Building Generalized Neo-Riemannian Groups of Musical Transformations as Extensions

Chords in musical harmony can be viewed as objects having shapes (major/minor/etc.) attached to base sets (pitch class sets). The base set and the shape set are usually given the structure of a group, more particularly a cyclic group. In a more general setting, any object could be defined by its position on a base set and by its internal shape or state. The goal of this paper is to determine the structure of simply transitive groups of transformations acting on such sets of objects with internal symmetries. In the main proposition, we state that, under simple axioms, these groups can be built as group extensions of the group associated to the base set by the group associated to the shape set, or the other way. By doing so, interesting groups of transformations are obtained, including the traditional ones such as the dihedral groups. The knowledge of the group structure and product allows to explicitly build group actions on the objects. In particular we differentiate between left and right group actions and we show how they are related to non-contextual and contextual transformations. Finally we show how group extensions can be used to build transformational models of time-spans and rhythms.Comment: 30 pages, 4 figures ; submitted to Journal of Mathematics and Music - v.4: corrected many errors, clarified some proposition

John Cage's Number Pieces as Stochastic Processes: a Large-Scale Analysis

The Number Pieces are a corpus of works by composer John Cage, which rely on a particular time-structure used for determining the temporal location of sounds, named the "time-bracket". The time-bracket system is an inherently stochastic process, which complicates the analysis of the Number Pieces as it leads to a large number of possibilities in terms of sonic content instead of one particular fixed performance. The purpose of this paper is to propose a statistical approach of the Number Pieces by assimilating them to stochastic processes. Two Number Pieces, "Four" and "Five", are studied here in terms of pitch-class set content: the stochastic processes at hand lead to a collection of random variables indexed over time giving the distribution of the possible pitch-class sets. This approach allows for a static and dynamic analysis of the score encompassing all the possible outcomes during the performance of these works.Comment: 25 pages, 9 figures, 5 tables; comments welcom

Using Monoidal Categories in the Transformational Study of Musical Time-Spans and Rhythms

Transformational musical theory has so far mainly focused on the study of groups acting on musical chords, one of the most famous example being the action of the dihedral group D24 on the set of major and minor chords. Comparatively less work has been devoted to the study of transformations of time-spans and rhythms. D. Lewin was the first to study group actions on time-spans by using a subgroup of the affine group in one dimension. In our previous work, the work of Lewin has been included in the more general framework of group extensions, and generalizations to time-spans on multiple timelines have been proposed. The goal of this paper is to show that such generalizations have a categorical background in free monoidal categories generated by a group-as-category. In particular, symmetric monoidal categories allow to deal with the possible interexchanges between timelines. We also show that more general time-spans can be considered, in which single time-spans are encapsulated in a "bracket" of time-spans, which allows for the description of complex rhythms.Comment: 17 pages; 7 figures - Minor corrections brought to the first versions; comments welcom

Exploiting the Time-Reversal Operator for Adaptive Optics, Selective Focusing and Scattering Pattern Analysis

We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The DORT method (Decomposition of the Time Reversal Operator) is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization and selective excitation of nanoparticles.Comment: 10 page

Diagrammatic approaches in Computational Musicology: Some theoretical and Philosophical Aspects

10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, ProceedingsInternational audienceDespite a long historical relationship between mathematics and music, the use of diagrammatic approaches in computational musicology is a relatively recent phenomenon. Within the different branches of formal methods in music analysis, the so-called "transformational" paradigm has progressively shifted from an object-oriented to a graph-theoretical and categorical approach. Both graph theory and category theory make large use of diagrams which enable the description of the inner relationships of musical structures. In the categorical framework recently proposed by the authors, whose results are summarized and discussed in this abstract, musical transformations are viewed as natural transformations between chords represented as labelled graphs with vertices corresponding to the notes and arrows corresponding to musical transpositions and inversions operations. The diagrammatic approach also provides a very powerful conceptual tool that can have crucial theoretical implications for music cognition. We discuss this aspect by showing some deep connections between transforma-tional music analysis and some mathematically-oriented directions in developmental psychology and cognition (such as Halford and Wilson's neostructural-istic approach, Ehresmann and Vanbremeersch's Memory Evolutive Systems, Phillips and Wilson's Categorical Compositionality, Fauconnier and Turner's Conceptual Blending and its structural extension proposed by Goguen) and epis-temology (Gaston-Granger's "objectal" and "operational" duality)

