Prediction of the relationship between body weight and body condition score in sheep

During the whole production cycle it is important to monitor the energy balance and to quantify body reserve changes of the ewes. This can be done, both in experimental settings and in the field, by estimating the body condition score (BCS) of the ewes and its variations. However, if this tool is used to balance the diets it is necessary to know the relationship between BCS and body weight (BW), which varies depending on the mature size of the breed and of the population considered within each breed. The relationship between BW and BCS has been studied only for some sheep breeds and populations. For this reason, this research aimed to develop a prediction model of this relationship in ewes for any breed or population

Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Cohomology and Support Varieties for Lie Superalgebras II

In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties for Kac supermodules for Type I Lie superalgebras and the simple supermodules for $\mathfrak{gl}(m|n)$. The latter result verifies our earlier conjecture for $\mathfrak{gl}(m|n)$. In our investigation we also delineate several of the major differences between Type I versus Type II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.Comment: 28 pages, the proof of Proposition 4.5.1 was corrected, several other small errors were fixe

Time to Vote?

Despite the centrality of voting costs to the paradox of voting, little effort has been made to accurately measure these costs outside of a few spatially limited case studies. In this paper, we apply Geographic Information Systems (GIS) tools to validated national election survey data from New Zealand. We calculate distance and travel time by road from the place of residence to the nearest polling place and combine our time estimate with imputed wages for all sample members. Using this new measure of the opportunity cost of voting to predict turnout at the individual level, we find that small increases in the opportunity costs of time can have large effects in reducing voter turnout.paradox of voting, opportunity cost, travel time

Invariant local twistor calculus for quaternionic structures and related geometries

New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all invariants and invariant operators arise from these universal operators and that they may be used to reduce all invariants problems to corresponding algebraic problems involving homomorphisms between modules of certain parabolic subgroups of Lie groups. Explicit application of the operators is illustrated by the construction of all non-standard operators between exterior forms on a large class of the geometries which includes the quaternionic structures.Comment: 44 page