Wales' Chief Scientific Adviser, Professor John Harries, says the £50-million investment should help build a team of top-level scientists and attract the best research projects to Wales.
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FIFA bosses will hear the FAW's case today after Wales fans wore poppies during a recent World Cup Qualifier.
More than a thousand youngsters in Wales were hospitalised for self-harming this year - an increase of over 40% in the past three years.
Twelve women in Wales have been killed, or suspected to have been killed, by men this year according to charity Welsh Women's Aid.