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[0] Schmidt EM, McIntosh JS, Durelli L, Bak MJ, Fine control of operantly conditioned firing patterns of cortical neurons.Exp Neurol 61:2, 349-69 (1978 Sep 1)[1] Serruya MD, Hatsopoulos NG, Paninski L, Fellows MR, Donoghue JP, Instant neural control of a movement signal.Nature 416:6877, 141-2 (2002 Mar 14)[2] Fetz EE, Operant conditioning of cortical unit activity.Science 163:870, 955-8 (1969 Feb 28)[3] Fetz EE, Finocchio DV, Operant conditioning of specific patterns of neural and muscular activity.Science 174:7, 431-5 (1971 Oct 22)[4] Fetz EE, Finocchio DV, Operant conditioning of isolated activity in specific muscles and precentral cells.Brain Res 40:1, 19-23 (1972 May 12)[5] Fetz EE, Baker MA, Operantly conditioned patterns on precentral unit activity and correlated responses in adjacent cells and contralateral muscles.J Neurophysiol 36:2, 179-204 (1973 Mar)

[0] Atallah HE, Lopez-Paniagua D, Rudy JW, O'Reilly RC, Separate neural substrates for skill learning and performance in the ventral and dorsal striatum.Nat Neurosci 10:1, 126-31 (2007 Jan)

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ref: -1992 tags: Linsker infomax Hebbian anti-hebbian linear perceptron unsupervised learning date: 08-04-2021 00:20 gmt revision:2 [1] [0] [head]

Local synaptic learning rules suffice to maximize mutual information in a linear network

  • Ralph Linsker, 1992.
  • A development upon {1545} -- this time with lateral inhibition trained through noise-contrast and anti-Hebbian plasticity.
  • {1545} does not perfectly maximize the mutual information between the input and output -- this allegedly requires the inverse of the covariance matrix, QQ .
    • As before, infomax principles; maximize mutual information MIH(Z)H(Z|S)MI \propto H(Z) - H(Z | S) where Z is the network output and S is the signal input. (note: minimize the conditional entropy of output given the input).
    • For a gaussian variable, H=12lndetQH = \frac{ 1}{ 2} ln det Q where Q is the covariance matrix. In this case Q=E|ZZ T|Q = E|Z Z^T |
    • since Z=C(S,N)Z = C(S,N) where C are the weights, S is the signal, and N is the noise, Q=CqC T+rQ = C q C^T + r where q is the covariance matrix of input noise and r is the cov.mtx. of the output noise.
    • (somewhat confusing): δH/δC=Q 1Cq\delta H / \delta C = Q^{-1}Cq
      • because .. the derivative of the determinant is complicated.
      • Check the appendix for the derivation. lndetQ=TrlnQln det Q = Tr ln Q and dH=1/2d(TrlnQ)=1/2Tr(Q 1dQ) dH = 1/2 d(Tr ln Q) = 1/2 Tr( Q^-1 dQ ) -- this holds for positive semidefinite matrices like Q.

  • From this he comes up with a set of rules whereby feedforward weights are trained in a Hebbian fashion, but based on activity after lateral activation.
  • The lateral activation has a weight matrix F=IαQF = I - \alpha Q (again Q is the cov.mtx. of Z). If y(0)=Y;y(t+1)=Y+Fy(t)y(0) = Y; y(t+1) = Y + Fy(t) , where Y is the feed-forward activation, then αy(inf)=Q 1Y\alpha y(\inf) = Q^{-1}Y . This checks out:
x = randn(1000, 10);
Q = x' * x;
a = 0.001;
Y = randn(10, 1);
y = zeros(10, 1); 
for i = 1:1000
	y = Y + (eye(10) - a*Q)*y;

y - pinv(Q)*Y / a % should be zero. 
  • This recursive definition is from Jacobi. αy(inf)=αΣ t=0 infF tY=α(IF) 1Y=Q 1Y\alpha y(\inf) = \alpha \Sigma_{t=0}^{\inf}F^tY = \alpha(I - F)^{-1} Y = Q^{-1}Y .
  • Still, you need to estimate Q through a running-average, ΔQ=1M(Y nY m+r nmQ NM)\Delta Q = \frac{ 1}{M}( Y_n Y_m + r_{nm} - Q_{NM} ) and since F=IαQF = I - \alpha Q , F is formed via anti-hebbian terms.

