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Address correspondence to: Emmanuel Agosto-Arroyo, MD, Department of Pathology and Laboratory Medicine, PO Box 365067, San Juan PR 00936. Email: [email protected] Objective: Routine Progesterone and Estrogen hormone receptor proteins and human epidermal growth factor receptor 2 (HER-2) analysis on invasive breast carcinomas provide therapeutic and prognostic values, revealing significant ...
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Proof. For the m = d case, first rotate the subspace W to become span(e1, . . . , ed) (via multiplication by an orthogonal matrix), and then project to the first d coordinates. This clearly preserves norms in W exactly. Now, assume there is an ε-subspace embedding Π ∈ Rm×n for m < d. Then, the map Π : W → Rm has a nontrivial kernel, in particular there is some w ∈ W,w 6= 0 such that Πw = 0. On ...
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ژورنال
عنوان ژورنال: Diacronie
سال: 2013
ISSN: 2038-0925
DOI: 10.4000/diacronie.121