Zeros near s=1 and the constant term of L′/L for L-functions in
the Selberg class
January 8, 2020
Mathematics
Number Theory
Let L(s)=∑n=1∞​an​n−s be an L-function in
the Selberg class, and qL​ its conductor. Let
ℓ0​(L) be the constant term of the Laurent expansion of
L′/L at $s=...
The LDBC Social Network Benchmark
January 7, 2020
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Computer Science
Databases
Performance
Social and Information Networks
The Linked Data Benchmark Council's Social Network Benchmark (LDBC SNB) is an
effort intended to test various functionalities of systems used for graph-like
data management. For this, LDBC SNB uses the recognizable scenario of operating
a s...
Resource-Efficient Neural Networks for Embedded Systems
January 7, 2020
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Statistics
Computer Science
Machine Learning
Machine Learning
While machine learning is traditionally a resource intensive task, embedded
systems, autonomous navigation, and the vision of the Internet of Things fuel
the interest in resource-efficient approaches. These approaches aim for a
carefully ch...
Sharp relations between volume growth, isoperimetry and escape
probability in vertex-transitive graphs
January 6, 2020
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Mathematics
Probability
Combinatorics
Group Theory
We prove sharp bounds on the probability that the simple random walk on a
vertex-transitive graph escapes the ball of radius r before returning to its
starting point. In particular, this shows that if the ball of radius r has
size sligh...
Review of the high-power vacuum tube microwave sources
January 6, 2020
Physics
Accelerator Physics
Applied Physics
Instrumentation and Detectors
Plasma Physics
Since the first vacuum tube (X-ray tube) was invented by Wilhelm R\"ontgen in
Germany, after more than one hundred years of development, the average power
density of the vacuum tube microwave source has reached the order of 108
[MW][GHz]2. ...
The Neumann Problem for Parabolic Hessian Quotient Equations
January 6, 2020
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Mathematics
Analysis of PDEs
In this paper, we consider the Neumann problem for parabolic Hessian quotient
equations. We show that the k-admissible solution of the parabolic Hessian
quotient equation exists for all time and converges to the smooth solution of
ellipti...
Sharp bounds on the Nusselt number in Rayleigh-B\'enard convection and a
bilinear estimate via Carleson measures
January 6, 2020
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Mathematics
Analysis of PDEs
We prove a conjecture in fluid dynamics concerning optimal bounds for heat
transportation in the infinite Prandtl number limit. Due to a maximum principle
property for the temperature exploited by Constantin-Doering and Otto-Seis,
this amou...
The troublesome kernel -- On hallucinations, no free lunches and the
accuracy-stability trade-off in inverse problems
January 5, 2020
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Computer Science
Machine Learning
Computer Vision and Pattern Recognition
Methods inspired by Artificial Intelligence (AI) are starting to
fundamentally change computational science and engineering through breakthrough
performances on challenging problems. However, reliability and trustworthiness
of such techniqu...
Normal crossing immersions, cobordisms and flips
January 4, 2020
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Mathematics
Geometric Topology
Combinatorics
We study various analogues of theorems from PL topology for cubical
complexes. In particular, we characterize when two PL homeomorphic cubulations
are equivalent by Pachner moves by showing the question to be equivalent to the
existence of ...
The Initial Value Problem for Singular SPDEs via Rough Paths
January 2, 2020
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Mathematics
Analysis of PDEs
In this contribution we develop a solution theory for singular quasilinear
stochastic partial differential equations subject to an initial condition. We
obtain our solution theory as a perturbation of the rough path approach
developed to ha...