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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] Schmidt EM, Single neuron recording from motor cortex as a possible source of signals for control of external devices.Ann Biomed Eng 8:4-6, 339-49 (1980)[1] 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)[2] Salcman M, Bak MJ, A new chronic recording intracortical microelectrode.Med Biol Eng 14:1, 42-50 (1976 Jan)

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ref: work-0 tags: distilling free-form natural laws from experimental data Schmidt Cornell automatic programming genetic algorithms date: 12-30-2021 05:11 gmt revision:7 [6] [5] [4] [3] [2] [1] [head]

Distilling free-form natural laws from experimental data

  • The critical step was to use the full set of all pairs of partial derivatives ( δx/δy\delta x / \delta y ) to evaluate the search for invariants.
  • The selection of which partial derivatives are held to be independent / which variables are dependent is a bit of a trick too -- see the supplemental information.
    • Even yet, with a 4D data set the search for natural laws took ~ 30 hours.
  • This was via a genetic algorithm, distributed among 'islands' on different CPUs, with mutation and single-point crossover.
  • Not sure what the IL is, but it appears to be floating-point assembly.
  • Timeseries data is smoothed with Loess smoothing, which fits a polynomial to the data, and hence allows for smoother / more analytic derivative calculation.
    • Then again, how long did it take humans to figure out these invariants? (Went about it in a decidedly different way..)
    • Further, how long did it take for biology to discover similar 'design equations'?
      • The same algorithm has been applied to biological data - a metabolic pathway - with some success pub 2011.
      • Of course evolution had to explore a much larger space - proteins and regulatory pathways, not simpler mathematical expressions / linkages.


Since his Phd, Michael Schmidt has gone on to found Nutonian, which produced Eurequa software, apparently without dramatic new features other than being able to use the cloud for equation search. (Probably he improved many other detailed facets of the software..). Nutonian received $4M in seed funding, according to Crunchbase.

In 2017, Nutonian was acquired by Data Robot (for an undisclosed amount), where Michael has worked since, rising to the title of CTO.

Always interesting to follow up on the authors of these classic papers!

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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].

____References____

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ref: -0 tags: coevolution fitness prediction schmidt genetic algorithm date: 09-14-2018 01:34 gmt revision:8 [7] [6] [5] [4] [3] [2] [head]

Coevolution of Fitness Predictors

  • Michael D. Schmidt and Hod Lipson, Member, IEEE
  • Fitness prediction is a technique to replace fitness evaluation in evolutionary algorithms with a light-weight approximation that adapts with the solution population.
    • Cannot approximate the full landscape, but shift focus during evolution.
    • Aka local caching.
    • Or adversarial techniques.
  • Instead use coevolution, with three populations:
    • 1) solutions to the original problem, evaluated using only fitness predictors;
    • 2) fitness predictors of the problem; and
    • 3) fitness trainers, whose exact fitness is used to train predictors.
      • Trainers are selected high variance solutions across the predictors, and predictors are trained on this subset.
  • Lightweight fitness predictors evolve faster than the solution population, so they cap the computational effort on that at 5% overall effort.
    • These fitness predictors are basically an array of integers which index the full training set -- very simple and linear. Maybe boring, but the simplest solution that works ...
    • They only sample 8 training examples for even complex 30-node solution functions (!!).
    • I guess, because the information introduced into the solution set is relatively small per generation, it makes little sense to over-sample or over-specify this; all that matters is that, on average, it's directionally correct and unbiased.
  • Used deterministic crowding selection as the evolutionary algorithm.
    • Similar individuals have to compete in tournaments for space.
  • Showed that the coevolution algorithm is capable of inferring even highly complex many-term functions
    • And, it uses function evaluations more efficiently than the 'exact' (each solution evaluated exactly) algorithm.
  • Coevolution algorithm seems to induce less 'bloat' in the complexity of the solutions.
  • See also {842}

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ref: Schmidt-1984.11 tags: spike sorting Schmidt date: 01-15-2012 05:45 gmt revision:5 [4] [3] [2] [1] [0] [head]

PMID-6392757[0] Instruments for sorting neuroelectric data: a review

  • Seems like it would be useful for me :-)
  • Amplifier bandwidth should be between 5 and 7.5kHz
  • High-pass between 100 and 600Hz, to reduce the 'baseline hash produced by the firing of distant neurons.
  • Electrodes generate Johnson noise (same as thermal noise): E=0.1219R×BμVrms E = 0.1219 \sqrt{R \times B} \mu V rms , where B = bandwidth in Hz and R = resistance in MOhm.
  • Modern low-noise FET amplifiers produce noise equivalent to a source resistance of 15K
  • Describe a number of nonlinear spike detection filters using switched amplifiers; these do not seem to have survived.
  • Analog window comparators described have been largely replaced with digital filtering techniques.
    • That said, the use of photo-detectors taped to an oscilloscope is an ingenious method for spike discrimination!
  • Note that audio output is useful, too. Ear is a good discriminator.

