Feb 052026
 

MAIN PhD Seminars 2026

 

Date Speaker Title
March, 4th  Filippo Concas Learning to Translate with Scarce Data Foundations and Recent Advances in Low-Resource NMT
March, 11th Luca Garau How to build a PhD: from 3D printing to advanced industrial fabrication
March, 18th  Marco Ferrara Implementing the Simply Typed Lambda Calculus with De Bruijn Levels
March, 25th  Davide Antonio Mura Bridging Modalities: Fusion Strategies and Vision-Language Alignment
April, 1st Roberta Angioni Healthcare Timetabling and Routing: State of the Art and Emerging AI-Driven Approaches
April, 8th Emily Priyadarshini DeFi Protocols and Attacks: A glimpse into the Wild West
April, 15th Simone Pinna Can machines deeply understand us? The role of AI in modern psychology
April, 22nd Giulio Casti Machine Learning Applications in Economics: Case Study on Startup Survival Prediction
April, 29th  Federico Meloni Third Year in the third dimension: a voyage into Volumetric Tetrahedral Maps
May, 6th Fabio Littera Beyond Static Profiling: Navigating User Intent with Conversational Agents and Reinforcement Learning
May, 13th Martina Salis Hybrid AI methods for data management and behavioral analysis
May, 20th Marco Murgia Challenges and strategies for robust AI-Generated Text Detection
May, 27th Marco Damele Problems on skew left braces
June, 3rd Andrea Cabriolu A Bayesian and heuristic approach to an optimization algorithm for the dynamic scheduling of astronomical observations
June, 10th Giuseppe Scarpi From uncertainty to formalisation: mitigating limits of Language Models in practical scenarios

All the seminars at 13:00 in Aula Magna di Fisica

 

Filippo Concas: Learning to Translate with Scarce Data Foundations and Recent Advances in Low-Resource NMT
Research Topic: Natural Language Processing

Neural Machine Translation (NMT) has shown strong performance in high-resource settings, where large and clean parallel corpora are available. These results, however, are harder to reproduce for low-resource languages, where data is scarce, heterogeneous, and often noisy or affected by domain mismatch. In this seminar, we introduce machine translation from its probabilistic formulation to modern neural approaches, highlighting the central role of training data and the assumptions underlying current NMT models.

We then focus on low-resource scenarios, discussing how data limitations influence training and evaluation, and reviewing common strategies such as data augmentation, transfer learning, and multilingual modeling. The seminar concludes by presenting recent research trends that adopt a data-centric perspective on neural machine translation, emphasizing data selection, filtering, and quality assessment as key components, and outlining open questions and directions for future research.

Luca Garau: How to build a PhD: from 3D printing to advanced industrial fabrication
Research Topic: Computer Graphics – Digital Fabrication

This seminar analyzes the evolution of digital manufacturing, comparing additive processes (based on material deposition) with subtractive ones (characterized by material removal). Positioned between these two techniques are casting processes, widely used in various industrial fields, which involve pouring molten material into molds. Starting with a general overview, the seminar will focus on the technical challenges related to the design of casting molds. We will delve into the unresolved problems affecting the efficiency and precision of reusable rigid molds, with particular emphasis on the fabrication of complex and unconventional geometries..

Marco Ferrara: Implementing the Simply Typed Lambda Calculus with De Bruijn Levels
Research Topic: Implementation of formal systems based on typed lambda calculus

The lambda calculus is a foundational formalism for describing computation, and it underlies many logical and programming systems. Its standard presentation relies on named variables, which are human-friendly but introduce complications related to alpha equivalence and substitution in formal and computational settings. Nameless representations of binding, such as de Bruijn levels, offer an alternative approach that avoids these issues while retaining a precise account of variable binding and scope. Using these representations, formalizations of logics based on the lambda calculus in a proof assistant such as Rocq provide an environment for establishing properties of programming and formal languages whose definitions or semantics are based on such logics.

Davide Antonio Mura: Bridging Modalities: Fusion Strategies and Vision-Language Alignment.
Research Topic: Computer Vision

In recent years, Deep Learning has revolutionized a multitude of tasks, yielding outstanding results in the analysis of single-modality data, such as images in Computer Vision or text in Natural Language Processing. However, many real-world applications require combining different types of information to capture complementary features and richer semantic context, making the analysis of multimodal data essential. This seminar introduces the fundamental concepts of Multimodal Deep Learning, presenting the main data types involved and demonstrating how neural models can effectively combine diverse information sources. The primary multimodal fusion techniques will be discussed, highlighting their characteristics, advantages, and limitations. Finally, the seminal architecture Contrastive Language–Image Pretraining (CLIP) will be examined as a concrete example of alignment between natural language and images in a shared representation space.

