FDA Disclosure of Safety and Effectiveness Data: A Legal and Policy Analysis

Syftet med studien är att genom analys av förskollärares berättelser beskriva hur barns sociala samspel och lek kan påverkas och utvecklas. Den empiriska studien baserar sig på åtta intervjuer med förskollärare som delat med sig av sina erfarenheter i sitt arbete med barns lek och sociala samspel. Den tidigare forskningen behandlar begreppen socialt samspel och lek. Vidare redovisas också olika faktorer som kan påverka barns samspelsutveckling i lek. Vi valde att göra en kvalitativ studie med tematisk analys för att besvara våra frågeställningar. Utifrån ett specialpedagogiskt synsätt har vi valt att utgå från tre teoretiska perspektiv, det kategoriska-, det relationella- och dilemmaperspektivet. Den tematiska analysen ledde fram till tre olika huvudteman. Det första temat handlar om hur viktiga pedagogers roll och deltagande är i leken. Det andra temat fokuserar på pedagogers erfarenheter hur lek och samspel kan påverkas utifrån hinder och möjligheter. Det tredje och sista temat behandlar organisationens och miljöns betydelse för utvecklingen i lek och samspel i förskolan

Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra

We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of randomized iterative algorithms based on similar principles to address a variety of common tasks in numerical linear algebra. From the point of view of numerical linear algebra, the main novelty of the Fast Randomized Iteration schemes described in this article is that they work in either linear or constant cost per iteration (and in total, under appropriate conditions) and are rather versatile: we will show how they apply to solution of linear systems, eigenvalue problems, and matrix exponentiation, in dimensions far beyond the present limits of numerical linear algebra. While traditional iterative methods in numerical linear algebra were created in part to deal with instances where a matrix (of size $\mathcal{O}(n^2)$) is too big to store, the algorithms that we propose are effective even in instances where the solution vector itself (of size $\mathcal{O}(n)$) may be too big to store or manipulate. In fact, our work is motivated by recent DMC based quantum Monte Carlo schemes that have been applied to matrices as large as $10^{108} \times 10^{108}$. We provide basic convergence results, discuss the dependence of these results on the dimension of the system, and demonstrate dramatic cost savings on a range of test problems.Comment: 44 pages, 7 figure

The Computational Complexity of Duality

We show that for any given norm ball or proper cone, weak membership in its dual ball or dual cone is polynomial-time reducible to weak membership in the given ball or cone. A consequence is that the weak membership or membership problem for a ball or cone is NP-hard if and only if the corresponding problem for the dual ball or cone is NP-hard. In a similar vein, we show that computation of the dual norm of a given norm is polynomial-time reducible to computation of the given norm. This extends to convex functions satisfying a polynomial growth condition: for such a given function, computation of its Fenchel dual/conjugate is polynomial-time reducible to computation of the given function. Hence the computation of a norm or a convex function of polynomial-growth is NP-hard if and only if the computation of its dual norm or Fenchel dual is NP-hard. We discuss implications of these results on the weak membership problem for a symmetric convex body and its polar dual, the polynomial approximability of Mahler volume, and the weak membership problem for the epigraph of a convex function with polynomial growth and that of its Fenchel dual.Comment: 14 page

Plethysm and lattice point counting

We apply lattice point counting methods to compute the multiplicities in the plethysm of $GL(n)$. Our approach gives insight into the asymptotic growth of the plethysm and makes the problem amenable to computer algebra. We prove an old conjecture of Howe on the leading term of plethysm. For any partition $\mu$ of 3,4, or 5 we obtain an explicit formula in $\lambda$ and $k$ for the multiplicity of $S^\lambda$ in $S^\mu(S^k)$.Comment: 25 pages including appendix, 1 figure, computational results and code available at http://thomas-kahle.de/plethysm.html, v2: various improvements, v3: final version appeared in JFoC

Effects of density on lek-site selection by Black Grouse <i>Tetrao tetrix</i> in the Alps

Capsule: The Black Grouse is a primarily lekking species, but low population density and lack of suitable habitat can lead to the establishment of non-lekking populations. Aims: To understand if differences in density could be related to differences in the lekking system, if there were differences in lek-site selection, and if there was a direct effect of habitat on the lek size. Methods: We compared lek sizes between two Black Grouse populations with different male population densities as estimated by distance sampling. We considered land-cover categories, landscape metrics and orographic variables and computed the Ivlev’s Electivity Index to evaluate habitat selection of males in the two study areas. A general linear model was used to assess the relationship between lek size and habitat variables. Results: We could not demonstrate the direct effect of density on the displaying behaviour but we found strongly different patterns of lek-site selection and different effects of habitat on lek size according to the population density. Conclusions: We concluded that habitat normally considered as high quality and habitat complexity may play different roles in selection by solitary versus lekking males when different population densities are considered

Nonnegative approximations of nonnegative tensors

We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious naive Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative PARAFAC, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Bregman divergences.Comment: 14 page