OBJECTIVE To estimate the prognostic value of T-cell subsets in Zambian patients initiating antiretroviral therapy (ART), and to assess the impact of a nutritional intervention on T-cell subsets. METHODS This was a sub-study of a randomised clinical trial of a nutritional intervention for malnourished adults initiating ART. Participants in a randomised controlled trial (NUSTART trial) were en...

We consider left-invariant control affine systems on the matrix Lie group SO (2, 1)0. A classification, under state space equivalence, of all such full-rank control systems is obtained. First, we identify certain subsets on which the group of Lie algebra automorphisms act transitively. We then systematically identify equivalence class representatives (for single-input, two-input and three-input...

1. ip is real-analytic; 2. the rank of <p equals p on an everywhere dense subset of U; 3. (f(U) is closed in V; 4. for each compact subset K C <p(U), there exists a compact subset H C U such that <p(H) = K. Then the composition subalgebra A? = {foip: f e C°°(V)} is closed in C°°(U), when this algebra carries its natural Frechet topology (convergence on compact subsets of the function and all it...

The Helton-Nie Conjecture (HNC) is the proposition that every convex semialgebraic set is a spectrahedral shadow. Here we prove that HNC is equivalent to another proposition related to quadratically constrained quadratic programming. Namely, that the convex hull of the rank-one elements of any spectrahedron is a spectrahedral shadow. In the case of compact convex semialgebraic sets, the spectra...

We investigate the large λ behavior of σ((p−λA)2) when the zero set of B = dA has a non-empty interior. With certain technical hypotheses we show that if either B is bounded away from zero for large |x| or periodic and certain quotients of standard homology groups are finite rank, then σ((p − λA)2) approaches a quasi-periodic orbit in the space of subsets of [0,∞).

Let ∆ be a thick building of type Xn = Cn,Dn. Let also Gk be the Grassmannian of k-dimensional singular subspaces of the associated polar space Π (of rank n). We write Gk for the corresponding shadow space of type Xn,k. Every bijective transformation of Gk preserving the class of base subsets (the shadows of apartments) is a collineation of Gk, and it is induced by a collineation of Π if n 6= 4...

The study of minimal complements in a group or semigroup was initiated by Nathanson. notion and being complement leads to the co-minimal pairs which considered prior work authors. In this article, we type subsets integers free abelian groups higher rank can be part pair. We show that majority lacunary sequences have property. From conditions established, one any infinite subset finitely generat...

Louviere et al. (2008, J. of Choice Modelling, 1, 126-163) present two main empirical examples in which a respondent rank orders the options in various choice sets by repeated best, then worst, choice. They expand the ranking data to various “implied” choices in subsets and fit the expanded data in various ways; they do not present models of the original rank data, except in one case (that of t...

In this work, we adapt the rank aggregation framework for the discovery of optimal course sequences at the university level. Each student provides a partial ranking of the courses taken throughout his or her undergraduate career. We compute pairwise rank comparisons between courses based on the order students typically take them, aggregate the results over the entire student population, and the...

We generalize the work of [13] on expansions of o-minimal structures with dense independent subsets, to the setting of geometric structures. We introduce the notion of an H-structure of a geometric theory T , show that H-structures exist and are elementarily equivalent, and establish some basic properties of the resulting complete theory T , including quantifier elimination down to “H-bounded” ...