### 2023

D. Lacker, K. Ramanan and R. Wu, “Local weak convergence for Large networks of interacting processes, “Annals of Applied Probability, Vol. 33, Number 2 (2023) 643-688, [Arvix, 2020].

C. Aistleitner, N. Gantert, Z. Kabluchko, J. Prochno and K. Ramanan

Large deviation principles for lacunary sums, “Transactions of the AMS, Vol. 376, Number 1 (2023) 507-553 [Arxiv, 2020].

### 2022

S S Kim, Y-T Liao and K Ramanan

An asymptotic thin shell condition and large deviations for multidimensional projections

*Advances in Applied Mathematics,* vol. **134**, 102306 (2022)

P Dupuis and Y Mao

Formulation and properties of a divergence used to compare probability measures without absolute continuity

J Birrell, P Dupuis, M A Katsoulakis, Y Pantazis, L Rey-Bellet

(f,Gamma)-Divergences: Interpolatin between f-divergences and integral probability metrics

P Dupuis and G S Medvedev

The large deviation principle for interacting dynamical systems on random graphs

### 2021

S V Lototsky, R Mikulevicius and B L Rozovsky

Intrusive and non-instrusive chaos approximation for a two-

dimensional steady state Navier-stokes system with random forcing.

R Atar, A Budhiraja, P Dupuis, and R Wu

Large Deviations for the Single-Server Queue and the Reneging Paradox

P Dupuis and G-J Wu

Large Deviation Properties of the E mpirical Measure of a Metastable Small Noise Diffusion

A Budhiraja, P Dupuis, P Nyquist, G-J Wu

Quasistationary distributions and ergodic control problems

J Birrell, P Dupuis, M A Katsoulakis, L Rey-Bellet and J Wang

Variational Representations and Neural Network Estimation of Renyi Divergences

### 2020

D. Lacker, K. Ramanan and R. Wu, “Local weak convergence for Large networks of interacting processes, “Annals of Applied Probability, Vol. 33, Number 2 (2023) 643-688, [Arvix, 2020].

C. Aistleitner, N. Gantert, Z. Kabluchko, J. Prochno and K. Ramanan

Large deviation principles for lacunary sums, “Transactions of the AMS, Vol. 376, Number 1 (2023) 507-553 [Arxiv, 2020].

J Klobusicky, G Menon and R L Pego

Two-dimensional grain boundary networks: stochastic particle models and kinetic limits.

Paul Dupius and Gjou-Jhen Wu

Large deviation properties of the empirical measure of a stochastic differential equation with small noise.

Rami Atar, Amarjit Budhiraja, Paul Dupuis and Ruoyu Wu

Robust bounds and optimization at the large deviations scale for queueing models via R\’enyl divergence.

Hongjie Dong and Doyoon Kim

Lp-estimates for time fractional parabolic equations in divergence form with measurable coefficients.

Hongjie Dong and Qi S. Zhang

Time analyticity for the heat equation and Navier-Stokes Equations.

Hongjie Dong and Chiara Gallarati

Higher-Order Parabolic Equations with VMO Assumptions and General Boundary Conditions with Variable Leading Coefficients.

Hongjie Dong and Zongyuan Li

Classical Solutions of Oblique Derivative Problem in Nonsmooth Domains with Mean Dini Coefficients.

Hongjie Dong and Kunrui Wang

Boundary e-Regularity Criteria for the Three-Dimensional Navier-Stokes Equations.

C. Dafermos

Wave scattering in hyperbolic balance laws and the zero relaxation limit.

A Volkening, MR Abbott, N Chandra, B Dubois, F Lim, D Sexton, and B Sandstede

Modeling stripe formation on growing zebrafish tailfins.

MR McGuirl, SP Smith, B Sandstede, and S Ramachandran

Detecting shared genetic architecture among multiple phenotypes by hierarchical clustering of gene-level association statistics.

JJ Bramburger and B Sandstede

Localized patterns in planar bistable weakly coupled lattice systems.

R Parker, PG Kevrekidis, and B Sandstede

Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems.

JJ Bramburger and B Sandstede

Spatially localized structures in lattice dynamical systems.

MR McGuirl, A Volkening, and B Sandstede

Topological data analysis of zebrafish patterns.

S. V. Lototsky and B. L. Rozovsky

Classical and generalized solutions of fractional stochastic differential equations.

### 2019

Shankar Bhamidi, Amarjit Budhiraja, Paul Dupuis and Ruoyu Wu

Rare event asymptotics for exploration processes for random graphs.

Jeremiah Birrell, Paul Dupuis, Markos A. Katsoulakis, Luc Rey-Bellet, and Jie Wang

Distributional Robustness and Uncertainty Quantification for Rare Events.

Rami Atar, Amarjit Budhiraja, Paul Dupuis, and Ruoyu Wu

Large Deviations for the Single Server Queue and the Reneging Paradox

Amarjit Budhiraja and Paul Dupuis

Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods

Amarjit Budhiraja and Paul Dupuis

Recursive Markov Systems with Small Noise.

Amarjit Budhiraja and Paul Dupuis

Relative Entropy and Tightness of Measures

Amarjit Budhiraja and Paul Dupuis

Stochastic Flows of Diffeomorphisms and Image Matching.

Amarjit Budhiraja and Paul Dupuis

Models with Special Features

Amarjit Budhiraja and Paul Dupuis

Examples of Representations and Their Application

Amarjit Budhiraja and Paul Dupuis

Rare Event Mote Carlo and Importance Sampling

Amarjit Budhiraja and Paul Dupuis

Large and Moderate Deviations for Finite Dimensional Systems.

Amarjit Budhiraja and Paul Dupuis

Representations for Continuous Time Processes.

