“Unmixing” Tissue Gene Expression Signatures from Tumor Biopsies

Emergent molecular measurement methods, such as DNA microarray, qRTPCR, and many others, offer tremendous promise for the personalized treatment of cancer. These technologies measure the amount of specific proteins, RNA, DNA or other molecular targets from tumor specimens with the goal of “fingerprinting” individual cancers. Tumor specimens are heterogeneous; an individual specimen typically contains unknown amounts of multiple tissues types. Thus, the measured molecular concentrations result from an unknown mixture of tissue types, and must be normalized to account for the composition of the mixture. For example, a breast tumor biopsy may contain normal, dysplastic and cancerous epithelial cells, as well as stromal components (fatty and connective tissue) and blood and lymphatic vessels. Our diagnostic interest focuses solely on the dysplastic and cancerous epithelial cells. The remaining tissue components serve to “contaminate” the signal of interest. The proportion of each of the tissue components changes as a function of patient characteristics (e.g., age), and varies spatially across the tumor region. Because each of the tissue components produces a different molecular signature, and the amount of each tissue type is specimen dependent, we must estimate the tissue composition of the specimen, and adjust the molecular signal for this composition. Using the idea of a chemical mass balance, we consider the total measured concentrations to be a weighted sum of the individual tissue signatures, where weights are determined by the relative amounts of the different tissue types. We develop a compositional source apportionment model to estimate the relative amounts of tissue components in a tumor specimen. We then use these estimates to infer the tissuespecific concentrations of key molecular targets for sub-typing individual tumors. We anticipate these specific measurements will greatly improve our ability to discriminate between different classes of tumors, and allow more precise matching of each patient to the appropriate treatment

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.

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

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

Vector pedagóxico e profesorado universitario : sentido e sensibilidade. 'Sector pedagógico y profesorado universitario : sentido y sensibilidad'.

Se apunta la necesidad de un cambio en relación con el modelo del profesorado en la universidad y con los métodos de enseñanza así como la necesidad de una formación pedagógica ante el impacto de las nuevas tecnologías para mejorar la calidad de la enseñanza superior. Se establecen las bases para un programa de formación señalándose objetivos y propuestas de acción posibles. Se consideran los aspectos de formación mínima, análisis institucional sobre la pertinencia y la calidad, las formas de estimular la participación del profesorado, validación de esa implicación y evaluación permanente de los procesos de formación e innovación docente.

Labour Motivation : an axiomatic vector model. 'Motivación en el trabajo : un modelo de vectores axiomáticos'.

Este artículo pertenece a una sección de la revista dedicada a psicología social