17 citations · 44 across the 18 of their papers we have counts for
5 papers · 1 filter
A multidimensional Law of Sines
Igor Rivin
We extend the Law of Sines to simplices in Euclidean spaces of any number of dimensions.
The amplitude modulation transform
Igor Rivin
Motivated by the study of the local extrema of sin(x)/x we define the \emph{Amplitude Modulation} transform of functions defined on (subsets of) the real line. We discuss certain p…
Another Simple Proof of a Theorem of Chandler Davis
Igor Rivin
In 1957, Chandler Davis proved that unitarily invariant convex functions on the space of hermitian matrices are precisely those which are convex and symmetrically invariant on the…
The performance of the batch learner algorithm
Igor Rivin
We analyze completely the convergence speed of the \emph{batch learning algorithm}, and compare its speed to that of the memoryless learning algorithm and of learning with memory.…
The moment zeta function and applications
Igor Rivin
Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the \emph{moment zeta function} of a probability…