[MURG] - emulation difficulties

[Joseph J. Strout]

At 2:43 PM -0700 9/12/03, digfarenough wrote:

>Granted, I don't know a lot about diff eq, I just worked through a 
>few chapters of a textbook to get some idea of how they work, some 
>time I should take a real class in them.

I'd recommend a class (or book) in numerical methods rather than one 
in diff eq.

>  But there's a relationship between timestep and instability, right?

Right: if the timestep is too large, the equations become unstable; 
if the timestep is sufficiently small, it stays stable.

>Personally, I'd want my upload to last forever, who's to say the end 
>of the universe is as far as we'll make it?

Umm, OK.  So?  The size of the timestep has nothing to do with how 
long the simulation can run.  Stay within the stable regime and it'll 
be stable forever.

>So I'm not sure if I'd be comfortable with a system that could allow 
>this slowly growing instability

There is no slowly growing instability.  Basically, the simulation 
either is stable or it isn't.  If it's unstable, you'll know because 
it'll blow up almost immediately.  If it's stable, then you're good 
forever.

>I may have used the wrong word in choosing "error." What I meant is 
>that with each timestep, the difference between the numeric solution 
>and the exact solution increases.

That's error all right.  But I see no reason to believe that this 
error is important in any way.

>That's not true; even the equations governing individual ion channels
>are differential. So are individual atoms, for that matter.
>Basically, all the universe works on differential equations. But
>this is not a serious problem.
>
>No, basically all the universe can be described by different 
>equations, that doesn't mean it works on them.

Well, now we seem to be picking nits.

>  Above the quantum level, everything seems to work by nice 
>deterministic equations (although I recall Penrose showing a few 
>exceptions).

Deterministic differential equations, yes.  (And you can safely 
ignore Penrose; he's a reasonably good mathematician but a complete 
moron at neuroscience.  He's looking to find God in quantum 
microtubules, and wants it badly enough to discredit himself in the 
attempt.)

>  At the quantum level things may or may not be deterministic (I read 
>a paper, but have forgotten the foreign name, of a physicist who 
>offered a deterministic quantum theory based on information loss). 
>But I may be getting off topic...

Right.

>The first way you outlined above (with the caveat that an accurate
>compartmental model is a great deal more complex than just the HH
>equations) will work.
>
>Right, I had intended on biologically realistic models, perhaps with 
>a number of compartments that'd put De Schutter's Purkinje cell 
>model to shame... (and boy would I hate to have to program those 
>models... luckily, there are undergrads).

Heh.  Well, eventually the models would be built automatically, from 
the scanned-in information.

>I've done simulations in both GENESIS and NEURON, and seem to be in 
>the minority in thinking that GENESIS is the superior program, 
>despite its occasional... unwelcome features.

Actually, I'm with you on that (i.e. I also used both and preferred 
GENESIS, though of course I preferred CONICAL even more).  But good, 
you're way ahead of most people then.  But if you've done simulations 
in these, then I would expect you'd have a good feeling for stability 
issues by now.  Or perhaps not; both of these use advanced 
integration techniques and automatic adjustment of the timestep, 
which causes them to be always stable unless you go out of your way 
to make them unstable.  So perhaps you've never seen a simulation 
blow up!

Instability would be a problem, except that it's easily solved, as 
tools like GENESIS show.  Accumulated error is a problem for 
astronomers attempting to predict exactly where Jupiter is going to 
be a few hundred millenia from now.  Accumulated error is not, 
however, a problem for us.  It would be ludicrous to try to predict 
the exact state of any person years in the future.  The brain has so 
many inputs, and is such a chaotic system, that any such error is 
meaningless.

Best,
- Joe



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