Machine Learning (ML) is forging a new era in Applied Mathematics (AM), leading to innovative and powerful methods. But the need for theoretical guarantees generates challenging, fundamental, deep mathematical questions. This great challenge can be addressed from the perspective of other, more mature areas of AM. CoDeFeL seeks to do so from the rich interface between Control Theory (CT) and ML, contributing to the analytical foundations of ML methods, significantly enlarging, and updating the range of applications of CT. As our recent results show, classification, regression, and prediction problems in Supervised Learning (SL) and the Universal Approximation Theorem can be successfully recast as the simultaneous or ensemble controllability property of Residual Neural Networks (ResNets). Following this path, we will develop ResNets of minimal complexity and cost, addressing the deep, intricate issue of linking the structure of the data set to be classified with the dynamics of the networks trained. Taking the turnpike principle as our inspiration, we will build new simplified ResNet architectures. This, however, raises major challenges for the genuinely nonlinear dynamics that ResNets represent.Adjoint methods will also be developed and applied, to understand the sensitivity of ResNets, and proposing techniques for Adversarial Training and computing Saliency Maps, applicable in Unsupervised Learning. The project is strongly inspired on the challenges arising in relevant applications in digital medicine and internet recommendation systems, among other areas. Accordingly, we will also develop a body of rich, hybrid, cutting-edge methods for data-aware modelling, combining ResNet surrogate models and those inspired on Mechanics, with the aid of Model Predictive Control strategies. New Federated Learning methodologies with privacy preservation guarantees will also be developed. The computational counterparts will be brought together in a new CoDeFeL GitHub repository.

So far, materials are seen as passive items. This project aims at providing a solution that can turn objects into matter that can perceive and communicate trigger events. If materials are turned capable of reporting their encountered history, this will significantly contribute to i) ensuring product safety and reliability, ii) making predictive maintenance possible, iii) making complex recycling fates of materials transparent, and iv) enabling autonomous, robot-controlled, resilient manufacturing (Industry 4.0). The key to realize this vision is to make use of smart magnetic particles, largely based on iron oxide (SmartRust). To achieve SmartRust, micron-sized (1-10 µm) supraparticles are composed of magnetic nano building blocks, the “signal transducers”, which are combined with other non-magnetic moieties, the “sensitizers”. A toolbox-like approach using spray-drying allows for nanoparticle assembly of a transducer and a sensitizer type of choice to specifically target a desired type of stimulus. The SmartRust particles are then integrated in materials` matrices. It is hypothesized – and yet an open research question! - that there is an interplay of two magnetic interaction principles: on a hierarchical level I, a trigger event will alter the intra-supraparticle magnetic interactions of the nanoparticles within individual supraparticles. On a hierarchical level II, a trigger event will alter the inter-supraparticle magnetic interactions among the supraparticles when the matrix of the materials, where the supraparticles are embedded in, is altered. The scientific idea is that this magnetic interaction information can be read out fast, easily, in a non-destructive way and from within a material, enabled by the technique magnetic particle spectroscopy (MPS). If this endeavour is successful in obtaining a meaningful signal-structure-trigger correlation, ultimately, design rules could be deduced how to create conscious matter using SmartRust.

