The g-theorem is a momentous result in combinatorics that gives a complete
numerical characterization of the face numbers of simplicial convex polytopes.
The g-conjecture asserts that the same numerical conditions given in the
g-theor...
Strongly Dependent Ordered Abelian Groups and Henselian Fields
June 11, 2017
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Mathematics
Logic
Group Theory
Strongly dependent ordered abelian groups have finite dp-rank. They are
precisely those groups with finite spines and ∣{p prime:[G:pG]=∞}∣<∞. We apply this to show that if K is a
strongly dependent field, then (K,v)...
Topology of irrationally indifferent attractors
June 8, 2017
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Mathematics
Dynamical Systems
Functional Analysis
Number Theory
Dynamical Systems
Functional Analysis
Number Theory
We study the post-critical set of a class of holomorphic systems with an
irrationally indifferent fixed point. We prove a trichotomy for the topology of
the post-critical set based on the arithmetic of the rotation number at the
fixed point...
Experiments of posture estimation on vehicles using wearable
acceleration sensors
June 6, 2017
Computer Science
Human-Computer Interaction
Distributed, Parallel, and Cluster Computing
In this paper, we study methods to estimate drivers' posture in vehicles
using acceleration data of wearable sensor and conduct a field test. Recently,
sensor technologies have been progressed. Solutions of safety management to
analyze vita...
Reversed Dickson polynomials of the (k+1)-th kind over finite fields,
II
June 5, 2017
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Mathematics
Number Theory
Number Theory
Let p be an odd prime. In this paper, we study the permutation behaviour of
the reversed Dickson polynomials of the (k+1)-th kind Dn,k(1,x) when
n=pl1+3, n=pl1+pl2+pl3, and
n=pl1+pl2+pl3+pl4, w...
On nonlinear instability of Prandtl's boundary layers: the case of
Rayleigh's stable shear flows
June 5, 2017
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Mathematics
Physics
Mathematical Physics
Mathematical Physics
Analysis of PDEs
In 1904, Prandtl introduced his famous boundary layer in order to describe
the behavior of solutions of Navier Stokes equations near a boundary as the
viscosity goes to 0. His Ansatz has later been justified for analytic data by
R.E. Cafl...
Mapping properties of the Hilbert and Fubini--Study maps in K\"ahler
geometry
May 31, 2017
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Mathematics
Differential Geometry
Differential Geometry
Suppose that we have a compact K\"ahler manifold X with a very ample line
bundle L. We prove that any positive definite hermitian form on the
space H0(X,L) of holomorphic sections can be written as an
L2-inner...
Birkhoff's Theorem for Quasi-Metric Gravity
May 31, 2017
Physics
General Relativity and Quantum Cosmology
Working within the quasi-metric framework (QMF), it is examined if the
gravitational field exterior to an isolated, spherically symmetric body is
necessarily metrically static, or equivalently, whether or not Birkhoff's
theorem holds for qu...
Counterfactual Multi-Agent Policy Gradients
May 24, 2017
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Computer Science
Artificial Intelligence
Multiagent Systems
Artificial Intelligence
Multiagent Systems
Cooperative multi-agent systems can be naturally used to model many real
world problems, such as network packet routing and the coordination of
autonomous vehicles. There is a great need for new reinforcement learning
methods that can effic...
Real models for the framed little n-disks operads
May 23, 2017
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Mathematics
Quantum Algebra
Algebraic Topology
Quantum Algebra
Algebraic Topology
We study the action of the orthogonal group on the little n-disks operads.
As an application we provide small models (over the reals) for the framed
little n-disks operads. It follows in particular that the framed little
n-disks opera...