相关论文: A Dual Approach to Triangle Sequences: A Multidime…
We describe Gauss-type maps as geometric realizations of certain codes in the monoid of nonnegative matrices in the extended modular group. Each such code, together with an appropriate choice of unimodular intervals in P^1R, determines a…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
The need to analyze information from streams arises in a variety of applications. One of its fundamental research directions is to mine sequential patterns over data streams. Current studies mine series of items based on the presence of the…
This paper aims to introduce high school students to the intriguing world of continued fractions, a mathematical concept that provides a unique representation of numbers. The study focuses on the exploration and development of the…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
This paper continues the author's previous studies on continued fractions and Heron's algorithm, as from his former JMM2017 presentation (see \cite{CF.HA}).\par\medskip Extending the notion of continued fraction to the $p$-adic fields, one…
Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…
By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphical representation of such information. A filtration might be determined by time in a set…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
The Tribonacci-Lucas sequence $\{S_n\}_{n\ge 0}$ is defined by the linear recurrence relation $S_{n+3} = S_{n+2} + S_{n+1} + S_n$, for $ n\ge 0 $, with the initial conditions $S_0 =S_2= 3$ and $S_1 = 1$. A palindromic number is a number…
In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the alpha-continued fraction transformations T_alpha and unimodal maps. This correspondence identifies…
A Lagrange Theorem in dimension 2 is proved, for a particular two-dimensional algorithm, with a very natural geometrical definition. Dirichlet-type properties for the convergence of the algorithm are also proved. These properties procced…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…
We propose a novel sequence prediction method for sequential data capturing node traversals in graphs. Our method builds on a statistical modelling framework that combines multiple higher-order network models into a single multi-order…