Sizing the European Shadow Banking System: A New Methodology

One of the critical unanswered questions relating to the shadow-banking system has been to quantify its scale in an industry where entities, by design, are opaque and often outside of regulated and publically shared frameworks. However almost all shadow banking entities, including hedge funds, private equity funds and special purpose vehicles ("SPVs"), interact with the financial markets via regulated investment banks. For example, many SPVs are in fact originated as part of investment banking business and hedge funds typically transact in financial markets exclusively via the "prime brokerage" division of investment banks. This interface with the regulated banking environment combines with the typical practise by investment banks of equalizing compensation (Including bonus) ratios to revenues globally which then allows identification of the implied difference in revenues and hence assets that represents the shadow banking system. The paper will present for critique the results of this methodology to estimate the UK shadow banking system including European business managed from the UK. The estimate will imply a larger scale of shadow banking than previous estimates at £548 billion which, when combined with hedge fund assets of £360 billion (FSA, 2011) gives total shadow banking assets of over £900 billion. It is proposed that the large gap between the estimates of this paper and other estimates reflects the huge, and previously unknown, scale of offshore activities of UK investment banks

Quasiconformal mappings that highly distort dimensions of many parallel lines

We construct a quasiconformal mapping of $n$-dimensional Euclidean space, $n \geq 2$, that simultaneously distorts the Hausdorff dimension of a nearly maximal collection of parallel lines by a given amount. This answers a question of Balogh, Monti, and Tyson.Comment: 12 page

Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group

We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean C2 -smooth surface in the Heisenberg group H away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean C2 -smooth curves on surfaces. These results are then used to prove a Heisenberg version of the Gauss–Bonnet theorem. An application to Steiner’s formula for the Carnot–Carathéodory distance in H is provided

Effects of nacelle shape on drag and weight of a supersonic cruising aircraft

The quantitive relationship of cruise drag and nacelle shape was investigated for a representative advanced supersonic transport configuration. Nacelle shape parameters were systematically varied, and the effects of these variations on wave and friction drag were determined. The effects of changes in vehicle drag, propulsion weight, and specific fuel consumption on vehicle takeoff gross weight were computed. Generally, it was found that nacelle shapes such that the maximum cross-sectional area occurred at or near the nozzle exit resulted in the lowest wave drag. In fact, nacelle shapes were found that produce favorable interference effects (drag reduction) of such magnitude as to nearly offset the friction drag of the nacelle

Spatial opinion dynamics and the effects of two types of mixing

Spatially situated opinions that can be held with different degrees of conviction lead to spatiotemporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and nonlocal interaction (“telephoning”), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations