Science > Physics > Independent/Dependent Phases 22: 196 Papers on Long Memory/Hysteresis
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
15 Oct 2005 12:58:55 AM |
| Object: |
Independent/Dependent Phases 22: 196 Papers on Long Memory/Hysteresis |
From Osher Doctorow
One of the most interesting "phase differences" is that between either
memoryless or one-step-back memory, on the one hand, and long-term or
long memory (2 or more steps back, usually more - even entire intervals
back).
There are at least 196 papers in arXiv and/or Front For the Mathematics
ArXiv under the search headings (keywords) long-memory, long memory,
hysteresis, with the preponderance under hysteresis in ArXiv (the
physics archive so to speak although it covers several other sciences).
In addition, outside either of the above sources, there is a very
large research literature that didn't get into either source for
various reasons (including preference since several researchers with
many papers published don't bother with either "archive").
This doesn't include psychology, where long-term memory (LTM) is
practically an institution and is commonly studied as well as
short-term memory (STM).
Guess where the mainstream Markov Chain people in mathematical
probability-statistics fall with regard to long memory versus short
memory or memoryless? Yes, you probably guessed it - they fall under
either short memory or memoryless.
Do the Markov people admit it? Heck no! They don't even talk about it
or write about it as far as I know, unless directly confronted (and
even then, they may never have thought about it!). I've heard several
excuses from Markov Chain people, including (a) Markov Chains are
simpler, so we can stick with them, (b) There aren't any
Non-Markov-Chain type of things (the Know-Nothing school!), (c) If it
ain't broke, don't fix it (the plumbing fixture branch of
engineering-related research).
For the uninitiated (there's recently been a spate of commenters on my
threads who claim or indirectly indicate that they haven't read any
previous postings of mine but who suddenly claim to have read posting n
with higher positive integer n in isolation), the issue here is the
difference between Probable Influence (PI) which is Non-Markov-Chain,
and Markov Chains which use (Bayesian) conditional probability (BCP as
I abbreviate it, although not all users of conditional probability are
technically Bayesians - that's a long story).
Readers should exert caution in looking up hysteresis, because if you
don't get a particularly conscious researcher so to speak, you may find
yourself in a feedback loop of indefinite type without ever learning
what hysteresis actually means. Yes, Virginia, there are Young
Alzheimers in Academia!
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Independent/Dependent Phases 22: 196 Papers on Long Memory/Hysteresis |
15 Oct 2005 01:17:35 AM |
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From Osher Doctorow
Take look at Gennady Samorodnitsky (Cornell U. School of Operations
Research and Industrial Engineering - you didn't really think
physicists or mathematicians would be leading this charge, did you :>),
"Extreme value theory, ergodic theory, and the boundary between short
memory and long memory for stationary stable processes," a 32 page
paper in math.PR/0410149 v1 6 Oct 2004 which was also published in the
extremely prestigious The Annals of Probability 2004, Vo. 32, No. 2,
1438-1468.
For those young lions who can't count to 2 or past, I remind you that 0
or 1 step back memory differs from 2 or more steps back memory, and
that if we call 0 or 1 steps back one phase, then 2 or more steps back
is a second phase, and we can put their "boundary" somewhere between 1
and 2. It gets more interesting when memory depends on the entire
(uncountable!) interval from the present to some older point in time in
the past, which is definitely in the second phase where Markov didn't
go.
Readers should also beware of a "trick" that the Markov Chain people
use. Since they can't express memory depending on two or more steps
(seconds, days, hours, years, etc.) backwards directly, they construct
2-step chains to go backwards to memory of 2 step back
things/events/processes. This is somewhat like an ant walking from a
to b and then from b to c since it can't go directly from a to c.
Needless to say, the Markov people specify their finite number of paths
from a to b to c, a to e to c, etc., which everybody has to follow, and
if asked why, "it's simpler this way."
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Independent/Dependent Phases 22: 196 Papers on Long Memory/Hysteresis |
15 Oct 2005 01:26:15 AM |
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From Osher Doctorow
To get a better idea of the difficulty that Markov Chain people have
gotten themselves into (with everybody except Academia!), try to find
the "last step before the present" in your own memory. If there were a
last step before the present, then there wouldn't be any time between
that step or that time and the present, which would mean that time
stopped at the previous step and then restarted at the present. If you
believe that, I have a great Brooklyn Bridge that I'd like to sell you
:>)
Osher Doctorow
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