In this digital ITEMS module, Dr. Stella Kim provides an overview of multidimensional item response theory (MIRT) equating. Traditional unidimensional (IRT) equating methods impose the sometimes untenable restriction on data that only a single ability is assessed. This module discusses potential sources multidimensionality and presents consequences To remedy these effects, MIRT can be used as v...

Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s ∈ N, we determine KmE/p sKmE as a (Z/pZ)[Gal(E/F )]-module. We also provide examples of extensions for which all of the possible nonzero summands in the decomposition are indeed nonzero. Let F be a field of characteristic p. Let KmF denote the mth Milnor K-group of F and kmF = KmF/pKmF . (See, for ins...

subject to (tf , x(tf )) ∈ S = [t0,∞)× S1 where S1 is a k dimensional manifold in Rn S1 = {x ∈ R : h1(x) = h2(x) = · · · = hn−k(x) = 0} where hi are C1 functions from Rn to R subject to ẋ = f(x, u), x(t0) = x0 for u ∈ C[t0, T ] and u(t) ∈ U ⊂ Rm with f and L being C1 functions. Let u∗ : [t0, tf ] → R be an optimal control with state trajectory x∗ : [t0, tf ] → Rn and a constant. Then there exis...

Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is ...