To this is added a 'sensing' learning and 'noise' unlearning phase -- one optimizes H(Z)H(Z) , the other minimizes H(Z|S)H(Z|S) . Everything is then applied, similar to before, to a gaussian-filtered one-dimensional white-noise stimuli. He shows this results in bandpass filter behavior -- quite weak sauce in an era where ML papers are expected to test on five or so datasets. Even if this was 1992 (nearly forty years ago!), it would have been nice to see this applied to a more realistic dataset; perhaps some of the following papers? Olshausen & Field came out in 1996 -- but they applied their algorithm to real images.

In both Olshausen & this work, no affordances are made for multiple layers. There have to be solutions out there...

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ref: Schmidt-1978.09 tags: Schmidt BMI original operant conditioning cortex HOT pyramidal information antidromic date: 03-12-2019 23:35 gmt revision:11 [10] [9] [8] [7] [6] [5] [head]

PMID-101388[0] Fine control of operantly conditioned firing patterns of cortical neurons.

  • Hand-arm area of M1, 11 or 12 chronic recording electrodes, 3 monkeys.
    • But, they only used one unit at a time in the conditioning task.
  • Observed conditioning in 77% of single units and 65% of combined units (multiunits?).
  • Trained to move a handle to a position indicated by 8 annular cursor lights.
    • Cursor was updated at 50hz -- this was just a series of lights! talk about simple feedback...
    • Investigated different smoothing: too fast, FR does not stay in target; too slow, cursor acquires target too slowly.
      • My gamma function is very similar to their lowpass filter used for smoothing the firing rates.
    • 4 or 8 target random tracking task
    • Time-out of 8 seconds
    • Run of 40 trials
      • The conditioning reached a significant level of performance after 2.2 runs of 40 trials (in well-trained monkeys); typically, they did 18 runs/day (720 trials)
  • Recordings:
    • Scalar mapping of unit firing rate to cursor position.
    • Filtered 600-6kHz
    • Each accepted spike triggered a generator that produced a pulse of of constant amplitude and width -> this was fed into a lowpass filter (1.5 to 2.5 & 3.5Hz cutoff), and a gain stage, then a ADC, then (presumably) the PDP.
      • can determine if these units were in the pyramidal tract by measuring antidromic delay.
    • recorded one neuron for 108 days!!
      • Neuronal activity is still being recorded from one monkey 24 months after chronic implantation of the microelectrodes.
    • Average period in which conditioning was attempted was 3.12 days.
  • Successful conditioning was always associated with specific repeatable limb movements
    • "However, what appears to be conditioned in these experiments is a movement, and the neuron under study is correlated with that movement." YES.
    • The monkeys clearly learned to make (increasingly refined) movement to modulate the firing activity of the recorded units.
    • The monkey learned to turn off certain units with specific limb positions; the monkey used exaggerated movements for these purposes.
      • e.g. finger and shoulder movements, isometric contraction in one case.
  • Trained some monkeys or > 15 months; animals got better at the task over time.
  • PDP-12 computer.
  • Information measure: 0 bits for missed targets, 2 for a 4 target task, 3 for 8 target task; information rate = total number of bits / time to acquire targets.
    • 3.85 bits/sec peak with 4 targets, 500ms hold time
    • With this, monkeys were able to exert fine control of firing rate.
    • Damn! compare to Paninski! [1]
  • 4.29 bits/sec when the same task was performed with a manipulandum & wrist movement
  • they were able to condition 77% of individual neurons and 65% of combined units.
  • Implanted a pyramidal tract electrode in one monkey; both cells recorded at that time were pyramidal tract neurons, antidromic latencies of 1.2 - 1.3ms.
    • Failures had no relation to over movements of the monkey.
  • Fetz and Baker [2,3,4,5] found that 65% of precentral neurons could be conditioned for increased or decreased firing rates.
    • and it only took 6.5 minutes, on average, for the units to change firing rates!
  • Summarized in [1].


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ref: Carpenter-1981.11 tags: STN subthalamic nucleus anatomy tracing globus_pallidus PPN substantia_nigra DBS date: 02-22-2012 22:01 gmt revision:7 [6] [5] [4] [3] [2] [1] [head]

PMID-7284825[0] Connections of the subthalamic nucleus in the monkey.

