A self-folding structure fabricated by additive manufacturing can be automatically folded into a demanding 3D shape by actuation mechanisms such as heating. However, 3D surfaces can only be fabricated by self-folding structures when they are flattenable. Most generally designed parts are not flattenable. To address the problem, we develop a shape optimization method to modify a non-flattenable ...

The mixed Dirichlet-Neumann problem for the Laplace equation in an unbounded plane domain with cuts (cracks) is studied. The Dirichlet condition is given on closed curves making up the boundary of the domain, while the Neumann condition is specified on the cuts. The existence of a classical solution is proved by potential theory and a boundary integral equation method. The integral representati...

We present a novel approach to segmenting video using iterated graph cuts based on spatio-temporal volumes. We use the mean shift clustering algorithm to build the spatio-temporal volumes with different bandwidths from the input video. We compute the prior probability obtained by the likelihood from a color histogram and a distance transform using the segmentation results from graph cuts in the...

We show how the holomorphic anomaly found in hep-th/0409245 can be used to efficiently compute certain classes of unitarity cuts of one-loop N = 4 amplitudes of gluons. These classes include all cuts of n-gluon one-loop MHV amplitudes and of n-gluon next-toMHV amplitudes with helicities (1, 2, 3, 4, . . . , n). As an application of this method, we present the explicit computation of the (1, 2, ...

Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve. This paper presents a first computational study of a disjunctive cutting plane method for stochastic mixed 0-1 programs that uses lift-and-project cuts based on the extensive form of the two-stage SMIP problem. An extension of the method based on where the data uncertainty appears in t...

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by constructing a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton ...

Type two cuts, bad cuts and very bad cuts are introduced in [KL] for studying the relationship between Loeb measure and U-topology of a hyper nite time line in an !1-saturated nonstandard universe. The questions concerning the existence of those cuts are asked there. In this paper we answer, fully or partially, some of those questions by showing that: (1) type-two cuts exist, (2) the @1-isomorp...