@article{shao_canner_everett_bekele-maxwell_kuerbis_stephenson_menda_morgenstern_banks_2023, title={A Comparison of Mathematical and Statistical Modeling with Longitudinal Data: An Application to Ecological Momentary Assessment of Behavior Change in Individuals with Alcohol Use Disorder}, volume={85}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-022-01097-1}, abstractNote={Ecological momentary assessment (EMA) has been broadly used to collect real-time longitudinal data in behavioral research. Several analytic methods have been applied to EMA data to understand the changes of motivation, behavior, and emotions on a daily or within-day basis. One challenge when utilizing those methods on intensive datasets in the behavioral field is to understand when and why the methods are appropriate to investigate particular research questions. In this manuscript, we compared two widely used methods (generalized estimating equations and generalized linear mixed models) in behavioral research with three other less frequently used methods (Markov models, generalized linear mixed-effects Markov models, and differential equations) in behavioral research but widely used in other fields. The purpose of this manuscript is to illustrate the application of five distinct analytic methods to one dataset of intensive longitudinal data on drinking behavior, highlighting the utility of each method.}, number={1}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Shao, Sijing and Canner, Judith E. E. and Everett, Rebecca A. and Bekele-Maxwell, Kidist and Kuerbis, Alexis and Stephenson, Lyric and Menda, Jennifer and Morgenstern, Jon and Banks, H. T.}, year={2023}, month={Jan} }
 @article{wootton_curtsdotter_jonsson_banks_bommarco_roslin_laubmeier_2022, title={Beyond body size-new traits for new heights in trait-based modelling of predator-prey dynamics}, volume={17}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0251896}, abstractNote={Food webs map feeding interactions among species, providing a valuable tool for understanding and predicting community dynamics. Using species’ body sizes is a promising avenue for parameterizing food-web models, but such approaches have not yet been able to fully recover observed community dynamics. Such discrepancies suggest that traits other than body size also play important roles. For example, differences in species’ use of microhabitat or non-consumptive effects of intraguild predators may affect dynamics in ways not captured by body size. In Laubmeier et al. (2018), we developed a dynamic food-web model incorporating microhabitat and non-consumptive predator effects in addition to body size, and used simulations to suggest an optimal sampling design of a mesocosm experiment to test the model. Here, we perform the mesocosm experiment to generate empirical time-series of insect herbivore and predator abundance dynamics. We minimize least squares error between the model and time-series to determine parameter values of four alternative models, which differ in terms of including vs excluding microhabitat use and non-consumptive predator-predator effects. We use both statistical and expert-knowledge criteria to compare the models and find including both microhabitat use and non-consumptive predator-predator effects best explains observed aphid and predator population dynamics, followed by the model including microhabitat alone. This ranking suggests that microhabitat plays a larger role in driving population dynamics than non-consumptive predator-predator effects, although both are clearly important. Our results illustrate the importance of additional traits alongside body size in driving trophic interactions. They also point to the need to consider trophic interactions and population dynamics in a wider community context, where non-trophic impacts can dramatically modify the interplay between multiple predators and prey. Overall, we demonstrate the potential for utilizing traits beyond body size to improve trait-based models and the value of iterative cycling between theory, data and experiment to hone current insights into how traits affect food-web dynamics.}, number={7}, journal={PLOS ONE}, author={Wootton, Kate L. and Curtsdotter, Alva and Jonsson, Tomas and Banks, H. T. and Bommarco, Riccardo and Roslin, Tomas and Laubmeier, Amanda N.}, year={2022}, month={Jul} }
 @article{white_yousefian_banks_alexanderian_mueller_2021, title={Inferring pore radius and density from ultrasonic attenuation using physics-based modeling}, volume={149}, ISSN={["1520-8524"]}, DOI={10.1121/10.0003213}, abstractNote={This work proposes the use of two physics-based models for wave attenuation to infer the microstructure of cortical bone-like structures. One model for ultrasound attenuation in porous media is based on the independent scattering approximation (ISA) and the other model is based on the Waterman Truell (WT) approximation. The microstructural parameters of interest are pore radius and pore density. Attenuation data are simulated for three-dimensional structures mimicking cortical bone using the finite-difference time domain package SimSonic. These simulated structures have fixed sized pores (monodisperse), allowing fine-tuned control of the microstructural parameters. Structures with pore radii ranging from 50 to 100  μm and densities ranging from 20 to 50 pores/mm3 are generated in which only the attenuation due to scattering is considered. From here, an inverse problem is formulated and solved, calibrating the models to the simulated data and producing estimates of pore radius and density. The estimated microstructural parameters closely match the values used to simulate the data, validating the use of both the ISA and WT approximations to model ultrasonic wave attenuation in heterogeneous structures mimicking cortical bone. Furthermore, this illustrates the effectiveness of both models in inferring pore radius and density solely from ultrasonic attenuation data.}, number={1}, journal={JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA}, author={White, R. D. and Yousefian, O. and Banks, H. T. and Alexanderian, A. and Mueller, M.}, year={2021}, month={Jan}, pages={340–347} }
 @article{banks_banks_catenacci_joyner_stark_2020, title={Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data}, volume={17}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2020091}, abstractNote={We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts [1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.}, number={2}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Banks, John E. and Catenacci, Jared and Joyner, Michele and Stark, John}, year={2020}, pages={1743–1756} }
 @article{banks_banks_myers_laubmeier_bommarco_2020, title={Lethal and sublethal effects of toxicants on bumble bee populations: a modelling approach}, volume={29}, ISSN={["1573-3017"]}, DOI={10.1007/s10646-020-02162-y}, abstractNote={Abstract Pollinator decline worldwide is well-documented; globally, chemical pesticides (especially the class of pesticides known as neonicotinoids) have been implicated in hymenopteran decline, but the mechanics and drivers of population trends and dynamics of wild bees is poorly understood. Declines and shifts in community composition of bumble bees (Bombus spp .) have been documented in North America and Europe, with a suite of lethal and sub-lethal effects of pesticides on bumble bee populations documented. We employ a mathematical model parameterized with values taken from the literature that uses differential equations to track bumble bee populations through time in order to attain a better understanding of toxicant effects on a developing colony of bumble bees. We use a delay differential equation (DDE) model, which requires fewer parameter estimations than agent-based models while affording us the ability to explicitly describe the effect of larval incubation and colony history on population outcomes. We explore how both lethal and sublethal effects such as reduced foraging ability may combine to affect population outcomes, and discuss the implications for the protection and conservation of ecosystem services.}, number={3}, journal={ECOTOXICOLOGY}, author={Banks, J. E. and Banks, H. T. and Myers, N. and Laubmeier, A. N. and Bommarco, R.}, year={2020}, month={Apr}, pages={237–245} }
 @article{banks_laubmeier_banks_2020, title={Modelling the effects of field spatial scale and natural enemy colonization behaviour on pest suppression in diversified agroecosystems}, volume={22}, ISSN={["1461-9563"]}, DOI={10.1111/afe.12354}, abstractNote={Diversifying agroecosystems by establishing or retaining natural vegetation in and around crop areas has long been recognized as a potentially effective means of bolstering pest control as a result of attracting more numerous and diverse natural enemies, although outcomes are inconsistent across species. Little is known about the underlying mechanisms driving such differences in species responses, creating challenges for determining how best to manage landscapes for maximizing environmental services such as biological control. The present study addresses gaps in our understanding of the link between noncrop vegetation in field margins and pest suppression by using a system of partial differential equations to model population‐level predator–prey interactions, as well as spatial processes, aiming to capture the dynamics of crop plants, herbivores and two generalist predators. We focus on differences in how two predators (a carabid and a ladybird beetle) colonize crop fields where they forage for prey, examining differences in how they move into the fields from adjacent vegetation as a potential driver of differences in overall pest suppression. The results obtained demonstrate that predator colonization behaviour and spatial scale are important factors with respect to determining the effectiveness of biological control.}, number={1}, journal={AGRICULTURAL AND FOREST ENTOMOLOGY}, author={Banks, John E. and Laubmeier, Amanda N. and Banks, H. Thomas}, year={2020}, month={Feb}, pages={30–40} }
 @article{banks_joyner_2019, title={ADAPTION OF AKAIKE INFORMATION CRITERION UNDER LEAST SQUARES FRAMEWORKS FOR COMPARISON OF STOCHASTIC MODELS}, volume={77}, ISSN={["1552-4485"]}, DOI={10.1090/qam/1542}, abstractNote={In this paper, we examine the feasibility of extending the Akaike Information Criterion (AIC) for deterministic systems as a potential model selection criteria for stochastic models. We discuss the implementation method for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). The effectiveness and limitations of implementing the AIC for comparison of stochastic models is demonstrated using simulated data from the three types of models and then applied to experimental longitudinal growth data for algae.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Joyner, Michele L.}, year={2019}, month={Dec}, pages={831–859} }
 @article{noorman_allen_musante_banks_2019, title={Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments}, volume={16}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2019052}, abstractNote={Non-alcoholic fatty liver disease is the most common cause of chronic liver disease. Precipitated by the build up of extra fat in the liver not caused by alcohol, it is still not understood why steatosis occurs where it does in the liver microstructure in non-alcoholic fatty liver disease. It is likely, however, that the location of steatosis is due, at least in part, to metabolic zonation (heterogeneity among liver cells in function and enzyme expression). Recently, there has been an influx of computational and mathematical models in order to investigate the relationship between metabolic zonation and steatosis in non-alcoholic fatty liver disease. Of interest among these models are "compartments-in-series" models. Compartments-in-series models include the spatial distribution of metabolite concentrations via series of compartments that are connected through some representation of blood flow. In this paper, we analyze one such model, focusing specifically at how the number of compartments and inclusion of dispersion in the flow affect simulation results. We find the number of compartments to have a much larger effect than the inclusion of dispersion, however this is likely due to numerical artifacts. Overall, we conclude that considering partial differential equations that are equivalent to compartments-in-series models would be beneficial both in computation and in theoretical analyses.}, number={3}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Noorman, Marcella and Allen, Richard and Musante, Cynthia J. and Banks, H. Thomas}, year={2019}, pages={1082–1114} }
 @article{curtsdotter_banks_banks_jonsson_jonsson_laubmeier_traugott_bommarco_2019, title={Ecosystem function in predator-prey food webs-confronting dynamic models with empirical data}, volume={88}, ISSN={["1365-2656"]}, DOI={10.1111/1365-2656.12892}, abstractNote={Abstract}, number={2}, journal={JOURNAL OF ANIMAL ECOLOGY}, author={Curtsdotter, Alva and Banks, H. Thomas and Banks, John E. and Jonsson, Mattias and Jonsson, Tomas and Laubmeier, Amanda N. and Traugott, Michael and Bommarco, Riccardo}, year={2019}, month={Feb}, pages={196–210} }
 @article{schacht_meade_banks_enderling_abate-daga_2019, title={Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model}, volume={16}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2019365}, abstractNote={In this effort we explain fundamental formulations for aggregate data inverse problems requiring estimation of probability distribution parameters. We use as a motivating example a class of CAR T-call cancer models in mice. After ascertaining results on model stability and sensitivity with respect to parameters, we carry out first elementary computations on the question how much data is needed for successful estimation of probability distributions.}, number={6}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Schacht, Celia and Meade, Annabel and Banks, H. T. and Enderling, Heiko and Abate-Daga, Daniel}, year={2019}, pages={7299–7326} }
 @article{murad_tran_banks_everett_rosenberg_2019, title={IMMUNOSUPPRESSANT TREATMENT DYNAMICS IN RENAL TRANSPLANT RECIPIENTS: AN ITERATIVE MODELING APPROACH}, volume={24}, ISSN={["1553-524X"]}, DOI={10.3934/dcdsb.2018274}, abstractNote={Finding the optimal balance between over-suppression and under-suppression of the immune response is difficult to achieve in renal transplant patients, all of whom require lifelong immunosuppression. Our ultimate goal is to apply control theory to adaptively predict the optimal amount of immunosuppression; however, we first need to formulate a biologically realistic model. The process of quantitively modeling biological processes is iterative and often leads to new insights with every iteration. We illustrate this iterative process of modeling for renal transplant recipients infected by BK virus. We analyze and improve on the current mathematical model by modifying it to be more biologically realistic and amenable for designing an adaptive treatment strategy.}, number={6}, journal={DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B}, author={Murad, Neha and Tran, H. T. and Banks, H. T. and Everett, R. A. and Rosenberg, Eric S.}, year={2019}, month={Jun}, pages={2781–2797} }
 @article{banks_bekele-maxwell_bociu_noorman_guidiboni_2019, title={LOCAL SENSITIVITY VIA THE COMPLEX-STEP DERIVATIVE APPROXIMATION FOR 1D PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS}, volume={9}, ISSN={["2156-8499"]}, DOI={10.3934/mcrf.2019044}, abstractNote={Poro-elastic systems have been used extensively in modeling fluid flow in porous media in petroleum and earthquake engineering. Nowadays, they are frequently used to model fluid flow through biological tissues, cartilages, and bones. In these biological applications, the fluid-solid mixture problems, which may also incorporate structural viscosity, are considered on bounded domains with appropriate non-homogeneous boundary conditions. The recent work in [ 12 ] provided a theoretical and numerical analysis of nonlinear poro-elastic and poro-viscoelastic models on bounded domains with mixed boundary conditions, focusing on the role of visco-elasticity in the material. Their results show that higher time regularity of the sources is needed to guarantee bounded solution when visco-elasticity is not present. Inspired by their results, we have recently performed local sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the boundary source of traction associated with the elastic structure [ 3 ]. Our results show that the solution is more sensitive to boundary datum in the purely elastic case than when visco-elasticity is present in the solid matrix. In this article, we further extend this work in order to include local sensitivities of the solution of the coupled system to the boundary conditions imposed on the Darcy velocity. Sensitivity analysis is the first step in identifying important parameters to control or use as control terms in these poro-elastic and poro-visco-elastic models, which is our ultimate goal.}, number={4}, journal={MATHEMATICAL CONTROL AND RELATED FIELDS}, author={Banks, H. Thomas and Bekele-Maxwell, Kidist and Bociu, Lorena and Noorman, Marcelle and Guidiboni, Giovanna}, year={2019}, month={Dec}, pages={623–642} }
 @article{rahman_bekele-maxwell_cates_banks_vaidya_2019, title={Modeling Zika Virus Transmission Dynamics: Parameter Estimates, Disease Characteristics, and Prevention}, volume={9}, ISSN={["2045-2322"]}, DOI={10.1038/s41598-019-46218-4}, abstractNote={Abstract}, journal={SCIENTIFIC REPORTS}, author={Rahman, Munsur and Bekele-Maxwell, Kidist and Cates, LeAnna L. and Banks, H. T. and Vaidya, Naveen K.}, year={2019}, month={Jul} }
 @article{banks_banks_cody_hoddle_meade_2019, title={Population model for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) over a ten-year period}, volume={13}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2019.1616839}, abstractNote={ABSTRACT The glassy-winged sharpshooter, Homalodisca vitripennis (Germar), is an invasive pest which presents a major economic threat to grape industries in California, because it spreads a disease-causing bacterium, Xylella fastidiosa. In this note we develop a time and temperature dependent mathematical model to analyze aggregate population data for H. vitripennis from a 10-year study consisting of biweekly monitoring of H. vitripennis populations on unsprayed citrus, during which H. vitripennis decreased significantly. This model was fitted to the aggregate H. vitripennis time series data using iterative reweighted weighted least squares (IRWLS) with assumed probability distributions for certain parameter values. Results indicate that the H. vitripennis model fits the phenological and temperature data reasonably well, but the observed population decrease may possibly be attributed to factors other than the abiotic effect of temperature. A key factor responsible for this decline but not analyzed here could be biotic, for example, potentially parasitism of H. vitripennis eggs by Cosmocomoidea ashmeadi. A biological control program targeting H. vitripennis utilizing the mymarid egg parasitoid Cosmocomoidea (formerly Gonatocerus) ashmeadi (Girault) is described.}, number={1}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Banks, John E. and Cody, Natalie G. and Hoddle, Mark S. and Meade, Annabel E.}, year={2019}, month={Jan}, pages={422–446} }
