mRNA diffusion explains protein gradients in Drosophila early development

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of _Drosophila_. In this model, we consider that _bicoid_ mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments.We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11 to 14 of the developing embryo of _Drosophila_. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of _bicoid_ mRNA is in the range 4.6 x 10^-12^ - 1.5 x10^-11^ m^2^s^-1^, in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of _bicoid_ mRNA in _Drosophila_ [Spirov _et al._ (2009) _Development_ 136:605-614]

The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and M{\o}ller operators

This paper deals with several issues concerning the algebraic quantization of the real Proca field in a globally hyperbolic spacetime and the definition and existence of Hadamard states for that field. In particular, extending previous work, we construct the so-called M\o ller $*$-isomorphism between the algebras of Proca observables on paracausally related spacetimes, proving that the pullback of these isomorphisms preserves the Hadamard property of corresponding quasifree states defined on the two spacetimes. Then, we pull-back a natural Hadamard state constructed on ultrastatic spacetimes of bounded geometry, along this $*$-isomorphism, to obtain a Hadamard state on a general globally hyperbolic spacetime. We conclude the paper, by comparing the definition of a Hadamard state, here given in terms of wavefront set, with the one proposed by Fewster and Pfenning, which makes use of a supplementary Klein-Gordon Hadamard form. We establish an (almost) complete equivalence of the two definitions.Comment: 45 pages --- accepted in Annales Henri Poincar\'

Measuring the risk appetite of bank-controlling shareholders: The Risk-Weighted Ownership index

This study proposes a measure of the risk appetite of a bank’s ownership structure and investigates whether ownership risk propensity is related to performance and default risk. Our indicator, the Risk-Weighted Ownership (RWO), assumes that credit risk is a proxy for shareholders’ risk appetite and assigns risk weights based on the Basel standard approach to the stakes held by the top 5, 10, and 20 controlling shareholders. We calculate the RWO index using a sample of 76 listed banks from the Eurozone and the United Kingdom from 2008 to 2017. The RWO correlates with bank fundamentals when we regress it with accounting- and market-based performance and risk measures. We present two major findings. First, the RWO index incorporates the risk appetite of controlling shareholders, and its variance is affected by the ownership structure. Second, a higher risk appetite among shareholders is associated with higher profitability but lower bank capitalization, implying a trade-off between performance and default risk. Overall, we find that the risk appetite of the ownership structure is an important driver of bank performance and risk

On the rectangular mesh and the decomposition of a Green's-function-based quadruple integral into elementary integrals

Computational electromagnetic problems require evaluating the electric and magnetic fields of the physical object under investigation, divided into elementary cells with a mesh. The partial element equivalent circuit (PEEC) method has recently received attention from academic and industry communities because it provides a circuit representation of the electromagnetic problem. The surface formulation, known as S-PEEC, requires computing quadruple integrals for each mesh patch. Several techniques have been developed to simplify the computational complexity of quadruple integrals but limited to triangular meshes as used in well-known methods such as the Method of Moments (MoM). However, in the S-PEEC method, the mesh can be rectangular and orthogonal, and new approaches must be investigated to simplify the quadruple integrals. This work proposes a numerical approach that treats the singularity and reduces the computational complexity of one of the two quadruple integrals used in the S-PEEC method. The accuracy and computational time are tested for representative parallel and orthogonal meshes.ISSN:0955-799