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While I agree that this neural-nets thread is getting slightly off the
techdiver path, I think there still remain a few interesting points
for techdiver.

John Erling Blad <johnbl@if*.ui*.no*> sez:
> ... but in diving you can't learn the
> model because none want's to risk theire life's while training the networks.
> Because of this the network must be trained from a model and it can't be any
> better than this. So if you already have the model, why use a NN?
> 
> >(you can derrive lots of info about potential error from
> >watching the ststistics during training).
> 
> Shure, but how can you obtain training data? I *don't* dive so I don't know,
> but I can't imagine anyone willing to risk theire life to train the network.
> So the network must be trained from a model, which it can't be better than.

This brings to light a common misconception about mathematical
modeling as it relates to dive tables: dive tables are not simply
models generated from first principles, but rather are models
generated to fit some empirical data.  The problem of obtaining data
for training a neural net is no different than obtaining data in order
to produce a new dive table model.  Translation: Yes, Virginia,
*people* were bent in order to generate your dive tables.  (Of course,
the people were volunteers, and they were immediately treated.)

While dive table research typically begins with some animal studies
(goats and rabbits are the popular choices), ultimately all table
algorithms must be tested on humans.  Most of the recent tables
(Buhlman, DCIEM, etc) have been worked out exclusively through testing
with human volunteers diving in both chambers and open water.  Of
course, they start from somewhere -- namely earlier research which has
shown the drastic limits.

> A good model is better simply because you know what it does. This is much
> like an accounting problem.

Do you?  Let's take a look at the development of the three most
important deco models in history and see.

(Before we start: *PLEASE* keep in mind that what follows is a vast
oversimlification of deco model building, particularly w.r.t. what
actually went on in the development of deco models.  What you should
take from this is the spirit of the process, not the actual events of
the various research efforts.)

First, Haldane began studying DCS with goats.  His experiments went
along the lines of compress some goats, see how many fell ill, record
the data, try a different depth, time, and deco schedule.  After
repeating this with many goats, he looked at the data to discern
patterns.  What he came up with was the idea that a body was composed
of several "compartments" each of which had a particular N2 saturation
rate, and that no compartment should ever exceed a supersaturation of
1.58.  Haldane had no way to study bubbling, so he went by presenting
symptoms alone; additionally, he assumed that gas uptake and
elimination were at equal rates.

What do we find appealing about Haldane's theory?  Well, there are
several factors which make it appealing when looked at from a physical
point of view:
	- We know that the body is made of many different types of
tissues, and the Haldane model has several compartments.
	- Gas in solution is exponential, which seems to fit well with
the physical universe.
	- Uptake and elimination are at the same rate, as why
shouldn't they be?
	- 1.58 is a "weird" number, but every theory needs a "weird"
number.
	- N2 is inert and the single largest component of air,
therefore it sort of makes sense that it is the cause of DCI.

When looked at from the above point of view, Haldane seems to have a
pretty decent understanding of DCS.  But if we flip the view around to
a mathematical oriented view, we realize that what Haldane did was
work out an equation of sufficient degree to fit his data.  (You can
always find an equation to fit any data, but you will need higher and
higher degrees[exponents] to make it fit.)  Of course, Haldane's model
comes with the above neat explanation, so it is seen as reasinable and
accepted.  After all, it does fit his data.

Fast forward to Buhlman: Buhlman decides that Haldane (and lots of
post-Haldane work, especially Workman) is not quite right; he seeks a
better and more general model.  Buhlman begins from first principles,
looking at determining 1/2 times and permitted saturation levels for
different real body tissue types (blood, skin, joints, etc).  Buhlman
also revises the original model to accomodate two coefficients per
halftime (compartment) which control the accepted supersaturation
(Workman's M-values, generalized from Haldane's 1.58, are replaced now
with pairs of coeffs).  In the beginning, Buhlman uses his
tissue-derrived coeffs.  But as his model development progresses, he
switches to determining the half times (compartments) and
corresponding coeff pairs via empirical studies involving human divers
in a wet chamber.

So, looking at the outcome of Buhlamn's research, what do we have in
the way of a model?
	- Gas uptake and elimination are exponential.
	- Gas elimination is at a different rate than absorption.
	- Coeffs for He are different than N2.
	- Acceptable saturation levels are now dependant on two
coeffs, in a slightly more complex formula.
	- Half times are different, with much longer half times on the
long end.