 @article{bokil_banks_cioranescu_griso_2018, title={A MULTISCALE METHOD FOR COMPUTING EFFECTIVE PARAMETERS OF COMPOSITE ELECTROMAGNETIC MATERIALS WITH MEMORY EFFECTS}, volume={76}, ISSN={["1552-4485"]}, DOI={10.1090/qam/1503}, abstractNote={We consider the problem of computing (macroscopic) effective properties of composite materials that are mixtures of complex dispersive dielectrics described by polarization and magnetization laws. We assume that the micro-structure of the composite material is described by spatially periodic and deterministic parameters. Mathematically, the problem is to homogenize Maxwell’s equations along with constitutive laws that describe the material response of the micro-structure comprising the mixture, to obtain an equivalent effective model for the composite material with constant effective parameters. The novel contribution of this paper is the homogenization of a hybrid model consisting of the Maxwell partial differential equations along with ordinary (auxiliary) differential equations modeling the evolution of the polarization and magnetization, as a model for the complex dielectric material. This is in contrast to our previous work (2006) in which we employed a convolution in time of a susceptibility kernel with the electric field to model the delayed polarization effects in the dispersive material. In this paper, we describe the auxiliary differential equation approach to modeling material responses in the composite material and use the periodic unfolding method to construct a homogenized model.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Bokil, V. A. and Banks, H. T. and Cioranescu, D. and Griso, G.}, year={2018}, month={Dec}, pages={713–738} }
 @article{banks_kabanikhin_krivorotko_yermolenko_2018, title={A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level}, volume={26}, ISSN={["1569-3945"]}, DOI={10.1515/jiip-2018-0019}, abstractNote={Abstract}, number={6}, journal={JOURNAL OF INVERSE AND ILL-POSED PROBLEMS}, author={Banks, H. Thomas and Kabanikhin, Sergey I and Krivorotko, Olga I and Yermolenko, Darya V}, year={2018}, month={Dec}, pages={859–873} }
 @article{rutter_banks_flores_2018, title={Estimating intratumoral heterogeneity from spatiotemporal data}, volume={77}, ISSN={["1432-1416"]}, DOI={10.1007/s00285-018-1238-6}, abstractNote={Glioblastoma multiforme (GBM) is a malignant brain cancer with a tendency to both migrate and proliferate. We propose modeling GBM with heterogeneity in cell phenotypes using a random differential equation version of the reaction-diffusion equation, where the parameters describing diffusion (D) and proliferation ([Formula: see text]) are random variables. We investigate the ability to perform the inverse problem to recover the probability distributions of D and [Formula: see text] using the Prohorov metric, for a variety of probability distribution functions. We test the ability to perform the inverse problem for noisy synthetic data. We then examine the predicted effect of treatment, specifically, chemotherapy, when assuming such a heterogeneous population and compare with predictions from a homogeneous cell population model.}, number={6-7}, journal={JOURNAL OF MATHEMATICAL BIOLOGY}, author={Rutter, E. M. and Banks, H. T. and Flores, K. B.}, year={2018}, month={Dec}, pages={1999–2022} }
 @article{laubmeier_wootton_banks_bommarco_curtsdotter_jonsson_roslin_banks_2018, title={From theory to experimental design-Quantifying a trait-based theory of predator-prey dynamics}, volume={13}, number={4}, journal={PLoS One}, author={Laubmeier, A. N. and Wootton, K. and Banks, J. E. and Bommarco, R. and Curtsdotter, A. and Jonsson, T. and Roslin, T. and Banks, H. T.}, year={2018} }
 @misc{rieger_allen_bystricky_chen_colopy_cui_gonzalez_liu_white_everett_et al._2018, title={Improving the generation and selection of virtual populations in quantitative systems pharmacology models}, volume={139}, ISSN={["0079-6107"]}, DOI={10.1016/j.pbiomolbio.2018.06.002}, abstractNote={Quantitative systems pharmacology (QSP) models aim to describe mechanistically the pathophysiology of disease and predict the effects of therapies on that disease. For most drug development applications, it is important to predict not only the mean response to an intervention but also the distribution of responses, due to inter-patient variability. Given the necessary complexity of QSP models, and the sparsity of relevant human data, the parameters of QSP models are often not well determined. One approach to overcome these limitations is to develop alternative virtual patients (VPs) and virtual populations (Vpops), which allow for the exploration of parametric uncertainty and reproduce inter-patient variability in response to perturbation. Here we evaluated approaches to improve the efficiency of generating Vpops. We aimed to generate Vpops without sacrificing diversity of the VPs' pathophysiologies and phenotypes. To do this, we built upon a previously published approach (Allen et al., 2016) by (a) incorporating alternative optimization algorithms (genetic algorithm and Metropolis-Hastings) or alternatively (b) augmenting the optimized objective function. Each method improved the baseline algorithm by requiring significantly fewer plausible patients (precursors to VPs) to create a reasonable Vpop.}, journal={PROGRESS IN BIOPHYSICS & MOLECULAR BIOLOGY}, author={Rieger, Theodore R. and Allen, Richard J. and Bystricky, Lukas and Chen, Yuzhou and Colopy, Glen Wright and Cui, Yifan and Gonzalez, Angelica and Liu, Yifei and White, R. D. and Everett, R. A. and et al.}, year={2018}, month={Nov}, pages={15–22} }
 @misc{banks_joyner_2018, title={Information content in data sets: A review of methods for interrogation and model comparison}, volume={26}, ISSN={["1569-3945"]}, DOI={10.1515/jiip-2017-0096}, abstractNote={Abstract}, number={3}, journal={JOURNAL OF INVERSE AND ILL-POSED PROBLEMS}, author={Banks, H. Thomas and Joyner, Michele L.}, year={2018}, month={Jun}, pages={423–452} }
 @article{banks_everett_murad_white_banks_cass_rosenheim_2018, title={OPTIMAL DESIGN FOR DYNAMICAL MODELING OF PEST POPULATIONS}, volume={15}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2018044}, abstractNote={We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Everett, R. A. and Murad, Neha and White, R. D. and Banks, J. E. and Cass, Bodil N. and Rosenheim, Jay A.}, year={2018}, month={Aug}, pages={993–1010} }
 @article{murad_tran_banks_2018, title={Optimal control of immunosuppressants in renal transplant recipients susceptible to BKV infection}, volume={40}, ISSN={0143-2087}, url={http://dx.doi.org/10.1002/oca.2478}, DOI={10.1002/oca.2478}, abstractNote={Summary}, number={2}, journal={Optimal Control Applications and Methods}, publisher={Wiley}, author={Murad, Neha and Tran, H.T. and Banks, H.T.}, year={2018}, month={Nov}, pages={292–309} }
 @article{banks_thompson_2018, title={RANDOM DELAY DIFFERENTIAL EQUATIONS AND INVERSE PROBLEMS FOR AGGREGATE DATA PROBLEMS}, volume={6}, ISSN={["2308-9822"]}, DOI={10.32523/2306-6172-2018-6-4-4-16}, abstractNote={We consider nonparametric estimation of probability measures for parameters in delay differential equation (DDE) problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [11, 17, 21, 26, 28]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random DDEs.}, number={4}, journal={EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS}, author={Banks, H. T. and Thompson, W. C.}, year={2018}, pages={4–16} }
 @article{yousefian_white_karbalaeisadegh_banks_muller_2018, title={The effect of pore size and density on ultrasonic attenuation in porous structures with mono-disperse random pore distribution: A two-dimensional in-silico study}, volume={144}, ISSN={["1520-8524"]}, DOI={10.1121/1.5049782}, abstractNote={This work proposes a power law model to describe the attenuation of ultrasonic waves in non-absorbing heterogeneous media with randomly distributed scatterers, mimicking a simplified structure of cortical bone. This paper models the propagation in heterogeneous structures with controlled porosity using a two-dimensional finite-difference time domain numerical simulation in order to measure the frequency dependent attenuation. The paper then fits a phenomenological model to the simulated frequency dependent attenuation by optimizing parameters under an ordinary least squares framework. Local sensitivity analysis is then performed on the resulting parameter estimates in order to determine to which estimates the model is most sensitive. This paper finds that the sensitivity of the model to various parameter estimates depends on the micro-architectural parameters, pore diameter (ϕ) and pore density (ρ). In order to get a sense for how confidently model parameters are able to be estimated, 95% confidence intervals for these estimates are calculated. In doing so, the ability to estimate model-sensitive parameters with a high degree of confidence is established. In the future, being able to accurately estimate model parameters from which micro-architectural ones could be inferred will allow pore density and diameter to be estimated via an inverse problem given real or simulated ultrasonic data to be determined.}, number={2}, journal={JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA}, author={Yousefian, Omid and White, R. D. and Karbalaeisadegh, Yasamin and Banks, H. T. and Muller, Marie}, year={2018}, month={Aug}, pages={709–719} }
 @article{banks_hu_rosenberg_2017, title={A dynamical modeling approach for analysis of longitudinal clinical trials in the presence of missing endpoints}, volume={63}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2016.07.002}, abstractNote={Randomized longitudinal clinical trials are the gold standard to evaluate the effectiveness of interventions among different patient treatment groups. However, analysis of such clinical trials becomes difficult in the presence of missing data, especially in the case where the study endpoints become difficult to measure because of subject dropout rates or/and the time to discontinue the assigned interventions are different among the patient groups. Here we report on using a validated mathematical model combined with an inverse problem approach to predict the values for the missing endpoints. A small randomized HIV clinical trial where endpoints for most of patients are missing is used to demonstrate this approach.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Hu, Shuhua and Rosenberg, Eric}, year={2017}, month={Jan}, pages={109–117} }
 @article{banks_doumic_kruse_2017, title={A numerical scheme for the early steps of nucleation-aggregation models}, volume={74}, ISSN={["1432-1416"]}, DOI={10.1007/s00285-016-1026-0}, abstractNote={In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nuclei. After this early step, the polymers are involved in a number of reactions such as polymerization, fragmentation and coalescence. Since there may be several orders of magnitude between the size of a particle and the size of an aggregate, building efficient numerical schemes to capture accurately the kinetics of the reaction is a delicate step of key importance. In this article, we propose a conservative scheme, based on finite volume methods on an adaptive grid, which is capable of simulating well the early steps of the reaction as well as the later chain reactions.}, number={1-2}, journal={JOURNAL OF MATHEMATICAL BIOLOGY}, author={Banks, Harvey Thomas and Doumic, Marie and Kruse, Carola}, year={2017}, month={Jan}, pages={259–287} }
 @article{banks_joyner_2017, title={AIC under the framework of least squares estimation}, volume={74}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2017.05.005}, abstractNote={In this note we explain the use of the Akiake Information Criterion and its related model comparison indices (usually derived for maximum likelihood estimator inverse problem formulations) in the context of least squares (ordinary, weighted, iterative weighted or “generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in biology.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Joyner, Michele L.}, year={2017}, month={Dec}, pages={33–45} }
 @article{rutter_banks_leblanc_flores_2017, title={Continuous Structured Population Models for Daphnia magna}, volume={79}, ISSN={0092-8240 1522-9602}, url={http://dx.doi.org/10.1007/S11538-017-0344-8}, DOI={10.1007/S11538-017-0344-8}, abstractNote={We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters. We present our confidence intervals on parameter estimates.}, number={11}, journal={Bulletin of Mathematical Biology}, publisher={Springer Science and Business Media LLC}, author={Rutter, Erica M. and Banks, H. T. and LeBlanc, Gerald A. and Flores, Kevin B.}, year={2017}, month={Sep}, pages={2627–2648} }
 @article{banks_bekele-maxwell_everett_stephenson_shao_morgenstern_2017, title={Dynamic Modeling of Problem Drinkers Undergoing Behavioral Treatment}, volume={79}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-017-0282-5}, abstractNote={We use dynamical systems modeling to help understand how selected intra-personal factors interact to form mechanisms of behavior change in problem drinkers. Our modeling effort illustrates the iterative process of modeling using an individual's clinical data. Due to the lack of previous work in modeling behavior change in individual patients, we build our preliminary model relying on our understandings of the psychological relationships among the variables. This model is refined and the psychological understanding is then enhanced through the iterative modeling process. Our results suggest that this is a promising direction in research in alcohol use disorders as well as other behavioral sciences.}, number={6}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Banks, H. T. and Bekele-Maxwell, Kidist and Everett, R. A. and Stephenson, Lyric and Shao, Sijing and Morgenstern, Jon}, year={2017}, month={Jun}, pages={1254–1273} }
 @article{banks_flores_langlois_serio_sindi_2017, title={Estimating the rate of prion aggregate amplification in yeast with a generation and structured population model}, volume={26}, ISSN={1741-5977 1741-5985}, url={http://dx.doi.org/10.1080/17415977.2017.1316498}, DOI={10.1080/17415977.2017.1316498}, abstractNote={Abstract Prions are a special class of proteins capable of adopting multiple (misfolded) conformations, some of which have been associated with fatal diseases in mammals such as bovine spongiform encephalopathy or Creutzfeldt–Jakob Disease. Prion diseases, like protein misfolding diseases in general, are caused by the formation and amplification of ordered aggregates of proteins called amyloids. While such diseases in mammals can take decades to form, yeast have a variety of prion phenotypes that occur over a few hours, making this system an ideal model for protein misfolding disease in general. Most experimental assays of colonies with yeast prions provide steady-state population observations which complicate the inference of biochemical parameters both by the inability to directly measure aggregate amplification and by obscuring heterogeneity between cells. We develop a mathematical and inverse problem formulation to determine the amplification rate with prion aggregates from single-cell measurements observed in propagon amplification experiments. We demonstrate the ability of our formulation to determine heterogeneous amplification rates on simulated and experimental data. Our results show that aggregate amplification rates for two prion variants are strongly bimodal, suggesting that the generational structure in the yeast population impacts the ability of prion aggregates to amplify.}, number={2}, journal={Inverse Problems in Science and Engineering}, publisher={Informa UK Limited}, author={Banks, H. T. and Flores, Kevin B. and Langlois, Christine R. and Serio, Tricia R. and Sindi, Suzanne S.}, year={2017}, month={Apr}, pages={257–279} }
 @article{banks_burns_2017, title={Inverse problems and techniques with applications in the biological sciences}, volume={26}, ISSN={1741-5977 1741-5985}, url={http://dx.doi.org/10.1080/17415977.2017.1318490}, DOI={10.1080/17415977.2017.1318490}, abstractNote={Each contribution to this special issue of Inverse Problems in Science and Engineering (IPSE) discusses some particular aspects of inverse problems and parameter estimation, from topics including mathematical model vs. statistical model misspecification, model discrepancy, uncertainty quantification in estimated parameters, to model identification vs. calibration, with applications to a wide variety of biological problems. These include dynamics of phytoplankton aggregates and their interaction with the environment in a well-mixed reactor or surface layer of a water column, population models with the Allee Effect, metabolic heat generation rate which quantifies either the presence or the absence of tumour as well as the degree of inflammations in the biological tissue, special classes of proteins capable of adopting multiple (misfolded) conformations (prions) which have been associated with fatal diseases (e.g. encephalopathy, Creutzfeldt-Jakob disease, etc.) caused by the formation and amplification of ordered aggregates of proteins called amyloids, uncertainty in clinical data from kidney transplant recipients infected with BK virus, uncertainty in mathematical epidemiology modelling (in data, as well as in parameters) illustrated with data from an ongoing community-acquired Methicillin-resistant Staphylococcus aureus epidemic in Chicago, and Bayesian model construction of densities for input parameters in a dynamic HIV infection and propagation model. Consistent with the IPSE journal’s procedures, all contributions were carefully evaluated by at least three (anonymous to the authors) reviewers, and subsequently accepted after suggested revisions. For these significant contributions of these reviewers to this special issue of IPSE, the organising editors are most grateful.}, number={2}, journal={Inverse Problems in Science and Engineering}, publisher={Informa UK Limited}, author={Banks, H. T. and Burns, J. A.}, year={2017}, month={Nov}, pages={151–151} }
