Local solution to an energy critical 2-D stochastic wave equation with
exponential nonlinearity in a bounded domain
January 23, 2019
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Mathematics
Probability
Analysis of PDEs
We prove the existence and the uniqueness of a local maximal solution to an
H1-critical stochastic wave equation with multiplicative noise on a smooth
bounded domain D⊂R2 with exponential
nonlinearity. First...
Effectiveness of Tree-based Ensembles for Anomaly Discovery: Insights,
Batch and Streaming Active Learning
January 23, 2019
| | |
Computer Science
Statistics
Machine Learning
Machine Learning
In many real-world AD applications including computer security and fraud
prevention, the anomaly detector must be configurable by the human analyst to
minimize the effort on false positives. One important way to configure the
detector is by...
Surface groups are flexibly stable
January 22, 2019
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Mathematics
Group Theory
Geometric Topology
Group Theory
Geometric Topology
We show that surface groups are flexibly stable in permutations. This is the
first non-trivial example of a non-amenable flexibly stable group. Our method
is purely geometric and relies on an analysis of branched covers of hyperbolic
surfac...
The self-concordant perceptron is efficient on a sub-family feasibility
instances
January 22, 2019
Computer Science
Data Structures and Algorithms
Strict linear feasibility or linear separation is usually tackled using
efficient approximation/stochastic algorithms (that may even run in sub-linear
times in expectation). However, today state of the art for solving
exactly/deterministica...
Generalization of Bertrand's Postulate for Gaussian Primes
January 21, 2019
Mathematics
Number Theory
Bertrand's Postulate states about the prime distribution for the real
numbers. The generalization of Bertrand's Postulate was proved by Das et al.
[Arxiv 2018]. In this paper, we have formalized this idea for the Gaussian
primes (or the pri...
Geoelectric field and seismicity changes preceding the 2018 Mw6.8
earthquake and the subsequent activity in Greece
January 20, 2019
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Physics
Geophysics
A strong earthquake of magnitude Mw6.8 struck Western Greece on 25 October
2018 with epicenter at 37.515N 20.564E. It was preceded by an anomalous
geolectric signal that was recorded on 2 October 2018 at a measuring station
70km away from t...
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural
Networks
January 19, 2019
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Computer Science
Statistics
Machine Learning
Machine Learning
We study the training process of Deep Neural Networks (DNNs) from the Fourier
analysis perspective. We demonstrate a very universal Frequency Principle
(F-Principle) -- DNNs often fit target functions from low to high frequencies
-- on high...
Great Circle Fibrations and Contact Structures on Odd-Dimensional
Spheres
January 18, 2019
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Mathematics
Differential Geometry
Geometric Topology
It is known that for every smooth great circle fibration of the 3-sphere, the
distribution of tangent 2-planes orthogonal to the fibres is a contact
structure, in fact a tight one, but we show here that, beginning with the
5-sphere, there e...
Coherent IC-sheaves on type An affine Grassmannians and dual
canonical basis of affine type A1
January 17, 2019
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Mathematics
Representation Theory
Algebraic Geometry
Quantum Algebra
The convolution ring
KGLn(O)⋊C×(GrGLn) was
identified with a quantum unipotent cell of the loop group LSL2 in
[Cautis-Williams, J. Amer. Math. Soc. 32 (2019), pp. 709-778]. We identify th...
Gap theorems in Yang-Mills theory for complete four-dimensional
manifolds with a weighted Poincar\'e inequality
January 16, 2019
Mathematics
Physics
Differential Geometry
Mathematical Physics
Mathematical Physics
In this paper we prove gap theorems in Yang-Mills theory for complete
four-dimensional manifolds with a weighted Poincar\'e inequality. We apply the
theorems to many examples of manifolds. We also prove a uniqueness theorem for
the basic in...