MAIN PhD Seminars 2024

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

Sandro Gabriele Tiddia: LLM Agents: Definitions and Real-World Applications

In this seminar, we explore the concept of ‘agents’ in artificial intelligence (AI), with a particular focus on the role of Large Language Models (LLMs) in powering these systems. The seminar begins by discussing a real-world application where LLMs are used to build a question-answering (QA) system, showing how LLMs can function as ‘agents’ within such a system. We then examine various definitions of ‘agent’ across AI subfields and consider how agents interact with their environment, make decisions, and pursue goals autonomously. Additionally, we revisit earlier works on agency in AI, reflecting on their original, more profound ideas, and connect them to recent developments and applications of LLM-powered agents. The seminar concludes by exploring experiments and use cases from recent literature, highlighting the capabilities and potential of LLM agents across different domains. The goal is to provide a clear introduction to the concept of LLM-powered agents, their role in AI systems, and how this concept has evolved from theoretical foundations to practical applications.

Andrea Azzarelli: Fractional Laplacian and ADMM for glyph extraction

In archaeology it is a common task to extract incisions or glyphs from a surface. This procedure is usually done manually and, therefore, it is prone to errors and it can be extremely time consuming. In this talk we present a variational model to automatically extract these incisions from a smooth surface. We provide a procedure to generate realistic synthetic data and we show the performances of the proposed method on this kind of data.

Valentino Artizzu: End-User Development for Extended Reality: Empowering Users to Create and Understand XR Environments

In this seminar we will see how to enable individuals without prior XR development experience to create and understand XR environments. It focuses on using End-User Development (EUD) techniques to allow users to design, build, and adapt XR systems. The research specifically explores methodologies and tools for non-programmers to construct XR environments. It examines how EUD can facilitate novice developers in comprehending existing VR environments for enhancement purposes. The study further investigates how EUD can empower domain experts to tailor these environments to meet diverse requirements. Additionally, it delves into how EUD can guide domain experts in configuring XR environments to support task learning and demonstration. The goal is to provide a clear overview of the topic using the experiences and the applications developed during the three years of a PhD career.

Nicola Piras: Global and local fit measures for latent class models and extensions

Latent class (LC) analysis is a powerful and flexible statistical tool for model-based clustering with categorical data. An important task in LC analysis is the choice of the number of clusters or classes. The choice of the number of classes is a selection model problem and usually Information Criteria are considered for this purpose. These are measures that weigh model fit (log-likelihood) and model complexity (based on the number of free parameters). The LC models formulation is subject to an assumption of conditional independence between the variables involved. Adherence to this assumption and the correct estimation of the parameters is central to evaluate how well the model fits to the data. While global selection and the goodness of fit is verified through Information Criteria, model conditions must also be checked. Specific statistics can be defined that allow to verify the local independence assumption. In the literature of LC analysis the statistics considered are the Bivariate residuals. The standard LC model can be modified to handle more complex data structures, and fit measures must be adapted to the new formulations. In this talk, after having briefly discussed the results in the standard formulation, I will also present the extension to the case in which data have a multilevel cross-classified structure. This structure is present when observations are simultaneously nested within two groups, for example, children nested within both schools and neighborhoods. An application is illustrated using an Italian dataset on the evaluation of students of their degree programmes, where degree programmes are nested in both universities and fields of study.

Foundations of Digital Systems and Applications

Dr. Zsolt Ercsey
University of Pécs, Hungary

Outline

1. Introduction to internet technology
2. Comparison of the business model of mobile operating systems (Android and iOS)
3. Introduction to a mobile tv recommendation system
4. Introduction to a sport shooting scheduling system
5. Solution of a human resource allocation problem

Schedule

Please register to the course through this form.

June 24th, 9.30-11.30 Aula F
June 25th, 9.30-12.30 Aula F
June 26th, 9.30-12.30 Aula F
June 28th, 9.30-11.30 Aula F (final test)

Exam

The final exam consists in a test, which will be taken on the last day of the course.

Boundary value problems with nonsmooth and multivalued terms

Prof. Vasile Staicu
University of Aveiro, Portugal

Abstract

The aim of this course is to present some methods and tools used in the study of nonlinear boundary value problems involving multivalued maps and nonsmooth functions and illustrate those methods with some recent results concerning existence and multiplicity of solutions. The course will be given during the period April 26 – May 16, 2023, under the support of Visiting Professor Program of INdAM.

