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)...
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...
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...
Corrigendum to "Model Theory of Fields with Virtually Free Group
Actions"
May 18, 2017
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Mathematics
Logic
There is an irreparable error in the proof of Theorem 3.26 in our "Model
Theory of Fields with Virtually Free Group Actions" paper and we withdraw the
claim of having proved that theorem. In fact, that theorem is false in a very
strong sens...
Subalgebras of the rank two semisimple Lie algebras
May 9, 2017
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Mathematics
Rings and Algebras
In this expository article, we describe the classification of the subalgebras
of the rank 2 semisimple Lie algebras. Their semisimple subalgebras are
well-known, and in a recent series of papers, we completed the classification
of the subal...
Discretisation of regularity structures
May 8, 2017
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Mathematics
Probability
Analysis of PDEs
We introduce a general framework allowing to apply the theory of regularity
structures to discretisations of stochastic PDEs. The approach pursued in this
article is that we do not focus on any one specific discretisation procedure.
Instead...