http://elea.unisa.it/xmlui/handle/10556/3005 2026-04-14T11:30:38Z 2026-04-14T11:30:38Z Serra, Domenico http://elea.unisa.it/xmlui/handle/10556/7330 2025-04-30T17:43:48Z 2023-02-14T00:00:00Z

Hidden Structures and Conflicting Items in Combinatorial Optimization Problems Serra, Domenico Combinatorial optimization-based methods are widely used to solve complex real life problems. In this thesis, we use some of these methods for addressing several emerging combinatorial opti- mization problems on graphs that can be classified in two macro areas: i) graph substructures identification problems; ii) combinatorial optimization problems with conflict constraints. In graph theory, graphs are defined as mathematical structures that describe entities of inter- est (as nodes) and their relationships (as edges). Many real-world problems can be described through the use of a graph. For example, graph theory finds application in: i) the context of social network analysis, where graphs are used to represent the interactions (edges) between users (nodes); and in ii) the study of biological networks, such as protein-protein interaction, where the nodes are proteins, and the edges represent their physical interactions. In graph analysis one common application is the identification of clusters (or communities) of nodes that are tightly connected. In social networks, a community could represent a set of users sharing the same interest, while in the protein-protein interaction networks it could represent a set of very similar proteins forming a protein complex. In this thesis, three problems related to identifying graph substructures have been tackled. The first problem addresses the 2-Edge-Connected Minimum Branch Vertices, that finds ap- plication in the design of optical networks. A graph is 2-Edge-Connected if by removing one edge, the graph is still connected. The problem looks for a spanning 2-edge connected subgraph having the minimum number of branch vertices that is vertices with degree strictly greater than two. In these networks, branch vertices are associated with switch devices that split the light signals and send them to the adjacent vertices. For this NP-complete problem we developed a genetic algorithm using ad-hoc designed operators. The second addressed problem arise in the social network analysis and aims to study how users influence the choices of their neighbours. In particular, we addressed the Collapsed k-Core Problem that seeks to identify a subset of critical users in the network whose choices would alter the cohesiveness of a community. To the best of our knowledge, this is the first attempt to formulate this problem using mathematical programming. We implemented multiple solution approaches and compared them on a set of benchmark instances. The last case studied is related to network clustering, where a cluster graph is a disjoint union of cliques. The Cluster Deletion problem is defined as the identification of the minimum number of edges to remove from a network to produce a cluster graph. This is a well-known NP-hard problem and we faced it using integer linear programming formulation and a heuristic approach based on edge contraction operation. Our results show the effectiveness of our methodology both on artificial and real-world biological networks. 4 Currently, the definition of many real-life problems, doesn’t always fully capture their com- plexity. Indeed, classical optimization problems encountered over the years, although extensively studied, do not always take into account additional limitations, such as incompatibility situa- tions, encountered in real-world problems. In this context, two or more elements of the problem cannot be chosen together to compose a feasible solution. Such incompatibilities are modelled by introducing conflict constraints in classical combinatorial optimization problems, leading to more realistic but often harder problems. Finally, three different combinatorial optimization problems with conflicts constraints are addressed. The first one is a variant of the set cover problem where pairwise conflicts are added among the subsets. In the formulation of this problem, two sets in conflict can belong to the same solution, provided that a non-negative penalty is paid. We introduced two mathematical formu- lations for the problem and offered a parallel Greedy Randomised Adaptive Search Procedure for its solution. The performance of our algorithm was evaluated through an extensive set of experiments. The results shown the effectiveness and efficiency of our methodology compared to the mathematical model solutions. The second problem is related to the Maximum Flow Problem with Conflict constraints on the edges, for which we present a matheuristic method based on the combination of two different approaches: Carousel Greedy and Kernel Search. The results shown that the Carousel Greedy selection substantially improves the effectiveness of the Kernel Search. The last problem is the Minimum Spanning Tree with Conflicts, that we solved by using a Kernel Search method. Also in this case, the results on benchmark instances shown that our methods identifies a better solution compared with existing methods. [edited by Author] 2021 - 2022

2023-02-14T00:00:00Z Rota, Paolo http://elea.unisa.it/xmlui/handle/10556/7328 2025-04-30T17:43:36Z 2023-04-17T00:00:00Z