 @article{banks_everett_hu_murad_tran_2017, place={Banks, R.A}, title={Mathematical and statistical model misspecifications in modelling immune response in renal transplant recipients}, volume={26}, ISSN={1741-5977 1741-5985}, url={http://dx.doi.org/10.1080/17415977.2017.1312363}, DOI={10.1080/17415977.2017.1312363}, abstractNote={We examine uncertainty in clinical data from a kidney transplant recipient infected with BK virus and investigate mathematical model and statistical model misspecifications in the context of least squares methodology. A difference-based method is directly applied to data to determine the correct statistical model that represents the uncertainty in data. We then carry out an inverse problem with the corresponding iterative weighted least squares technique and use the resulting modified residual plots to detect mathematical model discrepancy. This process is implemented using both clinical and simulated data. Our results demonstrate mathematical model misspecification when both simpler and more complex models are assumed compared to data dynamics.}, number={2}, journal={Inverse Problems in Science and Engineering}, publisher={Informa UK Limited}, author={Banks, H. T. and Everett, R. A. and Hu, Shuhua and Murad, Neha and Tran, H. T.}, year={2017}, month={Apr}, pages={203–222} }
 @article{banks_banks_bommarco_laubmeier_myers_rundlof_tillman_2017, title={Modeling bumble bee population dynamics with delay differential equations}, volume={351}, ISSN={["1872-7026"]}, DOI={10.1016/j.ecolmodel.2017.02.011}, abstractNote={Bumble bees are ubiquitous creatures and crucial pollinators to a vast assortment of crops worldwide. Bumble bee populations have been decreasing in recent decades, with demise of flower resources and pesticide exposure being two of several suggested pressures causing declines. Many empirical investigations have been performed on bumble bees and their natural history is well documented, but the understanding of their population dynamics over time, causes for observed declines, and potential benefits of management actions is poor. To provide a tool for projecting and testing sensitivity of growth of populations under contrasting and combined pressures, we propose a delay differential equation model that describes multi-colony bumble bee population dynamics. We explain the usefulness of delay equations as a natural modeling formulation, particularly for bumble bee modeling. We then introduce a particular numerical method that approximates the solution of the delay model. Next, we provide simulations of seasonal population dynamics in the absence of pressures. We conclude by describing ways in which resource limitation, pesticide exposure and other pressures can be reflected in the model.}, journal={ECOLOGICAL MODELLING}, author={Banks, H. T. and Banks, J. E. and Bommarco, Riccardo and Laubmeier, A. N. and Myers, N. J. and Rundlof, Maj and Tillman, Kristen}, year={2017}, month={May}, pages={14–23} }
 @article{banks_banks_rosenheim_tillman_2017, title={Modelling populations of Lygus hesperus on cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice}, volume={11}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2016.1143533}, abstractNote={ABSTRACT Understanding the population dynamics of herbivorous insects is critical to developing and implementing effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we explore the topic of model selection for an appropriate mathematical model and corresponding statistical models, and use techniques including ANOVA-based model comparison tests and residual plot analysis to make the best selections. In addition we explore the topic of data information content: in this example, we are testing the question of whether data, as it is currently collected, can support time-dependent parameter estimation. Furthermore, we investigate the statistical assumptions often haphazardly made in the process of parameter estimation and consider the implications of unfounded assumptions.}, number={1}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Banks, J. E. and Rosenheim, Jay and Tillman, Kristen}, year={2017}, month={Mar}, pages={25–39} }
 @article{banks_bekele-maxwell_bociu_noorman_guidoboni_2017, title={SENSITIVITY ANALYSIS IN PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS WITH RESPECT TO BOUNDARY DATA}, volume={75}, ISSN={["1552-4485"]}, DOI={10.1090/qam/1475}, abstractNote={In this article we consider poro-elastic and poro-visco-elastic models inspired by problems in medicine and biology, and we perform sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the imposed boundary data, which are the main drivers of the system. Moreover, we compare the results obtained in the elastic case vs. visco-elastic case, as it is known that structural viscosity of biological tissues decreases with age and disease. Sensitivity analysis is the first step towards optimization and control problems associated with these models, which is our ultimate goal.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Bekele-Maxwell, K. and Bociu, L. and Noorman, M. and Guidoboni, G.}, year={2017}, month={Dec}, pages={697–735} }
 @article{banks_bekele-maxwell_bociu_wang_2017, title={SENSITIVITY VIA THE COMPLEX-STEP METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH NON-SMOOTH INITIAL DATA}, volume={75}, ISSN={["1552-4485"]}, DOI={10.1090/qam/1458}, abstractNote={In this report, we use the complex-step derivative approximation technique to compute sensitivities for delay differential equations (DDEs) with non-smooth (discontinuous and even distributional) history functions. We compare the results with exact derivatives and with those computed using the classical sensitivity equations whenever possible. Our results demonstrate that the implementation of the complex-step method using the method of steps and the Matlab solver dde23 provides a very good approximation of sensitivities as long as discontinuities in the initial data do not cause loss of smoothness in the solution: that is, even when the underlying smoothness with respect to the initial data for the Cauchy-Riemann derivation of the method does not hold. We conclude with remarks on our findings regarding the complex-step method for computing sensitivities for simpler ordinary differential equation systems in the event of lack of smoothness with respect to parameters.}, number={2}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Bekele-Maxwell, Kidist and Bociu, Lorena and Wang, Chuyue}, year={2017}, month={Jun}, pages={231–248} }
 @article{banks_collins_flores_pershad_stemkovski_stephenson_2017, title={Statistical error model comparison for logistic growth of green algae (Raphidocelis subcapitata)}, volume={64}, ISSN={0893-9659}, url={http://dx.doi.org/10.1016/J.AML.2016.09.006}, DOI={10.1016/j.aml.2016.09.006}, abstractNote={We validate a model for the population dynamics, as they occur in a chemostat environment, of the green algae Raphidocelis subcapitata, a species that is often used as a primary food source in toxicity experiments for the fresh water crustacean Daphnia magna. We collected longitudinal data from 4 replicate population experiments with R. subcapitata. This data was fit to a logistic growth model to reveal patterns of the algae growth in a continuous culture. Overall, our results suggest that a proportional error statistical model is the most appropriate for logistic growth modeling of R. subcapitata continuous population growth.}, journal={Applied Mathematics Letters}, publisher={Elsevier BV}, author={Banks, H.T. and Collins, Elizabeth and Flores, Kevin and Pershad, Prayag and Stemkovski, Michael and Stephenson, Lyric}, year={2017}, month={Feb}, pages={213–222} }
 @article{banks_banks_everett_stark_2016, title={AN ADAPTIVE FEEDBACK METHODOLOGY FOR DETERMINING INFORMATION CONTENT IN STABLE POPULATION STUDIES}, volume={13}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2016013}, abstractNote={We develop statistical and mathematical based methodologies for determining (as the experiment progresses) the amount of information required to complete the estimation of stable population parameters with pre-specified levels of confidence. We do this in the context of life table models and data for growth/death for three species of Daphniids as investigated by J. Stark and J. Banks [17]. The ideas developed here also have wide application in the health and social sciences where experimental data are often expensive as well as difficult to obtain.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Banks, John E. and Everett, R. A. and Stark, John D.}, year={2016}, month={Aug}, pages={653–671} }
 @article{banks_catenacci_2016, title={Aggregate data and the Prohorov Metric Framework: Efficient gradient computation}, volume={56}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2015.12.004}, abstractNote={We discuss efficient methods for computing gradients in inverse problems for estimation of distributions for individual parameters in models where only aggregate or population level data is available. The ideas are illustrated with two examples arising in applications.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Catenacci, Jared}, year={2016}, month={Jun}, pages={1–9} }
 @article{andreev_banks_dulikravich_hofmann_kabanikhin_kuchuk_lesnic_nashed_neubauer_romanov_et al._2016, title={In celebration of the 60th birthday of Professor Alemdar Hasanoglu (Hasanov)}, volume={24}, number={2}, journal={Journal of Inverse and Ill-Posed Problems}, author={Andreev, V. B. and Banks, H. T. and Dulikravich, G. S. and Hofmann, B. and Kabanikhin, S. I. and Kuchuk, F. J. and Lesnic, D. and Nashed, M. Z. and Neubauer, A. and Romanov, V. G. and et al.}, year={2016}, pages={109–110} }
 @inbook{banks_banks_murad_rosenheim_tillman_2016, title={Modelling Pesticide Treatment Effects on Lygus hesperus in Cotton Fields}, ISBN={9783319557946 9783319557953}, ISSN={1868-4238 1868-422X}, url={http://dx.doi.org/10.1007/978-3-319-55795-3_8}, DOI={10.1007/978-3-319-55795-3_8}, abstractNote={We continue our efforts on modeling of the population dynamics of herbivorous insects in order to develop and implement effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we consider model selection for an appropriate mathematical model and corresponding statistical models, and use techniques to compare models. We address the question of whether data, as it is currently collected, can support time-dependent (as opposed to constant) parameter estimates.}, booktitle={IFIP Advances in Information and Communication Technology}, publisher={Springer International Publishing}, author={Banks, H. T. and Banks, J. E. and Murad, Neha and Rosenheim, J. A. and Tillman, K.}, year={2016}, pages={95–106} }
 @article{banks_hu_link_rosenberg_mitsuma_rosario_2016, title={Modelling immune response to BK virus infection and donor kidney in renal transplant recipients}, volume={24}, ISSN={["1741-5985"]}, DOI={10.1080/17415977.2015.1017484}, abstractNote={In this paper, we develop and validate with bootstrapping techniques a mechanistic mathematical model of immune response to both BK virus infection and a donor kidney based on known and hypothesized mechanisms in the literature. The model presented does not capture all the details of the immune response but possesses key features that describe a very complex immunological process. We then estimate model parameters using a least squares approach with a typical set of available clinical data. Sensitivity analysis combined with asymptotic theory is used to determine the number of parameters that can be reliably estimated given the limited number of observations.}, number={1}, journal={INVERSE PROBLEMS IN SCIENCE AND ENGINEERING}, author={Banks, H. T. and Hu, Shuhua and Link, Kathryn and Rosenberg, Eric S. and Mitsuma, Sheila and Rosario, Lauren}, year={2016}, month={Jan}, pages={127–152} }
 @article{banks_flores_sindi_2016, title={On analytical and numerical approaches to division and label structured population models}, volume={60}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2016.04.009}, abstractNote={Even among cells in the same population, the concentration of a protein or cellular constituent can vary considerably. This heterogeneity can arise from several sources, including differences in kinetic rates between cells and distribution of cellular constituents through cell division. Compartmental models have been used to describe the distribution of the number of divisions undergone by cells in a population. More recently, such models have been coupled with the dynamics of intracellular labels and analytical solutions to the division and label structured population equations have been found. However, such approaches have thus far focused on simple models of intracellular dynamics such as the decay of an intracellular label. In this work, we demonstrate that analytical solutions are possible for more general forms of intracellular dynamics offering the promise to lend mathematical insight into population dynamics in more realistic biological settings.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Flores, Kevin B. and Sindi, Suzanne S.}, year={2016}, month={Oct}, pages={81–88} }
 @article{banks_baraldi_catenacci_myers_2016, title={Parameter Estimation Using Unidentified Individual Data in Individual Based Models}, volume={11}, ISSN={["1760-6101"]}, DOI={10.1051/mmnp/201611602}, abstractNote={In physiological experiments, it is common for measurements to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (referred to as unidentified individual data in this work but often referred to as aggregate population data [5, Chapter 5]). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. This assumption leads to an overconfidence in model parameter values and model based predictions. We propose a novel method which accounts for inter-individual variability in experiments where only unidentified individual data is available. Both parametric and nonparametric methods for estimating the distribution of parameters which vary among individuals are developed. These methods are illustrated using both simulated data, and data taken from a physiological experiment. Taking the approach outlined in this paper results in more accurate quantification of the uncertainty attributed to inter-individual variability.}, number={6}, journal={MATHEMATICAL MODELLING OF NATURAL PHENOMENA}, author={Banks, H. T. and Baraldi, R. and Catenacci, J. and Myers, N.}, year={2016}, pages={9–27} }
 @article{wentworth_smith_banks_2016, title={Parameter Selection and Verification Techniques Based on Global Sens Analysis Illustrated for an HIV Model}, volume={4}, ISSN={["2166-2525"]}, DOI={10.1137/15m1008245}, abstractNote={We consider parameter selection and verification techniques for models having one or more parameters that are noninfluential in the sense that they minimally impact model outputs. We illustrate these techniques for a dynamic HIV model but note that the parameter selection and verification framework is applicable to a wide range of biological and physical models. To accommodate the nonlinear input to output relations, which are typical for such models, we focus on global sensitivity analysis techniques, including those based on the Pearson correlation coefficient, Sobol indices based on second-order model representations, and Morris indices, as well as a parameter selection technique based on standard errors. A significant objective is to provide verification strategies to assess the accuracy of those techniques, which we illustrate in the context of the HIV model.}, number={1}, journal={SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION}, author={Wentworth, Mami T. and Smith, Ralph C. and Banks, H. T.}, year={2016}, pages={266–297} }
 @article{banks_catenacci_criner_2016, title={Quantifying the degradation in thermally treated ceramic matrix composites}, volume={52}, ISSN={["1875-8800"]}, DOI={10.3233/jae-162168}, abstractNote={Reflectance spectroscopy obtained from a thermally treated silicon nitride carbon based ceramic matrix composite is used to quantity the oxidation products SiO2 and SiN. The data collection is described in detail in order to point out the potential biasing present in the data processing. A probability distribution is imposed on select model parameters, and then non-parametrically estimated. A non-parametric estimation is chosen since the exact composition of the material is unknown due to the inherent heterogeneity of ceramic composites. The probability distribution is estimated using the Prohorov metric framework in which the infinite dimensional optimization is reduced to a finite dimensional optimization using an approximating space composed of linear splines. A weighted least squares estimation is carried out, and uncertainty quantification is performed on the model parameters, including a piecewise asymptotic confidence band for the estimated probability density. Our estimation results indicate a distinguishable increase in the SiO2 present in the samples which were heat treated for 100 hours compared to 10 hours.}, number={1-2}, journal={INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS}, author={Banks, H. T. and Catenacci, Jared and Criner, Amanda}, year={2016}, pages={3–24} }
 @article{kojima_banks_2016, title={Statistical parameter estimation of dielectric materials using MCMC for nonlinear hierarchical models}, volume={52}, ISSN={["1875-8800"]}, DOI={10.3233/jae-162207}, abstractNote={This paper is concerned with material interrogation methods for homogeneous dielectric materials using statistical inversion. Frequency dispersions for homogeneous dielectric materials can be described by a classical Lorentz model. Taking into account that the reflection coefficients are indirectly measurable, the signal response model is given by a complex reflectance at the interface between free space and the dielectric medium. The problem considered here is to quantify uncertainties of the estimated dielectric parameters from the measurements obtained by a reflective interferometer. A computational method using Hamiltonian Monte Carlo sampling based on nonlinear hierarchical models is tested.}, number={1-2}, journal={INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS}, author={Kojima, Fumio and Banks, H. Thomas}, year={2016}, pages={49–54} }
