Universal excursion and bridge shapes in ABBM/CIR/Bessel processes

Baldassarri, Andrea

doi:10.1088/1742-5468/ac1404

Cited by 8 publications

(6 citation statements)

References 83 publications

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“…6 A,B. Note that, as expected, an exponent corresponds to a shape that is nearly parabolic (fully-connected system), while in the case of the 2D system the exponent corresponds to a more flattened shape 26 .…”

Section: Scaling Of the Shape Of Avalanchessupporting

confidence: 64%

Power spectrum and critical exponents in the 2D stochastic Wilson–Cowan model

Apicella

Scarpetta

Arcangelis

et al. 2022

Sci Rep

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The power spectrum of brain activity is composed by peaks at characteristic frequencies superimposed to a background that decays as a power law of the frequency, $$f^{-\beta }$$ f - β , with an exponent $$\beta $$ β close to 1 (pink noise). This exponent is predicted to be connected with the exponent $$\gamma $$ γ related to the scaling of the average size with the duration of avalanches of activity. “Mean field” models of neural dynamics predict exponents $$\beta $$ β and $$\gamma $$ γ equal or near 2 at criticality (brown noise), including the simple branching model and the fully-connected stochastic Wilson–Cowan model. We here show that a 2D version of the stochastic Wilson–Cowan model, where neuron connections decay exponentially with the distance, is characterized by exponents $$\beta $$ β and $$\gamma $$ γ markedly different from those of mean field, respectively around 1 and 1.3. The exponents $$\alpha $$ α and $$\tau $$ τ of avalanche size and duration distributions, equal to 1.5 and 2 in mean field, decrease respectively to $$1.29\pm 0.01$$ 1.29 ± 0.01 and $$1.37\pm 0.01$$ 1.37 ± 0.01 . This seems to suggest the possibility of a different universality class for the model in finite dimension.

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Section: Scaling Of the Shape Of Avalanchessupporting

confidence: 64%

Power spectrum and critical exponents in the 2D stochastic Wilson–Cowan model

Apicella

Scarpetta

Arcangelis

et al. 2022

Sci Rep

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show abstract

“…6A,B. Note that, as expected, an exponent γ 2 corresponds to a shape that is nearly parabolic (fully connected system), while in the case of the 2D system the exponent γ 1.3 corresponds to a more flattened shape [26].…”

Section: Fig 4 (A)supporting

confidence: 64%

Power spectrum and critical exponents in the 2D stochastic Wilson Cowan model

Apicella

Scarpetta

Arcangelis

et al. 2022

Preprint

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The power spectrum of brain activity is composed by peaks at characteristic frequencies superimposed to a background that decays as a power law of the frequency, f−β with an exponent β close to 1 (pink noise). This exponent is predicted to be connected with the exponent γ related to the scaling of the average size with the duration of avalanches of activity. “Mean field” models of neural dynamics predict exponents β and γ equal or near 2 at criticality (brown noise), including the simple branching model and the fully connected stochastic Wilson Cowan model. We here show that a 2D version of the stochastic Wilson Cowan model, where neuron connections decay exponentially with the distance, is characterized by exponents β and γ markedly different from those of mean field, respectively around 1 and 1.3. The exponents α and τ of avalanche size and duration distributions, equal to 1.5 and 2 in mean field, decrease respectively to 1.29 ± 0.01 and 1.37 ± 0.01. This seems to suggest the possibility of a different universality class for the model in finite dimension.

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“…Similarly, a "bridge" is the portion of a stochastic trajectory joining a chosen starting point to a given final one without further constraints. Both these quantities have been studied for a broad class of processes, with several applications in physics [43][44][45][46]. Stochastic thermodynamics represents an ideal framework where these studies could reveal their utility, for instance in comparing an excursion from an initial to a final configuration and its time reversed counterpart.…”

Section: A Brief Review Of Recent Approachesmentioning

confidence: 99%

“…In terms of the theory of stochastic processes, the avalanche of the process is called an excursion [45,69]. In a recent paper [46], for the case of a class of multiplicative stochastic processes (ABBM/CIR/Bessel processes), it has been shown that the average bridge shape is simply proportional to the average avalanche shape, suggesting that the two quantities (bridge and excursion) carry similar information about the time evolution of the process. Symmetric, as well asymmetric average avalanche shapes has been observed in several physical [70][71][72][73], geophysical [74] and biological [75] phenomena, but at the moment there is no general understanding of the meaning of such property.…”

Section: Pitfalls Of Linear Systemsmentioning

confidence: 99%

Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls

Lucente¹,

Baldassarri²,

Puglisi³

et al. 2022

Preprint

Self Cite

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Data from experiments and theoretical arguments are the two pillars sustaining the job of modelling physical systems through inference. In order to solve the inference problem, the data should satisfy certain conditions that depend also upon the particular questions addressed in a research. Here we focus on the characterization of systems in terms of a distance from equilibrium, typically the entropy production (time-reversal asymmetry) or the violation of the Kubo fluctuation-dissipation relation. We show how general, counter-intuitive and negative for inference, is the problem of the impossibility to estimate the distance from equilibrium using a series of scalar data which have a Gaussian statistics. This impossibility occurs also when the data are correlated in time, and that is the most interesting case because it usually stems from a multi-dimensional linear Markovian system where there are many time-scales associated to different variables and, possibly, thermal baths. Observing a single variable (or a linear combination of variables) results in a one-dimensional process which is always indistinguishable from an equilibrium one (unless a perturbation-response experiment is available). In a setting where only data analysis (and not new experiments) is allowed, we propose -as a way out -the combined use of different series of data acquired with different parameters. This strategy works when there is a sufficient knowledge of the connection between experimental parameters and model parameters. We also briefly discuss how such results emerge, similarly, in the context of Markov chains within certain coarse-graining schemes. Our conclusion is that the distance from equilibrium is related to quite a fine knowledge of the full phase space, and therefore typically hard to approximate in real experiments.

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Universal excursion and bridge shapes in ABBM/CIR/Bessel processes

Cited by 8 publications

References 83 publications

Power spectrum and critical exponents in the 2D stochastic Wilson–Cowan model

Power spectrum and critical exponents in the 2D stochastic Wilson–Cowan model

Power spectrum and critical exponents in the 2D stochastic Wilson Cowan model

Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls

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