Shall We (Math and) Dance?

Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and dance, and between music and categories. Then, we extend this formalism and diagrammatic thinking style to dance.Comment: preprin

Toxicity of Chloroanilines to the Earthworm "Eisenia fetida"

Toxicity of chloroanilines to "Eisenia foetida" was found by a filter paper contact test to range from 2.9 ng/cm2 to 100 ng/cm2. Toxicity increased by a factor two for increasing number of chlorine substituants (from di- to tetra-) in the aniline; that is increasing (kow) and decreasing (S). Little effect of isomer substitution pattern was observed. Correlation coefficients between acute toxicity (LC50) and Kow or S were too weak with r2 = 0.85 and r2 = 0.51, respectively, partly due to the uncertainty of LC50 data and partly due to artificial exposure during filter paper contact test.JRC.(EI)-Environment Institut

Musical pitch quantization as an eigenvalue problem

How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum mechanics with music and is consistent with music theory and seminal insights by Hermann von Helmholtz

Hypercube + Rubik’s Cube + Music = HyperCubeHarmonic

Musical chords and chord relations can be described through mathematics. Abstract permutations can be visualized through the Rubik’s cube, born as a pedagogical device [7,21]. Permutations of notes can also be heard through the CubeHarmonic, a novel musical instru- ment. Here, we summarize the basic ideas and the state of the art of the physical implementation of CubeHarmonic, discussing its conceptual lift- ing up to the fourth dimension, with the HyperCubeHarmonic (HCH). We present the basics of the hypercube theory and of the 4-dimensional Rubik’s cube, investigating its potential for musical applications. To gain intuition about HCH complexity, we present two practical implementa- tions of HCH based on the three-dimensional development of the hyper- cube. The first requires a laptop and no other devices; the second involves a physical Rubik’s cube enhanced through augmented and virtual reality and a specifically-designed mobile app. HCH, as an augmented musical instrument, opens new scenarios for STEAM teaching and performing, allowing us to hear the “sound of multiple dimensions.

CubeHarmonic: A new musical instrument based on Rubik{'}s cube with embedded motion sensor

A contemporary challenge involves scienti c education and the connection between new technologies and the heritage of the past. CubeHarmonic (CH) joins novelty and tradition, creativity and education, science and art. It takes shape as a novel musical instrument where magnetic 3D motion tracking technology meets musical performance and composition. CH is a Rubik’s cube with a note on each facet, and a chord or chord sequence on each face. The position of each facet is detected through magnetic 3D motion tracking. While scrambling the cube, the performer gets new chords and new chord sequences. CH can be used to compose, improvise,1 and teach music and mathematics (group theory, permutations) with colors and physical manipulation supporting abstract thinking. Further- more, CH allows visually impaired people to enjoy Rubik’s cube manipulation by using sounds instead of colors

Energy and SNR-Aware Robotic Swarm Coordination for Aquatic Cleaning Operations

We propose a network-based approach to mission planning for a swarm of robots. We model a search and rescue mission with a fleet of aquatic robots, coordinated with a computing central on a rowing boat, to minimize the environmental impact and avoid noticeable waves. We develop a theoretical yet implementable model for the mission management, taking into account energy and multi-robot communication issues. The considered mathematical tools come from network theory and multi-layered graphs. The chosen mission is aquatic cleaning, and in particular trash detection in canals of Venice. We schematize a specific canal as an example, the "Rio di Ca' Foscari."Computing centers are located in gondolas, and each of them is coordinated with a swarm of aquatic robots. In this context, we consider a newly-designed floating robot, RoboWood, equipped with GPS sensors, distance sensors, and an underwater camera to observe the ground of the canal and store images, to be analyzed onboard and offline. Finally, we discuss a sonification strategy to obtain human-friendly, auditory feedback from the robotic movements

CubeHarmonic: A New Musical Instrument Based on Rubik’s Cube with Embedded Motion Sensor

A contemporary challenge involves scientific education and the connection between new technologies and the heritage of the past. CubeHarmonic (CH) joins novelty and tradition, creativity and edu- cation, science and art. It takes shape as a novel musical instrument where magnetic 3D motion tracking technology meets musical per- formance and composition. CH is a Rubik’s cube with a note on each facet, and a chord or chord sequence on each face. The posi- tion of each facet is detected through magnetic 3D motion tracking. While scrambling the cube, the performer gets new chords and new chord sequences. CH can be used to compose, improvise,1 and teach music and mathematics (group theory, permutations) with colors and physical manipulation supporting abstract thinking. Further- more, CH allows visually impaired people to enjoy Rubik’s cube manipulation by using sounds instead of colors