Related papers: Binary Signed-Digit Integers, the Stern Diatomic S…

It is well known that the Bell numbers represent the total number of partitions of an n-set. Similarly, the Stirling numbers of the second kind, represent the number of k-partitions of an n-set. In this paper we introduce a certain…

This article introduces byteSteady -- a fast model for classification using byte-level n-gram embeddings. byteSteady assumes that each input comes as a sequence of bytes. A representation vector is produced using the averaged embedding…

A Sidon set is a set A of integers such that no integer has two essentially distinct representations as the sum of two elements of A. More generally, for every positive integer g, a B_2[g]-set is a set A of integers such that no integer has…

In a recent paper, Roland Bacher conjectured three identities concerning Stern's sequence and its twist. In this paper we prove Bacher's conjectures. Possibly of independent interest, we also give a way to compute the Stern value (or…

For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs) can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their…

We study some essential arithmetic properties of a new tree-based number representation, {\em hereditarily binary numbers}, defined by applying recursively run-length encoding of bijective base-2 digits. Our representation expresses giant…

The problem of storing large amounts of information safely for a long period of time has become essential. One of the most promising new data storage mediums are the polymer-based data storage systems, like the DNA-storage system. These…

Let $X$ be a $v$-set, $\B$ a set of 3-subsets (triples) of $X$, and $\B^+\cup\B^-$ a partition of $\B$ with $|\B^-|=s$. The pair $(X,\B)$ is called a simple signed Steiner triple system, denoted by ST$(v,s)$, if the number of occurrences of…

Coding theory and $t$-designs have close connections and interesting interplay. In this paper, we first introduce a class of ternary linear codes and study their parameters. We then focus on their three-weight subcodes with a special weight…

In the paper we study the structure of hyperplanes of so called binomial partial Steiner triple systems (BSTS's, in short) i.e. of configurations with $\binom{n}{2}$ points and $\binom{n}{3}$ lines, each line of the size $3$. Consequently,…

In this work we introduce a new polynomial representation of the Bernoulli numbers in terms of polynomial sums allowing on the one hand a more detailed understanding of their mathematical structure and on the other hand provides a…

Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we…

Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $\sum_{n\in{\rm NR}(a,b)}\lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${\rm…

We study representations of integers as sums of the form $\pm a_1\pm a_2\pm \dotsb \pm a_n$, where $a_1,a_2,\ldots$ is a prescribed sequence of integers. Such a sequence is called an Erd\H{o}s-Sur\'anyi sequence if every integer can be…

For each integer $d\ge 4$, we study the sequence of positive integers which are represented by one at least of the cyclotomic binary forms $\Phi_n(X,Y)$, with $n$ a positive integer satisfying $\varphi(n)\ge d$. The case $d=2$ was studied…

From a geometric perspective most nonlinear binary classification algorithms, including state of the art versions of Support Vector Machine (SVM) and Radial Basis Function Network (RBFN) classifiers, and are based on the idea of…

A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…

Using well-known mathematical problems for encryption is a widely used technique because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as…

The distribution of a given sequence in the set of all sequences with n ones and m = M - n zeros are found by relating the problem to the partitions of a natural number in m natural summands, taking into account the order. The formulas…

Numerically efficient and stable algorithms are essential for kernel-based regularized system identification. The state of art algorithms exploit the semiseparable structure of the kernel and are based on the generator representation of the…