Roberta Angioni: Healthcare Timetabling and Routing: State of the Art and Emerging AI-Driven Approaches
Research Topic: Hybrid Optimization Methods and Generative AI in Healthcare

The effective optimization of human and logistic resources constitutes a critical socio-economic imperative in the healthcare sector. This necessity drives the search for advanced solutions to complex combinatorial challenges, such as the Home Healthcare Routing and Scheduling Problem (HHCRSP) and the Integrated Healthcare Timetabling Problem (IHTP). The foundational work of Mankowska et al. (2014) and the benchmarks defined by the winning approaches of the Integrated Healthcare Timetabling Competition 2024 establish robust baselines for these problems; however, the application of exact solvers to these domains often faces limitations, and the NP-hard nature of these problems calls for continuous research to mitigate the intrinsic limitation of an intractable global optimality. 

Addressing these challenges, the seminar first provides a critical overview of state-of-the-art resolution methods, then the focus shifts to emerging AI-driven architectures: we investigate how Large Language Models (LLMs) can function as active heuristic components within frameworks based on classic metaheuristics and genetic algorithms, or within specific hybrid systems incorporating other AI techniques based on Monte Carlo methods. Finally, drawing from ongoing research efforts, an overview of the obtained experimental results is also provided, critically assessing both the competitive advantages of these AI-integrated solutions and the specific limitations that have emerged.

Emily Priyadarshini: DeFi Protocols and Attacks: A glimpse into the Wild West
Research Topic: Blockchain Security

Decentralized finance (DeFi) has enabled a suite of financial services to be offered without relying on trusted intermediaries. Ethereum, an account-based blockchain model, implements DeFi using smart contracts. In this seminar, we give an overview of the DeFi landscape through a few widespread DeFi protocols. Specifically, we use these protocols to witness how blockchains have given rise to new market dynamics and subsequently novel attack vectors. To conclude, we present a few general approaches and common tools used to mitigate such attacks and discuss some potential areas for research.

Simone Pinna: Can machines deeply understand us? The role of AI in modern psychology
Research Topic: AI in Psychology

In recent years, artificial intelligence has become increasingly present in the field of health, covering various care roles. However, when it comes to mental health, its intervention is still seen as taboo. This mistrust is motivated by valid reasons, which are examined by the most recent research, with the aim of breaking down the barriers to understanding between humans and machines. For example, Large Language Models are commonly used for their ability to mimic reasoning patterns expressed in human natural language. However, in the field of psychology, standard patterns are not always our ally, and an overly rigid interpretation can lead to risks and clinical misjudgments. This seminar will explore the ability of AI (LLMs in particular) to approach the sensitive issue of mental health and how this technology can be used in different roles (diagnostic hypotheses, emotion recognition, patient simulators, training for therapists, etc.). The fundamental rule remains the same as in medicine: the use of AI is not intended to replace experts but to improve their ability to treat patients by capturing the nuances in their language. There are many obstacles to the introduction of these new technologies into this world, including realism, adaptability, trust, explainability, ethics and a lack of data for privacy reasons. We will look at the most promising techniques for overcoming these obstacles and how they have evolved over time to refine the ability of computers to learn the pattern of our psyche.

Giulio Casti: Machine Learning Applications in Economics: Case Study on Startup Survival Prediction
Research Topic: Machine Learning in Economics

In the highly volatile startup ecosystem, the ability to predict the survival and growth of early-stage companies is a critical challenge for investors, policymakers, and entrepreneurs alike. Traditional economic evaluation methods, such as comparative analysis,  often struggle to account for intangible assets and extreme market uncertainty. This seminar presents an approach to predicting startup survival by leveraging advanced machine Learning methodologies applied to large-scale structured data from the PitchBook platform. The discussion focuses on a comparative analysis of different algorithmic architectures, highlighting their performance in binary classification tasks. Furthermore, we explore the application of survival analysis models to handle right-censored data, allowing for the analysis of survival probabilities as they evolve over time. Key findings report that factors beyond traditional financial indicators, such as team experience, lead investor counts, and competitive positioning, play a crucial role in business longevity. Finally, the seminar outlines future research directions, including the integration of deep learning models to capture temporal market dynamics and the development of real-time monitoring platforms for investors and entrepreneurs.

