Related papers: Describe the Fibonacci map by principal nests
We generalize the notions of $\beta$- and $\lambda$-maps to general selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normality, extremal disconnectedness,…
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.
We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article…
In this paper we prove that a matrix property of nettedness (all 2x2 cells satisfy a recurrence) is preserved for powers of such a matrix, where the coefficients are all instances of the same sequence. Also, we find an n-dimensional analog…
In this paper we provide some applications of the norm form in some quaternion division algebras over rational field and we give some properties of Fibonacci sequence and Fibonacci sequence in connection with quaternion elements. We define…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture…
We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
We introduce a framework for reasoning about what meaning is captured by the neurons in a trained neural network. We provide a strategy for discovering meaning by training a second model (referred to as an observer model) to classify the…
We use probability urn models to discover some known and unknown series identities involving Fibonacci numbers.
In this paper, we survey some properties, encoding, and bijections involving combinatorial maps, double occurrence words, and chord diagrams. We particularly study quasi-trees from a purely combinatorial point of view and derive a…
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of…
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the…
An $n$-valued map is a set-valued continuous function $f$ such that $f(x)$ has cardinality $n$ for every $x$. Some $n$-valued maps will "split" into a union of $n$ single-valued maps. Characterizations of splittings has been a major theme…
In this paper we use well-known results from linear algebra as tools to explore some properties of products of Fibonacci numbers. Specifically, we explore the behavior of the eigenvalues, eigenvectors, characteristic polynomials,…
We discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the…
The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space…
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.