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The zigzag product was introduced by Reingold, Vadhan & Wigderson (2000). When the zig-zag product was first introduced, it was used for the explicit construction of constant degree expanders and extractors. Later on, the zig-zag product was used in computational complexity theory to prove that symmetric logspace and logspace are equal ...
Tooth supported expanders allow the forces to be applied directly to the teeth of maxillary arch instead of the tissue. The most common tooth-borne expander is known as the Hyrax (hygienic rapid expander) or Biedermann appliance. This appliance was developed by Bidermann.
A palatal expander Upper and lower jaw functional expanders. A palatal expander is a device in the field of orthodontics which is used to widen the upper jaw [1] so that the bottom and upper teeth will fit together better. [2] [3] This is a common orthodontic procedure. The use of an expander is most common in children and adolescents 8–18 ...
Whatever the purpose, orthodontic headgear works by exerting tension on the braces via hooks, a facebow, coils, elastic bands, metal orthodontic bands, and other attachable appliances directly into the patient's mouth. It is most effective for children and teenagers because their jaws are still developing and can be easily manipulated.
Salil Vadhan is an American computer scientist. He is Vicky Joseph Professor of Computer Science and Applied Mathematics at Harvard University. [1] After completing his undergraduate degree in Mathematics and Computer Science at Harvard in 1995, he obtained his PhD in Applied Mathematics from Massachusetts Institute of Technology in 1999, where his advisor was Shafi Goldwasser. [2]
Therefore, a zig-zag product can also be used to construct families of expander graphs. If G is a ( n , d , λ 1 ) -graph and H is an ( m , d , λ 2 ) -graph, then the zig-zag product G H is a ( nm , d 2 , φ ( λ 1 , λ 2 )) -graph where φ has the following properties.
Zig-zag product This page was last edited on 18 December 2020, at 00:02 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 License ...
The company distributes its product throughout the United States, and in 2011 was named the fastest-growing health company in America by Inc. magazine. [27] [28] It has been reported that in 2017 its clear align system had been used to treat about 80,000 patients. [2] ClearCorrect was founded in Houston, Texas, by Willis Pumphrey, Jr., a dentist.