Federico Meloni: Third Year in the third dimension: a voyage into Volumetric Tetrahedral Maps
Research Topic: Computer Graphics – Geometry Processing

Volumetric tetrahedral maps are a key tool in geometry processing, enabling applications such as simulation, deformation, and volumetric texturing. Compared to surface parameterization, volumetric mapping poses additional challenges in ensuring bijectivity, controlling distortion, and achieving robustness on complex meshes. This seminar introduces the problem and surveys the main state-of-the-art approaches, outlining their strengths, limitations, and open challenges. In the second part, I will present my ongoing research on volumetric tetrahedral mapping, describing my methodological perspective, how it differs from existing techniques, and the contributions I am developing toward more robust and practical volumetric maps.

Fabio Littera: Beyond Static Profiling: Navigating User Intent with Conversational Agents and Reinforcement Learning
Research Topic: AI Agents and Reinforcement Learning

Traditional Recommender Systems often struggle to capture evolving user needs, particularly in “cold-start” scenarios where prior interaction data is missing. To address this limitation, Conversational Recommender Systems (CRS) have emerged as a solution, enabling users to express complex preferences through multi-turn natural language dialogues.

In this seminar, we present an Agentic AI architecture that frames the recommendation task as a sequential decision problem. We model the system as a Markov Decision Process (MDP), formally defining its State Space, Action Space, Transitions, and Reward functions to bridge the gap between language understanding and decision-making. To ensure efficient retrieval over large catalogs, we introduce a hybrid filtering mechanism that combines deterministic constraints (Hard Filters) with semantic embedding similarity (Soft Filters).

The core of our approach is a Reinforcement Learning Director, an agent trained to optimize the trade-off between exploration (eliciting preferences via questions) and exploitation (recommending items). This decision process is driven by the semantic uncertainty of the search space, modeled through embedding-based representations. Finally, we discuss the challenges of offline evaluation in conversational settings and demonstrate our validation strategy using an LLM-based User-Simulator.

Martina Salis: Hybrid AI methods for data management and behavioral analysis
Research Topic: Hybrid data analytics

The growing adoption of data-driven systems and artificial intelligence poses new challenges in data management, governance, and behavior analysis across heterogeneous domains.

In this seminar, we will present a set of works that leverage large language models (LLMs) to address these challenges through scalable and lightweight AI-based solutions.

Specifically, we will discuss a metadata-based technique for detecting similarity among data products, LLM-based methods for the automated verification of natural-language semantic rules (policies) on data products and a system that uses LLMs and sensor data from smart homes to recognize and explain anomalous behavior with respect to examples of normal daily activities.

Marco Murgia: Challenges and strategies for robust AI-Generated Text Detection

Research Topic: Generative AI

The exponential advancements in Large Language Models (LLMs) have revolutionized text generation, making it increasingly difficult to distinguish between human-produced and machine-generated content. This indistinguishability raises significant concerns in critical domains such as disinformation, academic integrity, and online content security. This seminar will explore the inherent challenges of AI-generated text detection, focusing on current methodologies and strategies to enhance the robustness and generalization of detection systems. Beginning with an understanding of the stylistic and statistical characteristics that differentiate AI text, we will study the state of art and analyze approaches based on fine-tuned language models and discuss findings from recent research, including personal contributions to developing detectors resilient to adversarial attacks. We will conclude by outlining the ethical implications and future directions of research in this rapidly evolving field, emphasizing the continuous ‘cat-and-mouse game’ between generation and detection capabilities.

Marco Damele: Problems on skew left braces
Research Topic: Algebra

Skew left braces are algebraic structures introduced to study set-theoretical solutions of the Yang–Baxter equation, with a one-to-one correspondence between solutions and skew braces. Recently, the concept has been extended to Lie groups.

Research on skew braces focuses on understanding the relationship between the additive and multiplicative groups, including the open Byott conjecture, which asserts that a skew brace with solvable additive group has a solvable multiplicative group. In the finite case, skew braces are also studied as single algebraic objects, with interest in properties such as solvability, supersolvability, and nilpotency, as well as analogues of the Cauchy and Sylow theorems. Another line of research uses permutation braces to analyze algebraic properties of set-theoretical solutions, such as indecomposability and irretractability. In this talk, I will provide an accessible introduction to skew left braces, explaining what they are and why they are interesting. I will then present the main lines of research in the area and discuss my recent contributions to the field.

Andrea Cabriolu: A Bayesian and heuristic approach to an optimization algorithm for the dynamic scheduling of astronomical observations
Research Topic: Heuristic algorithms, dynamic scheduling

In order to maximize the scientific time used by the Sardinia Radio Telescope a Dynamic Scheduling system will be developed. An all-encompassing architecture will be designed based on a careful top-down approach. A complete system will be presented, in which the weather tools, proposal tools, scheduling system, observing system and telescope management tools will all be integrated.

