firing neurons, namely avalanches. These waves' size and duration distributions have been experimentally shown to display a stable power-law profile, long-range correlations and $1/f^{b}$ power spectrum \textit{in vivo} and \textit{in vitro}. We study an avalanching biologically motivated model of mammals visual cortex and find an extended critical-like region -- a Griffiths phase -- characterized by divergent susceptibility and zero order parameter. This phase lies close to the expected experimental value of the \textit{excitatory postsynaptic potential} in the cortex suggesting that critical behavior may be found in the visual system. Avalanches are not perfectly power-law distributed, but it is possible to collapse the distributions and define a cutoff avalanche size that diverges as the network size is increased inside the critical region. The avalanches present long-range correlations and $1/f^{b}$ power spectrum, matching experiments. The phase transition is analytically determined by a mean-field approximation.

q-bio.NC↗

arXiv2013

Critical Avalanches and Subsampling in Map-based Neural Networks

We investigate the synaptic noise as a novel mechanism for creating critical avalanches in the activity of neural networks. We model neurons and chemical synapses by dynamical maps with a uniform noise term in the synaptic coupling. An advantage of utilizing maps is that the dynamical properties (action potential profile, excitability properties, post synaptic potential summation etc.) are not imposed to the system, but occur naturally by solving the system equations. We discuss the relevant neuronal and synaptic properties to achieve the critical state. We verify that networks of excitatory by rebound neurons with fast synapses present power law avalanches. We also discuss the measuring of neuronal avalanches by subsampling our data, shedding light on the experimental search for Self-Organized Criticality in neural networks.

cond-mat.dis-nn↗