Topological differential testing
K Ambrose, S Huntsman, M Robinson… - arXiv preprint arXiv …, 2020 - arxiv.org
We introduce topological differential testing (TDT), an approach to extracting the consensus
behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a …
behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a …
The rectangle complex of a relation
M Brun, LM Salbu - Mediterranean Journal of Mathematics, 2023 - Springer
The Rectangle Complex of a Relation | Mediterranean Journal of Mathematics Skip to main
content SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Mediterranean …
content SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Mediterranean …
From music to mathematics and backwards: introducing algebra, topology and category theory into computational musicology
M Andreatta - Imagine Math 6: Between Culture and Mathematics, 2018 - Springer
Despite a long historical relationship between mathematics and music, the interest of
mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based …
mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based …
Chordal Embeddings Based on Topology of the Tonal Space
A Ayzenberg, M Beketov, A Burashnikova… - … Intelligence in Music …, 2023 - Springer
In the classical western musical tradition, the mutual simultaneous appearance of two tones
in a melody is determined by harmony, ie the ratio of their frequencies. To perform NLP …
in a melody is determined by harmony, ie the ratio of their frequencies. To perform NLP …
Taking music seriously: on the dynamics of'mathemusical'research with a focus on Hexachordal Theorems
M Andreatta, C Guichaoua, N Juillet - SIGMA. Symmetry, Integrability and …, 2024 - emis.de
After presenting the general framework ofmathemusical'dynamics, we focus on one music-
theoretical problem concerning a special case of homometry theory applied to music …
theoretical problem concerning a special case of homometry theory applied to music …
Density Sensitive Bifiltered Dowker Complexes via Total Weight
N Hellmer, J Spaliński - arXiv preprint arXiv:2405.15592, 2024 - arxiv.org
In this paper, we introduce a density-sensitive bifiltration on Dowker complexes. Previously,
Dowker complexes were studied to address directional or bivariate data whereas density …
Dowker complexes were studied to address directional or bivariate data whereas density …
The bifiltration of a relation and extended Dowker duality
M Vaupel, B Dunn - arXiv preprint arXiv:2310.11529, 2023 - arxiv.org
We explain how homotopical information of two composeable relations can be organized in
two simplicial categories that augment the relations row and column complexes. We show …
two simplicial categories that augment the relations row and column complexes. We show …
The generative, analytic and instructional capacities of sound in architecture: fundamentals, tools and evaluation of a design methodology
J Llorca Bofí - 2018 - upcommons.upc.edu
The disciplines of space and time form two domains to which it is daring to compare, since it
is obvious that they are of a different nature. Music happens in time, while architecture …
is obvious that they are of a different nature. Music happens in time, while architecture …
Chordal Embeddings Based on Topology of the Tonal Space
In the classical western musical tradition, the mutual simultaneous appearance of two tones
in a melody is determined by harmony, ie the ratio of their frequencies. To perform NLP …
in a melody is determined by harmony, ie the ratio of their frequencies. To perform NLP …
Morphological links between formal concepts and hypergraphs
I Bloch - Mathematical Morphology and Its Applications to …, 2017 - Springer
Hypergraphs can be built from a formal context, and conversely formal contexts can be
derived from a hypergraph. Establishing such links allows exploiting morphological …
derived from a hypergraph. Establishing such links allows exploiting morphological …