arXiv subjects

Osame Kinouchi

Publications and source records attributed to Osame Kinouchi.

At least 19 recordsLinked to original sources

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↗

arXiv2023

Less is different: why sparse networks with inhibition differ from complete graphs

In neuronal systems, inhibition contributes to stabilizing dynamics and regulating pattern formation. Through developing mean field theories of neuronal models, using complete graph networks, inhibition is commonly viewed as one ``control parameter'' of the system, promoting an absorbing phase transition. Here, we show that for low connectivity sparse networks, inhibition weight is not a control parameter of the transition. We present analytical and simulation results using generic stochastic integrate-and-fire neurons that, under specific restrictions, become other simpler stochastic neuron models common in literature, which allow us to show that our results are valid for those models as well. We also give a simple explanation about why the inhibition role depends on topology, even when the topology has a dimensionality greater than the critical one. The absorbing transition independence of the inhibitory weight may be an important feature of a sparse network, as it will allow the network to maintain a near-critical regime, self-tuning average excitation, but at the same time, have the freedom to adjust inhibitory weights for computation, learning, and memory, exploiting the benefits of criticality.

cond-mat.dis-nn↗

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

Prime numbers and random walks in a square grid

In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we refer to as Prime Walk. The walk is constructed from a sequence of steps dictated by and dependent on the sequence of last digits of the primes. Despite the apparent randomness of this generating sequence, the resulting structure -- both in 2d and 3d -- created by the algorithm presents remarkable properties and regularities in its pattern that we proceed to analyze in detail.

math.NT↗

arXiv2020

Mechanisms of self-organized quasicriticality in neuronal networks models

The critical brain hypothesis states that there are information processing advantages for neuronal networks working close to the critical region of a phase transition. If this is true, we must ask how the networks achieve and maintain this critical state. Here we review several proposed biological mechanisms that turn the critical region into an attractor of a dynamics in network parameters like synapses, neuronal gains and firing thresholds. Since neuronal networks (biological and models) are nonconservative but dissipative, we expect not exact criticality but self-organized quasicriticality (SOqC), where the system hovers around the critical point.

cond-mat.dis-nn↗

arXiv2020

Physics of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality

Psychophysics try to relate physical input magnitudes to psychological or neural correlates. Microscopic models to account for macroscopic psychophysical laws, in the sense of statistical physics, are an almost unexplored area. Here we examine a sensory epithelium composed of two connected square lattices of stochastic integrate-and-fire cells. With one square lattice we obtain a Stevens's law $ρ\propto h^m$ with Stevens's exponent $m = 0.254$ and a sigmoidal saturation, where $ρ$ is the neuronal network activity and $h$ is the input intensity (external field). We relate Stevens's power law exponent with the field critical exponent as $m = 1/δ_h = β/σ$. We also show that this system pertains to the Directed Percolation (DP) universality class (or perhaps the Compact-DP class). With stacked two layers of square lattices, and a fraction of connectivity between the first and second layer, we obtain at the output layer $ρ_ 2 \propto h^{m_2}$, with $m_2 = 0.08 \approx m^2$, which corresponds to a huge dynamic range. This enhancement of the dynamic range only occurs when the layers are close to their critical point.

nlin.AO↗

arXiv2019

Citation network centrality: a scientific awards predictor?

The $K$-index is an easily computable centrality index in complex networks, such as a scientific citations network. A researcher has a $K$-index equal to $K$ if he or she is cited by $K$ articles that have at least $K$ citations. The $K$-index has several advantages over Hirsh's $h$-index and, in previous studies, has shown better correlation with Nobel prizes than any other index given by the {\em Web of Science}, including the $h$-index. It is plausible that researchers who are the most connected to other scientifically well-connected researchers are the most likely to be doing important work and more likely to be awarded major prizes in a given area. However, the correlation found does not imply causation. Here we perform an experiment using the $K$-index, producing a shortlist of twelve candidates for major scientific prizes, including the Physics Nobel award, in the near future. For example, our top-12 $K$-index list naturally selects the 2019 Nobel laureate, James Peebles. The list can be updated annually and should be compared to laureates of the following years

cs.DL↗

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

Character Networks and Book Genre Classification

We compare the social character networks of biographical, legendary and fictional texts, in search for marks of genre differentiation. We examine the degree distribution of character appearance and find a power law that does not depend on the literary genre or historical content. We also analyze local and global complex networks measures, in particular, correlation plots between the recently introduced Lobby (or Hirsh $H(1)$) index and Degree, Betweenness and Closeness centralities. Assortativity plots, which previous literature claims to separate fictional from real social networks, were also studied. We've found no relevant differences in the books for these network measures and we give a plausible explanation why the previous assortativity result is not correct.

