Scales are a fundamental concept of musical practice around the world. They commonly exhibit symmetry properties that are formally studied using cyclic groups in the field of mathematical scale theory. This paper proposes an axiomatic framework for mathema ...
Program synthesis was first proposed a few decades ago, but in the last decade it has gained increased momentum in the research community. The increasing complexity of software has dictated the urgent need for improved supporting tools that verify the soft ...
Humans are comparison machines: comparing and choosing an item among a set of alternatives (such as objects or concepts) is arguably one of the most natural ways for us to express our preferences and opinions. In many applications, the analysis of data con ...
The failure detector approach for solving distributed computing problems has been celebrated for its modularity. This approach allows the construction of algorithms using abstract failure detection mechanisms, defined by axiomatic properties, as building b ...
Detection of elongated structures in 2D images and 3D image stacks is a critical prerequisite in many applications and Machine Learning-based approaches have recently been shown to deliver superior performance. However, these methods essentially classify i ...
In this paper, we present Majority-Inverter Graph (MIG), a novel logic representation structure for efficient optimization of Boolean functions. An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented e ...
Using arguments developed by De Giorgi in the 1950's, it is possible to prove the regularity of the solutions to a vast class of variational problems in the Euclidean space. The main goal of the present thesis is to extend these results to the more abstrac ...
We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total order o ...
A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. The aim of this paper is to present some interesting weak metrics and to study some of their properties. In particular, we introduce a ...
