The Entropy/Influence conjecture, raised by Friedgut and Kalai (1996) [9], seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is “smeared out”, then the Fourier coefficients are concentrated on “high” levels. In this note we generalize the conjecture to biased product measures on the d...

3 Case study: Yeast cell cycle 2 3.1 Missing values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Standardisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 Statistical assessment of periodicity . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3.1 Choice of background model . . . . . . . . . . . . . . . . . . . . . . . . ...

Introduction: Target transformation and factor analysis techniques are applied to the data returned by the Planetary Fourier spectrometer (PFS) on board the ESA Mars Express (MEX) mission. The data analyzed were obtained by the long wavelength channel (LWC) of PFS, in the range roughly from 300 to 1300 cm

Synthetic aperture radar (SAR) raw signal simulation is a powerful tool for designing new sensors, testing processing algorithms, planning missions, and devising inversion algorithms. In this paper, a spotlight SAR raw signal simulator for distributed targets is presented. The proposed procedure is based on a Fourier domain analysis: a proper analytical reformulation of the spotlight SAR raw si...

In this paper we develop a correlation method for the template matching problem in pattern recognition which includes translations, rotations, and dilations in a natural way. The correlation method is implemented using Fourier analysis on the “discrete motion group” and fast Fourier transform methods. A brief introduction to Fourier methods on the discrete motion group is given and the efficien...

The region occupied by and the contour of a physical object in 3-dimensional space are in a way dual or interchangeable characteristics of the object: the contour is the region’s boundary and the region is contained inside the contour. In the same way the characterization of the object’s contour by its Fourier descriptors, and the reconstruction of its region from the object’s multidimensional ...

Identifying the projective group for patterns by developing the camera model, the projective Fourier transform and its inverse are obtained in analogy with the classical, that is, Euclidean Fourier analysis. Projectively adapted properties are demonstrated in a numerical test. Using the expression of the projective Fourier integral by a standard Fourier integral in the coordinates given by the ...

The non-Fourier effect in heat conduction is important in strong thermal environments and thermal shock problems. Generally, commercial FE codes are not available for analysis of non-Fourier heat conduction. In this study, a meshless formulation is presented for the analysis of the non-Fourier heat conduction in the materials. The formulation is based on the symmetric local weak form of the sec...

The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From this theory an entire branch of research has flourished: from the Short-Time or Windowed Fourier Transform to the Wavelets, the Frames, and lately the Gener...