### Recent Submissions

• #### Numerical modelling of the growth of glioblastoma cells in microfluidic devices ﻿

(Universitat Politècnica de Catalunya, 2022-06)
Master thesis
Open Access
Glioblastoma Multiform tumour (GBM) is the most common and aggressive of the primary gliomas. Therefore, special efforts are focused on the development of new drugs and therapies that can lead to a better prognosis. To ...
• #### Rings of differential operators on singular varieties ﻿

(Universitat Politècnica de Catalunya, 2022-07)
Master thesis
Open Access
This project will be centered in the study of rings of differential operators on singular varieties and the theory of D-modules. We will start with the ring of k-linear differential operators on a polynomial ring. We will ...
• #### Trajectory based map quality evaluation ﻿

(Universitat Politècnica de Catalunya, 2022-05)
Master thesis
Open Access
In this Thesis we approach a problem related with map generation. Automatically generated maps still have some room to improve in terms of precision or consistency. This is why we decided to study a method that could ...
• #### Asymptotics in the schema of simple varieties of trees ﻿

(Universitat Politècnica de Catalunya, 2022-05)
Master thesis
Open Access
We study the functional equation y(x) = xA(y(x)) satisfied by the generating functions in the schema of simple varieties of trees. The radii of convergence r, R of y, A respectively satisfy y(r) <= R. In the subcritical ...
• #### Control of synchronization phenomena in Complex Networks: The Kuramoto Model ﻿

(Universitat Politècnica de Catalunya, 2022-05)
Master thesis
Open Access
Covenantee:   Universitat Rovira i Virgili
The notion of Control in Complex Systems has started almost 60 years ago by Kalman. However, the results obtained were not sufficient for systems with complex topologies (Complex Networks) and non-linear dynamics. Thanks ...
• #### Shorter secret keys in multivariate cryptography through optimal subspace representations ﻿

(Universitat Politècnica de Catalunya, 2022-05)
Master thesis
Open Access
La criptografia multivariant (MVQC) és, actualment, una de les famílies d'esquemes criptogràfics més prometedores en l'àmbit postquàntic. Tanmateix, amb freqüència pateix de claus d'una mida excessiva o suposicions de ...
• #### Enumeration of chordal planar graphs and maps ﻿

(Universitat Politècnica de Catalunya, 2022-05)
Master thesis
Open Access
We determine the number of labelled chordal planar graphs with $n$ vertices, which is asymptotically $c_1\cdot n^{-5/2} \gamma^n n!$ for a constant $c_1>0$ and $\gamma \approx 11.89235$. We also determine the number of ...
• #### Solutions of linear equations in pseudorandom sets ﻿

(Universitat Politècnica de Catalunya, 2022-01)
Master thesis
Open Access
A common theme in modern combinatorics consists in proving sparse analogues of results known in the dense setting. We review some of these for linear systems of equations. We first prove sparse analogues for random sets ...
• #### Lung cancer model calibration using linearly constrained optimization ﻿

(Universitat Politècnica de Catalunya, 2022-01)
Master thesis
Open Access
When modeling cancer evolution to simulate possible future prevention strategies, it is of great importance to calibrate the model to make sure that it reproduces properly the present situation. This leads to a constrained ...
• #### On the number of periodic orbits in billiards with flat points ﻿

(Universitat Politècnica de Catalunya, 2022-01)
Master thesis
Open Access
A billiard is a map that describes the motion of a ball without mass in a closed region on the plane such that the collisions with the boundary are elastic. The region where the ball moves is the billiard table. In this ...
• #### Hopf and Neimark-Sacker bifurcations: applications to discrete-time hypercycles with functional shifts ﻿

(Universitat Politècnica de Catalunya, 2021-10)
Master thesis
Open Access
Hypercycles are cyclic catalytic sets of replicating macromolecules, where each one of the species catalyzes the replication of the next species of the set. This system has been widely studied within the framework of origins ...
• #### Efficient deep ensembles by averaging neural networks in parameter space ﻿

(Universitat Politècnica de Catalunya, 2021-10)
Master thesis
Open Access
Although deep ensembles provide large accuracy boosts relative to individual models, their use is not widespread in environments in which computational constraints are limited, as deep ensembles require storing M models ...