cs.SI↗

arXiv2017

A simple centrality index for scientific social recognition

We introduce a new centrality index for bipartite network of papers and authors that we call $K$-index. The $K$-index grows with the citation performance of the papers that cite a given researcher and can seen as a measure of scientific social recognition. Indeed, the $K$-index measures the number of hubs, defined in a self-consistent way in the bipartite network, that cites a given author. We show that the $K$-index can be computed by simple inspection of the Web of Science platform and presents several advantages over other centrality indexes, in particular Hirsch $h$-index. The $K$-index is robust to self-citations, is not limited by the total number of papers published by a researcher as occurs for the $h$-index and can distinguish in a consistent way researchers that have the same $h$-index but very different scientific social recognition. The $K$-index easily detects a known case of a researcher with inflated number of papers, citations and $h$-index due to scientific misconduct. Finally, we show that, in a sample of twenty-eight physics Nobel laureates and twenty-eight highly cited non-Nobel-laureate physicists, the $K$-index correlates better to the achievement of the prize than the number of papers, citations, citations per paper, citing articles or the $h$-index. Clustering researchers in a $K$ versus $h$ plot reveals interesting outliers that suggest that these two indexes can present complementary independent information.

cs.DL↗

arXiv2017

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality or SOSC) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and dragon king avalanches. We also find that neuronal gains can produce collective oscillations that coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

nlin.AO↗

arXiv2017

A precursor of the sciences of complexity in the XIX century

The sciences of complexity present some recurrent themes: the emergence of qualitatively new behaviors in dissipative systems out of equilibrium, the aparent tendency of complex system to lie at the border of phase transitions and bifurcation points, a historical dynamics which present punctuated equilibrium, a tentative of complementing Darwinian evolution with certain ideas of progress (understood as increase of computational power) etc. Such themes, indeed, belong to a long scientific and philosophical tradiction and, curiously, appear already in the work of Frederick Engels at the 70's of the XIX century. So, the apparent novelity of the sciences of complexity seems to be not situated in its fundamental ideas, but in the use of mathematical and computational models for illustrate, test and develop such ideas. Since politicians as the candidate Al Gore recently declared that the sciences of complexity have influenced strongly their worldview, perhaps it could be interesting to know better the ideas and the ideology related to the notion of complex adaptive systems.

physics.pop-ph↗

arXiv2017

Correlations Induced by Depressing Synapses in Critically Self-Organized Networks with Quenched Dynamics

In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the so-called annealed dynamics). Calculations agree with simulations of the annealed version, showing that the nominal \textit{branching ratio\/} $σ$ converges to unity in the thermodynamic limit, as expected of a self-organized critical system. However, the question remains whether the same results apply to the biological case where only the synapses of firing neurons are depressed (the so-called quenched dynamics). We show that simulations of the quenched model yield significant deviations from $σ=1$ due to spatial correlations. However, the model is shown to be critical, as the largest eigenvalue of the synaptic matrix approaches unity in the thermodynamic limit, that is, $λ_c = 1$ . We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.

nlin.AO↗

arXiv2015

Can dynamical synapses produce true self-organized criticality?

