Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems

Consider the classic infinite-horizon problem of stopping a one-dimensional diffusion to optimise between running and terminal rewards and suppose we are given a parametrised family of such problems. We provide a general theory of parameter dependence in infinite-horizon stopping problems for which threshold strategies are optimal. The crux of the approach is a supermodularity condition which guarantees that the family of problems is indexable by a set valued map which we call the indifference map. This map is a natural generalisation of the allocation (Gittins) index, a classical quantity in the theory of dynamic allocation. Importantly, the notion of indexability leads to a framework for inverse optimal stopping problems

The Wronskian parameterizes the class of diffusions with a given distribution at a random time

We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion theory. To illustrate we characterize the class of diffusions with the same distribution as Brownian motion at an exponentially distributed time

Parametric Set-Up of a Structural Model for FERMAT Configuration for Aeroelastic and Loads Analysis

The development of a structural finite element model for the generic aircraft configuration named FERMAT is presented. The geometry of the FERMAT configuration is based on the NASA Common Research Model (CRM). The CRM is a wing/body/nacelle/pylon/horizontal-tail configuration was originally developed for the the AIAA 4th Drag Prediction Workshop in 2009. It is based on a long-range, wide-body transonic transport. As far as the CRM is missing the vertical stabilizer as well as other well as the definition of overall aircraft characteristics, they are defined for the FERMAT configuration. For the development of the structural model a parametric modeling approach is applied, using methods from Computer Aided Geometric Design (CAGD). A design process is established, comprising the parametric modeling part, loads analysis, and the sizing of the structure considering structural and aeroelastic constraints. The parametric approach enables a wide range of variations while the the structural model for the wing-like components is as detailed as possible. The parametric design loop has three basic sequential steps. It starts with the set-up of parameterized simulation models (e.g. finite element model, aerodynamic model, mass models, and optimization model) for the given target flight shape. It follows an aeroelastic loads analysis using the condensed structural model for selected mass cases. And finally, the structural components are sized independently using the detailed structural models, where for the wing also aileron effectiveness is defined as constraints. After adapting the jig shape of the wing, the process is repeated until the structural sizing and the jig-shape converge. The structural dynamic characteristics are presented for two mass cases. The final flutter investigation is briefly described wherein advantage was derived from the parametric approach. In order to avoid the first flutter mode to be at the horizontal stabilizer, the structural concept of the load carrying structure of the horizontal stabilizer was modified and the design process repeated

Heavy Metal in Medieval Europe

How and why did plate armor come to be widely used in Medieval Europe? I trace the historical development of armor in Europe from antiquity to the middle ages, and then identify the main causes that pushed European warriors to develop and adopt plate armor from the 14th to the 16th centuries. I rely on prior research by scholars and historians of arms and armor, as well as primary source documents that describe arms and armor and their use in tournaments and on the battlefield. I conclude that a combination of social, political, military, and technical factors pushed European warriors to adopt plate armor. I also briefly discuss the demise of plate armor due to increasing use of firearms in the 16th century and the growth of professional armies

A simple hypergraph min cut algorithm

We present an algorithm for finding the minimum cut of an edge-weighted hypergraph. It is simple in every respect. It has a short and compact description, is easy to implement and has a surprisingly simple proof of correctness. The runtime is O(jV j 2 log jV j+jV j \Delta jjEjj) where jjEjj is the sum of the cardinalities of the hyperedges

Maximizing functionals of the maximum in the Skorokhod embedding problem and an application to variance swaps

The Az\'{e}ma-Yor solution (resp., the Perkins solution) of the Skorokhod embedding problem has the property that it maximizes (resp., minimizes) the law of the maximum of the stopped process. We show that these constructions have a wider property in that they also maximize (and minimize) expected values for a more general class of bivariate functions $F(W_{\tau},S_{\tau})$ depending on the joint law of the stopped process and the maximum. Moreover, for monotonic functions $g$, they also maximize and minimize $\mathbb {E}[\int_0^{\tau}g(S_t)\,dt]$ amongst embeddings of $\mu$, although, perhaps surprisingly, we show that for increasing $g$ the Az\'{e}ma-Yor embedding minimizes this quantity, and the Perkins embedding maximizes it. For $g(s)=s^{-2}$ we show how these results are useful in calculating model independent bounds on the prices of variance swaps. Along the way we also consider whether $\mu_n$ converges weakly to $\mu$ is a sufficient condition for the associated Az\'{e}ma-Yor and Perkins stopping times to converge. In the case of the Az\'{e}ma-Yor embedding, if the potentials at zero also converge, then the stopping times converge almost surely, but for the Perkins embedding this need not be the case. However, under a further condition on the convergence of atoms at zero, the Perkins stopping times converge in probability (and hence converge almost surely down a subsequence).Comment: Published in at http://dx.doi.org/10.1214/12-AAP893 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Tenth Amendment Challenges After Bond v. United States

In its recent decision in Bond v. United States, the Supreme Court explained that because the Tenth Amendment secures the freedom of the individual, private parties who otherwise satisfy Article III\u27s standing requirements and other prudential requirements may challenge federal laws as violating the Tenth Amendment. In so doing, the Court reversed the majority of circuit courts that have addressed the issue and removed a significant categorical bar to individual Tenth Amendment challenges. This Article explains Bond\u27s holding and explores its implications for future Tenth Amendment challenges by private parties. Although Bond contains some expansive language regarding the role of Tenth Amendment in protecting individual liberties, it should not be read too broadly. Bond clarified that the Tenth Amendment protects individual liberties and thus prudential, third-party standing principles do not prevent individuals from bringing a Tenth Amendment challenge against federal statutes that impair their liberties. But Bond also made clear that individual Tenth Amendment challenges must satisfy traditional Article III standing requirements and that not every violation of the Tenth Amendment automatically entails an impairment of individual liberty that supports standing. As a result, Article III standing requirements will hinder many individual Tenth Amendment challenges, and many individual challenges will not succeed without the support of states. Thus, despite the breadth of the Court\u27s language in Bond, states may significantly influence whether private parties can successfully assert the states\u27 sovereign interests in a Tenth Amendment challenge. Litigants must understand these limitations as they attempt to use Bond to challenge federal statutes that, until this point, have been protected from individual suits by the bar that most courts of appeals have imposed on private-party Tenth Amendment standing. Put succinctly, while Bond rightly removed the prudential bar to individual Tenth Amendment challenges, it did not confer Article III standing to each and every litigant alleging a Tenth Amendment injury. Litigants will still need to separately satisfy the Article III requirements, blunting the impact of Bond and likely insulating many federal statutes from individual Tenth Amendment challenges