Advanced Modeling of Microlensing Events Rota, Paolo The search for exoplanets is one of the most exciting challenges. From the first exoplanets discovered around the pulsar PSR B1 257+12 back in 1992 until today there are over 5200 exoplanets discovered. And the number will continue to rise in the coming years with the advent of the latest generation telescopes. There are various techniques for finding exoplanets such as transit, radial velocity, pulsar timing, direct imaging etc. But among these, gravitational microlensing is one of the most fascinating. Gravitational microlensing is a particular technique to detect exoplanets otherwise unavailable with other techniques such as transits or radial velocity. We have a microlensing event when the light from a distant source is deflected by a lens passing through the source and the observer. The result, in the simplest case, is a bell-shaped peak in the light curve. Planets can be detected studying the anomalies in the lightcurve (additional peaks or dips, longer distortions, etc.). But microlensing is not important only for exoplanets. The fact that with this technique it is possible to reach distances of the order of the galactic center allows us to discover objects ranging from the disk to the bulge allowing us to have a much more complete overview of the study of the stellar populations of our galaxy. And in particular with the study of binary systems we can detect faint objects that are impossible to reveal with other techniques, such as brown dwarfs, mysterious objects of which little is known yet and which are presumed to populate our galaxy in great abundance. Microlensing is undoubtedly the best method to discover these objects, since having extremely low luminosities they are difficult to see with telescopes except when they play the role of lens. Moreover, in some cases the orbital motions of the system can also be detected, allowing us to study their dynamics in more detail. The typology of microlensing events is enormous and in this thesis we will analyze some of the cases that can occur. In the first part we focus on the fundamental concepts of microlensing theory for the exoplanets search. The second part is dedicated to the modeling of microlensing events, which is based on the VBBinaryLensing code. In the third part we analyze some microlensing events, each with certain characteristics, to highlight how vast the case history of these events is. Finally there will be the conclusions where the results achieved and future prospects are discussed. [edited by Author] 2021 - 2022

2023-04-17T00:00:00Z Veronesi, Ilaria http://elea.unisa.it/xmlui/handle/10556/7309 2025-04-30T17:40:34Z 2023-05-16T00:00:00Z

The use of technologies in Mathematics Education research paths in the “Mathematical High School” Project Veronesi, Ilaria In the last twenty years the school has been hit by a succession of disruptive and unknown innovations. In particular, there is institutional talk for the first time of ascertaining competences in DPR 323-98 (reform of the state examinations of secondary school). Leaving aside the various indications that have followed one another very quickly, in the Regulations for the Reorganization of Higher Institutes (DPR 87, 88 and 89 of 2010) a disciplinary system centered on competences is envisaged, followed by the relative ministerial indications. Finally, we come to the much-discussed Law 107 of 2015 in which it is provided that the activity of School-Work Alternation is extended to all three-year courses of high schools. The PNSD states that “digital technologies intervene to support all dimensions of transversal skills. But they also fit vertically, as part of the literacy of our time and fundamental skills for a full, active and informed citizenship”, as anticipated by the Recommendation of the European Parliament and the Council of Europe and as even better emphasized by frameworks such as the 21st Century Skills, promoted by the “World Economic Forum” (Bellanca 2010). In fact, the S.T.E.M. curriculum incorporates the “four C’s” of 21st-century skills: creativity, critical thinking, collaboration and communication. Students work together to create innovative solutions to real-world problems and communicate their solutions with others. As they carry out their investigations and projects, they must access, analyze, and use the information they need to complete the learning tasks. While working through the task, students build important life and career skills by learning to manage their time, to become self-directed workers and to collaborate effectively with others. Using appropriate technology tools to complete their task, students discover the most effective and efficient ways to access and manage the world of digital information that is available to them (Beers 2011). The importance of new skills not included in the traditional school curricula was highlighted in numerous teaching conferences where it was emphasized that “Exemplary science education can offer a rich context for developing many 21st-century skills, such as critical thinking, problem-solving, and information literacy. These skills not only contribute to a well-prepared workforce of the future but also give all individuals life skills that help them succeed.” (NSTA 2011) The choice of the research group in mathematics education of the Department of Mathematics of the University of Salerno to develop educational paths that exploit the potential of technological tools for the training of teachers and laboratory activities for students of upper secondary school, is the natural evolution of an educational Didactic Design aimed at developing models and paths that can be proposed in the classroom thanks to the help of new technologies. The research group has been involved for years in updating the teaching of mathematics by bringing to the center of educational choices the close interconnection between the various disciplines and in particular the role of mathematics as a bridge between the two cultures, the scientific and the humanistic. In this interdisciplinary key that aims to become transdisciplinary, new technologies have the important task of allowing the reworking of in-depth paths on the various curricular themes through a laboratory activity and in particular experimental research. This vision of mathematics as a link between the various cultural areas and new technologies as the key to activating these interconnections, led the didactic research group in mathematics of Salerno to develop numerous training proposals at various levels. My research project in mathematics teaching aimed to • deepen the interrelationships of mathematics with other disciplinary areas, • prepare both informative and technical teaching material, both in the traditional format of dossiers and handouts • organize and structure educational paths for skills that provide for the presence of "mathematics with...”, or not monothematic paths where mathematics is linked to physics and chemistry, but transdisciplinar paths that tie mathematics to all the disciplines of the curriculum. In particular, the importance of mathematics in various historical contexts, in philosophical processes, interconnections with literature, art, music, religions, sport... • implement the use of new technologies and new learning processes also thanks to dedicated hardware and software. Young people are commonly called "digital natives", they are used to living with computer technology much more than previous generations and it is appropriate that they also find it in study paths, in order to learn that even non-"dedicated" tools can be portable laboratories (exactly as twenty years ago scientific calculators supplanted logarithmic and trigonometric tables ...). Inevitably the future will lead to an increasingly pushed and exasperated use. It therefore becomes essential that the world of education uses and makes its own the available tools and transforms them into an "accelerator of interest": only if teachers and students speak the same language, they can communicate. [edited by the Author] 2020 - 2021

