A conformal scalar n-point function in momentum space
January 15, 2020
Physics
High Energy Physics - Theory
We suggest a certain type of conformal n-point function of scalar primaries
where the scalar operators share the same scaling dimension. The conformal
correlation functions are obtained in momentum space, and we show that they
satisfy the...
Blow-up criteria below scaling for defocusing energy-supercritical NLS
and quantitative global scattering bounds
January 15, 2020
Mathematics
Physics
Analysis of PDEs
Mathematical Physics
Mathematical Physics
We establish quantitative blow-up criteria below the scaling threshold for
radially symmetric solutions to the defocusing nonlinear Schr\"odinger equation
with nonlinearity ∣u∣6u. This provides to our knowledge the first generic
results ...
The Bhargava greedoid as a Gaussian elimination greedoid
January 15, 2020
Mathematics
Computer Science
Combinatorics
Discrete Mathematics
Inspired by Manjul Bhargava's theory of generalized factorials, Fedor Petrov
and the author have defined the "Bhargava greedoid" -- a greedoid (a
matroid-like set system on a finite set) assigned to any "ultra triple" (a
somewhat extended v...
Safe Voting: Resilience to Abstention and Sybils
January 15, 2020
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Computer Science
Multiagent Systems
Social and Information Networks
Voting rules may implement the will of the society when all eligible voters
vote, and only them. However, they may fail to do so when sybil (fake or
duplicate) votes are present and when only some honest (non sybil) voters
actively particip...
Making deep neural networks right for the right scientific reasons by
interacting with their explanations
January 15, 2020
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Statistics
Computer Science
Machine Learning
Artificial Intelligence
Machine Learning
Deep neural networks have shown excellent performances in many real-world
applications. Unfortunately, they may show "Clever Hans"-like behavior --
making use of confounding factors within datasets -- to achieve high
performance. In this wo...
Tight Static Lower Bounds for Non-Adaptive Data Structures
January 14, 2020
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Computer Science
Data Structures and Algorithms
In this paper, we study the static cell probe complexity of non-adaptive data
structures that maintain a subset of n points from a universe consisting of
m=n1+Ω(1) points. A data structure is defined to be non-adaptive when
the ...
Resolving the induction problem: Can we state with complete confidence
via induction that the sun rises forever?
January 13, 2020
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Statistics
Other Statistics
Other Statistics
Induction is a form of reasoning that starts with a particular example and
generalizes to a rule, namely, a hypothesis. However, establishing the truth of
a hypothesis is problematic due to the potential occurrence of conflicting
events, al...
Computing isogenies from modular equations in genus two
January 13, 2020
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Mathematics
Algebraic Geometry
Number Theory
Algebraic Geometry
Number Theory
We present an algorithm solving the following problem: given two genus 2
curves over a field k with isogenous Jacobians, compute such an isogeny
explicitly. This isogeny can be either an l-isogeny or, in the real
multiplication case, an iso...
Motivated by the fact that most of the information relevant to the prediction
of target tokens is drawn from the source sentence S=s1,…,sS, we
propose truncating the target-side window used for computing self-attention by
making ...
On the dimension of the Fomin-Kirillov algebra and related algebras
January 13, 2020
Mathematics
Quantum Algebra
Rings and Algebras
In 1999, Fomin-Kirillov introduced the quadratic algebras Em in
terms of generators and relations which are the universal quadratic cover of
the algebra generated by divided difference operators ∂ij acting on
the po...