Neuronal networks can present activity described by power-law distributed avalanches presumed to be a signature of a critical state. Here we study a random-neighbor network of excitable cellular automata coupled by dynamical synapses. The model exhibits a very similar to conservative self-organized criticality (SOC) models behavior even with dissipative bulk dynamics. This occurs because in the stationary regime the model is conservative on average, and, in the thermodynamic limit, the probability distribution for the global branching ratio converges to a delta-function centered at its critical value. So, this non-conservative model pertain to the same universality class of conservative SOC models and contrasts with other dynamical synapses models that present only self-organized quasi-criticality (SOqC). Analytical results show very good agreement with simulations of the model and enable us to study the emergence of SOC as a function of the parametric derivatives of the stationary branching ratio.

nlin.AO↗

arXiv2015

The exoplanets analogy to the Multiverse

The idea of a Mutiverse is controversial, although it is a natural possible solution to particle physics and cosmological fine-tuning problems (FTPs). Here I explore the analogy between the Multiverse proposal and the proposal that there exist an infinite number of stellar systems with planets in a flat Universe, the Multiplanetverse. Although the measure problem is present in this scenario, the idea of a Multiplanetverse has predictive power, even in the absence of direct evidence for exoplanets that appeared since the 90s. We argue that the fine-tuning of Earth to life (and not only the fine-tuning of life to Earth) could predict with certainty the existence of exoplanets decades or even centuries before that direct evidence. Several other predictions can be made by studying only the Earth and the Sun, without any information about stars. The analogy also shows that theories that defend that the Earth is the unique existing planet and that, at the same time, is fine-tuned to life by pure chance (or pure physical necessity from a parameter free Theory of Everything) are misguided, and alike opinions about our Universe are similarly delusional.

physics.gen-ph↗

arXiv2015

Nonsynchronous updating in the multiverse of cellular automata

In this paper we study updating effects on cellular automata rule space. We consider a subset of 6144 order-3 automata from the space of 262144 bi-dimensional outer-totalistic rules. We compare synchronous to asynchronous and sequential updatings. Focusing on two automata, we discuss how update changes destroy typical structures of these rules. Besides, we show that the first-order phase-transition in the multiverse of synchronous cellular automata, revealed with the use of a recently introduced control parameter, seems to be robust not only to changes in update schema but also to different initial densities.

nlin.CG↗

arXiv2014

Conway's game of life is a near-critical metastable state in the multiverse of cellular automata

Conway's cellular automaton Game of LIFE has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. LIFE's mean-field return map predicts an absorbing vacuum phase ($ρ=0$) and an active phase density, with $ρ=0.37$, which contrasts with LIFE's absorbing states in a square lattice, which have a stationary density $ρ_{2D} \approx 0.03$. Here, we study and classify mean-field maps for $6144$ outer-totalistic CA and compare them with the corresponding behavior found in the square lattice. We show that the single-site mean-field approach gives qualitative (and even quantitative) predictions for most of them. The transition region in rule space seems to correspond to a nonequilibrium discontinuous absorbing phase transition instead of a continuous order-disorder one. We claim that LIFE is a quasicritical nucleation process where vacuum phase domains invade the alive phase. Therefore, LIFE is not at the "border of chaos," but thrives on the "border of extinction."

cond-mat.stat-mech↗

arXiv2013

Single-Neuron Criticality Optimizes Analog Dendritic Computation

Neurons are thought of as the building blocks of excitable brain tissue. However, at the single neuron level, the neuronal membrane, the dendritic arbor and the axonal projections can also be considered an extended active medium. Active dendritic branchlets enable the propagation of dendritic spikes, whose computational functions, despite several proposals, remain an open question. Here we propose a concrete function to the active channels in large dendritic trees. By using a probabilistic cellular automaton approach, we model the input-output response of large active dendritic arbors subjected to complex spatio-temporal inputs and exhibiting non-stereotyped dendritic spikes. We find that, if dendritic spikes have a non-deterministic duration, the dendritic arbor can undergo a continuous phase transition from a quiescent to an active state, thereby exhibiting spontaneous and self-sustained localized activity as suggested by experiments. Analogously to the critical brain hypothesis, which states that neuronal networks self-organize near a phase transition to take advantage of specific properties of the critical state, here we propose that neurons with large dendritic arbors optimize their capacity to distinguish incoming stimuli at the critical state. We suggest that "computation at the edge of a phase transition" is more compatible with the view that dendritic arbors perform an analog rather than a digital dendritic computation.

q-bio.NC↗