Coprimely packed rings

Bacterial chemoreceptor arrays are hexagonally packed trimers of receptor dimers networked by rings of kinase and coupling proteins.

Chemoreceptor arrays are supramolecular transmembrane machines of unknown structure that allow bacteria to sense their surroundings and respond by chemotaxis. We have combined X-ray crystallography of purified proteins with electron cryotomography of native arrays inside cells to reveal the arrangement of the component transmembrane receptors, histidine kinases (CheA) and CheW coupling proteins...

Differential Polynomial Rings of Triangular Matrix Rings

Are proteins well-packed?

The average packing density inside proteins is as high as in crystalline solids. Does this mean proteins are well-packed? We go beyond average densities, and look at the full distribution functions of free volumes inside proteins. Using a new and rigorous Delaunay triangulation method for parsing space into empty and filled regions, we introduce formal definitions of interior and surface packin...

Optimal Packed String Matching

In the packed string matching problem, each machine word accommodates α characters, thus an n-character text occupies n/α memory words. We extend the Crochemore-Perrin constantspace O(n)-time string matching algorithm to run in optimal O(n/α) time and even in real-time, achieving a factor α speedup over traditional algorithms that examine each character individually. Our solution can be efficie...

Polynomial Rings over Pseudovaluation Rings

Let R be a ring. Let σ be an automorphism of R. We define a σ-divided ring and prove the following. (1) Let R be a commutative pseudovaluation ring such that x ∈ P for any P ∈ Spec(R[x,σ]) . Then R[x,σ] is also a pseudovaluation ring. (2) Let R be a σ-divided ring such that x ∈ P for any P ∈ Spec(R[x,σ]). Then R[x,σ] is also a σ-divided ring. Let now R be a commutative Noetherian Q-algebra (Q i...