Els meus projectes
Càlcul d'òrbites periòdiques
Funcions i llibreries en C per trobar numèricament òrbites periòdiques d'alta precisió, com l'òrbita halo del punt de Lagrange L1 en el Problema Restringit de Tres Cossos (RTBP).
Codi FontQuatre en ratlla
Implementació en llenguatge C del clàssic joc del Quatre en Ratlla, dissenyat per ser executat en un terminal d'entorns Unix. L'oponent (ordinador) utilitza l'algorisme MiniMax amb optimitzacions.
Codi FontUnknotting number RL
A model that learns to solve a classic problem in low-dimensional topology: determining the unknotting number of a knot. The agent is trained using Deep Reinforcement Learning techniques to find a sequence of moves that simplifies a knot, represented as a braid word, into the unknot.
Codi FontSimulador de Partícules
Un simulador bàsic de N-cossos construït amb C i la llibreria Raylib per a la visualització. Explora la interacció gravitatòria entre partícules en un entorn 2D.
Codi FontTreballs de final de grau
Desfent nusos amb machine learning
In knot theory, a fundamental invariant is the unknotting number, denoted u(K), which is the minimum number of crossing changes required to transform a given knot K into the trivial knot (the unknot). Calculating this number is computationally hard (NP-hard). This project frames the unknotting problem as a game that a Reinforcement Learning agent can learn to play. The "game board" is the knot's representation as a braid word, and the "moves" are topological operations that preserve the knot type or simplify its structure.
Document PDFSymbolic ordinal analysis to explore the properties of the logistic map
Symbolic ordinal analysis has emerged as a recent technique to explore and characterize the statistical properties of complex data series and systems. Essentially, the idea is to discretize consecutive values of the data series into a reduced phase space of symbols according to their values. Despite its simplicity, such method allows one to map complex system dynamics into a low-dimensional space so turning their analysis feasible and often revealing nontrivial regular patterns that remain unperceivable from the original series. The objective of the work is to provide a general overview about the foundations of this technique and explore its applicability to a paradigmatic model of chaos and complexity, as is the logistic map.
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