相关论文: Geometric Aspects of Biological Sequence Compariso…

The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…

We consider quasi-perfect codes in $\mathbb{Z}^n$ over the $\ell_p$ metric, $2 \leq p < \infty$. Through a computational approach, we determine all radii for which there are linear quasi-perfect codes for $p = 2$ and $n = 2, 3$. Moreover,…

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

Edit distance similarity search, also called approximate pattern matching, is a fundamental problem with widespread database applications. The goal of the problem is to preprocess $n$ strings of length $d$, to quickly answer queries $q$ of…

Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in model representations has been shown to improve many tasks,…

In this paper, I introduce a Sequence-based Multiscale Model (SeqMM) for the biomolecular data analysis. With the combination of spectral graph method, I reveal the essential difference between the global scale models and local scale ones…

The goal of this paper is to study the similarity between sequences using a distance between the \emph{context} trees associated to the sequences. These trees are defined in the framework of \emph{Sparse Probabilistic Suffix Trees} (SPST),…

The article deals with the issue of modification of metric classification algorithms. In particular, it studies the algorithm k-Nearest Neighbours for its application to sequential data. A method of generalization of metric classification…

Measuring visual similarity between two or more instances within a data distribution is a fundamental task in image retrieval. Theoretically, non-metric distances are able to generate a more complex and accurate similarity model than metric…

Biological sequence comparison is a key step in inferring the relatedness of various organisms and the functional similarity of their components. Thanks to the Next Generation Sequencing efforts, an abundance of sequence data is now…

The class of 1-generator quasi-abelian codes over finite fields is revisited. Alternative and explicit characterization and enumeration of such codes are given. An algorithm to find all 1-generator quasi-abelian codes is provided. Two…

Cliquewidth is a dense analogue of treewidth. It can be deduced from recent results by Hickingbotham [arXiv:2501.10840] and Nguyen, Scott, and Seymour [arXiv:2501.09839] that graphs of bounded cliquewidth are quasi-isometric to graphs of…

We introduce a distance in the space of fully-supported probability measures on one-dimensional symbolic spaces. We compare this distance to the $\bar{d}$-distance and we prove that in general they are not comparable. Our projective…

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…

The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…

This paper addresses the challenge of modeling multi-way contingency tables for matched set data with ordinal categories. Although the complete symmetry and marginal homogeneity models are well established, they may not always provide a…

This paper focuses on systems of strongly coupled elliptic operators whose coefficients may be unbounded and are defined on a domain $\Omega \subseteq \mathbb{R}^d$. It is shown that a quasi-contractive semigroup in $L^p$-spaces can be…

Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…

In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for tree-like shapes and study metrics on the shape space. This shape space has singularities, corresponding to topological…

Pathogen genome data offers valuable structure for spatial models, but its utility is limited by incomplete sequencing coverage. We propose a probabilistic framework for inferring genetic distances between unsequenced cases and known…