Relative completed cohomologies and modular symbols
September 17, 2017
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Mathematics
Number Theory
Number Theory
Generalizing Emerton's completed cohomologies, we define relative completed
cohomologies of arithmetic manifolds. We also define modular symbols for them,
and show that the relative completed cohomology spaces interpolate the ``nearly
ordin...
A priori bounds for geodesic diameter. Part III. A Sobolev-Poincar\'e
inequality and applications to a variety of geometric variational problems
September 16, 2017
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Mathematics
Differential Geometry
Analysis of PDEs
Classical Analysis and ODEs
Based on a novel type of Sobolev-Poincar\'e inequality (for generalised
weakly differentiable functions on varifolds), we establish a finite upper
bound of the geodesic diameter of generalised compact connected
surfaces-with-boundary of arb...
1-Dimensional Intrinsic Persistence of Geodesic Spaces
September 15, 2017
Mathematics
Geometric Topology
Algebraic Topology
Metric Geometry
Given a compact geodesic space X we apply the fundamental group and
alternatively the first homology group functor to the corresponding Rips or
\v{C}ech filtration of X to obtain what we call a persistence. This paper
contains the theor...
On Early-stage Debunking Rumors on Twitter: Leveraging the Wisdom of
Weak Learners
September 13, 2017
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Computer Science
Social and Information Networks
Machine Learning
Recently a lot of progress has been made in rumor modeling and rumor
detection for micro-blogging streams. However, existing automated methods do
not perform very well for early rumor detection, which is crucial in many
settings, e.g., in c...
Low-Energy Effective Field Theory below the Electroweak Scale: Operators
and Matching
September 13, 2017
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Physics
High Energy Physics - Phenomenology
The gauge-invariant operators up to dimension six in the low-energy effective
field theory below the electroweak scale are classified. There are 70 Hermitian
dimension-five and 3631 Hermitian dimension-six operators that conserve baryon
and...
Spectral ACMS: A robust localized Approximated Component Mode Synthesis
Method
September 12, 2017
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
We consider finite element methods of multiscale type to approximate
solutions for two-dimensional symmetric elliptic partial differential equations
with heterogeneous L∞ coefficients. The methods are of Galerkin type
and follow the...
Is completeness necessary? Estimation in nonidentified linear models
September 11, 2017
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Mathematics
Economics
Statistics
Statistics Theory
Econometrics
Machine Learning
Statistics Theory
Statistics Theory
Econometrics
Machine Learning
Statistics Theory
Modern data analysis depends increasingly on estimating models via flexible
high-dimensional or nonparametric machine learning methods, where the
identification of structural parameters is often challenging and untestable. In
linear setting...
Quantum Drinfeld Modules and Ray Class Fields of Real Quadratic Global
Function Fields
September 11, 2017
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Mathematics
Number Theory
This is the second in a series of two papers presenting a solution to
Hilbert's 12th problem for real quadratic function fields in positive
characteristic, in the sense of proving an analog of the Theorem of
Weber-Fueter. We also offer a co...
The Asymptotic Binary Goldbach and Lemoine Conjectures
September 11, 2017
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Mathematics
Number Theory
In this paper we use the former of the authors developed theory of
\textbf{circles of partition} to investigate possibilities to prove the binary
Goldbach as well as the Lemoine conjecture. We state the \textit{squeeze
principle} and its co...
Learning to Detect Entanglement
September 11, 2017
Physics
Quantum Physics
Classifying states as entangled or separable is a fundamental, but expensive
task. This paper presents a method, the forest algorithm, to improve the amount
of resources needed to detect entanglement. Starting from 'optimized' methods
for u...