Amarjit Budhiraja and Paul Dupuis

Multilevel Splitting

Amarjit Budhiraja and Paul Dupuis

Systems Driven by an Infinite Dimensional Brownian Noise

Amarjit Budhiraja and Paul Dupuis

Moderate Deviations for Recursive Markov Systems

Amarjit Budhiraja and Paul Dupuis

Models with Special Features

Amarjit Budhiraja and Paul Dupuis

General Theory

Amarjit Budhiraja and Paul Dupuis

Abstract Sufficient Conditions for Large and Moderate Deviations in the Small Noise Limit

Amarjit Budhiraja and Paul Dupuis

Performance of an IS Scheme Based on a Subsolution

Amarjit Budhiraja and Paul Dupuis

Empirical Measure of a Markov Chain

Paul Dupuis, Vaios Laschos and Kavita Ramanan

Exit time risk-sensitive control for systems of cooperative agents

Paul Dupuis, Guo-jhen Wu, and Michael Snarski

Infinte Swapping using IID Samples

CM Dafermos

Uniqueness of Zero Relaxation Limit.

*SIAM Journal on Mathematical Analysis* 51 (3), 1999-2018

Hongjie Dong and Longjuan Xu

Hessian Estimates for Non-divergence form Elliptic Equations Arising from Composite Materials

Hongjie Dong and Doyoon Kim

Lp-estimates for time fractional parabolic equations with coefficients measurable in time.

Jongkeun Choi and Hongjie Dong

Gradient estimates for Stokes systems with Dini Mean oscillation coefficients.

Hongjie Dong and Longjuan Xu

Gradient estimates for divergence form elliptic systems arising from composite material.

Hongjie Dong, Tong Yang and Mingying Zhong

Exterior problem of the linear Vlasov-Poisson-Boltzmann System.

Jongkeun Choi, Hongjie Dong and Zhongyuan Li

Optimal Regularity for a Dirichlet-Conormal Problem in Reifenberg Flat Domain

Hongjie Dong and N. V. Kkrylov

Fully nonlinear elliptic and parabolic equations in weighted and mied-norm Sobolev spaces.

Hongjie Dong and Haigang Li

Optimal estimates for the conductivity probem by Green’s Function Method

Hongjie Dong and Hong Zhang

On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations

Jongjeun Choi and Hongjie Dong

Gradient estimates for Stokes systems in domains

Hongjie Dong and Seick Kim

Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A revisit

Hongjie Dong and Doyoon Kim

Lq-Estimates for stationary Stokes system with coefficients measurable in one direction

C. Dafermos

Uniqueness of zero relaxation limit”

SIAM J. Math. Anal., **51** (2019), 1999-2018.

S Dodson and B Sandstede

Determining the source of period-doubling instabilities in spiral waves.

X. Cao, B. Sandstede, and X Luo

A functional data method for causal dynamic network modeling of task-related fMRI.

W. Strauss, A. Constantin and E. Varvaruca

*Large-amplitude steady downstreamwater waves*.

W. Strauss and Y. Wu

*Rapidly rotating stars*.

W. Strauss and J. Jang and Y. Wu

*Existence of rotating magnetic stars.*

S Iyer and B Sandstede

Mixing in reaction-diffusion systems: large phase offsets.

T Aougab, M Beck, P Carter, S Desai, B Sandstede, M Stadt, and A Wheeler

Isolas versus snaking of localized rolls.

Cao, B Sandstede, and X Luo

A functional data method for causal dynamic network modeling of task-related fMRI.

### 2018

M. V. Ciocanel, B. Sandstede, S. P. Jeschonek and K. L. Mowry

Modeling microtubule-based transport and anchoring of mRNA.

Hongjie Dong and Doyoon Kim

On L*p*-Estimates for Elliptic and Parabolic Equations with A*p *Weights.

Hongjie Dong and Seick Kim

Fundamental Solutions for Second-Order Parabolic Systems with Drift Terms.

Hongjie Dong, Luis Escauriaza and Seick Kim

On C1, C2, and weak type-(1, 1) estimates for linear elliptic operators: Part II.

Jongkeun Choi, Hongjie Dong and Doyoon Kim

Green Functions of Cornmal Derivative Problems for Stationary Stokes System

Jongkeun Choi, Hongjie Dong and Doyoon Kim

Conormal Deriative Problems for Stationary Stokes System in Sobolev Spaces.

Hongjie Dong, Tianling Jin and Hong Zhang

Dini and Schauder Estimates for Nonlocal Fully Nonlinear Parabolic Equations with Drifts.

Hongjie Dong and Hong Zhang

Dini estimates for nonlocal fully nonlinear elliptic equations.

Hongjie Dong and Doyoon Kim

Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients.

Hongjie Dong and Chiara Gallarati

Higher-order elliptic and parabolic equatios with VMO assumptions and general boundary conditions.

F. Delarue, D. Lacker and K. Ramanan

From the master equation to mean field game limit theory: Large deviations and concentration of measure.

Constantine Dafermos

Hyperbolic balance laws with dissipative source relaxing to adiabatic conservation laws.

B. L. Rozovsky and S. V. Lototsky

Classical and Generalized Solutions of Fractional Stochastic Differential Equations.

B. Rozovskii , T. Chen, and C.-W. Shu

Numerical solutions of stochastic PDEs driven by arbitrary type of noise.

B. L. Rozovsky and S. V. Lototsky

Stochastic Evolution Systems. Linear Theory and Applications to Non-linear Filtering.

W. Strauss and S. W. So

Upper bound on the slope of steady water waves with small adverse vorticity

E Makrides and B Sandstede

Existence and stability of spatially localized patterns.

HM McNamara, S Dodson, Y-L Huang, EW Miller, B Sandstede, and AE Cohen

Geometry-dependent instabilities in electrically excitable tissues.

B de Rijk and B Sandstede

Diffusive stability against nonlocalized perturbations of planar wave trains in reaction-diffusion systems.

A Volkening and B Sandstede

Iridophores as a source of robustness in zebrafish stripes and variability in *Danio* patterns.

P Carter and B Sandstede

Unpeeling a homoclinic banana in the FitzHugh-Nagumo system.

B Barker, R Nguyen, B Sandstede, N Ventura, and C Wahl

Computing Evans functions numerically via boundary-value problems.

C M Dafermos

Hyperbolic balance laws with dissipative source relaxing to adiabatic conservation laws.

