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Machine learning on sets towards sequential output is an important and ubiquitous task, with applications ranging from language modeling and meta-learning to multi-agent strategy games and power grid optimization. Combining elements of…
Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns.…
An overview of current multiple alignment systems to date are described.The useful algorithms, the procedures adopted and their limitations are presented.We also present the quality of the alignments obtained and in which cases(kind of…
We provide an algorithm for computing semi-Fourier sequences for expressions constructed from arithmetic operations, exponentiations and integrations. The semi-Fourier sequence is a relaxed version of Fourier sequence for polynomials…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-10 expansions, Dedekind cuts and continued fractions.
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
Session A5 on numerical methods contained talks on colliding black holes, critical phenomena, investigation of singularities, and computer algebra.
By the sometimes so-called 'Main Theorem' of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of HYPERcomputation allow for the effective evaluation of also discontinuous…
This abstract extends on the previous work (arXiv:1407.2646, arXiv:1606.00075) on program induction using probabilistic programming. It describes possible further steps to extend that work, such that, ultimately, automatic probabilistic…
Gaussian Processes (GPs) are widely used tools in statistics, machine learning, robotics, computer vision, and scientific computation. However, despite their popularity, they can be difficult to apply; all but the simplest classification or…
The generalized Petersen graph $G(n, k)$ is a cubic graph with vertex set $V(G(n, k)) = \{v_i\}_{0 \leq i < n} \cup \{w_i\}_{0 \leq i < n}$ and edge set $E(G(n, k)) = \{v_i v_{i+1}\}_{0 \leq i < n} \cup \{w_i w_{i+k}\}_{0 \leq i < n} \cup…
We describe the results of the computation of aliquot sequences with small starting values. In particular all sequences with starting values less than a million have been computed until either termination occurred (at 1 or a cycle), or an…
The paper discusses numerical implementations of various inversion schemes for generalized V-line transforms on vector fields introduced in [6]. It demonstrates the possibility of efficient recovery of an unknown vector field from five…
Finding the $n$-th positive square number is easy, as it is simply $n^2$. But how do we find the complementary sequence, i.e., the $n$-th positive non-square number? For this case there is an explicit formula. However, for general…
The aim of this paper is to present a didactical sequence that fosters the development of meanings related to fractions, conceived as numbers that can be placed on the number line. The sequence was carried out in various elementary school…
This paper presents an expression to compute the exact period of a recursive random number generator based on d-sequences. Using the multi-recursive version of this generator we can produce large number of pseudorandom sequences.
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
Horadam sequences and their partial sums are computed via generating functions. The results are as simple as possible.
A new algebraic object is introduced - recurrent fractions, which is an n-dimensional generalization of continued fractions. It is used to describe an algorithm for rational approximations of algebraic irrational numbers. Some…