We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph ...

Abstract: A vertex set D ⊆ V is considered a dominating set of G if every vertex in V − D is adjacent to at least one vertex in D. We called a dominating set D as a paired-dominating set if the ...

With her hull straying against the pressure, the Norwegian icebreaker Kronprins Haakon floats through a frozen labyrinth of ice floes eight hundred kilometers north of the Arctic Circle. A brief ...

Singapore, India, Japan, China and South Korea, geographically distant from the polar circle, were granted observer status in 2013. Their arguments were compelling: As major players in global shipping ...

Apple improved the Math Notes feature in iOS 26 and iPadOS 26, allowing users to input equations to create graphs in three dimensions. Math Notes ...