On ends of finite-volume noncompact manifolds of nonpositive curvature
December 5, 2018
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Mathematics
Geometric Topology
Differential Geometry
In this paper we confirm a folklore conjecture which suggests that for a
complete noncompact manifold M of finite volume with sectional curvature −1≤K≤0, if the universal cover of M is a visibility manifold, then
the fundame...
Scalar probes on wormholes in Lovelock theories with unique vacuum
December 5, 2018
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Physics
High Energy Physics - Theory
General Relativity and Quantum Cosmology
In this paper we present a new family of wormhole geometries in Lovelock
theories with a unique vacuum, and study their stability under scalar field
perturbations. As the solutions already known in the literature for
Chern-Simons gravity on...
Optimal stability results and nonlinear duality for L∞ entropy
and L1 viscosity solutions
December 5, 2018
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Mathematics
Analysis of PDEs
We give a new and rigorous duality relation between two central notions of
weak solutions of nonlinear PDEs: entropy and viscosity solutions. It takes the
form of the nonlinear dual inequality: \begin{equation}\int |S_t u_0-S_t v_0|
\varphi...
Box-splines orthogonal projections
December 4, 2018
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Mathematics
Classical Analysis and ODEs
Classical Analysis and ODEs
Let P be orthogonal projection on B-splines of degree r−1 with equally
spaced knots. Sweldens and Piessens proved that P(xr)−xr is Bernoulli
polynomial. We generalize Sweldens ans Piessens's result for box-splines. It
gives the oppo...
On sequential structures in incompressible multidimensional networks
December 3, 2018
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Computer Science
Mathematics
Information Theory
Discrete Mathematics
Social and Information Networks
Information Theory
Logic
In order to deal with multidimensional structure representations of
real-world networks, as well as with their worst-case irreducible information
content analysis, the demand for new graph abstractions increases. This article
investigates i...
Trading T gates for dirty qubits in state preparation and unitary
synthesis
December 3, 2018
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Physics
Quantum Physics
Efficient synthesis of arbitrary quantum states and unitaries from a
universal fault-tolerant gate-set e.g. Clifford+T is a key subroutine in
quantum computation. As large quantum algorithms feature many qubits that
encode coherent quantum ...
MDU-Net: Multi-scale Densely Connected U-Net for biomedical image
segmentation
December 2, 2018
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Computer Science
Computer Vision and Pattern Recognition
Biomedical image segmentation plays a central role in quantitative analysis,
clinical diagnosis, and medical intervention. In the light of the fully
convolutional networks (FCN) and U-Net, deep convolutional networks (DNNs) have
made signif...
Learning Interpretable Characteristic Kernels via Decision Forests
November 30, 2018
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Statistics
Computer Science
Machine Learning
Machine Learning
Decision forests are widely used for classification and regression tasks. A
lesser known property of tree-based methods is that one can construct a
proximity matrix from the tree(s), and these proximity matrices are induced
kernels. While t...
Optimal Data Driven Resource Allocation under Multi-Armed Bandit
Observations
November 30, 2018
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Statistics
Computer Science
Machine Learning
Machine Learning
This paper introduces the first asymptotically optimal strategy for a multi
armed bandit (MAB) model under side constraints. The side constraints model
situations in which bandit activations are limited by the availability of
certain resour...
Limbs and Cospectral Vertices in Trees
November 29, 2018
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Mathematics
Combinatorics
We generalize Schwenk's result that almost all trees contain any given limb
to trees with positive integer vertex weights. The concept of characteristic
polynomial is extended to such weighted trees and we prove that the proportion
of n-v...