Programa de Doctorat en Matemàtica Aplicada: Recent submissions
Now showing items 21-40 of 200
Mathematical and computational modeling of active cellular flows
(English) During development, cellular tissues undergo dramatic reconfigurations as a result of organized flows driven by active forces. Depending on the system, cellular flows and active forces can be understood from a ...
Mechanics of epithelial tissue subjected to controlled pressure
(English) Epithelial sheets form specialized 3D structures suited to their physiological roles, such as branched alveoli in the lungs, tubes in the kidney, and villi in the intestine. To generate and maintain these structures, ...
Theta correspondences and arithmetic intersections
(English) The thesis is mainly divided into two parts. In essence, the first one is an extension of the paper [Ter22]. Using the regularized Siege-Weil formula of [GQT14] we obtain an explicit expression for the truncated ...
First order logic of random sparse structures
(English) This work is dedicated to the study several models of random structures from the perspective of first-order logic. We prove that the asymptotic probabilities of first-order statements converge in a general model ...
A theoretical and computational study of the active self-organization of nematic patterns in thin cytoskeletal layers and their effect on curvature
(English)The structure and dynamics of important biological systems, ranging from cytoskeletal gels to tissues, are controlled by an interplay between activity, dissipation, nematic order, density, and geometry. In particular, ...
Lattice-based zero-knowledge proofs of knowledge
(English) The main goal of this dissertation is to develop new lattice-based cryptographic schemes. Most of the cryptographic protocols that each and every one of us use on a daily basis are only secure under the assumption ...
Metric-aware optimization of high-order meshes for curved adaptivity
(English) To enhance the simulation accuracy when the solution presents sharp curved features, the community of high-order methods has started to curve not only the boundary but also the interior of unstructured high-order ...
Nodal distributions on the high-dimensional simplex for high-order interpolation and integration
(English) To simulate unsteady phenomena on complex moving geometry, computational scientists and engineers have been interested in unstructured space-time discretizations. These space-time discretizations aim to overcome ...
Robotic manipulation of cloth: mechanical modeling and perception
(Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present ...
Homoclinic and chaotic phenomena to L3 in the restricted 3-Body Problem
(English) The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies, called the primaries. If the primaries perform circular motions and the ...
Conformal n-dimensional bisection for local refinement of unstructured simplicial meshes
[English] In n-dimensional adaptive applications, conformal simplicial meshes must be lo cally modified. One systematic local modification is to bisect the prescribed simplices while surrounding simplices are bisected ...
Multiscale clutch models for cell mechanics
Integrin-based cell adhesion is a key mechanism in fundamental biological processes such as cell migration and wound healing, and in diseases like osteoporosis and cancer. For example, during migration, cells form adhesion ...
Local preconditioning for parallel iterative solvers
This thesis aims at improving the convergence of iterative solvers, used for algebraic systems coming from the discretization of partial differential equations (PDE), in the context of large scale simulations and high ...
Disentangling ecological networks in marine microbes
There is a myriad of microorganisms on Earth contributing to global biogeochemical cycles, and their interactions are considered pivotal for ecosystem function. Previous studies have already determined relationships between ...
p-adic L-functions, p-adic Gross-Zagier formulas and plectic points
In this work we generalize the construction of p-adic anticyclotomic L-functions associated to an elliptic curve E/F and a quadratic extension K/F, by defining a measure µ_f^p attached to K/F and an automorphic form. In ...
Probabilistic and extremal studies in additive combinatorics
The results in this thesis concern extremal and probabilistic topics in number theoretic settings. We prove sufficient conditions on when certain types of integer solutions to linear systems of equations in binomial ...
Geometrical aspects of contact mechanical systems and field theories
Many important theories in modern physics can be stated using the tools of differential geometry. It is well known that symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits ...
Threshold phenomena involving the connected components of random graphs and digraphs
We consider some models of random graphs and directed graphs and investigate their behavior near thresholds for the appearance of certain types of connected components. Firstly, we look at the critical window for the ...
A census for curves and surfaces with diophantine stability over finite fields
An algebraic variety defined over a field is said to have Diophantine stability for an extension of this field if the variety does not acquire new points in the extension. Diophantine stability has a growing interest due ...
A study on structure recovery and the broadcasting problem
The thesis contains a study of two problems of combinatorial statistics. The first one is structure learning for partial correlation graphs and the second one is the broadcasting problem on certain families of random ...
