Dessins, their delta-matroids and partial duals

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceeding

Generalized Dualities and Supergroups

Using a recently developed formulation of double field theory in superspace, the graviton, $B$-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic $O(D,D)$ duality group, and these act on all constituents of the supervielbein in an easily computable way. We first review conventional non-abelian T-duality in the Green-Schwarz superstring and describe the dual geometries in the language of double superspace. Since dualities are related to super-Killing vectors, this includes as special cases both abelian and non-abelian fermionic T-duality. We then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in arXiv:1912.11036. As an application, we construct the supergeometries associated with the integrable $\lambda$ and $\eta$ deformations of the $AdS_5 \times S^5$ superstring. The deformation parameters $\lambda$ and $\eta$ are identified with the possible one-parameter embeddings of the supergravity frame within the doubled supergeometry. In this framework, the Ramond-Ramond bispinors are directly computable purely from the algebraic data of the supergroup.Comment: 85 pages; v2: references added, additional comments in introduction and conclusio

Consistent Truncations and Dualities

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation is only the tip of the iceberg. Currently, the most general known classes of T-dualities (excluding mirror symmetry) are based on dressing cosets. But as we discuss, they can be further extended to the even larger class of generalised cosets. We prove that the latter give rise to consistent truncations for which the ansatz can be constructed systematically. Hence, we pave the way for many new examples of T-dualities and consistent truncations. The arising structures result in covariant tensors with more than two derivatives and we argue how they might be key to understand generalised T-dualities and consistent truncations beyond the leading two derivative level.Comment: 43 page

Picturing and modeling catchments by representative hillslopes

This study explores the suitability of a single hillslope as a parsimonious representation of a catchment in a physically based model. We test this hypothesis by picturing two distinctly different catchments in perceptual models and translating these pictures into parametric setups of 2-D physically based hillslope models. The model parametrizations are based on a comprehensive field data set, expert knowledge and process-based reasoning. Evaluation against streamflow data highlights that both models predicted the annual pattern of streamflow generation as well as the hydrographs acceptably. However, a look beyond performance measures revealed deficiencies in streamflow simulations during the summer season and during individual rainfall–runoff events as well as a mismatch between observed and simulated soil water dynamics. Some of these shortcomings can be related to our perception of the systems and to the chosen hydrological model, while others point to limitations of the representative hillslope concept itself. Nevertheless, our results confirm that representative hillslope models are a suitable tool to assess the importance of different data sources as well as to challenge our perception of the dominant hydrological processes we want to represent therein. Consequently, these models are a promising step forward in the search for the optimal representation of catchments in physically based models

Partitioning of on-demand electron pairs

We demonstrate the high fidelity splitting of electron pairs emitted on demand from a dynamic quantum dot by an electronic beam splitter. The fidelity of pair splitting is inferred from the coincidence of arrival in two detector paths probed by a measurement of the partitioning noise. The emission characteristic of the on-demand electron source is tunable from electrons being partitioned equally and independently to electron pairs being split with a fidelity of 90%. For low beam splitter transmittance we further find evidence of pair bunching violating statistical expectations for independent fermions

