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{842}  
Distilling freeform natural laws from experimental data
 
{305}  
PMID101388[0] Fine control of operantly conditioned firing patterns of cortical neurons.
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{1207} 
ref: 0
tags: Shenoy eye position BMI performance monitoring
date: 01252013 00:41 gmt
revision:1
[0] [head]


PMID18303802 Cortical neural prosthesis performance improves when eye position is monitored.
 
{1087} 
ref: Timmermann2003.01
tags: DBS double tremor oscillations DICS beamforming parkinsons
date: 02292012 00:39 gmt
revision:4
[3] [2] [1] [0] [head]


PMID12477707[0] The cerebral oscillatory network of parkinsonian resting tremor.
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{1132}  
PMID20400953 Dissolvable films of silk fibroin for ultrathin conformal biointegrated electronics.
 
{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 $\mathrm{SNR}(y)=\frac{\mathrm{Var}(x)}{\mathrm{Var}(\mathrm{err})}$ where $\mathrm{err}=xy$ . Note this is a ratio of powers; for the conventional SNR, ${\mathrm{SNR}}_{\mathrm{dB}}=10*{\mathrm{log}}_{10}\frac{\mathrm{Var}(x)}{\mathrm{Var}(\mathrm{err})}$ . $\mathrm{Var}(\mathrm{err})$ is also known as the meansquarederror (mse). Now, $\mathrm{Var}(\mathrm{err})=\sum (xy\overline{\mathrm{err}}{)}^{2}=\mathrm{Var}(x)+\mathrm{Var}(y)2\mathrm{Cov}(x,y)$ ; assume x and y have unit variance (or scale them so that they do), then $\frac{2\mathrm{SNR}(y{)}^{1}}{2}=\mathrm{Cov}(x,y)$ 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, $Q=\left[\begin{array}{cc}\mathrm{Var}(x)& \mathrm{Cov}(x,y)\\ \mathrm{Cov}(x,y)& \mathrm{Var}(y)\end{array}\right]$ $\mathrm{MI}=\frac{1}{2}\mathrm{log}\frac{\mathrm{Var}(x)\mathrm{Var}(y)}{\mathrm{det}(Q)}$ $\mathrm{Det}(Q)=1\mathrm{Cov}(x,y{)}^{2}$ Then $\mathrm{MI}=\frac{1}{2}{\mathrm{log}}_{2}[1\mathrm{Cov}(x,y{)}^{2}]$ or $\mathrm{MI}=\frac{1}{2}{\mathrm{log}}_{2}[\mathrm{SNR}(y{)}^{1}\frac{1}{4}\mathrm{SNR}(y{)}^{2}]$ 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}.  
{5} 
ref: bookmark0
tags: machine_learning research_blog parallel_computing bayes active_learning information_theory reinforcement_learning
date: 12312011 19:30 gmt
revision:3
[2] [1] [0] [head]


hunch.net interesting posts:
 
{968} 
ref: Bassett2009.07
tags: Weinberger congnitive efficiency beta band neuroimagaing EEG task performance optimization network size effort
date: 12282011 20:39 gmt
revision:1
[0] [head]


PMID19564605[0] Cognitive fitness of costefficient brain functional networks.
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{922}  
PMID20011034[0] A Wireless BrainMachine Interface for RealTime Speech Synthesis
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{252}  
PMID15022843[0] A simulation study of information transmission by multiunit microelectrode recordings key idea:
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{289}  
PMID11395017[0] Neuronal correlates of motor performance and motor learning in the primary motor cortex of monkeys adapting to an external force field
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{565} 
ref: Walker2005.12
tags: algae transfection transformation protein synthesis bioreactor
date: 03212008 17:22 gmt
revision:1
[0] [head]


Microalgae as bioreactors PMID16136314
 
{530}  
 
{520}  
http://www.dspguide.com/ch34.htm  awesome!!  
{344}  
PMID2027042[0] Making arm movements within different parts of space: the premotor and motor cortical representation of a coordinate system for reaching to visual targets.
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{294}  
PMID2376768[0] Making arm movements within different parts of space: dynamic aspects in the primate motor cortex
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{229} 
ref: notes0
tags: SNR MSE error multidimensional mutual information
date: 03082007 22:33 gmt
revision:2
[1] [0] [head]


http://ieeexplore.ieee.org/iel5/516/3389/00116771.pdf or http://hardm.ath.cx:88/pdf/MultidimensionalSNR.pdf
 
{7} 
ref: bookmark0
tags: book information_theory machine_learning bayes probability neural_networks mackay
date: 002007 0:0
revision:0
[head]


http://www.inference.phy.cam.ac.uk/mackay/itila/book.html  free! (but i liked the book, so I bought it :)  
{146} 
ref: van2004.11
tags: anterior cingulate cortex error performance monitoring 2004
date: 002007 0:0
revision:0
[head]


PMID15518940 Errors without conflict: implications for performance monitoring theories of anterior cingulate cortex.
 
{57}  
http://www.cs.rug.nl/~rudy/matlab/
 
{66} 
ref: bookmark0
tags: machine_learning classification entropy information
date: 002006 0:0
revision:0
[head]


http://iridia.ulb.ac.be/~lazy/  Lazy Learning. 