 @article{banks_catenacci_hu_2016, title={Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems}, volume={24}, number={4}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Catenacci, J. and Hu, S. H.}, year={2016}, pages={413–433} }
 @article{stemkovski_baraldi_flores_banks_2016, title={Validation of a mathematical model for green algae (Raphidocelis Subcapitata) growth and implications for a coupled dynamical system with Daphnia magna}, volume={6}, number={5}, journal={Applied Sciences-Basel}, author={Stemkovski, M. and Baraldi, R. and Flores, K. B. and Banks, H. T.}, year={2016} }
 @article{brewin_birch_mehta_reeves_shaw_kruse_whiteman_hu_kenz_banks_et al._2015, title={Characterisation of Elastic and Acoustic Properties of an Agar-Based Tissue Mimicking Material}, volume={43}, ISSN={["1573-9686"]}, DOI={10.1007/s10439-015-1294-7}, abstractNote={As a first step towards an acoustic localisation device for coronary stenosis to provide a non-invasive means of diagnosing arterial disease, measurements are reported for an agar-based tissue mimicking material (TMM) of the shear wave propagation velocity, attenuation and viscoelastic constants, together with one dimensional quasi-static elastic moduli and Poisson’s ratio. Phase velocity and attenuation coefficients, determined by generating and detecting shear waves piezo-electrically in the range 300 Hz–2 kHz, were 3.2–7.5 ms−1 and 320 dBm−1. Quasi-static Young’s modulus, shear modulus and Poisson’s ratio, obtained by compressive or shear loading of cylindrical specimens were 150–160 kPa; 54–56 kPa and 0.37–0.44. The dynamic Young’s and shear moduli, derived from fitting viscoelastic internal variables by an iterative statistical inverse solver to freely oscillating specimens were 230 and 33 kPa and the corresponding relaxation times, 0.046 and 0.036 s. The results were self-consistent, repeatable and provide baseline data required for the computational modelling of wave propagation in a phantom.}, number={10}, journal={ANNALS OF BIOMEDICAL ENGINEERING}, author={Brewin, M. P. and Birch, M. J. and Mehta, D. J. and Reeves, J. W. and Shaw, S. and Kruse, C. and Whiteman, J. R. and Hu, S. and Kenz, Z. R. and Banks, H. T. and et al.}, year={2015}, month={Oct}, pages={2587–2596} }
 @article{banks_catenacci_hu_2015, title={Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance}, volume={23}, number={5}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Catenacci, J. and Hu, S. H.}, year={2015}, pages={491–509} }
 @article{adoteye_banks_flores_leblanc_2015, title={Estimation of time-varying mortality rates using continuous models for Daphnia magna}, volume={44}, ISSN={["1873-5452"]}, DOI={10.1016/j.aml.2014.12.014}, abstractNote={Structured population models that make the assumption of constant demographic rates do not accurately describe the complex life histories seen in many species. We investigated the accuracy of using constant versus time-varying mortality rates within discrete and continuously structured models for Daphnia magna. We tested the accuracy of the models we considered using density-independent survival data for 90 daphnids. We found that a continuous differential equation model with a time-varying mortality rate was the most accurate model for describing our experimental D. magna survival data. Our results suggest that differential equation models with variable parameters are an accurate tool for estimating mortality rates in biological scenarios in which mortality might vary significantly with age.}, journal={APPLIED MATHEMATICS LETTERS}, author={Adoteye, Kaska and Banks, H. T. and Flores, Kevin B. and LeBlanc, Gerald A.}, year={2015}, month={Jun}, pages={12–16} }
 @inproceedings{criner_cherry_cooney_katter_banks_hu_catenacci_2015, title={Identification of thermal degradation using probabilistic models in reflectance spectroscopy}, volume={1650}, url={http://dx.doi.org/10.1063/1.4914816}, DOI={10.1063/1.4914816}, abstractNote={Different probabilistic models of molecular vibration modes are considered to model the reflectance spectra of chemical species through the dielectric constant. We discuss probability measure estimators in parametric and nonparametric models. Analyses of ceramic matrix composite samples that have been heat treated for different amounts of times are compared. We finally compare these results with the analysis of vitreous silica using nonparametric models.}, publisher={AIP Publishing LLC}, author={Criner, A. K. and Cherry, A. J. and Cooney, A. T. and Katter, T. D. and Banks, H. T. and Hu, Shuhua and Catenacci, Jared}, year={2015}, pages={1898–1906} }
 @article{banks_flores_hu_rosenberg_buzon_yu_lichterfeld_2015, title={Immuno-modulatory strategies for reduction of HIV reservoir cells}, volume={372}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2015.02.006}, abstractNote={Antiretroviral therapy is able to suppress the viral load to below the detection limit, but it is not able to eradicate HIV reservoirs. Thus, there is a critical need for a novel treatment to eradicate (or reduce) the reservoir in order to eliminate the need for a lifelong adherence to antiretroviral therapy, which is expensive and potentially toxic. In this paper, we investigate the possible pharmacological strategies or combinations of strategies that may be beneficial to reduce or possibly eradicate the latent reservoir. We do this via studies with a validated mathematical model, where the parameter values are obtained with newly acquired clinical data for HIV patients. Our findings indicate that the strategy of reactivating the reservoir combined with enhancement of the killing rate of HIV-specific CD8+ T cells is able to eradicate the reservoir. In addition, our analysis shows that a targeted suppression of the immune system is also a possible strategy to eradicate the reservoir.}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Banks, H. T. and Flores, Kevin B. and Hu, Shuhua and Rosenberg, Eric and Buzon, Maria and Yu, Xu and Lichterfeld, Matthias}, year={2015}, month={May}, pages={146–158} }
 @article{banks_doumic_kruse_prigent_rezaei_2015, title={Information content in data sets for a nucleated-polymerization model}, volume={9}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2015.1050465}, abstractNote={We illustrate the use of statistical tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, and model comparison techniques) in addition to sensitivity analysis that may be employed to determine the information content in data sets. We do this in the context of recent models [S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel, L.M. Tine, H. Rezaei, and M. Doumic, An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation, PLoS ONE 7 (2012), e43273. doi:10.1371/journal.pone.0043273.] for nucleated polymerization in proteins, about which very little is known regarding the underlying mechanisms; thus, the methodology we develop here may be of great help to experimentalists. We conclude that the investigated data sets will support with reasonable levels of uncertainty only the estimation of the parameters related to the early steps of the aggregation process.}, number={1}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Doumic, Marie and Kruse, Carola and Prigent, Stephanie and Rezaei, Human}, year={2015}, month={Jan}, pages={172–197} }
 @article{banks_banks_link_rosenheim_ross_tillman_2015, title={Model comparison tests to determine data information content}, volume={43}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2014.11.002}, abstractNote={In the context of inverse or parameter estimation problems we demonstrate the use of statistically based model comparison tests in several examples of practical interest. In these examples we are interested in questions related to information content of a particular given data set and whether the data will support a more complicated model to describe it. In the first example we compare fits for several different models to describe simple decay in a size histogram for aggregates in amyloid fibril formation. In a second example we investigate whether the information content in data sets for the pest Lygus hesperus in cotton fields as it is currently collected is sufficient to support a model in which one distinguishes between nymphs and adults. Finally in a third example with data for patients having undergone an organ transplant, we question whether the data content is sufficient to estimate more than 5 of the fundamental parameters in a particular dynamic model.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Banks, J. E. and Link, Kathryn and Rosenheim, J. A. and Ross, Chelsea and Tillman, K. A.}, year={2015}, month={May}, pages={10–18} }
 @article{banks_rubio_saintier_troparevsky_2015, title={OPTIMAL DESIGN FOR PARAMETER ESTIMATION IN EEG PROBLEMS IN A 3D MULTILAYERED DOMAIN}, volume={12}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2015.12.739}, abstractNote={The fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical D-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Rubio, D. and Saintier, N. and Troparevsky, M. I.}, year={2015}, month={Aug}, pages={739–760} }
 @article{adoteye_banks_flores_2015, title={Optimal design of non-equilibrium experiments for genetic network interrogation}, volume={40}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2014.09.013}, abstractNote={Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.}, journal={APPLIED MATHEMATICS LETTERS}, author={Adoteye, Kaska and Banks, H. T. and Flores, Kevin B.}, year={2015}, month={Feb}, pages={84–89} }
 @article{banks_banks_rinnovatore_jackson_2015, title={Optimal sampling frequency and timing of threatened tropical bird populations: A modeling approach}, volume={303}, ISSN={["1872-7026"]}, DOI={10.1016/j.ecolmodel.2015.02.005}, abstractNote={Abstract Conservation of threatened or endangered species relies critically on accurate population counts over time. In practice, many population censuses are conducted by non-governmental organizations or volunteer citizen scientists who are constrained by fiscal and temporal resources. Less than optimal sampling regimens (characterized by infrequent and/or irregular schedules) for conducting population censuses can result in woefully misleading population estimates – and thus have dire consequences for management and conservation. We illustrate this using an East African case study in which 14 years of bird data was collected in the Arabuko-Sokoke Forest in coastal Kenya. We first estimate life history parameters in a discrete matrix model. Desiring a data collection protocol which would lessen observation error and lend to a deeper understanding of population projections and dynamics of a threatened species, we carry out mathematical and statistical modeling efforts with an adaptation of a Leslie model for simulated population estimates stemming from different population sampling schemes. We illustrate how resource managers might take a strategic approach, using simple quantitative models, to develop an optimal sampling scheme that considers important species traits, such as breeding season, and balances the tradeoff between resources and accuracy.}, journal={ECOLOGICAL MODELLING}, author={Banks, J. E. and Banks, H. T. and Rinnovatore, K. and Jackson, C. M.}, year={2015}, month={May}, pages={70–77} }
 @article{adoteye_banks_cross_eytcheson_flores_leblanc_nguyen_ross_smith_stemkovski_et al._2015, title={Statistical validation of structured population models for Daphnia magna}, volume={266}, ISSN={0025-5564}, url={http://dx.doi.org/10.1016/j.mbs.2015.06.003}, DOI={10.1016/j.mbs.2015.06.003}, abstractNote={In this study we use statistical validation techniques to verify density-dependent mechanisms hypothesized for populations of Daphnia magna. We develop structured population models that exemplify specific mechanisms and use multi-scale experimental data in order to test their importance. We show that fecundity and survival rates are affected by both time-varying density-independent factors, such as age, and density-dependent factors, such as competition. We perform uncertainty analysis and show that our parameters are estimated with a high degree of confidence. Furthermore, we perform a sensitivity analysis to understand how changes in fecundity and survival rates affect population size and age-structure.}, journal={Mathematical Biosciences}, publisher={Elsevier BV}, author={Adoteye, Kaska and Banks, H.T. and Cross, Karissa and Eytcheson, Stephanie and Flores, Kevin B. and LeBlanc, Gerald A. and Nguyen, Timothy and Ross, Chelsea and Smith, Emmaline and Stemkovski, Michael and et al.}, year={2015}, month={Aug}, pages={73–84} }
 @article{banks_baraldi_cross_flores_mcchesney_poag_thorpe_2015, title={UNCERTAINTY QUANTIFICATION IN MODELING HIV VIRAL MECHANICS}, volume={12}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2015.12.937}, abstractNote={We consider an in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work [7]. We revisit the earlier model in light of progress over the last several years in understanding HIV-1 progression in humans. We then consider statistical models to describe the data and use these with residual plots in generalized least squares problems to develop accurate descriptions of the proper weights for the data. We use recent parameter subset selection techniques [5,6] to investigate the impact of estimated parameters on the corresponding selection scores. Bootstrapping and asymptotic theory are compared in the context of confidence intervals for the resulting parameter estimates.}, number={5}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Baraldi, Robert and Cross, Karissa and Flores, Kevin and Mcchesney, Christina and Poag, Laura and Thorpe, Emma}, year={2015}, month={Oct}, pages={937–964} }
 @article{banks_rehm_sutton_davis_hail_kuerbis_morgenstern_2014, title={DYNAMIC MODELING OF BEHAVIOR CHANGE}, volume={72}, ISSN={["1552-4485"]}, DOI={10.1090/s0033-569x-2014-01296-3}, abstractNote={We consider a conceptual and quantitative modeling approach for investigating dynamic behavior change. While the approach is applicable to behavior change in eating disorders, smoking, substance abuse and other behavioral disorders, here we present our novel dynamical systems modeling approach to understand the processes governing an individual’s behavior in the context of problem drinking. Recent advances in technology have resulted in large intensive longitudinal data sets which are particularly well suited for study within such frameworks. However, the lack of previous work in this area (specifically, on the interand intra-personal factors governing drinking behavior of individuals) renders this a daunting and unique challenge. As a result, issues which are typically routine in mathematical modeling require considerable effort such as the determination of key quantities of interest, and the timescale on which to represent them. We discuss the construction of an initial mathematical model for two starkly distinct individuals and make a case for the potential for such efforts to help in understanding the underlying mechanisms responsible for behavior change in problem drinkers. AMS Subject Classification: 91E10, 34K29, 62G10.}, number={2}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Rehm, Keri L. and Sutton, Karyn L. and Davis, Christine and Hail, Lisa and Kuerbis, Alexis and Morgenstern, Jon}, year={2014}, pages={209–251} }
 @inproceedings{banks_catenacci_hu_kenz_2014, title={Decomposition of permittivity contributions from reflectance using mechanism models}, booktitle={2014 american control conference (acc)}, author={Banks, H. T. and Catenacci, J. and Hu, S. H. and Kenz, Z. R.}, year={2014}, pages={367–372} }
 @article{banks_birch_brewin_greenwald_hu_kenz_kruse_maischak_shaw_whiteman_2014, title={High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling}, volume={98}, ISSN={["1097-0207"]}, DOI={10.1002/nme.4631}, abstractNote={SUMMARY}, number={2}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING}, author={Banks, H. T. and Birch, Malcolm J. and Brewin, Mark P. and Greenwald, Stephen E. and Hu, Shuhua and Kenz, Zackary R. and Kruse, Carola and Maischak, Matthias and Shaw, Simon and Whiteman, John R.}, year={2014}, month={Apr}, pages={131–156} }
 @article{banks_hu_kenz_kruse_shaw_whiteman_brewin_greenwald_birch_2014, title={MODEL VALIDATION FOR A NONINVASIVE ARTERIAL STENOSIS DETECTION PROBLEM}, volume={11}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2014.11.427}, abstractNote={A current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use one-dimensional shear wave experimental data from novel acoustic phantoms to validate a corresponding viscoelastic mathematical model. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.}, number={3}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. Thomas and Hu, Shuhua and Kenz, Zackary R. and Kruse, Carola and Shaw, Simon and Whiteman, John and Brewin, Mark P. and Greenwald, Stephen E. and Birch, Malcolm J.}, year={2014}, month={Jun}, pages={427–448} }
 @inproceedings{baraldi_cross_mcchesney_poag_thorpe_flores_banks_2014, title={Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions}, booktitle={2014 american control conference (acc)}, author={Baraldi, R. and Cross, K. and McChesney, C. and Poag, L. and Thorpe, E. and Flores, K. B. and Banks, H. T.}, year={2014}, pages={2753–2758} }
 @article{banks_catenacci_hu_2013, title={A Comparison of Stochastic Systems with Different Types of Delays}, volume={31}, ISSN={["1532-9356"]}, DOI={10.1080/07362994.2013.806217}, abstractNote={In this article, we investigate the effects of different types of delays, a fixed delay and a random delay, on the dynamics of stochastic systems as well as their relationship with each other in the context of a just-in-time network model. The specific example on which we focus is a pork production network model. We numerically explore the corresponding deterministic approximations for the stochastic systems with these two different types of delays. Numerical results reveal that the agreement of stochastic systems with fixed and random delays depend on the population size and the variance of the random delay, even when the mean value of the random delay is chosen the same as the value of the fixed delay. When the variance of the random delay is sufficiently small, the histograms of state solutions to the stochastic system with a random delay are similar to those of the stochastic model with a fixed delay regardless of the population size. We also compared the stochastic system with a Gamma distributed random delay to the stochastic system constructed based on the Kurtz's limit theorem from a system of deterministic delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the second system appear more dispersed than the corresponding ones obtained for the first case. In addition, we found that there is more agreement between the histograms of these two stochastic systems as the variance of the Gamma distributed random delay decreases.}, number={6}, journal={STOCHASTIC ANALYSIS AND APPLICATIONS}, author={Banks, H. T. and Catenacci, Jared and Hu, Shuhua}, year={2013}, month={Nov}, pages={913–955} }
