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ref: work-0 tags: distilling free-form natural laws from experimental data Schmidt Cornell automatic programming genetic algorithms date: 09-14-2018 01:34 gmt revision:5 [4] [3] [2] [1] [0] [head]

Distilling free-form natural laws from experimental data

  • There critical step was to use partial derivatives to evaluate the search for invariants. Even yet, with a 4D data set the search for natural laws took ~ 30 hours.
    • 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 invariants?
      • They claim elsewhere that the same algorithm has been applied to biological data - a metabolic pathway - with some success.
      • Of course evolution had to explore a much larger space - proteins and reculatory pathways, not simpler mathematical expressions / linkages.

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ref: work-2999 tags: autocorrelation poisson process test neural data ISI synchrony DBS date: 02-16-2012 17:53 gmt revision:5 [4] [3] [2] [1] [0] [head]

I recently wrote a matlab script to measure & plot the autocorrelation of a spike train; to test it, I generated a series of timestamps from a homogeneous Poisson process:

function [x, isi]= homopoisson(length, rate)
% function [x, isi]= homopoisson(length, rate)
% generate an instance of a poisson point process, unbinned.
% length in seconds, rate in spikes/sec. 
% x is the timestamps, isi is the intervals between them.

num = length * rate * 3; 
isi = -(1/rate).*log(1-rand(num, 1)); 
x = cumsum(isi); 
%%find the x that is greater than length. 
index = find(x > length); 
x = x(1:index(1,1)-1, 1); 
isi = isi(1:index(1,1)-1, 1); 

The autocorrelation of a Poisson process is, as it should be, flat:

Above:

  • Red lines are the autocorrelations estimated from shuffled timestamps (e.g. measure the ISIs - interspike intervals - shuffle these, and take the cumsum to generate a new series of timestamps). Hence, red lines are a type of control.
  • Blue lines are the autocorrelations estimated from segments of the full timestamp series. They are used to how stable the autocorrelation is over the recording
  • Black line is the actual autocorrelation estimated from the full timestamp series.

The problem with my recordings is that there is generally high long-range correlation, correlation which is destroyed by shuffling.

Above is a plot of 1/isi for a noise channel with very high mean 'firing rate' (> 100Hz) in blue. Behind it, in red, is 1/shuffled isi. Noise and changes in the experimental setup (bad!) make the channel very non-stationary.

Above is the autocorrelation plotted in the same way as figure 1. Normally, the firing rate is binned at 100Hz and high-pass filtered at 0.005hz so that long-range correlation is removed, but I turned this off for the plot. Note that the suffled data has a number of different offsets, primarily due to differing long-range correlations / nonstationarities.

Same plot as figure 3, with highpass filtering turned on. Shuffled data still has far more local correlation - why?

The answer seems to be in the relation between individual isis. Shuffling isi order obviuosly does not destroy the distribution of isi, but it does destroy the ordering or pair-wise correlation between isi(n) and isi(n+1). To check this, I plotted these two distributions:

-- Original log(isi(n)) vs. log(isi(n+1)

-- Shuffled log(isi_shuf(n)) vs. log(isi_shuf(n+1)

-- Close-up of log(isi(n)) vs. log(isi(n+1) using alpha-blending for a channel that seems heavily corrupted with electro-cauterizer noise.

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ref: Laubach-2003.03 tags: cluster matlab linux neurophysiology recording on-line data_analysis microstimulation nicolelis laubach date: 12-17-2011 00:38 gmt revision:4 [3] [2] [1] [0] [head]

IEEE-1215970 (pdf)

  • 2003
  • M. Laubach
  • Random Forests - what are these?
  • was this ever used??

follow up paper: http://spikelab.jbpierce.org/Publications/LaubachEMBS2003.pdf

  • discriminant pusuit algorithm & local regression basis (again what are these? lead me to find the lazy learning package: http://iridia.ulb.ac.be/~lazy/

____References____

Laubach, M. and Arieh, Y. and Luczak, A. and Oh, J. and Xu, Y. Bioengineering Conference, 2003 IEEE 29th Annual, Proceedings of 17 - 18 (2003.03)

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ref: notes-0 tags: data effectiveness Norvig google statistics machine learning date: 12-06-2011 07:15 gmt revision:1 [0] [head]

The unreasonable effectiveness of data.

