Related papers: A Reduced Forward Collatz Algorithm: How Binary St…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
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…
This paper investigates integer multiplication of continued fractions using geometric structures. In particular, this paper shows that integer multiplication of a continued fraction can be represented by replacing one triangulation of an…
Lossy compression algorithms take advantage of the inherent limitations of the human eye and discard information that cannot be seen. In the present paper, a technique termed as Lossy Data Compression using Logarithm (LDCL) is proposed to…
The interest in polar codes has been increasing significantly since their adoption for use in the 5$^{\rm th}$ generation wireless systems standard. Successive cancellation (SC) decoding algorithm has low implementation complexity, but…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
We study the problem of indexing text with wildcard positions, motivated by the challenge of aligning sequencing data to large genomes that contain millions of single nucleotide polymorphisms (SNPs)---positions known to differ between…
In this paper, we study the impact of locality on the decoding of binary cyclic codes under two approaches, namely ordered statistics decoding (OSD) and trellis decoding. Given a binary cyclic code having locality or availability, we…
In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this…
This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless…
This paper presents an algorithmic method that, given a positive integer $j$, generates the $j$-th convergence stair containing all natural numbers from where the Collatz conjecture holds by exactly $j$ applications of the Collatz function.…
Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to…
A construction of expander codes is presented with the following three properties: (i) the codes lie close to the Singleton bound, (ii) they can be encoded in time complexity that is linear in their code length, and (iii) they have a…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
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…
We developed a novel direct algorithm to derive the mass-ratio distribution (MRD) of short-period binaries from an observed sample of single-lined spectroscopic binaries (SB1). The algorithm considers a class of parameterized MRDs and finds…
We study small-loss bounds for adversarial multi-armed bandits with graph feedback, that is, adaptive regret bounds that depend on the loss of the best arm or related quantities, instead of the total number of rounds. We derive the first…