Let K =(K1€¦Kn) be a n-tuple ofconvex compact subsets in the Euclidean spaceRn, and let V (·) be the Euclidean volume inRn . The Minkowski polynomial VK is defined as VK(x1,€¦, xn)= V (λ1K1+€¦+λnKn) and the mixed volume V(K1,€¦,Kn) asV(K1€¦Kn) =ˆ‚n / ˆ‚λ1€¦ˆ‚λnVK(λ1K1+€¦Î»nKn).The mixed volume is one of the backbones of convexity theory.Aft...
Creator:
Gurvits, Leonid (Los Alamos National Laboratory)
Created:
2007-04-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The fundamental trade-off in coding theory is the onebetween the rate of the code (a measure of amount of redundancyintroduced) and the amount of errors that can be corrected. In thistalk, I will describe an explicit construction of codes that achievesthe optimal trade-off between these parameters, for a worst-case noise model where the channel ...
Creator:
Guruswami, Venkatesan (University of Washington)
Created:
2007-04-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.