### 2017

Paul Dupuis, J. Doll and P. Nyquist

Thermodynamic integration methods, infinite swapping and the calculation of generalized averages.

J Klobusicky, G Menon

Concentration inequalities for a removal-driven thinning process.

Paul Dupuis, J. Doll and P. Nyquist

A large deviations analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms.

P. Dupuis and D. Johnson

Moderate deviations based importance sampling for stochastic recursive equations

B. L. Rozovsky and S. Lototsky

Stochastic Partial Differential Equations.

W. Strauss and Y. Wu

*Steady states of rotating stars and galaxies.*

V Ciocanel, JA Kreiling, JA Gagnon, KL Mowry, and B Sandstede

Analysis of active transport by fluorescence recovery after photobleaching.

C Xia, C Cochrane, J DeGuire, G Fan, E Holmes, M McGuirl, P Murphy, J Palmer, P Carter, L Slivinski, and B Sandstede

Assimilating Eulerian and Lagrangian data in traffic-flow models.

### 2016

D Johnson-Chyzhykov and G Menon

The building game: from enumerative combinatorics to conformational diffusion

E. Russell and G Menon

Energy landscapes for the self-assembly of supramolecular polyhedra

G. Menon

The Airy function is a Fredholm determinant

G Menon and T Trogdon

Smoothed analysis for the conjugate gradient algorithm, SIGMA, 12 (2016)

R Abgrall, CW Shu, C Dafermos, EF Toro, TH Sonar, F Coquel, B Despres, et al.

Handbook of Numerical Methods for Hyperbolic Problems, Vol **17**. Handbook of Numerical Analysis

CM Dafermos

Hyperbolic balance laws with relaxation

CM Dafermos

BV Solutions for Systems of Balance Laws

CM Dafermos

Steady and Self-Similar Solutions in Multi-Space Dimensions

CM Dafermos

Scalar Conservation Laws in One Space Dimension

CM Dafermos

Construction of BV Solutions by the Vanishing Viscosity Method

CM Dafermos

The Cauchy Problem

CM Dafermos

Admissible Wave Fans and the Riemann Problem

CM Dafermos

Admissible Shocks

CM Dafermos

The L1 Theory for Scalar Conservation Laws

CM Dafermos

Entropy and the Stability of Classical Solutions

Hyperbolic Conservation Laws in Continuum Physics

CM Dafermos

BV Solutions for Hyperbolic Balance Laws with periodic initial data

Constantine Dafermos

BV solutions for hyperbolic balance laws with periodic initial data.

CM Dafermos

Introduction to the theory of hyperbolic conservation laws

Paul Dupuis, M. A. Katsoulakis, Y. Pantazis and P. Plechac

Path-space information bounds for uncertainty quantification and sensitivity analysis of stochastic dynamics.

R. Abgrall and Chi-Wang Shu (eds.) North Holland

Introduction to the Theory of Hyperbolic Conservation Laws.

*Handbook of Numerical Analysis*.

B. Rozovsky and R. Mikulevicius

On distribution free Skorokhod- Malliavin Calculus.

B. Rozovsky, G. E. Karniadakis, and Z. Zhang

Strong and weak convergence rate of finite element methods for semi-linear equations with additive white noise.

W. Strauss, A. Constantin and E. Varvaruca

Global bifurcation of steady gravity water waves with critical layers.

W. Strauss and M. Wheeler

Bound on the slope of steady water waves with favorable vorticity.

W. Strauss, D. Ambrose and D. Wright

Global bifurcation theory for periodic traveling interfacial gravity-capillary waves with critical layers.

W. Strauss and X. Chen

Convergence to equilibrium of a body moving in a kinetic sea.

P Carter, B de Rijk, and B Sandstede

Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system.

EA Powrie, V Ciocanel, JA Kreiling, JA Gagnon, B Sandstede, and KL Mowry

Using *in vivo* imaging to measure RNA mobility in *Xenopus laevis* oocytes.

### 2015

Paul Dupuis, A. Budhiraja, M. Rischer and K. Ramanan

Limits of relative entropies associated with weakly interacting particle systems.

B. Rozovsky, M Zheng, and G. E. Karniadakis

Adaptive Wick-Malliavin Approximation to Nonlinear SPDEs with Discrete random Variables.

W. Strauss, T. T. Nguyen, and T. V. Nguyen

Global magnetic confinement for the 1.5 D Vlasov-Maxwell system.

W. Strauss, E. Esenturk and H. J. Hwang

Stationary solutions of the Vlasov-Poisson system with diffusive boundary conditions.

W. Strauss and Xuwen Chen

Velocity reversal criterion of a body immersed in a sea of particles.

B Sandstede and T Theerakarn

Regularity of center manifolds via the graph transform.

A Volkening and B Sandstede

Modelling stripe formation in zebrafish: an agent-based approach.

J Guckenheimer, B Krauskopf, HM Osinga and B Sandstede

Invariant manifolds and global bifurcations.

P Carter and B Sandstede

Fast pulses with oscillatory tails in the FitzHugh-Nagumo system.

L Slivinski, E Spiller, A Apte, and B Sandstede

A hybrid particle-ensemble Kalman filter for Lagrangian data assimilation.

### 2014

B. Rozovskii, Z. Zhang, M. V. Tretyakov, and G. E. Karniadakis

Wiener chaos vs stochastic collocation methods for linear advection-diffusion quations with multiplicative white noise.

W. Strauss and Xuwen Chen

*Approach to equilibrium of a body colliding specularly and diffusely with a sea of particles*.

W. Strauss and T. Nguyen

*Linear stability analysis of a hot plasma in a solid torus.*

P Carter, PL Christiansen, YB Gaididei, C Gorria, B Sandstede, MP Sorensen, and J Starke

Multi-jam solutions in traffic models with velocity-dependent driver strategies.

K McQuighan and B Sandstede

Oscillons in the planar Ginzburg-Landau equation with 2:1 forcing.

M Beck, T Nguyen, B Sandstede and K Zumbrun

Nonlinear stability of source defects in the complex Ginzburg-Landau equation.

