Assuming Schanuel's Conjecture we prove that for any variety V over the
algebraic closure over the rational numbers, of dimension n and with dominant
projections, there exists a generic point in V. We obtain in this way many
instances of th...
Geometry, Computation, and Optimality in Stochastic Optimization
September 23, 2019
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Mathematics
Computer Science
Statistics
Optimization and Control
Information Theory
Machine Learning
Information Theory
Machine Learning
We study computational and statistical consequences of problem geometry in
stochastic and online optimization. By focusing on constraint set and gradient
geometry, we characterize the problem families for which stochastic- and
adaptive-grad...
Manifold Fitting under Unbounded Noise
September 23, 2019
|
Statistics
Computer Science
Machine Learning
Machine Learning
There has been an emerging trend in non-Euclidean statistical analysis of
aiming to recover a low dimensional structure, namely a manifold, underlying
the high dimensional data. Recovering the manifold requires the noise to be of
certain co...
Algebras for enriched ∞-operads
September 22, 2019
Mathematics
Algebraic Topology
Category Theory
Using the description of enriched ∞-operads as associative algebras in
symmetric sequences, we define algebras for enriched ∞-operads as
certain modules in symmetric sequences. For V a symmetric monoidal
model categ...
On the simplest static and stationary vacuum quadrupolar metrics
September 22, 2019
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Physics
General Relativity and Quantum Cosmology
In the present paper we argue that a special case of the Bach-Weyl metric
describing a static configuration of two Schwarzschild black holes gives rise,
after extending its parameter space to complex values, to a very simple
2-parameter mod...
Time Series, Persistent Homology and Chirality
September 21, 2019
Mathematics
Statistics
Probability
Algebraic Topology
Statistics Theory
Statistics Theory
We investigate the point process of persistent diagram for Brownian motions
with drift, obtaining some of its basic characteristics. Further we introduce
and study the refinement of the persistent homology, assigning to each bar its
chirali...
Efficient estimation of the modified Gromov-Hausdorff distance between
unweighted graphs
September 21, 2019
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Computer Science
Mathematics
Computational Geometry
Geometric Topology
Metric Geometry
Gromov-Hausdorff distances measure shape difference between the objects
representable as compact metric spaces, e.g. point clouds, manifolds, or
graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an
NP-Hard optimizatio...
Upper Ramification Groups for Arbitrary Valuation Rings
September 21, 2019
|
Mathematics
Number Theory
Algebraic Geometry
T. Saito established a ramification theory for ring extensions locally of
complete intersection. We show that for a Henselian valuation ring A with
field of fractions K and for a finite Galois extension L of K, the
integral closure ...
Supercuspidal representations of GLn(F) distinguished by a
unitary involution
September 20, 2019
|
Mathematics
Representation Theory
Number Theory
Representation Theory
Number Theory
Let F/F0 be a quadratic extension of non-archimedean locally compact
fields of residue characteristic p=2. Let R be an algebraically closed
field of characteristic different from p. For π a supercuspidal
representation of...
A Note on Fuzzy Automorphism and Inner Automorphism of Groups
September 20, 2019
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Mathematics
Group Theory
The fuzzification of classical set theory came into existence when Zadeh [1]
laid down the concept of a fuzzy set as a generalization of a crisp set. The
objective of this paper is to extend the concept of fuzzy endomorphism to fuzzy
automo...