Scattering and Sparse Partitions, and their Applications
January 13, 2020
Computer Science
Data Structures and Algorithms
Computational Geometry
A partition P of a weighted graph G is
(σ,τ,Δ)-sparse if every cluster has diameter at most Δ,
and every ball of radius Δ/σ intersects at most τ clusters.
Similarly, P is $(\s...
An adjunction inequality obstruction to isotopy of embedded surfaces in
4-manifolds
January 12, 2020
Mathematics
Differential Geometry
Geometric Topology
Consider a smooth 4-manifold X and a diffeomorphism f:X→X. We
give an obstruction in the form of an adjunction inequality for an embedded
surface in X to be isotopic to its image under f. It follows that the
minimal genus of...
Complements of Schubert polynomials
January 12, 2020
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Mathematics
Combinatorics
Let Sw​(x) be the Schubert polynomial for a permutation w of
{1,2,…,n}. For any given composition μ, we say that xμSw​(x−1) is the complement of Sw​(x) with respect
to μ. When...
Bayesian Semi-supervised learning under nonparanormality
January 11, 2020
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Statistics
Computer Science
Machine Learning
Machine Learning
Applications
Semi-supervised learning is a model training method that uses both labeled
and unlabeled data. This paper proposes a fully Bayes semi-supervised learning
algorithm that can be applied to any binary classification problem. We assume
the labe...
FBI Transform in Gevrey Classes and Anosov Flows
January 10, 2020
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Mathematics
Analysis of PDEs
Dynamical Systems
Spectral Theory
An analytic FBI transform is built on compact manifolds without boundary,
that satisfies all the expected properties. It enables the study of microlocal
analytic and Gevrey regularity on such manifolds. This tool is then used to
study the R...
Small Algebraic Central Values of Twists of Elliptic L-Functions
January 10, 2020
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Mathematics
Number Theory
We consider heuristic predictions for small non-zero algebraic central values
of twists of the L-function of an elliptic curve E/Q by Dirichlet
characters. We provide computational evidence for these predictions and
consequence...
Unbounded field operators in categorical extensions of conformal nets
January 9, 2020
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Mathematics
Physics
Quantum Algebra
Mathematical Physics
Mathematical Physics
Operator Algebras
Quantum Algebra
Mathematical Physics
Mathematical Physics
Operator Algebras
We prove the equivalence of VOA tensor categories and conformal net tensor
categories for the following examples: all WZW models; all lattice VOAs; all
unitary parafermion VOAs; type ADE discrete series W-algebras; their tensor
products...
Regular 3-polytopes of order 2np
January 9, 2020
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Mathematics
Combinatorics
In [Problems on polytopes, their groups, and realizations, Periodica Math.
Hungarica 53 (2006) 231-255] Schulte and Weiss proposed the following problem:
{\em Characterize regular polytopes of orders 2np for n a positive integer
and $p...
Towards Secure Over-The-Air Computation
January 9, 2020
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Computer Science
Mathematics
Information Theory
Information Theory
We propose a new method to protect Over-The-Air (OTA) computation schemes
against passive eavesdropping. Our method uses a friendly jammer whose signal
is -- contrary to common intuition -- stronger at the legitimate receiver than
it is at ...
Scrollar Invariants of Tropical Curves
January 8, 2020
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Mathematics
Algebraic Geometry
Algebraic Geometry
We define scrollar invariants of tropical curves with a fixed divisor of rank
1. We examine the behavior of scrollar invariants under specialization, and
provide an algorithm for computing these invariants for a much-studied family
of tropi...