The complexity and geometry of numerically solving polynomial systems

These pages contain a short overview on the state of the art of efficient numerical analysis methods that solve systems of multivariate polynomial equations. We focus on the work of Steve Smale who initiated this research framework, and on the collaboration between Stephen Smale and Michael Shub, which set the foundations of this approach to polynomial system--solving, culminating in the more recent advances of Carlos Beltran, Luis Miguel Pardo, Peter Buergisser and Felipe Cucker

Fluorescent probes for selective detection of ozone in plasma applications

This thesis presents an overview of the research activities undertaken during my PhD under the supervision of Dr. F. Iza from the School of Electronic, Electrical and Systems Engineering and Dr. B. Buckley from the Chemistry Department at Loughborough University. The thesis is divided as follows. The first chapter of the thesis presents an introduction to plasma and chemical probes as well as the motivation for developing fluorescent probes for plasma characterisation. Analytical techniques used during this work to analyse chemical substances are described in the second chapter. Results and discussions from the experiments are discussed in chapters 3 to 7. Conclusions and future work are presented in chapter 8. In chapter 9, experimental data is presented. In the last century, plasma has attracted the attention of numerous researchers. Due to the wide-range of applications of this ionised gas, people from different fields have focused their effort on studying plasma. Low-temperature plasmas have received growing attention in the last 50 years when the development in cold plasma devices made them more controllable. Plasma played (and continues to play) a critical role in the fabrication process of integrated circuits and recent advances in the generation of low-temperature atmospheric-pressure plasmas have resulted in the emergence of new applications including treatment of temperature sensitive surfaces and biological targets. During the first months at Loughborough I worked on the ozonolysis of various alkenes with air plasmas. This allowed me to familiarised myself with plasma as this was new to me and get a feeling of some of the challenges lying ahead. Nonetheless, the data I obtained was encouraging and I presented the results of batch and flow plasma-based ozonolysis of alkenes at the Technological Plasma Workshop held in Manchester in January 2012. Once I had familiarised myself with the plasma system, I worked on synthesising fluorescent probes to detect ozone, one of the many reactive species that are typically generated in oxygen containing plasmas. Details of the experiments conducted to date and most significant findings are discussed in this thesis

Elucidating Nucleation and Growth Behavior of Single-Walled Carbon Nanotubes obtained via Catalyzed Synthesis

The catalytic growth of single-walled carbon nanotubes (SWCNTs) is studied using reactive molecular dynamics (RMD) simulations and density functional theory (DFT) calculations. Computational calculations are performed in order to achieve a better understanding of the catalytic reaction mechanism at the initial stages of synthesis, where most of the structural characteristics are defined. Different process variables such as catalyst chemical composition and size, temperature, pressure, and the nature of catalyst support, can be optimized with the purpose of tuning the structure and physical properties of SWCNTs. Controlling the structure of SWCNTs during synthesis and avoiding additional purification and/or separation processes are critical for the direct use of SWCNTs in electronic devices. RMD simulations demonstrate that small catalyst particles favor the growth of lengthy nanotubes over catalyst encapsulation as a result of an increase of the curvature energies of the carbon capsule. Furthermore, simulations performed over deposited catalyst particles demonstrate that the catalyst-support adhesion must be controlled in order to grow nanotubes with high structural quality and avoid catalyst poisoning. Results herein reported suggest that growth conditions must be optimum to minimize the nucleation of topological defects in nanotubes. RMD trajectories prove the vital role played by the catalyst surface in healing defects via adsorption and diffusion. These results significantly impact the field of chirality control since the presence of defects introduce misorientation of hexagons, shifts the overall chiral angle, and therefore, modifies the physical properties of the nanotube. DFT calculations are employed to evaluate the interaction between SWCNTs and the ST-cut quartz substrate. The outstanding performance of CNT-based FET relies on the alignment of the horizontally grown nanotubes on silica substrates, as well as on the selective growth of semiconducting nanotubes. It is demonstrated that finite-length zigzag nanotubes are adsorbed stronger than armchair tubes on the quartz support. This suggests that the nanotube electronic band structure is a key factor on the preferential adsorption of zigzag tubes. DFT calculations suggest that patterns of unsaturated silicon atoms of silica surfaces define the crystallographic directions of preferential alignment. These patterns might be chemically altered in order to favor other directions of alignment

musicaiz: A Python Library for Symbolic Music Generation, Analysis and Visualization

In this article, we present musicaiz, an object-oriented library for analyzing, generating and evaluating symbolic music. The submodules of the package allow the user to create symbolic music data from scratch, build algorithms to analyze symbolic music, encode MIDI data as tokens to train deep learning sequence models, modify existing music data and evaluate music generation systems. The evaluation submodule builds on previous work to objectively measure music generation systems and to be able to reproduce the results of music generation models. The library is publicly available online. We encourage the community to contribute and provide feedback

Inserción de Colombia en la Cuenca del Pacifico: el nuevo eje de la economía mundial

El comercio internacional ha presentado, a lo largo de los años, un fuerte dinamismo que ha impulsado a las naciones del mundo ha desarrollar distintas estrategias para afrontar las nuevos cambios y desafíos que ha traído consigo la globalización. El centro económico mundial se ha trasladado, en el pasado, del Mediterráneo al Atlántico, y hoy parece seguir una nueva tendencia hacia el Pacífico. El enorme potencial de su mercado y los grandes avances para la cooperación comercial que se han logrado entre los países que conforman la Cuenca del Pacífico, confirma la importancia de esta región, que se ha convertido en el nuevo epicentro económico mundial. Colombia cuenta con una posición geográfica privilegiada que le permite tener un fácil acceso al comercio con los países de la Cuenca. Sin embargo, su inserción a este mercado ha sido débil y tardío, si se compara con otros países de América Latina como Chile, que cuenta con una participación activa en este bloque económico desde hace varias décadas. Es necesario, de esta manera, que el país implemente estrategias enfocadas a lograr un cambio en el enfoque en su política exterior, que le permita fortalecer las relaciones comerciales con la otras naciones que hacen parte de la Cuenca del pacífico, para aprovechar eficazmente las oportunidades y ventajas que se presentan en este mercado y que pueden ser determinantes para el desarrollo económico del país en el futuroThe international commerce has presented, over the years, a strong dynamism that has driven all nations over the world to develop different strategies to face the new changes and challenges that have come along with the process of globalization. The world´s economic center has moved for the Mediterranean to the Atlantic, in the past, and it seems that it follows a new trend towards the Pacific. The great potential of its market and the significant progress of the commercial cooperation between the countries within the Pacific basin, confirms the importance of this region that has become the new global economic center. Colombia has a privileged geographical position that provides the country with an important access to the commerce within the basin. However, its inclusion in this market has been weak and delayed, compared with other Latin American countries such as Chile, which has an active participation in this economic bloc through the past few decades. It has become necessary, that the country sets up new strategies aimed to achieve a change in its foreign policy. Theses will strengthen the commercial relations with other nations from the Pacific Basin, to take advantage of the opportunities that are present in this market and that can be crucial for the future economic development of the country