A Note on Support Vector Machines Degeneracy

When training Support Vector Machines (SVMs) over non-separable data sets, one sets the threshold $b$ using any dual cost coefficient that is strictly between the bounds of $0$ and $C$. We show that there exist SVM training problems with dual optimal solutions with all coefficients at bounds, but that all such problems are degenerate in the sense that the "optimal separating hyperplane" is given by ${f w} = {f 0}$, and the resulting (degenerate) SVM will classify all future points identically (to the class that supplies more training data). We also derive necessary and sufficient conditions on the input data for this to occur. Finally, we show that an SVM training problem can always be made degenerate by the addition of a single data point belonging to a certain unboundedspolyhedron, which we characterize in terms of its extreme points and rays.

Vector Fields

Exercises and solutions about vector fields. Diagrams for the questions are all together in the support.zip file, as .eps files

Vector Calculus

Exercises and solutions about vector calculus

Vector functions and curves

Exercises and solutions about vector functions and curves.

Adobe Photoshop : Adjustment and Fill Layers

Find out more about Photoshop Adjustment and Fill Layers with this share of video tutorials.

Uffington White Horse vector art files

Vector graphic files for the Uffington White Horse in PDF, AI (Adobe Illustrator EPS) and SVG formats. I manually traced these from a photo using Xara Xtreme.

University Logo in Vector and Raster

This is a selection of University of Southampton Logos in both vector (svg) and raster (png) formats. These are suitable for use on the web or in small documents and posters. You can open the SVG files using inkscape (http://inkscape.org/download/?lang=en) and edit them directly. The University logo should not be modified and attention should be paid to the branding guidelines found here: http://www.edshare.soton.ac.uk/10481 You must always leave a space the width of an capital O in Southampton on all 4 edges of the logo. The negative space makes it appear more prominently on the page.

University Logo in Vector and Raster (Smoother Version)

These are a range of logos created in the same way as Mr Patrick McSweeny http://www.edshare.soton.ac.uk/11157. The logo has been extracted from PDF documents and is smoother and accurate to the original logo design. Many thanks to to McSweeny for publishing the logo, in SVG originally, I struggled to find it anywhere else. Files are in Inkscape SVG, PDF and PNG. From Mr Patrick McSweeney: This is a selection of University of Southampton Logos in both vector (svg) and raster (png) formats. These are suitable for use on the web or in small documents and posters. You can open the SVG files using inkscape (http://inkscape.org/download/?lang=en) and edit them directly. The University logo should not be modified and attention should be paid to the branding guidelines found here: http://www.edshare.soton.ac.uk/10481 You must always leave a space the width of an capital O in Southampton on all 4 edges of the logo. The negative space makes it appear more prominently on the page.

School of Physics and Astronomy Logo - Vector and Raster

Logo for the school of Physics and Astronomy in Inkscape SVG, PDF and high-resolution PNG format

Relationship between siblings and psychological adjustment in adolescents:

This study evaluated the effect of parent-child relationship quality (acceptance and differential treatment) over dimensions of the quality of sibling relationships (warmth and conflict) and psychological adjustment in 69 adolescent sibling dyads. The effects of parent-child relationships were evaluated both at the individual and dyadic levels. In older siblings, the father-child relationship had a significant effect on both their perception of warmth in the sibling relationship and psychological adjustment. In younger siblings, there was a significant dyadic effect of the older sibling’s perceived acceptance by mother on their perception of warmth in the sibling relationship. Results are analyzed based on the literature and questions for future research are proposed.

Religion, Marketing and Market: An Adjustment in the Language of Faith

O presente trabalho se propõe fazer uma análise de categorias sociais que a primeira vista não tem proximidade, na verdade, podem, inclusive, parecer antagônicas. Trata-se das relações entre Religião, Marketing e Mercado. O trabalho se apóia num referencial teórico mais próximo das ciências sociais, todavia, considera a Religião, em sua expressão institucional –a igreja– como um empreendimento social, uma empresa dos tempos modernos. Procura demonstrar que, para aderir ao mundo moderno, plasmado pela idéia de competição e consumo da sociedade capitalista, a religião reorganizou sua linguagem para atender as exigências desses tempos, já considerados Pós-modernos. A análise é feita a partir do caso brasileiro que, como muitos paises da América Latina, acomodam no seu tecido social, as mais recentes expressões da religião cristã, em especial, os grupos evangélicos que pululam as periferias das grandes cidades desse  continente americano.

Seasonal adjustment and cointegration

El documento examina el efecto de filtros de ajuste en el tamaño y poder de prueba de cointegración que usan los residuales como pruebas ADF y PP, mediante procedimientos MonteCarlo y una aplicación empírica. Nuestros resultados indican que el uso de filtros distorsiona el tamaño y reduce el poder de estas pruebas.

Un metodo para conectar la proyección octogonal de un vector sobre un subespacio de R dotado de un producto escalar

Se trata de un estudio matemático sobre proyecciones octogonales. En el se analizan las diversas posibilidades y variables y se concluye con las posibles soluciones a aplicar al nuevo modelo vectorial.

Los medios de representación gráfica en la modelización en ciencias físicas : el caso del vector fuerza.

Resumen tomado de la publicación

Aproximación al vector histórico de la NEE sordoceguera en España.

Resumen tomado de la revista. Resumen en Inglés