On the eigenvalues of distance powers of circuits

Taking the d-th distance power of a graph, one adds edges between all pairs of vertices of that graph whose distance is at most d. It is shown that only the numbers -3, -2, -1, 0, 1, 2d can be integer eigenvalues of a circuit distance power. Moreover, their respective multiplicities are determined and explicit constructions for corresponding eigenspace bases containing only vectors with entries -1, 0, 1 are given.Comment: 14 page

Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups

It is shown that distance powers of an integral Cayley graph over an abelian group are again integral Cayley graphs over that group. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral spectrum

Pricing options and computing implied volatilities using neural networks

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly

To Use Constructed-Response Questions, Or Not To Use Constructed-Response Questions? That Is The Question

Advocates of Constructed Response (CR) questions argue that CR questions provide a different assessment of student knowledge than is available from Multiple Choice (MC) questions. If that is the case, and if the benefit in terms of improved assessment is substantial, then it follows that grade outcomes using CR questions should be different from those using MC questions. We investigate this using a large dataset composed of individual assessment results from thousands of students in introductory economics classes at a large public university. Empirical analysis of our large sample of students indicates that a switch to an all-MC format would result in grade changes that are in the “small” to moderate range when compared to grade changes that occur between assessments. This evidence suggests that CR questions could be abandoned at relatively little cost in grading accuracy. However, there are other arguments in favour of keeping CR questions. In particular, it has been suggested that students perceive a mix of CR and MC as “fairer” than an assessment composed exclusively of one or the other question type. Further, some instructors believe that CR questions encourage students to study harder. We provide survey evidence that supports both arguments.Principles of Economics Assessment; Multiple Choice; Constructed Response; Free Response; Essay

The metallicity dependence of WR winds

Wolf-Rayet (WR) stars are the most advanced stage in the evolution of the most massive stars. The strong feedback provided by these objects and their subsequent supernova (SN) explosions are decisive for a variety of astrophysical topics such as the cosmic matter cycle. Consequently, understanding the properties of WR stars and their evolution is indispensable. A crucial but still not well known quantity determining the evolution of WR stars is their mass-loss rate. Since the mass loss is predicted to increase with metallicity, the feedback provided by these objects and their spectral appearance are expected to be a function of the metal content of their host galaxy. This has severe implications for the role of massive stars in general and the exploration of low metallicity environments in particular. Hitherto, the metallicity dependence of WR star winds was not well studied. In this contribution, we review the results from our comprehensive spectral analyses of WR stars in environments of different metallicities, ranging from slightly super-solar to SMC-like metallicities. Based on these studies, we derived empirical relations for the dependence of the WN mass-loss rates on the metallicity and iron abundance, respectively.Comment: 5 pages, 4 figures, to be published in the Proceedings of the IAU Symposium No. 329 "The lives and death-throes of massive stars