22,601 research outputs found
Examples of M5-Brane Elliptic Genera
We determine the modified elliptic genus of an M5-brane wrapped on various
one modulus Calabi-Yau spaces, using modular invariance together with some
known Gopakumar-Vafa invariants of small degrees. As a bonus, we find
nontrivial relations among Gopakumar-Vafa invariants of different degrees and
genera from modular invariance.Comment: 13 page
Intrinsic Universal Measurements of Non-linear Embeddings
A basic problem in machine learning is to find a mapping from a low
dimensional latent space to a high dimensional observation space. Equipped with
the representation power of non-linearity, a learner can easily find a mapping
which perfectly fits all the observations. However such a mapping is often not
considered as good as it is not simple enough and over-fits. How to define
simplicity? This paper tries to make such a formal definition of the amount of
information imposed by a non-linear mapping. This definition is based on
information geometry and is independent of observations, nor specific
parametrizations. We prove these basic properties and discuss relationships
with parametric and non-parametric embeddings.Comment: work in progres
Geometric free energy of toric AdS4/CFT3 models
We study the supersymmetric free energy of three dimensional
Chern-Simons-matter theories holographically dual to AdS times toric
Sasaki-Einstein seven-manifolds. In the large limit, we argue that the
square of the free energy can be written as a quartic polynomial of trial
R-charges. The coefficients of the polynomial are determined geometrically from
the toric diagrams. We present the coefficients of the quartic polynomial
explicitly for generic toric diagrams with up to 6 vertices, and some
particular diagrams with 8 vertices. Decomposing the trial R-charges into
mesonic and baryonic variables, and eliminating the baryonic ones, we show that
the quartic polynomial reproduces the inverse of the Martelli-Sparks-Yau volume
function. On the gravity side, we explore the possibility of using the same
quartic polynomial as the prepotential in the AdS gauged supergravity.
Comparing Kaluza-Klein gravity and gauged supergravity descriptions, we find
perfect agreement in the mesonic sector but some discrepancy in the baryonic
sector.Comment: 39 pages, 21 figures; v2. references added, minor improvement
Power Spectrum Analysis of the 2dF QSO Sample Revisited
We revisit the power spectrum analysis of the complete sample of the two
degree field (2dF) QSO redshift (2QZ) survey, as a complementary test of the
work by Outram et al. (2003). A power spectrum consistent with that of the 2QZ
group is obtained. Differently from their approach, fitting of the power
spectrum is investigated incorporating the nonlinear effects, the geometric
distortion and the light-cone effect. It is shown that the QSO power spectrum
is consistent with the cold dark matter (CDM) model with the matter
density parameter . Our constraint on the density
parameter is rather weaker than that of the 2QZ group. We also show that the
constraint slightly depends on the equation of state parameter of the dark
energy. The constraint on from the QSO power spectrum is demonstrated,
though it is not very tight.Comment: 15 pages, 5 figures, accepted for publication in the Astrophysical
Journa
Subsampling in Smoothed Range Spaces
We consider smoothed versions of geometric range spaces, so an element of the
ground set (e.g. a point) can be contained in a range with a non-binary value
in . Similar notions have been considered for kernels; we extend them to
more general types of ranges. We then consider approximations of these range
spaces through -nets and -samples (aka
-approximations). We characterize when size bounds for
-samples on kernels can be extended to these more general
smoothed range spaces. We also describe new generalizations for -nets to these range spaces and show when results from binary range spaces can
carry over to these smoothed ones.Comment: This is the full version of the paper which appeared in ALT 2015. 16
pages, 3 figures. In Algorithmic Learning Theory, pp. 224-238. Springer
International Publishing, 201
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