Topology is Connectedness

k p Collins kpaulc at [----------]earthlink.net
Tue Feb 24 05:29:37 EST 2004


Since you're posting from a Yale Medical School
ID, I =presume= that it =may= be the case that
you're in Neuroscience at Yale, so, I've Obligation
with respect to your Education in Neuroscience(?)

Yes, as I've stated before, in our discourse [and
repeatedly, over the course of the 'years', here in b.n,
unless I RETRACT or CLARIFY this or that that
I've posted, I stand on everything I've ever posted.

The nervous system is a neural Topology that is
dynamically-configured.

It's active 'circuitry' varies as a function of the 'mo-
mentary' "supersystem configuration" [AoK, Ap5]
that has been converged-upon via "TD E/I-mini-
mization" [See AoK].

So, to comprehend what's going-on =anywhere=
within the nervous system, one must comprehend
the neural Topology of the 'momentary' "super-
system configuration" that has been converged-upon.

This simply cannot be done via a method that re-
sorts, exclusively, to 'time'-series analysis witnin
any 'isolated' functional sub-system [e.g. the cere-
bellum], be-cause the 'momentary' neural Topology
is configured as a function of =globally= integrated
TD E/I-minimization.

If one looks solely at this or that sub-system [e.g.
the cerebellum], one sees exactly nothing that
addresses the globally-integrated neural Topology
in a way that's sufficient to constitute anything other
than a "pretty picture".

Ever when one does a 'time'-series with respect to
the globally-integrated neural Topology, what one
is able to see in that 'time' =series= is insufficient,
be-cause of the nervous system's massive parallel-
ism. Looking at 'sequences' discloses exactly-no-
thing.

One must build-up the picture of the dynamics that
are occurring within the nervous system's massive-
parallelism. and the =only= way in which this can
be accomplished is by sorting-out, and invoking,
the neural Topology.

Which is what I said when I responded to the OP.

What I was doing, in that initial reply, was eliciting
interest, with respect to a much-larger discussion.

I do this, routinely, because I've Learned that it does
no good to just discuss Larger concepts if there's no
one who's accumulated sufficient "biological mass"
through prior study - if that's the case, then the
Larger discussion tends to 'pass-right-through', its
stuff remaining 'undetected'.

But, before anyone else had a chance to express-
interest, you started 'bashing' my Person, which
sent everything to Waste.

And the Work that I'd've, otherwise accomplished,
here in b.n, was left Undone, and my ability to Work,
here in b.n, has, at this 'point', still not recovered
from your 'shunting' it off into 'nothingness', =except=
for one thing - I've been Working to use our 'inter-
action' as an in-process example of the way that
'blindly'-automated TD E/I-minimization wreaks its
havoc within Human interactive dynamics.

The costs are always great, and, sometimes, they
stretch all the way out to Infinity, encompassing
all of Humanity.

The 'present' case is such an Infinite case.

I Forgive you, but I can only stand on what I've
posted it is Truth - while 'mourning' that which has
been Lost - that which could have Been.

"It's a slip and not a fall." {Abraham Lincoln]

As my Friend, K. W. Ford always said, "You got
to go through what you been through to get to
where you're goin'".

I've given you Opportunity to Learn.

What you do with it is up-to-you.

K. P. Collins

"Doktor DynaSoar" <targeting at OMCL.mil> wrote in message
news:is0l30182sgrpuruft07ijlrdnej40u9v8 at 4ax.com...
> On Mon, 23 Feb 2004 08:26:01 GMT, "k p  Collins"
> <kpaulc@[----------]earthlink.net> wrote:
>
> } I stand on what =I've= posted.
>
> All of it?
>
> "You're missing some crucial data that cross-correlates
> your 'time' series to the cerebellar topology.
>
> The cerebellum is a topographically-mapped subsystem.
>
> Any analysis must preserve, and incorporate, that mapping
> if the correlations are to be meaningful."
>
>
>
> From: "k p  Collins" <kpaulc@[----------]earthlink.net>
> Newsgroups:
> sci.nonlinear,sci.bio.technology,sci.math,bionet.neuroscience,sci.fractals
> References: <235b9607.0401210500.3ebedda5 at posting.google.com>
> Subject: Re: Practical problems with correlation dimension
> Lines: 68
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> Message-ID: <AhvPb.17594$q4.2672 at newsread3.news.atl.earthlink.net>
> Date: Wed, 21 Jan 2004 13:38:40 GMT
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> (Wed, 21 Jan 2004 05:38:40 PST)
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>
>
> "Karl" <karlknoblich at yahoo.de> wrote in message
> news:235b9607.0401210500.3ebedda5 at posting.google.com...
> > Hallo!
> >
> > I want to calculate the correlation dimension of a time serie.
> >
> > What I have done
> > I calculated the correlation integral C(r) (number of point having a
> > distance smaller than r) for different embedding dimensions. Taking
> > the slopes of the curve of log C(r) against log r for the different
> > embedding dimensions and plotting them against the embedding dimension
> > should result in a limes of the slopes: the correlation dimension.
> >
> > My problem
> > Which slope shall I take?
> >
> > In examples I saw in text books there is a nice limit of the slopes
> > with higher embedding dimensions. In my data I do not know which slope
> > I should take because the slope of the curve varies. If I take the
> > slope at a certain value of log r I can not get a limes.
> >
> > My curves (log C(r) against log r) can be seen in
> > http://karlknoblich.4t.com/korrdim.jpg
> >
> >
> > What to do? Does anybody knows such data and how to handle it?
> >
> > Hope somebody can help!
> >
> > Karl
>
> What I will say has not yet been accepted by others,
> so keep that in mind as you consider it.
>
> You're missing some crucial data that cross-correlates
> your 'time' series to the cerebellar topology.
>
> The cerebellum is a topographically-mapped subsystem.
>
> Any analysis must preserve, and incorporate, that mapping
> if the correlations are to be meaningful.
>
> And, then, to continue, one has to follow this mapping into
> the rest of the brain.
>
> It's a =big= problem, but the mapping is mapped :-] through
> the efforts of Neuroscientists, and all one has to do is 'grind'
> through it.
>
> There a couple of other things that make your analysis Difficult.
>
> One is that the data is virtually always, itself, a transformation.
>
> The other is that the activation that occurs within the cerebellum
> is extremely-dynamic, with a =lot= of different inputs converging
> and 'sliding' with respect to each other. There is such 'sliding'
> stuff with respect to every joint in the skelleton. [These enter
> into the way that the nervous system maintains it's 'awareness'
> of the body's orientation in 3-D space [climbing fibers from
> the inferior olive].] And this is only one set of such 'sliding-field'
> stuff that occurs within the cerebellum. There are hundreds
> [perhaps thousands] more.
>
> So your analysis is Hard.
>
>





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