This paper explores modeling the adaptive mechanisms of autonomous agents. The focus is on reflexive interaction as a looping action that creates a “self.” Imitation and play are adaptive components of reflexive interactions that can provide gradual modifications of the agent’s self. Little by little, the autonomous agent reinforces what seems to work and phases out other options through an int...

We discuss an unusual reflexive construction in which the Chinese reflexive ziji appears twice, once before the verb and once after. We demonstrate that this is a distinct construct with its own rules of construal and interpretation; it is not, for example, a combination of a simple ziji reflexive and an adverbial intensifier. Notably, their locality properties are also different: Double ziji d...

We consider the problem of executing conscious behavior i.e., of driving an agent’s actions and of allowing it, at the same time, to run concurrent processes reflecting on these actions. Toward this end, we express a single agent’s plans as reflexive dialogs in a multi-agent system defined by a virtual machine. We extend this machine’s planning language by introducing two specific operators for...

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1 free module, or R is Gorenstein and an isolated singularity (if R is complete, then it is even a simple hypersurface singularity). The crux of our proof is to...

In a recent paper [11] we answered to the negative a question raised in the book by Eklof and Mekler [8, p. 455, Problem 12] under the set theoretical hypothesis of ♦א1 which holds in many models of set theory. The Problem 12 in [8] reads as follows: If A is a dual (abelian) group of infinite rank, is A ∼= A⊕Z? The set theoretic hypothesis we made is the axiom ♦א1 which holds in particular in G...

Studio as a model of education is distinct from many other professional disciplines and although it can be quite rewarding on many levels it may also be an extremely unconstructive endeavor.1 The amount of time spent in studio typically far outweighs that spent for other courses and often at the expense of such other courses. The dedication that students bring to the studio is remarkable, yet m...

If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...