Abstract: We extend the concept of graph isomorphisms to multilayer networks with any number of “aspects” (i.e., types of layering). In developing this generalization, we identify multiple types of ...

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Abstract. Heisenberg reinvented matrices while discovering quantum mechanics, and the algebra generated by annihilation and creation operators obeying the canonical commutation relations was named ...

Formal and functional theories of language seem disparate, because formal theories answer the question of what a language is, while functional theories answer the question of what functions it serves.

The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously ...

Deciding whether two graphs are structurally identical, or isomorphic, is a classical algorithmic problem that has been studied since the early days of computing. Applications span a broad field of ...

Hurwitz’s theorem says that there are only 4 normed division algebras over the real numbers, up to isomorphism: the real numbers, the complex numbers, the quaternions, and the octonions. The proof was ...

Powerful insights arise from linking two fields of study previously thought separate. Examples include Descartes’s coordinates, which links geometry to algebra, Planck’s Quantum Theory, which links ...