Related papers: Patterns on the numerical duplication by their adm…

We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction…

Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization,…

We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…

We prove model completeness for the theory of addition and the Frobenius map for certain subrings of rational functions in positive characteristic. More precisely: Let $p$ be a prime number, $\mathbb{F}_{p}$ the prime field with $p$…

We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…

Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of…

In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational…

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…

We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…

Continuing the study of the structure of semirings, we turn to the spectrum of prime congruences. Joo and Mincheva developed an elegant theory in the special case of idempotent semirings, which is generalized here to ``semiring pairs,''…

Let R and S be differential graded algebras. In this paper we give a characterisation of when a differential graded R-S-bimodule M induces a full embedding of derived categories M\otimes - :D(S)--> D(R). In particular, this characterisation…

We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…

We show that, with some technical conditions, an abelian category can be embedded into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.

We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric…

We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws:…

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same…

A categoricity theorem is established for patterns of resemblance of order 2 showing that the order in which patterns arise in a wide range of hierarchies is the same.

A consecutive pattern in a permutation $\pi$ is another permutation $\sigma$ determined by the relative order of a subsequence of contiguous entries of $\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular…