Big mapping class groups and rigidity of the simple circle
July 18, 2019
| | |
Mathematics
Dynamical Systems
Group Theory
Geometric Topology
Dynamical Systems
Group Theory
Geometric Topology
Let Γ denote the mapping class group of the plane minus a Cantor set.
We show that every action of Γ on the circle is either trivial or
semi-conjugate to a unique minimal action on the so-called simple circle....
Joint Coverage and Power Control in Highly Dynamic and Massive UAV
Networks: An Aggregative Game-theoretic Learning Approach
July 18, 2019
| | |
Electrical Engineering and Systems Science
Computer Science
Systems and Control
Systems and Control
Unmanned aerial vehicles (UAV) ad-hoc network is a significant contingency
plan for communication after a natural disaster, such as typhoon and
earthquake. To achieve efficient and rapid networks deployment, we employ
noncooperative game th...
Maximum rectilinear convex subsets
July 17, 2019
| | | | | | | | | | and others
Computer Science
Computational Geometry
Discrete Mathematics
Computational Geometry
Discrete Mathematics
Let P be a set of n points in the plane. We consider a variation of the
classical Erd\H{o}s-Szekeres problem, presenting efficient algorithms with
O(n3) running time and O(n2) space complexity that compute: (1) A subset
S of P...
Siegel modular forms of degree three and invariants of ternary quartics
July 17, 2019
|
Mathematics
Number Theory
Algebraic Geometry
We determine the structure of the graded ring of Siegel modular forms of
degree 3. It is generated by 19 modular forms, among which we identify a
homogeneous system of parameters with 7 forms of weights 4, 12, 12, 14, 18, 20
and 30. We also...
Properties of the geometry of solutions and capacity of multi-layer
neural networks with Rectified Linear Units activations
July 17, 2019
| |
Physics
Computer Science
Statistics
Disordered Systems and Neural Networks
Machine Learning
Machine Learning
Rectified Linear Units (ReLU) have become the main model for the neural units
in current deep learning systems. This choice has been originally suggested as
a way to compensate for the so called vanishing gradient problem which can
undercut...
Aspects of Ω-deformed M-theory
July 15, 2019
|
Physics
High Energy Physics - Theory
We explore the properties of Ω-deformed M-theory, with particular
focus on the Cϵ1×Cϵ2×Cϵ3 background and coupling to Ω-deformed M2 and M5
brane world-v...
Lauricella hypergeometric functions, unipotent fundamental groups of the
punctured Riemann sphere, and their motivic coactions
July 15, 2019
|
Mathematics
Physics
Algebraic Geometry
High Energy Physics - Phenomenology
Mathematical Physics
Complex Variables
Mathematical Physics
Number Theory
The goal of this paper is to raise the possibility that there exists a
meaningful theory of `motives' associated to certain hypergeometric integrals,
viewed as functions of their parameters. It goes beyond the classical theory of
motives, b...
Markov-switching State Space Models for Uncovering Musical
Interpretation
July 14, 2019
| | | | | | |
Statistics
Applications
Methodology
Applications
Methodology
For concertgoers, musical interpretation is the most important factor in
determining whether or not we enjoy a classical performance. Every performance
includes mistakes -- intonation issues, a lost note, an unpleasant sound -- but
these ar...
Projectively and affinely invariant PDEs on hypersurfaces
July 14, 2019
| |
Mathematics
Differential Geometry
In [Alekseevsky, Gutt, Manno, Moreno: "A general method to construct
invariant PDEs on homogeneous manifolds", Communications in Contemporary
Mathematics (2021)] the authors have developed a method for constructing
G-invariant PDEs impose...
Skew Generalized Polycyclic Codes with Derivations
July 13, 2019
| | |
Computer Science
Mathematics
Information Theory
Information Theory
Information Theory
Information Theory
In this paper, we first consider the iterated skew polynomial ring
R[z1;τ1,δτ1]\\[z2;τ2,δτ2],
where R is a finite ring with unity. Then we use this structure for
the construction o...