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Aug 09, 2018
Numerical Analysis

A fast solver for spectral element approximation applied to fractiona…

We develop a fast solver for the spectral element method (SEM) applied to the two-sided fractional diffusion equation on uniform, geometric and grade…
Oct 29, 2017
Combinatorics

There are still many questions to be answered regarding the sets Sk(n,m) and R(n,m). For example, the number of 2-foldable words, |S2(n,m)|, is not known. A complete description of R(n,m) remains to be determined. We are particularly interested in t…

$k$-Foldability of Words

We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecu…
Dec 21, 2011
Combinatorics

Diameters of Graphs with Spectral Radius at most $3/2\sqrt{2}$

The spectral radius $\rho(G)$ of a graph $G$ is the largest eigenvalue of its adjacency matrix. Woo and Neumaier discovered that a connected graph $G…
May 02, 2019
Algebraic Geometry

A variety X with a surjective morphism η:X\leavevmodeto18.73pt\vboxto4.5pt\pgfpicture\makeatletterto0.0pt\pgfsys@beginscope\definecolorpgfstrokecolorrgb0,0,0\pgfsys@color@rgb@stroke000\pgfsys@color@rgb@fill000\pgfsys@setlinewidth0.4pt\nullfontto0.0p…

Birational self-maps of threefolds of (un)-bounded genus or gonality

We study the complexity of birational self-maps of a projective threefold $X$ by looking at the birational type of surfaces contracted. These surface…
Jan 19, 2018
Computational Physics
Numerical Analysis
Fluid Dynamics

An Exponential Time-Integrator Scheme for Steady and Unsteady Invisci…

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve mul…
Oct 17, 2017
Numerical Analysis

An ensemble algorithm for numerical solutions to deterministic and …

In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabo…
Jan 16, 2011
Differential Geometry
Dynamical Systems
Geometric Topology

Normal curvatures of asymptotically constant graphs and Caratheodory'…

We show that Caratheodory's conjecture, on umbilical points of closed convex surfaces, may be reformulated in terms of the existence of at least one …
Jun 21, 2018
Numerical Analysis

Fractional Gray-Scott Model: Well-posedness, Discretization, and Si…

The Gray-Scott (GS) model represents the dynamics and steady state pattern formation in reaction-diffusion systems and has been extensively studied i…
Nov 04, 2014
Statistics Theory

The authors wish to thank Stephane Gaiffas and László Györfi for various valuable suggestions and references, as well as the anonymous referees for their constructive comments.

Classification algorithms using adaptive partitioning

Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friend…
Nov 07, 2017
Numerical Analysis

Overlapping Localized Exponential Time Differencing Methods for Dif…

The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cel…
Dec 05, 2013
Differential Geometry
Geometric Topology
Metric Geometry

Total diameter and area of closed submanifolds

The total diameter of a closed planar curve $C\subset R^2$ is the integral of its antipodal chord lengths. We show that this quantity is bounded belo…
Jul 03, 2008
Numerical Analysis

Iteratively re-weighted least squares minimization for sparse recovery

We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We pro…
May 05, 2014
Number Theory

Our work began with ℓ=5, by inspecting the Jones-Roberts database of number fields [JR13] and finding patterns which called for explanation. However, for ℓ>5, this database does not contain enough fields for a reasonable test, and does not include t…

Identities for field extensions generalizing the Ohno-Nakagawa relati…

In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be vie…
Sep 15, 2014
Number Theory

Products of binomial coefficients and unreduced Farey fractions

This paper studies the product $\bar{G}_n$ of the binomial coefficients in the n-th row of Pascal's triangle, which equals the reciprocal of the prod…
Sep 24, 2017
Combinatorics
Discrete Mathematics

Analogies between the crossing number and the tangle crossing number

Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two l…
Mar 28, 2019
Combinatorics

On the cover Turán number of Berge hypergraphs

For a fixed set of positive integers $R$, we say $\mathcal{H}$ is an $R$-uniform hypergraph, or $R$-graph, if the cardinality of each edge belongs to…
Nov 20, 2018
Artificial Intelligence

On a hypergraph probabilistic graphical model

We propose a directed acyclic hypergraph framework for a probabilistic graphical model that we call Bayesian hypergraphs. The space of directed acycl…
May 26, 2017
Numerical Analysis

An efficient algorithm for simulating ensembles of parameterized flow…

Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical…
Jul 11, 2008
Populations and Evolution
Quantitative Methods

The reader may be curious as to where our proof for the log(n) lower bound on sequence length for testing under the finite-state model breaks down for the random cluster model. The crucial distinction is that the random cluster model fails to satisf…

Phylogenetic information complexity: Is testing a tree easier than …

Phylogenetic trees describe the evolutionary history of a group of present-day species from a common ancestor. These trees are typically reconstructe…
Jun 23, 2017
Numerical Analysis
Optimization and Control

Non-commutative Discretize-then-Optimize Algorithms for Elliptic PD…

In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite dif…
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