Inferring collective dynamical states from widely unobserved systems

Wilting, Jens; Priesemann, Viola

doi:10.1038/s41467-018-04725-4

Cited by 120 publications

(377 citation statements)

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“…This typically involves stochastic processes, such as (probabilistic) cellular automata [8][9][10], contact processes [10,11], or interacting Hawkes processes [12]. In particular, infectious diseases have been modeled by so-called susceptible-infectious models or generalizations thereof [13], whereas spikepropagation in neural networks has been modeled by socalled branching networks [14][15][16][17][18][19][20][21][22], Hawkes processes [23][24][25], or probabilistic integrate-and-fire networks [26,27]. These models can be either constructed as independentinteraction models (static interactions), or as threshold models with interactions depending on the states of the interacting partners [28].…”

Section: Introductionmentioning

confidence: 99%

Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

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Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network, or directly on the macroscopic level, assuming that microscopic contributions are negligible. The macroscopic characteristics of both descriptions are commonly assumed to be identical. In this work, we show that these characteristics of microscopic and macroscopic descriptions can be different due to coalescence, i.e., a node being activated at the same time by multiple sources. In particular, we consider a (microscopic) branching network (probabilistic cellular automaton) with annealed connectivity disorder, record the macroscopic activity, and then approximate this activity by a (macroscopic) branching process. In this framework, we analytically calculate the effect of coalescence on the collective dynamics. We show that coalescence leads to a universal non-linear scaling function for the conditional expectation value of successive network activity. This allows us to quantify the difference between the microscopic model parameter and established macroscopic estimates. To overcome this difference, we propose a non-linear estimator that correctly infers the model branching parameter for all system sizes.

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Section: Introductionmentioning

confidence: 99%

Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

et al. 2020

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“…DBI was not specifically designed to recover 839 envelope time series, and assumes basis functions to represent dynamics, but could be 840 applied to envelope dynamics inference. Additionally, the direct method can be 841 improved using multiple linear regressions and derivative estimates with various time 842 lags [62], in particular for linear dynamics. The passage method may find productive 843 applications in other parts of the neurosciences -for instance in the field of memory, 844 where beta and gamma bursts [63], and the duration of sharp wave ripples [64] have 845 been found to be related to memory -and beyond.…”

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Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson’s disease

Duchet

Ghezzi

Weerasinghe

et al. 2020

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1Parkinson's disease motor symptoms are associated with an increase in subthalamic 2 nucleus beta band oscillatory power. But these oscillations are phasic, and there is a 3 growing body of evidence suggesting that beta burst duration may be of critical 4 importance to motor symptoms, making insights into the dynamics of beta bursting 5 generation valuable. In this study, we ask the question "Can average burst duration 6 reveal how dynamics change between the ON and OFF medication states?". Our 7 analysis of local field potentials from the subthalamic nucleus demonstrates using linear 8 surrogates that the system generating beta oscillations acts in a more non-linear regime 9 OFF medication and that the change in the degree of non-linearity is correlated with 10 motor impairment. Further, we pinpoint specific dynamical changes responsible for 11 changes in the temporal patterning of beta oscillations between medication states by 12 fitting to data biologically inspired models, and simpler beta envelope models. Finally, 13 we show that the non-linearity can be directly extracted from average burst duration 14 profiles under the assumption of constant noise in envelope models. This reveals that 15 average burst duration profiles provide a window into burst dynamics, which may 16 underlie the success of burst duration as a biomarker. In summary, we demonstrate a 17 relationship between average burst duration profiles, dynamics of the system generating 18 beta oscillations, and motor impairment, which puts us in a better position to 19 understand the pathology and improve therapies such as deep brain stimulation. 20 April 27, 2020 1/39 65 OFF medication states to changes in dynamical properties of the system generating 66 beta oscillations? 67In previous studies, STN beta bursts have been mostly studied based on one 68 arbitrary threshold of the beta envelope as events above the threshold, potentially with 69April 27, 2020 2/39 a minimum duration condition (examples of various thresholds shown in Fig 1A). 70Average burst duration and amplitude profiles describing the average burst duration 71 and amplitude for a range of thresholds (see Fig 1A and Fig 1B for an illustration of 72 average burst duration profiles) have been introduced [13,14]. However, they played a 73 minor role and have not been considered systematically on an individual patient basis. 74 Here, we leave behind the arbitrary choice of a threshold by relying on profiles across 75 thresholds to provide an unbiased characterisation of beta oscillation temporal 76 patterning. It has been established that STN beta burst duration is a better metric 77 than burst amplitude to distinguish between the healthy and pathological states in an 78 animal model of PD [19]. We begin our study by investigating in STN recordings of PD 79 patients whether average burst duration profiles are better at distinguishing between the 80 ON and OFF medication states than average burst amplitude profiles. We only observe 81 changes in temporal patterning of beta oscillations in...

