Non-linear reduced modeling of dynamical systems using kernel methods
and low-rank approximation
October 30, 2017
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Statistics
Machine Learning
Machine Learning
Reduced modeling of a computationally demanding dynamical system aims at
approximating its trajectories, while optimizing the trade-off between accuracy
and computational complexity. In this work, we propose to achieve such an
approximation...
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....
Fixing the AdS3 metric from the pure state entanglement entropies of
CFT2
October 23, 2017
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Physics
High Energy Physics - Theory
Statistical Mechanics
General Relativity and Quantum Cosmology
Quantum Physics
High Energy Physics - Theory
Statistical Mechanics
General Relativity and Quantum Cosmology
Quantum Physics
In this paper, based on RT formula, by identifying the pure state UV and IR
entanglement entropies of a perturbed CFT2 with geodesic lengths in the
bulk, we demonstrate that the dual geometry is uniquely determined to be
asymptotically A...
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...