Are the Lessons from the Financial Crisis on Using Modern Finance Theory as the Intellectual Framework for Financial Regulation Reflected in Post-crisis Regulation?

Modern finance theory informed the approach to financial regulation before the financial crisis. However, the crisis exposed the inadequacy of using modern finance theory as the intellectual framework for financial regulation, providing important lessons for future reform. Since the crisis, regulators and policymakers have been seeking to strengthen the financial system to avoid a repeat of 2008. Therefore, it is apposite to ask whether regulators and policymakers are simply taking the same, flawed pre-crisis approach and using modern finance theory as the basis for financial regulation, or whether there has been a fundamental pivot in their approach. This article examines how modern finance theory informed the pre-crisis regulatory approach, how doing so contributed to the failure of the financial system and examines two examples of post-crisis regulation to understand how, and whether, the lessons from the financial crisis are being incorporated into regulators’ and policymakers’ post-crisis approach to financial regulation

Controlling a quantum system via its boundary conditions

We numerically study a particle in a box with moving walls. In the case where the walls are oscillating sinusoidally with a small amplitude, we show that states up to the fourth state can be populated with more than 80 percent population, while higher lying states can also be selectively excited. This work introduces a way of controlling quantum systems which does not rely on (dipole) selection rules

Assessing Alternatives for Directional Detection of a WIMP Halo

The future of direct terrestrial WIMP detection lies on two fronts: new, much larger low background detectors sensitive to energy deposition, and detectors with directional sensitivity. The former can large range of WIMP parameter space using well tested technology while the latter may be necessary if one is to disentangle particle physics parameters from astrophysical halo parameters. Because directional detectors will be quite difficult to construct it is worthwhile exploring in advance generally which experimental features will yield the greatest benefits at the lowest costs. We examine the sensitivity of directional detectors with varying angular tracking resolution with and without the ability to distinguish forward versus backward recoils, and compare these to the sensitivity of a detector where the track is projected onto a two-dimensional plane. The latter detector regardless of where it is placed on the Earth, can be oriented to produce a significantly better discrimination signal than a 3D detector without this capability, and with sensitivity within a factor of 2 of a full 3D tracking detector. Required event rates to distinguish signals from backgrounds for a simple isothermal halo range from the low teens in the best case to many thousands in the worst.Comment: 4 pages, including 2 figues and 2 tables, submitted to PR

The occurrence of the extinct shark genus Sphenodus in the Jurassic of Sicily

During the systematic revision of some historical collections containing Mesozoic ammonites, housed at the "G.G. Gemmellaro" Geological Museum of the Palermo University, a fossil shark’s tooth has been discovered. This specimen, indicated as Lamna in the original catalogue, can be attributed to the genus Sphenodus, an extinct cosmopolitan shark ranging from Lower Jurassic rocks to the Paleocene. The specimen is part of the Mariano Gemmellaro Collection which mainly consists of Middle-Upper Jurassic ammonites coming from Tardàra Mountain, between Menfi and Sambuca di Sicilia (Agrigento Province, Southwestern Sicily). Some of the ammonite specimens were listed, but not illustrated, by M. Gemmellaro in a note of 1919. The succession described in this area consists (from bottom to the top) of Lower Jurassic shallow-water carbonates followed by condensed ammonitic limestones of “Rosso ammonitico-type” (Middle-Late Jurassic in age), Calpionellid limestones (Upper Jurassic-Lower Cretaceous) and cherty calcilutites of Scaglia-type (Upper Cretaceous-Eocene). Since the exact stratigraphic level from which the shark tooth comes is not recorded, a thin section was made of the rock matrix surrounding the tooth. The sedimentological and paleontological analysis of the thin section has highlighted the presence of a microfacies characteristic of the Upper Jurassic condensed deposits of Rosso ammonitico-type, data that fits very well with the geology of the Tardàra area. The study of the Tardàra shark’s tooth has provided both the stimulus and opportunity to undertake a taxonomic review of the Jurassic specimens of Sphenodus collected from a range of Sicilian localities (Gemmellaro G.G., 1871; Seguenza G., 1887; Di Stefano & Cortese, 1891; Seguenza L., 1900; De Gregorio A., 1922) that, to date, have not been re-examined in the light of more recent scholarship. In particular, the specimens described and illustrated by G.G. Gemmellaro (1871), and stored in his eponymous museum, have been revised with the aim of providing a contribution to our knowledge of the genus Sphenodus in the Sicilian Mesozoic successions

A discrete Laplace-Beltrami operator for simplicial surfaces

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace-Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay triangulations of piecewise flat surfaces revised and expanded. References added. Some minor changes, typos corrected. v3: fixed inaccuracies in discussion of flip algorithm, corrected attributions, added references, some minor revision to improve expositio

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Skydiving to Bootstrap Islands

We study families of semidefinite programs (SDPs) that depend nonlinearly on a small number of "external" parameters. Such families appear universally in numerical bootstrap computations. The traditional method for finding an optimal point in parameter space works by first solving an SDP with fixed external parameters, then moving to a new point in parameter space and repeating the process. Instead, we unify solving the SDP and moving in parameter space in a single algorithm that we call "skydiving". We test skydiving on some representative problems in the conformal bootstrap, finding significant speedups compared to traditional methods

Association Between p.Leu54Met Polymorphism at the Paraoxonase-1 Gene and Plantar Fascia Thickness in Young Subjects With Type 1 Diabetes

OBJECTIVE— In type 1 diabetes, plantar fascia, a collagen-rich tissue, is susceptible to glycation and oxidation. Paraoxonase-1 (PON1) is an HDL-bound antioxidant enzyme. PON1 polymorphisms have been associated with susceptibility to macro- and microvascular complications. We investigated the relationship between plantar fascia thickness (PFT) and PON1 gene variants, p.Leu54Met, p.Gln192Arg, and c.-107C>T, in type 1 diabetes