  • counterpoint to Eugene Wigner's "The Unreasonable effectiveness of mathematics in the natural sciences"
    • that is, math is not effective with people.
    • we should not look for elegant theories, rather embrace complexity and make use of extensive data. (google's mantra!!)
  • in 2006 google released a trillion-word corpus with all words up to 5 words long.
  • document translation and voice transcription are successful mostly because people need the services - there is demand.
    • Traditional natural language processing does not have such demand as of yet. Furthermore, it has required human-annotated data, which is expensive to produce.
  • simple models and a lot of data triumph more elaborate models based on less data.
    • for translation and any other application of ML to web data, n-gram models or linear classifiers work better than elaborate models that try to discover general rules.
  • much web data consists of individually rare but collectively frequent events.
  • because of a huge shared cognitive and cultural context, linguistic expression can be highly ambiguous and still often be understood correctly.
  • mention project halo - $10,000 per page of a chemistry textbook. (funded by DARPA)
  • ultimately suggest that there is so so much to explore now - just use unlabeled data with an unsupervised learning algorithm.

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ref: life-0 tags: IQ intelligence Flynn effect genetics facebook social utopia data machine learning date: 10-02-2009 14:19 gmt revision:1 [0] [head]

src

My theory on the Flynn effect - human intelligence IS increasing, and this is NOT stopping. Look at it from a ML perspective: there is more free time to get data, the data (and world) has almost unlimited complexity, the data is much higher quality and much easier to get (the vast internet & world!(travel)), there is (hopefully) more fuel to process that data (food!). Therefore, we are getting more complex, sophisticated, and intelligent. Also, the idea that less-intelligent people having more kids will somehow 'dilute' our genetic IQ is bullshit - intelligence is mostly a product of environment and education, and is tailored to the tasks we need to do; it is not (or only very weakly, except at the extremes) tied to the wetware. Besides, things are changing far too fast for genetics to follow.

Regarding this social media, like facebook and others, you could posit that social intelligence is increasing, along similar arguments to above: social data is seemingly more prevalent, more available, and people spend more time examining it. Yet this feels to be a weaker argument, as people have always been socializing, talking, etc., and I'm not sure if any of these social media have really increased it. Irregardless, people enjoy it - that's the important part.

My utopia for today :-)

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ref: work-0 tags: yushin robot data date: 06-25-2009 18:35 gmt revision:3 [2] [1] [0] [head]

U141 LMV1032 microSMD-4 -2.23315 -0.03575 180. 9394. 27366. 1675. 
L7 INDUCTOR 0603 -1.7784 -0.7561 0. 13171. 34955. 1727. 
C86 0.1uf 0402 1.0946 -0.0347 360. 37107. 27524. 1710. 
TP8 TP TP 0.222 -1.0285 0. 29815. 37809. 1767. 
TP9 TP TP 0.7021 -1.2484 0. 33805. 40090. 1787. 
C67 1uf 0603 0.8146 -0.7047 270. 34758. 34540. 1752. 
C68 1uf 0603 1.1946 -0.7247 270. 37920. 34730. 1758. 
C69 1uf 0603 1.2747 -0.7247 90. 38576. 34742. 1759. 
R4 33 0402 1.6937 -0.1982 180. 42071. 29215. 1728. 
R17 10k 0402 -1.685 -0.6615 270. 13941. 33981. 1723. 
U92 LMV1032 microSMD-4 -2.53285 -0.03585 180. 6912. 27381. 1671. 
U96 LMV1032 microSMD-4 -2.23315 -0.89075 180. 9364. 36340. 1732. 
TP10 TP TP 0.222 -1.1685 0. 29811. 39233. 1776. 
TP11 TP TP 0.222 -1.3084 0. 29807. 40698. 1786. 
R23 33 0402 0.2834 0.6142 180. 30371. 20682. 1659. 
U105 LMV1032 microSMD-4 -2.23315 -0.71965 180. 9368. 34557. 1720. 
U117 LMV1032 microSMD-4 -2.23315 -0.49165 180. 9366. 32055. 1705. 
U124 LMV1032 microSMD-4 -2.18025 -0.37765 180. 9820. 30853. 1698. 
U127 LMV1032 microSMD-4 -2.18025 -0.32065 180. 9826. 30273. 1695. 
U128 LMV1032 microSMD-4 -2.28685 -0.26365 180. 8940. 29697. 1690. 
R10 50k 0402 -0.9607 -0.3308 180. 19983. 30430. 1709. 

