Corrigendum to "Model Theory of Fields with Virtually Free Group
Actions"
May 18, 2017
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Mathematics
Logic
There is an irreparable error in the proof of Theorem 3.26 in our "Model
Theory of Fields with Virtually Free Group Actions" paper and we withdraw the
claim of having proved that theorem. In fact, that theorem is false in a very
strong sens...
Subalgebras of the rank two semisimple Lie algebras
May 9, 2017
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Mathematics
Rings and Algebras
In this expository article, we describe the classification of the subalgebras
of the rank 2 semisimple Lie algebras. Their semisimple subalgebras are
well-known, and in a recent series of papers, we completed the classification
of the subal...
Discretisation of regularity structures
May 8, 2017
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Mathematics
Probability
Analysis of PDEs
We introduce a general framework allowing to apply the theory of regularity
structures to discretisations of stochastic PDEs. The approach pursued in this
article is that we do not focus on any one specific discretisation procedure.
Instead...
Existence of Infinite Product Measures
May 3, 2017
Mathematics
Functional Analysis
A construction of product measures is given for an arbitrary sequence of
measure spaces via outer measure techniques without imposing any condition on
the underlying measure spaces. This approach concludes finally the problem of
the existen...
Modulo quantifiers over functional vocabularies extending addition
April 30, 2017
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Computer Science
Logic in Computer Science
Logic in Computer Science
We show that first order logic (FO) and first order logic extended with
modulo counting quantifiers (FOMOD) over purely functional vocabularies which
extend addition, satisfy the Crane beach property (CBP) if the logic satisfies
a normal fo...
Maximizing free energy gain
April 28, 2017
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Physics
Statistical Mechanics
Quantum Physics
Statistical Mechanics
Quantum Physics
Maximizing the amount of work harvested from an environment is important for
a wide variety of biological and technological processes, from
energy-harvesting processes such as photosynthesisto energy storage systems
such as fuels and batter...
The phase transition in bounded-size Achlioptas processes
April 27, 2017
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Mathematics
Physics
Probability
Statistical Mechanics
Combinatorics
Probability
Statistical Mechanics
Combinatorics
Perhaps the best understood phase transition is that in the component
structure of the uniform random graph process introduced by Erd\H{o}s and
R\'enyi around 1960. Since the model is so fundamental, it is very interesting
to know which fea...
A Framework for Algorithm Stability
April 26, 2017
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Computer Science
Data Structures and Algorithms
Computational Geometry
Data Structures and Algorithms
Computational Geometry
We say that an algorithm is stable if small changes in the input result in
small changes in the output. This kind of algorithm stability is particularly
relevant when analyzing and visualizing time-varying data. Stability in general
plays a...
The First Syzygy of Hibi Rings Associated with Planar distributive
lattices
April 26, 2017
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Mathematics
Commutative Algebra
Let L be a finite distributive lattice and S=K[xα:α∈L] be a polynomial ring over a field K and $I=\langle x_\alpha
x_\beta - x_{\alpha\vee \beta} x_{\alpha\wedge\beta} : \alpha \nsim
\beta,\alpha,\b...
Vaidya Spacetime in the Diagonal Coordinates
April 23, 2017
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Physics
General Relativity and Quantum Cosmology
We have analyzed the transformation from initial coordinates (v,r) of the
Vaidya metric with light coordinate v to the most physical diagonal
coordinates (t,r). An exact solution has been obtained for the corresponding
metric tensor i...