On the asymptotic normality of persistent Betti numbers
March 7, 2019
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Mathematics
Statistics
Probability
Statistics Theory
Statistics Theory
Persistent Betti numbers are a major tool in persistent homology, a subfield
of topological data analysis. Many tools in persistent homology rely on the
properties of persistent Betti numbers considered as a two-dimensional
stochastic proce...
A face cover perspective to ℓ1 embeddings of planar graphs
March 7, 2019
Computer Science
Data Structures and Algorithms
Computational Geometry
It was conjectured by Gupta et al. [Combinatorica04] that every planar graph
can be embedded into ℓ1 with constant distortion. However, given an
n-vertex weighted planar graph, the best upper bound on the distortion is
only $O(\sqrt...
Infinitely many solutions for a Schrodinger equation with sign-changing
potential and nonlinear term
March 7, 2019
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Mathematics
Functional Analysis
Analysis of PDEs
We propose a new variational approach to finding multiple critical points for
strongly indefinite problems without assuming the weak upper semicontinuity on
the variational functionals. By this approach, we obtain the existence of
infinitel...
On the Time-Range Dependency of the Beampatterns Produced by Arbitrary
Antenna Arrays: Discussions on the Misplaced Expectations from Frequency
Diverse Arrays
March 6, 2019
Physics
Classical Physics
In the recent years constructing time-invariant spatial-focusing beampatterns
by using frequency diverse arrays (FDAs) is conveyed in several papers. Further
than time-invariant spatial-focusing beampatterns, the unfeasibility of
constructi...
Observing evolution from steady state
March 6, 2019
Physics
General Physics
The time-translation symmetry of the conformal FLRW frame gˉ=a−2g
allows reinterpretation of cosmological observation in the static space of a
stationary universe, where constant matter density
$\bar{\rho}_{\textrm{m}}=\rho_{\text...
Fibers of maps to totally nonnegative spaces
March 4, 2019
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Mathematics
Combinatorics
Geometric Topology
Representation Theory
Combinatorics
Geometric Topology
Representation Theory
This paper undertakes a study of the structure of the fibers of the Chevalley
exponentiation maps f(i1,…,id). The fibers of these maps
f(i1,…,id) encode the nonnegative real relations amongst
exponentiated Chevalley ...
Albatross: An optimistic consensus algorithm
March 4, 2019
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Computer Science
Cryptography and Security
Cryptography and Security
The consensus protocol is a critical component of distributed ledgers and
blockchains. Achieving consensus over a decentralized network poses challenges
to transaction finality and performance. Currently, the highest-performing
consensus al...
A duality theorem for harmonic maps into inner symmetric spaces
March 3, 2019
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Mathematics
Differential Geometry
In this note, we show that for any harmonic map into a non-compact symmetric
space one can find naturally a "dual" harmonic map into a compact symmetric
space which can be constructed from the same basic data (called "potentials" in
the loo...
Uniform exponential mixing for congruence covers of convex cocompact
hyperbolic manifolds
March 2, 2019
Mathematics
Dynamical Systems
Geometric Topology
Spectral Theory
Let Γ be a Zariski dense convex cocompact subgroup contained in an
arithmetic lattice of SO(n,1)∘. We prove uniform
exponential mixing of the geodesic flow for congruence covers of the hyperbolic
manifold $\G...
Model-Based Reinforcement Learning for Atari
March 1, 2019
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Computer Science
Statistics
Machine Learning
Machine Learning
Model-free reinforcement learning (RL) can be used to learn effective
policies for complex tasks, such as Atari games, even from image observations.
However, this typically requires very large amounts of interaction --
substantially more, i...