Among all the components that compose the relationships between the system’s actors, the “Optimizer” component plays a key role. A central element of the entire architecture, its main role is to create long- and short-term schedules, basing its choices with Bayesian and heuristic approaches on various parameters, such as weather forecast data, antenna availability, scientific constraints, and the like.

Basically, Optimizer will involve a set of algorithms with the aim to validate if the conditions and the constraints defined by astronomers at proposal phase would be met at a specific time. Some of the tasks managed by Optimizer aim to predict observation-relevant parameters using information such as real-time weather data and time series; others assign appropriate weight to parameters; still others calculate long- and short-term schedules.

Optimizer must maximize a specific parameter called “figure of merit”, related to the semester. These are metrics that statistically establish the desired success rate for projects of various levels or the efficiency of telescope time use. Therefore, the “figure of merit” governs the quality of astronomical observation arrangements, prioritizing specific characteristics so that the activities carried out can meet the objectives established by the Observatory.

Giuseppe Scarpi: From uncertainty to formalisation: mitigating limits of Language Models in practical scenarios
Research Topic: Language Models

It was clear from the beginning, but now we are interiorizing it: language models are neither totally stochastic, nor totally deterministic. Thus, they can’t be creative, but not even completely reliable.

With the increasing integration of LM in critical applications, undestanding and mitigating their limits has become very important. In this seminar we will examine some countermeasures – like PLD formalization, usage of ontologies/nomenclatures, delegation of critical functions to deterministic software – and some practical applications of synthetic data generation and genuine data analysis.

 Scritto da in 5 Febbraio 2026  Senza categoria  Commenti disabilitati su MAIN PhD Seminars 2026
Gen 162026
 

Symbolic AI and SMT solving

Dott. Enrico Lipparini
University of Cagliari

Abstract

Symbolic AI is an approach to Artificial Intelligence that relies on deductive reasoning to produce exact, explainable solutions to well-defined problems. This contrasts with sub-symbolic methods (e.g., machine learning, NNs, and LLMs), which use statistical learning to address a wide range of (possibly vaguely defined) tasks, producing plausible but not always correct results that are typically hard to explain. Integrating symbolic and sub-symbolic techniques is a hot topic in AI (neuro-symbolic AI).

SMT (Satisfiability Modulo Theories) solvers are automated tools for reasoning about and rigorously solving problems involving arithmetic, arrays, bit vectors, and more. They are widely used in industrial settings for tasks such as program verification, planning, and testing.

In this short course, we introduce Z3, an efficient and user-friendly SMT solver developed by Microsoft. We will compare it to both hand-written algorithms and LLM-based approaches on a simple illustrative problem, such as solving a Sudoku. Then, we will show how SMT solving can be used for program verification (i.e., checking whether a program satisfies a given specification), discussing some applications in smart contract security.

Throughout the course, students will actively engage with the material by working on a series of simple, guided exercises that will be assigned during the session, allowing them to experiment directly with the tool and reinforce the concepts discussed.

Schedule
February 5th, 9:00-14:00, Lab Pes

Exam
The final assessment consists of a small project developed using the Z3 Python APIs.

Dic 112025
 

Foundations of Open, Rigorous and Reproducible Research

Dott. Mirko Marras
University of Cagliari

Abstract
This course equips participants with the conceptual and practical foundations required to conduct open, rigorous, and reproducible research, aligned with the evolving expectations of the scientific community. Integrating methodological principles with applied examples, the course examines the major challenges that arise when research lacks transparency, from restricted accessibility and ambiguous analytic workflows to irreproducible findings and diminished scientific credibility. Students will learn to design studies and experiments thoughtfully, plan analyses in advance, document methodological decisions in detail, and adopt best practices for data collection, preprocessing, visualization, simulation, and analysis, for improving the overall transparency. The course also addresses strategies for making research materials openly available, including datasets, proofs and derivations, code, computational environments, and documentation, while navigating ethical and practical constraints related to privacy, confidentiality, and intellectual property. These practices are discussed in the broader context of contemporary research, including as examples the requirements for openess mandated by funding agencies, the increasing use of transparency and reproducibility checklists in scientific call for papers, and community-wide initiatives advancing open science and responsible research practices. Emphasis is placed on modular, tractable, and domain-agnostic techniques that can be applied across theoretical, algorithmic, and empirical work. By the end of the course, participants will develop the core competence and mindset needed to meet these emerging standards and to produce research that is robust, transparent, verifiable, and ultimately more suitable for dissemination.

