Space-Efficient Prime Knot 7-Mosaics

Efficient Super-Resolution and Applications to Mosaics

Mosaicing and super resolution are two ways to combine information from multiple frames in video sequences. Mosaicing displays the information of multiple frames in a single panoramic image. Super-resolution uses regions which appear in multiple frames to improve resolution and reduce noise. The aim of this work is constructing a high resolution mosaic from a video sequence in an efficient way....

A Prime Strongly Positive Amphicheiral Knot Which Is Not Slice

Efficient Generation of Prime Numbers

The generation of prime numbers underlies the use of most public-key schemes, essentially as a major primitive needed for the creation of key pairs or as a computation stage appearing during various cryptographic setups. Surprisingly, despite decades of intense mathematical studies on primality testing and an observed progressive intensification of cryptographic usages, prime number generation ...

Polygonal Knot Space near Ropelength-minimized Knots

For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r < R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which we can see small trefoil and figure-eight su...

A Space-eecient Fast Prime Number Sieve

We present a new algorithm that nds all primes up to n using at most O(n= log log n) arithmetic operations and O(n=(log n log log n)) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of (log n). In addition, we present the results of our imp...