Works (20)

Updated: July 5th, 2023 15:04

2023 article

NON-LINEAR SINGULARITY FORMATION FOR CIRCULAR VORTEX SHEETS

Murray, R., & Wilcox, G. (2023, May 3). QUARTERLY OF APPLIED MATHEMATICS, Vol. 5.

By: R. Murray n  & G. Wilcox n

co-author countries: United States of America 🇺🇸
Sources: Web Of Science, ORCID
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.

By: L. Bungert *, N. Trillos * & R. Murray n 

co-author countries: Germany 🇩🇪 United States of America 🇺🇸
author keywords: adversarial training; nonlocal perimeter; nonlocal total variation; existence of solutions; regularity
Sources: Web Of Science, ORCID
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.

By: B. Swenson*, R. Murray n , H. Poor * & S. Kar *

co-author countries: United States of America 🇺🇸
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
Sources: ORCID, Web Of Science
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.

By: N. Trillos *, R. Murray n  & M. Thorpe*

co-author countries: United Kingdom of Great Britain and Northern Ireland 🇬🇧 United States of America 🇺🇸
Sources: Web Of Science, ORCID
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.

By: M. Molina-Fructuoso*  & R. Murray* 

author keywords: statistical depths; robust statistics; Hamilton-Jacobi equations; viscosity solutions
Sources: ORCID, Web Of Science
Added: May 12, 2022

2021 journal article

Dropout Fails to Regularize Nonparametric Learners

JOURNAL OF STATISTICAL THEORY AND PRACTICE, 15(2).

By: R. Murray n  & E. Fokoue*

co-author countries: United States of America 🇺🇸
author keywords: Dropout; Nonparametric statistics; Deep learning; Regularization
Sources: ORCID, Web Of Science
Added: January 21, 2021

2020 journal article

Neutral competition in a deterministically changing environment: Revisiting continuum approaches

JOURNAL OF THEORETICAL BIOLOGY, 486.

By: R. Murray n  & G. Young *

co-author countries: United States of America 🇺🇸
MeSH headings : Population Dynamics; Probability
Sources: Web Of Science, ORCID
Added: February 10, 2020

2020 journal article

On self-similar solutions to the incompressible Euler equations

JOURNAL OF DIFFERENTIAL EQUATIONS, 269(6), 5142–5203.

By: A. Bressan * & R. Murray n 

co-author countries: United States of America 🇺🇸
Sources: Web Of Science, ORCID
Added: June 29, 2020

2020 journal article

Regular potential games

Games and Economic Behavior, 124, 432–453.

By: B. Swenson*, R. Murray n  & S. Kar *

co-author countries: United States of America 🇺🇸
author keywords: Game theory; Potential games; Generic games; Regular equilibria; Multi-agent systems
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.

By: N. Trillos & R. Murray* 

author keywords: empirical risk minimization; graph Laplacian; discrete to continuum; nonparametric regression
Sources: ORCID, Web Of Science
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.

By: G. Leoni * & R. Murray n 

co-author countries: United States of America 🇺🇸
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.

By: R. Murray* , B. Swenson* & S. Kar *

co-author countries: United States of America 🇺🇸
author keywords: Gradient methods; machine learning; nonconvex optimization; optimization
Source: ORCID
Added: December 6, 2019

2018 journal article

A model for system uncertainty in reinforcement learning

Systems & Control Letters, 122, 24–31.

By: R. Murray*  & M. Palladino *

co-author countries: Italy 🇮🇹 United States of America 🇺🇸
author keywords: Dynamic programming; Learning systems; Machine learning; Adaptive control
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.

By: B. Swenson*, R. Murray* , S. Kar * & H. Poor *

co-author countries: United States of America 🇺🇸
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.

By: B. Swenson*, R. Murray*  & S. Kar *

co-author countries: United States of America 🇺🇸
author keywords: game theory; learning; best-response dynamics; fictitious play; potential games; convergence rate
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.

By: N. Trillos * & R. Murray* 

co-author countries: United States of America 🇺🇸
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.

By: R. Murray*  & R. Pego *

co-author countries: United States of America 🇺🇸
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.

By: R. Murray*  & R. Pego *

co-author countries: United States of America 🇺🇸
author keywords: coagulation-fragmentation equations; rate of decay to equilibrium; interpolation inequalities
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.

By: G. Leoni * & R. Murray* 

co-author countries: United States of America 🇺🇸
Source: ORCID
Added: December 6, 2019