In this paper we implement a Fourier method to estimate high-frequency correlation matrices from small data sets. The Fourier estimates are shown to be considerably less noisy than the standard Pearson correlation measures and thus capable of detecting subtle changes in correlation matrices with just a month of data. The evolution of correlation at different time scales is analyzed from the ful...

The coherent anti-Stokes Raman scattering (CARS) process with two different-color phase-fluctuating fields was studied experimentally and theoretically. It was found that the efficiency of this process depends strongly on the cross correlation between the phases of the driving fields. Depending on the detuning from Raman resonance, the CARS signal can be either enhanced or suppressed with respe...

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so tur...

This essay compares the performance of two types of correlation measures in triggering trades in a pairs trading application in the presence of high-frequency stock prices. One correlation measure is the commonly-used Pearson correlation and the other is a robust correlation measure called Maronna correlation. These correlation measures are used to define three methods of initiating trades – ca...

The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational correlation tensor terms as compared with the Einstein equations of general relativity. This correlation tensor satisfies a system of structure and field equatio...