Functional connectivity between two voxels or regions of voxels can be measured by the correlation between voxel measurements from either PET CBF or BOLD fMRI images in 3D. We propose to look at the entire 6D matrix of correlations between all voxels and search for 6D local maxima. The main result is a new theoretical formula, based on random eld theory, for the p-value of these local maxima, t...

We present a procedure that can estimate – with statistical consistency guarantees – any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or modal-sets, of any bounded shape or dimension, including usual point-modes. In practice, modal-sets can arise as dense low-dimensional structures in noisy data, and more generally serve to be...

To estimate positions of individual trees in high– resolution aerial photographs we use circular templates derived from an optical tree crown model and the geometry at image acquisition. Local maxima are found for the correlation function for the successively transposed templates over the whole image. Using auxilliary information on the exact or approximate number of trees in the stand regarded...

Functional connectivity between two voxels or regions of voxels can be measured by the correlation between voxel measurements from either PET CBF or BOLD fMRI images in 3D. We propose to look at the entire 6D matrix of correlations between all voxels and search for 6D local maxima. The main result is a new theoretical formula based on random field theory for the p-value of these local maxima, w...

We present a new continuity correction to the P value for local maxima of a statistical parametric map that bridges the gap between small FWHM, when the Bonferroni correction is accurate, and large FWHM, when random field theory is accurate. The new method, based on discrete local maxima, is always an upper bound (like the Bonferroni), but lower and hence more accurate for large FWHM, without i...

Air-sea-ice interaction processes in the Southern Ocean are investigated utilizing space-observed surface winds, sea ice concentration, and sea surface temperature (SST) from September through December, 1996. The sea ice edge (SIE) shows three ice-extent maxima around the Antarctic during September and October when sea ice coverage is maximum. They are located in the central Indian Ocean, east ...

Example : (Local maxima) Let Z = (Z1, ..., Zn) be i.i.d. U(0, 1) random variables and let Sn be the number of local maxima in Z. Then Sn/ √ V ar(Sn)→d N (0, 1) as n→∞. CLT is so strong due to its universality and a natural question is whether there are other laws that own the same property. Tracy-Widom distribution and its variants form such a class and they appear in several statistics of rand...

The Expectation-Maximization (EM) algorithm is a very popular technique for maximum likelihood estimation in incomplete data models. When the expectation step cannot be performed in closed{form, a stochastic approximation of EM (SAEM) can be used. Under very general conditions, the authors have shown that the attractive stationary points of the SAEM algorithm correspond to the global and local ...

We study universality in the kinetics of spinodal phase separation in unstable thin liquid films, via simulations of the thin film equation. It is shown that, in addition to morphology and free energy, the number density of local maxima in the film profile can also be used to identify the early, late, and intermediate stages of spinodal phase separation. A universal curve between the number den...

QBI in 162 directions (b=4500 s/mm2). In panel a), colors encode principal sheet direction and both techniques show good qualitative agreement. However, closer inspection of the SNDFs shows intravoxel sheet crossing which cannot be resolved with conventional DTI. Panel b) illustrates this for the framed voxel from a), where the DTI sheet normal direction lies in between two distinct sheet popul...