New results in the geometry of random fields, with applications to CMB and galaxy density

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New results in the geometry of random fields,
with applications to CMB and galaxy density

• Keith Worsley,
• Hugo Drouin, Pauline Klein
• Department of Mathematics and Statistics,
• McConnell Brain Imaging Centre,
• Montreal Neurological Institute,
• McGill University

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Milky way
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(No Transcript)
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The 2dF Galaxy Redshift Survey spectra and
redshifts Mon. Not. R. Astron. Soc. 328,
10391063 (2001)
Milky way
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(No Transcript)
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fMRI data 120 scans, 3 scans each of hot, rest,
warm, rest, hot, rest,
T (hot warm effect) / S.d. t110 if no
effect
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Gaussianized ?2 field?
EC
Gaussian threshold
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Gaussianized T field?
EC
Gaussian threshold
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EC for WMAP, unsmoothed, FWHM 1.6o
2500
Observed
2000
Expected
10
1500
0
1000
500
-10
-8
-7
-6
-5
-4
0
EC
20
-500
-1000
10
-1500
0
4
5
6
7
8
-2000
-2500
-5
-4
-3
-2
-1
0
1
2
3
4
5
Gaussian threshold
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Observed Expected EC, with Poisson sd in tails
EC
Gaussian threshold
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EC for WMAP smoothed to FWHMo (expected)
no smoothing
scale space
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Simulation (expected)
no smoothing
scale space
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Scale space WMAP data
2000
Observed
Expected
o
o

1.6

20.5
1500
1000
10
0
500
EC
-10
-4.5
-4
-3.5
0
20
10
-500
0
3.5
4
4.5
5
-1000
-5
-4
-3
-2
-1
0
1
2
3
4
5
Gaussian threshold