2. Beyond the Gaussian (theory and examples from time series in econophysics):
sums of independent random variables; from Bernoulli to Binomial; from Binomial to Gaussian; the Central Limit Theorem; random walks versus empirical log-return distributions in financial markets; alpha-stable distributions and their asymptotic properties; non-Gaussian attractors and the Generalized Central Limit Theorem; stylised facts of univariate financial time series.

3. Beyond independence (in multivariate time series and correlation matrices):
correlation matrices (definition and examples from multivariate time series in financial markets and neuroscience); correlation networks; Random Matrix Theory, the Wishart ensemble and the Marcenko-Pastur eigenvalue distribution; interpretation of empirical eigenvalue and eigenvectors of correlation matrices; decomposition of correlation matrices in random, group, and global modes; community detection for correlation matrices.

4. Beyond ensemble equivalence:
Definitions of equivalence of canonical and microcanonical ensembles in statistical physics (measure, macrostate and thermodynamic equivalence); evidences for the breakdown of ensemble equivalence in physical systems and in networks; generalized correspondence between ensembles; minimum description length of canonical and microcanonical models.

5. Beyond Shannon entropy:
Shannon-Khinchin and Shore-Johnson axioms; generalizations of the axioms; the Uffink family of entropies and Renyi entropy; the uninformativeness axiom and the maximum-likelihood estimation of the entropic parameter; the generalized maximum-entropy principle; the q-exponential distribution.

6. Beyond the separation of time-scales in in network dynamics:
(de)coupling dynamics and structure in network models; the Bak-Sneppen model and self-organized criticality; the fitness network model; feedback between dynamics and topology in self-organized network models; the Bouchaud-Mezard model and real-world networks.

7. Beyond the separation of structural scales in networks:
challenges around coarse-graining in networks; different approaches to network coarse-graining: geometric, Laplacian and multiscale network renormalization; applications of multiscale network renormalization in the quenched and annealed settings.

27.10.2025 – Gen AI & Scuola: come educare all’AI
Reflection on educational practices and challenges in teaching responsible AI use.

30.10.2025 – L’impatto della comunicazione nel XXI secolo
Exploration of relational paradigms, nonviolent communication, and structural violence in digital society.

07.11.2025 – Il futuro della Fama nel mondo digitale
Discussion on fame, technology, and power through literature, graphic art, and digital culture.

10.11.2025 – Visione del film “Ex Machina” e discussione
Viewing and debate on artificial intelligence, consciousness, and ethics in cinema.

11.11.2025 – The Doctorate Blueprint: Una Guida Pratica e Completa per Laureati e Giovani Accademici in Discipline scientifiche e Ingegneria
Presentation of a practical guide to doctoral research, supervision, and career development in science and engineering.

20.11.2025 – Io, chatbot: le leggi della robotica di Asimov nel mondo di oggi
Live readings and musical reflections on Asimov’s legacy and contemporary AI ethics.

25.11.2025 – L’evoluzione dei Motori di Ricerca: da Strumenti a Smart Assistants
Overview of the technological transformation from early search engines to intelligent digital agents.

04.12.2025 – Dottorato in Italia: Il ruolo dell’ADI tra rappresentanza, tutela ed ascolto
Open dialogue on rights, representation, and community building within Italian doctoral education.

12.12.2025 – Esplorare gli impatti sociali della digitalizzazione con il gioco di ruolo dal vivo
Experiential workshop using live-action role-play to reflect on the personal and social effects of digital transformation.

2) Biological databases

3) Pairwise sequence alignments

4) Basic Local Alignment Search Tool (BLAST)

5) Multiple sequence Alignment

6) Molecular Phylogenetics

7) Protein domains and proteome modularity

8) Protein structure analysis, alignments and classification

9) Protein structure prediction

10) Biomolecular interaction networks

11) hands-on (based on available freely available webservers and softwares): a) sequence alignments, b) protein structure analysis and prediction, c) molecular interaction network analysis (visualization, annotation and functional enrichment)

– Motivational, introductory notions of statistical inference and probabilistic approaches to cognition. Sampling vs inferring. The Markov Chain Monte Carlo method. Statistical ensembles and emergence. Correlations, cumulants, partial correlations, and interactions: the cumulant expansion. Variational free energy. Relation between the Gaussian and Ising models.
– The inverse problem: Bayesian estimators. Maximum entropy inference: two applications. Unsupervised learning in energy-based neural networks. Expectation-Maximisation learning. Elements of Bayesian model selection. Principal Component Analysis (PCA) as a probabilistic model. Model selection in PCA. Elements of random matrix ensembles. Bayesian inference of correlation and precision matrices. Model selection and clustering: Latent Dirichlet Allocation. Variational inference. Notions of probabilistic models of cognition. The Hierarchical Gaussian Filter.
– Elements of information theory: information and entropy (Shannon entropy, Fisher information, mutual information, differential information, the data processing inequality). The o-information. Model selection and Minimum Description Length. Information relevance. Model selection and inference of higher-order interaction tensors.

