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From: Tom Kurtzman <simpleliquid.gmail.com>

Date: Tue, 30 Aug 2016 11:07:36 -0400

Hi Roman, in response to your comment "In my opinion this is not possible

since the track is made of 0 and 1, so the autocorrelation cannot be < 0."

Often correlation functions (including autocorrelation functions) are

normalized so that their initial values are 1 and absence of correlation is

zero so instead of calculating

<A(t)A(t')> they actually calculate This is the same as calculating

<[A(t) -<A>][A(t')-<A>]> = <A(t)A(t')> - <A>^2. This allows for negative

numbers and ensures that the limit as t --> \infty is zero. Often the

function is then divided by its initial value to give an initial value

(upper bound) value of unity.

For the no-covariance calculation, I assume that the average values are not

subtracted and hence the limit and infinite time approaches <A>^2 which is

positive.

It is not unusual for autocorrelation functions to have negative values nor

to have long time non-zero tails (the velocity autocorrelation function is

a famous example of both of these) however, I'm not sure whether the long

time tail you are seeing is

1) real

2) fluctuations about zero due to sampling limitations (noise)

3) an artifact of an incorrectly calculated quantity.

Without seeing the data, I would initially suspect it's just noise.

Tom

On Mon, Aug 29, 2016 at 9:05 AM, Osman, Roman <roman.osman.mssm.edu> wrote:

*> Hello Amberites,
*

*>
*

*> I was wondering whether anybody has used an autocorrelation of hydrogen
*

*> bonds.
*

*> Here is a cpptraj input that I ran:
*

*>
*

*> # Read in trajectory
*

*>
*

*> trajin mcmrjp_free_nw.dcd
*

*>
*

*> hbond HB out mcmrjp_free_hb.dat :17,252,67,206,159,272,27,32,
*

*> 228,245,262,267,165
*

*> ,183,34,138,239,290,39,143,207,204,162 series uuseries mcmrjp_free_hb.dat
*

*> avgout
*

*> mcmrjp_free_avg.dat printatomnum
*

*> run
*

*> runanalysis lifetime HB[solutehb] out mcmrjp_free_lifet.dat
*

*> autocorr HB[solutehb] out mcmrjp_free_auc.dat lagmax 14500
*

*> run
*

*>
*

*>
*

*> The surprising thing is that I get in the aucorrelation function negative
*

*> numbers towards the end of the track.
*

*> In my opinion this is not possible since the track is made of 0 and 1, so
*

*> the autocorrelation cannot be < 0.
*

*>
*

*> In fact if I run with
*

*> autocorr HB[solutehb] out mcmrjp_free_auc.dat lagmax 14500 nocovar
*

*>
*

*> The autocorrelations become positive.
*

*>
*

*> Am I doing something wrong?
*

*>
*

*> Thanks for your help.
*

*>
*

*> PS: I can provide the trajectory (large) and the output from the
*

*> autocorrelation.
*

*>
*

*> Roman Osman
*

*> Professor of Structural and Chemical Biology
*

*> Mount Sinai School of Medicine
*

*> New York, NY 10029
*

*> (212) 659-8627
*

*> roman.osman.mssm.edu<mailto:roman.osman.mssm.edu>
*

*>
*

*>
*

*> _______________________________________________
*

*> AMBER mailing list
*

*> AMBER.ambermd.org
*

*> http://lists.ambermd.org/mailman/listinfo/amber
*

*>
*

Date: Tue, 30 Aug 2016 11:07:36 -0400

Hi Roman, in response to your comment "In my opinion this is not possible

since the track is made of 0 and 1, so the autocorrelation cannot be < 0."

Often correlation functions (including autocorrelation functions) are

normalized so that their initial values are 1 and absence of correlation is

zero so instead of calculating

<A(t)A(t')> they actually calculate This is the same as calculating

<[A(t) -<A>][A(t')-<A>]> = <A(t)A(t')> - <A>^2. This allows for negative

numbers and ensures that the limit as t --> \infty is zero. Often the

function is then divided by its initial value to give an initial value

(upper bound) value of unity.

For the no-covariance calculation, I assume that the average values are not

subtracted and hence the limit and infinite time approaches <A>^2 which is

positive.

It is not unusual for autocorrelation functions to have negative values nor

to have long time non-zero tails (the velocity autocorrelation function is

a famous example of both of these) however, I'm not sure whether the long

time tail you are seeing is

1) real

2) fluctuations about zero due to sampling limitations (noise)

3) an artifact of an incorrectly calculated quantity.

Without seeing the data, I would initially suspect it's just noise.

Tom

On Mon, Aug 29, 2016 at 9:05 AM, Osman, Roman <roman.osman.mssm.edu> wrote:

-- ************************************************ Tom Kurtzman, Ph.D. Assistant Professor Department of Chemistry Lehman College, CUNY 250 Bedford Park Blvd. West Bronx, New York 10468 718-960-8832 http://www.lehman.edu/faculty/tkurtzman/ <http://www.lehman.edu/faculty/tkurtzman/index.html> ************************************************ _______________________________________________ AMBER mailing list AMBER.ambermd.org http://lists.ambermd.org/mailman/listinfo/amberReceived on Tue Aug 30 2016 - 09:30:03 PDT

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