2023-05-16T00:00:00Z Tedesco, Antonio http://elea.unisa.it/xmlui/handle/10556/7291 2025-04-30T17:38:28Z 2023-01-02T00:00:00Z

Orbital motion, periastron advance and galaxy rotation curves beyond General Relativity Tedesco, Antonio The Extended Theories of Gravity (ETG) have become one of the most investigated the- oretical proposals among the alternative explanations for the observed flatness of galaxy rotation curves, related to the dark matter problem, as well as for the accelerated expan- sion of the universe, related to the dark energy problem. The reason lies in the fact that ETG’s can provide predictions consistent with the observational surveys without implicating invisible matter. In this framework, these phenomena are explained as a physical manifes- tation of extra-curvature terms of the geometry of the Universe. In the first part, we focus on this class of theories which are a curvature-based extension of GR. Higher order scalar curvature invariants are included in the Einstein-Hilbert action giving rise to the Higher Order Theories and corresponding field equations. For the extension of GR, we consider the Scalar-Tensor-Fourth-Order Gravity (STFOG) in metric formalism as a representative general class for the ETG, obtained from combination of Fourth Order Gravity plus a cou- pled scalar field. The NonCommutative Spectral Gravity is a special case of STFOG. Other Higher Order Theories, like the f(R)-gravity models, are sub-classes of it. In this scenario to analyse the orbital motion of interacting objects constituting astro- physical gravitating systems, like the Solar System or galaxies, is a very important issue for making new predictions and testing theories. We discuss the fundamentals of the physical regime given by the Weak Field limit, Newtonian and Post-Newtonian limits, and their cor- responding expansions as a mathematical procedure to solve the field equations in STFOG. This makes it possible to deal with the problems of motion for a system of many parti- cles and reproduce many physical configurations. We solve the linearized field equations of STFOG stemming from the weak field limit, and this is done in the Standard Post- Newtonian gauge, which is the suitable choice for the purpose. Then we find the space-time metric and the potentials connected to each metric component that give rise to the gravi- tational field. Their behaviour presents a modification to the Newtonian potential induced by the Yukawa-like potential terms (5th force) of the type V (r) = α e−βr r . Finally, in the context of the STFOG, we determine the relativistic Lagrangian leading to the equations of orbital motion for a system of N-body and involving the Post-Newtonian fields. This allows 1 to find out the equations governing the dynamics of a generic N-body system, like those in the Solar System, binary systems (when N = 2) or possibly the S-stars cluster around Sagittarius A*, thus providing a theoretical reference for Relativistic Celestial Mechanics beyond General Relativity and the possibility to study realistic astrophysical models and gravitational tests. In the second part, we expose the problem of anomalistic precession and deal with the analysis of the periastron shift. We consider the Adkins & MacDonell integrals and making use of the data coming from the precession of planets, we deduce constraints on the param- eters of the STFOG, therefore also of Non-Commutative Spectral Gravity (NCSG) (as par- ticular case), including a study for the Quintessence Field (deformation of the Schwarzschild geometry induced by a dark energy) related to a power-law potential. We show that the periastron shift of planets allows us to improve the bounds on the range of interaction β by several orders of magnitude. Then we develop a new resolution method for the determina- tion of the periastron advance by relying on the epicyclic perturbation, which includes also the Post-Newtonian contributions and can be applied to theories beyond GR like the ETG, or models within, without the necessity of numerical integration. Using it, we obtain the final results and then deduce the full analytic expressions for the advance relative to the examined ETG. We carry out the preceding analysis once more, and further improvements on the bounds are achieved. In the last part, by resorting to the Newtonian limit, we provide the theoretical galaxy rotation curves in the context of the f(R)-theory, the more general STFOG and the a NonCommutative Spectral Gravity. Therefore, the first analysis of galaxy rotation curves in NCSG is conducted. Through the parametric fits with observed data, we derive direct predictions on the physical parameters (total mass and mass-to-light ratio) for an unexplored sample of spiral galaxies of the THINGS catalogue. Good reproductions are obtained for these theories as well as numerical predictions on the physical parameters characterizing a galaxy. The predictions are directly comparable with the observations. We compare the numerical outcomes for the metric f(R)-theory with those of the Palatini formalism and, in the end, we make a comparison of the results relative to the examined ETG with the observed astronomical estimations. [edited by Author] 2021 - 2022

2023-01-02T00:00:00Z