Relations between Reeb graphs, systems of hypersurfaces and epimorphisms
onto free groups
February 6, 2020
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Mathematics
Group Theory
Geometric Topology
We construct a correspondence between epimorphisms φ:π1(M)→Fr from the fundamental group of a compact manifold M onto the free
group of rank r, and systems of r framed non-separating hypersurfaces in
M, which ...
Analysis of Blocking in mmWave Cellular Systems: Application to Relay
Positioning
February 5, 2020
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Electrical Engineering and Systems Science
Computer Science
Mathematics
Signal Processing
Information Theory
Information Theory
Signal Processing
Information Theory
Information Theory
Within the framework of 5G, blockage effects occurring in the mmWave band are
critical. Previous works describe the effects of blockages in isolated and
multiple links for simple blocking objects, modeled with mathematical tools
such as sto...
Function approximation by neural nets in the mean-field regime: Entropic
regularization and controlled McKean-Vlasov dynamics
February 5, 2020
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Computer Science
Mathematics
Statistics
Machine Learning
Optimization and Control
Probability
Machine Learning
We consider the problem of function approximation by two-layer neural nets
with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler
divergence. Our setting is the mean-field limit, where the finite population of
neuro...
An upper bound conjecture for the Yokota invariant
February 5, 2020
Mathematics
Geometric Topology
We conjecture an upper bound on the growth of the Yokota invariant of
polyhedral graphs, extending a previous result on the growth of the
6j-symbol. Using Barrett's Fourier transform we are able to prove this
conjecture in a large family ...
A lower bound for the modulus of the Dirichlet eta function on a
partition P from 2-D principal component analysis and transitive
composition
February 5, 2020
Mathematics
General Mathematics
The present manuscript aims to derive an expression for the lower bound of
the modulus of the Dirichlet eta function on vertical lines ℜ(s)=α.
The approach employs concepts of two-dimensional principal component analysis
built on a...
Global Bifurcation of Periodic Solutions in Delay Equations with
Symmetric Monotone Feedback
February 4, 2020
Mathematics
Dynamical Systems
We study the periodic solutions of the delay equation
x˙(t)=f(x(t),x(t−1)), where f scalar is strictly monotone in the
delayed component and has even-odd symmetry. We completely describe the global
bifurcation structure of periodic...
Exploratory Machine Learning with Unknown Unknowns
February 4, 2020
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Computer Science
Statistics
Machine Learning
Artificial Intelligence
Machine Learning
In conventional supervised learning, a training dataset is given with
ground-truth labels from a known label set, and the learned model will classify
unseen instances to known labels. This paper studies a new problem setting in
which there ...
On hybrid order dimension
February 4, 2020
Mathematics
Combinatorics
The notion of interval order was introduced by Norbert Wiener \cite{wie} in
order to clarify the relation between the notion of an instant of time and that
of a period of time. This was a problem on which Bertrand Russell \cite{rus}
worked ...
The relative isoperimetric inequality for minimal submanifolds with free
boundary in the Euclidean space
February 3, 2020
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Mathematics
Differential Geometry
Analysis of PDEs
In this paper, we mainly consider the relative isoperimetric inequalities for
minimal submanifolds with free boundary. We first generalize ideas of
restricted normal cones introduced by Choe-Ghomi-Ritor\'e in \cite{CGR06} and
obtain an opti...
Operations on the Hochschild Bicomplex of a Diagram of Algebras
February 3, 2020
Mathematics
Category Theory
Algebraic Topology
Rings and Algebras
A diagram of algebras is a functor valued in a category of associative
algebras. I construct an operad acting on the Hochschild bicomplex of a diagram
of algebras. Using this operad, I give a direct proof that the Hochschild
cohomology of a...