We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ , or are weakly rigid. As a consequence we obtain tha...

The category of von Neumann correspondences from B to C (or von Neumann B–C–modules) is dual to the category of von Neumann correspondences from C to B via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel’s Eilenberg-Watts theorem (on functors between the categories of represen...

Signal crossing is a significant problem within von Neumann cellular automata (29-states); only three solutions are known. This paper gives a thorough examination of these three solutions, including discussion of performance and the effective means of construction, including the mechanism of autoinitialisation. Application of these solutions within self-replicators is then examined for Nobili a...

All rings considered are associative with identity and all occurring modules are unital right modules. We denote by Mod R the category of all R-modules. The spectrum of a ring R is known to be the “set” of isomorphism classes of indecomposable injective right R-modules. When R is right-Noetherian the spectrum describes all injective Rmodules, since each injective module is a direct sum of indec...

The aim of this paper is to prove that, if R is a commutative regular ring in which 2 is a unit, then the reduced theory of quadratic forms with invertible coefficients in R, modulo a proper preorder T , satisfies Marshall’s signature conjecture and Milnor’s Witt ring conjecture (for precise statements, see Section 1 below). For that purpose we use the theory of special groups (abbreviated SG),...

We define five properties of symbol representations (called the Five M's) that together provide a powerful and flexible symbol processing facility. Our ideal symbol structures arc Mobile, Memorable, Meaningful, Malleable, and Modifiable. Conventional symbol processing architectures, such as Lisp on von Neumann machines, support some of these properties, but others seem to require flexibility an...

A very general commentary on the program camex, accompanied by an assortment of experiments which can be performed using the cam/pc board. These include the use of one, two, and three dimensional automata, although the primary utility of the board lies with two dimensional automata evolving on a 256x256 screen. Binary Moore and von Neumann neighborhoods are possible in each of the two half-cam'...