It is well known that a discrete band-limited signal can be made broad-banded if we randomly permute its entries. In this paper, we study the efficacy of such spectral whitening procedure and its application to Sigma Delta quantization in Compressed Sensing. As a side result, we show that a similar whitening phenomenon can be observed in a broad class of non-Fourier orthogonal transformations.

We investigate the relation between supersymmetry and geometry for two dimensional sigma models with target spaces of arbitrary signature, and Lorentzian or Euclidean world-sheets. In particular, we consider twisted forms of the two-dimensional (p, q) supersymmetry algebra. Superspace formulations of the (p, q) heterotic sigma-models with twisted or untwisted supersymmetry are given. For the tw...

Let $D$ be the open disk $|x|< R$ of a complete ultrametric algebraically closed field $\mathbb K$. We define growth order $\rho(f)$, type $\sigma(f)$ cotype $\psi(f)$ and another expression $\theta(f)$ an analytic function in we show relations between number zeros $f$ ``maximum modulus'' involving $\rho,\sigma,\psi$. Then $\rho(f)$ lies $[\theta(f)-1, \theta(f)]$. Moreover, if $0< \rho(f)< +\i...

We consider the U(1) sigma model in the two dimensional spacetime S × R, which is a field-theoretical model possessing a nontrivial topology. It is pointed out that its topological structure is characterized by the zero-mode and the winding number. A new type of commutation relations is proposed to quantize the model respecting the topological nature. Hilbert spaces are constructed to be repres...

We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two dimensions are intimately related to the minimal surfaces in a flat pseudo Riemannian 3-space. We define two dimensional surfaces conformally related to the minimal s...

In Analog-to-digital (A/D) conversion on oversampled bandlimited functions, integration of samples in blocks before down-sampling, known as decimation, has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. In particular, when coupled with the Σ∆ quantization scheme, the reconstruction error decays exponentially with respect to the bit-rate. Here, a s...

When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong fluctuations, the condensation skyrmion textures order parameter fields can lead to superconductivity. In this work, we address mechanism considering scattering between $(2+1)$-dimensional Weyl and hedgehog-type tunneling configurations parameters that violate skyrmion-number conservation law. We show quant...