Fundamentals of Geographical Information Systems
Geographic coordinates systems
Vector data model
Trajectories
Spatial Tessellations
Flows
Digital spatial and mobility data
Mobile Phone Data
GPS data
Social media data
Other data (POIs, Road Networks, etc.)
Preprocessing mobility data
filtering compression
stop detection
trajectory segmentation
trajectory similarity and clustering

MODULE 2: Mobility Patterns and Laws

individual mobility laws and models
collective mobility laws and models

MODULE 3: Predictive and Generative Models

Next-location prediction
Spatial interpolation

Lesson 2 Recommender systems: a recap. Overview of the main technologies related to recommender systems.

Lesson 3 The Human-AI Feedback Loop. Exploration and formalisation of feedback loops in ML models, with practical examples from social media, online retail, urban mapping, and chatbot platforms. (4 hours)

Lesson 4 Types of Experiments. An overview of experimental methods to evaluate feedback loop impacts, illustrated with examples from diverse human-AI ecosystems. (4 hours)

Lesson 5 Unintended Consequences in Social Media. Case studies of unintended AI recommendation effects on platforms like Facebook, Twitter, and YouTube.

Lesson 6 Unintended Consequences in Online Retail. Real-world examples of AI recommendation impacts on platforms like Amazon and Spotify.

Lesson 7 Unintended Consequences in Urban Mapping. Analysis of unintended effects of AI recommendations on platforms such as Google Maps and Airbnb.

Lesson 8 Unintended Consequences in Chatbots. Examples of challenges posed by AI-generated chatbots like LLAMA and ChatGPT.

Lesson 9 Open Challenges in Human-AI Coevolution. A discussion of unresolved technical, legal, and political issues in measuring human-AI coevolution.

Lesson 10 Pratice and discussion.

2) Unsupervised learning methods: : methods and hands-on exercises
Pattern Mining and Association Rules: basic concepts and a-priori algorithm
Tutorials: practical exercises on simple case studies using Python libraries

3) Supervised learning: methods and practical exercises
Classification: introduction, performance evaluation. A first simple classifier:Decision tree
Exercises: hands-on practice on simple case studies using Python libraries
Overview of advanced methods: Random Forest, Support Vector Machine
Introduction to Neural Networks, project description and assignment
Exercises: hands-on practice on advanced classification methods and Neural Networks withPyTorch

4) Introduction to Deep Learning architectures: methods and hands-on exercises
Convolutional Neural Networks, theory and practice with PyTorch
Recurrent Neural Networks
Adversarial Generative Networks
Transformers
Graph Neural Networks

5) Design principles and Trustworthy issues in AI-based systems

– Introduce the concepts of minimization algorithms for a scalar functional (the loss function).
– Provide the necessary tools for practical course execution, such as Python, Tensorflow, and Pytorch.
– Cover dense neural networks and examples of their applications in physics.
– Explore convolutional neural networks and examples of their applications in physics.
– Discuss recurrent neural networks and examples of their applications in physics.
– Investigate graph neural networks: inductive bias and examples of their applications in physics.
– Examine attention mechanisms: transformers and examples of their applications in physics.
– Study generative neural networks and examples of their applications in physics.
– Provide an overview of differentiable programming.

The course encompasses these topics to provide students with a comprehensive understanding of machine learning algorithms in the context of physics applications.

2. From small to large systems:
quick overview of the three-body problem; the magnetic pendulum; emergent randomness; empirical “principles” of thermodynamics; kinetic theory; statistical thermodynamics; principles of statistical physics (ergodicity, metric transitivity, equal a-priori probability, ensembles versus trajectories); entropy in thermodynamics and physics.

3. Entropy in Information Theory and Statistical Inference:
Shannon-Khinchin axioms; Shannon Entropy; Jaynes’ Maximum-Entropy Principle; statistical inference; the Maximum Likelihood principle; canonical and microcanonical ensembles; entropy-likelihood relationships; canonical covariance of the constraints.