P van Heijster and B Sandstede

Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system.

E Makrides and B Sandstede

Predicting the bifurcation structure of localized snaking patterns.

Hongjie Dong and Seick Kim

Green’s functions for parabolic systems of second order in time-varying domains

Hongjie Dong and Jinggang Xiong

Boundary gradient estimates for parabolic and elliptic systems from linear laminates

Hongjie Dong

On a multi-dimensional transport equation with nonlocal velocity.

Hongjie Dong and Xumin Gu

Boundary partial regularity for the high dimensional Navier-Stokes equations.

Hongjie Dong and Doyoon Kim

On the impossibility of $W_p^2$ estimates for elliptic equations with piecewise constant coefficients.

Hongjie Dong and Doyoon Kim

Parabolic equations in simple convex polytopes with time irregular coefficients.

Hongjie Dong and Hong Zhang

Schauder estimates for higher-order parabolic systems with time irregular coefficients.

Govind Menon, D. Gracias, D. Johnson, R. Kaplan, J. Klobusicky, and S. Pandey

Self-assembly of mesoscale isomers: the role of pathways and degrees of freedom.

Govind Menon, P. Deift, S. Olver, and T. Trogdon

Universality in numerical computations with random data.

Govind Menon, D. Gracias, R. Kaplan, J. Klobusicky, and S. Pandey

Building polyhedra by self-assembly: theory and experiment.

Harold Kushner

A partial history of the early development of continuous-time nonlinear stochastic systems theory.

### 2013

W. Strauss and T. Nyugen

Stability analysis of collisionless plasmas with specularly reflecting boundary.

*SIAM J. Math. Anal.* **45** (2013), 777-808.

S McCalla and B Sandstede

Spots in the Swift-Hohenberg equation.

*SIAM Journal on Applied Dynamical Systems* **12** (2013) 831-877.

HJ Hupkes and B Sandstede

Stability of pulse solutions for the discrete FitzHugh-Nagumo system.

*Transactions of the American Mathematical Society* **365**(2013) 251-301.

Hongjie Dong and N. V. Krylov

On the existence of smooth solutions for fully nonlinear parabolic equations with measurable “coefficients” without convexity assumptions

*Comm. Partial Differential Equations*, **38** (2013), no. 6, 1038–1068

Hongjie Dong and Doyoon Kim

Schauder estimates for a class of nonlocal elliptic equations

*Discrete Contin. Dyn. Syst.-A* **33** (2013) no. 6, 2319-2347

Hongjie Dong and Dong Li

Global $\dot H^1 \cap \dot H^{-1}$ solutions to a logarithmically regularized 2D Euler equation

*J. Math. Fluid Mech*., 2013

Hongjie Dong and Dong Li

On a one-dimensional $\alpha$-patch model with nonlocal drift and fractional dissipation

*Trans. Amer. Math. Soc.*, **366** (2014), no. 4, 2041–2061

Hongjie Dong

On elliptic equations in a half space or in convex wedges with irregular coefficients

*Adv. Math.,* **238** (2013), 24–49

Hongjie Dong and Dong Li

On a generalized maximum principle for a transport-diffusion model with log-modulated fractional dissipation

*Discrete Contin. Dyn. Syst.-A* **34** (2013), no.9, 3437–3454

Govind Menon, with Andrew Sageman-Furnas, Parikshit Goswami and Stephen Russell

The Sphereprint: An approach to quantifying the conformability of flexible materials.

*Journal of Textile Research, (*2013).

Govind Menon, with Helen Li.

Numerical solution of Dyson Brownian motion and a sampling scheme for invariant matrix ensembles.

*J. Stat. Phys. *Vol **153**, (2013).

Govind Menon, with C. Pfrang and Percy Deift

How long does it take to compute the eigenvalues of a random symmetric matrix?

Featured in *MSRI volume on random matrix theory.*

Paul Dupuis and Y. Cai

Analysis of an interacting particle method for rare event estimation.

*Queueing Systems 73(4), April 2013.*

### 2012

W. Strauss

Vorticity jumps in steady water waves.

*Disc. Cont. Dyn. Sys.-B* **17** (2012), 1101-1113

B Sandstede and Y Xu

Snakes and isolas in non-reversible conservative systems.

*Dynamical Systems* **27** (2012) 317-329.

P van Heijster and B Sandstede

Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system.

*RIMS Kokyuroku Bessatsu* **B31** (2012) 135-155.

B Sandstede, A Scheel, G Schneider and H Uecker

Diffusive mixing of periodic wave trains in reaction-diffusion systems.

*Journal of Differential Equations* **252** (2012) 3541-3574.

M Beck, T Nguyen, B Sandstede and K Zumbrun

Toward nonlinear stability of sources via a modified Burgers equation.

*Physica D* **241** (2012) 382-392.

Constantine Dafermos

Maximal dissipation in equations of evolution

*J. Diff. Equations ***252 **(2012), 567-587

Constantine Dafermos

N-waves in hyperbolic balance laws.

*Journal of Hyperbolic Equations, 9, 2, 339-354, 2012.*

Constantine Dafermos

Hyperbolic Conservation Laws: Analytical Properties*
Encyclopedia of Applied and Computational Mathematics*. B. Engquist (ed.) Springer-Verlag, Berlin.

Constantine Dafermos

Regularity of solutions to the equations of thermoelasticity

*Encyclopedia of Thermal Stresses*. R. Hetnarski (ed.) Springer-Verlag, Berlin.

