1,586 research outputs found
Probing the dynamics of identified neurons with a data-driven modeling approach
In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach
Revisiting chaos in stimulus-driven spiking networks: signal encoding and discrimination
Highly connected recurrent neural networks often produce chaotic dynamics,
meaning their precise activity is sensitive to small perturbations. What are
the consequences for how such networks encode streams of temporal stimuli? On
the one hand, chaos is a strong source of randomness, suggesting that small
changes in stimuli will be obscured by intrinsically generated variability. On
the other hand, recent work shows that the type of chaos that occurs in spiking
networks can have a surprisingly low-dimensional structure, suggesting that
there may be "room" for fine stimulus features to be precisely resolved. Here
we show that strongly chaotic networks produce patterned spikes that reliably
encode time-dependent stimuli: using a decoder sensitive to spike times on
timescales of 10's of ms, one can easily distinguish responses to very similar
inputs. Moreover, recurrence serves to distribute signals throughout chaotic
networks so that small groups of cells can encode substantial information about
signals arriving elsewhere. A conclusion is that the presence of strong chaos
in recurrent networks does not prohibit precise stimulus encoding.Comment: 8 figure
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses
We present a mathematical analysis of a networks with Integrate-and-Fire
neurons and adaptive conductances. Taking into account the realistic fact that
the spike time is only known within some \textit{finite} precision, we propose
a model where spikes are effective at times multiple of a characteristic time
scale , where can be \textit{arbitrary} small (in particular,
well beyond the numerical precision). We make a complete mathematical
characterization of the model-dynamics and obtain the following results. The
asymptotic dynamics is composed by finitely many stable periodic orbits, whose
number and period can be arbitrary large and can diverge in a region of the
synaptic weights space, traditionally called the "edge of chaos", a notion
mathematically well defined in the present paper. Furthermore, except at the
edge of chaos, there is a one-to-one correspondence between the membrane
potential trajectories and the raster plot. This shows that the neural code is
entirely "in the spikes" in this case. As a key tool, we introduce an order
parameter, easy to compute numerically, and closely related to a natural notion
of entropy, providing a relevant characterization of the computational
capabilities of the network. This allows us to compare the computational
capabilities of leaky and Integrate-and-Fire models and conductance based
models. The present study considers networks with constant input, and without
time-dependent plasticity, but the framework has been designed for both
extensions.Comment: 36 pages, 9 figure
Learning to Recognize Actions from Limited Training Examples Using a Recurrent Spiking Neural Model
A fundamental challenge in machine learning today is to build a model that
can learn from few examples. Here, we describe a reservoir based spiking neural
model for learning to recognize actions with a limited number of labeled
videos. First, we propose a novel encoding, inspired by how microsaccades
influence visual perception, to extract spike information from raw video data
while preserving the temporal correlation across different frames. Using this
encoding, we show that the reservoir generalizes its rich dynamical activity
toward signature action/movements enabling it to learn from few training
examples. We evaluate our approach on the UCF-101 dataset. Our experiments
demonstrate that our proposed reservoir achieves 81.3%/87% Top-1/Top-5
accuracy, respectively, on the 101-class data while requiring just 8 video
examples per class for training. Our results establish a new benchmark for
action recognition from limited video examples for spiking neural models while
yielding competetive accuracy with respect to state-of-the-art non-spiking
neural models.Comment: 13 figures (includes supplementary information
Transition to chaos in random neuronal networks
Firing patterns in the central nervous system often exhibit strong temporal
irregularity and heterogeneity in their time averaged response properties.
Previous studies suggested that these properties are outcome of an intrinsic
chaotic dynamics. Indeed, simplified rate-based large neuronal networks with
random synaptic connections are known to exhibit sharp transition from fixed
point to chaotic dynamics when the synaptic gain is increased. However, the
existence of a similar transition in neuronal circuit models with more
realistic architectures and firing dynamics has not been established.
In this work we investigate rate based dynamics of neuronal circuits composed
of several subpopulations and random connectivity. Nonzero connections are
either positive-for excitatory neurons, or negative for inhibitory ones, while
single neuron output is strictly positive; in line with known constraints in
many biological systems. Using Dynamic Mean Field Theory, we find the phase
diagram depicting the regimes of stable fixed point, unstable dynamic and
chaotic rate fluctuations. We characterize the properties of systems near the
chaotic transition and show that dilute excitatory-inhibitory architectures
exhibit the same onset to chaos as a network with Gaussian connectivity.
Interestingly, the critical properties near transition depend on the shape of
the single- neuron input-output transfer function near firing threshold.
Finally, we investigate network models with spiking dynamics. When synaptic
time constants are slow relative to the mean inverse firing rates, the network
undergoes a sharp transition from fast spiking fluctuations and static firing
rates to a state with slow chaotic rate fluctuations. When the synaptic time
constants are finite, the transition becomes smooth and obeys scaling
properties, similar to crossover phenomena in statistical mechanicsComment: 28 Pages, 12 Figures, 5 Appendice
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