Works (21)
Updated: April 4th, 2024 08:39
2024 article
NON-LINEAR SINGULARITY FORMATION FOR CIRCULAR VORTEX SHEETS (vol 82, pg 81, 2024)
Murray, R., & Wilcox, G. (2024, February 6). QUARTERLY OF APPLIED MATHEMATICS, Vol. 2.
Sources: Web Of Science, NC State University Libraries
Added: February 19, 2024
2023 article
NON-LINEAR SINGULARITY FORMATION FOR CIRCULAR VORTEX SHEETS
Murray, R., & Wilcox, G. (2023, May 3). QUARTERLY OF APPLIED MATHEMATICS, Vol. 5.
arxiv.org (repository)
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: June 5, 2023
2023 article
The geometry of adversarial training in binary classification
Bungert, L., Trillos, N. G., & Murray, R. (2023, January 13). INFORMATION AND INFERENCE-A JOURNAL OF THE IMA, Vol. 1.
author keywords: adversarial training; nonlocal perimeter; nonlocal total variation; existence of solutions; regularity
Sources: Web Of Science, NC State University Libraries
Added: February 6, 2023
2022 journal article
Adversarial classification: Necessary conditions and geometric flows
Journal of Machine Learning Research, 23(187), 1–38.
Source: ORCID
Added: November 10, 2022
2022 journal article
Distributed Gradient Flow: Nonsmoothness, Nonconvexity, and Saddle Point Evasion
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 67(8), 3949–3964.
author keywords: Optimization; Convergence; Linear programming; Manifolds; Standards; Heuristic algorithms; Trajectory; Distributed optimization; gradient descent; gradient flow; nonconvex optimization; nonsmooth optimization; saddle point; stable manifold
TL;DR:
It is shown that if agents’ objective functions are assumed to be smooth and nonconvex, then DGF can only converge to a saddle point from a zero-measure set of initial conditions.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 28, 2022
2022 article
From Graph Cuts to Isoperimetric Inequalities: Convergence Rates of Cheeger Cuts on Data Clouds
Trillos, N. G., Murray, R., & Thorpe, M. (2022, April 8). ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Vol. 4.
TL;DR:
In this work, careful estimates of interpolation operators which lift empirical Cheeger cuts to the continuum, as well as continuum stability estimates for isoperimetric problems are obtained, the first of their kind.
(via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: April 25, 2022
2022 journal article
Tukey Depths and Hamilton-Jacobi Differential Equations
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE, 4(2), 604–633.
author keywords: statistical depths; robust statistics; Hamilton-Jacobi equations; viscosity solutions
TL;DR:
It is proved that this equation possesses a unique viscosity solution, and that this solution always bounds the Tukey depth from below.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: May 12, 2022
2021 journal article
Dropout Fails to Regularize Nonparametric Learners
JOURNAL OF STATISTICAL THEORY AND PRACTICE, 15(2).
author keywords: Dropout; Nonparametric statistics; Deep learning; Regularization
TL;DR:
This work studies the theory of dropout from a nonparametric viewpoint, which is considered a proxy for the deepest layers of a neural network.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
4. Quality Education
(OpenAlex)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: January 21, 2021
2020 journal article
Neutral competition in a deterministically changing environment: Revisiting continuum approaches
JOURNAL OF THEORETICAL BIOLOGY, 486.
MeSH headings : Population Dynamics; Probability
TL;DR:
A classical, competitive Moran model is extended to incorporate an environment that fluctuates periodically in time to investigate the effects of the magnitude and frequency of environmental fluctuations on two important population statistics: the probability of fixation and the mean time to fixation.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land
(Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: February 10, 2020
2020 journal article
On self-similar solutions to the incompressible Euler equations
JOURNAL OF DIFFERENTIAL EQUATIONS, 269(6), 5142–5203.
