Publications (21)
An AI system to help scientists write expert-level empirical software
Eser Aygün, Anastasiya Belyaeva, Gheorghe Comanici +39
The cycle of scientific discovery is frequently bottlenecked by the slow, manual creation of software to support computational experiments\cite{hannay2009how}. To address this, we…
Tukey's transformational ladder for portfolio management
Philip Ernst, James Thompson, Yinsen Miao
Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted S\&P 500 portfolio as well as the often overlooke…
Derivatives of Feynman-Kac Semigroups
James Thompson
We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the lo…
Convex geometries representable by at most 5 circles on the plane
PolyMath REU Convex Geometries Collaboration, Kira Adaricheva, Madina Bolat +18
A convex geometry is a closure system satisfying the anti-exchange property. In this work we document all convex geometries on 4- and 5-element base sets with respect to their repr…
Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces
Anton Thalmaier, James Thompson
In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the…
First Order Feynman-Kac Formula
Xue-Mei Li, James Thompson
We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and fo…
Functional inequalities for Feynman-Kac semigroups
James Thompson
Using the tools of stochastic analysis, we prove various gradient estimates and Harnack inequalities for Feynman-Kac semigroups with possibly unbounded potentials. One of the main…
Brownian bridges to submanifolds
James Thompson
We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete…
Deep Learning Framework for Detecting Ground Deformation in the Built Environment using Satellite InSAR data
Nantheera Anantrasirichai, Juliet Biggs, Krisztina Kelevitz +5
The large volumes of Sentinel-1 data produced over Europe are being used to develop pan-national ground motion services. However, simple analysis techniques like thresholding canno…
Uniform gradient estimates on manifolds with a boundary and applications
Li-Juan Cheng, Anton Thalmaier, James Thompson
We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperime…
Portfolio Selection: The Power of Equal Weight
Philip Ernst, James Thompson, Yinsen Miao
We empirically show the superiority of the equally weighted S\&P 500 portfolio over Sharpe's market capitalization weighted S\&P 500 portfolio. We proceed to consider the MaxMedian…
Soil Property and Class Maps of the Conterminous US at 100 meter Spatial Resolution based on a Compilation of National Soil Point Observations and Machine Learning
Amanda Ramcharan, Tomislav Hengl, Travis Nauman +4
With growing concern for the depletion of soil resources, conventional soil data must be updated to support spatially explicit human-landscape models. Three US soil point datasetsw…
Derivative and divergence formulae for diffusion semigroups
Anton Thalmaier, James Thompson
For a semigroup generated by an elliptic operator on a smooth manifold , we use straightforward martingale arguments to derive probabilistic formulae for , not…
Approximation of Riemannian measures by Stein's method
James Thompson
In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the…
Quantitative -estimates by Bismut formulae
Li-Juan Cheng, Anton Thalmaier, James Thompson
For a function and an elliptic operator , we prove a quantitative estimate for the derivative in terms of local bounds on and . An integral version of thi…
Bounded-Memory Parallel Image Pulling for Large Container Images
Sri Saran Balaji Vellore Rajakumar, Henry Wang, Ankur Singh +1
AI/ML workloads increasingly run as containers, where a container image must be downloaded to the host before the workload can start. This cold image pull lands on the critical pat…
Functional inequalities on manifolds with non-convex boundary
Li-Juan Cheng, Anton Thalmaier, James Thompson
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalitie…
Seekable OCI: Lazy-Loading Container Images via Range-Request Indexing
James Thompson, Wayne Mesard, Jesse Butler +2
Container image pulling accounts for the majority of pod startup time in Kubernetes environments. Standard pull downloads the entire image before the container can start, even when…
Convex geometries representable with colors, by ellipses on the plane, and impossible by circles
Kira Adaricheva, Evan Daisy, Ayush Garg +5
A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of K. Adaricheva and M. Bolat (2016) and the Polymath REU 2020 team, con…
Ultrafast Processes in 1,2-Dichloroethene measured with a Universal XUV probe
Henry G. McGhee, Henry J. Thompson, James Thompson +8
The presence of two chlorine atoms in 1,2-dichloroethene allows for isomerisation around the double bond. This isomerisation can lead to rich photochemistry. We present a time-reso…
Brownian motion and the distance to a submanifold
James Thompson
We present a study of the distance between a Brownian motion and a submanifold of a complete Riemannian manifold. We include a variety of results, including an inequality for the L…