Works (22)

Updated: May 1st, 2024 05:32

2024 article

EIKONAL DEPTH: AN OPTIMAL CONTROL APPROACH TO STATISTICAL DEPTHS

Molina-Fructuoso, M., & Murray, R. (2024, April). FOUNDATIONS OF DATA SCIENCE, Vol. 4.

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

author keywords: Multivariate analysis; data depth; outlier detection; adversarial ro- bustness; non-Euclidean depth
UN Sustainable Development Goal Categories
13. Climate Action (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: April 29, 2024

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.

By: R. Murray n & G. Wilcox*

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.

By: R. Murray n & G. Wilcox n

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.

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

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.

Ryan Murray

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*

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)
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.

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

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.

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

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).

By: R. Murray n & E. Fokoue*

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
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.

By: R. Murray n & G. Young*

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.

By: A. Bressan* & R. Murray n

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.

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

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.

By: N. Trillos & R. Murray*

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.

By: G. Leoni* & R. Murray n

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*

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.

By: R. Murray* & M. Palladino*

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.

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

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.

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

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.

By: N. Trillos* & R. Murray*

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*

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*

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.

By: G. Leoni* & R. Murray*

Source: ORCID
Added: December 6, 2019

Citation Index includes data from a number of different sources. If you have questions about the sources of data in the Citation Index or need a set of data which is free to re-distribute, please contact us.

Certain data included herein are derived from the Web of Science© and InCites© (2024) of Clarivate Analytics. All rights reserved. You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.