A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation.Comment: 26 page

High-Precision Entropy Values for Spanning Trees in Lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed slightly. 2nd revision corrects first displayed equatio

Comparison of FDMA and CDMA for second generation land-mobile satellite communications

Code Division Multiple Access (CDMA) and Frequency Division Multiple Access (FDMA) (both analog and digital) systems capacities are compared on the basis of identical link availabilities and physical propagation models. Parameters are optimized for a bandwidth limited, multibeam environment. For CDMA, the benefits of voice activated carriers, antenna discrimination, polarization reuse, return link power control and multipath suppression are included in the analysis. For FDMA, the advantages of bandwidth efficient modulation/coding combinations, voice activated carriers, polarization reuse, beam placement, and frequency staggering were taken into account

Discrete analogue computing with rotor-routers

Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is spread throughout the system). It is also possible to efficiently check that a computation has been carried out correctly in less time than the computation itself required, provided one has a certificate that can itself be computed by the rotor-router network. Rotor-router networks can be viewed as both discrete analogues of continuous linear systems and deterministic analogues of stochastic processes.Comment: To appear in Chaos Special Focus Issue on Intrinsic and Designed Computatio

Specialized Accreditation in Collegiate Aviation: A Case Study On Evaluative Inquiry Practices Required by the Aviation Accreditation Board International

Market changes within the aviation industry have increased the demand for aviation professionals worldwide (Christensen, 2013). The Aviation Accreditation Board International (AABI) represents the only specialized accrediting organization in the world for non-engineering collegiate aviation programs (Council for Higher Education Accreditation [CHEA], 2020), and their mission is to advance quality aviation education in partnership with industry (AABI, 2019b). In 2019, AABI expanded its continuous assessment criteria despite issuing citations previously to accredited collegiate aviation programs for non-compliance predominately with continuous assessment and improvement requirements (AABI, 2020). Program accreditation through AABI has demonstrated value to students (Bjerke et al., 2016; Christensen, 2013; Prather, 2007; Radigan, 2011; Smith et al., 2017); however, contextual variables may influence the efficacy and sustainability of continuous assessment (Elliott & Goh, 2013; Staub, 2019). Using a social constructivist theoretical framework, the purpose of this study was to investigate the value of continuous assessment and improvement practices, specifically AABI Criterion 3.10, as perceived by collegiate aviation administrators and faculty at AABI-accredited collegiate aviation programs. Four programs, based on size and experience with AABI accreditation, were chosen. Interviews, supporting accreditation documents, and online data were analyzed concurrently with data collection. The findings suggested that most participating programs remained non-compliant with AABI Criterion 3.10; therefore, programs did not satisfy existing assessment requirements and were not in compliance with the newly revised criterion. Participants believed that faculty experience and workload most influenced assessment practices. They assigned the value of assessment to increased industry involvement and environmental adaptability. Overall, organizational improvements in response to continuous assessment activities generated expanded social interactions among stakeholders during unprecedented academic and industry conditions

Asteraceae

Senior Project submitted to The Division of Languages and Literature of Bard College