Spectral and Hodge theory of `Witt' incomplete cusp edge spaces

Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Assuming such a space is Witt, we construct a fundamental solution to the heat equation, and using a precise description of its asymptotic behavior at the singular set, we prove that the Hodge-Laplacian on differential forms is essentially self-adjoint, with discrete spectrum satisfying Weyl asymptotics. We go on to prove bounds on the growth of $L^2$-harmonic forms at the singular set and to prove a Hodge theorem, namely that the space of $L^2$-harmonic forms is naturally isomorphic to the middle-perversity intersection cohomology. Moreover, we develop an asymptotic expansion for the heat trace near $t = 0$

It’s All About Race: How State Legislators Respond to Immigrant Constituents

How do elected representatives respond to the needs of immigrant constituents? We report the results of a field experiment on U.S. state legislators in which the nativity, likelihood of voting, and race/ethnicity of a hypothetical constituent are independently manipulated. The experimental design allows us to contribute new insights by isolating the various elements that may impede the connection between immigrants and elected representatives. Moreover, we explore racial/ethnic identities beyond black and white by including Latino and Asian aliases. Contrary to expectations, nativity and voting status do not affect response rates. Instead, legislator behavior appears to be driven by racial/ethnic bias. Whites benefit from the highest response rate, while blacks, Hispanics, and Asians all receive lower rates, respectively. This bias follows a partisan logic. The low response rate for Hispanic constituents comes primarily from Republican legislators, whereas Asians experience bias from representatives of both parties. We argue that this difference may result from Hispanic identity sending a stronger signal about partisan affiliation, or from a prejudicial view of Asians as outsiders. In this last interpretation, rather than the model minority, Asians become the excluded minority

Holocene vegetation change, Aboriginal wetland use and the impact of European settlement on the Fleurieu Peninsula, South Australia

© ArnoldA fossil pollen and charcoal record from a cyperaceous swamp on the Fleurieu Peninsula, South Australia, was investigated to provide a history of pre- and post-European settlement vegetation change. It was found that the swamp initiated sometime before 8220 calibrated years BP. High rates of peat development and the expansion of swamp species between 7000 BP and 4500 cal. BP indicated wet conditions at that time. The swamp became drier in the late Holocene and some peat may have been lost through deflation. Macroscopic charcoal and Typha pollen suggested that Aborigines deliberately burned the upland wetlands during the mid to late Holocene. Prior to European settlement climate changes generated community shifts in the terrestrial vegetation. The record revealed a transition from an early-Holocene Eucalyptus woodland to an Allocasuarina wet-heath in the humid mid-Holocene, a community type with no modern analogue in the region. In the drier late Holocene, a Eucalyptus -dominated woodland returned. The impacts of European settlement were clearly seen in changes in sedimentation rates and in both terrestrial and wetland flora. Allocasuarina verticillata declined early in the European period and fire-tolerant species were promoted, before the almost complete removal of native vegetation through broad-scale land clearance and its replacement with nonnative pasture species. Compositional changes to the swamp flora were marked through the European phase with Acacia expanding early in settlement and later being replaced by Leptospermum, in response to changed fire and regional hydrological regimes. The impact of European land use is discussed in relation to Holocene climate-driven vegetation changes and aspects of Aboriginal land use.Sophia Bickford and Peter Gel

Wetland and terrestrial vegetation change since European settlement on the Fleurieu Peninsula, South Australia

Copyright © 2008 SAGE PublicationsMicrofossil, sediment and documentary records provide a history of European land use and its impact on the vegetation of the Fleurieu Peninsula, South Australia. Two sedimentary cores were analysed for their fossil pollen and charcoal composition. Chronologies were established using a combination of 210Pb, 14C and microfossil markers. Primary and secondary evidence for the spatial expansion of land uses in the region were compiled providing local-, bioregional- and regional-scaled European settlement histories. The settlement and land-use histories of the major vegetation types in the region were different and were closely determined by the nature of the vegetation itself. The sedimentary and microfossil records indicate that wetland and terrestrial vegetation have undergone sequential changes of composition. There is evidence of a decline in fire-sensitive understorey species and the decline is likely due to intensive firing and grazing of scleropyllous woodlands and forests early in European settlement. Early-settlement native forestry practices were intensive, however they did not alter overstorey tree composition. Mid-twentieth-century wholesale vegetation clearance is clearly marked in the pollen record by a decline in Eucalyptus and increase in herbaceous species. Wetland vegetation was highly impacted by European land practices through changes to sediment inputs and hydrological conditions that began prior to catchment clearance, during the phase of intensive firing and grazing. Through the integration of multiscaled, ecosystem-specific historical settlement histories and palaeoecological analysis, correlations between past land uses and biotic responses can be confidently demonstrated.Sophia Bickford, Peter Gell and Gary J. Hancoc