In this work, we prove the criterion of Banach-Grunblum and the principle of
selection of Bessaga-Pe\l{}czy\'nski for normed spaces. As applications of
these results, we show the Principle of Selection of Bessaga-Pe\l{}czy\'nski
for normed ...
Minimum Quadratic Helicity States
June 19, 2018
| |
Physics
Mathematics
Fluid Dynamics
Solar and Stellar Astrophysics
Differential Geometry
Building on previous results on the quadratic helicity in
magnetohydrodynamics (MHD) we investigate particular minimum helicity states.
Those are eigenfunctions of the curl operator and are shown to constitute
solutions of the quasi-station...
Kiselyov's geometry
June 18, 2018
Mathematics
History and Overview
The book is a unique phenomenon in Russian geometry education. It was first
published in 1892; there have been more than 40 revised editions, and dozens of
millions of copies (by these parameters it is trailing only Euclid's Elements).
Ou...
Synthetic G-jet-structures in modal homotopy type theory
June 15, 2018
|
Mathematics
Differential Geometry
Algebraic Geometry
Category Theory
Differential Geometry
Algebraic Geometry
Category Theory
This article constructs the moduli stack of torsionfree G-jet-structures in
homotopy type theory with one monadic modality. This yields a construction of
this moduli stack for any ∞-topos equipped with any stable factorization
syst...
The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang-Mills matrix
models
June 15, 2018
|
Physics
High Energy Physics - Theory
We consider the SO(4,1)-covariant fuzzy hyperboloid Hn4 as a solution
of Yang-Mills matrix models, and study the resulting higher-spin gauge theory.
The degrees of freedom can be identified with functions on classical H4
taking val...
The committee machine: Computational to statistical gaps in learning a
two-layers neural network
June 14, 2018
| | | | |
Statistics
Physics
Computer Science
Machine Learning
Computational Physics
Statistical Mechanics
Disordered Systems and Neural Networks
Machine Learning
Heuristic tools from statistical physics have been used in the past to locate
the phase transitions and compute the optimal learning and generalization
errors in the teacher-student scenario in multi-layer neural networks. In this
contribut...
The e-vector of a simplicial complex
June 13, 2018
|
Mathematics
Combinatorics
We study the exponential Hilbert series (both coarsely- and finely-graded) of
the Stanley-Reisner ring of an abstract simplicial complex, Δ, and we
introduce the e-vector of Δ, which relates to the coefficients of the
expone...
On a scalar field of time and electromagnetism
June 13, 2018
Physics
General Physics
It is possible to describe a universal scalar field of time but not a
universal coordinate of time and to attribute its non-geodesic alignment to the
electromagnetic phenomena. A very surprising outcome is that not only mass
generates gravi...
Covariance constraints for stochastic inverse problems of computer
models
June 9, 2018
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Mathematics
Statistics
Statistics Theory
Statistics Theory
Statistics Theory
Statistics Theory
Stochastic inverse problems considered in this article consist of estimating
the probability distributions of intrinsically random inputs of computer
models. These estimations are based on observable outputs affected by model
noise, and suc...
Mixed ℓ-adic complexes for schemes over number fields
June 8, 2018
Mathematics
Algebraic Geometry
If X is a variety over a number field, Annette Huber has defined a category
of "horizontal" (or "almost everywhere unramified") ℓ-adic complexes and
ℓ-adic perverse sheaves on X. For such objects, the notion of weights
makes s...