How paper folds: bending with local constraints

(Non)existence of Pleated Folds: How Paper Folds Between Creases

We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zero-thickness paper. In contrast, we show that the model can be folded with additional creases, suggesting that real paper “folds” into this model via small such creases. We conjecture that the circular versi...

Collection Processing with Constraints, Monads, and Folds

We propose an intermediate form based on monad-algebra comprehensions (to represent queries), folds (to represent computation), and setoids over polynomial datatypes (to represent data), suitable for use in collection processing. Such an intermediate form captures, in a uniform way, large fragments of many recent largescale collection processing languages such as MapReduce, PIG, DryadLINQ, and ...

How TriC Folds Tricky Proteins

How chaperonins orchestrate the successful folding of even the most elaborate of proteins is a question of central importance. In two recent studies in Cell by Joachimiak et al. and Freund et al., a new class of TRiC substrate is identified, and how the chaperonin exploits its different subunits to extend its substrate repertoire and direct productive folding is revealed.

How Folds Cut a Scene

We consider the interactions between edges and intensity distributions in semi-open image neighborhoods surrounding them. Locally this amounts to a kind of figure-ground problem, and we analyze the case of smooth figures occluding arbitrary backgrounds. Techniques from differential topology permit a classification into what we call folds (the side of an edge from a smooth object) and cuts (the ...

Bending and buckling of wet paper