We shall show that there exist only finitely many nondegenerate three-term
Machin-type formulae and give explicit upper bounds for the sizes of variables....
The electron self-energy in QED at two loops revisited
November 22, 2018
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Physics
High Energy Physics - Phenomenology
High Energy Physics - Phenomenology
We reconsider the two-loop electron self-energy in quantum electrodynamics.
We present a modern calculation, where all relevant two-loop integrals are
expressed in terms of iterated integrals of modular forms. As boundary points
of the iter...
How to find MH370?
November 22, 2018
Electrical Engineering and Systems Science
Signal Processing
The disappearance of flight MH370 is possibly the greatest mystery in
aviation history. A large zone in the Southern Indian Ocean was searched
unsuccessfully leaving an open case and an unacceptable situation for the
family members. We disc...
Abstract Bivariant Cuntz Semigroups II
November 21, 2018
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Mathematics
Operator Algebras
Operator Algebras
We previously showed that abstract Cuntz semigroups form a closed symmetric
monoidal category. This automatically provides additional structure in the
category, such as a composition and an external tensor product, for which we
give concret...
Operator-norm homogenisation estimates for the system of Maxwell
equations on periodic singular structures
November 21, 2018
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Mathematics
Physics
Analysis of PDEs
Mathematical Physics
Mathematical Physics
For arbitrarily small values of ε>0, we formulate and analyse the
Maxwell system of equations of electromagnetism on ε-periodic sets
Sε⊂R3. Assuming that a family of Borel measures
$\mu^...
The geometric Cauchy problem for rank-one submanifolds
November 20, 2018
Mathematics
Differential Geometry
Given a smooth distribution D of m-dimensional planes along a
smooth regular curve γ in Rm+n, we consider the following
problem: to find an m-dimensional rank-one submanifold of Rm+n,
that ...
State of the Art in Fair ML: From Moral Philosophy and Legislation to
Fair Classifiers
November 20, 2018
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Computer Science
Statistics
Computers and Society
Machine Learning
Machine Learning
Machine learning is becoming an ever present part in our lives as many
decisions, e.g. to lend a credit, are no longer made by humans but by machine
learning algorithms. However those decisions are often unfair and
discriminating individual...
Combinatorial modifications of Reeb graphs and the realization problem
November 19, 2018
Mathematics
Geometric Topology
We prove that, up to homeomorphism, any graph subject to natural necessary
conditions on orientation and the cycle rank can be realized as the Reeb graph
of a Morse function on a given closed manifold M. Along the way, we show that
the Re...
Unifying lower bounds for algebraic machines, semantically
November 16, 2018
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Computer Science
Computational Complexity
Logic in Computer Science
This paper presents a new abstract method for proving lower bounds in
computational complexity. Based on the notion of topological and measurable
entropy for dynamical systems, it is shown to generalise three previous lower
bounds results f...
A Spectral View of Adversarially Robust Features
November 15, 2018
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Computer Science
Statistics
Machine Learning
Machine Learning
Given the apparent difficulty of learning models that are robust to
adversarial perturbations, we propose tackling the simpler problem of
developing adversarially robust features. Specifically, given a dataset and
metric of interest, the go...