[gmx-users] What is the autocorrelation time

[Erik Marklund]

Hi Patrick,

There is a fast decay of the hbond acf for liquid water on a 100-200 fs timescale that traditionally is associated with the librational motion of water molecules. There's a good paper by Omer Markovich and Noam Agmon in J. Chem. Phys. 129 084505 2008 where this effect is discussed, although it's not the main focus of that paper. Then, after 10 ps or so, there's a regime where the acf falls of as a power law. As a consequence the correlation time is not really derived from a purely exponential acf and the interpretation might be misleading to some extent if you imply exponential behaviour.

Best,

Erik

21 maj 2012 kl. 14.07 skrev Patrick Fuchs:

> Hi Erik,
> your examples on H-bond acfs are interesting. I'm wondering about the "distinct features which are non-exponential" in your examples. What do you mean exactly? Could these features be due to rare (H-bonding) events, or in other words to poor sampling?
> Intuitively, I'd say that the interpretation of the acf (at least for the decay and the decorelation) is always valid unless maybe if you have very poor statistics.
> Ciao,
> 
> Patrick
> 
> Le 20/05/2012 16:12, Erik Marklund a écrit :
>> Dear Chris,
>> 
>> As I see it there one can interpret the acf and correlatation time
>> further for certain types of data. I'll use the h-bond autocorrelation
>> function as an example. Here the data is time series of logical true and
>> false, represented as ones and zeros. This type of acf can be direcly
>> interpreted as a probablity, and some quantities derived from the acf
>> can bear further meaning because of this.
>> 
>> I also thought that the nature of the data may be such there is a
>> non-exponential part, which makes the autocorreltaion time less valid,
>> or less connected to other intuitive concepts. Again, the h-bond acf has
>> distinct features which are non-exponential and the autocorreltaion time
>> derived from such acfs may in fact be misleading when the h-bond
>> kinetics is to be determined.
>> 
>> Hope that makes sense. I's be happy to hear from you if you disagree.
>> 
>> Best,
>> 
>> Erik
>> 
>> 19 maj 2012 kl. 04.01 skrev Christopher Neale:
>> 
>>> Dear Erik:
>>> 
>>> I thought about your comment for a while and I have come to understand
>>> that you are correct. The exponential (or integral) autocorrelation
>>> time is a mathematical construct and is defined as such. What I was
>>> looking for was an interpretation of the autocorrelation time in terms
>>> of the time required to decorrelate the sampling.
>>> 
>>> As to whether or not this will depend on the nature of the data, I
>>> don't really understand your conjecture. If the interpretation of the
>>> autocorrelation time depends on the nature of the data, then that
>>> implies to me that a single scalar value is useless in this case. I
>>> don't understand how it could be useful to represent the
>>> autocorrelation time by a single number if that number does not mean
>>> anything on its own. If you have time, I would appreciate if you could
>>> elaborate on this point.
>>> 
>>> Thank you,
>>> Chris.
>>> 
>>> -- original message --
>>> 
>>> Aren't you looking for an interpretation rather than a definition? And
>>> will this not depend on the nature of the data?
>>> 
>>> Best,
>>> 
>>> Erik
>>> 
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>> 
>> -----------------------------------------------
>> Erik Marklund, PhD
>> Dept. of Cell and Molecular Biology, Uppsala University.
>> Husargatan 3, Box 596, 75124 Uppsala, Sweden
>> phone: +46 18 471 6688 fax: +46 18 511 755
>> erikm at xray.bmc.uu.se <mailto:erikm at xray.bmc.uu.se>
>> http://www2.icm.uu.se/molbio/elflab/index.html
>> 
>> 
>> 
> 
> -- 
> _______________________________________________________________________
> Patrick FUCHS
> Dynamique des Structures et Interactions des Macromolécules Biologiques
> INTS, INSERM UMR-S665, Université Paris Diderot,
> 6 rue Alexandre Cabanel, 75015 Paris
> Tel : +33 (0)1-44-49-30-57 - Fax : +33 (0)1-43-06-50-19
> E-mail address: patrick.fuchs at univ-paris-diderot.fr
> Web Site: http://www.dsimb.inserm.fr/~fuchs
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-----------------------------------------------
Erik Marklund, PhD
Dept. of Cell and Molecular Biology, Uppsala University.
Husargatan 3, Box 596,    75124 Uppsala, Sweden
phone:    +46 18 471 6688        fax: +46 18 511 755
erikm at xray.bmc.uu.se
http://www2.icm.uu.se/molbio/elflab/index.html

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