Topology of Networks in Generalized Musical Spaces

The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this foundation, I generalize the concept of musical spaces as networks and derive functional principles of compositional design by the direct analysis of the network topology. This approach provides a novel framework for the analysis and quantification of similarity of musical objects and structures, and suggests a way to relate such measures to the human perception of different musical entities. Finally, the analysis of a single work or a corpus of compositions as complex networks provides alternative ways of interpreting the compositional process of a composer by quantifying emergent behaviors with well-established statistical mechanics techniques. Interpreting the latter as probabilistic randomness in the network, I develop novel compositional design frameworks that are central to my own artistic research

Quantum mechanics in fractional and other anomalous spacetimes

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the fact that ordinary time and spatial translations are broken and the dynamics is not unitary, the theory is in one-to-one correspondence with a unitary one, thus allowing us to employ standard tools of analysis. These features are illustrated in the examples of the free particle and the harmonic oscillator. While fractional (and the more general anomalous-spacetime) free models are formally indistinguishable from ordinary ones at the classical level, at the quantum level they differ both in the Hilbert space and for a topological term fixing the classical action in the path integral formulation. Thus, all non-unitarity in fractional quantum dynamics is encoded in a contribution depending only on the initial and final state.Comment: 22 pages, 1 figure. v2: typos correcte

Topology of Networks in Generalized Musical Spaces

Leonardo Music Journal, Massachusetts Institute of Technology Press (MIT Press): Arts & Humanities Titles etc, In press. Publication date: December 2020The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this foundation, I generalize the concept of musical spaces as networks and derive functional principles of compositional design 15 by the direct analysis of the network topology. This approach provides a novel framework for the analysis and quantification of similarity of musical objects and structures, and suggests a way to relate such measures to the human perception of different musical entities. Finally, the analysis of a single work or a corpus of compositions as complex networks provides alternative ways of interpreting the compositional process of a composer by quantifying emergent behaviors with 20 well-established statistical mechanics techniques. Interpreting the latter as probabilistic randomness in the network, I develop novel compositional design frameworks that are central to my own artistic research. One Sentence Summary: Network theory is an innovative tool for the classification of generalized musical spaces and provides a framework for the discovery or generation of functional 25 principles of compositional design

MUSICNTWRK: data tools for music theory, analysis and composition

International audienceWe present the API for MUSICNTWRK, a python library for pitch class set and rhythmic sequences classification and manipulation, the generation of networks in generalized music and sound spaces, deep learning algorithms for timbre recognition, and the sonification of arbitrary data. The software is freely available under GPL 3.0 and can be downloaded at www.musicntwrk.com

Giant spin Hall Effect in two-dimensional monochalcogenides

One of the most exciting properties of two dimensional materials is their sensitivity to external tuning of the electronic properties, for example via electric field or strain. Recently discovered analogues of phosphorene, group-IV monochalcogenides (MX with M = Ge, Sn and X = S, Se, Te), display several interesting phenomena intimately related to the in-plane strain, such as giant piezoelectricity and multiferroicity, which combine ferroelastic and ferroelectric properties. Here, using calculations from first principles, we reveal for the first time giant intrinsic spin Hall conductivities (SHC) in these materials. In particular, we show that the SHC resonances can be easily tuned by combination of strain and doping and, in some cases, strain can be used to induce semiconductor to metal transitions that make a giant spin Hall effect possible even in absence of doping. Our results indicate a new route for the design of highly tunable spintronics devices based on two-dimensional materials