Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

Gollo, Leonardo L.; Kinouchi, Osame; Copelli, Mauro

doi:10.1103/physreve.85.011911

Cited by 25 publications

(53 citation statements)

References 76 publications

(136 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This question is explored here through the use of both analytic and numerical tools and is the main focus of the present work. Similar issues have been examined in other recent works [27,28] although the geometry of the model and the dynamics differ significantly from the present case.…”

Section: Introductionsupporting

confidence: 81%

Scaling behavior in probabilistic neuronal cellular automata

2013

View full text Add to dashboard Cite

We study a neural network model of interacting stochastic discrete two-state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean-field theory.

show abstract

Section: Introductionsupporting

confidence: 81%

Scaling behavior in probabilistic neuronal cellular automata

2013

View full text Add to dashboard Cite

show abstract

“…Much work has been done to investigate how topology determines the capability of single neurons to detect intensity of stimulus [14], to reliably detect dendritic spikes [15], to discriminate input patterns [16], and to perform other forms of dendritic computation [17,18]. There has been some attempts to study this problem analytically [19,20]. However, given the complexity of the task, they are usually limited to regular or oversimplified dendritic structure [19].…”

Section: Introductionmentioning

confidence: 99%

Spatially resolved dendritic integration: Towards a functional classification of neurons

Kirch

Gollo

2019

Preprint

View full text Add to dashboard Cite

The vast tree-like dendritic structure of neurons allow them to receive and integrate input from many neurons. A wide variety of neuronal morphologies exist, however, their role in dendritic integration, and how it shapes the response of the neuron, is not yet fully understood. Here, we study the evolution and interactions of dendritic spikes in excitable neurons with complex real branch structures. We focus on dozens of digitally reconstructed illustrative neurons from the online repository NeuroMorpho.org, which contains over 100,000 neurons. Yet, our methods can be promptly extended to any other neuron. This approach allows us to estimate and map the heterogeneity of activity patterns observed across extensive dendritic trees with thousands of compartments. We propose a classification of neurons based on the location of the soma (centrality) and the dendritic topology (number of branches connected to the soma). These are key topological factors in determining the neuron's energy consumption, dynamics, and the dynamic range, which quantifies the range in synaptic input rate that can be reliably encoded by the neuron's firing rate. Moreover, we find that bifurcations, the structural building blocks of complex dendrites, play a major role in increasing the dynamic range of neurons. Our results provide a better understanding of the effects of neuronal morphology in the diversity of neuronal dynamics and function.

show abstract

“…(18)], we use the common Glauber dynamics [13,40,57] with asynchronous updates according to which the state of a randomly chosen neuron n is set to v n ¼ AE1 with probability…”

Section: E Capacity Of Stochastic Hopfield Network With Nonadditivementioning

confidence: 99%

“…The propagation of dendritic spikes in branched dendrites with steplike activation functions has been studied in Ref. [18], providing the somatic input as a numerical solution to a highdimensional system of nonlinear equations.…”

Section: Introduction: Nonadditive Dendritic Input Processing In Nmentioning

confidence: 99%

Statistical Physics of Neural Systems with Nonadditive Dendritic Coupling

2014

View full text Add to dashboard Cite

How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly by the dendritic compartments. Yet, single-neuron experiments report pronounced supralinear dendritic summation of sufficiently synchronous and spatially close-by inputs. Here, we provide a statistical physics approach to study the impact of such nonadditive dendritic processing on single-neuron responses and the performance of associative-memory tasks in artificial neural networks. First, we compute the effect of random input to a neuron incorporating nonlinear dendrites. This approach is independent of the details of the neuronal dynamics. Second, we use those results to study the impact of dendritic nonlinearities on the network dynamics in a paradigmatic model for associative memory, both numerically and analytically. We find that dendritic nonlinearities maintain network convergence and increase the robustness of memory performance against noise. Interestingly, an intermediate number of dendritic branches is optimal for memory functionality

show abstract

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

Cited by 25 publications

References 76 publications

Scaling behavior in probabilistic neuronal cellular automata

Scaling behavior in probabilistic neuronal cellular automata

Spatially resolved dendritic integration: Towards a functional classification of neurons

Statistical Physics of Neural Systems with Nonadditive Dendritic Coupling

Contact Info

Product

Resources

About