Self-Organized Bistability Associated with First-Order Phase Transitions

Santo, Serena Di; Burioni, Raffaella; Vezzani, A.; Muñoz, Miguel A.

doi:10.1103/physrevlett.116.240601

Cited by 59 publications

(92 citation statements)

References 48 publications

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“…Our identification of a symmetrical (in time), parabolic profile for neuronal avalanches in vivo supports results in simulations of critical neural networks 35,56 and identifies constraints for other generative models proposed for avalanche dynamics 37 . Models fine-tuned to produce power laws for size and duration distributions via bi-stable dynamics combined with a locally expansive dynamical term 39 or purely external uncorrelated driving 38 reveal profiles that deviate from a symmetric parabola. The parabolic profile also differentiates neuronal avalanches from stochastic processes with no memory which typically display a semicircle motif 72 .…”

Section: Discussionmentioning

confidence: 99%

“…Variable and asymmetric profiles have been reported for neuronal cultures 35,36 , and profiles seem to depend on avalanche duration in humans 18 . Identifying the correct profile of neuronal avalanches will provide insights into the temporal evolution of brain activity, will distinguish between different models of avalanche generation [37][38][39][40] and, importantly, might provide a biomarker given recent findings that profiles predict recovery from brain insults 41,42 . A second prediction from critical theory is that the avalanche parabola can be collapsed over many avalanche durations with a scaling exponent, χ, larger than 1.5 (Refs.…”

Section: Introductionmentioning

confidence: 99%

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The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

Miller

Plenz

2019

Preprint

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Miller et al.The temporal profile of neuronal avalanches 2 ABSTRACT Activity cascades are found in many complex systems. In the cortex, they arise in the form of neuronal avalanches which capture ongoing and evoked neuronal activities at many spatial and temporal scales. The scale-invariant nature of avalanches suggests that the brain is in a critical state, yet predictions from critical theory on the temporal unfolding of avalanches have yet to be confirmed in vivo. Here we show in awake nonhuman primates that the temporal profile of avalanches, which describes how avalanches initiate locally, extend spatially and shrink as they evolve in time, follows a symmetrical, inverted parabola spanning up to hundreds of milliseconds. Parabolas of different durations can be collapsed with a scaling exponent close to 2 supporting critical generational models of neuronal avalanches. Spontaneously emerging, transient γ-oscillations coexist with and modulate these avalanche parabolas thereby providing a temporal segmentation to inherently scale-invariant, critical dynamics. Our results identify avalanches and oscillations as dual principles in the temporal organization of brain activity. Significance StatementThe most common framework for understanding the temporal organization of brain activity is that of oscillations, or "brain waves". In oscillations, distinct physiological frequencies emerge at well-defined temporal scales, dividing brain activity into time segments underlying cortex function. Here, we identify a fundamentally different temporal parsing of activity in cortex. In awake Macaque monkeys, we demonstrate the motif of an inverted parabola that governs the temporal unfolding of brain activity in the form of neuronal avalanches. This symmetrical motif is scale-invariant, that is, it is not tied to time segments, and exhibits a scaling exponent close to 2 in line with prediction from theory of critical systems. We suggest that oscillations provide a Miller et al.The temporal profile of neuronal avalanches 3 transient "wrinkle" of regularity in an otherwise scale-invariant temporal organization pervading cortical activity at numerous scales.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

Miller

Plenz

2019

Preprint

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“…Furthermore, the sandpile model-a prototypical model for SOC [14]-can also be viewed as the repetition of such switching between the buildup of large gradients (forcing) and the sandpile's collapse beyond some critical gradient (dissipation). In fact, recent work by di Santo et al [24] attempted to formally adapt SOC to bistable systems by invoking self-organized bistability. Our work was motivated to present a different way of understanding disorder-to-order and order-to-disorder transitions in bistable systems, highlighting asymmetry between these two processes.…”

Section: Introductionmentioning

confidence: 99%

Geometric structure and information change in phase transitions

Kim

Hollerbach

2017

Phys. Rev. E

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We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale τ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation γ of a control parameter from the critical state in BPs while increasing logarithmically with γ in FPs. L scales as | ln D| and D −1/2 in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with γ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).

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“…To this end, we investigate a bistable stochastic system that is often invoked as a canonical model of self-regulating systems, e.g., in electric circuits [17], in various cellular processes such as cycles, differentiation and apoptosis, regulation of heart, brain, etc. [18][19][20][21][22][23]. In this model, we calculate time-dependent Probability Density Function (PDF) and the total number of statistically different states that the system undergoes in time.…”

Section: Introductionmentioning

confidence: 99%

Information Geometry of Non-Equilibrium Processes in a Bistable System with a Cubic Damping

Hollerbach

Kim

2017

Entropy

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A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic systems and information geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate the information geometry of non-equilibrium processes involved in disorder-order transitions between the critical and subcritical states in a bistable system. Specifically, we compute time-dependent PDFs, information length, the rate of change in information length, entropy change and Fisher information in disorder-to-order and order-to-disorder transitions and discuss similarities and disparities between the two transitions. In particular, we show that the total information length in order-to-disorder transition is much larger than that in disorder-to-order transition and elucidate the link to the drastically different evolution of entropy in both transitions. We also provide the comparison of the results with those in the case of the transition between the subcritical and supercritical states and discuss implications for fitness.

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Self-Organized Bistability Associated with First-Order Phase Transitions

Cited by 59 publications

References 48 publications

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

Geometric structure and information change in phase transitions

Information Geometry of Non-Equilibrium Processes in a Bistable System with a Cubic Damping

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