4. Ensembles of random graphs:
canonical and microcanonical graph ensembles; the Erdös-Rényi model; link stub reconnection; the local rewiring algorithm; the Chung-Lu model; the Park-Newman model.

5. Maximum-entropy (re)formulation of network models:
canonical ensembles with given number of links and given degree sequence (the canonical Binary Undirected Configuration Model).

6. The Configuration Model at work:
pattern detection (assortativity and clustering) using the Binary Undirected Configuration Model; graph modelling (the International Trade Network) using the Binary Undirected Configuration Model; the Binary Directed Configuration Model: derivation and use for pattern detection.

7. Network Reconstruction:
the “fitness ansatz” for economic and financial networks; reconstruction of interbank and interfirm networks from aggregate input and output flows.

8. Reciprocity:
introduction to reciprocity in directed networks; definition of reciprocity indicators; joint and conditional reciprocation probabilities; (non-)reciprocated degrees; the Binary Reciprocal Configuration Model; use of the model for triadic motif detection.

9. Triadic motifs detection:
applications to food webs, international trade, supply networks, interbank networks.

3) The last and most important section is instead completely dedicated to neural networks and follows the main path traced by Amit, Gutfreund & Sompolinsky: after a minimal description (always in mathematical terms) of the key mechanisms of spike emission in biological neuron models -e.g. Stein’s integrate&fire (as well as their electronic implementation, e.g. Rosenblatt’s perceptron) – and the propagation of information between them through axons and dendrites, we will see the limits of single-neuron computation by looking at it from different perspectives (e.g. Minsky & Papert’s criticism in the construction of logic gates as i.e. the XOR, etc.). Having shifted the focus from the subject (the neuron) to its interactions (neural networks), we will then build neural networks and study their information processing emergent properties (namely those not immediately deducible solely by looking at the behavior of the single neuron), persisting in a statistical mechanics perspective. Specifically, we will try to see how these networks are able to learn and abstract “archetypes” by looking at examples supplied by the external world. Subsequently, we will show how these networks use what they have learned to respond appropriately, when stimulated, to the external world by carrying out tasks such as “pattern recognition”, “associative memory”, “pattern disentanglement”, etc.
We will also understand how these processes can sometimes go wrong, and why.
Using Hopfield & Hinton’s neural networks as leitmotif for several variations on this theme, the section will close by showing the deep structural and computational equivalence between these two theories, Hopfield’s pattern recognition and Hinton’s statistical learning, unifying these pillars of the discipline in a single and coherent scenario for the whole phenomenon of “cognition”: ideally – and hopefully – at the end of the course the student should be able to independently continue in the study of these topics. In particular, the student should be able, interacting in a team in the future, to play a complementary role to the figures of the computer scientist and the information engineer, taking an interest in their same topics, but offering a different perspective, intrinsically more abstract and synthetic (that is, where the myriad of algorithmic recipes that we produce every day find a natural placement) helping in the optimization of a research group itself.

Ability to create digital twin models of products and processes, integrating computer aided design and real geometrical data with computer aided engineering tools. Both high-fidelity (model-based) simulations and data-driven (artificial neural networks) models are presented and discussed with practical examples.

Lecture Contents:

Introduction to digital twins and their use in technology (1h, Marco Paggi)
Data-driven models based on artificial neural networks: neurons, activation functions, cost functions, back-propagation algorithm for a simple artificial neural network (1h, Marco Paggi)
Artificial neural networks for linear and nonlinear classification problems (1h, Marco Paggi)
Time series networks (1h, Marco Paggi)
Convolutional neural networks (1h, Marco Paggi)
From Computer Aided Design (CAD) or real geometrical data (from images, laser scanner, etc.) to Computer Aided Engineering (CAE): how to integrate realistic object geometries in simulation tools (3h, Maria Rosaria Marulli)
Digital twins for cultural heritage (2h, Maria Rosaria Marulli)
User element routines for model-based simulations of surface problems (5h, Maria Rosaria Marulli)
Interfaces between different CAE software (1h, Andrea Mola)
Integrating functions from software libraries in CAE simulation tools (2h, Andrea Mola)
Integrating data driven information in numerical models (2h, Andrea Mola)

Teaching Method:
The lectures will feature both lessons delivered using standard presentations, and hands-on interactive examples.

Bibliography:
Specific didactic material tailored to the course contents will be provided to the students before the scheduled lessons.

