Polynomial progressions in topological fields
October 2, 2022
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Mathematics
Number Theory
Classical Analysis and ODEs
Combinatorics
Let be polynomials with distinct degrees, no
constant terms and coefficients in a general locally compact topological field
. We give a quantitative count of the number of polynomial progressions $x,
x+P_1(y),...
Analysis of Gradient Descent with Varying Step Sizes using Integral Quadratic Constraints
October 2, 2022
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Mathematics
Computer Science
Electrical Engineering and Systems Science
Optimization and Control
Systems and Control
Systems and Control
The framework of Integral Quadratic Constraints (IQCs) is used to perform an
analysis of gradient descent with varying step sizes. Two performance metrics
are considered: convergence rate and noise amplification. We assume that the
step siz...
Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements
October 2, 2022
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Mathematics
Combinatorics
Group Theory
Let be a free hyperplane arrangement. In 1989, Ziegler showed
that the restriction of to any hyperplane endowed
with the natural multiplicity is then a free multiarrangement. In
2024, the fir...
Stochastic optimization on matrices and a graphon McKean-Vlasov limit
October 2, 2022
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Mathematics
Computer Science
Statistics
Probability
Machine Learning
Machine Learning
We consider stochastic gradient descents on the space of large symmetric
matrices of suitable functions that are invariant under permuting the rows and
columns using the same permutation. We establish deterministic limits of these
random cu...
A flexible model for correlated count data, with application to multi-condition differential expression analyses of single-cell RNA sequencing data
October 2, 2022
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Statistics
Methodology
Applications
Detecting differences in gene expression is an important part of single-cell
RNA sequencing experiments, and many statistical methods have been developed
for this aim. Most differential expression analyses focus on comparing
expression betw...
Generic mean curvature flows with cylindrical singularities
October 2, 2022
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Mathematics
Differential Geometry
Analysis of PDEs
Dynamical Systems
This paper examines the dynamics of mean curvature flow as it approaches a
cylindrical singularity. We reveal the mechanism for the isolatedness of
cylindrical singularities in terms of the normal form of the asymptotic
expansion of the res...
Learning Algorithm Generalization Error Bounds via Auxiliary Distributions
October 2, 2022
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Computer Science
Mathematics
Statistics
Machine Learning
Information Theory
Information Theory
Machine Learning
Generalization error bounds are essential for comprehending how well machine
learning models work. In this work, we suggest a novel method, i.e., the
Auxiliary Distribution Method, that leads to new upper bounds on expected
generalization e...
Raman spectroscopic characterization of crater walls formed upon single-shot high energy femtosecond laser irradiation of dimethacrylate polymer doped with plasmonic gold nanorods
October 2, 2022
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Physics
Optics
Plasma Physics
The bonding configuration of the crater walls formed in urethane
dimethacrylate-based polymer doped with plasmonic gold nanorods upon
irradiation with a single-shot high-energy femtosecond laser pulse has been
studied by Raman spectroscopy....
Speed Up the Cold-Start Learning in Two-Sided Bandits with Many Arms
October 1, 2022
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Computer Science
Statistics
Machine Learning
Machine Learning
Machine Learning
Machine Learning
Multi-armed bandit (MAB) algorithms are efficient approaches to reduce the
opportunity cost of online experimentation and are used by companies to find
the best product from periodically refreshed product catalogs. However, these
algorithms...
Results on a Strong Multiplicity One Theorem
October 1, 2022
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Mathematics
Representation Theory
Differential Geometry
Spectral Theory
Representation Theory
Differential Geometry
Spectral Theory
We prove an analogue of the strong multiplicity one theorem in the context of
-spherical representations of the group appearing
in for uniform torsion-free lattices $\Gamma_i, i
= 1, ...