 @article{banks_kapraun_thompson_peligero_argilaguet_meyerhans_2013, title={A novel statistical analysis and interpretation of flow cytometry data}, volume={7}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2013.812753}, abstractNote={A recently developed class of models incorporating the cyton model of population generation structure into a conservation-based model of intracellular label dynamics is reviewed. Statistical aspects of the data collection process are quantified and incorporated into a parameter estimation scheme. This scheme is then applied to experimental data for PHA-stimulated CD4+T and CD8+T cells collected from two healthy donors. This novel mathematical and statistical framework is shown to form the basis for accurate, meaningful analysis of cellular behaviour for a population of cells labelled with the dye carboxyfluorescein succinimidyl ester and stimulated to divide.}, number={1}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Kapraun, D. F. and Thompson, W. Clayton and Peligero, Cristina and Argilaguet, Jordi and Meyerhans, Andreas}, year={2013}, month={Dec}, pages={96–132} }
 @article{greenwald_banks_birch_brewin_hu_kenz_kruse_mehta_reeves_shaw_et al._2013, title={Acoustic localisation of coronary artery stenosis: Wave propagation in soft tissue mimicking gels}, volume={7}, ISSN={1872-9312}, url={http://dx.doi.org/10.1016/J.ARTRES.2013.10.081}, DOI={10.1016/J.ARTRES.2013.10.081}, abstractNote={WAVE PROPAGATION IN SOFT TISSUE MIMICKING GEL H. Thomas Banks, Malcolm J. Birch, Mark P. Brewin, Steve E. Greenwald, Shuhua Hu, Zack R. Kenz, Carola Kruse, Dwij Mehta, Simon Shaw, John R. Whiteman Blizard Institute, Barts and The London School of Medicine and Dentistry, Queen Mary, University of London, UK; Clinical Physics, Barts Health NHS Trust, London, UK; Institute of Computational Mathematics, Brunel University, UK; Department of Mathematics, North Carolina State University, Raleigh NC, USA}, number={3-4}, journal={Artery Research}, publisher={Atlantis Press}, author={Greenwald, S.E. and Banks, H.T. and Birch, M.J. and Brewin, M.P. and Hu, S. and Kenz, Z.R. and Kruse, C. and Mehta, D. and Reeves, J. and Shaw, S. and et al.}, year={2013}, month={Sep}, pages={124} }
 @article{banks_rehm_2013, title={Experimental design for distributed parameter vector systems}, volume={26}, ISSN={0893-9659}, url={http://dx.doi.org/10.1016/j.aml.2012.08.003}, DOI={10.1016/j.aml.2012.08.003}, abstractNote={We formulate an optimal design problem for the selection of best states to observe and optimal sampling times and locations for parameter estimation or inverse problems involving complex nonlinear partial differential systems. An iterative algorithm for implementation of the resulting methodology is proposed.}, number={1}, journal={Applied Mathematics Letters}, publisher={Elsevier BV}, author={Banks, H.T. and Rehm, K.L.}, year={2013}, month={Jan}, pages={10–14} }
 @article{banks_rehm_2013, title={Experimental design for vector output systems}, volume={22}, ISSN={1741-5977 1741-5985}, url={http://dx.doi.org/10.1080/17415977.2013.797973}, DOI={10.1080/17415977.2013.797973}, abstractNote={We formulate an optimal design problem for the selection of best states to observe and optimal sampling times for parameter estimation or inverse problems involving complex non-linear dynamical systems. An iterative algorithm for implementation of the resulting methodology is proposed. Its use and efficacy are illustrated on two applied problems of practical interest: (i) dynamic models of HIV progression and (ii) modelling of the Calvin cycle in plant metabolism and growth.}, number={4}, journal={Inverse Problems in Science and Engineering}, publisher={Informa UK Limited}, author={Banks, H.T. and Rehm, K.L.}, year={2013}, month={May}, pages={557–590} }
 @article{banks_hu_kenz_kruse_shaw_whiteman_brewin_greenwald_birch_2013, title={Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology}, volume={21}, number={1}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Hu, S. H. and Kenz, Z. R. and Kruse, C. and Shaw, S. and Whiteman, J. R. and Brewin, M. P. and Greenwald, S. E. and Birch, M. J.}, year={2013}, pages={25–57} }
 @article{banks_cintron-arias_kappel_2013, title={Parameter selection methods in inverse problem formulation}, volume={2064}, journal={Mathematical modeling and validation in physiology: applications to the cardiovascular and respiratory systems}, author={Banks, H. T. and Cintron-Arias, A. and Kappel, F.}, year={2013}, pages={43–73} }
 @article{banks_choi_huffman_nardini_poag_thompson_2013, title={Quantifying CFSE label decay in flow cytometry data}, volume={26}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2012.12.010}, abstractNote={We developed a series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester (CFSE) is used as a staining agent. Data collected from two healthy patients were used to validate the models and to compare the models with the Akiake Information Criteria. The distinguishing features of multiple decay rates in the data are readily characterized and explained via time dependent decay models such as the logistic and Gompertz models.}, number={5}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Choi, A. and Huffman, T. and Nardini, J. and Poag, L. and Thompson, W. C.}, year={2013}, month={May}, pages={571–577} }
 @article{shaw_whiteman_greenwald_kruse_banks_birch_kenz_reeves_hu_brewin_2013, title={Towards computational diagnosis of coronary artery disease}, volume={7}, ISSN={1872-9312}, url={http://dx.doi.org/10.1016/J.ARTRES.2013.10.079}, DOI={10.1016/J.ARTRES.2013.10.079}, number={3-4}, journal={Artery Research}, publisher={Atlantis Press}, author={Shaw, S. and Whiteman, J.R. and Greenwald, S.E. and Kruse, C. and Banks, H.T. and Birch, M.J. and Kenz, Z.R. and Reeves, J. and Hu, S. and Brewin, M.P.}, year={2013}, month={Sep}, pages={123–124} }
 @article{banks_hu_joyner_broido_canter_gayvert_link_2012, title={A COMPARISON OF COMPUTATIONAL EFFICIENCIES OF STOCHASTIC ALGORITHMS IN TERMS OF TWO INFECTION MODELS}, volume={9}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2012.9.487}, abstractNote={In this paper, we investigate three particular algorithms: a stochastic simulation algorithm (SSA), and explicit and implicit tau-leaping algorithms. To compare these methods, we used them to analyze two infection models: a Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunodeficiency Virus (HIV) within host infection model. While the first has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative efficiency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational efficiency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.}, number={3}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. Thomas and Hu, Shuhua and Joyner, Michele and Broido, Anna and Canter, Brandi and Gayvert, Kaitlyn and Link, Kathryn}, year={2012}, month={Jul}, pages={487–526} }
 @article{banks_tompson_peligero_giest_argilaguet_meyerhans_2012, title={A DIVISION-DEPENDENT COMPARTMENTAL MODEL FOR COMPUTING CELL NUMBERS IN CFSE-BASED LYMPHOCYTE PROLIFERATION ASSAYS}, volume={9}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2012.9.699}, abstractNote={Some key features of a mathematical description of an immune response are an estimate of the number of responding cells and the manner in which those cells divide, differentiate, and die. The intracellular dye CFSE is a powerful experimental tool for the analysis of a population of dividing cells, and numerous mathematical treatments have been aimed at using CFSE data to describe an immune response [30,31,32,37,38,42,48,49]. Recently, partial differential equation structured population models, with measured CFSE fluorescence intensity as the structure variable, have been shown to accurately fit histogram data obtained from CFSE flow cytometry experiments [18,19,52,54]. In this report, the population of cells is mathematically organized into compartments, with all cells in a single compartment having undergone the same number of divisions. A system of structured partial differential equations is derived which can be fit directly to CFSE histogram data. From such a model, cell counts (in terms of the number of divisions undergone) can be directly computed and thus key biological parameters such as population doubling time and precursor viability can be determined. Mathematical aspects of this compartmental model are discussed, and the model is fit to a data set. As in [18,19], we find temporal and division dependence in the rates of proliferation and death to be essential features of a structured population model for CFSE data. Variability in cellular autofluorescence is found to play a significant role in the data, as well. Finally, the compartmental model is compared to previous work, and statistical aspects of the experimental data are discussed.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Tompson, W. Clayton and Peligero, Cristian and Giest, Sandra and Argilaguet, Jordi and Meyerhans, Andreas}, year={2012}, month={Oct}, pages={699–736} }
 @article{banks_holm_kappel_2012, title={A Monte Carlo based analysis of optimal design criteria}, volume={20}, ISSN={["1569-3945"]}, DOI={10.1515/jip-2012-0201}, abstractNote={Abstract.}, number={1}, journal={JOURNAL OF INVERSE AND ILL-POSED PROBLEMS}, author={Banks, H. T. and Holm, Kathleen J. and Kappel, Franz}, year={2012}, month={Mar}, pages={1–37} }
 @book{banks_2012, title={A functional analysis framework for modeling, estimation, and control in science and engineering}, DOI={10.1201/b12209}, abstractNote={Introduction to Functional Analysis in Applications Example 1: Heat Equation Some Preliminaries: Hilbert, Banach, and Other Spaces Useful in Operator Theory Return to Example 1: Heat Equation Example 2: General Transport Equation Example 3: Delay Systems-Insect/Insecticide Models Example 4: Probability Measure Dependent Systems - Maxwell's Equations Example 5: Structured Population Models Semigroups and Infinitesimal Generators Basic Principles of Semigroups Infinitesimal Generators Generators Introduction to Generation Theorems Hille-Yosida Theorems Results from the Hille-Yosida Proof Corollaries to Hille-Yosida Lumer-Phillips and Dissipative Operators Examples Using Lumer-Phillips Theorem Adjoint Operators and Dual Spaces Adjoint Operators Dual Spaces and Strong, Weak, and Weak* Topologies Examples of Spaces and Their Duals Return to Dissipativeness for General Banach Spaces More on Adjoint Operators Examples of Computing Adjoints Gelfand Triple, Sesquilinear Forms, and Lax-Milgram Example 6: The Cantilever Beam The Beam Equation in the Form x derivative = Ax + F Gelfand Triples Sesquilinear Forms Lax-Milgram (Bounded Form) Lax-Milgram (Unbounded Form) Summary Remarks and Motivation Analytic Semigroups Example 1: The Heat Equation (again) Example 2: The Transport Equation (again) Example 6: The Beam Equation (again) Summary of Results on Analytic Semigroup Generation by Sesquilinear Forms Tanabe Estimates (on "Regular Dissipative Operators") Infinitesimal Generators in a General Banach Space Abstract Cauchy Problems General Second-Order Systems Introduction to Second-Order Systems Results for sigma2 V-elliptic Results for sigma2 H-semielliptic Stronger Assumptions for sigma2 Weak Formulations for Second-Order Systems Model Formulation Discussion of the Model Theorems 9.1 and 9.2: Proofs Inverse or Parameter Estimation Problems Approximation and Convergence Some Further Remarks "Weak" or "Variational Form" Finite Element Approximations and the Trotter-Kato Theorems Finite Elements Trotter-Kato Approximation Theorem Delay Systems: Linear and Nonlinear Linear Delay Systems and Approximation Modeling of Viral Delays in HIV Infection Dynamics Nonlinear Delay Systems State Approximation and Convergence for Nonlinear Delay Systems Fixed Delays versus Distributed Delays Weak* Convergence and the Prohorov Metric in Inverse Problems Populations with Aggregate Data, Uncertainty, and PBM A Prohorov Metric Framework for Inverse Problems Metrics on Probability Spaces Example 5: The Growth Rate Distribution Model and Inverse Problem in Marine Populations The Prohorov Metric in Optimization and Optimal Design Problems Two Player Min-Max Games with Uncertainty Optimal Design Techniques Generalized Curves and Relaxed Controls of Variational Theory Preisach Hysteresis in Smart Materials NPML and Mixing Distributions in Statistical Estimation Control Theory for Distributed Parameter Systems Motivation Abstract Formulation Infinite Dimensional LQR Control: Full State Feedback The Finite Horizon Control Problem The Infinite Horizon Control Problem Families of Approximate Control Problems The Finite Horizon Problem Approximate Control Gains The Infinite Horizon Problem Approximate Control Gains References Index}, publisher={Boca Raton: CRC Press}, author={Banks, H. T.}, year={2012} }
 @article{banks_kenz_thompson_2012, title={A review of selected techniques in inverse problem nonparametric probability distribution estimation}, volume={20}, number={4}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Kenz, Z. R. and Thompson, W. C.}, year={2012}, pages={429–460} }
 @article{banks_hu_2012, title={A zero-sum electromagnetic evader-interrogator differential game with uncertainty}, volume={91}, ISSN={["1563-504X"]}, DOI={10.1080/00036811.2012.667081}, abstractNote={We consider dynamic electromagnetic evasion-interrogation games in which the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies to enhance detection. The resulting problem is formulated as a two-player zero-sum dynamic differential game in which the cost functional is based on the expected value of the intensity of the reflected signal. We show that there exists a saddle point for the relaxed form of this dynamic differential game in which the relaxed controls appear bilinearly in the dynamics governed by a partial differential equation. We also present a computational framework for construction of approximate saddle point strategies in feedback form for a special case of this relaxed differential game with strategies and payoff in the sense of Berkovitz.}, number={4}, journal={APPLICABLE ANALYSIS}, author={Banks, H. T. and Hu, Shuhua}, year={2012}, pages={645–674} }
 @article{avery_banks_basu_cheng_eager_khasawinah_potter_rehm_2012, title={Experimental design and inverse problems in plant biological modeling}, volume={20}, number={2}, journal={Journal of Inverse and Ill-Posed Problems}, author={Avery, M. and Banks, H. T. and Basu, K. and Cheng, Y. S. and Eager, E. and Khasawinah, S. and Potter, L. and Rehm, K. L.}, year={2012}, pages={169–191} }
 @article{banks_clayton thompson_2012, title={Mathematical Models of Dividing Cell Populations: Application to CFSE Data}, volume={7}, ISSN={0973-5348 1760-6101}, url={http://dx.doi.org/10.1051/mmnp/20127504}, DOI={10.1051/mmnp/20127504}, abstractNote={Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental tool which can be used in conjunction with mathematical modeling to quantify the dynamic behavior of a population of lymphocytes. In this survey we begin by providing an overview of the mathematically relevant aspects of the data collection procedure. We then present an overview of the large body of mathematical models, along with their assumptions and uses, which have been proposed to describe the dynamics of proliferating cell populations. While much of this body of work has been aimed at modeling the generation structure (cells per generation) of the proliferating population, several recent models have considered the more fundamental task of modeling CFSE histogram data directly. Such models are analyzed and recent results are discussed. Finally, directions for future research are suggested.}, number={5}, journal={Mathematical Modelling of Natural Phenomena}, publisher={EDP Sciences}, author={Banks, H.T. and Clayton Thompson, W.}, year={2012}, pages={24–52} }
 @article{banks_hu_jang_kwon_2012, title={Modelling and optimal control of immune response of renal transplant recipients}, volume={6}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2012.655328}, abstractNote={We consider the increasingly important and highly complex immunological control problem: control of the dynamics of immunosuppression for organ transplant recipients. The goal in this problem is to maintain the delicate balance between over-suppression (where opportunistic latent viruses threaten the patient) and under-suppression (where rejection of the transplanted organ is probable). First, a mathematical model is formulated to describe the immune response to both viral infection and introduction of a donor kidney in a renal transplant recipient. Some numerical results are given to qualitatively validate and demonstrate that this initial model exhibits appropriate characteristics of primary infection and reactivation for immunosuppressed transplant recipients. In addition, we develop a computational framework for designing adaptive optimal treatment regimes with partial observations and low-frequency sampling, where the state estimates are obtained by solving a second deterministic optimal tracking problem. Numerical results are given to illustrate the feasibility of this method in obtaining optimal treatment regimes with a balance between under-suppression and over-suppression of the immune system.}, number={2}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Hu, Shuhua and Jang, Taesoo and Kwon, Hee-Dae}, year={2012}, pages={539–567} }
 @article{banks_bocharov_grossman_meyerhans_2012, title={Preface. Distributed Parameter Systems in Immunology}, volume={7}, ISSN={0973-5348 1760-6101}, url={http://dx.doi.org/10.1051/mmnp/20127501}, DOI={10.1051/mmnp/20127501}, number={5}, journal={Mathematical Modelling of Natural Phenomena}, publisher={EDP Sciences}, author={Banks, H.T. and Bocharov, G. and Grossman, Z. and Meyerhans, A.}, year={2012}, pages={1–3} }
