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Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

Understanding the laws that govern a phenomenon is the core of scientific progress. This is especially true when the goal is to model the interplay between different aspects in a causal fashion. Indeed, causal inference itself is…

Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…

We provide an algorithm to check whether two rational space curves are related by a similarity. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a computer algebra…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…

Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions,…

We intend to identify relationships between cancer cases and pollutant emissions and attempt to understand whether cancer in children is typically located together with some specific chemical combinations or is independent. Co-location…

Though the mediums for visualization are limited, the potential dimensions of a dataset are not. In many areas of scientific study, understanding the correlations between those dimensions and their uncertainties is pivotal to mining useful…

Accurate maps are a prerequisite for virtually all mobile robot tasks. Most state-of-the-art maps assume a static world; therefore, dynamic objects are filtered out of the measurements. However, this division ignores movable but non-moving…

This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…

Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for…

Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordinate is one of the topological data analysis techniques…

Determining changes in global temperature and precipitation that may indicate climate change is complicated by annual variations. One approach for finding potential climate change indicators is to train a model that predicts the year from…

Finding inherent or processed links within a dataset allows to discover potential knowledge. The main contribution of this article is to define a global framework that enables optimal knowledge discovery by visually rendering co-occurences…

The appearance of the world varies dramatically not only from place to place but also from hour to hour and month to month. Every day billions of images capture this complex relationship, many of which are associated with precise time and…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…

Entanglement in continuous-variable non-Gaussian states provides irreplaceable advantages in many quantum information tasks. However, the sheer amount of information in such states grows exponentially and makes a full characterization…

Self-organizing maps (SOMs) are a technique that has been used with high-dimensional data vectors to develop an archetypal set of states (nodes) that span, in some sense, the high-dimensional space. Noteworthy applications include weather…