Meter networks: a categorical framework for metrical analysis

This paper develops a framework based on category theory which unifies the simultaneous consideration of timepoints, metrical relations, and meter inclusion founded on the category Rel of sets and binary relations. Metrical relations are defined as binary relations on the set of timepoints, and the subsequent use of the monoid they generate and of the corresponding functor to Rel allows us to define meter networks, i.e. networks of timepoints (or sets of timepoints) related by metrical relations. We compare this to existing theories of metrical conflict, such as those of Harald Krebs and Richard Cohn, and illustrate that these tools help to more effectively combine displacement and grouping dissonance and reflect analytical claims concerning nineteenth-century examples of complex hemiola and twentieth-century polymeter. We show that meter networks can be transformed into each other through meter network morphisms, which allows us to describe both meter displacements and meter inclusions. These networks are applied to various examples from the nineteenth and twentieth century.Accepted manuscrip

Finite size effects, super-and sub-poissonian noise in a nanotube connected to leads

The injection of electrons in the bulk of carbon nanotube which is connected to ideal Fermi liquid leads is considered. While the presence of the leads gives a cancellation of the noise cross-correlations, the auto-correlation noise has a Fano factor which deviates strongly from the Schottky behavior at voltages where finite size effects are expected. Indeed, as the voltage is increased from zero, the noise is first super-poissonian, then sub-poissonian, and eventually it reaches the Schottky limit. These finite size effects are also tested using a diagnosis of photo-assisted transport, where a small AC modulation is superposed to the DC bias voltage between the injection tip and the nanotube. When finite size effects are at play, we obtain a stepwise behavior for the noise derivative, as expected for normal metal systems, whereas in the absence of finite size effects, due to the presence of Coulomb interactions, a smoothed staircase is observed. The present work shows that it is possible to explore finite size effects in nanotube transport via a zero frequency noise measurement

Eco-feedback performance exploration for Eco-feedback design

'Parmi les efforts actuels pour encourager une utilisation plus écologique des produits, la mise en place d'un système de retour d'information en temps réel (ou « ecofeedback ») du produit vers l'utilisateur semble être une voie prometteuse. Néanmoins, l’efficacité de ces systèmes peut se dégrader au fil du temps. La nature de l' « ecofeedback » dépend de différents facteurs comme le type de produits concernés ou le message à faire passer. Des pistes pour comprendre ces relations ont été identifiées dans la littérature. De plus, ce que nous appelons l''éco-profil' de l'utilisateur joue un rôle dans la dynamique de l'« ecofeedback » et par conséquent influence son efficacité. Dans cet article, nous présentons une étude réalisée afin de comprendre l'impact d'un « ecofeedback » dans le cas de l'utilisation d'un ordinateur mis à disposition d'étudiants et sa relation avec les éco-profils des utilisateurs. Les ordinateurs sont installés dans une salle de classe et utilisés couramment par des groupes de 12 à 15 étudiants. Pendant l'expérimentation deux groupes de 12 étudiants chacun ont été observés pendant 2 mois. L'un des deux groupes a été sensibilisé afin d'éteindre les ordinateurs et leur écran après utilisation, tandis que le deuxième groupe est resté sans « écofeedback » tout au long de l'observation. L’expérimentation se compose de trois phases d’observation : avant, pendant et après l’affichage de l’ »ecofeedback ». Les étudiants ont été interrogés dans le but de caractériser leur éco-profil. Une discussion proposée sur les relations entre les éco-profils des utilisateurs, la nature du message et son efficacité. Cette étude fait partie d'une expérimentation se déroulant sur deux ans (2012-2013) et vise à mieux comprendre les « ecofeedbacks » sur le long terme.

The European AntibotABE Framework Program and Its Update: Development of Innovative Botulinum Antibodies

The goal of the AntiBotABE Program was the development of recombinant antibodies that neutralize botulinum neurotoxins (BoNT) A, B and E. These serotypes are lethal and responsible for most human botulinum cases. To improve therapeutic efficacy, the heavy and light chains (HC and LC) of the three BoNT serotypes were targeted to achieve a synergistic effect (oligoclonal antibodies). For antibody isolation, macaques were immunized with the recombinant and non-toxic BoNT/A, B or E, HC or LC, followed by the generation of immune phage-display libraries. Antibodies were selected from these libraries against the holotoxin and further analyzed in in vitro and ex vivo assays. For each library, the best ex vivo neutralizing antibody fragments were germline-humanized and expressed as immunoglobulin G (IgGs). The IgGs were tested in vivo, in a standardized model of protection, and challenged with toxins obtained from collections of Clostridium strains. Protective antibody combinations against BoNT/A and BoNT/B were evidenced and for BoNT/E, the anti-LC antibody alone was found highly protective. The combination of these five antibodies as an oligoclonal antibody cocktail can be clinically and regulatorily developed while their high “humanness” predicts a high tolerance in humans.Peer reviewe