  • STN projects to both segments of the globus pallidus in a laminar and organized fashion.
    • most fibers projected to the lateral pallidal segment (aka GPe).
  • also projected to specific thalamic nuclei (VAmc, VLm, DMpl).
  • the major projection of PPN is to SN.
  • striatum projects to the substantia nigra pars reticulata (SNr). interesting.
  • see also: PMID-1707079[1]
    • "Anterograde transport in fibers and terminal fields surrounded retrogradely labeled cells in the LPS (GPe), suggesting a reciprocal relationship [to the STN]"
  • These data suggest that the STN receives its major subcortical input from cell of the LPS (GPe) arranged in arrays which have a rostrocaudal organization.
  • No cells of the MPS (GPi) or SN project to the STN.
  • The output of the STN is to both segments of the GP and SNpr.
  • Major subcortical projections to PPN arise from the MPS (GPi) and SNpr (output of the BG) , but afferents also arise from other sources.
    • The major projection of PPN is to SN.
    • HRP injected into PPN produced profuse retrograde transport in cells of the MPS and SNpr and distinct label in a few cells of the zona incerta and STN.


[0] Carpenter MB, Carleton SC, Keller JT, Conte P, Connections of the subthalamic nucleus in the monkey.Brain Res 224:1, 1-29 (1981 Nov 9)
[1] Carpenter MB, Jayaraman A, Subthalamic nucleus of the monkey: connections and immunocytochemical features of afferents.J Hirnforsch 31:5, 653-68 (1990)

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ref: Sato-2000.01 tags: globus_pallidus anatomy STN GPi GPe SNr substantia nigra tracing DBS date: 01-26-2012 17:20 gmt revision:6 [5] [4] [3] [2] [1] [0] [head]

PMID-10660885[0] Single-axon tracing study of neurons of the external segment of the globus pallidus in primate.

  • wow, check out the computerized tracing! the neurons tend to project to multiple areas, usually. I didn't realize this. I imagine that it is relatively common in the brain.
  • complicated, tree-like axon collateral projection from GPe to GPi.
    • They look like the from through some random-walk process; paths are not at all efficient.
    • I assume these axons are mylenated? unmylenated?
  • dendritic fields in the STN seem very dense.
  • study done in cyno. rhesus


[0] Sato F, Lavallée P, Lévesque M, Parent A, Single-axon tracing study of neurons of the external segment of the globus pallidus in primate.J Comp Neurol 417:1, 17-31 (2000 Jan 31)

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ref: Breit-2006.1 tags: parkinsons basal_ganglia palladium substantia_nigra motor_control striate date: 01-24-2012 22:10 gmt revision:1 [0] [head]

I wish i could remember where i got these notes from, so as to verify the somewhat controversial statements. I found them written on the back of a piece of scrap paper.

  • neurophysiological recordings in animals show that over half of basal ganglia neurons fire in response to motor activity but none are triggered by passive limb movement.
  • in parkinson's disease (PD), the substantia nigra actually becomes pale to the eye.
  • stimulation of the striatum does not result in low-threshold movements like stimulation of the cortex does.
  • palladium does not seem linked to motor planning. (just execution?)
  • stimulation of the caudate causes movement, i.e. head turning, while stimulation of the ventromedial caudate produces arrest and crouching movements. (Delgado etc)
  • large bilateral striatal leasions cause inattention.
  • striatal units appear to signal movement, not generate/compute it (really?)
  • in parkinson's disease, motor learning appears normal - it is the initial slowness that is abnormal :: PD relates to the quality of movement, not the quality of the motor commands. Thus, perhaps PD is a disease of gating/attention?
  • in PD, all reflexes except the Hoffman-reflex appear normal.
    • The primary difference between the H-reflex and the spinal stretch reflex is that the H-reflex bypasses the muscle spindle and, therefore, is a valuable tool in assessing modulation of monosynaptic reflex activity in the spinal cord. The H-reflex is an estimate of alpha motoneuron ( alphaalpha MN) excitability when presynaptic inhibition and intrinsic excitability of the alphaalpha MNs remain constant.
  • A lesion of the PPN (pedunculo pontine nucleus) was shown to restore decreased activity levels in the SNr and STN of a rat model of parkinson's (lesion of the SNc) PMID-17042796

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ref: Atallah-2007.01 tags: striatum skill motor learning VTA substantia nigra basal ganglia reinforcement learning date: 12-31-2011 18:59 gmt revision:3 [2] [1] [0] [head]

PMID-17187065[0] Separate neural substrates for skill learning and performance in the ventral and dorsal striatum.

