We initiate the axiomatic study of affine oriented matroids (AOMs) on
arbitrary ground sets, obtaining fundamental notions such as minors,
reorientations and a natural embedding into the frame work of Complexes of
Oriented Matroids. The res...
Subgroup induction property for branch groups
November 26, 2020
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Mathematics
Group Theory
The subgroup induction property is a property of self-similar groups acting
on rooted trees introduced by Grigorchuk and Wilson in 2003 that appears to
have strong implications on the structure of the groups possessing it. It was
for exampl...
Finite 2-groups with exactly three automorphism orbits
November 25, 2020
| | |
Mathematics
Group Theory
Group Theory
We give a complete classification of the finite 2-groups G for which the
automorphism group Aut(G) acting naturally on G has three
orbits. There are two infinite families and one additional group, of order
29. All ...
Pure point diffraction and entropy beyond the Euclidean space
November 25, 2020
Mathematics
Dynamical Systems
Number Theory
For Euclidean pure point diffractive Delone sets of finite local complexity
and with uniform patch frequencies it is well known that the patch counting
entropy computed along the closed centred balls is zero. We consider such sets
in the se...
The Quillen model structure on the category of diffeological spaces
November 25, 2020
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Mathematics
Algebraic Topology
We construct on the category of diffeological spaces a Quillen model
structure having smooth weak homotopy equivalences as the class of weak
equivalences....
Computation of Feedback Control Laws Based on Switched Tracking of
Demonstrations
November 25, 2020
|
Computer Science
Electrical Engineering and Systems Science
Systems and Control
Systems and Control
A common approach in robotics is to learn tasks by generalizing from special
cases given by a so-called demonstrator. In this paper, we apply this paradigm
and present an algorithm that uses a demonstrator (typically given by a
trajectory o...
AI Discovering a Coordinate System of Chemical Elements: Dual
Representation by Variational Autoencoders
November 24, 2020
|
Computer Science
Physics
Machine Learning
Chemical Physics
Machine Learning
Chemical Physics
The periodic table is a fundamental representation of chemical elements that
plays essential theoretical and practical roles. The research article discusses
the experiences of unsupervised training of neural networks to represent
elements o...
Double EPW sextics associated to Gushel-Mukai surfaces
November 24, 2020
|
Mathematics
Algebraic Geometry
Algebraic Geometry
Works by O'Grady allow to associate to a 2-dimensional Gushel-Mukai variety,
which is a K3 surface, a double EPW sextic. We characterize the K3 surfaces
whose associated double EPW sextic is smooth. As a consequence, we are able to
produce ...
Homotopies and transcendental extensions in colouring problems
November 24, 2020
Mathematics
Combinatorics
We develop the technique of geometric realizations with algebraically
independent (over the field of real algebraic numbers) coordinates of vertices
and combine it with the oriented volume method inspired by work of McLennan and
Tourky on t...
Automatic Clustering for Unsupervised Risk Diagnosis of Vehicle Driving
for Smart Road
November 24, 2020
| | | | |
Computer Science
Machine Learning
Artificial Intelligence
Early risk diagnosis and driving anomaly detection from vehicle stream are of
great benefits in a range of advanced solutions towards Smart Road and crash
prevention, although there are intrinsic challenges, especially lack of ground
truth,...