Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts.Comment: The final version of this paper has been published by the Journal of Mathematics and Musi

On algebraic supergroups, coadjoint orbits and their deformations

In this paper we study algebraic supergroups and their coadjoint orbits as affine algebraic supervarieties. We find an algebraic deformation quantization of them that can be related to the fuzzy spaces of non commutative geometry.Comment: 37 pages, AMS-LaTe

The moduli space of matroids

In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective matroid theories. Moreover, fuzzy rings are ordered blueprints and lie in the intersection of tracts with ordered blueprints; we call the objects of this intersection pastures. In the second part, we construct moduli spaces for matroids over pastures. We show that, for any non-empty finite set $E$, the functor taking a pasture $F$ to the set of isomorphism classes of rank-$r$ $F$-matroids on $E$ is representable by an ordered blue scheme $Mat(r,E)$, the moduli space of rank-$r$ matroids on $E$. In the third part, we draw conclusions on matroid theory. A classical rank-$r$ matroid $M$ on $E$ corresponds to a $\mathbb{K}$-valued point of $Mat(r,E)$ where $\mathbb{K}$ is the Krasner hyperfield. Such a point defines a residue pasture $k_M$, which we call the universal pasture of $M$. We show that for every pasture $F$, morphisms $k_M\to F$ are canonically in bijection with $F$-matroid structures on $M$. An analogous weak universal pasture $k_M^w$ classifies weak $F$-matroid structures on $M$. The unit group of $k_M^w$ can be canonically identified with the Tutte group of $M$. We call the sub-pasture $k_M^f$ of $k_M^w$ generated by ``cross-ratios' the foundation of $M$,. It parametrizes rescaling classes of weak $F$-matroid structures on $M$, and its unit group is coincides with the inner Tutte group of $M$. We show that a matroid $M$ is regular if and only if its foundation is the regular partial field, and a non-regular matroid $M$ is binary if and only if its foundation is the field with two elements. This yields a new proof of the fact that a matroid is regular if and only if it is both binary and orientable.Comment: 83 page

Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism

We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure sheaves of coordinatization coefficients in the attempt to probe the Quantum world. Interpretational aspects of the proposed scheme are discussed with respect to a functorial formulation of information exchange, as well as, quantum logical considerations. Finally, the sheaf theoretical construction suggests an opearationally intuitive method to develop differential geometric concepts in the quantum regime.Comment: 25 pages, Late

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

Disentangling agglomeration and network externalities : a conceptual typology

Agglomeration and network externalities are fuzzy concepts. When different meanings are (un)intentionally juxtaposed in analyses of the agglomeration/network externalities-menagerie, researchers may reach inaccurate conclusions about how they interlock. Both externality types can be analytically combined, but only when one adopts a coherent approach to their conceptualization and operationalization, to which end we provide a combinatorial typology. We illustrate the typology by applying a state-of-the-art bipartite network projection detailing the presence of globalized producer services firms in cities in 2012. This leads to two one-mode graphs that can be validly interpreted as topological renderings of agglomeration and network externalities

Interactive semantic mapping: Experimental evaluation

Robots that are launched in the consumer market need to provide more effective human robot interaction, and, in particular, spoken language interfaces. However, in order to support the execution of high level commands as they are specified in natural language, a semantic map is required. Such a map is a representation that enables the robot to ground the commands into the actual places and objects located in the environment. In this paper, we present the experimental evaluation of a system specifically designed to build semantically rich maps, through the interaction with the user. The results of the experiments not only provide the basis for a discussion of the features of the proposed approach, but also highlight the manifold issues that arise in the evaluation of semantic mapping