Bootstrap percolation with inhibition

Einarsson, Hafsteinn; Lengler, Johannes; Mousset, Frank; Παναγιώτου, Κωνσταντίνος; Steger, Angelika

doi:10.1002/rsa.20854

Cited by 7 publications

(8 citation statements)

References 20 publications

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“…This difference is analogous to (Koulakov, Hromádka, & Zador, ) and (Roxin et al, ) on the single neuron level. With respect to the emergence of normal NBs, it has been shown in a model of asynchronous spike transmission in random networks that normally distributed NBs with small standard deviation occur if inhibition is strong enough to stop the spread of activity (Einarsson, Lengler, Panagiotou, Mousset, & Steger, ), consistent with the observation that inhibition dominates during NBs in vitro (Hájos et al, ). Further, supporting normally distributed NB size, the distribution of SPW amplitude has been observed to follow a truncated normal distribution (where the truncation stems from the SPW detection threshold) (see Sullivan et al, ), however, the relation between SPW amplitude and NB size is not clear.…”

Section: Discussionmentioning

confidence: 53%

“…Our model investigates synchronous spike transmission propagated over one synaptic layer. Synchronous spike transmission over multiple layers has been studied in the context of synfire‐chains (Abeles, ) where it has been shown that in the absence of homeostatic plasticity the activity diverges quickly (Weissenberger, Meier, Lengler, Einarsson, & Steger, ) and the distribution of activity is very broad (Einarsson et al, ). Such divergence is consistent with our work: the tail of the input distribution is amplified over one synaptic layer and iterative amplification over multiple layers results in explosions of activity.…”

Section: Discussionmentioning

confidence: 99%

“…There, it was shown that a recurrent network of bursting neurons interconnected by synapses with a lognormal weight distribution spontaneously emits NBs whose size distri- Fitting the mean μ X and the standard deviation σ X of normally distributed NB size X such that the mean squared error between the distribution of the resulting SE size Y and data depicted in (Buzsáki & Mizuseki, 2014, Figure 2B) is minimized Our model investigates synchronous spike transmission propagated over one synaptic layer. Synchronous spike transmission over multiple layers has been studied in the context of synfire-chains (Abeles, 2012) where it has been shown that in the absence of homeostatic plasticity the activity diverges quickly (Weissenberger, Meier, Lengler, Einarsson, & Steger, 2017) and the distribution of activity is very broad (Einarsson et al, 2014). Such divergence is consistent with our work: the tail of the input distribution is amplified over one synaptic layer and iterative amplification over multiple layers results in explosions of activity.…”

Section: Related Computational Modelsmentioning

confidence: 99%

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On the origin of lognormal network synchrony in CA1

et al. 2018

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The sharp wave ripple complex in rodent hippocampus is associated with a network burst in CA3 (NB) that triggers a synchronous event in the CA1 population (SE). The number of CA1 pyramidal cells participating in a SE has been observed to follow a lognormal distribution. However, the origin of this skewed and heavy-tailed distribution of population synchrony in CA1 remains unknown. Because the size of SEs is likely to originate from the size of the NBs and the underlying neural circuitry, we model the CA3-CA1 circuit to study the underlying mechanisms and their functional implications. We show analytically that if the size of a NB in CA3 is distributed according to a normal distribution, then the size of the resulting SE in CA1 follows a lognormal distribution. Our model predicts the distribution of the NB size in CA3, which remains to be tested experimentally. Moreover, we show that a putative lognormal NB size distribution leads to an extremely heavy-tailed SE size distribution in CA1, contradicting experimental evidence. In conclusion, our model provides general insight on the origin of lognormally distributed network synchrony as a consequence of synchronous synaptic transmission of normally distributed input events.

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Section: Discussionmentioning

confidence: 53%

Section: Discussionmentioning

confidence: 99%

Section: Related Computational Modelsmentioning

confidence: 99%

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On the origin of lognormal network synchrony in CA1

et al. 2018

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“…some vertices are vaccinated or have a higher threshold for infection. See for example [18] for some recent work in this vein.…”

Section: Discussionmentioning

confidence: 99%

Bootstrap percolation in random geometric graphs

Falgas–Ravry¹,

Sarkar²

2021

Preprint

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Following Bradonjić and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the 2-dimensional torus. In this model, the expected number of vertices of the graph is n, and the expected degree of a vertex is a log n for some fixed a > 1. Each vertex is added with probability p to a set A 0 of initially infected vertices. Vertices subsequently become infected if they have at least θa log n infected neighbours. Here p, θ ∈ [0, 1] are taken to be fixed constants.We show that if θ < (1 + p)/2, then a sufficiently large local outbreak leads with high probability to the infection spreading globally, with all but o(n) vertices eventually becoming infected. On the other hand, for θ > (1 + p)/2, even if one adversarially infects every vertex inside a ball of radius O( √ log n), with high probability the infection will spread to only o(n) vertices beyond those that were initially infected.In addition we give some bounds on the (a, p, θ) regions ensuring the emergence of large local outbreaks or the existence of islands of vertices that never become infected. We also give a complete picture of the (surprisingly complex) behaviour of the analogous 1-dimensional bootstrap percolation model on the circle. Finally we raise a number of problems, and in particular make a conjecture on an 'almost no percolation or almost full percolation' dichotomy which may be of independent interest.

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“…In particular, it was shown that for a range of the parameters, the process percolates on the combined graph but not on the random graph G n,p without local edges. In [16] the authors considered bootstrap percolation process on G n,p with vertices of two different types.…”

Section: Introductionmentioning

confidence: 99%

A modified bootstrap percolation on a random graph coupled with a lattice

Janson

Kozma

Ruszinkó

et al. 2019

Discrete Applied Mathematics

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In this paper a random graph model G Z 2 N ,p d is introduced, which is a combination of fixed torus grid edges in (Z/N Z) 2 and some additional random ones. The random edges are called long, and the probability of having a long edge between vertices u, v ∈ (Z/N Z) 2 with graph distance d on the torus grid is p d = c/N d, where c is some constant. We show that, whp, the diameter D(G Z 2 N ,p d ) = Θ(log N ). Moreover, we consider a modified non-monotonous bootstrap percolation on G Z 2 N ,p d . We prove the presence of phase transitions in mean-field approximation and provide fairly sharp bounds on the error of the critical parameters.

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Bootstrap percolation with inhibition

Cited by 7 publications

References 20 publications

On the origin of lognormal network synchrony in CA1

On the origin of lognormal network synchrony in CA1

Bootstrap percolation in random geometric graphs

A modified bootstrap percolation on a random graph coupled with a lattice

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