Related papers: The Pitch-class Integer Theorem
We present a graded modal type theory, a dependent type theory with grades that can be used to enforce various properties of the code. The theory has $\Pi$-types, weak and strong $\Sigma$-types, natural numbers, an empty type, and a…
The PCT theorem is shown to be valid in quantum field theory formulated on noncommutative spacetime by exploiting the properties of the Wightman functions defined in such a set up.
Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from…
Music autotagging, an established problem in Music Information Retrieval, aims to alleviate the human cost required to manually annotate collections of recorded music with textual labels by automating the process. Many autotagging systems…
In many everyday categories (sets, spaces, modules, ...) objects can be both added and multiplied. The arithmetic of such objects is a challenge because there is usually no subtraction. We prove a family of cases of the following principle:…
We initiate a search for non-perturbative consistency conditions in M theory. Some non-perturbative conditions are already known in Type I theories; we review these and search for others. We focus principally on possible anomalies in…
We deal with relatives of GCH which are provable. In particular we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice are assumed but some of the results gives…
Rhythm is ubiquitous in human culture and in nature, but hard to capture in all its complexity. A key dimension of rhythm, integer ratio categories occur when the relationship between temporal intervals can be expressed as small-integer…
We propose music tagging with classifier chains that model the interplay of music tags. Most conventional methods estimate multiple tags independently by treating them as multiple independent binary classification problems. This treatment…
Mixtures of coherent states are commonly regarded as classical. Here we show that there is a quantum advantage in discriminating between coherent states in a mixture, implying the presence of quantum properties in the mixture, which are…
Out of the scope of the usual positions of computing in the field of music and musicology, one notices the emergence of human-computer systems that do exist by breaking off. Though these singular systems take effect in the usual fields of…
Music information is often conveyed or recorded across multiple data modalities including but not limited to audio, images, text and scores. However, music information retrieval research has almost exclusively focused on single modality…
Quantum instruments represent the most general type of quantum measurement, as they incorporate processes with both classical and quantum outputs. In many scenarios, it may be desirable to have some "on-demand" device that is capable of…
The Omitting Types Theorem in model theory and the Baire Category Theorem in topology are known to be closely linked. We examine the precise relation between these two theorems. Working with a general notion of logic we show that the…
Music information retrieval distinguishes between low- and high-level descriptions of music. Current generative AI models rely on text descriptions that are higher level than the controls familiar to studio musicians. Pitch strength, a…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
For more than a century, Cantor's theory of transfinite numbers has played a pivotal role in set theory, with ramifications that extend to many areas of mathematics. This article extends earlier findings with a fresh look at the critical…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…