After more than three centuries, a geometry problem that originated with a royal bet has been solved. Imagine you’re holding two equal-size dice. Is it possible to bore a tunnel through one die that’s ...

Can you drill a hole in a cube that an identical cube could fall through? Prince Rupert of the Rhine first asked this question in the 17th century, and he soon found out the answer is yes. One can ...

Sir Isaac Newton once wrote, in what must be one of the most oft-quoted lines in the history of science, "If I have seen further it is by standing upon the shoulders of giants." Well, any of us who ...

James Chen, CMT is an expert trader, investment adviser, and global market strategist. Cierra Murry is an expert in banking, credit cards, investing, loans, mortgages, and real estate. She is a ...

Taking the minkowski sum where an operand is concave causes a significant performance regression in Manifold mode. We implement minkowski by first decomposing operands into convex operands, then ...

Abstract: Digital images are easily corrupted during transmission. Most image denoising methods cannot perform well on restoring the secret image extracted from a corrupted stego image. To deal with ...

Abstract: The probabilistic gradient estimator (PAGE) algorithm allows switching between vanilla SGD and variance-reduced methods in a flexible probabilistic manner. This motivates us to develop novel ...