# Tentative schedule for the courses of the XXXVIII cycle

The following courses are planned for the first two years of the cycle. The precise dates will be made available at the beginning of the academic year 2022-2023.

*Each course includes a final test to certify the knowledge and skills acquired by the students.*

### Math and Computer Science Courses

**Declarative Problem-solving with Answer Set Programming**, Prof. Francesco Ricca and Prof. Simona Perri, 3CFU*Abstract.*Answer Set Programming (ASP) is a powerful AI formalism for knowledge representation and reasoning that has been developed in the field of logic programming and nonmonotonic reasoning. After more than twenty years after the introduction of ASP, the theoretical properties of the language are well understood and the solving technology has become mature for practical applications. The high modeling power of ASP makes it ideal for solving several complex problems arising in both academic and industrial applications of AI. Problems are modeled and solved in a declarative fashion by specifying a set of logic rules and resorting to an ASP system to compute solutions. In this course, we first present the basics of the ASP language and ASP solving techniques, and, then, we concentrate on its usage for knowledge representation and reasoning in several contexts. In particular, we illustrate methodologies and tools for the development of ASP-based applications, possibly mentioning some relevant extensions of ASP for ontological reasoning, combinatorial optimization, planning, neural-symbolic reasoning, explainable AI, and more. We also report on the development of both academic and industry-level applications of ASP developed with the ASP system DLV.

**An introduction to GPGPU Programming in CUDA**, Prof. Donato D'Ambrosio, 3CFU*Abstract.*Nvidia CUDA is currently one of the most diffuse technologies and programming models for General-Purpose computing on Graphics Processing Units (GPGPU), representing one of the best options to speed up computer applications in various scientific fields, including Numerical Simulation, Artificial Intelligence, and Data Science. This course provides an operative introduction to CUDA through simple examples. It also illustrates the parallelization of the SciddicaT cellular automaton, a simple but effective Computational Fluid Dynamics (CFD) model for landslides simulations.

**An introduction to Kubernetes**, Prof. Mario Alviano, 3CFU*Abstract.*Kubernetes is widely used in data-centers to abstract away the hardware infrastructure, and to expose a whole data-center as a single enormous computational resource. Software components, often microservices, are deployed and run without having to know about the actual servers underneath. Kubernetes autonomously selects a server for each component, deploys it, and enables it to easily find and communicate with all the other components of your application. This course introduces the main concepts required to effectively develop and run applications in a Kubernetes environment.

**Inductive and deductive AI techniques: overview, limitations, innovative solutions and real-world applications**, Pierangela Bruno, Francesco Pacenza, Jessica Zangari, 3CFU*Abstract.*In recent years, AI techniques can be envisioned in two main classes: inductive and deductive ones. The course will survey some innovative approaches in both categories, also discussing their limitations. On the inductive side, the course will mainly discuss Deep Learning (DL), a widely used approach in several application scenarios thanks to its ability in identifying complex relationships within huge amounts of data and in detecting latent patterns; in particular, the course will present DL-based applications in healthcare contexts. However, the lack of proper means to explain the decision-making process is still a relevant issue in DL approaches, while deductive methods are somehow complementary, as they are often ”explainable by design”. The course will hence provide an overview of them, mostly focusing on Answer Set Programming (ASP). In particular, the course will cover very recent advancements in incremental evaluation techniques purposely conceived to further extend ASP applicability. Indeed, these new ASP features make it attractive also in real-world contexts such as Stream Reasoning.

**Artificial Intelligence in highly dynamic environments**, Prof. Giovambattista Ianni, 3CFU*Abstract.*The course introduces the audience to techniques of design and integration of automated reasoning modules in unknown environments, possibly partially structured or not structured at all, where requirements on timing performance are very strict. These environments include stream reasoning, robotic applications, and real-time videogames. The course overviews reactive reasoning systems, deliberative systems, hybridizations of these, and integration techniques in real applications; then some use cases, related to videogames and robotics are described. A collective discussion on related open and challenging research problems closes the course.

