Related papers: Intrinsic Harmonic Spaces: A Solution to the Ancie…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
In this paper, we present a toolbox for a specific optimization problem that frequently arises in bioinformatics or genomics. In this specific optimisation problem, the state space is a set of words of specified length over a finite…
The determination of musical key is a fundamental aspect of music theory and perception, providing a harmonic context for melodies and chord progressions. Automating this process, known as automatic key detection, is a significant task in…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…
An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit…
Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
Digital advances have transformed the face of automatic music generation since its beginnings at the dawn of computing. Despite the many breakthroughs, issues such as the musical tasks targeted by different machines and the degree to which…
We revisit the problems of pitch spelling and tonality guessing with a new algorithm for their joint estimation from a MIDI file including information about the measure boundaries. Our algorithm does not only identify a global key but also…
This paper proves that arrangement of music is NP-hard when subject to various constraints: avoiding musical dissonance, limiting how many notes can be played simultaneously, and limiting transition speed between chords. These results imply…
We determine hidden conformal symmetries behind the evolution equations of black hole perturbations in a vector-tensor theory of gravity. Such hidden symmetries are valid everywhere in the exterior region of a spherically symmetric,…
Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of…
Advancements in the digital technologies have enabled researchers to develop a variety of Computational Music applications. Such applications are required to capture, process, and generate data related to music. Therefore, it is important…
The automated creation of accurate musical notation from an expressive human performance is a fundamental task in computational musicology. To this end, we present an end-to-end deep learning approach that constructs detailed musical scores…
A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…
The three-disk system, which for many years has served as a paradigm for the usefulness of cycle expansion methods, represents an extremely hard problem to semiclassical quantization when the disks are moved closer and closer together,…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
We consider systems of ordinary differential equations with known first integrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary set of discrete gradients. Integrators which exactly…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…