Generalising maximum mean discrepancy: kernelised functional Bregman divergences

Author

Modesto, Lenon Romano and Ogun Ramalhete, Ezgi and Ravasi, Stefano and Pezzoli, Stefano and Sharma, Mukesh and Nath, Dibyojyoty and Yucel, Icsil and Moons, Jannes and Melcore, Marie and Vershinina, Anna and Tait, Natasha and Ogunmefun, Segun and Reutina, Uliana and Colliaux, David and Mozos, Ignacio B and Willey, Neil J and Ieropoulos, Ioannis A and Cristiani, Pierangela and Hanappe, Peter and Barriuso, Jorge and Schmidt, Markus R and Armstrong, Rachel

Abstract

Urban environments need low-input cultivation systems that integrate plants into buildings while improving resource efficiency and circularity. This report presents the technical validation of the first operational Microbial--Hydroponic (Mi-Hy) prototype, known as SPIKA, which combines microbial fuel cells (MFCs), vertical hydroponics, and continuous sensing within an architectural-scale installation. The system was stress-tested for seven months (May--December 2025) in a demanding public setting at the Triennale Milano to evaluate its operational stability and robustness. A vertical hydroponic tower and an MFC stack were operated as parallel subsystems under a low-input, recirculating regime, supporting nine ornamental and aromatic plant species. Continuous sensing and imaging provided a longitudinal phenotypic record, enabling a semi-quantitative assessment of plant performance, including growth, flowering, and visual health. Results show stable physicochemical conditions (mean pH 7.1 $\pm$ 0.5; mean EC 510 $\pm$ 35 µS cm -1 ) and consistent plant growth without interruption. Over seven months, the system required 35 water refills (52.5 L) and 12 nutrient additions (190 mL). The 12-module MFC stack exhibited open-circuit voltages of 550--620 mV per module. These findings validate the operational reliability of the Mi-Hy framework and establish a baseline for future prototypes integrating nutrient recovery into hydroponic cultivation, advancing toward a fully coupled circular metabolism.