Title: A Library for Fast Kernel Expansions with Applications to Computer Vision and Deep Learning.

Institutions: Carnegie Mellon (Pittsburgh (Pennsylvania); United States of America); City University of Hong Kong (Hong Kong).

Description:

The main contribution of the thesis is the development of a fast library for approximating kernel expansions, which enables the use of Kernel Methods in large-scale datasets. Kernel Methods are computational costly for big data, this library enables the use of nonlinear features in log-linear time. This approximation is based on the Walsh Hadamard. A SIMD implementation of the Fast Walsh Hadamard that outperforms current state-of-the-art methods has been developed. The thesis contains interesting applications to Computer Vision and Deep Learning which can serve as guideline for novel researchers in statistical learning.

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Title: Construction and Performance of Network Codes.

Institutions: Universitat Autònoma de Barcelona (Cerdanyola del Vallès, Catalunya); Universitat Politècnica de Catalunya (Barcelona, Catalunya).

Description:

The main goal of this work is to implement and provide a theoretical description for different schemes of Physical-layer Network Coding. Using a basic scheme as starting point, the project presents the construction and performance of different systems of communications with increasing complexity. The project is structured in different parts: first, an introduction to Physical-layer Network Coding and Lattice Network Codes is done. Next, the mathematical tools needed to understand the system of Compute and Forward (C&F) are presented. Further, the first basic scheme is analysed and implemented. The next step consists on implementing a vectorial C&F System and a HAMMING q-ary coded version. Finally, different approaches to improve the matrix coefficient A are studied and implemented.

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