Hongjie Dong

Solvability of second-order equations with hierarchically partially BMO coefficients

*Trans. Amer. Math. Soc.*, **364 **(2012) no. 1, 493–517

Hongjie Dong, N. V. Krylov and X. Li

On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients

*Algebra i Analis (St. Petersburg Math. J.)*, **24 **(2012) no. 1

Paul Dupuis, Y. Liu, N. Plattner and J. D. Doll

On the infinite swapping limit for parallel tempering

Paul Dupuis, K. Spiliopoulos and H. Wang

Importance sampling for multiscale diffusions

*SIAM J. on Multiscale Modeling and Simulation, 10 (1) 1 – 27, 2012.*

Paul Dupuis, B. Kaynar, A. Ridder, R. Rubinstein and Radislav Vaisman

Counting with combined splitting and capture-recapture methods

Paul Dupuis and K. Chowdhary

Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification

*ESAIM: Mathematical Modeling and Numerical Analysis*

Paul Dupuis and K. Spiliopoulos

Large deviations for multiscale diffusions via weak convergence methods

*Stochastic Processes and Their Applications, 122(4), 2010.*

Paul Dupuis and M. Fischer

On the construction of Lyapunov functions for nonlinear Markov processes via relative entropy

Paul Dupuis, A. Budhiraja and M. Fischer

Large deviation properties of weakly interacting processes via weak convergence methods

Justin Holmer (with Quanhui Lin)

Phase-driven interaction of widely separated nonlinear Schroedinger solitons

Justin Holmer (with Svetlana Roudenko) *
*Blow-up solutions on a sphere for the 3d quintic NLS in the energy space

*Analysis and PDE*

Justin Holmer *
*Dynamics of KdV solitons in the presence of a slowly varying potential

Harold Kushner

Modeling and Approximations for Stochastic Systems with State-Dependent Singular Controls and Wide-Band Noise

*2012 IEEE CDC Conference on Decision and Control*

Harold Kushner

Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations

*Applied Math and Optimization, Vol. 66, 2012, pages 77-54 *

Harold Kushner

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

*Applied Math and Optimization, Vol. 66, 2012, pages 55-80*

Govind Menon, (in honor of Constantine Dafermos)

Lesser known miracles of Burgers equation

*Acta Mathematica Scientia*, Vol. **32** (2012)

Govind Menon

Complete integrability of shock clustering and Burgers turbulence

*Arch. Rational Mech. Anal. *Vol. **203**, (2012).

Govind Menon with M. Hadzic

Gradient flow structure for domain relaxation in Langmuir Films

*Q. App. Math. *Vol. **70** (2012).

B Sandstede, A Scheel, G Schneider and H Uecker

Diffusive mixing of periodic wave trains in reaction-diffusion systems

*Journal of Differential Equations* (2012)

P van Heijster and B Sandstede

Coexistence of stable spots and fronts in a three-component Fitzhugh-Nagumo system

*RIMS Kokyuroku Bessatsu*, (2012), **B31**, 135-155.

HJ Hupkes and B Sandstede

Stability of pulse solutions for the discrete FitzHugh-Nagumo system

*Transactions of the American Mathematical Society (2012).*

M Beck, T Nguyen, B Sandstede and K Zumbrun

Toward nonlinear stability of sources via a modified Burgers equation

*Physica D 241 (2012) 382-292 *

Harold Kushner

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

*Appl Math Optim* (2012) **66**:55-80

### 2011

W. Strauss and A. Constantin

Periodic traveling gravity waves with discontinuous vorticity.

Arch. Rat. Mech. Anal.**202** (2011), 133-175.

P van Heijster and B Sandstede

Planar radial spots in a three-component FitzHugh-Nagumo system.

*Journal of Nonlinear Science* **21** (2011) 705-745.

HJ Hupkes, D Pelinovsky and B Sandstede

Propagation failure in the discrete Nagumo equation.

*Proceedings of the American Mathematical Society* **139**(2011) 3537-3551.

J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht

Isolas of 2-pulse solutions in homoclinic snaking scenarios.

*Journal of Dynamics and Differential Equations* **23**(2011) 93-114.

G Derks, S Maad and B Sandstede

Perturbations of embedded eigenvalues for the planar bilaplacian.

*Journal of Functional Analysis* **260** (2011) 340-398.

Constantine Dafermos

Generalized characteristics and the Hunter-Saxton equation

Journal of Hyperbolic Equations, **8 **(2011), 159-168

Hongjie Dong

The aggregation equation with power-law kernels: ill-posedness, mass concentration and similarity solutions

*Comm. Math. Phys. ***304 **(2011) no. 3, 649–664

Hongjie Dong and D. Kim

Parabolic and elliptic systems in divergence form with variably partially BMO coefficients.

*SIAM J. Math. Anal.*, **43 **(2011) no. 3, 1075–1098

Hongjie Dong and D. Kim

Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth

*Comm. Partial Differential Equations*, **36 **(2011) no. 10, 1750–1777

Hongjie Dong, S. Cho and S. Kim

Global estimates for Green’s matrix of second order parabolic systems with application to elliptic systems in two dimensional domains

*Potential Anal. (2011)*

Hongjie Dong

On similarity solutions to the multidimensional aggregation equation*
SIAM J. Math.Anal.*,

**43**(2011) no. 4, 1995–2008

Hongjie Dong and D. Kim

Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

*J. Funct. Anal.*, **261 **(2011) no. 11, 3279–3327

Hongjie Dong and D. Kim

On *Lp*-estimates for a class of nonlocal elliptic equations

*J. Funct. Anal.*, (2011), doi:10.1016/j.jfa.2011.11.002

Hongjie Dong

Parabolic equations with variably partially VMO coefficients

*Algebra i Analis (St. Petersburg Math. J.) ***23 **(2011) no.3, 150–174

Hongjie Dong and S. Kim

Partial Schauder estimate for second-order elliptic and parabolic equations

*C**alc. Var. Partial Differential Equations*, **40 **(2011) no. 3–4, 481–500

Hongjie Dong and D. Li

On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces

*J. Differential Equations ***248 **(2010), no. 11, 2684–2702

Hongjie Dong and D. Kim*
Lp *solvability of divergence type parabolic and elliptic systems with partially BMO coefficient

*Calc. Var. Partial Differential Equations*

**40**(2011) no. 3–4, 357–389

Hongjie Dong and and D. Kim

On the *Lp*-solvability of higher order parabolic and elliptic systems with BMO coefficients

