Does generalization in infant learning implicate abstract algebra-like rules?

Does generalization in infant learning implicate abstract algebra-like rules?

Two recent papers in Science [1, 2] suggest that infants well under a year old can learn from exposure to relatively short samples of language-like sequences of syllables. The first of these two papers, by Saffran and colleagues [1], suggested that infants were sensitive to the statistical structure of syllable sequences that they heard, in that they tended to listen longer to syllable sequence...

Learning Abstract Rules for Swarm Systems

Rule abstraction is an intuitive new tool that we propose for implementing swarm systems. The methods presented in this paper encourage a new paradigm for designing swarm applications: engineers can interact with a swarm at the abstract (swarm) level instead of the individual (agent) level. This is made possible by modeling and learning how particular swarm-level properties arise from low-level...

Lie triple derivation algebra of Virasoro-like algebra

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

Abstract Algebra

Algebra

Lectures in abstract algebra