Hopf Algebras and Invariants of the Johnson Cokernel

We show that if H is a cocommutative Hopf algebra, then there is a natural action of Aut(F_n) on the nth tensor power of H which induces an Out(F_n) action on a quotient \overline{H^{\otimes n}}. In the case when H=T(V) is the tensor algebra, we show that the invariant Tr^C of the cokernel of the Johnson homomorphism studied in [J. Conant, The Johnson cokernel and the Enomoto-Satoh invariant, Algebraic and Geometric Topology, 15 (2015), no. 2, 801--821.] projects to take values in the top dimensional cohomology of Out(F_n) with coefficients in \overline{H^{\otimes n}}. We analyze the n=2 case, getting large families of obstructions generalizing the abelianization obstructions of [J. Conant, M. Kassabov, K. Vogtmann, Higher hairy graph homology, Journal of Topology, Geom. Dedicata 176 (2015), 345--374.]

Affine forward variance models

We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterized by the affine form of their cumulant generating function, which can be obtained as solution of a convolution Riccati equation. We further introduce the class of affine forward order flow intensity (AFI) models, which are structurally similar to AFV models, but driven by jump processes, and which include Hawkes-type models. We show that the cumulant generating function of an AFI model satisfies a generalized convolution Riccati equation and that a high-frequency limit of AFI models converges in distribution to the AFV model

Ariel - Volume 8 Number 5

Executive Editor James W. Lockard. Jr. Business Manager Neeraj K. Kanwal University News Martin Trichtinger World News Doug Hiller Opinions Elizabeth A. McGuire Features Patrick P. Sokas Sports Desk Shahab S. Minassian Managing Editor Edward H. Jasper Managing Associate Brenda Peterson Photography Editor Robert D. Lehman, Jr. Graphics Christine M. Kuhnl

Helicopter pilots' views of air traffic controller responsibilities: A mismatch

Controllers and pilots must work together to ensure safe and efficient helicopter flight within the London control zone. Subjective ratings of pilot perception of controller responsibility for five key flight tasks were obtained from thirty helicopter pilots. Three types of airspace were investigated. Results indicate that there is variation in pilot understanding of controller responsibility compared to the formal regulations that define controller responsibility. Significant differences in the perception of controller responsibility were found for the task of aircraft separation in class D airspace and along helicopter routes. Analysis of the patterns of response suggests that task type rather than the airspace type may be the key factor. Results are framed using the concept of a shared mental model. This research demonstrates that pilots flying in complex London airspace have an expectation of controller responsibility for certain flight tasks, in certain airspace types that is not supported by aviation regulation

Consumer Credit in America: Past, Present, and Future

In September 2016, in conjunction with Law & Contemporary Problems at Duke University School of Law, we organized a symposium on Consumer Credit in America. We sought to assess the state of consumer credit in America — to review and examine its recent history, to consider arguments for and against regulation, and to discuss the potential for future innovation. This is the introduction to the volume of articles coming out of that symposium

Delamination initiation and propagation modelling with an enriched shell element formulation

For achieving good predictability of the deformation of structural composite components in crash simulations, a proper modelling of the delamination process is crucial. However, due to industrial restrictions on the simulation time of crash simulations, detailed modelling of each ply by separate elements through the thickness is not feasible. A potential remedy is to adopt the concept of adaptive shell elements which can be enriched whenever delaminations need to be accounted for. Hence, a structural model of a thinwalled laminate can thereby initially be built up from a single layer of shell elements through the thickness. During loading, the model is then enriched locally in critical areas where delamination is predicted. In this con- tribution, we show the potential of such an approach, where delamination cracks are adaptively introduced in the analysis based on a stress criterion in terms of the transverse stresses. A specific challenge is that these stresses are predicted with low accuracy in the FE model, whereby a post-processing step is proposed where an improved prediction is reconstructed based on the momentum balance equations. We show the potential of the proposed methodologys ability to capture initiating and propagating delaminations, and can conclude that the proposed methodology appears to be suitable for the simulation of thin-walled structures undergoing substantial delaminations