A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

Second Screen User Profiling and Multi-level Smart Recommendations in the context of Social TVs

In the context of Social TV, the increasing popularity of first and second screen users, interacting and posting content online, illustrates new business opportunities and related technical challenges, in order to enrich user experience on such environments. SAM (Socializing Around Media) project uses Social Media-connected infrastructure to deal with the aforementioned challenges, providing intelligent user context management models and mechanisms capturing social patterns, to apply collaborative filtering techniques and personalized recommendations towards this direction. This paper presents the Context Management mechanism of SAM, running in a Social TV environment to provide smart recommendations for first and second screen content. Work presented is evaluated using real movie rating dataset found online, to validate the SAM's approach in terms of effectiveness as well as efficiency.Comment: In: Wu TT., Gennari R., Huang YM., Xie H., Cao Y. (eds) Emerging Technologies for Education. SETE 201

Comment on "Novel Convective Instabilities in a Magnetic Fluid"

Comment on the paper "Novel Convective Instabilities in a Magnetic Fluid" by W. Luo, T. Du, and J. Huang, Phys. Rev. Lett., v.82, p.4134 (1999).Comment: 1 page, 1 figure, To appear in Phys. Rev. Lett. (2001