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## Different levels of Ih determine distinct temporal integration in bursting and regular-spiking neurons in rat subiculum

van Welie, Ingrid; Remme, Michiel W H; van Hooft, Johannes A; Wadman, Wytse J
Fonte: Blackwell Science Inc Publicador: Blackwell Science Inc
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.77%
Pyramidal neurons in the subiculum typically display either bursting or regular-spiking behaviour. Although this classification into two neuronal classes is well described, it is unknown how these two classes of neurons contribute to the integration of input to the subiculum. Here, we report that bursting neurons posses a hyperpolarization-activated cation current (Ih) that is two-fold larger (conductance, 5.3 ± 0.5 nS) than in regular-spiking neurons (2.2 ± 0.6 nS), whereas Ih exhibits similar voltage-dependent and kinetic properties in both classes of neurons. Bursting and regular-spiking neurons display similar morphology. The difference in Ih between the two classes of neurons is not responsible for the distinct firing patterns, as neither pharmacological blockade of Ih nor enhancement of Ih using a dynamic clamp affects the qualitative firing patterns. Instead, the difference in Ih between bursting and regular-spiking neurons determines the temporal integration of evoked synaptic input from the CA1 area. In response to stimulation at 50 Hz, bursting neurons, with a large Ih, show ∼50% less temporal summation than regular-spiking neurons. The amount of temporal summation in both neuronal classes is equal after pharmacological blockade of Ih. A computer simulation model of a subicular neuron with the properties of either a bursting or a regular-spiking neuron confirmed the pivotal role of Ih in temporal integration of synaptic input. These data suggest that in the subicular network...

## Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

Buesing, Lars; Bill, Johannes; Nessler, Bernhard; Maass, Wolfgang
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.69%
The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution...

## Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

Torres Agudo, Joaqu??n J.; Elices, Irene; Marro Borau, Joaqu??n
Fonte: Public Library of Science (PLOS) Publicador: Public Library of Science (PLOS)
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.39%
We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances???that naturally balances the network with excitatory and inhibitory synapses???and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios...

## Adaptive Reduction of Large Spiking Neurons

Du, Bosen
Tipo: Thesis; Text Formato: application/pdf
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66.58%
This thesis develops adaptive reduction approaches for various models of large spiking neurons. Most neurons are like dendritic trees with many branches, and they communicate by nonlinear spiking behaviors. However, with the exception of Kellems' Strong-Weak model, most existing reduction approaches compromise the active ionic mechanisms that cause the spiking dynamics. The Strong-Weak model can predict the spikes caused by suprathreshold input traveling from the dendritic branches to the spike initiation zone (SIZ), but it is not able to reproduce the back propagation from SIZ to the dendritic branches after spikes. This thesis develops a new model called QAact, the mechanisms to incorporate QAact into the hybrid model to capture the back propagation behavior, and different model reduction techniques for each part of the new hybrid model where they are most advantageous. Computational tests of QAact and the new hybrid model as well as corresponding model reduction techniques on FitzHugh-Nagumo system, active nonuniform cable, and branched cell LGMD, demonstrate a significant reduction of dimension, computational complexity and running time.

## Macroscopic description for networks of spiking neurons

Montbrió, Ernest; Pazó, Diego; Roxin, Alex
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.69%
A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the underlying microscopic state of the spiking neurons. This has largely constrained the range of applicability of such macroscopic descriptions, particularly when trying to describe neuronal synchronization. Here we provide the derivation of a set of exact macroscopic equations for a network of spiking neurons. Our results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network. The resulting equations exactly describe all possible macroscopic dynamical states of the network...

## Efficient transmission of subthreshold signals in complex networks of spiking neurons

Torres, Joaquin J.; Elices, Irene; Marro, J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.39%
We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances -- that naturally balances the network with excitatory and inhibitory synapses -- and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios...

## Optimal Design of Minimum-Power Stimuli for Spiking Neurons

Dasanayake, Isuru; Li, Jr-Shin
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.67%
In this article, we study optimal control problems of spiking neurons whose dynamics are described by a phase model. We design minimum-power current stimuli (controls) that lead to targeted spiking times of neurons, where the cases with unbounded and bounded control amplitude are considered. We show that theoretically the spiking period of a neuron, modeled by phase dynamics, can be arbitrarily altered by a smooth control. However, if the control amplitude is bounded, the range of possible spiking times is constrained and determined by the bound, and feasible spiking times are optimally achieved by piecewise continuous controls. We present analytic expressions of these minimum-power stimuli for spiking neurons and illustrate the optimal solutions with numerical simulations.; Comment: 8 pages, 10 figures

## Response of electrically coupled spiking neurons: a cellular automaton approach

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.39%
Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.; Comment: 11 pages...

