TheD4Root System Is Not Universally Optimal
نویسندگان
چکیده
منابع مشابه
The D 4 Root System Is Not Universally Optimal
We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a constr...
متن کامل. M G ] 9 S ep 2 00 8 THE D 4 ROOT SYSTEM IS NOT UNIVERSALLY OPTIMAL
We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a constr...
متن کاملEssentially Optimal Universally Composable Oblivious Transfer
Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We provide the first oblivious transfer protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust t...
متن کاملColor filters: When "optimal" is not optimal
It is well known that many more than three or four spectral measurements are required for accurate measurement of color. Previous work has shown seven to ten measurements can yield accurate results on average, but with significant numbers of errors above the threshold of obvious visual detection. Furthermore, the filters used for these measurements are very difficult to fabricate. We show that ...
متن کاملUniversally Optimal Distribution of Points on Spheres
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m distances between distinct points in it and it is a spherical (2m− 1)-design. We prove that every sharp configuration minimizes potential energy for all compl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2007
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2007.10129008