Bayesian multi-trait kernel methods improve multi-environment genome based prediction

When multi-trait data are available, the preferred models are those that are able to account for correlations between phenotypic traits because when the degree of correlation is moderate or large, this increases the genomic prediction accuracy. For this reason, in this paper we explore Bayesian multi-trait kernel methods for genomic prediction and we illustrate the power of these models with three real datasets. The kernels under study were the linear, Gaussian, polynomial and sigmoid kernels; they were compared with the conventional Ridge regression and GBLUP multi-trait models. The results show that, in general, the Gaussian kernel method outperformed conventional Bayesian Ridge and GBLUP multi-trait linear models by 2.2 to 17.45% (datasets 1 to 3) in terms of prediction performance based on the mean square error of prediction. This improvement in terms of prediction performance of the Bayesian multi-trait kernel method can be attributed to the fact that the proposed model is able to capture non-linear patterns more efficiently than linear multi-trait models. However, not all kernels perform well in the datasets used for evaluation, which is why more than one kernel should be evaluated to be able to choose the best kernel.

Characterizing the vertical concentration profiles of ship plumes with a microscale model - is it all Gaussian?

<p>Accurate modeling of ship emissions is a topic of increasing interest due to the ever-growing global fleet and its emission of air pollutants. With the increasing calculation power of modern computers, numerical grid models can nowadays be used to analyze effects of shipping emissions from global to local scales. However, modeling entire ports and larger domains still requires a good representation for the vertical concentration profile of single ship plumes. As the shape of the plume strongly varies depending on parameters like plume temperature, ship-induced turbulence and meteorological conditions, the plume dilution does not always appear to be represented by a simple Gaussian distribution. In this work, the microscale model MITRAS is used to calculate vertical concentration profiles of ship plumes under varying technical and meteorological scenarios. The resulting curves are fitted with different mathematical curves (e.g. Gaussian, Polynomial and Gamma distribution) by a least square minimization approach and the best representations for individual scenarios are discussed.</p>

When are subset sums equidistributed modulo m?

For a triple $(n,t,m)$ of positive integers, we attach to each $t$-subset $S=\{a_1,\ldots ,a_t\}\subseteq \{1,\ldots ,n\}$ the sum $f(S)=a_1+\cdots +a_t$ (modulo $m$). We ask: for which triples $(n,t,m)$ are the ${n\choose t}$ values of $f(S)$ uniformly distributed in the residue classes mod $m$? The obvious necessary condition, that $m$ divides ${n\choose t}$, is not sufficient, but a $q$-analogue of that condition is both necessary and sufficient, namely: $${{q^m-1}\over {q-1}}\quad \text{divides the Gaussian polynomial}\quad \binom{n}{t}_q.$$ We show that this condition is equivalent to: for each divisor $d>1$ of $m$, we have $t\ {\rm mod}\, d>n\ {\rm mod}\, d$. Two proofs are given, one by generating functions and another via a bijection. We study the analogous question on the full power set of $[n]$: given $(n,m)$; when are the $2^n$ subset sums modulo $m$ equidistributed into the residue classes? Finally we obtain some asymptotic information about the distribution when it is not uniform, and discuss some open questions.

Some identities for terminating q-series

We present the following sequence of polynomial identities: is the Gaussian polynomial denned to be zero for m < 0 or m > N, one for m = 0 or N and