## Fluctuations and information filtering in coupled populations of spiking neurons with adaptation

Deger, Moritz; Schwalger, Tilo; Naud, Richard; Gerstner, Wulfram
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.54%
Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal description of neurons with adaptation. We derive an integral equation with colored noise that governs the stochastic dynamics of the population activity in response to time-dependent stimulation and calculate the spectral density in the asynchronous state. We show that systems of coupled populations with adaptation can generate a frequency band in which sensory information is preferentially encoded. The theory is applicable to fully as well as randomly connected networks, and to leaky integrate-and-fire as well as to generalized spiking neurons with adaptation on multiple time scales.

## On the Dynamical Complexity of Small-World Networks of Spiking Neurons

Shanahan, Murray
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.32%
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected clusters and then applying a probabilistic rewiring method reminiscent of the Watts-Strogatz procedure to make inter-cluster connections. Causal density, which counts the number of independent significant interactions among a system's components, is used to assess dynamical complexity. This measure was chosen because it employs lagged observations, and is therefore more sensitive to temporally smeared evidence of segregation and integration than its alternatives. The results broadly support the hypothesis that small-world topology promotes dynamical complexity, but reveal a narrow parameter range within which this occurs for the network topology under investigation, and suggest an inverse correlation with phase synchrony inside this range.; Comment: Accepted for Physical Review E

## Bayesian Inference with Spiking Neurons

Paulin, Michael G.; van Schaik, Andre
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.32%
Humans and other animals behave as if we perform fast Bayesian inference underlying decisions and movement control given uncertain sense data. Here we show that a biophysically realistic model of the subthreshold membrane potential of a single neuron can exactly compute the numerator in Bayes rule for inferring the Poisson parameter of a sensory spike train. A simple network of spiking neurons can construct and represent the Bayesian posterior density of a parameter of an external cause that affects the Poisson parameter, accurately and in real time.

## A theoretical basis for efficient computations with noisy spiking neurons

Jonke, Zeno; Habenschuss, Stefan; Maass, Wolfgang
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.6%
Network of neurons in the brain apply - unlike processors in our current generation of computer hardware - an event-based processing strategy, where short pulses (spikes) are emitted sparsely by neurons to signal the occurrence of an event at a particular point in time. Such spike-based computations promise to be substantially more power-efficient than traditional clocked processing schemes. However it turned out to be surprisingly difficult to design networks of spiking neurons that are able to carry out demanding computations. We present here a new theoretical framework for organizing computations of networks of spiking neurons. In particular, we show that a suitable design enables them to solve hard constraint satisfaction problems from the domains of planning - optimization and verification - logical inference. The underlying design principles employ noise as a computational resource. Nevertheless the timing of spikes (rather than just spike rates) plays an essential role in the resulting computations. Furthermore, one can demonstrate for the Traveling Salesman Problem a surprising computational advantage of networks of spiking neurons compared with traditional artificial neural networks and Gibbs sampling. The identification of such advantage has been a well-known open problem.; Comment: main paper: 21 pages...

## Simulation of networks of spiking neurons: A review of tools and strategies

Brette, R.; Rudolph, M.; Carnevale, T.; Hines, M.; Beeman, D.; Bower, J. M.; Diesmann, M.; Morrison, A.; Goodman, P. H.; Harris Jr., F. C.; Zirpe, M.; Natschlager, T.; Pecevski, D.; Ermentrout, B.; Djurfeldt, M.; Lansner, A.; Rochel, O.; Vieville, T.; Mul
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.49%
We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.; Comment: 49 pages...

