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Aug 04, 2015
Differential Geometry
Analysis of PDEs

In this final section, we explain how the double approximators uε,σ converge to the arrival time u of the mean curvature flow of K0, and how the estimates of Theorem 3.1 and Theorem 4.1 can be passed to the limit. This will be done in two steps, fir…

Singularities of mean convex level set flow in general ambient manifo…

We prove two new estimates for the level set flow of mean convex domains in Riemannian manifolds. Our estimates give control - exponential in time - …
Jun 16, 2016
Algebraic Geometry

The computations below were verified symbolically with Macaulay2 [GS]. Code is available on the arXiv as an ancillary file. For speed of computation we work over the finite field F5, explaining at the end of the section how to lift to characteristic…

Cubic fourfolds fibered in sextic del Pezzo surfaces

We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. …
Nov 04, 2011
Algebraic Geometry

From now on, we assume k is a finite field of odd characteristic and B≃P1. We retain the notation of Sections 3 and 4, so X→P1 is a quadric surface fibration with square-free discriminant of degree Δ=2g+2. Let C be the discriminant curve and F→C the…

Spaces of sections of quadric surface fibrations over curves

We consider quadric surface fibrations over curves, defined over algebraically closed and finite fields. Our goal is to understand, in geometric term…
Jul 29, 2015
Metric Geometry
Differential Geometry

Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds a…

We construct bi-Lipschitz embeddings into Euclidean space for manifolds and orbifolds of bounded diameter and curvature. The distortion and dimension…
Nov 25, 2015
Metric Geometry
Discrete Mathematics
Combinatorics

From Tarski's plank problem to simultaneous approximation

A {\em slab} (or plank) of width $w$ is a part of the $d$-dimensional space that lies between two parallel hyperplanes at distance $w$ from each othe…
May 29, 2019
Numerical Analysis

Factorization of the translation kernel for fast rigid image alignment

An important component of many image alignment methods is the calculation of inner products (correlations) between an image of $n \times n$ pixels an…
Dec 08, 2017
Analysis of PDEs

Global bifurcation of rotating vortex patches

We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as…
Mar 11, 2014
Numerical Analysis

Rational approximation, oscillatory Cauchy integrals and Fourier tr…

We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new er…
Oct 26, 2014
Machine Learning

Differentially- and non-differentially-private random decision trees

We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works …
Oct 04, 2007
Chaotic Dynamics

Information flow within stochastic dynamical systems

Information flow or information transfer is an important concept in dynamical systems which has applications in a wide variety of scientific discipli…
Nov 10, 2013
Analysis of PDEs
Mathematical Physics

Modified scattering for the cubic Schrödinger equation on product s…

We consider the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^d$. We prove modified scattering and …
Oct 07, 2015
Mathematical Physics
Probability

Local density for two-dimensional one-component plasma

We study the classical two-dimensional one-component plasma of $N$ positively charged point particles, interacting via the Coulomb potential and conf…
Aug 08, 2016
Biological Physics
Soft Condensed Matter
Fluid Dynamics

Scattering of biflagellate microswimmers from surfaces

We use a three-bead-spring model to investigate the dynamics of bi-flagellate micro-swimmers near a surface. While the primary dynamics and scatterin…
Sep 05, 2017
Numerical Analysis

A fluctuating boundary integral method for Brownian suspensions

We present a fluctuating boundary integral method (FBIM) for Brownian Dynamics of suspensions of rigid particles of complex shape immersed in a Stoke…
Jun 06, 2011
Combinatorics
Computational Geometry

$k$-quasi planar graphs

A topological graph is \emph{$k$-quasi-planar} if it does not contain $k$ pairwise crossing edges. A topological graph is \emph{simple} if every pair…
Aug 20, 2013
Combinatorics

Entanglement-assisted zero-error source-channel coding

We study the use of quantum entanglement in the zero-error source-channel coding problem. Here, Alice and Bob are connected by a noisy classical one-…
May 23, 2017
Machine Learning

Community Detection with Graph Neural Networks

We study data-driven methods for community detection in graphs. This estimation problem is typically formulated in terms of the spectrum of certain o…
May 24, 2013
Mathematical Physics
Numerical Analysis

A numerical dressing method for the nonlinear superposition of soluti…

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation.…
Jun 07, 2014
Machine Learning

Logarithmic Time Online Multiclass prediction

We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time compl…
Mar 25, 2017
Information Theory

Regularized Gradient Descent: A Nonconvex Recipe for Fast Joint Blind…

We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their con…
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