Toxic comment classification using convolutional and recurrent neural networks

This thesis aims to provide a reasonable solution for categorizing automatically sentences into types of toxicity using different types of neural networks. There are six types of categories: Toxic, severe toxic, obscene, threat, insult and identity hate. Three different implementations have been studied to accomplish the objective: LSTM (Long Short-Term Memory), GRU (Gated Recurrent Unit) and convolutional neural networks. The thesis is not thought to aim on improving the performance of every individual model but on the comparison between them in terms of natural language processing adequacy. In addition, one differential aspect about this project is the research of LSTM neurons activations and thus the relationship of the words with the final sentence classificatory decision. In conclusion, the three models performed almost equally and the extraction of LSTM activations provided a very accurate and visual understanding of the decisions taken by the network.Esta tesis tiene como objetivo aportar una buena solución para la categorización automática de comentarios abusivos haciendo uso de distintos tipos de redes neuronales. Hay seis categorías: Tóxico, muy tóxico, obsceno, insulto, amenaza y racismo. Se ha hecho una investigación de tres implementaciones para llevar a cabo el objetivo: LSTM (Long Short-Term Memory), GRU (Gated Recurrent Unit) y redes convolucionales. El objetivo de este trabajo no es intentar mejorar al máximo el resultado de la clasificación sino hacer una comparación de los 3 modelos para los mismos parámetros e intentar saber cuál funciona mejor para este caso de procesado de lenguaje. Además, un aspecto diferencial de este proyecto es la investigación sobre las activaciones de las neuronas en el modelo LSTM y su relación con la importancia de las palabras respecto a la clasificación final de la frase. En conclusión, los tres modelos han funcionado de forma casi idéntica y la extracción de las activaciones han proporcionado un conocimiento muy preciso y visual de las decisiones tomadas por la red.Aquesta tesi té com a objectiu aportar una bona solució per categoritzar automàticament comentaris abusius usant diferents tipus de xarxes neuronals. Hi ha sis tipus de categories: Tòxic, molt tòxic, obscè, insult, amenaça i racisme. S'ha fet una recerca de tres implementacions per dur a terme l'objectiu: LSTM (Long Short-Term Memory), GRU (Gated Recurrent Unit) i xarxes convolucionals. L'objectiu d'aquest treball no és intentar millorar al màxim els resultats de classificació sinó fer una comparació dels 3 models pels mateixos paràmetres per tal d'esbrinar quin funciona millor en aquest cas de processat de llenguatge. A més, un aspecte diferencial d'aquest projecte és la recerca sobre les activacions de les neurones al model LSTM i la seva relació amb la importància de les paraules respecte la classificació final de la frase. En conclusió, els tres models han funcionat gairebé idènticament i l'extracció de les activacions van proporcionar un enteniment molt acurat i visual de les decisions preses per la xarxa

Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schr\"odinger equations

We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using Fast Fourier Transforms. To split the system into the quantum harmonic oscillator problem and the remaining part allows to get higher accuracies in many cases, but it requires to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build new methods which combine the advantages of using Fourier methods while solving the timedependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition).Comment: 12 pages of RevTex4-1, 8 figures; substantially revised and extended versio

Immigrant’s Characteristics and their different effects on bilateral trade. Evidence from Spain.

This paper tests for the impact of immigration on bilateral trade using Spanish data from 1995 to 2003. It also explores some possible mechanisms behind this link. It uses a gravity equation for trade augmented with an immigrants stock variable and a set of control variables. The immigrants variable enters the estimated equation in different ways depending on immigrant relevant characteristics both individual and non individual-specific. Results show that there is a positive link between immigration and both exports and imports. We find evidence for the trade transaction cost channel but not for the preference one. The mechanisms behind this link are the information effect – immigrant’s additional information about product and about social and political institutions - and the social o ethnic network effect - immigrants with a medium level of education and those related to business activities are the one who have a positive effect on bilateral trade.International Trade, Migration.

The link between immigration and trade in developing countries

International trade can foster economic development. This paper examines the link between immigration from developing countries to OECD countries and their bilateral trade; it also explores some possible mechanism behind this link. It uses a gravity equation for trade augmented by an immigrant stock variable and a set of control variables. The immigrants’ variable enters the estimated equation in different ways depending on immigrants’ relevant characteristics both individual and non individual-specific. Results show that in developing countries there is a positive link between immigration and both exports and imports. We find evidence for the trade transaction cost channel but not for the preference one. We identify the social or ethnic network effect as the mechanism behind this link since immigrants related to business activities are the ones who have a positive effect on bilateral trade.International Trade, Migration, Economic Development.

Splitting and composition methods in the numerical integration of differential equations

We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE can be decomposed into several pieces and each of them is integrable. This class of integrators are explicit, simple to implement and preserve structural properties of the system. In consequence, they are specially useful in geometric numerical integration. In addition, the numerical solution obtained by splitting schemes can be seen as the exact solution to a perturbed system of ODEs possessing the same geometric properties as the original system. This backward error interpretation has direct implications for the qualitative behavior of the numerical solution as well as for the error propagation along time. Closely connected with splitting integrators are composition methods. We analyze the order conditions required by a method to achieve a given order and summarize the different families of schemes one can find in the literature. Finally, we illustrate the main features of splitting and composition methods on several numerical examples arising from applications.Comment: Review paper; 56 pages, 6 figures, 8 table

Does Immigration Help to Explain Intra-Industry Trade? Evidence for Spain

This paper argues and provides evidence that the stock of immigrants in a country have a positive effect on the share of its bilateral intra-industry trade (IIT). The paper links the literatures about immigration and trade and about IIT determinants. The key is that immigration contributes to trade transaction costs reduction and this would benefit more intra than inter-industry trade. We test this hypothesis using Spanish data and departing from the models developed by Helpman (1987). Immigration helps more IIT in manufactures and IIT between Spain and less developed countries. Results are robust both to different estimation methods and specifications.Intra-industry trade, immigration.

Characteristics of immigrants and bilateral trade

This paper tests the impact of immigration on bilateral trade using Spanish data from 1995 to 2003. It also explores some possible mechanisms behind this link. It uses a gravity equation for trade augmented with an immigrant’s stock variable and a set of control variables. The immigrants variable enters the estimated equation in different ways depending on immigrant relevant characteristics both individual and non individualspecific. Results show that there is a positive link between immigration and both exports and imports. We find evidence for the trade transaction cost channel but not for the preference one. The mechanisms behind this link are the information effect –immigrant’s additional information about products and about social and political institutions– and the social or ethnic network effect –immigrants with a medium level of education and those related to business activities are the ones who have a positive effect on bilateral trade.International Trade, migration

Immigrant’s Characteristics and its different effects on bilateral trade

This paper tests for the impact of immigration on bilateral trade using Spanish data from 1995 to 2003. It also explores some possible mechanisms through which the stock of immigrants in a country can contribute to its trade. It uses a gravity equation for trade augmented with an immigrants stock variable and a set of control variables. The immigrants variable enters the estimated equation in different ways depending on immigrant relevant characteristics. Results show that there is a positive link between immigration and both exports and imports. We find evidence for the trade transaction cost channel but not for the preference one. We find evidence that support that the mechanisms behind this link are the information effect - additional information about product and about social and political institutions brought by immigrants - and the social o ethnic network effect - since immigrants with a medium level of education and those who are related to business activities are the one who have a positive effect on bilateral trade.International Trade, Migration