**Parallel Computing Optimization Techniques in Computational Science**, Prof. William Spataro, 3CFU*Abstract.*Computational Science is a field of Mathematics that adopts techniques, tools, and theories by exploiting the computing power of advanced parallel computers. Typical applications are found Science and Engineering, and regard among others Complex Systems, Bioinformatics, Data Science, and Modelling and Simulation in general. After a rapid overview of parallel computing and High Performance Computing paradigms, the course presents optimization techniques that are adopted to further speed-up di performances of computational models on parallel machines. As support, simple computational fluid dynamics (CFD) models, referred to landslide and lava flow simulation, are adopted to illustrate the presented methods.

**A second introduction to Algebraic Topology: the de Rham Cohomology**, Prof. Francesco Polizzi, 3CFU*Abstract.*The course is a gentle introduction to differential forms in Algebraic Topology. We intend to discuss: the de Rham complex and the de Rham cohomology; the Mayer-Vietoris exact sequence; Orientation and Integration; the Stokes' theorem; the Poincaré lemma; the de Rham-Cech complex and the de Rham-Cech isomorphism; the Künneth formula. We will also discuss some applications to the Differential Geometry of manifolds, such as the Euler-Poincaré characteristic and the Lefschetz Fixed Point Theorem.

**Classic algorithms: past, present and future**, Dott.ssa Annarosa Serpe, 3CFU*Abstract.*The course offers a historical background to algorithmic practice. Specifically, it focuses attention on the structure of Euclid’s algorithm which often represents for mathematical the prototype of the algorithmic procedure and that has relevance to date. Euclid’s algorithm can be useful not only in the search for the greatest common divisor -as described from Euclid himself- but also, by adapting the procedure, in the solution of indeterminate equations, which leads to the identity of Bézout. This algorithm allowed al-Khwarizmi (ca 780 - ca 850) to compare two ratios, or to prove that they were the same; all this appears even more clearly in the writing of the continuous fractions which have been systematically studied by Euler. Finally, what may appear surprising, the algorithm can be used in Sturm's method for determining the number of real roots of an algebraic equation.

**Metric Fixed Point Theory**, Dott. Vittorio Colao, 3CFU*Abstract.*Banach-Caccioppoli Fixed Point Theorem, also known as Contraction Principle, can be considered one of the most important and celebrated theorems in Analysis. Indeed its direct application ensures the existence, uniqueness, and iterative approximation of solutions to functional equations. Anyway, even a small relaxation of the contractive hypothesis leads into losing at least one of the above-cited properties of the solutions. Starting from the above result, we will explore several results concerning generalizations of contraction mappings in several directions. In particular, we will analyze the cases when existence and uniqueness can be recollected and explore the structure of the fixed point set. Iterative approximations will be also part of the program. Several applications to Ordinary and Partial Differential Equations and to Optimization as well as open problems will be discussed.

**Nonlinear (Finsler) Anisotropic PDEs**, Prof. Luigi Montoro, 3CFU*Abstract.*Recently great attention has been focused on the study of quasilinear elliptic equations involving the quasilinear anisotropic Finsler operator that arises in many applications. From the mathematical point of view, the anisotropy is responsible for a richer geometric structure than the classical Euclidean case. On the other hand, different applications come from several real phenomena where anisotropic media naturally arise. Motivated by this increasing interest, this course deals with an introduction to some classical arguments addressed to the problem of the existence/nonexistence and regularity of the solutions, in the Finsler framework.

**Introduction to Information Theory and Coding**, Prof. Francesco Dell'Accio, 3CFU*Abstract.*The goal of the course is to give an introduction on the Inverse Distance Weighting-Partition of Unity methods for scattered data interpolation and on their applications to the numerical solutions of PDEs by collocation. These methods are based on the Little’s observation about the possibility to improve the precision and the behavior of the classical Shepard interpolants only by fixing triangulations of the scattered nodes and by blending local linear interpolants on the vertices of triangles with Shepard like basis functions based on those triangles. The main advantage of the Little interpolants is their explicit expressions that do not make use of any derivative data (exact or approximated). Moreover, it is possible to provide algorithms for their fast computation based on a criterion of the choice of triangles (which may overlap or being disjoint) and on a searching technique to detect and select the nearest points. Further improvements of such interpolants require the solution of two main problems: the partitioning of the node set in ordered subsets that guarantees the existence and accuracy of approximation of local interpolation polynomials of fixed total degree and the possibility to compute them in a stable way. There is evidence that such interpolants are useful in the numerical solution of elliptic PDEs via collocation, due to their explicit representation in terms of the function values which reflects in a low condition number of the collocation matrix.