*Arch. Rational Mech. Anal. ***199 **(2011) no. 3, 889–941

Paul Dupuis, N. Plattner, J. D. Doll, H. Wang, Y. Liu, and J. Gubernatis

An infinite swapping approach to the rare-event sampling problem

*J. of Chemical Physics, 135, (2011), 134111*

Paul Dupuis, A. Budhiraja and V. Maroulas

Variational representations for continuous time processes

*Annales de l.Institut Henri Poincaré, 47, (2011), 725-747*

Paul Dupuis and T. Dean

The design and analysis of a generalized RESTART/DPR algorithm for rare event simulation

*Annals of OR, 189, (2011), 63-02*

Yan Guo and I. Tice

Rayleigh-Taylor instability for compressible inviscid fluids

*Indiana University Math. (2011)*

Yan Guo, R. Esposito and R. Marra

Validity of the Boltzmann equation with an external field

*Kinet. Relat. Models* **4** (2011), no. 2, 499-515

Yan Guo and B. Pausader

Global smooth ion dynamics in the Euler-Poisson system

*Commun. Math. Phys. 303 (2011), no. 1, 89-125*

Yan Guo and T. Nguyen

A note on Prandtl layer problem

*Comm. Pure Appl. Math., 64, (2011) no. 10, 1416-143*8

Yan Guo and R. Strain

Momentum regularity and stability of the relativistic Vlasov-Maxwell-Boltzmann system

*Commun. Math. Phys.* (2011)

Yan Guo

The Vlasov-Poisson-Landau system in a periodic box

*Journal of AMS* (2011)

Justin Holmer (with Galina Perelman and Maciej Zworski, and an appendix by Bernd Sturmfels)

Effective dynamics of double solitons for perturbed mKdV

*Communications in Mathematical Physics 305 (2011) pp. 363-425 *

Justin Holmer and Svetlana Roudenko

A class of solutions to the 3d cubic nonlinear Schroedinger equation that blow-up on a circle

*AMRX Appl Math Res Express* 2011 (**1**): 23-94

HJ Hupkes, D Pelinovsky and B Sandstede

Propagation failure in the discrete Nagumo equation

*Proceedings of the American Mathematical Society 139 (2011) 3537-3551*

J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht

Isolas of 2-pulse solutions in homoclinic snaking scenarios

*Journal of Dynamics and Differential Equations 23 (2011) 93-114*

Harold Kushner

Numerical Methods for Stochastic Singular Control Problems with State-Dependent Control

*SIAM J on Control and Optimization*

Harold Kushner**
**Numerical Methods for Controls for Nonlinear Stochastic Systems With Delays and Jumps: Applications to Admission Control

*Stochastics: An International Journal of Probability and Statistics, Vol.*

**83**, 2011, pages 277-310

John Mallet-Paret and R. D. Nussbaum

Inequivalent measures of noncompactness and the Radius of the Essential Spectrum

*Proc. Amer. Math. Soc. 139 (2011), pp. 917–930*

John Mallet-Paret and R. D. Nussbaum

Inequivalent measures of noncompactness

*Annali di Matematica 190 (2011), pp. 453–488*

John Mallet-Paret and R. D. Nussbaum

Superstability and rigorous asymptotics in singularly perturbed state-dependent delay differential equations

*J. Diff. Eq. 250 (2011), pp. 4037–4084*

Govind Menon, with S. Pandey, M. Ewing, D. Kunas, N. Hguyan and D. Gracias

Algorithmic design of self-folding polyhedra.

*PNAS *( Oct. 28, 2011).

Weining Kang and Kavita Ramanan**
**Characterization of Stationary Distributions of Reflected Diffusions

P van Heijster and B Sandstede

Planar radial spots in a three-component FitzHugh-Nagumo system

*Journal of Nonlinear Science 21 (2011) 705-745*

Hui Wang, N. Plattner, J. Doll, P. Dupuis, Y. Liu, and J. E. Gubernatis

An infinite swapping approach to the rare-event sampling problem

*J. Chem. Phys*. **135**, 134111, 2011

Hui Wang, P. Dupuis and K. Spiliopoulos

Rare event simulation for rough energy landscapes

*Proceeding of the 2011 Winter Simulation Conference, *2011

Hui Wang and L. Setayeshgar

Large deviations for a feedforward network

*Adv. Appl. Prob. ***43**, 545-571, 2011

### 2010

W. Strauss and A. Constantin

Trochoidal solutions to the incompressible two-dimensional Euler equations.

J. Math. Fluid Mech.**12** (2010), 181-201.

W. Strauss, D. Ambrose, M. Lopes Filho and H. Nussenzveig Lopes

Transport of interfaces with surface tension by 2D viscous flows.

Interfaces and Free Boundaries**12** (2010), 23-44.

W. Strauss and A. Constantin

Pressure and trajectories beneath a Stokes wave.

Comm. Pure Appl. Math.**63** (2010), 533-557.

W. Strauss

Steady water waves.

Bull. AMS.**47** (2010), 671-694.

HJ Hupkes and B Sandstede

Travelling pulses for the discrete FitzHugh-Nagumo system.

*SIAM Journal on Applied Dynamical Systems* **9** (2010) 827-882.

D Avitabile, DJB Lloyd, J Burke, E Knobloch and B Sandstede

To snake or not to snake in the planar Swift-Hohenberg equation.

*SIAM Journal on Applied Dynamical Systems* **9** (2010) 704-733.

S McCalla and B Sandstede

Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study.

*Physica D* **239** (2010) 1581-1592.

D Obeid, JM Kosterlitz and B Sandstede

State selection in the noisy stabilized Kuramoto-Sivashinsky equation.

*Physical Review E* **81** (2010) 066205.

M Beck, B Sandstede and K Zumbrun

Nonlinear stability of time-periodic viscous shocks.

*Archive for Rational Mechanics and Analysis* **196** (2010) 1011-1076.

M Beck, HJ Hupkes, B Sandstede and K Zumbrun

Nonlinear stability of semidiscrete shocks for two-sided schemes.

*SIAM Journal on Mathematical Analysis* **42** (2010) 857-903.