The quiet Sun average Doppler shift of coronal lines up to 2 MK

The average Doppler shift shown by spectral lines formed from the chromosphere to the corona reveals important information on the mass and energy balance of the solar atmosphere, providing an important observational constraint to any models of the solar corona. Previous spectroscopic observations of vacuum ultra-violet (VUV) lines have revealed a persistent average wavelength shift of lines formed at temperatures up to 1 MK. At higher temperatures, the behaviour is still essentially unknown. Here we analyse combined SUMER/SoHO and EIS/Hinode observations of the quiet Sun around disk centre to determine, for the first time, the average Doppler shift of several spectral lines formed between 1 and 2 MK, where the largest part of the quiet coronal emission is formed. The measurements are based on a novel technique applied to EIS spectra to measure the difference in Doppler shift between lines formed at different temperatures. Simultaneous wavelength-calibrated SUMER spectra allow establishing the absolute value at the reference temperature of 1 MK. The average line shifts at 1 MK < T < 1.8 MK are modestly, but clearly bluer than those observed at 1 MK. By accepting an average blue shift of about (-1.8+/-0.6) km/s at 1 MK (as provided by SUMER measurements), this translates into a maximum Doppler shift of (-4.4+/-2.2) km/s around 1.8 MK. The measured value appears to decrease to about (-1.3+/-2.6) km/s at the Fe XV formation temperature of 2.1 MK. The measured average Doppler shift between 0.01 and 2.1 MK, for which we provide a parametrisation, appears to be qualitatively and roughly quantitatively consistent with what foreseen by 3-D coronal models where heating is produced by dissipation of currents induced by photospheric motions and by reconnection with emerging magnetic flux.Comment: 9 pages, 10 figures. Astronomy and Astrophysics (in press

It is Hobbes, not Rousseau:an experiment on voting and redistribution

We perform an experiment which provides a laboratory replica of some important features of the welfare state. In the experiment, all individuals in a group decide whether to make a costly effort, which produces a random (independent) outcome for each one of them. The group members then vote on whether to redistribute the resulting and commonly known total sum of earnings equally amongst themselves. This game has two equilibria, if played once. In one of them, all players make effort and there is little redistribution. In the other one, there is no effort and nothingWe thank Iris Bohnet, Tim Cason, David Cooper, John Duffy, Maia Guell, John Van Huyck and Robin Mason for helpful conversations and encouragement. The comments of the Editor and two referees helped improve the paper. We gratefully acknowledge the financial support from Spain’s Ministry of Science and Innovation under grants CONSOLIDER INGENIO 2010 CSD2006-0016 (all authors), ECO2009-10531 (Cabrales), ECO2008-01768 (Nagel) and the Comunidad de Madrid under grant Excelecon (Cabrales), the Generalitat de Catalunya and the CREA program (Nagel), and project SEJ2007-64340 of Spain’s Ministerio de Educación y Ciencia (Rodríguez Mora).Publicad

A road to reality with topological superconductors

Topological states of matter are a source of low-energy quasiparticles, bound to a defect or propagating along the surface. In a superconductor these are Majorana fermions, described by a real rather than a complex wave function. The absence of complex phase factors promises protection against decoherence in quantum computations based on topological superconductivity. This is a tutorial style introduction written for a Nature Physics focus issue on topological matter.Comment: pre-copy-editing, author-produced version of the published paper: 4 pages, 2 figure

Prolonged NCX activation prevents SOD1 accumulation, reduces neuroinflammation, ameliorates motor behavior and prolongs survival in a ALS mouse model

Imbalance in cellular ionic homeostasis is a hallmark of several neurodegenerative diseases including Amyotrophic Lateral Sclerosis (ALS). Sodium-calcium exchanger (NCX) is a membrane antiporter that, operating in a bidirectional way, couples the exchange of Ca2+ and Na + ions in neurons and glial cells, thus controlling the intracellular homeostasis of these ions. Among the three NCX genes, NCX1 and NCX2 are widely expressed within the CNS, while NCX3 is present only in skeletal muscles and at lower levels of expression in selected brain regions. ALS mice showed a reduction in the expression and activity of NCX1 and NCX2 consistent with disease progression, therefore we aimed to investigate their role in ALS pathophysiology. Notably, we demonstrated that the pharmacological activation of NCX1 and NCX2 by the prolonged treatment of SOD1G93A mice with the newly synthesized compound neurounina: (1) prevented the reduction in NCX activity observed in spinal cord; (2) preserved motor neurons survival in the ventral spinal horn of SOD1G93A mice; (3) prevented the spinal cord accumulation of misfolded SOD1; (4) reduced astroglia and microglia activation and spared the resident microglia cells in the spinal cord; (5) improved the lifespan and mitigated motor symptoms of ALS mice. The present study highlights the significant role of NCX1 and NCX2 in the pathophysiology of this neurodegenerative disorder and paves the way for the design of a new pharmacological approach for ALS