We study properties of a C2-cofinite vertex operator algebra V = ⊕ ∞ i=0Vi of CFT type. If it is also rational (i.e. all modules are completely reducible) and V ′ ∼= V , then the rigidity of the tensor category of modules has been proved by Huang [11], where V ′ denotes the restricted dual of V . However, when we treat irrational C2cofinite VOAs, the rigidity is too strong, because it is almost...

Two methods for the extension of neuro-modules are introduced resulting in a new behavioral functionality. We call them restricted and semi-restricted module expansion. These methods are developed and applied using a modular neuro-dynamics approach to behavior control of autonomous mobile robots. Evolved neuro-controllers which solve an obstacle avoidance task are expanded to show in addition a...

Exercise 1 Let A be a domain, α an injective endomorphism of A, D = A[∂;α, β] a skew polynomial ring, E ∈ An×n and F ∈ An×n, R = ∂ In − E ∈ Dn×n and R′ = ∂ In − F two matrices with entries in D, M = D1×n/(D1×nR) and M ′ = D1×n/(D1×nR′) two left D-modules respectively finitely presented by R and R′. 1. Describe the left D-modules M and M ′ in terms of generators and relations. 2. Prove that any ...

Laminins are a major constituent of all basement membranes. The polymerisation of laminins at the cell surface is mediated by the three short arms of the cross-shaped laminin heterotrimer. The short arms contain repeats of laminin-type epidermal growth factor-like (LE) domains, interspersed with globular domains of unknown function. A single LF domain is inserted between LE5 and LE6 of the lami...

Protein-based therapeutics feature large interacting surfaces. Protein folding endows structural stability to localised surface epitopes, imparting high affinity and target specificity upon interactions with binding partners. However, short synthetic peptides with sequences corresponding to such protein epitopes are unstructured in water and promiscuously bind to proteins with low affinity and ...

We describe a class of non-central extensions of the diffeomorphism algebra in N -dimensional spacetime, and construct lowest-energy modules thereof, thus generalizing work of Eswara-Rao and Moody. There is one representation for each representation of V ir⋉̃k0 ĝl(N) (an extension of the semi-direct product). Similar modules are constructed for gauge algebras.

Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann’s zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis. For simplicity, G here denotes a classical semi-simple algebraic group defined over the field Q of rationals. With a fixed Borel, as usual, ∆0 stands...