We study the performance of finite frames for the encoding of vectors by applying first-order sigma-delta quantization to the frame coefficients. Our discussion is restricted to families of uniform tight frames, given by N vectors in d-dimensional Hilbert spaces, and mostly concerns the use of quantizers that assume only integer multiples of a step-size δ (mid-tread). We prove upper and lower b...

The quark sigma model describes the quarks interacting via exchange the pions and sigma meson fields. A new version of mesonic potential is suggested in the frame of some aspects of the quantum chromodynamics (QCD). The field equations have been solved in the mean-field approximation for the hedgehog baryon state. The obtained results are compared with previous works and other models. We conclu...

A central problem of dynamical systems theory is to identify a reduced description of the dynamical process one can deal easier. In this paper we present a systematic method of identifying those closed sub-systems of a given discrete time dynamical system in the frame of operator theory. It is shown that this problem is closely related to finding invariant sigma algebras of the dynamics. Index ...

Suppose that the collection {ei}i=1 forms a frame for R, where each entry of the vector ei is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We show that an arbitrary signal in R can be recovered from its quantized frame coefficients up to an error which decays root-exponentially in the oversampling rate m/k. Here the...

The GOES-R Flight Project has developed an Image Navigation and Registration (INR) Performance Assessment Tool Set (IPATS) for measuring Advanced Baseline Imager (ABI) and Geostationary Lightning Mapper (GLM) INR performance metrics in the post-launch period for performance evaluation and long term monitoring. For ABI, these metrics are the 3-sigma errors in navigation (NAV), channel-to-channel...

Genome sequence analysis of the bacterium Xylella fastidiosa revealed the presence of two genes, named rpoE and rseA, predicted to encode an extracytoplasmic function (ECF) sigma factor and an anti-sigma factor, respectively. In this work, an rpoE null mutant was constructed in the citrus strain J1a12 and shown to be sensitive to exposure to heat shock and ethanol. To identify the X. fastidiosa...

The second order Sigma-Delta (Σ∆) scheme with linear quantization rule is analyzed for quantizing finite unit-norm tight frame expansions for Rd. Approximation error estimates are derived, and it is shown that for certain choices of frames the quantization error is of order 1/N2, where N is the frame size. However, in contrast to the setting of bandlimited functions there are many situations wh...