Related papers: Well-Orderedness of the Bashicu Matrix System
It is proved that positive entropy implies mean Li-Yorke chaos for a G-system, where G is a countable infinite discrete bi-orderable amenable group. Examples are given for the cases of integer lattice groups and groups of integer unipotent…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…
A prefix grammar is a context-free grammar whose nonterminals generate prefix-free languages. A prefix grammar $G$ is an ordinal grammar if the language $L(G)$ is well-ordered with respect to the lexicographic ordering. It is known that…
The set of idempotents of a regular semigroup is given an abstract characterization as a regular biordered set in [2], and in [4] it is shown how a biordered set can be associated with a complemented modular lattice. Von Neumann has shown…
Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum…
Human recursive numeral systems (i.e., counting systems such as English base-10 numerals), like many other grammatical systems, are highly regular. Following prior work that relates cross-linguistic tendencies to biases in learning, we ask…
Matrix grammars are one of the first approaches ever proposed in regulated rewriting, prescribing that rules have to be applied in a certain order. Originally, they have been introduced by \'Abrah\'am on linguistic grounds. In traditional…
Inspired by Leivant's work on absolute predicativism, Bellantoni and Cook in 1992 introduced a structurally restricted form of recursion called predicative recursion. Using this recursion scheme on the inductive structures of natural…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…
Bayesian networks (BNs) are graphical \emph{first-order} probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a…
Given a rank one measure-preserving system defined by cutting and stacking with spacers, we produce a rank one binary sequence such that its orbit closure under the shift transformation, with its unique {nonatomic} invariant probability, is…
Self-assembled patterns obtained from a drying nanosphere suspension are investigated by computer simulations and simple experiments. Motivated by the earlier experimental results of Sasaki and Hane and Schope, we confirm that more ordered…
A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order…
We studied the relationships between Collins-Roscoe mechanism and D-spaces, proved that well-ordered (F) spaces are D-spaces. This positively answered a question asked by D.Soukup and Y.Xu before.
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
We show that if a context-free grammar generates a language whose lexicographic ordering is well-ordered of type less than $\omega^2$, then its order type is effectively computable.
Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by…
A circular program contains a data structure whose definition is self-referential or recursive. The use of such a definition allows efficient functional programs to be written and can avoid repeated evaluations and the creation of…
As neural language models approach human performance on NLP benchmark tasks, their advances are widely seen as evidence of an increasingly complex understanding of syntax. This view rests upon a hypothesis that has not yet been empirically…