 @article{banks_hu_2012, title={Propagation of Growth Uncertainty in a Physiologically Structured Population}, volume={7}, ISSN={0973-5348 1760-6101}, url={http://dx.doi.org/10.1051/mmnp/20127503}, DOI={10.1051/mmnp/20127503}, abstractNote={In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described two recent approaches that have been investigated in the literature to describe this growth uncertainty/variability in a physiologically structured population. One involves formulating growth as a Markov diffusion process while the other entails imposing a probabilistic structure on the set of possible growth rates across the entire population. Both approaches lead to physiologically structured population models with nontrivial dispersion. Even though these two approaches are conceptually quite different, they were found in [] to have a close relationship: in some cases with properly chosen parameters and coefficient functions, the resulting stochastic processes have the same probability density function at each time.}, number={5}, journal={Mathematical Modelling of Natural Phenomena}, publisher={EDP Sciences}, author={Banks, H.T. and Hu, S.}, year={2012}, pages={7–23} }
 @article{banks_criner_2012, title={Thermal based methods for damage detection and characterization in porous materials}, volume={28}, ISSN={0266-5611 1361-6420}, url={http://dx.doi.org/10.1088/0266-5611/28/6/065021}, DOI={10.1088/0266-5611/28/6/065021}, abstractNote={In this effort we consider damage detection algorithms using thermal probes. The techniques proposed employ models derived from homogenization theory as the model solution in parameter estimation procedures for simulated data for heat flow in a porous medium. We consider data simulated from a model on a perforated domain with isotropic flow and data simulated from a model on a homogeneous domain with anisotropic flow. We report on ordinary least squares methods combined with the method of mappings to detect the presence of damage and to characterize the geometry of the damage.}, number={6}, journal={Inverse Problems}, publisher={IOP Publishing}, author={Banks, H T and Criner, Amanda Keck}, year={2012}, month={May}, pages={065021} }
 @misc{banks_hu_kenz_2011, title={A Brief Review of Elasticity and Viscoelasticity for Solids}, volume={3}, ISSN={["2075-1354"]}, DOI={10.4208/aamm.10-m1030}, abstractNote={Abstract}, number={1}, journal={ADVANCES IN APPLIED MATHEMATICS AND MECHANICS}, author={Banks, Harvey Thomas and Hu, Shuhua and Kenz, Zackary R.}, year={2011}, month={Feb}, pages={1–51} }
 @article{ortiz_banks_castillo-chavez_chowell_wang_2011, title={A DETERMINISTIC METHODOLOGY FOR ESTIMATION OF PARAMETERS IN DYNAMIC MARKOV CHAIN MODELS}, volume={19}, ISSN={["1793-6470"]}, DOI={10.1142/s0218339011003798}, abstractNote={ A method for estimating parameters in dynamic stochastic (Markov Chain) models based on Kurtz's limit theory coupled with inverse problem methods developed for deterministic dynamical systems is proposed and illustrated in the context of disease dynamics. This methodology relies on finding an approximate large-population behavior of an appropriate scaled stochastic system. The approach leads to a deterministic approximation obtained as solutions of rate equations (ordinary differential equations) in terms of the large sample size average over sample paths or trajectories (limits of pure jump Markov processes). Using the resulting deterministic model, we select parameter subset combinations that can be estimated using an ordinary-least-squares (OLS) or generalized-least-squares (GLS) inverse problem formulation with a given data set. The selection is based on two criteria of the sensitivity matrix: the degree of sensitivity measured in the form of its condition number and the degree of uncertainty measured in the form of its parameter selection score. We illustrate the ideas with a stochastic model for the transmission of vancomycin-resistant enterococcus (VRE) in hospitals and VRE surveillance data from an oncology unit. }, number={1}, journal={JOURNAL OF BIOLOGICAL SYSTEMS}, author={Ortiz, A. R. and Banks, H. T. and Castillo-Chavez, C. and Chowell, G. and Wang, X.}, year={2011}, month={Mar}, pages={71–100} }
 @article{banks_sutton_thompson_bocharov_doumic_schenkel_argilaguet_giest_peligero_meyerhans_2011, title={A new model for the estimation of cell proliferation dynamics using CFSE data}, volume={373}, ISSN={["1872-7905"]}, DOI={10.1016/j.jim.2011.08.014}, abstractNote={CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al. (2009), Luzyanina et al. (2007), a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.}, number={1-2}, journal={JOURNAL OF IMMUNOLOGICAL METHODS}, author={Banks, H. T. and Sutton, Karyn L. and Thompson, W. Clayton and Bocharov, Gennady and Doumic, Marie and Schenkel, Tim and Argilaguet, Jordi and Giest, Sandra and Peligero, Cristina and Meyerhans, Andreas}, year={2011}, month={Oct}, pages={143–160} }
 @article{banks_holm_kappel_2011, title={Comparison of optimal design methods in inverse problems}, volume={27}, ISSN={0266-5611 1361-6420}, url={http://dx.doi.org/10.1088/0266-5611/27/7/075002}, DOI={10.1088/0266-5611/27/7/075002}, abstractNote={Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst–Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667–77; De Gaetano A and Arino O 2000 J. Math. Biol. 40 136–68; Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979–90).}, number={7}, journal={Inverse Problems}, publisher={IOP Publishing}, author={Banks, H T and Holm, K and Kappel, F}, year={2011}, month={Jun}, pages={075002} }
 @article{banks_hu_ito_muccio_2011, title={Dynamic evasion-interrogation games with uncertainty in the context of electromagetics}, volume={4}, number={3}, journal={Numerical Mathematics: Theory, Methods and Applications}, author={Banks, H. T. and Hu, S. H. and Ito, K. and Muccio, S. G.}, year={2011}, pages={359–378} }
 @article{banks_sutton_thompson_bocharov_roose_schenkel_meyerhans_2011, title={Estimation of Cell Proliferation Dynamics Using CFSE Data}, volume={73}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-010-9524-5}, abstractNote={Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57–89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1–26, 2007) contain a mathematical model with fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Here, this model and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations suggest that the new decay/label loss and time dependent effective proliferation and death rates do indeed provide improved fits of the model to data. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics model should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences.}, number={1}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Banks, H. T. and Sutton, Karyn L. and Thompson, W. Clayton and Bocharov, Gennady and Roose, Dirk and Schenkel, Tim and Meyerhans, Andreas}, year={2011}, month={Jan}, pages={116–150} }
 @article{wendelsdorf_dean_hu_nordone_banks_2011, title={Host immune responses that promote initial HIV spread}, volume={289}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2011.08.012}, abstractNote={The host inflammatory response to HIV invasion is a necessary component of the innate antiviral activity that vaccines and early interventions seek to exploit/enhance. However, the response is dependent on CD4+ T-helper cell 1 (Th1) recruitment and activation. It is this very recruitment of HIV-susceptible target cells that is associated with the initial viral proliferation. Hence, global enhancement of the inflammatory response by T-cells and dendritic cells will likely feed viral propagation. Mucosal entry sites contain inherent pathways, in the form of natural regulatory T-cells (nTreg), that globally dampen the inflammatory response. We created a model of this inflammatory response to virus as well as inherent nTreg-mediated regulation of Th1 recruitment and activation. With simulations using this model we sought to address the net effect of nTreg activation and its specific functions as well as identify mechanisms of the natural inflammatory response that are best targeted to inhibit viral spread without compromising initial antiviral activity. Simulation results provide multiple insights that are relevant to developing intervention strategies that seek to exploit natural immune processes: (i) induction of the regulatory response through nTreg activation expedites viral proliferation due to viral production by nTreg itself and not to reduced Natural Killer (NK) cell activity; (ii) at the same time, induction of the inflammation response through either DC activation or Th1 activation expedites viral proliferation; (iii) within the inflammatory pathway, the NK response is an effective controller of viral proliferation while DC-mediated stimulation of T-cells is a significant driver of viral proliferation; and (iv) nTreg-mediated DC deactivation plays a significant role in slowing viral proliferation by inhibiting T-cell stimulation, making this function an aide to the antiviral immune response.}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Wendelsdorf, K. and Dean, G. and Hu, Shuhua and Nordone, S. and Banks, H. T.}, year={2011}, month={Nov}, pages={17–35} }
 @article{banks_cioranescu_criner_winfree_2011, title={Parameter estimation for the heat equation on perforated domains}, volume={19}, number={6}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Cioranescu, D. and Criner, A. K. and Winfree, W. P.}, year={2011}, pages={825–857} }
 @article{david_tran_banks_2011, title={Receding Horizon Control of HIV}, volume={32}, ISSN={["1099-1514"]}, DOI={10.1002/oca.969}, abstractNote={Abstract}, number={6}, journal={OPTIMAL CONTROL APPLICATIONS & METHODS}, author={David, John and Tran, Hien and Banks, H. T.}, year={2011}, pages={681–699} }
 @article{ortiz_banks_castillo-chavez_chowell_wang_2010, title={A discrete events delay differential system model for transmission of Vancomycin-resistant enterococcus (VRE) in hospitals}, volume={18}, number={7}, journal={Journal of Inverse and Ill-Posed Problems}, author={Ortiz, A. and Banks, H. T. and Castillo-Chavez, C. and Chowell, G. and Wang, X. H.}, year={2010}, pages={787–821} }
 @article{banks_rehm_sutton_2010, title={DYNAMIC SOCIAL NETWORK MODELS INCORPORATING STOCHASTICITY AND DELAYS}, volume={68}, ISSN={["1552-4485"]}, DOI={10.1090/s0033-569x-2010-01201-x}, abstractNote={Networks are typically studied via computational models, and often investigations are restricted to the static case. Here we extend the work in Banks, Karr, Nguyen and Samuels (2008), which demonstrated a simple dynamical system framework in which to study social network behavior, to include a discrete delay. This delay represents the time lag that is likely required for an agent to change his/her own characteristics (e.g., opinions, viewpoints or behavior) after interacting with an agent possessing different characteristics. Thus this modification adds significantly to the relevance of the model in many potential applications. We have shown that the delays can be incorporated into a stochastic differential equations (SDE) framework in an efficient and computationally tractable way. Through numerical studies, we see novel outcomes when stochasticity, delay, or both are considered, demonstrating the need to include these features should they be present in the network application.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Rehm, Keri and Sutton, Karyn L.}, year={2010}, month={Dec}, pages={783–802} }
 @article{banks_hu_thompson_2010, title={Electromagnetic interrogation and the Doppler shift using the method of mappings}, volume={51}, ISSN={["0895-7177"]}, DOI={10.1016/j.mcm.2009.12.013}, abstractNote={We consider the electromagnetic detection of hidden moving or oscillating conductive targets. The resulting mathematical problem involves computation of a Doppler shift for an electromagnetic wave reflecting from a moving interface. This entails solving Maxwell’s equations on a domain changing in time. We employ the method of mappings to transform the problem to one of computing solutions of a Maxwell system with time dependent coefficients on a fixed reference domain. Thus we obtain a problem that is eminently tractable with finite element or finite difference time domain methods. The accuracy of numerical solutions is illustrated with computations for a number of different velocities for the moving interface.}, number={5-6}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Hu, Shuhua and Thompson, W. Clayton}, year={2010}, month={Mar}, pages={389–399} }
 @article{banks_dediu_ernstberger_kappel_2010, title={Generalized sensitivities and optimal experimental design}, volume={18}, number={1}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Dediu, S. and Ernstberger, S. L. and Kappel, F.}, year={2010}, pages={25–83} }
 @article{banks_charles_jauffret_sutton_thompson_2010, title={Label structured cell proliferation models}, volume={23}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2010.07.009}, abstractNote={We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.}, number={12}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Charles, Frederique and Jauffret, Marie Doumic and Sutton, Karyn L. and Thompson, W. Clayton}, year={2010}, month={Dec}, pages={1412–1415} }
 @article{banks_holm_robbins_2010, title={Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping}, volume={52}, ISSN={["0895-7177"]}, DOI={10.1016/j.mcm.2010.06.026}, abstractNote={We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.}, number={9-10}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Holm, Kathleen and Robbins, Danielle}, year={2010}, month={Nov}, pages={1610–1625} }
 @article{banks_boudreaux_criner_foster_uttal_vogel_winfree_2010, title={Thermal-based damage detection in porous materials}, volume={18}, ISSN={["1741-5977"]}, DOI={10.1080/17415977.2010.498912}, abstractNote={We report here on the use of the heat equation to simulate a thermal interrogation method for detecting damage in a heterogeneous porous material. We first use probability schemes to randomly generate pores in a sample material; then we simulate flash heating of the compartment along one of its boundaries. Temperature data along the source and back boundaries are recorded and then analysed to distinguish differences between the undamaged and damaged materials. These results suggest that it is possible to detect damage of a certain size within a porous medium using thermal interrogation.}, number={6}, journal={INVERSE PROBLEMS IN SCIENCE AND ENGINEERING}, author={Banks, H. T. and Boudreaux, Brittany and Criner, Amanda Keck and Foster, Krista and Uttal, Cerena and Vogel, Thomas and Winfree, William P.}, year={2010}, pages={835–851} }
 @article{sutton_banks_castillo-chavez_2010, title={Using inverse problem methods with surveillance data in pneumococcal vaccination}, volume={51}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2009.12.014}, abstractNote={The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods.}, number={5-6}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Sutton, Karyn L. and Banks, H. T. and Castillo-Chavez, Carlos}, year={2010}, month={Mar}, pages={369–388} }
 @article{banks_davis_ernstberger_hu_artimovich_dhar_browdy_2009, title={A comparison of probabilistic and stochastic formulations in modelling growth uncertainty and variability}, volume={3}, ISSN={1751-3758 1751-3766}, url={http://dx.doi.org/10.1080/17513750802304877}, DOI={10.1080/17513750802304877}, abstractNote={We compare two approaches for inclusion of uncertainty/variability in modelling growth in size-structured population models. One entails imposing a probabilistic structure on growth rates in the population while the other involves formulating growth as a stochastic Markov diffusion process. We present a theoretical analysis that allows one to include comparable levels of uncertainty in the two distinct formulations in making comparisons of the two approaches.}, number={2-3}, journal={Journal of Biological Dynamics}, publisher={Informa UK Limited}, author={Banks, H. T. and Davis, J. L. and Ernstberger, S. L. and Hu, Shuhua and Artimovich, E. and Dhar, A. K. and Browdy, C. L.}, year={2009}, month={May}, pages={130–148} }
 @article{banks_holm_wanner_cintron-arias_kepler_wetherington_2009, title={A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system}, volume={50}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2009.02.007}, abstractNote={We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.}, number={7-8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Holm, Kathleen and Wanner, Nathan C. and Cintron-Arias, Ariel and Kepler, Grace M. and Wetherington, Jeffrey D.}, year={2009}, month={Oct}, pages={959–974} }
 @article{kepler_banksa_davidian_rosenberg_2009, title={A model for HCMV infection in immunosuppressed patients}, volume={49}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2008.06.003}, abstractNote={We propose a model for HCMV infection in healthy and immunosuppressed patients. First, we present the biological model and formulate a system of ordinary differential equations to describe the pathogenesis of primary HCMV infection in immunocompetent and immunosuppressed individuals. We then investigate how clinical data can be applied to this model. Approximate parameter values for the model are derived from data available in the literature and from mathematical and physiological considerations. Simulations with the approximated parameter values demonstrates that the model is capable of describing primary, latent, and secondary (reactivated) HCMV infection. Reactivation simulations with this model provide a window into the dynamics of HCMV infection in (D-R+) transplant situations, where latently-infected recipients (R+) receive transplant tissue from HCMV-naive donors (D-).}, number={7-8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Kepler, G. M. and Banksa, H. T. and Davidian, M. and Rosenberg, E. S.}, year={2009}, month={Apr}, pages={1653–1663} }
 @article{cintron-arias_banks_capaldi_lloyd_2009, title={A sensitivity matrix based methodology for inverse problem formulation}, volume={17}, ISSN={["1569-3945"]}, DOI={10.1515/JIIP.2009.034}, abstractNote={Abstract We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.}, number={6}, journal={JOURNAL OF INVERSE AND ILL-POSED PROBLEMS}, author={Cintron-Arias, A. and Banks, H. T. and Capaldi, A. and Lloyd, A. L.}, year={2009}, month={Aug}, pages={545–564} }
 @article{banks_bokil_gibson_2009, title={Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Dispersive Media}, volume={25}, ISSN={["0749-159X"]}, DOI={10.1002/num.20379}, abstractNote={Abstract}, number={4}, journal={NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS}, author={Banks, H. T. and Bokil, V. A. and Gibson, N. L.}, year={2009}, month={Jul}, pages={885–917} }