Schedule
The course will be held in June or July 2026, delivered over approximately 8 lectures for a total of 16 hours.

Exam
The final assessment consists of one of two options, to be selected in agreement with the instructor based on the student’s attendance and research needs. Students may either (i) engage with a published paper by producing a report assessing its transparency, evaluating how reproducible the study appears, and reflecting on any challenges they would expect to encounter while performing a full replication or (ii) they may prepare a plan for enabling openness, rigor, and reproducibility in one study within their doctoral research (or a closely related use case), aligning it as closely as possible with the principles and best practices introduced in the course.

Enrolment
Prospective participants should contact the instructor by email (mirko.marras@unica.it) to express their interest in attending no later than April 30, 2025.

 Scritto da in 11 Dicembre 2025  Senza categoria  Commenti disabilitati su PhD Course: Foundations of Open, Rigorous and Reproducible Research
Nov 302025
 

The Dichotomy of Global Existence and Blow-up in Chemotaxis Systems

Dott. Rafael Díaz Fuentes

Università di Cagliari

Abstract

This course provides a comprehensive analysis of systems of nonlinear partial differential equations, primarily of parabolic and elliptic type, that arise in the modeling of chemotaxis. The curriculum is structured around the fundamental dichotomy between two possible fates for solutions: global existence and finite-time blow-up. The analysis focuses on the critical thresholds in mass, dimension, and model parameters that determine the outcome of a dynamic competition between stabilizing forces (diffusion, logistic damping) and destabilizing forces (aggregation). Beginning with the classical theory, the course progresses to several advanced topics, including: the mechanisms that enforce global regularity, the long-term behavior of such solutions, and the modern analytical tools required to establish well-posedness in challenging low-regularity settings.

Schedule

The course will be held in April-May 2026, delivered over 8 lectures for a total of 14-16 hours.

Exam

The final assessment consists of one of the two choices: a seminar on a topic building on the content of the course or a written elaborate on selected topics of the course.

References

  • Bellomo, N., Belloquid, A., Tao, Y., & Winkler, M. (2015). Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Mathematical Models and Methods in Applied Sciences, 25(9), 1663-1763.
  • Brezis, H. (2011). Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer.
  • Evans, L. C. (2010). Partial Differential Equations (2nd ed.). American Mathematical Society.
  • Horstmann, D. (2003). From 1970 until now: the Keller-Segel model in chemotaxis and its consequences. I. Jahresbericht der Deutschen Mathematiker-Vereinigung, 105(3), 103-165.
  • Lankeit, J., Winkler, M. (2017). Facing Low Regularity in Chemotaxis Systems. Jahresbericht der Deutschen Mathematiker-Vereinigung, 122, 35-64.
  • Winkler, M. (2010). Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. Journal of Differential Equations, 248(12), 2889-2905.
Nov 262025
 

Extreme Value Theory

Dr. Amir Khorrami Chokami

Università di Cagliari

Abstract

This doctoral course provides a comprehensive introduction to Extreme Value Theory (EVT), covering both classical probabilistic foundations and modern statistical modeling tools, with particular attention to dependence structures and applications to real data.
We begin with the fundamental limit theorems for maxima and the characterization of max-stable laws (described by the so-called Generalised Extreme-Value family of distributions). We then introduce the Point-Process approach to extremes and the Peaks-over-Threshold (POT) method (leading to the Generalised Pareto Distribution). The probabilistic foundations of extremes are followed by the statistical aspects of the theory, including parameter estimation and diagnostic techniques, all implemented in the R software. A fundamental topic of the course regards the behavior of extremes under dependence. We study how to describe the tail dependence of multiple variables and the connections with the multivariate extreme value distributions. We then address extremes of stationary sequences, including mixing conditions, the extremal index and the clustering of extreme events.

Outline

  • Fundamentals of Extreme Value Theory and Max-stable Distributions
  • Point Process Representation of Extremes
  • Peaks-over-Threshold Method and the Generalized Pareto Distribution
  • Statistical Inference: Estimation, Diagnostics
  • Tail Dependence and Multivariate Extremes
  • Extremes of Stationary Processes: Mixing, Clustering, Extremal Index
  • Applications and R Implementations

Schedule

  • 2/03, 16:30 – 18:30 (Room A)
  • 9/03, 16:30 – 18:30 (Room A)
  • 19/03, 16:30 – 18:30 (Room C)
  • 26/03, 16:30 – 18:30 (Room C)

Exam

The final assessment consists of reading and presenting a research article selected from a list provided during the course.

