Hi Denis,

Thanks very much for clarifying what the ADF is actually doing. I have
a much better idea of what's going on now, and I agree completely that
our concerns at Nevis may not be a real problem. And our "solutions"
should only be taken to indicate that we're thinking about the
problem - not as proposals. However, I think that we need to consider
this matter carefully before declaring it to be "solved".

To aid in this process (I hope) I will post comments off the Dec-12
meeting agenda page.

http://www.nevis.columbia.edu/~evans/l1cal/meetings/meetings.html

Let me expand a bit on our view of the problem.

The real issue is that we need to include somehow measurements of TTs
that have fluctuated below the pedestal in our sums. Since there is an
approximately equal probability for a TT's energy to end up above or
below the pedestal in the absence of a signal, then "positive" and
"negative" fluctuations will cancel in the sum. If negative
fluctuations get truncated to the pedestal (whatever it is) then this
will not work, and we will induce a positive bias into all of our
sums. This is obviously a problem for the hadronic veto in the EM
algorithm, for example.

Now, this would not normally be a problem because an offset can be
added to the TT input signal at various points in the chain (as you
mentioned in your previous mail). Negative fluctuations in the noise
are then just signals below the pedestal that we have chosen. We have
to worry about this pedestal when summing 2560 TTs to get the total
Et, but that's another story.

A *possible* difficulty arises, however, because the peak detection
algorithm sets any TT signal that is not a peak to the
pedestal. Again, this does not produce problems to zeroth order,
because noise doesn't normally produce a peak - so both positive and
negative fluctuations are set to the pedestal symmetrically. The
problem comes for those noise signals that are detected as a peak. It
is very improbable that a negative fluctuation would be seen as a
peak: three samples in a row would have to fluctuate downward, with
the middle one fluctuating less negatively than the other
two. Positive fluctuations, on the other hand, could relatively easily
produce small-magnitude peaks.

So, because of the asymmetry in probability for positive and negative
fluctuations to be found as peaks, fluctuations above pedestal will
tend to be reported as their true energy (>pedestal) while negative
fluctuations will be reported as the pedestal, and a positive bias
will be introduced into sums.

The big question here is: how big is this effect? We certainly need
any input we can get into this question before we embark on any
serious study of it using MC.

Note that MC studies of this issue are complicated because, without
being very clever, we would have to consider information from previous
bunch crossings to understand the effect in the BC under consideration.

Thanks again for your thoughts on this issue. Everyone else is
encouraged to weigh in as well.

Regards  -  Hal