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Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
Let $E$ be an elliptic curve with complex multiplication by a ring $R$, where $R$ is an order in an imaginary quadratic field or quaternion algebra. We define sesquilinear pairings ($R$-linear in one variable and $R$-conjugate linear in the…
Outsourcing data in the cloud has become nowadays very common. Since -- generally speaking -- cloud data storage and management providers cannot be fully trusted, mechanisms providing the confidentiality of the stored data are necessary. A…
We examine several aspects of explicability of a classification system built from neural networks. The first aspect is the pairwise explicability, which is the ability to provide the most accurate prediction when the range of possibilities…
Determining if two sets are related - that is, if they have similar values or if one set contains the other - is an important problem with many applications in data cleaning, data integration, and information retrieval. A particularly…
We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph $G$ and an integer $k$, ask whether $G$ has two (maximum/perfect) matchings whose symmetric difference is at least $k$. Diverse Pair of…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
Secure pairing is essential for trustworthy deployment and operation of Internet of Things (IoT) devices. However, traditional pairing methods are unsuitable due to the lack of user interfaces such as keyboards. Proximity-based approaches…
Clustering is a fundamental analysis tool aiming at classifying data points into groups based on their similarity or distance. It has found successful applications in all natural and social sciences, including biology, physics, economics,…
A connected matching in a graph G consists of a set of pairwise disjoint edges whose covered vertices induce a connected subgraph of G. While finding a connected matching of maximum cardinality is a well-solved problem, it is NP-hard to…
Natural phenomena show that many creatures form large social groups and move in regular patterns. Previous In this paper, we first propose an efficient distributed mining algorithm to jointly identify a group of moving objects and discover…
Visual identification of gunmen in a crowd is a challenging problem, that requires resolving the association of a person with an object (firearm). We present a novel approach to address this problem, by defining human-object interaction…
A pair-trading strategy is an approach that utilizes the fluctuations between prices of a pair of stocks in a short-term time frame, while in the long-term the pair may exhibit a strong association and co-movement pattern. When the prices…
This note describes some cryptographic issues related to multi-located parties. In general, multi-located parties make it difficult for the eavesdropper to mount the man-in-the-middle attack. Conversely, they make it easier to address…
Re-Pair is an effective grammar-based compression scheme achieving strong compression rates in practice. Let $n$, $\sigma$, and $d$ be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original…
Signature verification, as a crucial practical documentation analysis task, has been continuously studied by researchers in machine learning and pattern recognition fields. In specific scenarios like confirming financial documents and legal…
A pair $(a, b)$ of positive integers is a pythagorean pair if $a^2 + b^2 = \Box$ (i.e., $a^2 + b^2$ is a square). A pythagorean pair $(a, b)$ is called a double-pythapotent pair if there is another pythagorean pair $(k,l)$ such that…
A popular paradigm for 3D point cloud registration is by extracting 3D keypoint correspondences, then estimating the registration function from the correspondences using a robust algorithm. However, many existing 3D keypoint techniques tend…
Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by…
We introduce NetworKit, an open-source software package for analyzing the structure of large complex networks. Appropriate algorithmic solutions are required to handle increasingly common large graph data sets containing up to billions of…