References

  1. Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J., Statistics of Extremes: Theory and Applications, Wiley, 2004
  2. Coles, S., An Introduction to Statistical Modeling of Extreme Values, Springer, 2001
  3. de Haan, L., Ferreira, A., Extreme Value Theory: An Introduction, Springer, 2006
  4. Resnick, S. I., Extreme Values, Regular Variation and Point Processes, Springer, 1987
Nov 192025
 

Riemann Surfaces

Prof. Roberto Mossa
University of Cagliari, Italy

Abstract

This 16-hour PhD course is devoted to algebraic functions on Riemann surfaces, following Forster’s Lectures on Riemann Surfaces up to §8 (Algebraic Functions), with emphasis on the construction of the associated Riemann surfaces and on Puiseux expansions near branch points.

In the final part we will explain how these classical tools naturally appear in recent problems in Kähler geometry, notably in the study of Nash–algebraic functions, simultaneous normalization, and rigidity of holomorphic isometries into Kähler manifolds. As a case study we will discuss the paper A. Loi, R. Mossa, Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds, Proc. Amer. Math. Soc. 152 (2024), no. 7.

Schedule

The course will take place in January-February 2026. The course consists of 16 hours divided into 8 lectures.

  • 27/01, 11:45–13:45 (Room III)

  • 28/01, 11:00–13:00 (Room C)

  • 29/01, 11:00–13:00 (Room C)

  • 30/01, 11:00–13:00 (Room C)

  • 03/02, 11:45–13:45 (Room II)

  • 04/02, 11:00–13:00 (Room II)

  • 05/02, 11:00–13:00 (Room II)

  • 06/02, 11:00–13:00 (Room C)

Exam

The final exam consists in a seminar on a topic building on the content of the course. The topic for the final exam may be proposed by the students themselves or chosen from a list provided at the end of the lectures.

 Scritto da in 19 Novembre 2025  Senza categoria  Commenti disabilitati su PhD Course: Riemann Surfaces
Set 262025
 

Insights and Algorithms for Ill-Posed Problems

Prof. Lothar Reichel and Prof. Laura Dykes
Kent State University, USA

Abstract

The aim of this course is to introduce Master’s and Ph.D. students to linear ill-posed problems. Their properties and applications will be discussed. The focus of the lectures will be on solution methods for linear discrete ill-posed problems and on the numerical linear algebra required for the solution of these problems.

While there are no prerequisites, a basic knowledge of numerical linear algebra, least squares, LU, QR and SVD factorizations, and Matlab programming will be helpful for successfully following the lessons.

Outline

  1. Linear discrete ill-posed problems: Definition, properties, applications
  2. Solution methods for small to moderately sized problems: Regularization, Tikhonov regularization, the singular value decomposition, the generalized singular value decomposition, choice of regularization matrix.
  3. Solution methods for large problems: Iterative methods based on the Lanczos process, the Arnoldi process, and Golub-Kahan bidiagonalization. Regularization by Tikhonov’s method and truncated iteration. Iterative methods for general regularization matrices.
  4. lp-lq minimization for image restoration.

Schedule

  • Monday September 29, 15-18, room B
  • Thursday October 2, 15-18, room 2
  • Friday October 3, 15-18, room 2
  • Monday October 6, 15-18, room B

The first four lectures will be broadcast on Microsoft Teams for students who cannot attend in person.

The final two lectures, each lasting two hours, will be delivered on Teams after the instructors return to their offices. The schedule will be released during the lectures.

Anyone interested in participating in the course should contact the organizers, Alessandro Buccini and Giuseppe Rodriguez.

Exam

TBA

Acknowledgements

The course is partially supported by the INdAM Visiting Professors Program.

 Scritto da in 26 Settembre 2025  Senza categoria  Commenti disabilitati su PhD Course: Insights and Algorithms for Ill-Posed Problems
Mag 232025
 

Qualitative Properties of Solutions of Uniformly Parabolic Equations

Prof. Daniele Castorina
Università di Napoli Federico II

Dott. Simone Ciani
Università di Bologna

Abstract

The course is divided in two sections:

Section 1 – Second Order Parabolic Equations (Ciani)
In the first lectures we will follow Ch. VII of [1], by setting up a definition of solution of parabolic uniformly elliptic equations. In the sequel we will prove existence and uniqueness for the Cauchy-Dirichlet problem, thanks to the method of Galerkin approximations and a priori estimates. Then we will approach regularity theory: first we will prove that the unique solution to the boundary value problem proposed improves its regularity as much as the initial value datum allows, until we reach the smoothness C-infinity by a bootstrap argument. In the last lecture, time permitting, we will comment on the lack of regularity when the coefficients and the data are rough; and give a glimpse of the possible minimal regularity properties affordable, following Chap XI-XII of [2].

