1. Vishnu V. Zutshi for the NICADD/NIU group
Potpourri
Vishnu V. Zutshi
for the
NICADD/NIU group

2. Cluster Separability
AHCal Meeting,DESY,Oct03
10/28/2003

3. Separability
For any two classes or clusters the classification rule can basically be stated as:
P(c1|x) > P(c2|x)
The separability of two clusters or classification error probability depends on the difference between P(c1|x) and P(c2|x)
Many measures can be constructed to quantify this
AHCal Meeting,DESY,Oct03
10/28/2003

4. For Example…..
For best separability clusters should have small within class
variance and large between class distance.
J = trace{Sw-1 Sm} where Sw = S PiSi
Si is the covariance matrix for cluster ci
Sm is the covariance matrix w.r.t. the global mean
AHCal Meeting,DESY,Oct03
10/28/2003

5. Track Parameters
AHCal Meeting,DESY,Oct03
10/28/2003

6. ‘Separability’ vs. Distance
AHCal Meeting,DESY,Oct03
10/28/2003

7. Another Measure…. B = a*(mi-mk)T *({Si+Sk}/2)-1 *(mi-mk) +
b*ln{(|(Si+Sk)/2|)/sqrt(| Si || Sk |)}
m = mean and S = covariance
the first term gives the separation due to mean difference
the second term due to covariance difference
AHCal Meeting,DESY,Oct03
10/28/2003

8. ‘Separability’ vs. Distance
AHCal Meeting,DESY,Oct03
10/28/2003

9. Ratio of measures (m x m/n x n)
AHCal Meeting,DESY,Oct03
10/28/2003

10. Ratio of measures (m x m/n x n)
3x3/1x1
5x5/3x3
AHCal Meeting,DESY,Oct03
10/28/2003

11. ‘Resolution’
3x3
1x1
5x5
AHCal Meeting,DESY,Oct03
10/28/2003

12. Test-beam Geometry Implemented in G4 HCal Tail-catcher ECal
AHCal Meeting,DESY,Oct03
10/28/2003

13. G4 Setup GEANT 4.5.2.p01 Mokka physics lists
For convenience General Particle Source linked in
Aggregate hits by cell with track contributions
ASCII output format (others can be put in)
AHCal Meeting,DESY,Oct03
10/28/2003

14. Data Format EVENT evt_no ECAL no_hits
layer_no … x y z cell_edep abs_edep ntrak
track_no track_edep …
HCAL …
TAILCATCHER
AHCal Meeting,DESY,Oct03
10/28/2003

15. HCal Face & Side View
AHCal Meeting,DESY,Oct03
10/28/2003

16. Charged Pion Event
AHCal Meeting,DESY,Oct03
10/28/2003

17. Tail-catcher
AHCal Meeting,DESY,Oct03
10/28/2003

18. Extruder Line
AHCal Meeting,DESY,Oct03
10/28/2003

19. Extruded Strip w/ 10 holes
AHCal Meeting,DESY,Oct03
10/28/2003

20. 10-hole Die
AHCal Meeting,DESY,Oct03
10/28/2003

21. Tail-catcher Next Steps
Steel from Fermilab ?
Need to have a stable design to go hunting
With the simulation now ready this should happen soon
AHCal Meeting,DESY,Oct03
10/28/2003