Annualy the PhD board propose new training activites that will be supported by Università degli Studi dell’Insubria. 

Etica dell'IA, IA spiegabile e ruolo del processo decisionale umano  
Il corso si propone di definire ed esplorare le questioni etiche inerenti all'uso dell'intelligenza artificiale (IA), di fornire modelli di explanability di IA e di combinarli con modelli e definizioni di processi decisionali. Il corso si occupa di una serie di questioni e argomenti attuali attraverso l'applicazione di importanti teorie morali. Questo corso si propone di definire ed esplorare le questioni etiche inerenti all'uso dell'intelligenza artificiale (IA), di fornire modelli di explanability di IA e di combinarli con modelli e definizioni di processi decisionali. Gli argomenti trattati includono, ad esempio, la nozione di responsabilità, le questioni etiche nella progettazione e nella gestione dell'IA, gli aspetti etici dei rischi tecnici, la distribuzione della responsabilità nell'ingegneria, nel design e nell'architettura e il rapporto tra sostenibilità, etica e tecnologia.

PDE su grafi metrici: teoria spettrale degli operatori differenziali, propagazione delle onde e  
applicazioni  
Il corso fornisce un'introduzione alla teoria delle equazioni differenziali parziali (PDE) su grafi metrici ed è suddiviso in quattro parti. La prima parte introduce le definizioni di base e la nozione di operatore differenziale selfadjoint su un grafo metrico. Include una descrizione delle varie realizzazioni di operatori selfadjoint del Laplaciano e una rassegna dei principali risultati della teoria spettrale. La seconda parte si concentra sull'analisi della dinamica lineare delle onde su grafi metrici, con particolare attenzione all'equazione lineare di Schrödinger. La terza parte del corso si concentra sull'equazione di Schrödinger non lineare, in particolare sull'analisi delle soluzioni stazionarie e della loro stabilità. Infine, l'ultima parte del corso esamina alcuni risultati sul problema della giustificazione dei modelli di grafi metrici come approssimazioni per la dinamica delle narrow tube network.

Interpolation theory for differential forms  
Nowadays, differential forms are an across-the-board instrument in mathematics and physics. As a consequence, their numerical representation and approximation is essential. In this course we will understand the main challenges of interpolation of differential forms. To do so, techniques based on integration on simplices (i.e. on the construction of weights – a suitable selection of currents) are presented. Crucial steps involve the identification of unisolvent sets and their comparison in terms of appropriate functionals, called k-Lebesgue constants, that are discussed and characterised. Numerical linear algebraic features are also identified and studied. At the end of the course, the student is in a position to deal with the existing literature and aware of modern challenges in the field.

Topological Data Analysis  
The need for analyzing enormous amounts of data has increased dramatically over the last years. The typical approach to this problem is of quantitative nature, and uses tools from Statistics. A different approach, of a more qualitative nature, has been introduced in 2002. The main idea is to focus on the identification and the recognition of shapes, and patterns, in data. This approach is known as Topological Data Analysis, and is a branch of computational topology. The invariants associated to the shape of data are codified by persistence homology groups, a parametrized version of singular homology groups. Both the storage of the data in a way which easily enables the computation of persistence homology groups, and the computation itself, have a strong computational flavor: for instance, one needs efficient algorithms to row-reduce matrices with coefficients in Z2.

Systems, Modelling, Simulations  
Learning Organization and Strategic Knowledge Management means, for an organization, the acquisition of a mental model (Peter Senge 1990). To perceive such a challenging objective it is necessary to identify, clarify and improve our inner worldview and understand how the dynamics of the organization structure evolve and govern critical variables (levers) in order to better support actions and decisions. Thanks to the understanding of influence relationships between world “participants” and an integrated and complex view of phenomena (systems), which is supported by a correct management of information universe, it is possible to develop System Dynamics (J. W. Forrester) models and use simulations to be aware of what are the possible alternative consequences of our decisions. Such a paradigm allows us to acquire a real Systems Thinking approach and to recognize relationships between time ‘variables’, instead of finding out, statically, simple structures. System Dynamics (SD) modeling has been used in many different contexts, For example, in ICT domain can be applied in Project Management (PM) process control. In particular an innovative and original application could be in engaging Agile SW development approach through a SD modeling analysis and hence building a simulation model in order to best support alternative PM decisions, also in relation to present/ideal organizational environment. Many Small-Medium Enterprise (SME) Decision Support Systems are also developed involving SD simulation models in order to build the so called Enterprise Dashboards and support medium- top managers in overall enterprise strategic decisions.

Flipping strategies for large linear systems: spectral analysis and computational results  
Consider a Toeplitz matrix T_n that is a matrix whose coefficient are constant along the diagonals and assume that T_n is real and nonsymmetric. Even assuming that the coefficients stem as Fourier coefficients of a given smooth function f, the spectral features of T_n=T_n(f) are very complicate. The latter property makes notable solvers (as GMRES) for the related non-symmetric linear systems very difficult to analyze.   One decade ago Pestana and Whathen proposed solving a real non-symmetric Toeplitz linear system T_n(f)x = b by (preconditioned) MINRES applied to the symmetrized linear system H_n(f)x = Y_n b, H_n(f)=Y_n T_n(f) has some advantages over solving the original system through either direct methods or iterative methods for non-symmetric Toeplitz matrices, Y_n being the flipping matrix (or anti-diagonal matrix).  

The course focuses on the theoretical and algorithmic aspects of the flipping strategy, by testing it on notewhorty applications such as approximated evolutionary differential equations and deblurring problems in imaging. The course is divided in the following sections: 

• Spectral analysis of the flipped matrices and flipped matrix-sequences in the the sense of localization and distributional results; 
• Preconditioning in various matrix algebras and clustering results; 
• Application of the flipping stategy to approximated evolutionary differential equations; 
• Application of the flipping stategy to deblurring problems in imaging with various boundary conditions (BCs) including reflective and anti-reflective BCs.