Final Exam:
The final exam will be based on the evaluation of an application of the taught methodologies to one case study of relevance for the PhD student’s research.

Prerequisites:
The course is self-contained. Fundamentals of algebra are required. A general knowledge on CAD and CAE software is recommended, but not essential.

– PDAI 2-ML introduces students to the components of typical data analysis processes and machine learning pipelines. It first builds the necessary toolset by introducing popular Python libraries for data manipulation/visualization (NumPy, Pandas, Seaborn, scikit-learn) with simple applications. The toolset is then applied to a more complex case study on the classification of benign and malignant breast cancer, including aspects of data preprocessing, dimensionality reduction, clustering, and classification. The course will conclude with one research-driven topics like process-oriented data science (Process Mining).

– PDAI 2-PM introduces students to recent data-driven techniques where the main component is the process that generated the data (the data generating process). This is a particularly hot topic, with many companies and researchers involved (see, e.g., the list of industrial that sponsored the reference conference in 2023 https://icpmconference.org/2023/sponsor-and-exhibition/). We will consider techniques known as Process Mining, in which logs generated during the execution of a process (e.g., an industrial production process, business processes, social system ‘processes’) are used to infer the structure of the process. Questions of interest are, e.g.: What is the actual process being executed? Are there possibilities for improvement? Does the actual process conform to the intended reference process?

Module 1
– Unsupervised classification; Clustering methods
– Unsupervised dimension reduction; Principal Components Analysis and related techniques
– Supervised classification methods
– Non-parametric regression methods
– Resampling methods, Cross Validation, the Bootstrap and permutation-based techniques.

Module 2
– Feature selection and regularization techniques for high-dimensional Linear and Generalized Linear Models
– Feature screening algorithms for ultra-high dimensional supervised problems
– Supervised dimension reduction; Sufficient Dimension Reduction and related techniques
– Subsampling/partitioning approaches for ultra-high sample sizes
– Under- and oversampling approaches for data rebalancing

Materials: Our main reference texts will be (a) An Introduction to Statistical Learning (James, Witten, Hastie, Tibshirani; see https://www.statlearning.com/); (b) Computer Age Statistical Inference (Efron, Hastie). Links to lecture notes, practicum materials and further materials will be provided.

Evaluation: Evaluation will be based on project presentations and written reports to be held/handed in at the end of the course. Each project will revolve around a dataset, to which students will apply techniques and approaches described during the course – thus building an overall analysis to be summarized in the final presentation and report. Ideally, students will work on datasets of their own choice. These could be related to their own research, or selected from public sources.

Prerequisites: A working knowledge of basic statistical inference procedures (point estimation, confidence intervals, testing) and linear and generalized linear models. For Module 2, a working knowledge of the methods comprised in Module 1.

1. Understand and apply normative principles of welfare theory to public policy analysis.
2. Critically evaluate efficiency, equity and sustainability in policy design.
3. Integrate formal welfare economics analysis with the challenges posed by environmental and intergenerational sustainability.

Structure of the course:

Lecture 1 – Introduction to welfare economics and sustainability
• Normative vs. positive economics: conceptual differences and implications for policy
• Utility, preferences and well-being: individualistic and collective approaches
• Sustainability as a normative criterion: intergenerational well-being and ecological constraints
Lecture 2 – Paretian efficiency and the fundamental theorems of welfare economics
• Paretian efficiency: definition, implications and limitations
• First and second theorems of welfare economics: formulation and proof
• Criticisms of the applicability of theorems in sustainability contexts
Lesson 3 – Equity, social choice and collective welfare criteria
• Functions of social welfare: utilitarianism, egalitarianism, Rawls, Sen
• Arrow’s impossibility theorem and its limitations
• Capabilities approach and pluralism in evaluation criteria
Lecture 4 – Market failures and sustainability.
• Environmental externalities, public goods, and imperfect information
• The “second best” and systemic constraints in policy design
• Regulatory tools for sustainability: environmental taxation, tradable permits, standards
Lesson 5 – Rethinking well-being: normative perspectives for sustainability
• Critique of standard models of well-being and growth
• Alternative indicators: natural capital, subjective well-being, wealth accounting
• The role of welfare economics in the ecological transition

Verranno proposti esercizi di analisi critica di testi specialistici e casi di studio per stimolare la riflessione autonoma e l’elaborazione di idee originali.

Sono inoltre previste attività di laboratorio per l’applicazione pratica degli strumenti di analisi automatica del testo e di valutazione della traduzione neurale.