Optimal Algorithm for the Planar Two-Center Problem
July 17, 2020
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Computer Science
Computational Geometry
We study a fundamental problem in Computational Geometry, the planar
two-center problem. In this problem, the input is a set S of n points in
the plane and the goal is to find two smallest congruent disks whose union
contains all points...
Convolution Bounds on Quantile Aggregation
July 17, 2020
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Quantitative Finance
Mathematics
Risk Management
Optimization and Control
Probability
Mathematical Finance
Quantile aggregation with dependence uncertainty has a long history in
probability theory with wide applications in finance, risk management,
statistics, and operations research. Using a recent result on inf-convolution
of quantile-based ri...
Parameter estimation for Gibbs distributions
July 17, 2020
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Computer Science
Mathematics
Data Structures and Algorithms
Computational Complexity
Discrete Mathematics
Probability
We consider Gibbs distributions, which are families of probability
distributions over a discrete space Ω with probability mass function of
the form μβΩ(ω)∝eβH(ω) for β in
an interval $[\...
Exponential periods and o-minimality
July 16, 2020
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Mathematics
Number Theory
Number Theory
Let α∈C be an exponential period. We show that the real
and imaginary part of α are up to signs volumes of sets definable in the
o-minimal structure generated by Q, the real exponential function
and ${\...
Bounds on the revenue gap of linear posted pricing for selling a
divisible item
July 16, 2020
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Computer Science
Computer Science and Game Theory
Selling a perfectly divisible item to potential buyers is a fundamental task
with apparent applications to pricing communication bandwidth and cloud
computing services. Surprisingly, despite the rich literature on single-item
auctions, reve...
Homotopy groups and quantitative Sperner-type lemma
July 16, 2020
Mathematics
Algebraic Topology
Combinatorics
Geometric Topology
We consider a generalization of Sperner's lemma for a triangulation T of
(m+1)-discs D whose vertices are colored in c=n+2 colors. A proper
coloring of T on the boundary of D determines a simplicial mapping f:Sm→Sn and t...
A characterization of equivalent martingale probability measures in a
mixed renewal risk model with applications in Risk Theory
July 16, 2020
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Mathematics
Probability
If a given aggregate process S is a compound mixed renewal process under a
probability measure P, we provide a characterization of all probability
measures Q on the domain of P such that Q and P are progressively
equivalent and ...
Affine Pavings of Hessenberg Ideal Fibers
July 16, 2020
Mathematics
Algebraic Geometry
Representation Theory
We define certain closed subvarieties of the flag variety, Hessenberg ideal
fibers, and prove that they are paved by affines. Hessenberg ideal fibers are a
natural generalization of Springer fibers. In type G2, we give explicit
descripti...
String Sanitization Under Edit Distance: Improved and Generalized
July 16, 2020
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Computer Science
Data Structures and Algorithms
Let W be a string of length n over an alphabet Σ, k be a
positive integer, and S be a set of length-k substrings of W.
The ETFS problem asks us to construct a string XED such that: (i)
no string of...
Maximally Nonlinear and Nonconservative Quantum Circuits
July 15, 2020
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Physics
Classical Physics
Quantum Physics
Classical Physics
Quantum Physics
In this article, we introduce an algorithmic method to find the conservative
energy and non-conservative power of a large class of maximally nonlinear
electric circuits (including Josephson tunnel junctions, coherent quantum phase
slips, an...