144 research outputs found
Evidence accumulation and change rate inference in dynamic environments
In a constantly changing world, animals must account for environmental
volatility when making decisions. To appropriately discount older, irrelevant
information, they need to learn the rate at which the environment changes. We
develop an ideal observer model capable of inferring the present state of the
environment along with its rate of change. Key to this computation is an update
of the posterior probability of all possible changepoint counts. This
computation can be challenging, as the number of possibilities grows rapidly
with time. However, we show how the computations can be simplified in the
continuum limit by a moment closure approximation. The resulting
low-dimensional system can be used to infer the environmental state and change
rate with accuracy comparable to the ideal observer. The approximate
computations can be performed by a neural network model via a rate-correlation
based plasticity rule. We thus show how optimal observers accumulate evidence
in changing environments, and map this computation to reduced models which
perform inference using plausible neural mechanisms.Comment: 43 pages, 8 figures, in pres
Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients
Electro-cortical activity in patients with epilepsy may show abnormal
rhythmic transients in response to stimulation. Even when using the same
stimulation parameters in the same patient, wide variability in the duration of
transient response has been reported. These transients have long been
considered important for the mapping of the excitability levels in the
epileptic brain but their dynamic mechanism is still not well understood.
To understand the occurrence of abnormal transients dynamically, we use a
thalamo-cortical neural population model of epileptic spike-wave activity and
study the interaction between slow and fast subsystems.
In a reduced version of the thalamo-cortical model, slow wave oscillations
arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region
of bistability between a high amplitude oscillatory rhythm and the background
state. In vicinity of the bistability in parameter space, the model has
excitable dynamics, showing prolonged rhythmic transients in response to
suprathreshold pulse stimulation. We analyse the state space geometry of the
bistable and excitable states, and find that the rhythmic transient arises when
the impending FoC bifurcation deforms the state space and creates an area of
locally reduced attraction to the fixed point. This area essentially allows
trajectories to dwell there before escaping to the stable steady state, thus
creating rhythmic transients. In the full thalamo-cortical model, we find a
similar FoC bifurcation structure.
Based on the analysis, we propose an explanation of why stimulation induced
epileptiform activity may vary between trials, and predict how the variability
could be related to ongoing oscillatory background activity.Comment: http://journal.frontiersin.org/article/10.3389/fncom.2017.00025/ful
A neural population model of the bi-phasic EEG-power spectrum during general anaesthesia
International audienceThe neuronal mechanisms of general anaesthesia are still poorly understood, though the induction of analgesia, amnesia, immobility and loss of consciousness by anaesthetic agents is well-established in hospital practice. To shed some light onto these mysterious effects, the chapter analyzes mathematically a neural field model describing the neural population dynamics by an integro-differential equation. The power spectrum is derived and compared to experimental results
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