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Three classes of finite structures are related by extremal properties: complete d-partite d-uniform hypergraphs, d-dimensional affine cubes of integers, and families of 2 d sets forming a d-dimensional Boolean algebra. We review extremal results for each of these classes and derive new ones for Boolean algebras and hypergraphs, several obtained by employing(More)
Responsive behavior, which is intrinsic to natural systems, is becoming a key requirement for advanced artificial materials and devices, presenting a substantial scientific and engineering challenge. We designed dynamic actuation systems by integrating high-aspect-ratio silicon nanocolumns, either free-standing or substrate-attached, with a hydrogel layer.(More)
Dedicated to the memory of Paul Erd} os. Abstract A minimal detour subgraph of the n-dimensional cube is a spanning subgraph G of Q n having the property that for vertices x, y of Q n , distances are related by d G (xx y) d Qn (xx y) + 2. For a spanning subgraph G of Q n to bea local detour subgraph, we require only that the above inequality be satissed(More)