Transparent display with diffuser-backed microtextured illuminating device and method of manufacture therefor

A substantially planar illuminating device, a visual display and a method of manufacture therefor. The illuminating device includes: (1) a light source (210) and (2) a transparent substrate (220) having a pair of substantially parallel major surfaces (230,240) and an entry point (250) for accepting light from the light source, the substrate functioning as a guide for the light, one of the pair of surfaces textured with a plurality of microelements (260) for scattering the light from the substrate, the microelements having a side wall with a side wall area, the side wall area being a function of a distance of the microelements from the entry point to enhance a uniformity of the scattering of the light over an area of the pair of surfaces.Published versio

A geometric study of Wasserstein spaces: Hadamard spaces

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity) probability measures on any (not too wild) metric space X, called its Wasserstein space W(X). In this paper we investigate the geometry of W(X) when X is a Hadamard space, by which we mean that $X$ has globally non-positive sectional curvature and is locally compact. Although it is known that -except in the case of the line- W(X) is not non-positively curved, our results show that W(X) have large-scale properties reminiscent of that of X. In particular we define a geodesic boundary for W(X) that enables us to prove a non-embeddablity result: if X has the visibility property, then the Euclidean plane does not admit any isometric embedding in W(X).Comment: This second version contains only the first part of the preceeding one. The visibility properties of W(X) and the isometric rigidity have been split off to other articles after a referee's commen

Evolutionary dynamics of incubation periods

The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms. For typhoid fever, polio, measles, leukemia and many other diseases, the incubation period is highly variable. Some affected people take much longer than average to show symptoms, leading to a distribution of incubation periods that is right skewed and often approximately lognormal. Although this statistical pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here we propose an explanation based on evolutionary dynamics on graphs. For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk. Unlike previous explanations that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease.Comment: 24 pages, 8 figures, 1 tabl

Comparing the correlation length of grain markets in China and France

In economics comparative analysis plays the same role as experimental research in physics. In this paper we closely examine several methodological problems related to comparative analysis by investigating the specific example of grain markets in China and France respectively. This enables us to answer a question in economic history which has so far remained pending, namely whether or not market integration progressed in the 18th century. In economics as in physics, before being accepted any new result has to be checked and re-checked by different researchers. This is what we call the replication and comparison procedures. We show how these procedures should (and can) be implemented.Comment: 16 pages, 7 figures, to appear in International Journal of Modern Physics

Protonolysis of a Ruthenium–Carbene Bond and Applications in Olefin Metathesis

The synthesis of a ruthenium complex containing an N-heterocylic carbene (NHC) and a mesoionic carbene (MIC) is described wherein addition of a Brønsted acid results in protonolysis of the Ru–MIC bond to generate an extremely active metathesis catalyst. Mechanistic studies implicated a rate-determining protonation step in the generation of the metathesis-active species. The activity of the NHC/MIC catalyst was found to exceed those of current commercial ruthenium catalysts