M Oh and B Sandstede

Evans functions for periodic waves on infinite cylindrical domains.

*Journal of Differential Equations* **248** (2010) 544-555.

W.H.Fleming, H. Kaise and S-J. Sheu

Max-plus Stochastic Control and Risk Sensitivity

W.H. Fleming and D. Hernandez-Hernandez

On the Value of Stochastic Differential Games

Harold Kushner

Numerical Methods for the Optimization of Nonlinear Stochastic Delay Systems, and an Application to Internet Regulation

*Proceedings of the 49th Conference on Decision and Control, 2010, IEEE Press, New York*

Govind Menon

A kinetic theory of shock clustering in scalar conservation laws

*Oberwolfach Reports *Vol** 7**, Issue 3, (2010).

Govind Menon with R. Srivivasan

Kinetic theory and Lax equations for shock clustering and Burgers turbulence

*J. Stat. Phys. ***140**, (2010).

Govind Menon, B. Niethammer and R. Pego

Dynamics and self-similarity in min-driven clustering

*Trans. AMS *Vol. **362** (2010)

### 2009

W. Strauss and B. Pausader

Analyticity of the scattering operator for fourth-order nonlinear waves.

Disc. Cont. Dyn. Sys.**25** (2009), 617-625.

V Manukian, N Costanzino, CKRT Jones and B Sandstede

Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations.

*Journal of Dynamics and Differential Equations* **21**(2009) 607-622.

HJ Hupkes and B Sandstede

Modulated wave trains in lattice differential systems.

*Journal of Dynamics and Differential Equations* **21**(2009) 417-485.

V Manukian and B Sandstede

Multi-hump pulses in systems with reflection and phase invariance.

*Journal of Differential Equations* **247** (2009) 1866-1898.

M Beck, J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht

Snakes, ladders, and isolas of localised patterns.

*SIAM Journal on Mathematical Analysis* **41** (2009) 936-972.

A Doelman, B Sandstede, A Scheel and G Schneider

The dynamics of modulated wave trains.

*Memoirs of the American Mathematical Society, ***199 **(934) (2009).

M Beck, A Ghazaryan and B Sandstede

Nonlinear convective stability of traveling fronts near Turing and Hopf instabilities.

*Journal of Differential Equations* **246** (2009) 4371-4390.

BG Bale, N Kutz and B Sandstede

Optimizing waveguide array mode-locking for high-power fiber lasers.

*IEEE Journal of Selected Topics in Quantum Electronics ***15** (2009) 210-231.

DJB Lloyd and B Sandstede

Localized radial solutions of the Swift-Hohenberg equation.

*Nonlinearity* **22** (2009) 485-524.

Harold Kushner

Numerical Methods for Optimal Controls for Nonlinear Stochastic Systems With Delays: Algorithms and Data

*IEEE Trans on Automatic Control, Vol. 55, 2010, pages 2170-2176*

Harold Kushner

Large Deviations for Two-Time-Scale Diffusions, With Delays

### 2008

W. Strauss and J. Ko

Effect of vorticity on steady water waves.

J. Fluid Mech.**608** (2008), 197-215.

W. Strauss and Z. Lin

A sharp stability criterion for the Vlasov-Maxwell system.

Inventiones Math.** 173** (2008), 497-546.

W. Strauss and J. Ko

Large-amplitude steady rotational water waves.

Eur. J. Mech. B Fluids**27** (2008), 96-109.

W. Strauss and P. Karageorgis*
Instability of steady states for nonlinear wave and heat equations.
J. Diff. Eqns*.

**241**(2007), 184-205.

DJB Lloyd, B Sandstede, D Avitabile and AR Champneys

Localized hexagon patterns of the planar Swift-Hohenberg equation.

*SIAM Journal on Applied Dynamical Systems* **7 **(2008) 1049-1100.

G Derks, S Maad and B Sandstede

Perturbations of embedded eigenvalues for the bilaplacian on a cylinder.

*Discrete and Continuous Dynamical Systems A* **21**(2008) 801-821.

B Sandstede and A Scheel

Hopf bifurcation from viscous shock waves.

*SIAM Journal on Mathematical Analysis* **39** (2008) 2033-2052.

N Kutz and B Sandstede

Theory of passive harmonic mode-locking using waveguide arrays.

*Optics Express* **16** (2008) 636-650.

B Sandstede and A Scheel

Relative Morse indices, Fredholm indices, and group velocities.

*Discrete and Continuous Dynamical Systems A* **20**(2008) 139-158.

Abdelkader Boucherif

Nonlocal Problems for Parabolic Inclusions

Abdelkader Boucherif, Zehour Benbouziane, and Sidi Mohamed Bouguima

Existence Result for Impulsive Third Order Periodic Boundary Value Problems

Hongjie Dong and Dong Li

Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations

*Comm. Math. Sci. (2008)*

Hongjie Dong and Dong Li

Finite time singularities for a class of generalized surface quasi-geostropic equations

*Proc. Amer. Math., 136 (2008), 2555–2563*

Hongjie Dong and Seick Kim

Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains

*Trans. Amer. Math. Soc. (2008)*

Hongjie Dong

Well-posedness for a transport equation with nonlocal velocity

*J. Funct. Anal, (2008)*

Hongjie Dong and Doyoon Kim

Parabolic and elliptic systems with VMO coefficients

Hongjie Dong and Natas Pavlovic

Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces

*Comm. Math. Phys. (2008)*

Hongjie Dong and Nicolai V. Krylov

Second-order elliptic and parabolic equations with *B(R2, VMO)* coefficients

Hongjie Dong, Seick Kim and Mikhail Safonov

On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equation

*Comm. Partial Differential Equations 33 (2008), no. 2, 177-188*

Paul Dupuis and Thomas Dean

The design and analysis of a generalized DPR algorithm for rare event simulation

Yan Guo and Mahir Hadzic

Stability in the Stefan problem with surface tension (I)

