Definability in self-referential systems.

The Dynamics of Cross-coupled, Self-referential Linear Systems

This article presents the central ideas behind cross-coupled, self-referential linear systems—dual systems where each system in the pair provides the other system with reference or control signals using a form of state feedback. Such systems are ubiquitous in nature, the most noteworthy being the mammalian brain. Although complex systems and feedback mechanisms have several decades worth of lit...

Contingent robot behaviors from self-referential dynamical systems

The self-organization of behavior is both a striking phenomenon in living beings and a challenging objective for autonomous robots. In our earlier work we introduced homeokinesis – the dynamical pendant of homeostasis – as a general domain invariant principle for behavioral self-creation. The present paper continues these investigations under a more pragmatic aspect. We start from the formulati...

Differential electrophysiological response during rest, self-referential, and non-self-referential tasks in human posteromedial cortex.

The electrophysiological basis for higher brain activity during rest and internally directed cognition within the human default mode network (DMN) remains largely unknown. Here we use intracranial recordings in the human posteromedial cortex (PMC), a core node within the DMN, during conditions of cued rest, autobiographical judgments, and arithmetic processing. We found a heterogeneous profile ...

Transformations between Self-Referential Sets

Self-Referential Definition of Orthogonality

There has for longer been an interest in finding equivalent conditions which define inner product spaces, and the respective literature is considerable, see for instance Amir, which lists 350 such results. Here, in this tradition, an alternative definition of orthogonality is presented which does not make use of any inner product. This definition, in the spirit of the recently developed non-wel...