Related papers: $LCSk$++: Practical similarity metric for long str…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…
We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…
In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…
Tools that effectively analyze and compare sequences are of great importance in various areas of applied computational research, especially in the framework of molecular biology. In the present paper, we introduce simple geometric criteria…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
Measuring the similarity of short written contexts is a fundamental problem in Natural Language Processing. This article provides a unifying framework by which short context problems can be categorized both by their intended application and…
How do we know if two systems - biological or artificial - process information in a similar way? Similarity measures such as linear regression, Centered Kernel Alignment (CKA), Normalized Bures Similarity (NBS), and angular Procrustes…
Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…
This paper presents a new algorithm, the Modified Moving Contracting Window Pattern Algorithm (CMCWPM), for the calculation of field similarity. It strongly relies on previous work by Yang et al. (2001), correcting previous work in which…
Due to the increased availability of large datasets of biological sequences, the tools for sequence comparison are now relying on efficient alignment-free approaches to a greater extent. Most of the alignment-free approaches require the…
Data similarity (or distance) computation is a fundamental research topic which fosters a variety of similarity-based machine learning and data mining applications. In big data analytics, it is impractical to compute the exact similarity of…
Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…
This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…
Large language models (LLMs) are increasingly expected to tackle complex tasks, driven by their expanding applications and users' growing proficiency in crafting sophisticated prompts. However, as the number of explicitly stated…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
For graph learning tasks, many existing methods utilize a message-passing mechanism where vertex features are updated iteratively by aggregation of neighbor information. This strategy provides an efficient means for graph features…
The advent of "next-generation" DNA sequencing (NGS) technologies has meant that collections of hundreds of millions of DNA sequences are now commonplace in bioinformatics. Knowing the longest common prefix array (LCP) of such a collection…
Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider…
This paper describes a linear-time algorithm that finds the longest stretch in a sequence of real numbers (``scores'') in which the sum exceeds an input parameter. The algorithm also solves the problem of finding the longest interval in…