362,110 research outputs found
D2-brane Chern-Simons theories: F-maximization = a-maximization
We study a system of N D2-branes probing a generic Calabi-Yau three-fold
singularity in the presence of a non-zero quantized Romans mass n. We argue
that the low-energy effective N = 2 Chern-Simons quiver gauge theory flows to a
superconformal fixed point in the IR, and construct the dual AdS_4 solution in
massive IIA supergravity. We compute the free energy F of the gauge theory on
S^3 using localization. In the large N limit we find F = c(nN)^{1/3}a^{2/3},
where c is a universal constant and a is the a-function of the "parent"
four-dimensional N = 1 theory on N D3-branes probing the same Calabi-Yau
singularity. It follows that maximizing F over the space of admissible
R-symmetries is equivalent to maximizing a for this class of theories.
Moreover, we show that the gauge theory result precisely matches the
holographic free energy of the supergravity solution, and provide a similar
matching of the VEV of a BPS Wilson loop operator.Comment: 19 pages; v2: minor correction
Submodular Welfare Maximization
An overview of different variants of the submodular welfare maximization
problem in combinatorial auctions. In particular, I studied the existing
algorithmic and game theoretic results for submodular welfare maximization
problem and its applications in other areas such as social networks
Neural Expectation Maximization
Many real world tasks such as reasoning and physical interaction require
identification and manipulation of conceptual entities. A first step towards
solving these tasks is the automated discovery of distributed symbol-like
representations. In this paper, we explicitly formalize this problem as
inference in a spatial mixture model where each component is parametrized by a
neural network. Based on the Expectation Maximization framework we then derive
a differentiable clustering method that simultaneously learns how to group and
represent individual entities. We evaluate our method on the (sequential)
perceptual grouping task and find that it is able to accurately recover the
constituent objects. We demonstrate that the learned representations are useful
for next-step prediction.Comment: Accepted to NIPS 201
- …