Shimizu and Takahashi have shown that every decreasing sequence of nonempty,
bounded, closed, convex subsets of a complete, uniformly Takahashi convex
metric space has nonempty intersection. It is well known that the Menger
convexity is a g...
Compact manifolds of dimension n≥12 with positive isotropic
curvature
September 26, 2019
|
Mathematics
Differential Geometry
Differential Geometry
We prove the following result: Let (M,g0) be a compact manifold of
dimension n≥12 with positive isotropic curvature. Then M is
diffeomorphic to a spherical space form, or the total space of an orbifiber
bundle over S1...
Metal-insulator transition in CaCu3Fe4O12
September 26, 2019
| | |
Physics
Strongly Correlated Electrons
Materials Science
We study structurally-triggered metal-insulator transition in
CaCu3Fe4O12 by means of local density approximation (LDA) +U and
LDA+dynamical mean-field theory (DMFT). The ferrimagnetic insulating phase is
essentially the same w...
Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control
September 26, 2019
| |
Statistics
Physics
Electrical Engineering and Systems Science
Computer Science
Machine Learning
Computational Physics
Systems and Control
Systems and Control
Machine Learning
In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning
framework which can infer the dynamics of a physical system, given by an
ordinary differential equation (ODE), from observed state trajectories. To
achieve better gen...
A Facet Enumeration Algorithm for Convex Polytopes
September 25, 2019
|
Mathematics
Optimization and Control
Combinatorics
Optimization and Control
Combinatorics
This paper proposes a novel and simple algorithm of facet enumeration for
convex polytopes. The complexity of the algorithm is discussed. The algorithm
is implemented in Matlab. Some simple polytopes with known H-representations
and V-repre...
A weak version of the Strong Exponential Closure
September 23, 2019
| | | | |
Mathematics
Logic
Logic
Assuming Schanuel's Conjecture we prove that for any variety V over the
algebraic closure over the rational numbers, of dimension n and with dominant
projections, there exists a generic point in V. We obtain in this way many
instances of th...
Geometry, Computation, and Optimality in Stochastic Optimization
September 23, 2019
| |
Mathematics
Computer Science
Statistics
Optimization and Control
Information Theory
Machine Learning
Information Theory
Machine Learning
We study computational and statistical consequences of problem geometry in
stochastic and online optimization. By focusing on constraint set and gradient
geometry, we characterize the problem families for which stochastic- and
adaptive-grad...
Manifold Fitting under Unbounded Noise
September 23, 2019
|
Statistics
Computer Science
Machine Learning
Machine Learning
There has been an emerging trend in non-Euclidean statistical analysis of
aiming to recover a low dimensional structure, namely a manifold, underlying
the high dimensional data. Recovering the manifold requires the noise to be of
certain co...
Algebras for enriched ∞-operads
September 22, 2019
Mathematics
Algebraic Topology
Category Theory
Using the description of enriched ∞-operads as associative algebras in
symmetric sequences, we define algebras for enriched ∞-operads as
certain modules in symmetric sequences. For V a symmetric monoidal
model categ...
On the simplest static and stationary vacuum quadrupolar metrics
September 22, 2019
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Physics
General Relativity and Quantum Cosmology
In the present paper we argue that a special case of the Bach-Weyl metric
describing a static configuration of two Schwarzschild black holes gives rise,
after extending its parameter space to complex values, to a very simple
2-parameter mod...