____References____

[0] Schmidt EM, Instruments for sorting neuroelectric data: a review.J Neurosci Methods 12:1, 1-24 (1984 Nov)

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ref: Schmidt-1980.01 tags: BMI 1980 SUA M1 prosthetics Schmidt MEA date: 01-04-2012 22:59 gmt revision:14 [13] [12] [11] [10] [9] [8] [head]

PMID-6794389[0] Single neuron recording from motor cortex as a possible source of signals for control of external devices

  • also [1]
  • I guess this was the first published article claiming that motorneurons could be used to drive a prosthesis, and first clear attempt at long-term array recording (?)
  • recorded via arrays for up to 37 months!
    • only 2 of the 11 eelctrodes were recording at the time of sacrifice.
  • trained the monkey to perform an 8 target tracking task
    • with cortical neurons: 2.45 bits/second
    • with wrist flexion/extension: 4.48 bits/second
  • electrodes: {946} A new chronic recording intracortical microelectrode (1976!)
    • 25um iridium wires electropolished to a 1um tip; 1.5mm long.
    • electrodes float on the cortex; signals transmitted through 25um gold wire, which is in turn connected to a head-mounted connector.
    • iridium and gold are insulated with vapor-deposited parylene-C
    • electrode tips are exposed with a HV arc. (does this dull them? from the electromicrograph, it seems that it just makes them rougher.)
    • arrays of 12.
    • 1M impedance (average)
  • interesting: neural activity was recorded from at least 8 different neurons with this electrode during the course of the implant, indicating that it was migrating through cortical tissue.
    • the average recording time from the same electrode was 8 days; max 23 days.
  • second implant was more successful: maximium time recording from the same neuron was 108 days.
  • failure is associated with cracks in the parylene insulation (which apparently occurred on the grain boundaries of the iridium). "still only marginally reliable" (and still.. and still..)
  • they have operantly trained cortical units in another, earlier study.
  • have, effectively, 8 levels of activity, with feedback monkey has to match the proscribed firing rate.
  • > 50% rewarded trials = success for them; 26/28 of the neurons tested were eventually conditioned successfully.
  • looks like the monkey can track the target firing rate rather accurately. "the output of cortical cells can provide information output rates moderately less precise than the intact motor system. "
  • Monkey can also activated sequences of neurons: A, then AB, then B.
  • people have also tried conditioning individual EMG units; it is sometimes possible to control 2 different motor units in the same muscle independently, but in general only a single channel of information can be obtained from one muscle, and gross EMGs are fine for this.
    • Thus surface EMG is preferred.
    • you can get ~ 2.73 bits/sec with gross EMG on a human; 2.99 bits/sec (max) with a monkey.
  • they remind us, of course, that an enormous amount of work remains to be done.

____References____

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ref: Schmidt-1984.12 tags: Schmidt spike sorting PCA date: 12-20-2011 23:34 gmt revision:1 [0] [head]

PMID-6396456[0] Computer separation of multi-unit neuroelectric data: a review

  • goes through the standard, by then well-established ideas: template matching, PCA, spike amplitude, peak-to-peak amplitude, Fourier analysis, curve fitting, spike area, rms value.
  • These are all useful features, though template matching seems the standard now..
  • Gerstein and Clark 1964 -- stored spikes on tape, then sampled the tape until a threshold was exceeded. 32 samples of the waveform around threshold crossing were stored for analysis on the computer; up to 7000 points could be saved.
  • also looked at cross-correlation of a spike with a template -- back in 1968 on a LINC-8!
  • Reviews a good number of other very clever spike sorting techniques for using the lmiited hardware available.
  • Talk about template realignment and resampling Mambrito and De Luca 1983

____References____

[0] Schmidt EM, Computer separation of multi-unit neuroelectric data: a review.J Neurosci Methods 12:2, 95-111 (1984 Dec)