We prove the lower bound R(Mm) ≥ 3 2 m² − 2 on the border rank of m × m matrix multiplication by exhibiting explicit representation theoretic (occurence) obstructions in the sense of Mulmuley and Sohoni’s geometric complexity theory (GCT) program. While this bound is weaker than the one recently

; social theory; social morphology INTRODUCTION The network society is a speci c form of social structure tentatively identied by empirical research as being characteristic of the Information Age. By social structure I understand the organizational arrangements of humans in relationships of production

Abstract. We show that most arithmetic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique (Nisan–Wigderson), the results of Razborov

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a

of geometric obstructions (the Levi problem) that in dimension 1 are irrelevant. A good candidate kernel for the higher dimensional setting was first identified by Jean Leray in the context of a C ∞ -smooth, convex domain D: while these conditions on D can be relaxed a bit, if the domain is less than C 2

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with implementation, our study identified that completing the bundle within an hour was not straightforward. Our emergent theory suggested that rather than being an apparently simple sequence of six steps, the Sepsis Six actually involved a complex trajectory comprising multiple interdependent tasks that required

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The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main

tend to contain easier or more familiar concepts than the academic subjects. In fact, there was some evidence for this latter explanation: there was a high positive correlation of .54 (p Ͻ.01) between the nonacademic subjects and the occurrence of these extratextual referentials. Three rhetorical