Discrimination in the Private Sphere. A subjective Right or a Legal Abuse. An European North American Legal Comparative Study

En el presente trabajo se estudian los límites de la autonomía privada desde la perspectiva del derecho a la igualdad y del principio de no discriminación tanto en el derecho norteamericano como en el europeo, con especial incidencia a la doctrina española. Por un lado se plantea si la piedra angular a la hora de establecer límites a la autonomía privada debe ser el concepto de dignidad o el de igualdad, por otro superando dicho debate se propone un acercamiento al problema entendido como una colisión entre derechos fundamentales en la que en cada concreto supuesto ha de estudiarse cual debe prevalecer. Finalmente se estima conveniente seguir el modelo de la Constitución de Sudáfrica y entender que los derechos fundamentales afectan directamente tanto a las relaciones horizontales como verticales, es decir tanto al ámbito público como privado.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Sliding Window Persistence of Quasiperiodic Functions

A function is called quasiperiodic if its fundamental frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window point clouds of such functions can be shown to be dense in tori with dimension equal to the number of independent frequencies. In this paper, we develop theoretical and computational techniques to study the persistent homology of such sets. Specifically, we provide parameter optimization schemes for sliding windows of quasiperiodic functions, and present theoretical lower bounds on their Rips persistent homology. The latter leverages a recent persistent K\"{u}nneth formula. The theory is illustrated via computational examples and an application to dissonance detection in music audio samples.Comment: 31 pages, 11 figure

How to leverage outward FDI for development? A six-step guide for policymakers

OFDI can increasingly serve as an additional channel for countries to achieve their development goals. This Perspective proposes a six-step framework to help policymakers think through how best to facilitate, support and promote OFDI to maximize the benefits for the home economy

FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way that the base space accounts for the large scale topology, while the fibers account for the local geometry. This allows one to reduce the dimensionality of the fibers, while preserving the large scale topology. We formalize this point of view and, as an application, we describe a dimensionality reduction algorithm based on topological inference for vector bundles. The algorithm takes as input a dataset together with an initial representation in Euclidean space, assumed to recover part of its large scale topology, and outputs a new representation that integrates local representations obtained through local linear dimensionality reduction. We demonstrate this algorithm on examples coming from dynamical systems and chemistry. In these examples, our algorithm is able to learn topologically faithful embeddings of the data in lower target dimension than various well known metric-based dimensionality reduction algorithms