Abstract The graphical description of morphisms in rigid monoidal categories, in particular in ribbon categories, is summarized. It is illustrated with various examples of algebraic structures in such categories, like algebras, (weak) bi-algebras, Frobenius algebras, and modules and bimodules. Nakayama automorphisms of Frobenius algebras are introduced; they are inner iff the algebra is symmetric.

An important problem in computer vision is to determine how features extracted from images are connected to an existing model. In this paper, we focus on solving the registration problem, i.e. obtaining rigid transformation parameters between several 3D data sets, whether partial or exhaustive. The di culty of this problem is to obtain a method which is robust with respect to outliers and at th...

The general stress response of Bacillus subtilis provides a protective resistance to a variety of pressures. The key molecule is a subunit of RNA polymerase, sigma(B), which confers promoter specificity and is regulated by two signalling modules. Each module comprises protein kinases and phosphatases and 'switch' protein substrates for the kinase and phosphatase. The phosphorylation state of th...

In two-component signal transduction, an input triggers phosphorylation of receiver domains that regulate the status of output modules. One such module is the AAA+ ATPase domain in bacterial enhancer-binding proteins that remodel the sigma(54) form of RNA polymerase. We report X-ray solution scattering and electron microscopy structures of the activated, full-length nitrogen-regulatory protein ...

Symbolic architectures are effective at complex cognitive reasoning, but typically are incapable of important forms of sub-cognitive processing – such as perception – without distinct modules connected to them via low-bandwidth interfaces. Neural architectures, in contrast, may be quite effective at the latter, but typically struggle with the former. Sigma has been designed to leverage the stat...

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.

We introduce the notion of Burch submodules and weakly m-full modules over a local ring (R,m) study their properties. One our main results shows that satisfy 2-Tor rigid test also show (R,m), submodule M finitely generated R-module X, such either M=mX or M(⊆mX) is in 1-Tor rigid, module provided X faithful (and X∕M has finite length when m-full). As an application, we give some new class rings ...

Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is...