Let $\go{g}$ be a finite-dimensional semi-simple Lie algebra, $\go{h}$ a Cartan subalgebra of $\go{g}$, and $W$ its Weyl group. The group $W$ acts diagonally on $V:=\go{h}\oplus\go{h}^*$, as well as on $\mathbb{C}[V]$. The purpose of this article is to study the Poisson homology of the algebra of invariants $\mathbb{C}[V]^W$ endowed with the standard symplectic bracket. To begin with, we give g...

There is a known connection between the multinomial and the Poisson likelihoods. This, in turn, means that a Poisson regression may be transformed into a logit model and vice versa. In this paper, I show the data transformations required to implement this transformation. Several examples are used as illustrations.

rice husk ash (rha) is natural pozzolan containing reactive silica and/or aluminum. when the material is mixed with lime in powdered form and in the presence of water, it will set and harden like cement. this work uses osadebe’s optimization model to optimize the shear modulus of concrete made from rha. the strengths predicted by the model are in good agreement with their corresponding experime...

There are many studies that have been done to examine what types of voting behavior or patterns are present when voting for environmental ballot measures. This paper examines what characteristics of people are likely to cause them to support Proposition 37 in California, an initiative that, if passed, would require GMOlabeling on all genetically modified foods. Using voting data at a zip code l...

This study proposes a new use of goal programming for empirically estimating a regression quantile hyperplane. The approach can yield regression quantile estimates that are less sensitive to not only non-Gaussian error distribut.ions but also a small sample size t.han conventional regression quantile methods. The performance of regression quantile estimates is compared with least absolute value...

The Poisson likelihood with rectified linear function as non-linearity is a physically plausible model to discribe the stochastic arrival process of photons or other particles at a detector. At low emission rates the discrete nature of this process leads to measurement noise that behaves very differently from additive white Gaussian noise. To address the intractable inference problem for such m...