In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras
of conjugacy classes of symmetric groups Sn admit a stabilization (in a
non-obvious sense) as n→∞. We extend their construction to a class of
pairs of...
Principal Sub-manifolds
April 14, 2016
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Statistics
Methodology
We propose a novel method of finding principal components in multivariate
data sets that lie on an embedded nonlinear Riemannian manifold within a
higher-dimensional space. Our aim is to extend the geometric interpretation of
PCA, while bei...
Connecting Through Obstruction; Relating Gauge Gravity and String Theory
April 13, 2016
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Physics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
General Relativity and Quantum Cosmology
High Energy Physics - Theory
In this article we provide a more detailed account of the geometry and
topology of the composite bundle formalism introduced by Tresguerres in Phys.
Rev. D 66 (2002) 064025 [1] to accommodate gravitation as a gauge theory. In
the first half...
Proposal for an experiment to verify Wigner's rotation at
non-relativistic speeds with massive spin-1/2 particles
April 12, 2016
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Physics
Quantum Physics
Quantum Physics
The Wigner rotation of quantum particles with spin is one of the fascinating
consequences of interplay between special relativity and quantum mechanics. In
this paper we show that a direct experimental verification of Wigner's rotation
is i...
Squircular Calculations
April 8, 2016
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Mathematics
General Mathematics
General Mathematics
The Fernandez-Guasti squircle is a plane algebraic curve that is an
intermediate shape between the circle and the square. It has qualitative
features that are similar to the more famous Lam\'e curve. However, unlike the
Lam\'e curve which h...
Reductive group actions
April 4, 2016
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Mathematics
Representation Theory
Algebraic Geometry
In this paper, we study rationality properties of reductive group actions
which are defined over an arbitrary field of characteristic zero. Thereby, we
unify Luna's theory of spherical systems and Borel-Tits' theory of reductive
groups. In ...
A note on the affine-invariant plank problem
April 2, 2016
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Mathematics
Metric Geometry
Metric Geometry
Suppose that C is a bounded, convex subset of Rn, and that
P1,…,Pk are planks which cover C in respective directions v1,…,vk and with widths w1,…,wk. In 1951, Bang conjectured that
the sum of re...
Beyond matroids: Secretary Problem and Prophet Inequality with general
constraints
April 1, 2016
Computer Science
Data Structures and Algorithms
Computer Science and Game Theory
We study generalizations of the "Prophet Inequality" and "Secretary Problem",
where the algorithm is restricted to an arbitrary downward-closed set system.
For {0,1}-values, we give O(log n)-competitive algorithms for both problems.
This is...
A Chernoff bound for branching random walk
March 31, 2016
Mathematics
Probability
Concentration inequalities, which prove to be very useful in a variety of
fields, provide fairly tight bounds for large deviation probability while
central limit theorem (CLT) describes the asymptotic distribution around the
mean (within sc...
Estimating Treatment Effects using Multiple Surrogates: The Role of the
Surrogate Score and the Surrogate Index
March 30, 2016
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Statistics
Economics
Methodology
Econometrics
Machine Learning
Estimating the long-term effects of treatments is of interest in many fields.
A common challenge in estimating such treatment effects is that long-term
outcomes are unobserved in the time frame needed to make policy decisions. One
approach ...