Publications

N. E. Pacheco, C. G. Henry, A. Arnold, L. Fichera (2025) Virtual palpation: a novel method to identify the physical properties of tissue for laser surgery.

D. Calvetti, A. Arnold, G. Davico, A. Hoover, E. Somersalo (2024) Separable hierarchical priors applied to analysis of synergies in human locomotion.

S. Amato, A. Arnold (2024) Data-driven modeling and prediction of microglial cell dynamics in the ischemic penumbra. [arXiv]

C. Ho, A. Arnold (2024) Integrating physics-informed deep learning and numerical methods for robust dynamics discovery and parameter estimation. [arXiv]

S. Amato, A. Arnold (2025) A data-informed mathematical model of microglial cell dynamics during ischemic stroke in the middle cerebral artery. Bulletin of Mathematical Biology, 87, 31. [link] [pdf]

A. Fitzpatrick, M. Folino, A. Arnold (2024) Fourier series-based approximation of time-varying parameters in ordinary differential equations. Inverse Problems, 40 (3), 035004. [link] [pdf]

A. Arnold (2024) Virtual Sonia Kovalevsky Day mathematics outreach events for middle school girls. PRIMUS, 34 (5), 555-570. [link]

A. Arnold (2023) When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems. Inverse Problems, 39 (1), 014002. [link] [pdf]

^ Included in the "Emerging Talents 2021" Special Issue of Inverse Problems. 

A. Arnold, L. Fichera (2022) Identification of tissue optical properties during thermal laser-tissue interactions: an ensemble Kalman filter-based approach. International Journal for Numerical Methods in Biomedical Engineering, 38 (4), e3574. [link] [pdf]

L. Mitchell, A. Arnold (2021) Analyzing the effects of observation function selection in ensemble Kalman filtering for epidemic models. Mathematical Biosciences, 339, 108655. [link] [pdf]

S. Amato, A. Arnold (2021) Modeling microglia activation and inflammation-based neuroprotectant strategies during ischemic stroke. Bulletin of Mathematical Biology, 83, 72. [link] [pdf]

K. Campbell, L. Staugler, A. Arnold (2020) Estimating time-varying applied current in the Hodgkin-Huxley model. Applied Sciences, 10 (2), 550. [link] [pdf] 

A. Arnold, A. L. Lloyd (2018) An approach to periodic, time-varying parameter estimation using nonlinear filtering. Inverse Problems, 34 (10), 105005. [link] 

A. D. Marquis, A. Arnold, C. Dean-Bernhoft, B. E. Carlson, M. S. Olufsen (2018) Practical identifiability and uncertainty quantification of a pulsatile cardiovascular model. Mathematical Biosciences, 304, 9-24. [link] 

A. Arnold, C. Battista, D. Bia, Y. Zócalo German, R. L. Armentano, H. Tran, M. S. Olufsen (2017) Uncertainty quantification in a patient-specific one-dimensional arterial network model: EnKF-based inflow estimator. ASME Journal of Verification, Validation and Uncertainty Quantification, 2 (1), 011002. [link] 

A. Arnold, D. Calvetti, A. Gjedde, P. Iversen, E. Somersalo (2015) Astrocytic tracer dynamics estimated from [1-11C]-acetate PET measurements. Mathematical Medicine & Biology, 32 (4), 367-382. First published online November 24, 2014. [link]

A. Arnold, D. Calvetti, E. Somersalo (2014) Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter. Inverse Problems, 30 (10), 105008. [link] 

^ Included in the Inverse Problems 2014 Highlights collection. Papers are selected on the basis of referee endorsement, novelty and scientific impact. 

A. Arnold, D. Calvetti, E. Somersalo (2013) Linear multistep methods, particle filtering and sequential Monte Carlo. Inverse Problems, 29 (8), 085007. [link]

S. Amato, A. Arnold (2024) Sparse model identification and prediction of microglial cells during ischemic stroke. In: 8th International Conference on Computational and Mathematical Biomedical Engineering (P. Nithiarasu and R. Lohner eds) Arlington, VA, USA, pp. 322-325. [link] [pdf]

A. Arnold (2020) Using Monte Carlo particle methods to estimate and quantify uncertainty in periodic parameters. In: Advances in Mathematical Sciences: AWM Research Symposium, Houston, TX, April 2019 (B. Acu, D. Danielli, M. Lewicka, A. N. Pati, S. Ramanathapuram Vancheeswara, and M. I. Teboh-Equngkem eds) Springer, pp. 213-226. [link] [pdf]

A. Arnold, H. Tran (2020) An ensemble Kalman filtering approach for discrete-time inverse optimal control problems. In: Transactions on Engineering Technologies, IMECS 2018 (S. I. Ao, H. Kim, O. Castillo, A. Chan, H. Katagiri eds) Springer, Singapore, pp. 1-12. First published online October 11, 2019. [link]

A. Arnold (2019) Exploring the effects of uncertainty in parameter tracking estimates for the time-varying external voltage parameter in the FitzHugh-Nagumo model. In: 6th International Conference on Computational and Mathematical Biomedical Engineering (P. Nithiarasu, M. Ohta, and M. Oshima eds) Sendai, Japan, pp. 512-515. [link] [pdf]

A. Arnold, H. Tran (2018) Ensemble Kalman filtering for inverse optimal control. In: Proceedings of International MultiConference of Engineers and Computer Scientists 2018 Vol II, IMECS 2018, March 12-16, 2018, Hong Kong, pp. 526-530. [link] [pdf] 

^ Received “Best Paper Award of the 2018 IAENG International Conference on Control and Automation”. 

A. Arnold, D. Calvetti, E. Somersalo (2015) Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs. In: Dynamical Systems and Differential Equations, AIMS Proceedings 2015 (M. de León, W. Feng, Z. Feng, X. Lu, J. M. Martell, J. Parcet, D. Peralta-Salas and W. Ruan eds) Madrid, Spain, pp. 75-84. [link] 

C. Battista, A. Arnold, M. U. Qureshi, M. S. Olufsen (2015) Estimating boundary conditions for one-dimensional modeling of blood flow and pressure in arterial networks. In: 4th International Conference on Computational and Mathematical Biomedical Engineering (P. Nithiarasu and E. Budyn eds) Cachan, France, pp. 307-310. [link]

A. Arnold (2014) Sequential Monte Carlo parameter estimation for differential equations. Ph.D. Thesis, Case Western Reserve University, Cleveland, OH. [link]