## A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics

Cessac, B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.32%
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (raster plots''). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.; Comment: 56 pages, 1 Figure, to appear in Journal of Mathematical Biology

## Thermodynamic Order Parameters and Statistical-Mechanical Measures for Characterization of the Burst and Spike Synchronizations of Bursting Neurons

Kim, Sang-Yoon; Lim, Woochang
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.65%
We are interested in characterization of population synchronization of bursting neurons which exhibit both the slow bursting and the fast spiking timescales, in contrast to spiking neurons. Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments. The instantaneous population firing rate (IPFR) $R(t)$, which may be directly obtained from the raster plot of spikes, is often used as a realistic collective quantity describing population behaviors in both the computational and the experimental neuroscience. For the case of spiking neurons, realistic thermodynamic order parameter and statistical-mechanical spiking measure, based on $R(t)$, were introduced in our recent work to make practical characterization of spike synchronization. Here, we separate the slow bursting and the fast spiking timescales via frequency filtering, and extend the thermodynamic order parameter and the statistical-mechanical measure to the case of bursting neurons. Consequently, it is shown in explicit examples that both the order parameters and the statistical-mechanical measures may be effectively used to characterize the burst and spike synchronizations of bursting neurons.; Comment: arXiv admin note: text overlap with arXiv:1403.1255

## Mean-Field Analysis of Orientation Selectivity in Inhibition-Dominated Networks of Spiking Neurons

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.32%
Mechanisms underlying the emergence of orientation selectivity in the primary visual cortex are highly debated. Here we study the contribution of inhibition-dominated random recurrent networks to orientation selectivity, and more generally to sensory processing. By simulating and analyzing large-scale networks of spiking neurons, we investigate tuning amplification and contrast invariance of orientation selectivity in these networks. In particular, we show how selective attenuation of the common mode and amplification of the modulation component take place in these networks. Selective attenuation of the baseline, which is governed by the exceptional eigenvalue of the connectivity matrix, removes the unspecific, redundant signal component and ensures the invariance of selectivity across different contrasts. Selective amplification of modulation, which is governed by the operating regime of the network and depends on the strength of coupling, amplifies the informative signal component and thus increases the signal-to-noise ratio. Here, we perform a mean-field analysis which accounts for this process.; Comment: 19 figures

## Frequency-Domain Order Parameters for the Burst And Spike Synchronization Transitions of Bursting Neurons

Kim, Sang-Yoon; Lim, Woochang
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.75%
We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) $R(t)$, which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on $R(t)$, was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR $R(t)$ of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR $R(t)$ into the instantaneous population bursting rate $R_b(t)$ (describing the bursting behavior) and the instantaneous population spike rate $R_s(t)$ (describing the spiking behavior) via frequency filtering, and extend the realistic order parameter to the case of bursting neurons. Thus, we develop the frequency-domain bursting and spiking order parameters which are just the bursting and spiking "coherence factors" $\beta_b$ and $\beta_s$ of the bursting and spiking peaks in the power spectral densities of $R_b$ and $R_s$ (i.e....

## Distribution of Orientation Selectivity in Recurrent Networks of Spiking Neurons with Different Random Topologies

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.36%
Neurons in the primary visual cortex are more or less selective for the orientation of a light bar used for stimulation. A broad distribution of individual grades of orientation selectivity has in fact been reported in all species. A possible reason for emergence of broad distributions is the recurrent network within which the stimulus is being processed. Here we compute the distribution of orientation selectivity in randomly connected model networks that are equipped with different spatial patterns of connectivity. We show that, for a wide variety of connectivity patterns, a linear theory based on firing rates accurately approximates the outcome of direct numerical simulations of networks of spiking neurons. Distance dependent connectivity in networks with a more biologically realistic structure does not compromise our linear analysis, as long as the linearized dynamics, and hence the uniform asynchronous irregular activity state, remain stable. We conclude that linear mechanisms of stimulus processing are indeed responsible for the emergence of orientation selectivity and its distribution in recurrent networks with functionally heterogeneous synaptic connectivity.; Comment: 12 figures

## Generalized activity equations for spiking neural network dynamics

Buice, Michael A.; Chow, Carson C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.67%
Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time scales - the spike duration time is much shorter than the inter-spike time, which is much shorter than any learning time scale. In numerical analysis, this is a classic stiff problem. Spiking neurons are also much more difficult to study analytically. One possible approach to making spiking networks more tractable is to augment mean field activity models with some information about spiking correlations. For example, such a generalized activity model could carry information about spiking rates and correlations between spikes self-consistently. Here, we will show how this can be accomplished by constructing a complete formal probabilistic description of the network and then expanding around a small parameter such as the inverse of the number of neurons in the network. The mean field theory of the system gives a rate-like description. The first order terms in the perturbation expansion keep track of covariances.

## Modeling networks of spiking neurons as interacting processes with memory of variable length

Galves, A.; Löcherbach, E.