  • good paper. via SCLin's blog. slightly confusing anatomical terminology.
  • tested in rats, which has a anatomically different basal ganglia system than primates.
  • Rats had to choose which driection in a Y maze based on olfactory cues. Normal rats figure it out in 60 trials.
  • ventral striatum (nucleus accumbens here in rats) connects to the ventral prefrontal cortices (for example, the orbitofrontal cortex)
    • in primates, includes the medial caudate, which has been shown in fMRI to respond to reward prediction error. Neural activity in the caudate is attenuated when a monkey reaches optimal performance.
  • dorsal parts of the striatum (according to web: caudate, putamen, globus pallidus in primates) connect to the dorsal prefrontal and motor cortices
    • (according to them:) this corresponds to the putamen in primates. Activity in the putamen reflects performance but not learning.
    • activity in the putamen is highest after successful learning & accurate performance.
  • used muscimol (GABAa agonist, silences neural activity) and AP-5 (blocks NMDA based plasticity), in each of the target areas.
  • dorsal striatum is involved in performance but not learning
    • Injection of muscimol during acquisition did not impair test performance
    • Injection of muscimol during test phase did impair performance
    • Injection of AP-5 during acquisition had no effect.
    • in acquisition sessions, muscimol blocked instrumental response (performance); but muscimol only has a small effect when it was injected after rats perfected the task.
      • Idea: consistent behavior creates a stimulus-response association in extrastriatal brain areas, e.g. cerebral cortex. That is, the basal ganglia is the reinforcement signal, the cortex learns the association due to feedback-driven behavior? Not part of the habit system, but make and important contribution to goal-directed behavior.
      • This is consistent with the observation that behavior is initially goal driven but is later habitual.
    • Actually, other studies show that plasticity in the dorsal striatum may be detrimental to instrumental learning.
    • The number of neurons that fire just before the execution of a response is larger in the putamen than the caudate.
  • ventral striatum is involved in learning and performance.
    • Injection of AP-5 or muscimol during acquisition (learning behavior) impairs test performance.
    • Injection of AP-5 during test performance has no effect , but muscimol impairs performance.
  • Their data support an actor-director-critic architecture of the striatum:
    • Actor = dorsal striatum; involved in performance, but not in learning them.
    • Director = ventral striatum; quote "it somehow learns the relevant task demands and directs the dorsal striatum to perform the appropriate action plans, but, crucially, it does not train the dorsal striatum"
      • ventrai striatum acts through the orbitofrontal cortex that mantains representations of task-reward contingencies.
      • ventral striatum might also select action selection through it's projections to the substantia nigra.
    • Critic = dopaminergic inputs from the ventral tegmental area and substantia nigra.


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ref: Shidara-2002.05 tags: anterior cingulate ACC 2002 reward anticipation ODC date: 12-07-2011 04:12 gmt revision:1 [0] [head]

PMID-12040201[0] Anterior cingulate: single neuronal signals related to degree of reward expectancy

  • feelings of increasing anticipation experienced as we work toward a predicted outcome may be traceable to a reward expectancy signal; in OCD, the brain may be 'hijacked' by runaway signals in the reward expectancy circuit.
    • brain imaging studies have detected abnormal activation of ACC in OCD


[0] Shidara M, Richmond BJ, Anterior cingulate: single neuronal signals related to degree of reward expectancy.Science 296:5573, 1709-11 (2002 May 31)

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ref: life-0 tags: princeton postmodern education kirn atlantic essay poetry undergrad date: 05-20-2009 05:32 gmt revision:1 [0] [head]

http://www.theatlantic.com/doc/200501/kirn -- goood.

  • quote: "Would it be possible someday—through drugs, maybe, or esoteric Buddhism, or some profound, postapocalyptic languor—to stop coming up with ideas of what we are and then laboring to live up to them?" -- from "The Autumn of the Multitasker". (The title makes me think of "Delta Autumn" by Faulkner, which I love...)

