On Ordinal Invariants in Well Quasi Orders and Finite Antichain Orders
November 1, 2017
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Mathematics
Logic
Combinatorics
We investigate the ordinal invariants height, length, and width of well quasi
orders (WQO), with particular emphasis on width, an invariant of interest for
the larger class of orders with finite antichain condition (FAC). We show that
the w...
Sophisticated and small versus simple and sizeable: When does it pay off
to introduce drifting coefficients in Bayesian VARs?
November 1, 2017
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Statistics
Economics
Methodology
Econometrics
Applications
Computation
We assess the relationship between model size and complexity in the
time-varying parameter VAR framework via thorough predictive exercises for the
Euro Area, the United Kingdom and the United States. It turns out that
sophisticated dynamics...
Efficient computation of minimum-area rectilinear convex hull under
rotation and generalizations
October 30, 2017
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Computer Science
Mathematics
Computational Geometry
Combinatorics
Computational Geometry
Combinatorics
Let P be a set of n points in the plane. We compute the value of
θ∈[0,2π) for which the rectilinear convex hull of P, denoted by
RHθ(P), has minimum (or maximum) area in optimal O(nlogn)
time and $O(n...
Cosmological constant as quantum error correction from generalised gauge
invariance in double field theory
October 29, 2017
Physics
High Energy Physics - Theory
The holographic principle and its realisation as the AdS/CFT correspondence
leads to the existence of the so called precursor operators. These are boundary
operators that carry non-local information regarding events occurring deep
inside th...
Paley--Wiener theorems on the Siegel upper half-space
October 27, 2017
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Mathematics
Complex Variables
In this paper we study spaces of holomorphic functions on the Siegel upper
half-space U and prove Paley-Wiener type theorems for such spaces.
The boundary of U can be identified with the Heisenberg group
Hn....
The Implicit Bias of Gradient Descent on Separable Data
October 27, 2017
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Statistics
Computer Science
Machine Learning
Machine Learning
We examine gradient descent on unregularized logistic regression problems,
with homogeneous linear predictors on linearly separable datasets. We show the
predictor converges to the direction of the max-margin (hard margin SVM)
solution. The...
The cohomology of projective unitary groups
October 25, 2017
Mathematics
Algebraic Topology
The projective unitary group PU(n) is the quotient of the unitary group U(n)
by its center. We compute the integral cohomology ring of PU(n) using explicit
constructed generators....
Pm Interior Penalty Nonconforming Finite Element Methods
for 2m-th Order PDEs in Rn
October 20, 2017
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
Numerical Analysis
Numerical Analysis
In general n-dimensional simplicial meshes, we propose a family of interior
penalty nonconforming finite element methods for 2m-th order partial
differential equations, where m≥0 and n≥1. For this family of
nonconforming f...
A factorisation theory for generalised power series and omnific integers
October 19, 2017
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Mathematics
Rings and Algebras
Logic
We prove that in every ring of generalised power series with non-positive
real exponents and coefficients in a field of characteristic zero, every series
admits a factorisation into finitely many irreducibles of infinite support, the
number...
BPZ equations for higher degenerate fields and non-perturbative
Dyson-Schwinger equations
October 18, 2017
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Physics
High Energy Physics - Theory
In the two-dimensional Liouville conformal field theory, correlation
functions involving a degenerate field satisfy partial differential equations
due to the decoupling of the null descendant field. On the other hand, the
instanton partitio...