Automorphy lifting for residually reducible-adic Galois representations, II

We revisit the paper [Automorphy lifting for residually reducible$l$-adic Galois representations, J. Amer. Math. Soc. 28 (2015), 785–870] by the third author. We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.This work was partially conducted during the period that J.T. served as a Clay Research Fellow. J.T.’s work received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714405). J.T. would like to thank Lue Pan for pointing out an error in [Tho15], which is addressed here in §3.1 below. P.A. was supported by Simons Foundation Collaboration Grant 527275 and NSF grant DMS- 1902155

The mean free path for electron conduction in metallic fullerenes

We calculate the electrical resistivity due to electron-phonon scattering for a model of A3C60 (A= K, Rb), using an essentially exact quantum Monte-Carlo calculation. In agreement with experiment, we obtain exceptionally large metallic resistivities at large temperatures T. This illustrates that the apparent mean free path can be much shorter than the separation of the molecules. An interpretation of this result is given. The calculation also explains the linear behavior in T at small T.Comment: 4 pages, RevTeX, 3 eps figure, additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene

The latitudinal diversity gradient of tetrapods across the Permo-Triassic mass extinction and recovery interval

The decline in species richness from the equator to the poles is referred to as the latitudinal diversity gradient (LDG). Higher equatorial diversity has been recognized for over 200 years, but the consistency of this pattern in deep time remains uncertain. Examination of spatial biodiversity patterns in the past across different global climate regimes and continental configurations can reveal how LDGs have varied over Earth history and potentially differentiate between suggested causal mechanisms. The Late Permian–Middle Triassic represents an ideal time interval for study, because it is characterized by large-scale volcanic episodes, extreme greenhouse temperatures and the most severe mass extinction event in Earth history. We examined terrestrial and marine tetrapod spatial biodiversity patterns using a database of global tetrapod occurrences. Terrestrial tetrapods exhibit a bimodal richness distribution throughout the Late Permian–Middle Triassic, with peaks in the northern low latitudes and southern mid-latitudes around 20–40° N and 60° S, respectively. Marine reptile fossils are known almost exclusively from the Northern Hemisphere in the Early and Middle Triassic, with highest diversity around 20° N. Reconstructed terrestrial LDGs contrast strongly with the generally unimodal gradients of today, potentially reflecting high global temperatures and prevailing Pangaean super-monsoonal climate system during the Permo-Triassic

The Depressed Brain: An Evolutionary Systems Theory

Major depression is a debilitating condition characterised by diverse neurocognitive and behavioural deficits. Nevertheless, our species-typical capacity for depressed mood implies that it serves an adaptive function. Here we apply an interdisciplinary theory of brain function to explain depressed mood and its clinical manifestations. Combining insights from the free-energy principle (FEP) with evolutionary theorising in psychology, we argue that depression reflects an adaptive response to perceived threats of aversive social outcomes (e.g., exclusion) that minimises the likelihood of surprising interpersonal exchanges (i.e., those with unpredictable outcomes). We suggest that psychopathology typically arises from ineffectual attempts to alleviate interpersonal difficulties and/or hyper-reactive neurobiological responses to social stress (i.e., uncertainty), which often stems from early experience that social uncertainty is difficult to resolve

Stable Heterogeneity for the Production of Diffusible Factors in Cell Populations

The production of diffusible molecules that promote survival and growth is common in bacterial and eukaryotic cell populations, and can be considered a form of cooperation between cells. While evolutionary game theory shows that producers and non-producers can coexist in well-mixed populations, there is no consensus on the possibility of a stable polymorphism in spatially structured populations where the effect of the diffusible molecule extends beyond one-step neighbours. I study the dynamics of biological public goods using an evolutionary game on a lattice, taking into account two assumptions that have not been considered simultaneously in existing models: that the benefit of the diffusible molecule is a non-linear function of its concentration, and that the molecule diffuses according to a decreasing gradient. Stable coexistence of producers and non-producers is observed when the benefit of the molecule is a sigmoid function of its concentration, while strictly diminishing returns lead to coexistence only for very specific parameters and linear benefits never lead to coexistence. The shape of the diffusion gradient is largely irrelevant and can be approximated by a step function. Since the effect of a biological molecule is generally a sigmoid function of its concentration (as described by the Hill equation), linear benefits or strictly diminishing returns are not an appropriate approximations for the study of biological public goods. A stable polymorphism of producers and non-producers is in line with the predictions of evolutionary game theory and likely to be common in cell populations

Metal-insulator transition in vanadium dioxide nanobeams: probing sub-domain properties of strongly correlated materials

