Related papers: 2-Free Tetranacci Sequences

The syntactic structure of a sentence is often represented using syntactic dependency trees. The sum of the distances between syntactically related words has been in the limelight for the past decades. Research on dependency distances led…

A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…

The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number of other spectral sequences. Our goal is to show how the higher terms of such spectral sequences are determined…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

We prove an upper bound for the least prime in an irrational Beatty sequence. This result may be compared with Linnik's theorem on the least prime in an arithmetic progression.

In the classic sequential testing problem, we are given a system with several components each of which fails with some independent probability. The goal is to identify whether or not some component has failed. When the test costs are…

In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent…

We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The…

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…

We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to…

We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent…

A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…

We propose a general scheme to create time sequences that fulfill given constraints but are random otherwise. Significance levels for nonlinearity tests are as usually obtained by Monte Carlo resampling. In a new scheme, constraints…

The notion of 'bifurcating continued fractions' is introduced. Two coupled sequences of non-negative integers are obtained from an ordered pair of positive real numbers in a manner that generalizes the notion of continued fractions. These…

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…

In this short article, we study different problems described as initial value problems of discrete differential equations and develop a a transform method called the sigma transform, a discrete version of the continuous Laplace transform to…

The Fibonacci numbers are a sequence of integers in which every number after the first two, 0 and 1, is the sum of the two preceding numbers. These numbers are well known and algorithms to compute them are so easy that they are often used…

Consider a binary tree, to the vertices of which are assigned independent Bernoulli random variables with mean $p\leq1/2$. How many of these Bernoullis one must look at in order to find a path of length $n$ from the root which maximizes, up…

Let $s$ be a finite sequence over a field of length $n$. It is well-known that if $s$ satisfies a linear recurrence of order $d$ with non-zero constant term, then the reverse of $s$ also satisfies a recurrence of order $d$ (with…

Sequences diverge either because they head off to infinity or because they oscillate. Part 1 \cite{Part1} of this paper laid the pure mathematics groundwork by defining Archimedean classes of infinite numbers as limits of smooth sequences.…