Motivated by (and using tools from) communication complexity, we investigate the relationship between the following two ranks of a 0-1 matrix: its nonnegative rank and its binary rank (the log of the latter being the unambiguous nondeterministic communication complexity). We prove that for partial 0-1 matrices, there can be an exponential separation. For total 0-1 matrices, we show that if the ...

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. The Econometric Society is collaborating with JSTOR to di...

Andreas-Stephan ELSENHANS a and Jörg JAHNEL a a Universität Göttingen, Mathematisches Institut, Bunsenstraße 3–5, D-37073 Göttingen, Germany 1 Abstract. We construct explicit examples of K3 surfaces over Q which are of degree 2 and the geometric Picard rank of which is equal to 1. We construct, particularly, examples in the form w2 = det M where M is a symmetric (3× 3)-matrix of ternary quadrat...