Section 2 – The Alexandrov-Bakelman-Pucci method and its applications (Castorina)
The classical Alexandrov-Bakelman-Pucci (or ABP) estimate is a uniform bound for strong solutions of second order uniformly parabolic operators with bounded measurable coefficients written in nondivergence form. Its main feature is being a basic tool in the regularity theory for fully nonlinear parabolic equations. However, the ABP method is fairly general and it can be adapted to a wide variety of different issues such as obtaining a maximum principle in domains of small measure, as well as simplifying the proofs of several isoperimetric and Sobolev inequalitiees. The aim of this second part course is to introduce the ABP method in detail, discuss some of its generalizations and refinements and to give a detailed and complete overview of its applications, explicitly highlighting the improvements of using this technique with respect to previous and more classical tools.

Outline

  1. Existence and Uniqueness
  2. Regularity Theory I – Improvement of Regularity
  3. Minimal Regularity II – Hölder Continuity, Harnack inequality and Applications
  4. The Alexandrov-Bakelman-Pucci estimate
  5. The Maximum Principle in small domains
  6. The Gidas-Ni-Nirenberg Theorem and Isoperimetric and Sobolev inequalities

Schedule

  • 8/7/2025 11:00 – 13:00 and 15:00 – 17:00 room A
  • 9/7/2025 11:00 – 13:00 and 15:00 – 17:00 room A
  • 10/7/2025 11:00 – 13:00 and 15:00 – 17:00 room A

Exam

The final assessment consists of one of the two choices: a list of exercises to solve (during the course) and a seminar; or a written elaborate on selected topics of the course.

References

  1. L. Evans, Partial Differential Equations, Second Edition, AMS, 1998.
  2. E. DiBenedetto, U. Gianazza, Partial Differential Equations, Third Edition, Birkhäuser, 2023.
  3. Berestycki, H., Nirenberg, L. On the method of moving planes and the sliding method, Bol. Soc. Brasil. Mat. (N.S.) 22, 1991, 1–37.
  4. Berestycki, H., Nirenberg, L., Varadhan, S. R. S. The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47,1994, 47–92.
  5. Cabré, X. On the Alexandrov-Bakelman-Pucci estimate and the reversed Holder inequality for solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 48, 1995, 539–570.
  6. Cabré, X., Ros-Oton, X. Sobolev and isoperimetric inequalities with monomial weights, J. Differential Equations 255, 2013, 4312–4336.
  7. Cabré, X., Ros-Oton, X., Serra, J. Sharp isoperimetric inequalities via the ABP method, J. Eur. Math. Soc. 18, 2016, 2971–2998.
  8. Gilbarg, D., Trudinger, N. S. Elliptic Partial Differential Equations of Second Order. 2nd ed., Springer-Verlag, Berlin-New York, 1983.
Mar 232025
 

Introduction to Compositional Data Analysis and Modelling

Prof. Fabio Divino
Università del Molise & University of Jyväskylä

Abstract

This course introduces the fundamental concepts of compositional data analysis, including the algebraic structure of the simplex and its main properties. It will then cover the basic tools for analysis before presenting the main regression models:
(a) compositional data as a predictor;
(b) compositional data as a response variable;
(c) compositional data as both predictor and response.

All topics will be explored through hands-on lab sessions in R using real data and simulations.

Outline

  • Lecture 1: Introduction to Compositional Data Analysis. ALR, ILR, and CLR Transformations
  • Lecture 2: Descriptive Analysis in the Simplex. Introduction to Regression Models
  • Lecture 3: Regression Models with Compositional Data

Schedule

The course consists of a total of 6 hours, scheduled as follows:

  • March 17, 15:00-17:00 – Aula A
  • March 19, 11:00-13:00 – Aula A
  • March 21, 15:00-17:00 – Aula A

Exam

The final exam consists of a presentation on a specific topic covered in the course.

