28 research outputs found
Inference-Based Decisions in a Hidden State Foraging Task:Differential Contributions of Prefrontal Cortical Areas
Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise
We discuss control techniques for noisy self-sustained oscillators with a
focus on reliability, stability of the response to noisy driving, and
oscillation coherence understood in the sense of constancy of oscillation
frequency. For any kind of linear feedback control--single and multiple delay
feedback, linear frequency filter, etc.--the phase diffusion constant,
quantifying coherence, and the Lyapunov exponent, quantifying reliability, can
be efficiently controlled but their ratio remains constant. Thus, an
"uncertainty principle" can be formulated: the loss of reliability occurs when
coherence is enhanced and, vice versa, coherence is weakened when reliability
is enhanced. Treatment of this principle for ensembles of oscillators
synchronized by common noise or global coupling reveals a substantial
difference between the cases of slightly non-identical oscillators and
identical ones with intrinsic noise.Comment: 10 pages, 5 figure
Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises
Dynamics of an ensemble of -unit FitzHugh-Nagumo (FN) neurons subject to
white noises has been studied by using a semi-analytical dynamical mean-field
(DMF) theory in which the original -dimensional {\it stochastic}
differential equations are replaced by 8-dimensional {\it deterministic}
differential equations expressed in terms of moments of local and global
variables. Our DMF theory, which assumes weak noises and the Gaussian
distribution of state variables, goes beyond weak couplings among constituent
neurons. By using the expression for the firing probability due to an applied
single spike, we have discussed effects of noises, synaptic couplings and the
size of the ensemble on the spike timing precision, which is shown to be
improved by increasing the size of the neuron ensemble, even when there are no
couplings among neurons. When the coupling is introduced, neurons in ensembles
respond to an input spike with a partial synchronization. DMF theory is
extended to a large cluster which can be divided into multiple sub-clusters
according to their functions. A model calculation has shown that when the noise
intensity is moderate, the spike propagation with a fairly precise timing is
possible among noisy sub-clusters with feed-forward couplings, as in the
synfire chain. Results calculated by our DMF theory are nicely compared to
those obtained by direct simulations. A comparison of DMF theory with the
conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice
Citric water as an alternative to water restriction for high-yield mouse behavior
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