In a quantum money scheme, a bank can issue money that users cannot
counterfeit. Similar to bills of paper money, most quantum money schemes assign
a unique serial number to each money state, thus potentially compromising the
privacy of the...
Generalized maps between diffeological spaces
February 26, 2020
Mathematics
Algebraic Topology
By utilizing the idea of Colombeau's generalized function, we introduce a
notion of asymptotic map between arbitrary diffeological spaces. The category
consisting of diffeological spaces and asymptotic maps is enriched over the
category of ...
Extreme Value Theory with Spectral Techniques: application to a simple
attractor
February 25, 2020
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Mathematics
Physics
Dynamical Systems
Chaotic Dynamics
Dynamical Systems
Chaotic Dynamics
We give a brief account of application of extreme value theory in dynamical
systems by using perturbation techniques associated to the transfer operator.
We will apply it to the baker's map and we will get a precise formula for the
extremal...
Modular Exercises for Four-Point Blocks -- I
February 25, 2020
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Physics
Mathematics
High Energy Physics - Theory
Number Theory
Quantum Algebra
High Energy Physics - Theory
Number Theory
Quantum Algebra
The well-known modular property of the torus characters and torus partition
functions of (rational) vertex operator algebras (VOAs) and 2d conformal field
theories (CFTs) has been an invaluable tool for studying this class of
theories. In t...
Big Quantum cohomology of orbifold spheres
February 25, 2020
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Mathematics
Symplectic Geometry
We construct a Kodaira-Spencer map from the big quantum cohomology of a
sphere with three orbifold points to the Jacobian ring of the mirror
Landau-Ginzburg potential function. This is constructed via the Lagrangian
Floer theory of the Seid...
General elephants for threefold extremal contractions with
one-dimensional fibers: exceptional case
February 25, 2020
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Mathematics
Algebraic Geometry
Let (X,C) be a germ of a threefold X with terminal singularities along a
connected reduced complete curve C with a contraction f:(X,C)→(Z,o)
such that C=f−1(o)red and −KX is f-ample. Assume that
eac...
Biased Stochastic First-Order Methods for Conditional Stochastic
Optimization and Applications in Meta Learning
February 25, 2020
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Mathematics
Computer Science
Statistics
Optimization and Control
Machine Learning
Machine Learning
Conditional stochastic optimization covers a variety of applications ranging
from invariant learning and causal inference to meta-learning. However,
constructing unbiased gradient estimators for such problems is challenging due
to the compo...
A-polynomials, Ptolemy equations and Dehn filling
February 24, 2020
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Mathematics
Geometric Topology
Symplectic Geometry
The A-polynomial encodes hyperbolic geometric information on knots and
related manifolds. Historically, it has been difficult to compute, and
particularly difficult to determine A-polynomials of infinite families of
knots. Here, we compute ...
On minimal entanglement wedge cross section for holographic entanglement
negativity
February 24, 2020
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Physics
High Energy Physics - Theory
We demonstrate the equivalence of two different conjectures in the literature
for the holographic entanglement negativity in AdS3/CFT2, modulo certain
constants. These proposals involve certain algebraic sums of bulk geodesics
homolog...
Courant-Dorfman algebras of differential operators and Dorfman
connections of Courant algebroids
February 24, 2020
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Mathematics
Differential Geometry
We construct an algebra and a complex of multidifferential operators on
tensor products of a Courant algebroid E with values in the endomorphism bundle
of a smooth vector bundle B, predual of E, extending the standard complex of
the Courant...