This article reports on a series of mathe-musical experiments based on the dynamic behavior of a musical quantum model of C-major tonality. The model reinterprets empirical pitch-class profiles of tonal attraction in C-major as the probability wave function of a one-dimensional stationary ground state within a perturbed quantum harmonic oscillator. By solving the associated time-dependent Schrödinger equation, we assign specific temporal evolutions to any given initial state. We explore two distinct sonification strategies: First, the time-evolutions of various initial states—in particular deflections of the ground state and higher excited states—are used to drive a stroboscopic stratification of musical hierarchies and to set them into Minimal Music-inspired travelling note patterns. Secondly, we implement rich continuous sound processes that rely on the uninterrupted flow of the wave function. Crucially, these approaches bypass the simulation of quantum measurements; instead, they leverage the full theoretical information of the wave function’s evolution.
Phosphogypsum is a by-product of the wet production process of phosphoric acid from phosphate minerals. Since the 1950s, many industries in Europe used this process to produce fertilizers and detergents. Processing residues and waste were often dumped near production facilities or dispersed in sensitive areas such as river estuaries or coastal lagoons, resulting in the release of toxic substances into the environment and damage to the ecosystem. In Europe, to this day, there are still many areas with non-contained phosphogypsum deposits, which pose significant environmental, social and economic problems. Phosphogypsum is mainly composed of a calcium sulfate matrix and contains natural radionuclides (mainly 226Ra, 210Pb, 210Po) in different concentrations, depending on the composition of the starting mineral; it can also contain elements such as phosphorus and fluorine, heavy metals as zinc, copper, chromium, cadmium, and some rare-earth elements (REEs). From the perspective of circular economy, it is therefore increasingly considered a resource from which it is possible to extract new raw materials. In this work, the main options currently under study for the valorization of phosphogypsum through circular economy processes are evaluated and the activities planned within the Horizon Europe Fic-FIGHTERS project are presented.
The conventional paradigm of network science, reducing complex systems to dyadic interactions, is fundamentally inadequate for capturing the rich, multi-agent dynamics that define real-world complexity. From neural assemblies and ecological webs to social collectives and technological infrastructures, many systems are governed by higher-order interactions (HOIs) that transcend pairwise descriptions. At the same time, self-organization, the autonomous emergence of order and function from internal dynamics, remains a defining principle of adaptive complexity. The convergence of self-organization and HOIs is not merely an incremental advance; it is a transformative frontier that redefines how we model, predict, and control emergent behavior in natural and engineered systems. This special issue presents a landmark collection of cutting-edge research at this critical intersection. By unifying rigorous theoretical frameworks with groundbreaking applications, it demonstrates that embracing higher-order representations unlocks unprecedented insight into collective phenomena, system resilience, and phase transitions. Spanning physics, mathematics, neuroscience, computer science, social science, and engineering, this issue establishes a new interdisciplinary benchmark and charts the course for the next generation of complex systems science.
