On the well-posedness of a class of McKean Feynman-Kac equations
October 24, 2018
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Mathematics
Probability
We analyze the well-posedness of a so called McKean Feynman-Kac Equation
(MFKE), which is a McKean type equation with a Feynman-Kac perturbation. We
provide in particular weak and strong existence conditions as well as pathwise
uniqueness c...
Stabilization distance bounds from link Floer homology
October 22, 2018
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Mathematics
Geometric Topology
We consider the set of connected surfaces in the 4-ball with boundary a fixed
knot in the 3-sphere. We define the stabilization distance between two surfaces
as the minimal g such that we can get from one to the other using
stabilizations...
A Model Theoretic Perspective on Matrix Rings
October 21, 2018
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Mathematics
Logic
Rings and Algebras
Logic
Rings and Algebras
In this paper natural necessary and sufficient conditions for quantifier
elimination of matrix rings Mn(K) in the language of rings expanded by two
unary functions, naming the trace and transposition, are identified. This is
used togethe...
A family of cohomological complex projective spaces
October 21, 2018
Mathematics
Algebraic Geometry
Algebraic Topology
We exhibit a family of complex manifolds, which has a member at each odd
complex dimension and which has the same cohomology groups as the complex
projective space at that dimension, but not homotopy equivalent to it. We also
analyze the ev...
Hardy-Sobolev-Rellich, Hardy-Littlewood-Sobolev and
Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
October 20, 2018
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Mathematics
Functional Analysis
In this paper we establish a number of geometrical inequalities such as
Hardy, Sobolev, Rellich, Hardy-Littlewood-Sobolev, Caffarelli-Kohn-Nirenberg,
Gagliardo-Nirenberg inequalities and their critical versions for an ample class
of sub-ell...
Federated Learning in Distributed Medical Databases: Meta-Analysis of
Large-Scale Subcortical Brain Data
October 19, 2018
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Statistics
Computer Science
Quantitative Biology
Machine Learning
Machine Learning
Neurons and Cognition
Quantitative Methods
Machine Learning
Machine Learning
Neurons and Cognition
Quantitative Methods
At this moment, databanks worldwide contain brain images of previously
unimaginable numbers. Combined with developments in data science, these massive
data provide the potential to better understand the genetic underpinnings of
brain diseas...
Elemental Abundance Analysis of Single and Binary Late-B Stars Using
Sub-meter Class Telescopes: HR 342, HR 769, HR 1284, and HR 8705
October 19, 2018
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Physics
Solar and Stellar Astrophysics
We test the capabilities of 0.4 m telescopes equipped with an \'{e}chelle
spectrograph to derive fundamental parameters and elemental abundances of four
late-B type stars: HR 342, HR 769, HR 1284, and HR 8705. The medium resolution
(R~14000...
Concerning a conjecture of Taketomi-Tamaru
October 18, 2018
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Mathematics
Differential Geometry
Differential Geometry
We study the setting of 2-step nilpotent Lie groups in the particular case
that its type (p,q) is not exceptional. We demonstrate that, generically, the
orbits of R>0×Aut0 in GL(n)/O(n) are congruent even when
a Ricci ...
Heegaard Floer Homology and Balanced Presentations of Groups
October 18, 2018
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Mathematics
Geometric Topology
Let G be a group with a finite balanced presentation P. We associate a
Heegaard Floer homology group HFP(G) with the pair (G,P) based
on some extra choices and technical assumptions. We show that
HFP(G) is in...
A Sharpened Rearrangement Inequality for Convolution on the Sphere
October 16, 2018
Mathematics
Classical Analysis and ODEs
One may define a trilinear convolution form on the sphere involving two
functions on the sphere and a monotonic function on the interval [−1,1]. A
symmetrization inequality of Baernstein and Taylor states that this form is
maximized when ...