Intrinsic Volumes and Gaussian Polytopes: The Missing Piece of the Jigsaw

The dad deficit the missing piece of the maternity jigsaw.

Intrinsic Volumes and Lattice Points of Crosspolytopes

Hadwiger showed by computing the intrinsic volumes of a regular simplex that a rectangular simplex is a counterexample to Wills’s conjecture for the relation between the lattice point enumerator and the intrinsic volumes in dimensions not less than 441. Here we give formulae for the volumes of spherical polytopes related to the intrinsic volumes of the regular crosspolytope and of the rectangul...

استفاده از فنّاوری‌های نمونه‌سازی سریع در بازسازی بخش‌های مفقود آثار شیشه‌ای با رویکرد استفاده در شیشه‌های تاریخی

Abstract Although nowadays the advancements in technologies and preservation methods have led to effective conservation of historical and ancient glass works, it is still necessary to develop much less-destructive methods in conservation practices. Rapid prototyping technique (RPT) in recent years has been increasingly implemented in Engineering, Medical, Industrial Design and Architecture fie...

Programmed-assembly system using DNA jigsaw pieces.

A novel method for assembling multiple DNA origami structures has been developed by using designed 2D DNA origami rectangles, so-called "DNA jigsaw pieces" that have sequence-programmed connectors. Shape and sequence complementarity were introduced to the concavity and convex connectors in the DNA rectangles for selective connection with the help of nonselective pi-stacking interactions between...

Learning Image Representations by Completing Damaged Jigsaw Puzzles

In this paper, we explore methods of complicating selfsupervised tasks for representation learning. That is, we do severe damage to data and encourage a network to recover them. First, we complicate each of three powerful self-supervised task candidates: jigsaw puzzle, inpainting, and colorization. In addition, we introduce a novel complicated self-supervised task called “Completing damaged jig...