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PMID16425835[0] Reliability of signals from a chronically implanted, siliconbased electrode array
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PMID19050033[0] Levodopa enhances synaptic plasticity in the substantia nigra pars reticulata of Parkinson's disease patients
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{828} 
ref: RodriguezOroz2001.09
tags: STN SNr parkinsons disease single unit recording spain 2001 tremor oscillations DBS somatotopy organization
date: 02222012 18:24 gmt
revision:12
[11] [10] [9] [8] [7] [6] [head]


PMID11522580[0] The subthalamic nucleus in Parkinson's disease: somatotopic organization and physiological characteristics
Old notes:
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PMID10660885[0] Singleaxon tracing study of neurons of the external segment of the globus pallidus in primate.
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{255} 
ref: BarGad2003.12
tags: information dimensionality reduction reinforcement learning basal_ganglia RDDR SNR globus pallidus
date: 01162012 19:18 gmt
revision:3
[2] [1] [0] [head]


PMID15013228[] Information processing, dimensionality reduction, and reinforcement learning in the basal ganglia (2003)
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{806}  
I've recently tried to determine the bitrate of conveyed by one gaussian random process about another in terms of the signaltonoise ratio between the two. Assume $x$ is the known signal to be predicted, and $y$ is the prediction. Let's define $SNR(y) = \frac{Var(x)}{Var(err)}$ where $err = xy$ . Note this is a ratio of powers; for the conventional SNR, $SNR_{dB} = 10*log_{10 } \frac{Var(x)}{Var(err)}$ . $Var(err)$ is also known as the meansquarederror (mse). Now, $Var(err) = \sum{ (x  y  sstrch \bar{err})^2 estrch} = Var(x) + Var(y)  2 Cov(x,y)$ ; assume x and y have unit variance (or scale them so that they do), then $\frac{2  SNR(y)^{1}}{2 } = Cov(x,y)$ We need the covariance because the mutual information between two jointly Gaussian zeromean variables can be defined in terms of their covariance matrix: (see http://www.springerlink.com/content/v026617150753x6q/ ). Here Q is the covariance matrix, $Q = \left[ \array{Var(x) & Cov(x,y) \\ Cov(x,y) & Var(y)} \right]$ $MI = \frac{1 }{2 } log \frac{Var(x) Var(y)}{det(Q)}$ $Det(Q) = 1  Cov(x,y)^2$ Then $MI =  \frac{1 }{2 } log_2 \left[ 1  Cov(x,y)^2 \right]$ or $MI =  \frac{1 }{2 } log_2 \left[ SNR(y)^{1}  \frac{1 }{4 } SNR(y)^{2} \right]$ This agrees with intuition. If we have a SNR of 10db, or 10 (power ratio), then we would expect to be able to break a random variable into about 10 different categories or bins (recall stdev is the sqrt of the variance), with the probability of the variable being in the estimated bin to be 1/2. (This, at least in my mind, is where the 1/2 constant comes from  if there is gaussian noise, you won't be able to determine exactly which bin the random variable is in, hence log_2 is an overestimator.) Here is a table with the respective values, including the amplitude (not power) ratio representations of SNR. "
Now, to get the bitrate, you take the SNR, calculate the mutual information, and multiply it by the bandwidth (not the sampling rate in a discrete time system) of the signals. In our particular application, I think the bandwidth is between 1 and 2 Hz, hence we're getting 1.63.2 bits/second/axis, hence 3.26.4 bits/second for our normal 2D tasks. If you read this blog regularly, you'll notice that others have achieved 4bits/sec with one neuron and 6.5 bits/sec with dozens {271}.  
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ref: notes0
tags: sorting SNR correlation coefficient expectation maximization tlh24
date: 01062012 03:07 gmt
revision:5
[4] [3] [2] [1] [0] [head]


Description: red is the perchannel crossvalidated correlation coeifficent of prediction. Blue is the corresponding number of clusters that the unit was sorted into, divided by 10 to fit on the same axis. The variable being predicted is cartesian X position. note 32 channels were dead (from PP). The last four (most rpedictive) channels were: 71 (1 unit), 64 (5 units), 73 (6 units), 67 (1 unit). data from sql entry: clem 20070308 18:59:27 timarm_log_20070308_185706.out ;Looks like this data came from PMD region. Description: same as above, but for the yaxis. Description: same as above, but for the zaxis. Conclusion: sorting seems to matter & have a nonnegligible positive effect on predictive ability.  
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http://delsys.com/KnowledgeCenter/FAQ_EMGSensor.html
 
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ref: notes0
tags: SNR MSE error multidimensional mutual information
date: 03082007 22:33 gmt
revision:2
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http://ieeexplore.ieee.org/iel5/516/3389/00116771.pdf or http://hardm.ath.cx:88/pdf/MultidimensionalSNR.pdf
 
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