Related papers: Algorithmic classification of noncorrelated binary…

When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…

A tournament on 8 or more vertices may be intrinsically linked as a directed graph. We begin the classification of intrinsically linked tournaments by examining their score sequences. While many distinct tournaments may have the same score…

If the list of binary numbers is read by upward-sloping diagonals, the resulting ``sloping binary numbers'' 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) have some surprising properties. We give formulae for the n-th…

Exact string matching has been a fundamental problem in computer science for decades because of many practical applications. Some are related to common procedures, such as searching in files and text editors, or, more recently, to more…

With reference to a previous work, the problem of the experimental detection of non-causal synordination patterns between two series of physical events is examined. It is necessary that the patterns in question act in a reproducible, or at…

The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset…

Binary code similarity approaches compare two or more pieces of binary code to identify their similarities and differences. The ability to compare binary code enables many real-world applications on scenarios where source code may not be…

One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…

Sequence comparison is a widely used computational technique in modern molecular biology. In spite of the frequent use of sequence comparisons the important problem of assigning statistical significance to a given degree of similarity is…

The binary string matching problem consists in finding all the occurrences of a pattern in a text where both strings are built on a binary alphabet. This is an interesting problem in computer science, since binary data are omnipresent in…

Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two…

The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to…

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…

The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…

The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study the density of the positivity set of a given linear recurrence sequence, that is the question of how…

We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…

We show how binary classification methods developed to work on i.i.d. data can be used for solving statistical problems that are seemingly unrelated to classification and concern highly-dependent time series. Specifically, the problems of…

Recently, a short and elegant proof was presented showing that a binary word of length $n$ contains at most $n-3$ runs. Here we show, using the same technique and a computer search, that the number of runs in a binary word of length $n$ is…

Our study revisits the problem of accuracy-fairness tradeoff in binary classification. We argue that comparison of non-discriminatory classifiers needs to account for different rates of positive predictions, otherwise conclusions about…

It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…