Yan Guo and R. Strain

Decay for soft potentials near Maxwellian

*Arch. Rational Mech. Anal., 187 no. 2, 287-339. (2008)*

Yan Guo and H. Hwang

Pattern formation (I): The Keller-Segel model

*JDE, (2008)*

Yan Guo and Z. Lin

Unstable and stable galaxy models

*Commun. Math. Phys. (2008)*

Harold Kushner

Stochastic Approximation: A Survey

*Brown University, November, 2008, ***PDF**

Bjorn Sandstede, A. Doelman, A. Scheel and G. Schneider

The dynamics of modulated wave trains

*Memoirs of the American Mathematical Society (2008)*

Bjorn Sandstede, D. J. B. Lloyd, D. Avitabile and A.R. Champneys

Localized hexagon patterns of the planar Swift-Hohenberg equation

*SIAM Journal on Applied Dynamical Systems 7 (2008) 1049-1100*

PDFHexagon movie Ladder movie)

Bjorn Sandstede, G. Derks, and S. Maad

Perturbations of embedded eigenvalues for the bilaplacian on a cylinder

*Discrete and Continuous Dynamical Systems A 21 (2008) 801-821*

Bjorn Sandstede and A. Scheel

Hopf bifurcation from viscous shock waves

*SIAM Journal on Mathematical Analysis 39 (2008) 2033-2052*

B Sandstede and N. Kutz

Theory of passive harmonic mode-locking using waveguide arrays

*Optics Express 16 (2008) 636-650*

Bjorn Sandstede and A. Scheel

Relative Morse indices, Fredholm indices, and group velocities

*Discrete and Continuous Dynamical Systems A 20 (2008) 139-158*

Hui Wang and Paul Dupuis

Importance Sampling for Jackson Networks

Hui Wang, Paul Dupuis and Kevin Leder

Importance Sampling for Weighted-Serve-the-Longest-Queue

### 2007

W. Strauss and P. Karageorgis

Instability of steady states for nonlinear wave and heat equations.

J. Diff. Eqns.**241** (2007), 184-205.

W. Strauss and A. Constantin

*Rotational steady water waves near stagnation
Phil. Trans. Roy. Soc.*

**365**(2007), 2227-2239.

W. Strauss and A. Constantin*
Stability properties of steady water waves with vorticity.
Comm. Pure Appl. Math*.

**60**(2007), 911-950.

W. Strauss and Z. Lin*
Linear stability and instability of relativistic Vlasov-Maxwell systems
Comm. Pure Appl. Math*.

**60**(2007), 724-787.

W. Strauss and Z. Lin*
Nonlinear stability and instability of relativistic Vlasov-Maxwell systems.
Comm. Pure Appl. Math*.

**60**(2007), 789-837.

B Sandstede

Evans functions and nonlinear stability of travelling waves in neuronal network models.

*International Journal of Bifurcation and Chaos* **17** (2007) 2693-2704.

B Sandstede and A Scheel

Period doubling of spiral waves and defects.

*SIAM Journal on Applied Dynamical Systems* **6** (2007) 494-547.

A Ghazaryan and B Sandstede

Nonlinear convective instability of Turing-unstable fronts near onset: A case study.

*SIAM Journal on Applied Dynamical Systems* **6** (2007) 319-347.

JDM Rademacher, B Sandstede and A Scheel.

Computing absolute and essential spectra using continuation.

*Physica D* **229** (2007) 166-183

Hongjie Dong and Dapeng Du

Global well-posedness and a decay estimate for the critical quasi-geostrophic equation

*Discrete Contin. Dyn. Syst., Vol. 21, 4, (2008) *

Hongjie Dong, Sungwon Cho and Seick Kim

On the fundamental solutions for strongly parabolic systems of second order

Hongjie Dong and N. Pavlovic

A regularity criterion for the dissipative quasi-geostrophic equations.

Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulasz

Large Deviations for Stochastic Flows of Diffeomorphisms.

Paul Dupuis, Kevin Leder, and Hui Wang

Large deviations and importance sampling for a tandem network with slow-down

Paul Dupuis, Kevin Leder and Hui Wang

On the Large Deviations Properties of the Weighted-Serve-the-Longest-Queue Policy

*Progress in Probability*

Thomas Dean, and Paul Dupuis

Splitting for Rare Event Simulation: A Large Deviations Approach to Design and Analysis

Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulas (March 2007)

Large Deviations for Infinite Dimensional Stochastic Dynamical Systems

Yan Guo and G. Rein

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

*Commun. Math. Phys., 271 (2007) 489-509*

Yan Guo, C. Hallstrom and D. Spirn

Dynamics near unstable, interfacial fluids

*Commun. Math. Phys., 270 (2007), 635-689*

Yan Guo and H. Hwang

Pattern formation (II): The Turing instability

*Proc. AMS, 135 (2007), 2855-2866*

Henrik Hult and Gennady Samorodnitsky

Tail probabilities for infinite series of regularly varying random vectors

Harold J. Kushner

Numerical Approximations to Optimal Nonlinear Filters

S. V. Lototsky and B. L. Rozovskii

Stochastic Partial Differential Equations Driven by Purely Spatial Noise

*Submitted to SIAM Journal on Mathematical Analysis, 2007*

S. V. Lototsky and B. L. Rozovskii

Stochastic Parabolic Equations of Full Second-Order

*Book chapter in ” Topics in Stochastic Analysis and Nonparametric Estimation,” Ed. P.- L. Chow et al., 199-210,
The IMA Volumes in Mathematics and its Applications, Springer, 2007*

S. V. Lototsky and B. L. Rozovskii

A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral

*Submitted to Probability Theory and Related Topics, 2007*

Govind Menon

Mathematical approaches to dynamic scaling

*J. Non-Newtonian Fluid Mech., 2007, doi:10.1016/j.jnnfm.2007.01.003*

Govind Menon and R. Pego

Universality classes in Burgers turbulence

*Comm. Math. Phys., 2007, doi:10.1007/s00220-007-0251-1*

Govind Menon and R. Pego

The scaling attractor and ultimate dynamics for Smoluchowski’s *coagulation equations*

*J. Nonlinear Sci., 2007.*