The project aims to fabricate and characterise novel type of multilayered scaffolds suitable for interface tissue engineering applications, in particular for osteochondral segment regeneration. Osteochondral defects imply injury in cartilage, bone and bone-cartilage interface tissues, characteristic of all the joints of human body, its causes could be both traumatic and due to aging-related pathologies. The project will be focused on the integration of several scaffold fabrication techniques for the development of novel electrospun multilayered scaffolds. In particular, considering the well-known effects of bioactive glass on osteogenesis, angiogenesis and its antibacterial activity, electrospun bioactive glass mats will be fabricated. Moreover, bioactive glass particles will be dispersed in a polymeric solution before the electrospinning for the fabrication of bioactive glass-doped mats. These two kind of scaffold will be used for the fabrication of the multilayered structures. Innovative solutions will be adopted for the obtainment of the stratified samples, integrating different technologies as the electrospinning, freeze-drying and foam replica method. The training of the researcher in the host Institution will be focus on the development of skills related to cell culture management and in particular on cell culture for tissue engineering. The training will start with cell viability tests and cell seeding on several kind of scaffolds. Several cell lines will be used and it will be also investigated stem cells differentiation. The use of co-culture systems and dynamic cell culture will also be evaluated and eventually applied to the multilayered scaffolds. An innovative approach will be used in the investigation of scaffold mechanical properties, in fact mechanical tests will be performed on the multilayered samples and on each single layer to evaluate the deposition of ECM on the seeded scaffolds and how it affects scaffold mechanical properties.

The overarching goal of the Hy-solFullGraph project is to undertake, from a molecular level, the synthesis of new functional hybrid materials based on carbon allotropes with outstanding properties. Synthetic carbon allotropes (SCAs) are regarded to be among the most promising candidates for future high performance materials. Precise control of the derivatisation will play a key role in tailoring their solubility and reactivity to maximise the advantages of their outstanding properties. We propose herein 1) to selectively functionalise C60 fullerenes with different substituents (hydrophobic, hydrophilic, and polyfluorinated) to tune their solubility and their superstructured assembly. 2) By controlling the addition pattern, we will include an additional functional group which will facilitate their covalent attachment to other carbon allotropes such as graphene or CNT. In this way, new Hybrid-SCAs will be synthesised for the very first time and the interactions between the hybrid allotropes will be unravelled. 3) Moreover, by changing the chemical decoration around the allotropes, we will be able to endow them with different functionality for their application in optoelectronic and biomedical fields. For optoelectronic applications, such as the development of solar cells, we propose to tune the electronic interactions and energy levels of fullerene and graphene and to control the energy transfer processes and packing behaviours between the allotropes by well-designed chemical functionalisation. Furthermore, we will use the hydrophilic fullerenes to prepare functional biomaterials by taking advantage of their electrical properties to ultimately assist nerve tissue regeneration. The project will be developed at the crossroads of organic and supramolecular chemistry, materials science, nanotechnology and physical chemistry to produce novel synthetic hybrid carbon allotropes with tailored properties towards new nanomaterials for optolectronical and biomedical applications

The existence of an intergalactic magnetic field (IGMF) remains elusive and only upper limits on its strength are known from limits on the rotation of polarization angles of radio waves. Its measurement would provide crucial information about large scale structure formation, since the IGMF is thought to act as a seed field for magnetic fields in galaxies and galaxy clusters, how the Universe evolved, and how charged cosmic rays and electromagnetic waves propagate through intergalactic space. Here, I propose a new search for IGMF signatures using observations of a high-energy gamma-ray cascades from distant galaxies. Gamma rays interact with background radiation fields to produce electron-positron pairs. These pairs up-scatter cosmic-microwave photons to gamma-ray energies, initiating the cascade. The IGMF morphology is imprinted on the cascade through a deflection of the pairs in the IGMF. A novel combination of observations with imaging air Cherenkov telescopes and the Fermi Large Area Telescope, using both spectral and spatial information, combined with precise model predictions of the cascade, promise an unprecedented sensitivity for detection of the cascade signal and the IGMF. Strong constraints on the IGMF strength will be possible if no cascade is detected. Furthermore, I will also search for a gamma-ray and neutrino signal from cascades initiated by cosmic rays from active galaxies. This will yield an independent probe of the IGMF and, additionally, constraints on the cosmic-ray acceleration power of such galaxies. As part of this work, I will also make predictions how the future Cherenkov Telescope Array (CTA) can further improve the detection of or constraints on the IGMF and the cosmic-ray acceleration power of active galaxies. This will result in an optimized observation strategy for the extragalactic survey and the blazar monitoring program, which are both planned with CTA.