Outline

We start by introducing some notions of multivalued analysis: multivalued maps and their continuity. Then we introduce some elements of nonsmooth analysis that we use to develop nonsmooth critical point theory succeeded in extending a big part of the smooth theory to nonsmooth functionals: the main tool in the variational method for solving boundary value problems, which consists of trying to find solutions for a given boundary value problem by looking for stationary points of a real functional defined on a space of functions in which the solution of the boundary value problem is assumed to lie.

Degree theory is a basic tool of nonlinear analysis and produces powerful existence and multiplicity results for nonlinear boundary value problems. We present a generalization of Brouwer degree theory to multivalued perturbations of monotone type maps, developed in a joint paper with Aizicovici and Papageorgiou (Mem. Amer. Math. Soc., 196, 2008). Then we consider a nonlinear Dirichlet problem with nonsmooth potential (hemivariational inequality) and use variational method to prove two constant sign solutions (one positive and another negative) and then by using degree theoretical approach we prove the existence of a third one, nontrivial solution, distinct from the previous two.

We present several existence and multiplicity results, with sign information for the solutions of nonlinear boundary value problems driven by the Laplacian, the p-Laplacian and then try to extend such results to nonlinear boundary value problems driven by fractional order differential operators and to nonlocal pseudo-differential inclusions, possibly including obstacles or constraints. It is reasonable to expect that the pairing of nonlocal diffusion operators and set-valued reaction will provide a more realistic model for applications to such problems as quantum mechanics, image restoration, and financial mathematics, which typically present a high degree of uncertainty, rather than elliptic equations with smooth, single-valued reactions.

Schedule

27/4 11-13 28/4 9-11 2/5 11-13 5/5 9-11 9/5 11-13 11/5 11-13 12/5 9-11 16/5 11-13 (room F)

References

Vasile Staicu, Lecture Notes, 2023

Open questions will be considered and analyzed with the Ph. D. students.

Factorizations in monoids and rings

Laura Cossu
University of Graz

Outline

Many problems in algebra involve the decomposition of certain elements of a ring (or more generally of a monoid) into a product of certain other elements (hereinafter generically referred to as building blocks) that are in some sense minimal. The classical theory of factorization investigates factorizations in which the building blocks are atoms, i.e., non-unit elements of a monoid that are not products of two non-units. For example, it is well known that every non-zero non-unit of a Dedekind domain (more generally, of a Noetherian domain) can be written as a finite product of atoms and that in general such decompositions are not unique. On the other hand, examples of factorizations that lie beyond the scope of the classical theory include additive decompositions into multiplicative units in rings; cyclic decompositions of permutations in the symmetric group of degree n; idempotent factorizations of the “singular elements” of a monoid; and so on.

After an introductory overview of the history and main results in the classical framework, in this course, we combine the language of monoids and preorders (partial orders that are not necessarily antisymmetric) to make first steps towards the construction of a “unified theory of factorization”. In particular, we prove an abstract existence theorem that recover, among others, a classical theorem of Cohn on atomic factorizations in cancellative monoids, a classical result by Anderson and Valdes-Leon on “irreducible factorizations” in commutative monoids, but also a theorem by Erdos on idempotent factorizations of square singular matrices over fields. We also introduce a notion of “minimal factorization”, suitable for the new abstract setting, and we qualify and quantify the related non-uniqueness properties in specific cases but also in some generality. Examples will help to motivate and illustrate the theory.

Prerequisites: Standard knowledge of (basic) algebraic structures and (binary) relations.

Duration of the course: 10 hours.

Schedule

– November 28, 16:00-18:00 (Aula B)
– November 29, 16:00-18:00 (Aula A)
– November 30, 16:00-18:00 (Aula A)
– December 1, 16:00-18:00 (Aula A)
– December 2, 16:00-18:00 (Aula A)

Exam

Written. Writing of a short essay.

References

1. L. Cossu and S. Tringali, Abstract Factorization Theorems with Applications to Idempotent Factorizations, e-print (Aug. 2021), arXiv:2108.12379.
2. L. Cossu and S. Tringali, Factorization under Local Finiteness Conditions, e-print (Aug. 2022), arXiv:2208.05869.
3. A. Geroldinger and F. Halter-Koch, Non-Unique Factorizations. Algebraic, Combinatorial and Analytic Theory, Pure Appl. Math. 278, Chapman & Hall/CRC, Boca Raton (FL), 2006.
4. S. Tringali, An Abstract Factorization Theorem and Some Applications, J. Algebra 602 (2022), 352–380.