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ref: Corlett-2007.09 tags: delusions pFC substantia nigra date: 09-23-2008 06:15 gmt revision:0 [head]

PMID-17690132 Disrupted prediction-error signal in psychosis: evidence for an associative account of delusions.

  • Hypothesis: the creation and maintenance of psychotic or delusional beliefs is caused by (or causally related to) malfunction in the predictive error circuitry in the brain. (namely, the prefrontal cortex, substantia nigra, and striatum).
  • Previous studies have shown that administering Ketamine, a dissociative drug that can cause delusions, effects this same pathway.
  • The authors tested the hypothesis by training control and psychotic subjects in an associative task: subjects had to determine if a fictitious patient would be allergic to a meal given example meals and resulting allergic reaction.
  • Both sets had about the same behavioral performance; however, activation of the prefrontal cortex, substantia nigra, and left striatum was less in the psychotic (some drug treated) subjects. This comparison of activation was measured between control trials (no prediction error) and violation trials (prediction violated) as well as unovershadowing (a and b causes allergy, but a or b separately do not)

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ref: notes-0 tags: DSP filter quantize lowpass elliptic matlab date: 09-02-2007 15:20 gmt revision:0 [head]

So, in order to measure how quantizing filter coeficients affects filter response, I quantized the coefficients of a 8th order bandpass filter designed with:

[B1, A1] = ellip(4,0.8,70, [600/31.25e3 6/31.25]);
here is a function that quantizes & un-quantizes the filter coeff, then compares the frequency responses:
function [Bq, Aq, Bcoef, Acoef] = filter_quantize(B, A) 
% quantize filter coeficients & un-quantize so as to get some idea to
% the *actual* fixed-point filter performance. 
% assume that everything in broken into biquads. 
base = 10; 
Aroots = roots(A); 
Broots = roots(B); 
order = length(Aroots)/2; % the number of biquads.
scale = B(1).^(1/order); % distribute the gain across the biquads. 
for o = 0:order-1
	Acoef_biquad(o+1, :) = poly(Aroots(o*2+1 : o*2+2));
	Bcoef_biquad(o+1, :) = poly(Broots(o*2+1 : o*2+2))*scale; 
Bcoef = round(Bcoef_biquad .* 2^base); 
Acoef = round(Acoef_biquad .* 2^base); 
% now, reverse the process. 
Bq2 = Bcoef ./ 2^base; 
Aq2 = Acoef ./ 2^base; 
for o = 0:order-1
	Arootsq(o*2+1: o*2+2) = roots(Aq2(o+1, :)); 
	Brootsq(o*2+1: o*2+2) = roots(Bq2(o+1, :)); 
Aq = poly(Arootsq); 
Bq = poly(Brootsq).*B(1); 
[H, W] = freqz(B, A); 
[Hq, Wq] = freqz(Bq, Aq); 
plot(W, db(abs(H)), 'b')
hold on
plot(W, db(abs(Hq)), 'r')
axis([0 pi -100 0])
The result: high frequency is not much affected

but low frequency is strongly affected.

But this is at a quatization to 10 bits - quantization to 15 bits lead to reasonably good performance. I'm not sure if this conclusively indicates / counterindicates downsampling prior to highpassing for my application, but i would say that it does, as if you downsample by 2 the highpass cutoff frequency will be 2x larger hence the filter will be less senitive to quantization errors which affect low frequencies.

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ref: neuro notes-0 tags: SNr SNc substantia nigra anatomy tracing date: 02-06-2007 05:40 gmt revision:0 [head]

Patterns of axonal branching of neurons of the substantia nigra pars reticulata and pars lateralis in the rat.

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ref: Wichmann-1999.04 tags: parkinsons basal ganglia substantia nigra date: 0-0-2007 0:0 revision:0 [head]

PMID-10323285 Comparison of MPTP-induced changes in spontaneous neuronal discharge in the internal pallidal segment and in the substania nigra pars reticulata

  • putamen = motor portion of the striatum.
  • basal ganglia output is directed toward the ventral anterior, ventrolateral, and centromedial nuclei of the thalamus, which, in turn, project back to the cortex. Plus, the output of the basal ganglia project to the cortex.
  • MPTP induces excessive 3-8 Hz bursts in the GPi (e.g. correlated with tremor).