 @article{valdez-jasso_haider_banks_santana_german_armentano_olufsen_2009, title={Analysis of Viscoelastic Wall Properties in Ovine Arteries}, volume={56}, ISSN={["1558-2531"]}, DOI={10.1109/TBME.2008.2003093}, abstractNote={In this paper, we analyze how elastic and viscoelastic properties differ across seven locations along the large arteries in 11 sheep. We employ a two-parameter elastic model and a four-parameter Kelvin viscoelastic model to analyze experimental measurements of vessel diameter and blood pressure obtained in vitro at conditions mimicking in vivo dynamics. Elastic and viscoelastic wall properties were assessed via solutions to the associated inverse problem. We use sensitivity analysis to rank the model parameters from the most to the least sensitive, as well as to compute standard errors and confidence intervals. Results reveal that elastic properties in both models (including Young's modulus and the viscoelastic relaxation parameters) vary across locations (smaller arteries are stiffer than larger arteries). We also show that for all locations, the inclusion of viscoelastic behavior is important to capture pressure-area dynamics.}, number={2}, journal={IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING}, author={Valdez-Jasso, Daniela and Haider, Mansoor A. and Banks, H. T. and Santana, Daniel Bia and German, Yanina Zocalo and Armentano, Ricardo L. and Olufsen, Mette S.}, year={2009}, month={Feb}, pages={210–219} }
 @article{banks_samuels_2009, title={Detection of arterial occlusions using viscoelastic wave propagation}, volume={1}, number={1}, journal={Advances in Applied Mathematics & Mechanics}, author={Banks, H. T. and Samuels, J. R.}, year={2009}, pages={1–28} }
 @article{banks_banks_joyner_2009, title={Estimation in time-delay modeling of insecticide-induced mortality}, volume={17}, ISSN={["1569-3945"]}, DOI={10.1515/JIIP.2009.012}, abstractNote={Abstract We present a mathematical and statistical computational framework for inverse problems involving delay or hysteretic differential equations. We demonstrate efficacy of the methodology in the context of models for insect maturation and mortality due to insecticide exposure.}, number={2}, journal={JOURNAL OF INVERSE AND ILL-POSED PROBLEMS}, author={Banks, H. T. and Banks, J. E. and Joyner, S. L.}, year={2009}, month={Mar}, pages={101–125} }
 @article{banks_davis_ernstberger_hu_artimovich_dhar_2009, title={Experimental design and estimation of growth rate distributions in size-structured shrimp populations}, volume={25}, ISSN={0266-5611 1361-6420}, url={http://dx.doi.org/10.1088/0266-5611/25/9/095003}, DOI={10.1088/0266-5611/25/9/095003}, abstractNote={We discuss inverse problem results for problems involving the estimation of probability distributions using aggregate data for growth in populations. We begin with a mathematical model describing variability in the early growth process of size-structured shrimp populations and discuss a computational methodology for the design of experiments to validate the model and estimate the growth-rate distributions in shrimp populations. Parameter-estimation findings using experimental data from experiments so designed for shrimp populations cultivated at Advanced BioNutrition Corporation are presented, illustrating the usefulness of mathematical and statistical modeling in understanding the uncertainty in the growth dynamics of such populations.}, number={9}, journal={Inverse Problems}, publisher={IOP Publishing}, author={Banks, H T and Davis, Jimena L and Ernstberger, Stacey L and Hu, Shuhua and Artimovich, Elena and Dhar, Arun K}, year={2009}, month={Aug}, pages={095003} }
 @book{banks_tran_2009, title={Mathematical and experimental modeling of physical and biological processes}, ISBN={9781420073379}, publisher={Boca Raton : CRC Press}, author={Banks, H. T. and Tran, H. T.}, year={2009} }
 @article{sutton_banks_castillo-chavez_2009, title={Public vaccination policy using an age-structured model of pneumococcal infection dynamics}, volume={4}, ISSN={1751-3758 1751-3766}, url={http://dx.doi.org/10.1080/17513750903023715}, DOI={10.1080/17513750903023715}, abstractNote={Public health professionals are charged with the task of designing prevention programs for the effective control of biologically intricate infectious diseases at a population level. The effective vaccination of a population for pneumococcal diseases (infections caused by Streptococcus pneumoniae) remains a relevant question in the scientific community. It is complicated by heterogeneity in individuals’ responses to exposure to the bacterium and their responses to vaccination. Due to these complexities, most modelling efforts in this area have been on the cellular/bacteria level. Here, we introduce an age-structured SEIS-type model of pneumococcal diseases and their vaccination. We discuss the use of this framework in predicting the impact of vaccine strategies, with pneumococcal diseases as an example. Using parameter values reasonable for a developed country, we discuss the effects of targeting the colonization and/or infection stages on the age profiles of morbidity in a population.}, number={2}, journal={Journal of Biological Dynamics}, publisher={Informa UK Limited}, author={Sutton, Karyn L. and Banks, H. T. and Castillo-Chavez, Carlos}, year={2009}, month={Jun}, pages={176–195} }
 @article{cintron-arias_castillo-chavez_bettencourt_lloyd_banks_2009, title={THE ESTIMATION OF THE EFFECTIVE REPRODUCTIVE NUMBER FROM DISEASE OUTBREAK DATA}, volume={6}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2009.6.261}, abstractNote={We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.}, number={2}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Cintron-Arias, Ariel and Castillo-Chavez, Carlos and Bettencourt, Luis M. A. and Lloyd, Alun L. and Banks, H. T.}, year={2009}, month={Apr}, pages={261–282} }
 @article{valdez-jasso_banks_haider_bia_zocalo_armentano_olufsen_2009, title={Viscoelastic models for passive arterial wall dynamics}, volume={1}, number={2}, journal={Advances in Applied Mathematics & Mechanics}, author={Valdez-Jasso, D. and Banks, H. T. and Haider, M. A. and Bia, D. and Zocalo, Y. and Armentano, R. L. and Olufsen, M. S.}, year={2009}, pages={151–165} }
 @article{banks_pedersen_2009, title={Well-posedness of inverse problems for systems with time dependent parameters}, volume={34}, number={1D}, journal={Arabian Journal for Science and Engineering}, author={Banks, H. T. and Pedersen, M.}, year={2009}, pages={39–58} }
 @misc{banks_2008, title={A brief review of some approaches to hysteresis in viscoelastic polymers}, volume={69}, ISSN={["1873-5215"]}, DOI={10.1016/j.na.2008.02.103}, abstractNote={We give a brief review of hysteresis in viscoelastic polymers. The efforts surveyed range from phenomenological to molecular modelling with applications involving recent efforts on elastomers to biotissue.}, number={3}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Banks, H. T.}, year={2008}, month={Aug}, pages={807–815} }
 @article{banks_hood_medhin_2008, title={A molecular based model for polymer viscoelasticity: Intra- and inter-molecular variability}, volume={32}, ISSN={["1872-8480"]}, DOI={10.1016/j.apm.2007.09.018}, abstractNote={We develop dynamic equations for rubber viscoelasticity based on a stick-slip continuum molecular-based model. The model developed is a continuum tube reptation model in which a chemically cross-linked (CC) system of molecules act as constraint box per unit volume for a physically constrained (PC) system of molecules. The CC-system carries along the PC-system during instantaneous step deformations. The subsequent relaxation of the PC-system is determined by the configuration of the CC-system, its own configuration and confirmation, and external force fields. Conversely, the deformation of the PC-system acts as an internal variable affecting the deformations of the constraining CC-system. We model the relationship between these processes to derive a model of viscoelasticity in rubber deformation. In developing a relaxation process for the PC-system, we start from the fact that the PC-system is composed of long molecular chains. The dynamics of these molecular chains are developed by modelling them as chains of beads connected by springs, which represent inter-molecular potentials. Various segments of the molecular chains relax at different rates. In addition, variability in relaxation times across molecular chains is permitted.}, number={12}, journal={APPLIED MATHEMATICAL MODELLING}, author={Banks, H. T. and Hood, J. B. and Medhin, N. G.}, year={2008}, month={Dec}, pages={2753–2767} }
 @article{banks_hood_medhin_samuels_2008, title={A stick-slip/Rouse hybrid model for viscoelasticity in polymers}, volume={9}, ISSN={["1468-1218"]}, DOI={10.1016/j.nonrwa.2007.06.015}, abstractNote={A Rouse model for polymer chains is incorporated into the linear continuous stick-slip molecular-based tube reptation ideas of Doi–Edwards and Johnson–Stacer. This treats the physically constrained (PC) molecular stretches as internal strain variables for the overall PC/chemically cross-linked (CC) system. It yields an explicit system of stress–strain equations for the system permitting simple calculations of complex stress–strain relations. The model that is developed here treats PC molecule as entrapped within a constraining tube, which is comprised of both CC and PC molecules. The model is compared with experimental data sets from the literature.}, number={5}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, H. T. and Hood, J. B. and Medhin, N. G. and Samuels, J. S., Jr.}, year={2008}, month={Dec}, pages={2128–2149} }
 @article{banks_banks_joyner_stark_2008, title={Dynamic models for insect mortality due to exposure to insecticides}, volume={48}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2007.10.005}, abstractNote={Ordinary differential equation models for insecticide induced sublethal damage and delayed death in insect populations are considered. It is shown that such models with time-varying mortality rates provide excellent fits to experimental data for populations subjected to numerous levels of insecticide exposure. The effects on fecundity rates are also examined.}, number={1-2}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Banks, John E. and Joyner, Sarah Lynn and Stark, John D.}, year={2008}, month={Jul}, pages={316–332} }
 @article{sutton_banks_castillo-chavez_2008, title={Estimation of invasive pneumococcal disease dynamics parameters and the impact of conjugate vaccination in Australia}, volume={5}, DOI={10.3934/mbe.2008.5.175}, abstractNote={Pneumococcal diseases, or infections from the etiological agent Streptococcus pneumoniae, have long been a major cause of morbidity and mortality worldwide. Recent advances in the development of vaccines for these infections have raised questions concerning their widespread and/or long-term use. In this work, we use surveillance data collected by the Australian National Notifiable Diseases Surveillance system to estimate parameters in a mathematical model of pneumococcal infection dynamics in a population with partial vaccination. The parameters obtained are of particular interest as they are not typically available in reported literature or measurable. The calibrated model is then used to assess the impact of the recent federally funded program that provides pneumococcal vaccines to large risk groups. The results presented here suggest the state of these infections may be changing in response to the programs, and warrants close quantitative monitoring.}, number={1}, journal={Mathematical Biosciences and Engineering}, author={Sutton, K. L. and Banks, H. T. and Castillo-Chavez, C.}, year={2008}, pages={175–204} }
 @article{banks_medhin_pinter_2008, title={Modeling of viscoelastic shear: A nonlinear stick-slip formulation}, volume={17}, number={2}, journal={Dynamic Systems and Applications}, author={Banks, H. T. and Medhin, N. G. and Pinter, G. A.}, year={2008}, pages={383–405} }
 @article{banks_davidian_hu_kepler_rosenberg_2008, title={Modelling HIV immune response and validation with clinical data}, volume={2}, ISSN={1751-3758 1751-3766}, url={http://dx.doi.org/10.1080/17513750701813184}, DOI={10.1080/17513750701813184}, abstractNote={A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain features that have been shown to be important by recent experimental research are incorporated in the model. These include the role of CD4+memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. We show that this more biologically detailed model can exhibit the phenomenon of transient viremia experienced by some patients on therapy with viral load levels suppressed below the detection limit. We also show that the loss of CD4+T-cell help in the generation of CD8+memory cells leads to larger peak values for the viral load during transient viremia. Censored clinical data is used to obtain parameter estimates. We demonstrate that using a reduced set of 16 free parameters, obtained by fixing some parameters at their population averages, the model provides reasonable fits to the patient data and, moreover, that it exhibits good predictive capability. We further show that parameter values obtained for most clinical patients do not admit multiple locally a.s off-treatment equilibria. This suggests that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower (or zero) viral load is not possible for these patients.}, number={4}, journal={Journal of Biological Dynamics}, publisher={Informa UK Limited}, author={Banks, H. T. and Davidian, M. and Hu, Shuhua and Kepler, Grace M. and Rosenberg, E. S.}, year={2008}, month={Oct}, pages={357–385} }
 @article{banks_luke_2008, title={Modelling of propagating shear waves in biotissue employing an internal variable approach to dissipation}, volume={3}, number={3}, journal={Communications in Computational Physics}, author={Banks, H. T. and Luke, N. S.}, year={2008}, pages={603–640} }
 @article{banks_davis_2008, title={QUANTIFYING UNCERTAINTY IN THE ESTIMATION OF PROBABILITY DISTRIBUTIONS}, volume={5}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2008.5.647}, abstractNote={We consider ordinary least squares parameter estimation problems where the unknown parameters to be estimated are probability distributions. A computational framework for quantification of uncertainty (e.g., standard errors) associated with the estimated parameters is given and sample numerical findings are presented.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Davis, Jimena L.}, year={2008}, month={Oct}, pages={647–667} }
 @article{banks_karr_nguyen_samuels_2008, title={Sensitivity to noise variance in a social network dynamics model}, volume={66}, ISSN={["1552-4485"]}, DOI={10.1090/S0033-569X-08-01124-0}, abstractNote={Abstract : The dynamics of social networks are modeled with a system of continuous Stochastic Ordinary Differential Equations (SODE). With the proper amount of noise input, the SODE model captures dynamic features that are lacking in the corresponding deterministic ODE model. Therefore, sensitivity to noise levels is investigated by considering four different regimes: essentially deterministic, noise-enriched, noise-enlarged, and noise-dominated. Each regime is defined based on the behavior of solutions of the SODE, and the geometry of the regimes is categorized with stochastic simulations.}, number={2}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Karr, A. F. and Nguyen, H. K. and Samuels, J. R., Jr.}, year={2008}, pages={233–247} }
 @article{banks_dick_banks_stark_2008, title={Time-varying vital rates in ecotoxicology: Selective pesticides and aphid population dynamics}, volume={210}, ISSN={["0304-3800"]}, DOI={10.1016/j.ecolmodel.2007.07.022}, abstractNote={Population dynamics models are useful predictive tools in applied ecology, and especially toxicological risk assessment. Many models that are useful for capturing deterministic constant-parameter dynamics are inadequate for dealing with temporally variable life history parameter values typical of many anthropogenic disturbances, including those associated with toxicological insults. Using aphid-insecticide population data as an example, here we show that constant-parameter versions of commonly used population dynamics models (a matrix model and a simple differential equation model) do not adequately capture the population dynamics of aphids subjected to a selective pesticide. However, a simple modification of the differential equation model with time-varying mortality rates provides a highly accurate fit to aphid population data. Our results suggest that variable coefficient differential equation models with time-dependent parameters provide an accurate and simple means of assessing the effects of disturbances on populations in cases where the effects of disturbance vary significantly through time. We suggest that this approach has potential for a wide range of ecological applications.}, number={1-2}, journal={ECOLOGICAL MODELLING}, author={Banks, J. E. and Dick, L. K. and Banks, H. T. and Stark, J. D.}, year={2008}, month={Jan}, pages={155–160} }
 @article{banks_davis_2007, title={A comparison of approximation methods for the estimation of probability distributions on parameters}, volume={57}, ISSN={["1873-5460"]}, DOI={10.1016/j.apnum.2006.07.016}, abstractNote={In this paper, we compare two computationally efficient approximation methods for the estimation of growth rate distributions in size-structured population models. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Furthermore, we compare the results from a spline based approximation method and a delta function based approximation method for the inverse problem involving the estimation of the distributions of growth rates in size-structured mosquitofish populations. Convergence as well as sensitivity of the estimates with respect to noise in the data are discussed for both approximation methods.}, number={5-7}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Banks, H. T. and Davis, Jimena L.}, year={2007}, pages={753–777} }
 @article{kepler_nguyen_webster-cyriaque_banks_2007, title={A dynamic model for induced reactivation of latent virus}, volume={244}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2006.08.020}, abstractNote={We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms.}, number={3}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Kepler, G. M. and Nguyen, H. K. and Webster-Cyriaque, J. and Banks, H. T.}, year={2007}, month={Feb}, pages={451–462} }
 @article{adams_banks_davidian_rosenberg_2007, title={Estimation and prediction with HIV-treatment interruption data}, volume={69}, ISSN={["0092-8240"]}, DOI={10.1007/s11538-006-9140-6}, abstractNote={We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.}, number={2}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Adams, B. M. and Banks, H. T. and Davidian, M. and Rosenberg, E. S.}, year={2007}, month={Feb}, pages={563–584} }
