Related papers: Unified Music Theories for General Equal-Temperame…
We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with…
Conventional Music Notation (CMN) is the well-established foundation for the written communication of musical information, such as rhythm, harmony, or timbre. However, CMN suffers from the complexity of its visual encoding and the need for…
Quantum typicality refers to the phenomenon that the expectation values of any given observable are nearly identical for the overwhelming majority of all normalized vectors in a sufficiently high-dimensional Hilbert (sub-)space. As a…
String theory is the leading candidate for a unified theory of the standard model and gravity. In the last few years theorists have realized that there is a unique structure underlying string theory. In this unification a prominent role is…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
Semantic embeddings play a crucial role in natural language-based information retrieval. Embedding models represent words and contexts as vectors whose spatial configuration is derived from the distribution of words in large text corpora.…
This study argues that electronic tones routinely used in contemporary popular music - including 808-style bass and power chords - are structurally and perceptually equivalent to multiphonics in contemporary classical music. Using listening…
In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled…
String theory is at the moment the only advanced approach to a unification of all interactions, including gravity. But, in spite of the more than thirty years of its existence, it does not make any empirically testable predictions, and it…
We develop a new master equation as a unified description of the effects of both quantum noise (system-bath interaction) and classical noise on a system's dynamics, using a two-dimensional series expansion method. When quantum and classical…
We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…
In recent years, the task of Automatic Music Transcription (AMT), whereby various attributes of music notes are estimated from audio, has received increasing attention. At the same time, the related task of Multi-Pitch Estimation (MPE)…
This is a brief overview on the current status of string theory for non-specialists. The purpose is to give an aspect on the nature of string theory as a unified theory of all interactions including quantum gravity and to discuss future…
The broadly applied notions of Lie bialgebras, Manin triples, classical $r$-matrices and $\mathcal{O}$-operators of Lie algebras owe their importance to the close relationship among them. Yet these notions and their correspondences are…
We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of…
From a general abstract system theoretical perspective, a quantum-like system description in the spirit of a generalized Quantum Theory may appear to be simpler and more natural than a classically inspired description. We investigate the…
What makes two computational systems equivalent? Topos theory answers with classifying toposes: a system's semantic content is encoded in the geometric theory it classifies, and two presentations are equivalent when their classifying…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
Mathematical music theory has assumed without proof that musical notes can be associated with the equivalence classes of $\mathbb{Z}_n$. We contest the triviality of this assertion, which we call the Pitch-class Integer Theorem (PCIT).…