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We present an origami construction of a maximum equilat-eral triangle inscribed in an origami, and an automated proof of the cor-rectness of the construction. The construction and the correctness proof are achieved by a computational origami system called Eos (E-origami system). In the construction we apply the techniques of geometrical constraint solving,… (More)

We describe Huzita's origami axioms from the logical and algebraic points of view. Observing that Huzita's axioms are statements about the existence of certain origami constructions, we can generate basic origami constructions from those axioms. Origami construction is performed by repeated application of Huzita's axioms. We give the logical specification… (More)

Computational origami is the computer assisted study of origami geometry. An origami is constructed by a finite sequence of fold steps, each consisting in folding along a fold line or unfolding. We base the fold methods on a formal system called Huzita's axiom system, and show how folding an origami can be formulated by a conditional rewrite system. A… (More)

We present a computational origami construction of Mor-ley's triangles and automated proof of correctness of the generalized Morley's theorem in a streamlined process of solving-computing-proving. The whole process is realized by a computational origami system being developed by us. During the computational origami construction, geometric constraints in… (More)

We formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system (<i>O</i>, ↬), where <i>O</i> is the set of abstract origami's and ↬ is a binary relation on <i>O</i>, called <i>fold</i>. An abstract origami is a triplet (Π, ∽, ≻), where Π is a set of faces… (More)

Sensor fusion of millimeter-wave radar and a camera is beneficial for advanced driver assistance functions such as obstacle avoidance and Stop&Go. However, millimeter-wave radar has low directional resolution which engenders low measurement accuracy of object position and difficulty of calibration between radar and camera. In this paper, we first propose a… (More)

Computational origami is the computer assisted study of origami as a branch of science of shapes. The origami construction is a countably finite sequence of fold steps, each consisting in folding along a line. In this paper, we formalize origami construction. We model origami paper by a set of faces over which we specify relations of overlay and ad-jacency.… (More)

- Hidekazu Takahashi, Caining Jin, Hasan Rajabi, Sean Pitroda, Maroof Alam, Rehan Ahmad +7 others
- Oncogene
- 2015

The mucin 1 (MUC1) oncoprotein has been linked to the inflammatory response by promoting cytokine-mediated activation of the NF-κB pathway. The TGF-β-activated kinase 1 (TAK1) is an essential effector of proinflammatory NF-κB signaling that also regulates cancer cell survival. The present studies demonstrate that the MUC1-C transmembrane subunit induces… (More)