more data!

U136 LMV1032 microSMD-4 -2.18025 -0.14965 180. 9860. 28534. 1682. 
R47 20k 0402 1.1822 -1.3883 90. 37828. 41612. 1797. 
R48 20k 0402 0.942 -1.0284 270. 35838. 37757. 1771. 
U139 LMV1032 microSMD-4 -2.18025 -0.09265 180. 9863. 27964. 1678. 
C72 10nf 0603 1.3546 -0.6248 270. 39284. 33694. 1750. 
R45 12.5k 0402 1.1021 -1.3883 90. 37161. 41608. 1796. 
C37 33nF 0402 -1.0956 -0.7067 360. 18894. 34462. 1730. 
R46 12.5k 0402 1.0221 -1.0284 270. 36505. 37759. 1772. 
L7 INDUCTOR 0603 -1.7784 -0.7561 0. 13210. 34933. 1725. 
U142 LMV1032 microSMD-4 -2.18025 -0.03575 180. 9865. 27310. 1674. 
L8 INDUCTOR 0603 0.1745 -0.6447 270. 29446. 33849. 1738. 
C87 0.047uf 0402 -2.3611 -0.8811 360. 8363. 36186. 1729. 
R53 9.2k 0402 1.062 -1.3883 90. 36817. 41587. 1796. 
R36 3.3k 0402 1.9546 -0.8747 270. 44273. 36230. 1772. 
C88 0.047uf 0402 -2.361 -0.8241 360. 8356. 35593. 1725. 
R54 9.2k 0402 1.062 -1.0284 270. 36838. 37762. 1772. 
R38 3.3k 0603 0.8646 -0.8147 360. 35200. 35636. 1757. 
R37 3.3k 0402 1.9546 -1.1347 270. 44266. 38878. 1788. 
TP1 TP TP 1.302 -1.3882 0. 38828. 41596. 1797. 
C89 0.047uf 0402 -2.361 -0.7671 360. 8358. 35023. 1721. 
C83 0.1uf 0402 1.2246 -0.5147 0. 38206. 32492. 1741. 
C12 1uf 0402 0.8182 0.1876 270. 34842. 25228. 1692. 
R39 3.3k 0402 1.5146 -0.8747 90. 40609. 36213. 1767. 
TP3 TP TP 1.302 -1.2484 0. 38835. 40039. 1788. 
C85 0.1uf 0402 0.2946 -0.0348 180. 30497. 27541. 1701. 
C29 0.01uf 0402 -1.5749 -0.1575 270. 14907. 28634. 1690. 
TP4 TP TP 0.8219 -1.1684 0. 34852. 39172. 1778. 
C15 1uf 0402 1.6037 0.0518 270. 41377. 26681. 1709. 
TP5 TP TP 0.8219 -1.3084 0. 34835. 40731. 1787. 
C86 0.1uf 0402 1.0946 -0.0347 360. 37136. 27478. 1709. 
TP6 TP TP 1.3021 -1.1085 0. 38832. 38563. 1779. 
TP7 TP TP 0.7021 -1.3883 0. 33824. 41561. 1791. 
TP8 TP TP 0.222 -1.0285 0. 29855. 37751. 1763. 
C19 1uf 0402 -0.6901 -0.0599 90. 22286. 27662. 1693. 
TP9 TP TP 0.7021 -1.2484 0. 33830. 40042. 1782. 
C90 0.047uf 0402 -2.361 -0.7101 360. 8360. 34449. 1718. 
R40 3.3k 0402 1.5146 -1.1347 90. 40602. 38842. 1784. 
C28 7pf 0402 -1.0306 -0.562 270. 19447. 32944. 1722. 
C36 0.01uf 0402 -1.1968 0.0315 0. 18064. 26795. 1682. 
