Hyperinvariant subspaces for normaloid essential isometric operators
February 21, 2020
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Mathematics
Functional Analysis
In this article, we prove the existence of a non-trivial hyperinvariant
subspace for a subclass of compact perturbations of scalar multiple of a
partial isometry. Later, we illustrate that this class contains several
important classes of op...
Misspecification-robust likelihood-free inference in high dimensions
February 21, 2020
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Statistics
Computation
Methodology
Machine Learning
Likelihood-free inference for simulator-based statistical models has
developed rapidly from its infancy to a useful tool for practitioners. However,
models with more than a handful of parameters still generally remain a
challenge for the Ap...
Realization of manifolds as leaves using graph colorings
February 20, 2020
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Mathematics
Geometric Topology
Dynamical Systems
Geometric Topology
Dynamical Systems
It is proved that any (repetitive) Riemannian manifold of bounded geometry
can be realized as a leaf of some (minimal) Riemannian matchbox manifold
without holonomy. Our methods can be adapted to achieve Cantor transversals or
a prescribed ...
A mean-field model of Integrate-and-Fire neurons: non-linear stability
of the stationary solutions
February 20, 2020
Mathematics
Probability
Analysis of PDEs
We investigate a stochastic network composed of Integrate-and-Fire spiking
neurons, focusing on its mean-field asymptotics. We consider an invariant
probability measure of the McKean-Vlasov equation and establish an explicit
sufficient cond...
Evolution of Cosmological Total Energy Density and Transient Periods in
Cosmology
February 20, 2020
Physics
General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
The evolution of the Universe is traditionally examined by monitoring how its
material content evolves as it expands. This model of an isolated system is
expressed as the equation of motion of the bulk but segmented into different
epochs. I...
Adaptive Graph Auto-Encoder for General Data Clustering
February 20, 2020
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Computer Science
Statistics
Machine Learning
Machine Learning
Graph-based clustering plays an important role in the clustering area. Recent
studies about graph convolution neural networks have achieved impressive
success on graph type data. However, in general clustering tasks, the graph
structure of ...
Lojasiewicz exponent of a surface: an intrinsic view
February 20, 2020
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Mathematics
Algebraic Geometry
In this paper we observe that the {\L}ojasiewicz exponent L0(X)
of an ADE-type singularity X can be computed by means of invariants of
certain ideals in the local ring OX,0. After extending the
notion of {\L}o...
Cominuscule subvarieties of flag varieties
February 19, 2020
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Mathematics
Algebraic Geometry
Differential Geometry
Algebraic Geometry
Differential Geometry
We show that every flag variety contains a natural choice of homogeneous
cominuscule subvariety. From the Dynkin diagram of the flag variety, we compute
the Dynkin diagram of that subvariety....
The complexity of knapsack problems in wreath products
February 19, 2020
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Mathematics
Computer Science
Group Theory
Computational Complexity
Group Theory
Computational Complexity
We prove new complexity results for computational problems in certain wreath
products of groups and (as an application) for free solvable group. For a
finitely generated group we study the so-called power word problem (does a
given expressi...
Bandits with Mean Bounds
February 19, 2020
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Computer Science
Statistics
Machine Learning
Machine Learning
We study a variant of the bandit problem where side information in the form
of bounds on the mean of each arm is provided. We prove that these translate to
tighter estimates of subgaussian factors and develop novel algorithms that
exploit t...