A new class of alternative dual frames is introduced in the setting of finite frames for Rd. These dual frames, called Sobolev duals, provide a high precision linear reconstruction procedure for Sigma-Delta (Σ∆) quantization of finite frames. The main result is summarized as follows: reconstruction with Sobolev duals enables stable rth order Sigma-Delta schemes to achieve deterministic approxim...

Introduction: Bacteria have at least one sigma factor (σ-factor) that transcribes the genes required for cell viability. Usually, transcription of σ-factors occurs and changes in response to a variety of environmental stresses. Expression of σ-factors is one of the strategies which is used in response to different stress conditions. This study was aimed to evaluate the effects...

By frame of reference transformations, an input variable in one coordinate system is transformed into an output variable in a different coordinate system depending on another input variable. If the variables are represented as neural population codes, then a sigma–pi network is a natural way of coding this transformation. By multiplying two inputs it detects coactivations of input units, and by...

let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

sigma B (sigma 37) is a secondary species of RNA polymerase sigma factor found in the gram-positive bacterium Bacillus subtilis. To study the function of sigma B genetically, we sought mutations that block the expression of a gene (ctc) known to be transcribed by sigma B-containing RNA polymerase in vitro. One such mutation, called crl, was found to map in or near the structural gene (sigB) for...

Quantization is a necessary intermediate step in any digital processing device. The Memoryless Scalar quantization and the Sigma Delta quantization are two well known quantization schemes with different emphasis. In this talk, I will discuss the quantization problem raised in frame theory and compressed sensing, and explain the benefit that Sigma Delta quantization can deliver. In particular, w...