C67 1uf 0603 0.8146 -0.7047 270. 34787. 34503. 1750. 
R13 25 0402 -1.57 -0.34 0. 14940. 30478. 1701. 
C68 1uf 0603 1.1946 -0.7247 270. 37950. 34725. 1755. 
C38 0.01uf 0402 -0.9763 -0.1733 270. 19894. 28829. 1697. 
R14 25 0402 -1.5749 -0.4094 270. 14897. 31177. 1705. 
C69 1uf 0603 1.2747 -0.7247 90. 38616. 34707. 1755. 
R16 25 0402 -1.1956 -0.8867 180. 18053. 36282. 1739. 
R1 33 0402 1.4961 0.0314 90. 40482. 26822. 1709. 
R5 220k 0402 -0.5628 -0.1852 90. 23338. 28986. 1701. 
R3 33 0402 1.6937 -0.1282 180. 42120. 28451. 1721. 
R4 33 0402 1.6937 -0.1982 180. 42116. 29193. 1725. 
R28 2.2k 0402 1.9346 -1.4048 90. 44069. 41754. 1804. 
R29 2.2k 0402 1.8346 -1.4047 90. 43249. 41818. 1804. 
C70 1uf 0603 1.2747 -0.6246 270. 38619. 33709. 1749. 
R2 100k 0402 1.4173 0.0315 90. 39826. 26815. 1708. 
C42 0.01uf 0402 -1.1955 -0.7166 180. 18052. 34552. 1730. 
R43 3k 0402 1.242 -1.3085 270. 38319. 40701. 1792. 
C73 1uf 0603 1.8646 -0.7147 0. 43527. 34646. 1761. 
R44 3k 0402 0.882 -1.1085 90. 35337. 38556. 1776. 
R49 33k 0402 1.202 -1.2285 270. 37988. 39816. 1787. 
C77 1uf 0603 0.7446 -0.9347 0. 34197. 36870. 1764. 
C32 1uf 0402 -0.8976 -0.6615 180. 20551. 34005. 1729. 
C79 1uf 0603 0.8646 -0.8747 180. 35198. 36251. 1761. 
R30 2.2k 0402 1.7347 -1.4047 90. 42427. 41804. 1803. 
C35 1uf 0402 -1.2913 0.0315 180. 17298. 26781. 1681. 
R31 2.2k 0402 1.6346 -1.4047 90. 41584. 41800. 1802. 
R50 33k 0402 0.9345 -1.1548 90. 35772. 39028. 1779. 
R11 10k 0402 -0.0001 0.126 90. 28025. 25843. 1690. 
C46 1uf 0402 -1.1955 -0.6766 180. 18053. 34138. 1727. 
R12 10k 0402 0.0001 0.5196 90. 28038. 21612. 1662. 
R9 10k 0402 0.0001 0.2835 270. 28031. 24093. 1677. 
R17 10k 0402 -1.685 -0.6615 270. 13974. 33945. 1741. 
R18 10k 0402 -1.5998 -0.4875 90. 14688. 32018. 1710. 
C14 0.001uf 0402 -0.96 -0.26 0. 20044. 29712. 1703. 
U92 LMV1032 microSMD-4 -2.53285 -0.03585 180. 6926. 27289. 1670. 
R55 6.5k 0402 0.9821 -1.3883 90. 36150. 41583. 1795. 
R56 6.5k 0402 1.142 -1.0284 270. 37502. 37773. 1774. 
R19 22K 0402 -0.9958 -0.6867 90. 19712. 34257. 1729. 
C2 0.1uf 0402 1.6237 -0.2581 270. 41530. 29787. 1728. 
C30 5pf 0402 -1.1907 -0.562 90. 18114. 32929. 1720. 