References

  • K. Gerald van den Boogaart & Raimon Tolosana-Delgado, Analyzing Compositional Data with R, Springer, 2013.
 Scritto da in 23 Marzo 2025  Senza categoria  Commenti disabilitati su PhD Course: Introduction to Compositional Data Analysis and Modelling
Mar 122025
 

Introduction to Algorithmic Fairness: Principles, Methods and Regulatory Perspectives

Dr. Erasmo Purificato
European Commission, Joint Research Centre (JRC), Italy

Abstract

The course provides a comprehensive introduction to algorithmic fairness, exploring key concepts such as definitions, bias characterisation and the potential sources of unfairness in machine learning models. Initially, we will thoroughly examine fairness criteria, bias detection metrics, and the limitation of fairness evaluation in binary scenarios. Then, we will analyse the emerging multiclass and multigroup approaches, and cover bias mitigation techniques and their practical trade-offs. Finally, the course will examine legal and ethical frameworks governing algorithmic fairness, with a focus on EU regulations such as the GDPR, DSA, and AI Act, as well as global policies.

Outline

  • Lecture 1: Foundation of Algorithmic Fairness
    • Why fairness matters in AI and ML
    • Defining fairness and bias
    • Potential causes of unfairness in ML
    • Fairness criteria
    • Conflicts between fairness goals
  • Lecture 2 – Measuring Bias and Fairness
    • Bias detection metrics
    • Challenges in binary scenarios
    • Extending fairness metrics to multiclass and multigroup scenarios
  • Lecture 3 – Mitigating Bias
    • Bias mitigation strategies
    • Choosing the right fairness intervention
    • Trade-offs and practical implementations
  • Lecture 4 – Legal and Ethical Frameworks for Fairness in AI
    • Overview of EU Regulations affecting AI and ML (i.e., GDPR, DSA and AI Act)
    • Fairness principles in EU Regulations
    • Fairness principles in global regulations
    • The future of algorithmic fairness and open research challenges

Schedule

The course will have a total duration of 10 hours, scheduled as follows:

  • May 21, 14:00-18:00 Aula II
  • May 22, 10:30-12:30 Aula F
  • May 22, 14:00-16:00 Aula F
  • May 23, 10:00-12:00 Aula F

Exam

The final exam consists either in a seminar presentation focusing on a specific topic studied during the course or in a test held on the last day of the course. The definitive format will be announced when the schedule is finalized. The course will be held in person. Please contact me if you are interested in joining.

References

The content of the course is based (but not limited to) the following articles:

  1. Simon Caton and Christian Haas. Fairness in Machine Learning: A Survey. ACM Comput. Surv. 56, 7, Article 166 (2024). https://dl.acm.org/doi/10.1145/3616865
  2. Corbett-Davies, Sam, Johann D. Gaebler, Hamed Nilforoshan, Ravi Shroff, and Sharad Goel. The measure and mismeasure of fairness. Journal of Machine Learning Research 24, no. 312 (2023). https://jmlr.org/papers/v24/22-1511.html
  3. Dana Pessach and Erez Shmueli. A Review on Fairness in Machine Learning. ACM Comput. Surv. 55, 3, Article 51 (2023). https://doi.org/10.1145/3494672
  4. Sahil Verma and Julia Rubin. Fairness definitions explained. In Proceedings of the International Workshop on Software Fairness (FairWare 2018). https://doi.org/10.1145/3194770.3194776
  5. Purificato, Erasmo, Ludovico Boratto, and Ernesto William De Luca. Toward a responsible fairness analysis: from binary to multiclass and multigroup assessment in graph neural network-based user modeling tasks. Minds and Machines 34, no. 3 (2024). https://doi.org/10.1007/s11023-024-09685-x
  6. Regulation (EU) 2016/679 of the European Parliament and of the Council of 27 April 2016 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing Directive 95/46/EC (General Data Protection Regulation),
    2016, OJ L119/1. http://data.europa.eu/eli/reg/2016/679/oj
  7. Regulation (EU) 2022/2065 of the European Parliament and of the Council of 19 October 2022 on a Single Market For Digital Services and amending Directive 2000/31/EC (Digital Services Act), 2022, OJ L277/1. http://data.europa.eu/eli/reg/2022/2065/oj
  8. Regulation (EU) 2024/1689 of the European Parliament and of the Council of 13 June 2024 laying down harmonised rules on artificial intelligence and amending Regulations (EC) No 300/2008, (EU) No 167/2013, (EU) No 168/2013, (EU) 2018/858, (EU) 2018/1139 and (EU) 2019/2144 and
    Directives 2014/90/EU, (EU) 2016/797 and (EU) 2020/1828 (Artificial Intelligence Act), 2024, http://data.europa.eu/eli/reg/2024/1689/oj
 Scritto da in 12 Marzo 2025  Senza categoria  Commenti disabilitati su PhD Course: Introduction to Algorithmic Fairness
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