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Margot edited MethodsThe_Hindmarsh_Rose_ModelThe_Hindmarsh__.html
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replacing the applied current, I, with an estimated response function,
x=y-ax^3+bx^2-z+\hat{r}(t)
\hat{r}(t) = h(t) \star s(t)
where
h(t) is a linear filter, s(t) is the stimulus, and $\star$ is
convolution. This adjustment allows us to fit the HR model to in vivo
neuron recording data.
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Genetic
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Mathematical
models such as the HR-neuron provide researchers a framework to understand and
predict qualities of a given system of interest. Researchers have developed
...
processing environment. Rather than having one chain randomly sampling
the posterior distribution, the ensemble sampler has hundreds of small
chains sampling at once. These features should allow the sampler to
converge on good parameter estimations more quickly than standard MCMC algorithms.
Evaluating Fitness
We evaluated the fitness of our models by using the SPIKE synchronization metric (Kruez et al, 2015). This metric calculates time similarity between spike trains by counting up the number of coincidences between. The metric is calculated,
SYNC = \frac{1}{M}\sum_{k=1}^{M}C_k
\[C_i^{(n,m)} = \left \{\begin{matrix}
1 if min_j(|t_i^m-t_j^m)|) <\tau_{i,j}& \\
0 > otherwise &
\end{matrix}\]
where M is number of possible coincidences, C is the coincidence factor for pairs of spikes, and $\tau$ is the coincidence window.
This metric provides some advantages over other commonly used spike-train similarity metrics, such as van-Rossum distance (van Rossum, 2001). It is time-scale independent, requires no parameter optimization, and very computationally efficient because it requires no convolutions.
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Method
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Method Validation - Twin Data Analysis
We demonstrate
the effectiveness of both MCMC and genetic algorithms for solving DSTRF HR-neuron
models by means of “twin data” analysis (Toth et al., 2011). We set the
parameters of an HR-neuron model to known fixed values and integrated across
...
the same manner from MCMC and genetic algorithm estimates of the DSTRF model.
When an MCMC or genetic algorithm generated spike train bests matches our original
spike train based on some fitness function, we inspect and compare parameter
estimates.
estimates.
