On the calculation of minimum variance estimators for unobservable dependent variables

The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored

Numerical experiments in semi-infinite programming

A quasi-Newton algorithm for semi-infinite programming using an L∞ exact penalty function is described, and numerical results are presented. Comparisons with three Newton algorithms and one other quasi-Newton algorithm show that the algorithm is very promising in practice

A direct search conjugate directions algorithm for unconstrained minimization

A direct search algorithm for unconstrained minimization of smooth functions is described. The algorithm minimizes the function over a sequence of successively finer grids. Each grid is defined by a set of basis vectors. From time to time these basis vectors are updated to include available second derivative information by making some basis vectors mutually conjugate. Convergence to one or more stationary points is shown, and the finite termination property of conjugate direction methods on strictly convex quadratics is retained. Numerical results show that the algorithm is effective on a variety of problems including ill-conditioned problems

Effect of limited precision on the BFGS quasi-Newton algorithm

Some claim that updating approximate Hessian information via the BFGS formula with a Cholesky factorisation offers greater numerical stability than the more straightforward approach of performing the update directly. Others claim that no such advantage exists and that any such improvement is probably due to early implementations of the DFP formula in conjunction with low accuracy line searches. We find no discernible advantage in choosing factorised implementations (over non-factorised implementations) of BFGS methods when approximate Hessian information is available to full machine precision. However, the type of implementation may have significant effects when approximate Hessian information is only available to limited precision. Furthermore, a conjugate directions factorisation outperforms the other methods explored (including Cholesky factorisation)

Historical changes in the phenology of British Odonata are related to climate

Responses of biota to climate change take a number of forms including distributional shifts, behavioural changes and life history changes. This study examined an extensive set of biological records to investigate changes in the timing of life history transitions (specifically emergence) in British Odonata between 1960 and 2004. The results show that there has been a significant, consistent advance in phenology in the taxon as a whole over the period of warming that is mediated by life history traits. British odonates significantly advanced the leading edge (first quartile date) of the flight period by a mean of 1.51 ±0.060 (SEM, n=17) days per decade or 3.08±1.16 (SEM, n=17) days per degree rise in temperature when phylogeny is controlled for. This study represents the first review of changes in odonate phenology in relation to climate change. The results suggest that the damped temperature oscillations experienced by aquatic organisms compared with terrestrial organisms are sufficient to evoke phenological responses similar to those of purely terrestrial taxa

Resolvin rvd2 reduces hypothalamic inflammation and rescues mice from diet-induced obesity

Diet-induced hypothalamic inflammation is an important mechanism leading to dysfunction of neurons involved in controlling body mass. Studies have shown that polyunsaturated fats can reduce hypothalamic inflammation. Here, we evaluated the presence and function of RvD2, a resolvin produced from docosahexaenoic acid, in the hypothalamus of mice. Methods: Male Swiss mice were fed either chow or a high-fat diet. RvD2 receptor and synthetic enzymes were evaluated by real-time PCR and immunofluorescence. RvD2 was determined by mass spectrometry. Dietary and pharmacological approaches were used to modulate the RvD2 system in the hypothalamus, and metabolic phenotype consequences were determined. Results: All enzymes involved in the synthesis of RvD2 were detected in the hypothalamus and were modulated in response to the consumption of dietary saturated fats, leading to a reduction of hypothalamic RvD2. GPR18, the receptor for RvD2, which was detected in POMC and NPY neurons, was also modulated by dietary fats. The substitution of saturated by polyunsaturated fats in the diet resulted in increased hypothalamic RvD2, which was accompanied by reduced body mass and improved glucose tolerance. The intracerebroventricular treatment with docosahexaenoic acid resulted in increased expression of the RvD2 synthetic enzymes, increased expression of anti-inflammatory cytokines and improved metabolic phenotype. Finally, intracerebroventricular treatment with RvD2 resulted in reduced adiposity, improved glucose tolerance and increased hypothalamic expression of anti-inflammatory cytokines. Conclusions: Thus, RvD2 is produced in the hypothalamus, and its receptor and synthetic enzymes are modulated by dietary fats. The improved metabolic outcomes of RvD2 make this substance an attractive approach to treat obesity14511

Direct search methods for nonlinearly constrained optimization using filters and frames

Abstract. A direct search method for nonlinear optimization problems with nonlinear inequality constraints is presented. A filter based approach is used, which allows infeasible starting points. The constraints are assumed to be continuously differentiable, and approximations to the constraint gradients are used. For simplicity it is assumed that the active constraint normals are linearly independent at all points of interest on the boundary of the feasible region. An infinite sequence of iterates is generated, some of which are surrounded by sets of points called bent frames. An infinite subsequence of these iterates is identified, and its convergence properties are studied by applying Clarke's non-smooth calculus to the bent frames. It is shown that each cluster point of this subsequence is a Karush-Kuhn-Tucker point of the optimization problem under mild conditions which include strict differentiability of the objective function at each cluster point. This permits the objective function to be non-smooth, infinite, or undefined away from these cluster points. When the objective function is only locally Lipschitz at these cluster points it is shown that certain directions still have interesting properties at these cluster points

Construction of Strand-seq libraries in open nanoliter arrays

Single-cell Strand-seq generates directional genomic information to study DNA repair, assemble genomes, and map structural variation onto chromosome-length haplotypes. We report a nanoliter-volume, one-pot (OP) Strand-seq library preparation protocol in which reagents are added cumulatively, DNA purification steps are avoided, and enzymes are inactivated with a thermolabile protease. OP-Strand-seq libraries capture 10%-25% of the genome from a single-cell with reduced costs and increased throughput