On the Concept of a Notational Variant

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic

String Supported Wormhole Spacetimes and Causality Violations

We construct a static axisymmetric wormhole from the gravitational field of two Schwarzschild particles which are kept in equilibrium by strings (ropes) extending to infinity. The wormhole is obtained by matching two three-dimensional timelike surfaces surrounding each of the particles and thus spacetime becomes non-simply connected. Although the matching will not be exact in general it is possible to make the error arbitrarily small by assuming that the distance between the particles is much larger than the radius of the wormhole mouths. Whenever the masses of the two wormhole mouths are different, causality violating effects will occur.Comment: 12 pages, LaTeX, 1 figur

The lightcone of G\"odel-like spacetimes

A study of the lightcone of the G\"odel universe is extended to the so-called G\"odel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces is defined by metrics of the form $ds^2=-(dt+H(x)dy)^2+D^2(x)dy^2+dx^2+dz^2$, together with the requirement of spacetime homogeneity, and includes the G\"odel metric. The quasi-periodic refocussing of cone generators with startling lens properties, discovered by Ozsv\'{a}th and Sch\"ucking for the lightcone of a plane gravitational wave and also found in the G\"odel universe, is a feature of the whole G\"odel family. We discuss geometrical properties of caustics and show that (a) the focal surfaces are two-dimensional null surfaces generated by non-geodesic null curves and (b) intrinsic differential invariants of the cone attain finite values at caustic subsets.Comment: 19 pages, 1 figur

Enhancing photoluminescence yields in lead halide perovskites by photon recycling and light out-coupling

In lead halide perovskite solar cells, there is at least one recycling event of electron-hole pair to photon to electron-hole pair at open circuit under solar illumination. This can lead to a significant reduction in the external photoluminescence yield from the internal yield. Here we show that, for an internal yield of 70%, we measure external yields as low as 15% in planar films, where light out-coupling is inefficient, but observe values as high as 57% in films on textured substrates that enhance out-coupling. We analyse in detail how externally measured rate constants and photoluminescence efficiencies relate to internal recombination processes under photon recycling. For this, we study the photo-excited carrier dynamics and use a rate equation to relate radiative and non-radiative recombination events to measured photoluminescence efficiencies. We conclude that the use of textured active layers has the ability to improve power conversion efficiencies for both LEDs and solar cells.We acknowledge financial support from the Engineering and Physical Sciences Research Council of the U.K. (EPSRC). J.M.R. and M.T. thank the Winton Programme for the Physics of Sustainability (University of Cambridge). L.M.P.-O. thanks the Cambridge Home European Scheme for financial support. L.M.P.-O. and J.P.H.R. also thank the Nano Doctoral Training Center (NanoDTC) of the EPSRC for financial support. M.A.-J. thanks Nyak Technology Limited for a PhD scholarship. F.D. acknowledges funding from a Herchel Smith Research Fellowship

Microtubule Associated Protein 1b (MAP1B) Is a Marker of the Microtubular Cytoskeleton in Podocytes but Is Not Essential for the Function of the Kidney Filtration Barrier in Mice.

Podocytes are essential for the function of the kidney glomerular filter. A highly differentiated cytoskeleton is requisite for their integrity. Although much knowledge has been gained on the organization of cortical actin networks in podocyte's foot processes, less is known about the molecular organization of the microtubular cytoskeleton in primary processes and the cell body. To gain an insight into the organization of the microtubular cytoskeleton of the podocyte, we systematically analyzed the expression of microtubule associated proteins (Maps), a family of microtubules interacting proteins with known functions as regulator, scaffold and guidance proteins. We identified microtubule associated protein 1b (MAP1B) to be specifically enriched in podocytes in human and rodent kidney. Using immunogold labeling in electron microscopy, we were able to demonstrate an enrichment of MAP1B in primary processes. A similar association of MAP1B with the microtubule cytoskeleton was detected in cultured podocytes. Subcellular distribution of MAP1B HC and LC1 was analyzed using a double fluorescent reporter MAP1B fusion protein. Subsequently we analyzed mice constitutively depleted of MAP1B. Interestingly, MAP1B KO was not associated with any functional or structural alterations pointing towards a redundancy of MAP proteins in podocytes. In summary, we established MAP1B as a specific marker protein of the podocyte microtubular cytoskeleton

Chronology protection in stationary three-dimensional spacetimes

We study chronology protection in stationary, rotationally symmetric spacetimes in 2+1 dimensional gravity, focusing especially on the case of negative cosmological constant. We show that in such spacetimes closed timelike curves must either exist all the way to the boundary or, alternatively, the matter stress tensor must violate the null energy condition in the bulk. We also show that the matter in the closed timelike curve region gives a negative contribution to the conformal weight from the point of view of the dual conformal field theory. We illustrate these properties in a class of examples involving rotating dust in anti-de Sitter space, and comment on the use of the AdS/CFT correspondence to study chronology protection.Comment: 20 pages. V2: minor corrections, Outlook expanded, references added, published versio