The market model of interest rates specifies simple forward or Libor rates as log-normally distributed, their stochastic dynamics has a linear volatility function. In this paper, the model is extended to quadratic volatility functions which are the product of a quadratic polynomial and a level-independent covariance matrix. The extended Libor market models allow for closed form cap pricing form...

in this study, a total of 101,147 monthly test day records of somatic cell count collected from 13,977 first lactation holstein cows (in 183 herds) calved between 2002 and 2006 were used. for the genetic analysis, a random regression test day model was utilized. somatic cell score (scs) was calculated based on natural logarithm of somatic cell count. in the model, fixed effect of contemporary g...

We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including entries of covariance matrix, entries of precision matrix, quadratic forms, log-determinant, eigenvalues in the Bayesian Gaussian covariance/precision matrix estim...

In a paper of Kim, Chan, and Rhagavan, the universal ternary classical quadratic forms over quadratic fields of positive discriminant were discovered. Here a proof of the universality of some of these quadratic forms is given using a technique of Liouville. Another quadratic form over the field of discriminant 8 is shown universal by a different elementary approach. Mathematics Subject Classifi...

A useful discriminant vector for pattern classification is one that maximizes the minimum separation of discriminant function values for two pattern classes. This optimality criterion can prove valuable in many situations because it emphasizes the class elements that are most difficult to classify. A method for computing this discriminant vector by quadratic programming is derived. The resultin...

In the first two articles of this series, we investigated various higher analogues of Gauss composition, and showed how several algebraic objects involving orders in quadratic and cubic fields could be explicitly parametrized. In particular, a central role in the theory was played by the parametrizations of the quadratic and cubic rings themselves. These parametrizations are beautiful and easy ...