C25 0.001uf 0402 0.2835 0.0787 180. 30398. 26352. 1694. 
C20 33pf 0402 -0.5628 -0.3352 90. 23328. 30458. 1712. 
C13 8pf 0402 1.6877 -0.4299 270. 42062. 31517. 1741. 
C27 0.001uf 0402 -0.9763 -0.5039 90. 19900. 32258. 1718. 
C17 8pf 0402 1.4476 -0.4299 90. 40063. 31519. 1738. 
C71 0.1uf 0603 1.3545 -0.7247 90. 39280. 34701. 1756. 
C49 2.2uf 0402 -2.2324 -0.9436 0. 9413. 36840. 1734. 
C50 2.2uf 0402 -2.4802 -0.9455 0. 7350. 36852. 1732. 
C51 2.2uf 0402 -2.4779 0.0152 0. 7399. 26905. 1670. 
C52 2.2uf 0402 -2.2347 0.0184 0. 9423. 26881. 1672. 
C40 0.001uf 0402 -1.1956 -0.7568 180. 18050. 34938. 1732. 
C53 2.2uf 0402 -1.9398 -0.7554 0. 11855. 34916. 1725. 
C54 2.2uf 0402 -1.6317 -0.315 270. 14433. 30225. 1700. 
C48 2.2nF 0402 -0.9154 -0.9464 90. 20377. 36919. 1747. 
C55 2.2uf 0402 -1.8616 -0.7549 180. 12506. 34903. 1726. 
C56 0.012uf 0402 -1.7107 -0.7353 270. 13762. 34716. 1726. 
C57 0.012uf 0402 -1.6956 -0.8478 90. 13875. 35886. 1733. 
R7 90k 0402 -0.8225 -0.266 90. 21176. 29782. 1704. 
C58 0.012uf 0402 -1.8891 -0.8466 90. 12274. 35834. 1731. 
R57 22k 0402 0.942 -1.3883 90. 35826. 41602. 1795. 
TP10 TP TP 0.222 -1.1685 0. 29847. 39154. 1772. 
C22 10uf 0603 -0.6428 -0.1653 360. 22687. 28750. 1700. 
TP11 TP TP 0.222 -1.3084 0. 29820. 40682. 1781. 
C23 10uf 0603 -0.7429 -0.1652 180. 21854. 28745. 1699. 
TP12 TP TP 0.7022 -1.1085 0. 33848. 38556. 1773. 
C61 2.2uf 0402 -1.8422 -0.8468 90. 12664. 35859. 1732. 
C62 2.2uf 0402 -2.0357 -0.8464 90. 11053. 35837. 1730. 
C63 2.2uf 0402 -2.0001 -0.0836 270. 11363. 27899. 1681. 
C64 2.2uf 0402 -2.0025 -0.1862 90. 11350. 28924. 1688. 
C44 1.5pF 0402 -0.8357 -0.8065 180. 21045. 35478. 1739. 
C65 0.012uf 0402 -1.8247 -0.9119 0. 12808. 36505. 1736. 
C66 0.012uf 0402 -2.0181 -0.913 0. 11198. 36540. 1734. 
C39 0.1uf 0402 -1.3229 -0.6772 180. 16993. 34136. 1726. 
R6 825k 0402 -0.5628 -0.2651 90. 23329. 29784. 1706. 
C41 0.1uf 0402 -1.1023 0.0314 180. 18851. 26789. 1683. 
C45 0.1uf 0402 -0.9763 -0.0787 90. 19897. 27845. 1691. 
R34 327k 0402 1.9046 -0.8747 270. 43856. 36228. 1771. 
R35 327k 0402 1.9046 -1.1347 90. 43849. 38858. 1788. 
R51 47k 0402 1.202 -1.3085 270. 37985. 40700. 1792. 