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“…All parameters of the model, the sampling and the 61 analysis are closely matched to those known from experiments 62 (see Methods).63Branching dynamics on a local 2D topology 64 In order to evaluate sampling effects, we want to precisely 65 set the underlying dynamics. Therefore, we employ the es-66 tablished branching model, which is well understood analyti-67 cally [9,25,32,33]. Inspired by biological neuronal networks, 68 we simulate the branching dynamics on a dense 2D topology 69 with N = 160 000 neurons where each neuron is connected 70 to ≈ 1000 local neighbors.…”

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confidence: 99%

“…In particular, the reverberating regime covers a specific range ideal baseline [25] from which brain areas or neural circuits can 357 adapt to meet task demands [35,[46][47][48][49][50][51][52].…”

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A unified picture of neuronal avalanches arises from the understanding of sampling effects

Neto

Spitzner

Priesemann

2019

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To date, it is still impossible to sample the entire mammalian brain with single-neuron precision. This forces one to either use spikes (focusing on few neurons) or to use coarse-sampled activity (averaging over many neurons, e.g. LFP). Naturally, the sampling technique impacts inference about collective properties. Here, we emulate both sampling techniques on a spiking model to quantify how they alter observed correlations and signatures of criticality. We discover a general effect: when the inter-electrode distance is small, electrodes sample overlapping regions in space, which increases the correlation between the signals. For coarse-sampled activity, this can produce power-law distributions even for non-critical systems. In contrast, spikes enable one to distinguish the underlying dynamics. This explains why coarse measures and spikes have produced contradicting results in the past -that are now all consistent with a slightly subcritical regime. Introduction 1For more than two decades, it has been argued that the cor-2 tex might operate at a critical point [1][2][3][4][5][6]. The criticality hy-3 pothesis states that by operating at a critical point, neuronal 4 networks could benefit from optimal information-processing 5 properties. Properties maximized at criticality include the cor-6 relation length [7], the autocorrelation time [6], the dynamic 7 range [8] and the richness of spatio-temporal patterns [9, 10]. 8 Evidence for criticality in the brain often derives from mea-9 surements of neuronal avalanches. Neuronal avalanches are 10 cascades of neuronal activity that spread in space and time. If a 11 system is critical, the probability distribution of avalanche size 12 ( ) follows a power law ( ) ∼ − [7, 11]. Such power-13 law distributions have been observed repeatedly in experiments 14 since they were first reported by Beggs & Plenz in 2003 [1]. 15 However, not all experiments have produced power laws 16 and the criticality hypothesis remains controversial. It turns 17 out that results for cortical recordings in vivo differ systemati-18 cally: 19 Studies that use what we here call coarse-sampled activity 20 typically produce power-law distributions [1, 12-21]. In con-21 trast, studies that use sub-sampled activity typically do not [14, 22 22-26]. Coarse-sampled activity include LFP, M/EEG, fMRI 23 and potentially calcium imaging, while sub-sampled activity is 24 front-most spike recordings. We hypothesize that the apparent 25 contradiction between coarse-sampled (LFP-like) data and sub-26 sampled (spike) data can be explained by the differences in the 27 recording and analysis procedures.28In general, the analysis of neuronal avalanches is not 29 straightforward. In order to obtain avalanches, one needs to de-30 fine discrete events. While spikes are discrete events by nature, 31 a coarse-sampled signal has to be converted into a binary form. 32This conversion hinges on thresholding the signal, which can be 33 problematic [27][28][29][30]. Furthermore, events have to be grouped 34 into avalanches, and th...

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Inferring collective dynamical states from widely unobserved systems

Cited by 120 publications

References 72 publications

Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson’s disease

A unified picture of neuronal avalanches arises from the understanding of sampling effects

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