Related papers: Elementary properties of circle map sequences

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…

The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…

The kernel of a pair of linear systems is studied in the framework of commutative ring theory with applications to behavioral perspective of linear systems

We examine the structure of Farey maps, which are a class of maps (graph embeddings on surfaces) that have received significant attention recently. We describe how they are related to each other through regular coverings and parallel…

We study the functorial and growth properties of closed orbits for maps. By viewing an arbitrary sequence as the orbit-counting function for a map, iterates and Cartesian products of maps define new transformations between integer…

While important properties of word vector representations have been studied extensively, far less is known about the properties of sentence vector representations. Word vectors are often evaluated by assessing to what degree they exhibit…

We show that the use of the main characteristics of the circle map leads naturally to establish a few statements on primes and pseudoprimes. In this way a Fermat's theorem on primes and some interesting properties of pseudoprimes are…

Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…

This paper proposes a simple test for compositionality (i.e., literal usage) of a word or phrase in a context-specific way. The test is computationally simple, relying on no external resources and only uses a set of trained word vectors.…

We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particular forms of these matrices.

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

In this work, we investigate the transfer of some homological properties from a ring $R$ to his amalgamated duplication along some ideal $I$ of $R$, and then generate new and original families of rings with these properties.

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…

We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…

Traditional sentence embedding models encode sentences into vector representations to capture useful properties such as the semantic similarity between sentences. However, in addition to similarity, sentence semantics can also be…

The detailed analysis of molecular structures and properties holds great potential for drug development discovery through machine learning. Developing an emergent property in the model to understand molecules would broaden the horizons for…

Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…