Polynomial progressions in topological fields

October 2, 2022

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Mathematics
Number Theory
Classical Analysis and ODEs
Combinatorics
Let P1,,PmK[y]P_1, \ldots, P_m \in K[y] be polynomials with distinct degrees, no constant terms and coefficients in a general locally compact topological field KK. 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 A\mathcal A be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction A"\mathcal A" of A\mathcal A to any hyperplane endowed with the natural multiplicity κ\kappa 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 τn\tau_n-spherical representations of the group G=SO(2,1)G = SO(2,1)^\circ appearing in L2(Γi\G)L^2(\Gamma_i \backslash G) for uniform torsion-free lattices $\Gamma_i, i = 1, ...