R52 47k 0402 0.9221 -1.1083 90. 35661. 38566. 1776. 
C74 4.7uf 0603 1.9346 -1.0047 360. 44101. 37581. 1780. 
C75 4.7uf 0603 1.9346 -0.9447 360. 44103. 36957. 1776. 
C76 4.7uf 0603 1.9346 -1.0648 180. 44099. 38174. 1784. 
R41 327k 0402 1.5646 -0.8747 90. 41026. 36215. 1768. 
C78 4.7uf 0603 1.7346 -0.7947 0. 42442. 35463. 1765. 
R42 327k 0402 1.5645 -1.1347 270. 41018. 38856. 1784. 
C59 0.1uf 0402 -1.8046 -0.2246 270. 12986. 29320. 1692. 
U124 LMV1032 microSMD-4 -2.18025 -0.37765 180. 9843. 30773. 1696. 
U127 LMV1032 microSMD-4 -2.18025 -0.32065 180. 9845. 30296. 1692. 
C80 4.7uf 0603 1.5346 -0.9447 360. 40773. 36984. 1772. 
C81 4.7uf 0603 1.5346 -1.0648 180. 40769. 38149. 1780. 
R10 50k 0402 -0.9607 -0.3308 180. 20034. 30408. 1706. 
C82 4.7uf 0603 1.5346 -1.0047 360. 40771. 37546. 1776. 
C84 4.7uf 0603 0.1746 -0.5347 270. 29464. 32629. 1732. 
C60 0.1uf 0402 -1.8032 -0.0862 270. 13012. 27892. 1683. 
R15 50k 0402 -1.1956 -0.7967 180. 18055. 35380. 1734. 
U130 LMV1032 microSMD-4 -2.18025 -0.26365 180. 9857. 29685. 1689. 
2.9mm_hole VAL** 2.9mm_hole -2.325 0.2 0. 8698. 24995. 1658. 
U133 LMV1032 microSMD-4 -2.18025 -0.20665 180. 9849. 29114. 1685. 
C47 1pF 0402 -0.8158 -0.7565 90. 21212. 34950. 1736. 

counts spaced at exactly 1mm:
0 -13206.000000
1 -12795.000000
2 -12349.000000
3 -11983.000000
4 -11545.000000
5 -11117.000000
6 -10710.000000
7 -10262.000000
8 -9813.000000
9 -9395.000000
10 -8957.000000
11 -8561.000000
12 -8154.000000
13 -7726.000000
14 -7298.000000
15 -6897.000000
16 -6477.000000
17 -6093.000000
18 -5700.000000
19 -5309.000000
20 -4871.000000
21 -4453.000000
22 -4046.000000
23 -3639.000000
24 -3232.000000
25 -2836.000000
26 -2429.000000
27 -2011.000000
28 -1594.000000
29 -1187.000000
30 -780.000000
31 -352.000000
32 65.000000
33 472.000000
34 900.000000
35 1318.000000
36 1708.000000
37 2104.000000
38 2490.000000
39 2908.000000
40 3325.000000

{11}
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ref: bookmark-0 tags: plexon documenation data file structure reading plx date: 0-0-2006 0:0 revision:0 [head]

http://hardcarve.com/wikipic/PlexonDataFileStructureDocumentation.pdf