8,317 research outputs found
Computation of generalized equivariant cohomologies of Kac-Moody flag varieties
In 1998, Goresky, Kottwitz, and MacPherson showed that for certain projective
varieties X equipped with an algebraic action of a complex torus T, the
equivariant cohomology ring H_T(X) can be described by combinatorial data
obtained from its orbit decomposition. In this paper, we generalize their
theorem in three different ways. First, our group G need not be a torus.
Second, our space X is an equivariant stratified space, along with some
additional hypotheses on the attaching maps. Third, and most important, we
allow for generalized equivariant cohomology theories E_G^* instead of H_T^*.
For these spaces, we give a combinatorial description of E_G(X) as a subring of
\prod E_G(F_i), where the F_i are certain invariant subspaces of X. Our main
examples are the flag varieties G/P of Kac-Moody groups G, with the action of
the torus of G. In this context, the F_i are the T-fixed points and E_G^* is a
T-equivariant complex oriented cohomology theory, such as H_T^*, K_T^* or
MU_T^*. We detail several explicit examples.Comment: 19 pages, 6 figures, this is a new and completely modified version of
DG/040207
Exact Solutions for Boson-Fermion Stars in (2+1) dimensions
We solve Einstein equations coupled to a complex scalar field with infinitely
large self-interaction, degenerate fermions, and a negative cosmological
constant in dimensions. Exact solutions for static boson-fermion stars
are found when circular symmetry is assumed. We find that the minimum binding
energy of boson-fermion star takes a negative value if the value of the
cosmological constant is sufficiently small.Comment: 19 pages, 5 figures, RevTeX 3.0, second revised versio
Cluster decomposition, T-duality, and gerby CFT's
In this paper we study CFT's associated to gerbes. These theories suffer from
a lack of cluster decomposition, but this problem can be resolved: the CFT's
are the same as CFT's for disconnected targets. Such theories also lack cluster
decomposition, but in that form, the lack is manifestly not very problematic.
In particular, we shall see that this matching of CFT's, this duality between
noneffective gaugings and sigma models on disconnected targets, is a worldsheet
duality related to T-duality. We perform a wide variety of tests of this claim,
ranging from checking partition functions at arbitrary genus to D-branes to
mirror symmetry. We also discuss a number of applications of these results,
including predictions for quantum cohomology and Gromov-Witten theory and
additional physical understanding of the geometric Langlands program.Comment: 61 pages, LaTeX; v2,3: typos fixed; v4: writing improved in several
sections; v5: typos fixe
Liquid Polymorphism and Density Anomaly in a Lattice Gas Model
We present a simple model for an associating liquid in which polymorphism and
density anomaly are connected. Our model combines a two dimensional lattice gas
with particles interacting through a soft core potential and orientational
degrees of freedom represented through thermal \char`\"{}ice
variables\char`\"{} . The competition between the directional attractive forces
and the soft core potential leads to a phase diagram in which two liquid phases
and a density anomaly are present. The coexistence line between the low density
liquid and the high density liquid has a positive slope contradicting the
surmise that the presence of a density anomaly implies that the high density
liquid is more entropic than the low density liquid
Developing a Virtual Community of Practice Framework for a Dispersed Group of Innovation Practitioners
This project lays the groundwork for establishing a virtual community of practice (VCoP) for innovation professionals within my organization across 8 countries and multiple business units. The literature review includes definitions of communities of practice, how they vary from other types of groups and teams, the benefits they provide to the organization and to the individual, as well best practices and considerations for building and launching a VCoP. The deliverable is a proposal that will be submitted to the global leadership of the organization for review and approval
Learning feed-forward one-shot learners
One-shot learning is usually tackled by using generative models or
discriminative embeddings. Discriminative methods based on deep learning, which
are very effective in other learning scenarios, are ill-suited for one-shot
learning as they need large amounts of training data. In this paper, we propose
a method to learn the parameters of a deep model in one shot. We construct the
learner as a second deep network, called a learnet, which predicts the
parameters of a pupil network from a single exemplar. In this manner we obtain
an efficient feed-forward one-shot learner, trained end-to-end by minimizing a
one-shot classification objective in a learning to learn formulation. In order
to make the construction feasible, we propose a number of factorizations of the
parameters of the pupil network. We demonstrate encouraging results by learning
characters from single exemplars in Omniglot, and by tracking visual objects
from a single initial exemplar in the Visual Object Tracking benchmark.Comment: The first three authors contributed equally, and are listed in
alphabetical orde
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