All of the above aspects fit well with what we now know about
physiology and physics, and so we say that Buhlman knows a lot about
what is going on to cause DCI.  In short, we are tempted to say that
looking at the model, we know how DCI works.  But do we?  Of course
not!  Some important points:
	- The final half times and coeffs in the Buhlman model *do
not* correspond to real tissue types (despite what the Aladin Pro
manual tells you!).
	- It's too simple, and only considers raw N2/He loading.

So fast forward again, this time to DCIEM.  UDT (commissioned by
DCIEM) undertakes building a new, safer deco model to generate a large
variety of tables.  They believe that a serial model of tissue loading
is more appropriate, given that inert gas uptake and elimination is
one of linear diffusion.  So their model starts with a veriety of
compartments which fill and unload in a serial order, as opposed to
the parallel fill and unload of Haldane/Workman/Buhlman.

UDT performs some animal studies (primarily to convert the body of
Haldane/Buhmal knowledge to a serial model), then commences with human
trials for refinement.  For refinement, UDT makes use of hard working
dives in cold water, to better approximate the ultimate usage environ
of the tables.  Large changes are made to the original model, in some
situations replacing sections of the general algorithm with specific
fudge factors to fit the data they gather.  Following the trials,
tables are published, thoug the model itself is not (after all, the
model is no longer a simple mathematical formula, but rather a model
with lots of contingencies).

So once again we ask: what does the DCIEM/UDT model tell us about DCI,
and why do we believe it?  Well, the idea of serial compartments is
defensible from a physics point of view, as we can easily argue that
gas loading is a linear diffusion problem.  Also, we still like the
notion of a variety of tissue types, each with their own coeffs, and
of course, the exponential nature is not in dispute from rational
people.

But the real reason we like the DCIEM/UDT tables is that they are not
simple models; rather, they we developed with a very heavy empirical
bent.  In short, through much refinement in real world diving, they
have been proven.  What do the DCIEM/UDT tables tell us about the
workings of DCI?  If anything, it is that DCI is a very complex
process, not easily modeled with a simple model.  Can we understand
how the DCIEM/UDT model works? No, as there is no model (in the form
of a simple equation) to speak of.

So now I ask, how different is what DCIEM/UDT did from using a neural
net to develop a model?  Not very, with one big exception: determining
when you are bent.

Prime Rat <shelps@ac*.ma*.ad*.ed*.au*> sez:
> How do you decide in an empirical way who has DCI?  Note also that I'm using 
> a different terminology to you.  You are using the old 'mechanistic 
> terminology' which isn't very useful once you actually have symptoms which 
> need treating.  I guess these are the ones people want to know about.  Who 
> cares about symptoms that don't need treating?
> 
> >cases where there would be no DCS, and another large number of cases
> >where DCS would be quite probable.  There would also be a large number
> >where DCS probability would be marginal, and the training would
> >require people to be bent so that the network would learn how to
> >discriminate. 
> 
> A fantastic concept. What criteria for discrimination would you use?  As far 
> as I am aware there are no objective criteria for deciding whether or not 
> someone has DCI.  Even the presence of intravascular bubbles is often 
> without symptoms.

Now that we have looked at how data for building deco models is
gathered (with people volunteering to be bent), lets think a little
about what a dive table is, and what it isn't.

Every dive table built so far has two regions, one a lot bigger than
the other:
	- Dives which are "on the table"
	- Dives which are not on the table
Question: If you perform a dive which is not on the table, are you
bent?  Flip side: if you perform a dive on the table, are you bent?

Answer to both questions: maybe.  With some (unstated) probability in
both cases. (With a "yes you are bent" probability higher in one
case.)

So who decided where to draw the boundary between these two regions of
the table, and what criteria did they use?  a) the table compiler, and
b) unstated.  b) is a big part of why we can not say what the
probability of being bent is, just by looking at a dive profile.

What has happened, of course, is that the table compiler built a
model, gathered lots of data, refined the model, then built a table
which incorporated their idea of "safe" dives.  But the table
compilers just provide the end result, a hard black line between
"table compiler sez its a safe dive" and "table compiler sez its not a
safe dive".  The table compiler does not tell you the criteria, or
even the relative safety of the two table regions.

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