**Optimization under Uncertainty and Risk**, Prof.ssa Patrizia Beraldi, 3CFU*Abstract.*Several decision making problems arising in engineering, science, and economics involve uncertain parameters whose values are not known when the decisions are made. Uncertainty may arise from incomplete data, measurement errors or the inherent stochastic nature of the problems. Neglecting uncertainty can lead to inferior solutions that perform poorly in practice. The goal of this course is to introduce optimization models and methodologies for addressing uncertainty-affected decision making problems. The course will introduce fundamental techniques from stochastic programming, robust optimization, and distributionally robust optimization, also discussing the relevance of the introduction of risk measures in mathematical formulations. The theory will be presented through concrete examples from portfolio optimization and energy system management.

**The Scheduling Problems: mathematical formulations and solution approaches**, Prof.ssa Francesca Guerriero, 3CFU*Abstract.*Scheduling is the process of assigning operations to resources over time to optimize one or more criteria. It is basically a decision-making process for the allocation of resources. The objective functions used in most of the research works can be categorized as time related, job related, and multiple objectives. Scheduling problems arise in a variety of settings. More specifically, they are defined by three separate elements: the machine environment, the optimality criterion, and a set of side constraints and characteristics. In this course we will focus on flexible flow shop (FFS) scheduling problems in a complex machine environment, their variants based on several real-world constraints and multiple objectives, and exact and heuristic solution approaches. We first present the simplest machine environment and introduce a variety of optimality criteria and side constraints. Then, we introduce and discuss more complex machine environments, as FFS scheduling problems which can be generalized by two fundamental scheduling problems, i.e., the flow shop scheduling and the parallel machines scheduling problems. 1. The scheduling problems: introduction and applications; 2. Some basic mathematical formulations of scheduling problems: single objective and multi-objective; 3. Flow shop and Job shop scheduling problems: state of the art, constraints, applications; 4. Flexible job shop scheduling: state of the art, constraints; 5. Flexible job shop scheduling: exact solution approaches and heuristics.

**The Vehicle Routing Problem and its innovative variants**, Prof.ssa Francesca Guerriero, 3CFU*Abstract.*The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which aims at finding optimal routes for multiple vehicles visiting a set of locations. The VRP is one of the most important applications of optimization since it helps delivery company to plan their routes for maximizing the efficiency of the fleet and minimizing the costs. Last mile delivery, which is the last length of the delivery process, is the most expensive part of the fulfillment chain; hence optimizing the routes, avoiding failed deliveries and errors, is a challenging issue for the companies. In this course, we will focus on the VRP and its variants, using innovative technologies and paradigms, which allow to consider several real-life constraints, and pursue different, often conflicting, goals (minimizing costs, maximizing quality of service, minimizing negative environmental impacts). After introducing the VRP and the VRP with time windows, we will focus on the green VRP, the VRP with crowd-shipping, and the Drone VRP. 1. The vehicle routing problems: introduction and applications; 2. The vehicle routing problem: formulation, heuristics, and exact approaches; 3. The crowd-shipping in the delivery process: state of the art, constraints, approaches, and future perspectives; 3. The drone routing problem: state of the art, constraints, approaches, and future perspectives.

**Reading course in algebraic geometry**, Prof.ssa Concettina Galati, 3CFU*Abstract.*During the course, we will read together with the students an article or part of an algebraic geometry text. The topic of the course may vary from year to year, depending on students' interests and proposals. The course could cover classical results of Brill Neother's theory, singularity theory, rationality problems, etc. The level of the course and its content will depend on students' knowledge of algebraic geometry. Students will be required to actively participate in lectures by solving previously assigned classroom exercises or expounding part of the lecture.

### Transdisciplinary Courses:

Please check the University Catalogue available at https://www.unical.it/didattica/offerta-formativa/dottorati/attivita-didattiche-dei-corsi-di-dottorato/