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: June 29, 2020
2020 journal article
Regular potential games
Games and Economic Behavior, 124, 432–453.
author keywords: Game theory; Potential games; Generic games; Regular equilibria; Multi-agent systems
TL;DR:
It is shown that almost all potential games are regular, except for a closed subset with Lebesgue measure zero, which proves an oddness result for potential games: in almost all possible games, the number of Nash equilibrium strategies is finite and odd.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(Web of Science)
Source: ORCID
Added: October 2, 2020
2020 journal article
y A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE, 2(3), 705–739.
author keywords: empirical risk minimization; graph Laplacian; discrete to continuum; nonparametric regression
TL;DR:
The argument relies on a simple, yet powerful, maximum principle for the graph Laplacian, which gives the explicit dependence of the rates in terms of the parameter $\varepsilon_n$, the strength of regularization $\beta_n$ and the number of data points $n$.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: September 13, 2020
2019 journal article
Local minimizers and slow motion for the mass preserving Allen–Cahn equation in higher dimensions
Proceedings of the American Mathematical Society, 147(12), 5167–5182.
author keywords: Second-order Gamma-convergence; rearrangement; Cahn-Hilliard functional; slow motion; Allen-Cahn equation; Cah-Hilliard equation
Source: ORCID
Added: December 6, 2019
2019 journal article
Revisiting Normalized Gradient Descent: Fast Evasion of Saddle Points
IEEE Transactions on Automatic Control, 64(11), 4818–4824.
author keywords: Gradient methods; machine learning; nonconvex optimization; optimization
TL;DR:
A global convergence-time bound is established for NGD under mild assumptions because it is shown that NGD “almost never” converges to saddle points and the time required to escape from a ball of radius is small.
(via Semantic Scholar)
Source: ORCID
Added: December 6, 2019
2018 journal article
A model for system uncertainty in reinforcement learning
Systems & Control Letters, 122, 24–31.
author keywords: Dynamic programming; Learning systems; Machine learning; Adaptive control
TL;DR:
This model provides one possible framework for studying the tradeoff between exploration and exploitation in reinforcement learning and can be seem as a variant of either Bayesian reinforcement learning or adaptive control.
(via Semantic Scholar)
Source: ORCID
Added: December 6, 2019
2018 article
Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points
Swenson, B., Murray, R., Kar, S., & Poor, H. V. (2018, October). 2018 52nd Asilomar Conference on Signals, Systems, and Computers.
TL;DR:
Under relatively mild assumptions it is shown that BR dynamics may only converge to an interior saddle-point from a measure-zero set of initial conditions, which provides a weak stable manifold theorem in this context.
(via Semantic Scholar)
Source: ORCID
Added: December 6, 2019
2018 journal article
On Best-Response Dynamics in Potential Games
SIAM Journal on Control and Optimization, 56(4), 2734–2767.
author keywords: game theory; learning; best-response dynamics; fictitious play; potential games; convergence rate
TL;DR:
The paper studies the convergence properties of (continuous-time) best-response dynamics from game theory to find out if they are convergent or non-convergent.
(via Semantic Scholar)
Source: ORCID
Added: December 6, 2019
2017 journal article
A new analytical approach to consistency and overfitting in regularized empirical risk minimization
European Journal of Applied Mathematics, 28(6), 886–921.
author keywords: Overfitting; empirical risk minimization; graph total variation; discrete to continuum; classification
Source: ORCID
Added: December 6, 2019
2017 journal article
Cutoff estimates for the linearized Becker–Döring equations
Communications in Mathematical Sciences, 15(6), 1685–1702.
author keywords: coagulation-fragmentation equations; spectrum; cutoff estimates
Source: ORCID
Added: December 6, 2019
2016 journal article
Algebraic Decay to Equilibrium for the Becker--Döring Equations
SIAM Journal on Mathematical Analysis, 48(4), 2819–2842.
author keywords: coagulation-fragmentation equations; rate of decay to equilibrium; interpolation inequalities
TL;DR:
Algebraic rates of decay are established when initial perturbations of equilibrium have polynomial moments, proved by using new dissipation estimates in polynomially weighted $\ell^1$ spaces, operator decomposition techniques from kinetic theory, and interpolation estimates from the study of traveling waves.
(via Semantic Scholar)
Source: ORCID
Added: December 6, 2019
2015 journal article
Second-Order Γ-limit for the Cahn–Hilliard Functional
Archive for Rational Mechanics and Analysis, 219(3), 1383–1451.
Source: ORCID
Added: December 6, 2019
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