Many strongly correlated electronic materials, including high-temperature superconductors, colossal magnetoresistance and metal-insulator-transition (MIT) materials, are inhomogeneous on a microscopic scale as a result of domain structure or compositional variations. An important potential advantage of nanoscale samples is that they exhibit the homogeneous properties, which can differ greatly from those of the bulk. We demonstrate this principle using vanadium dioxide, which has domain structure associated with its dramatic MIT at 68 degrees C. Our studies of single-domain vanadium dioxide nanobeams reveal new aspects of this famous MIT, including supercooling of the metallic phase by 50 degrees C; an activation energy in the insulating phase consistent with the optical gap; and a connection between the transition and the equilibrium carrier density in the insulating phase. Our devices also provide a nanomechanical method of determining the transition temperature, enable measurements on individual metal-insulator interphase walls, and allow general investigations of a phase transition in quasi-one-dimensional geometry.Comment: 9 pages, 3 figures, original submitted in June 200

Supporting Roma Voices

The Supporting Roma Voice project has aimed to address emerging knowledge gaps in the way in which the inclusion of migrant Roma in the UK is being addressed. Specifically, research by Brown, Scullion and Martin (2013) identified a demand from public authorities for social inclusion work directed towards migrant Roma communities to be developed and delivered by members of migrant Roma communities themselves. However, what was also lacking was an adequate evidence base about the settlement of migrant Roma in the UK and the varied experiences associated with this transition. This report explores the views and experiences of a large number of Roma people who have migrated to the UK in recent years. The research was designed in partnership with a team of researchers from the Roma communities and undertaken wholly by these researchers. The research study aimed to explore the following issues: - The settlement and integration experiences of Roma migrants living in areas across the UK. - The specific areas of community relations, housing, education, employment and social welfare and their role in settlement in the UK. - The provision of knowledge that would enable local authorities and other services to enhance the settlement experience of Roma migrants now and in the future. A total of 159 people participated in 19 focus groups, which took place in the following locations: Glasgow, Leicester, London, Oldham, Salford and Sheffield. It should be noted that owing to the heterogeneity of the Roma population this report does not attempt to make definitive statements about the situation and views of all Roma migrants in the UK. This report was co-authored by members of the academic team in partnership with community researchers. The fieldwork was undertaken in early 2016 prior to the UK’s referendum on staying in the European Union

Carrier-mediated magnetoelectricity in complex oxide heterostructures

While tremendous success has been achieved to date in creating both single phase and composite magnetoelectric materials, the quintessential electric-field control of magnetism remains elusive. In this work, we demonstrate a linear magnetoelectric effect which arises from a novel carrier-mediated mechanism, and is a universal feature of the interface between a dielectric and a spin-polarized metal. Using first-principles density functional calculations, we illustrate this effect at the SrRuO$_3$/SrTiO$_3$ interface and describe its origin. To formally quantify the magnetic response of such an interface to an applied electric field, we introduce and define the concept of spin capacitance. In addition to its magnetoelectric and spin capacitive behavior, the interface displays a spatial coexistence of magnetism and dielectric polarization suggesting a route to a new type of interfacial multiferroic

Climate-carbon cycle uncertainties and the Paris Agreement

The Paris Agreement aims to address the gap between existing climate policies and policies consistent with ‘holding the increase in global average temperature to well below 2C’. The feasibility of meeting the target has been questioned both in terms of the possible requirement for negative emissions, and ongoing debate on the sensitivity of the climate-carbon cycle system. Using a sequence of ensembles of a fully dynamic three-dimensional climate-carbon cycle model, forced by emissions from an integrated assessment model of regional-level climate policy, economy, and technological transformation, we show that a reasonable interpretation of the Paris Agreement is still technically achievable. Specifically, limiting peak (decadal) warming to less than 1.7°C, or end-century warming to less than 1.54°C, occurs in 50% of our simulations in a policy scenario without net negative emissions or excessive stringency in any policy domain. We evaluate two mitigation scenarios, with 200 GTC and 307 GTC post-2017 emissions, quantifying spatio-temporal variability of warming, precipitation, ocean acidification and marine productivity. Under rapid decarbonisation decadal variability dominates the mean response in critical regions, with significant implications for decision making, demanding impact methodologies that address non-linear spatio-temporal responses. Ignoring carbon-cycle feedback uncertainties (explaining 47% of peak warming uncertainty) becomes unreasonable under strong mitigation conditions.We acknowledge C-EERNG and Cambridge Econometrics for support, and funding from EPSRC (to J.-F.M., fellowship number EP/ K007254/1); the Newton Fund (to J.-F.M., P.S. and J.E.V., EPSRC grant number EP/N002504/1 and ESRC grant number ES/N013174/1), NERC (to N.R.E., P.H. and H.P., grant number NE/P015093/1), CONICYT (to P.S.), the Philomathia Foundation (to J.E.V.) and Horizon 2020 (to H.E.P. and J.-F.M., the Sim4Nexus project)