Plethysm and cohomology representations of external and symmetric products

We prove refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients, e.g., (complexes of) constructible or coherent sheaves, or (complexes of) mixed Hodge modules on spaces such as (possibly singular) complex quasi-projective varieties. These formulae generalize our previous results for symmetric and alternating powers of such coefficients, and apply also to other Schur functors. The proofs of these results are reduced via an equivariant K\"{u}nneth formula to a more general generating series identity for abstract characters of tensor powers $\mathcal{V}^{\otimes n}$ of an element $\mathcal{V}$ in a suitable symmetric monoidal category $A$. This abstract approach applies directly also in the equivariant context for spaces with additional symmetries (e.g., finite group actions, finite order automorphisms, resp., endomorphisms), as well as for introducing an abstract plethysm calculus for symmetric sequences of objects in $A$

The Economy and Loss Given Default: Evidence from Two UK Retail Lending Datasets

Loss given default (LGD) models predict losses as a proportion of the outstanding loan, in the event a debtor goes into default. The literature on corporate sector LGD models suggests LGD is correlated to the economy and so changes in the economy could translate into different predictions of losses. In this work, the role of macroeconomic variables in loan-level retail LGD models is examined by testing the inclusion of macroeconomic variables in two different retail LGD models: a two-stage model for a residential mortgage loans data set and an ordinary least squares model for an unsecured personal loans data set. To improve loan-level predictions of LGD, indicators relating to the macroeconomy are considered with mixed results: the selected macroeconomic variable seemed able to improve the predictive performance of mortgage loan LGD estimates, but not for personal loan LGD. For mortgage loan LGD, interest rate was most beneficial but only predicted better during downturn periods, underestimating LGD during non-downturn periods. For personal loan LGD, only net lending growth is statistically significant but including this variable did not bring any improvement to R2

Scope for Credit Risk Diversification

This paper considers a simple model of credit risk and derives the limit distribution of losses under different assumptions regarding the structure of systematic risk and the nature of exposure or firm heterogeneity. We derive fat-tailed correlated loss distributions arising from Gaussian risk factors and explore the potential for risk diversification. Where possible the results are generalised to non-Gaussian distributions. The theoretical results indicate that if the firm parameters are heterogeneous but come from a common distribution, for sufficiently large portfolios there is no scope for further risk reduction through active portfolio management. However, if the firm parameters come from different distributions, then further risk reduction is possible by changing the portfolio weights. In either case, neglecting parameter heterogeneity can lead to underestimation of expected losses. But, once expected losses are controlled for, neglecting parameter heterogeneity can lead to overestimation of risk, whether measured by unexpected loss or value-at-risk

The arabidopsis DNA polymerase δ has a role in the deposition of transcriptionally active epigenetic marks, development and flowering

DNA replication is a key process in living organisms. DNA polymerase α (Polα) initiates strand synthesis, which is performed by Polε and Polδ in leading and lagging strands, respectively. Whereas loss of DNA polymerase activity is incompatible with life, viable mutants of Polα and Polε were isolated, allowing the identification of their functions beyond DNA replication. In contrast, no viable mutants in the Polδ polymerase-domain were reported in multicellular organisms. Here we identify such a mutant which is also thermosensitive. Mutant plants were unable to complete development at 28°C, looked normal at 18°C, but displayed increased expression of DNA replication-stress marker genes, homologous recombination and lysine 4 histone 3 trimethylation at the SEPALLATA3 (SEP3) locus at 24°C, which correlated with ectopic expression of SEP3. Surprisingly, high expression of SEP3 in vascular tissue promoted FLOWERING LOCUS T (FT) expression, forming a positive feedback loop with SEP3 and leading to early flowering and curly leaves phenotypes. These results strongly suggest that the DNA polymerase δ is required for the proper establishment of transcriptionally active epigenetic marks and that its failure might affect development by affecting the epigenetic control of master genes.Fil: Iglesias, Francisco Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Bruera, Natalia Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Dergan Dylon, Leonardo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Marino, Cristina Ester. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Lorenzi, Hernán. J. Craig Venter Institute; Estados UnidosFil: Mateos, Julieta Lisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; Argentina. Max Planck Institute for Plant Breeding Research; AlemaniaFil: Turck, Franziska. Max Planck Institute for Plant Breeding Research; AlemaniaFil: Coupland, George. Max Planck Institute for Plant Breeding Research; AlemaniaFil: Cerdan, Pablo Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; Argentina. Universidad de Buenos Aires. Departamento de Ciencias Exactas; Argentin