100,274 research outputs found
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 . 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 . 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
Halpern-Huang directions in effective scalar field theory
Halpern and Huang recently showed that there are relevant directions in the
space of interactions at the Gaussian fixed point. I show that their result can
be derived from Polchinski's form of the Wilson renormalization group. The
derivation shows that the existence of these directions is independent of the
cutoff function used.Comment: 6 pages, plain Te
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