 @article{banks_banks_dick_stark_2007, title={Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides}, volume={69}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-007-9207-z}, abstractNote={With newer, more environmentally friendly and, subsequently less lethal, pesticides in use, evaluating efficacy of a pesticide now requires more than simply counting deaths after treatment. A discrete, age-structured matrix model that incorporates a species' life history traits (such as birth rate, death rate and fecundity) has previously been used by ecologists. This model will be presented and discussed along with an alternative continuous, age-structured model which offers significant advantage in considering sublethal damage. We use this continuous model to estimate time-dependent mortality parameters in an ordinary least-squares technique. Confidence intervals are given and results from tests for statistical significance of added parameters are presented.}, number={7}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Banks, H. T. and Banks, John E. and Dick, Lara K. and Stark, John D.}, year={2007}, month={Oct}, pages={2139–2180} }
 @article{banks_bokil_hu_2007, title={Monotone approximation for a nonlinear size and class age structured epidemic model}, volume={8}, ISSN={["1468-1218"]}, DOI={10.1016/j.nonrwa.2006.03.008}, abstractNote={In this paper, we study a nonautonomous size and class age structured epidemic model with nonlinear and nonlocal boundary conditions. We establish a comparison principle and construct convergent monotone sequences to prove the existence of solutions. Uniqueness of solutions is also established.}, number={3}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, H. T. and Bokil, V. A. and Hu, Shuhua}, year={2007}, month={Jul}, pages={834–852} }
 @article{banks_medhin_pinter_2007, title={Multiscale Considerations in Modeling of Nonlinear Elastomers}, volume={8}, ISSN={1550-2287 1550-2295}, url={http://dx.doi.org/10.1080/15502280601149346}, DOI={10.1080/15502280601149346}, abstractNote={We present a survey of results from an extended project focused on the understanding of the dynamic behavior of elastomers or filled rubbers. This entailed experimental, modeling, computational and theoretical efforts. Of particular emphasis are the nonlinear and hysteretic aspects of dynamic deformations.}, number={2}, journal={International Journal for Computational Methods in Engineering Science and Mechanics}, publisher={Informa UK Limited}, author={Banks, H. T. and Medhin, Negash G. and Pinter, Gabriella A.}, year={2007}, month={Feb}, pages={53–62} }
 @article{banks_lewis_tran_2007, title={Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach}, volume={37}, ISSN={["1573-2894"]}, DOI={10.1007/s10589-007-9015-2}, abstractNote={State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design and synthesis methods of nonlinear feedback controllers and estimators for a broad class of nonlinear regulator problems. In essence, the SDRE approach involves mimicking standard linear quadratic regulator (LQR) formulation for linear systems. In particular, the technique consists of using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficient matrices. Theoretical advances have been made regarding the nonlinear regulator problem and the asymptotic stability properties of the system with full state feedback. However, there have not been any attempts at the theory regarding the asymptotic convergence of the estimator and the compensated system. This paper addresses these two issues as well as discussing numerical methods for approximating the solution to the SDRE. The Taylor series numerical methods works only for a certain class of systems, namely with constant control coefficient matrices, and only in small regions. The interpolation numerical method can be applied globally to a much larger class of systems. Examples will be provided to illustrate the effectiveness and potential of the SDRE technique for the design of nonlinear compensator-based feedback controllers.}, number={2}, journal={COMPUTATIONAL OPTIMIZATION AND APPLICATIONS}, author={Banks, H. T. and Lewis, B. M. and Tran, H. T.}, year={2007}, month={Jun}, pages={177–218} }
 @article{banks_dediu_nguyen_2007, title={Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space}, volume={4}, DOI={10.3934/mbe.2007.4.403}, abstractNote={We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.}, number={3}, journal={Mathematical Biosciences and Engineering}, author={Banks, H. T. and Dediu, S. and Nguyen, H. K.}, year={2007}, pages={403–430} }
 @article{bai_banks_dediu_govan_last_lloyd_nguyen_olufsen_rempala_slenning_2007, title={Stochastic and deterministic models for agricultural production networks}, volume={4}, url={https://publons.com/publon/12886434/}, DOI={10.3934/mbe.2007.4.373}, abstractNote={An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.}, number={3}, journal={Mathematical Biosciences and Engineering}, author={Bai, P. and Banks, H. T. and Dediu, S. and Govan, A. Y. and Last, M. and Lloyd, Alun and Nguyen, H. K. and Olufsen, M. S. and Rempala, G. and Slenning, B. D.}, year={2007}, pages={373–402} }
 @article{banks_dediu_nguyen_2007, title={Time delay systems with distribution dependent dynamics}, volume={31}, ISSN={["1367-5788"]}, DOI={10.1016/j.arcontrol.2007.02.002}, abstractNote={General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measures for computational purposes is surveyed.}, number={1}, journal={ANNUAL REVIEWS IN CONTROL}, author={Banks, H. T. and Dediu, Sava and Nguyen, Hoan K.}, year={2007}, pages={17–26} }
 @article{rosenberg_davidian_banks_2007, title={Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection}, volume={88}, ISSN={["1879-0046"]}, DOI={10.1016/j.drugalcdep.2006.12.024}, abstractNote={The goal of this article is to suggest that mathematical models describing biological processes taking place within a patient over time can be used to design adaptive treatment strategies. We demonstrate using the key example of treatment strategies for human immunodeficiency virus type-1 (HIV) infection. Although there has been considerable progress in management of HIV infection using highly active antiretroviral therapies, continuous treatment with these agents involves significant cost and burden, toxicities, development of drug resistance, and problems with adherence; these latter complications are of particular concern in substance-abusing individuals. This has inspired interest in structured or supervised treatment interruption (STI) strategies, which involve cycles of treatment withdrawal and re-initiation. We argue that the most promising STI strategies are adaptive treatment strategies. We then describe how biological mechanisms governing the interaction over time between HIV and a patient's immune system may be represented by mathematical models and how control methods applied to these models can be used to design adaptive STI strategies seeking to maintain long-term suppression of the virus. We advocate that, when such mathematical representations of processes underlying a disease or disorder are available, they can be an important tool for suggesting adaptive treatment strategies for clinical study.}, journal={DRUG AND ALCOHOL DEPENDENCE}, author={Rosenberg, Eric S. and Davidian, Marie and Banks, H. Thomas}, year={2007}, month={May}, pages={S41–S51} }
 @article{banks_luke_samuels_2007, title={Viscoelasticity in polymers: Phenomenological to molecular mathematical modeling}, volume={23}, ISSN={["1098-2426"]}, DOI={10.1002/num.20250}, abstractNote={Abstract}, number={4}, journal={NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS}, author={Banks, H. T. and Luke, N. S. and Samuels, J. R., Jr.}, year={2007}, month={Jul}, pages={817–831} }
 @article{banks_kwon_toivanen_tran_2006, title={A state-dependent Riccati equation-based estimator approach for HIV feedback control}, volume={27}, ISSN={["1099-1514"]}, DOI={10.1002/oca.773}, abstractNote={Abstract}, number={2}, journal={OPTIMAL CONTROL APPLICATIONS & METHODS}, author={Banks, HT and Kwon, HD and Toivanen, JA and Tran, HT}, year={2006}, pages={93–121} }
 @article{banks_ito_toivanen_2006, title={Determination of interrogating frequencies to maximize electromagnetic backscatter from objects with material coatings}, volume={1}, number={2}, journal={Communications in Computational Physics}, author={Banks, H. T. and Ito, K. and Toivanen, J.}, year={2006}, pages={362–382} }
 @article{banks_gibson_2006, title={Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters}, volume={64}, ISSN={["1552-4485"]}, DOI={10.1090/S0033-569X-06-01036-X}, abstractNote={Abstract : We consider electromagnetic interrogation problems for complex materials involving distributions of polarization mechanisms and also distributions for the parameters in these mechanisms. a theoretical and computational framework for such problems is given. Computational results for specific problems with multiple Debye mechanisms are given in the case of discrete, uniform, log-normal, and log-Bi-Gaussian distributions.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Gibson, N. L.}, year={2006}, month={Dec}, pages={749–795} }
 @article{banks_bokil_cioranescu_gibson_griso_miara_2006, title={Homogenization of periodically varying coefficients in electromagnetic materials}, volume={28}, ISSN={["1573-7691"]}, DOI={10.1007/s10915-006-9091-y}, abstractNote={In this paper, we employ the periodic unfolding method for simulating the electromagnetic field in a composite material exhibiting heterogeneous microstructures which are described by spatially periodic parameters. We consider cell problems to calculate the effective parameters for a Debye dielectric medium in the case of a circular microstructure in two dimensions. We assume that the composite materials are quasi-static in nature, i.e., the wavelength of the electromagnetic field is much larger than the relevant dimensions of the microstructure.}, number={2-3}, journal={JOURNAL OF SCIENTIFIC COMPUTING}, author={Banks, H. T. and Bokil, V. A. and Cioranescu, D. and Gibson, N. L. and Griso, G. and Miara, B.}, year={2006}, month={Sep}, pages={191–221} }
 @article{banks_ito_kepler_toivanen_2006, title={Material surface design to counter electromagnetic interrogation of targets}, volume={66}, ISSN={["1095-712X"]}, DOI={10.1137/040621430}, abstractNote={Utilization of controllable ferromagnetic layers coating a conducting object to provide an attenuation capability against electromagnetic interrogation is discussed. The problem is formulated as a differential game and/or a robust optimization. The scattered field due to interrogation can be attenuated with the assumption of an uncertainty in the interrogation wave numbers. The controllable layer composed of ferromagnetic materials [H. How and C. Vittoria, Implementation of Microwave Active Nulling, private communication; H. How and C. Vittoria, IEEE Trans. Microwave Theory Tech., 52 (2004), pp. 2177-2182] is incorporated in a mathematical formulation based on the time-harmonic Maxwell equation. Fresnel's law for the reflectance index is extended to the electromagnetic propagation in anisotropic composite layers of ferromagnetic and electronic devices and is used to demonstrate feasibility of control of reflections. Our methodology is also tested for a nonplanar geometry of the conducting object (an NACA ...}, number={3}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Banks, HT and Ito, K and Kepler, GM and Toivanen, JA}, year={2006}, pages={1027–1049} }
 @article{banks_nguyen_2006, title={Sensitivity of dynamical systems to Banach space parameters}, volume={323}, ISSN={["0022-247X"]}, DOI={10.1016/j.jmaa.2005.09.084}, abstractNote={We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is presented.}, number={1}, journal={JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, author={Banks, H. T. and Nguyen, Hoan K.}, year={2006}, month={Nov}, pages={146–161} }
 @article{banks_gibson_2006, title={Void detection in foam with knit lines using THz pulse interrogation}, volume={44}, ISSN={["0895-7177"]}, DOI={10.1016/j.mcm.2006.02.014}, abstractNote={We model the electromagnetic interrogation of a polyurethane foam using the transverse electric (TE) mode of the two-dimensional (2D) Maxwell’s equations reduced to the wave equation for a fixed frequency in the terahertz (THz) regime. The foam block target contains knit lines which are modeled by modifying the speed of propagation, i.e., by altering the index of refraction. We describe our efforts to estimate the dielectric constant in the knit lines, as well as in the surrounding foam, by use of the classical Clausius–Mossotti equation, assuming only a change in density. We compare the numerical simulations accounting for knit lines to those in which knit lines are neglected, each in the context of modeling reflections of plane waves in foam with voids.}, number={9-10}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Gibson, N. L.}, year={2006}, month={Nov}, pages={807–815} }
 @article{banks_bokil_2005, title={A computational and statistical framework for multidimensional domain acoustooptic material interrogation}, volume={63}, ISSN={["0033-569X"]}, DOI={10.1090/S0033-569X-05-00949-0}, abstractNote={Abstract : We consider an electromagnetic interrogation technique in two and three dimensions for identifying the dielectric parameters (including the permittivity, the conductivity and the relaxation time) of a Debye medium. In this technique a travelling acoustic pressure wave in the Debye medium is used as a virtual reflector for an interrogating microwave electromagnetic pulse that is generated in free space. The reflections of the microwave pulse from the air-Debye interface and from the acoustic pressure wave are recorded at a remote antenna. the data is used in an inverse problem to estimate the locally pressure dependent dielectric parameters of the Debye medium. We present a time domain formulation that is solved using finite differences (FDTD) in time and in space. Perfectly matched layer (PML) absorbing boundary conditions are used to absorb outgoing waves at the finite boundaries of the computational domain, preventing spurious reflections from reentering the domain. Using the method of least squares for the parameter identification problem, we compare two different algorithms (the gradient based Levenberg-Marquardt method, and the gradient free, simplex based Nelder-Mead method) in solving an inverse problem to calculate estimates for two or more dielectric parameters. Finally we use statistical error analysis to construct confidence intervals for all the presented estimates, thereby providing a probabilistic statement about the computational procedure with uncertainty aspects of estimates.}, number={1}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, HT and Bokil, VA}, year={2005}, month={Mar}, pages={156–200} }
 @article{banks_grove_hu_ma_2005, title={A hierarchical Bayesian approach for parameter estimation in HIV models}, volume={21}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/21/6/001}, abstractNote={A hierarchical Bayesian approach is developed to estimate parameters at both the individual and the population levels in a HIV model, with the implementation carried out by Markov Chain Monte Carlo (MCMC) techniques. Sample numerical simulations and statistical results are provided to demonstrate the feasibility of this approach.}, number={6}, journal={INVERSE PROBLEMS}, author={Banks, HT and Grove, S and Hu, S and Ma, YY}, year={2005}, month={Dec}, pages={1803–1822} }
 @article{banks_bortz_2005, title={A parameter sensitivity methodology in the context of HIV delay equation models}, volume={50}, ISSN={["1432-1416"]}, DOI={10.1007/s00285-004-0299-x}, abstractNote={A sensitivity methodology for nonlinear delay systems arising in one class of cellular HIV infection models is presented. Theoretical foundations for a typical sensitivity investigation and illustrative computations are given.}, number={6}, journal={JOURNAL OF MATHEMATICAL BIOLOGY}, author={Banks, HT and Bortz, DM}, year={2005}, month={Jun}, pages={607–625} }
 @article{banks_pinter_2005, title={A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue}, volume={3}, ISSN={["1540-3467"]}, DOI={10.1137/040603693}, abstractNote={Motivated by a problem involving wave propagation through viscoelastic biotissue, we present a theoretical framework for treating hysteresis as multiscale phenomena which must be averaged across distributions of internal variables. The resulting systems entail probability measure-dependent partial differential equations for which we establish well-posedness in a framework that leads readily to computationally useful approximations.}, number={2}, journal={MULTISCALE MODELING & SIMULATION}, author={Banks, HT and Pinter, GA}, year={2005}, pages={395–412} }
 @article{banks_gibson_winfree_2005, title={Gap detection with electromagnetic terahertz signals}, volume={6}, ISSN={["1468-1218"]}, DOI={10.1016/j.nonrwa.2004.09.004}, abstractNote={We apply an inverse problem formulation to determine characteristics of a defect from a perturbed electromagnetic interrogating signal. A defect (gap) inside of a dielectric material causes a disruption, via reflections and refractions at the material interfaces, of the windowed interrogating signal. We model the electromagnetic waves inside the material with Maxwell's equations. This leads to a non-standard, nonlinear optimization problem for the dimensions and location of the defect. Using simulations as forward solves, we employ a Newton-based, iterative optimization scheme to a novel modified least-squares objective function. Numerical results are given in tables and plots, standard errors are calculated, and computational issues are addressed.}, number={2}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, HT and Gibson, NL and Winfree, WP}, year={2005}, month={Apr}, pages={381–416} }
 @article{adams_banks_davidian_kwon_tran_wynne_rosenberg_2005, title={HIV dynamics: Modeling, data analysis, and optimal treatment protocols}, volume={184}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2005.02.004}, abstractNote={We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ideas relevant to Structured Treatment Interruptions (STI). Among these are model development and validation procedures including parameter estimation, data reduction and representation, and optimal control relative to STI. Results from initial attempts in each of these areas by an interdisciplinary team of applied mathematicians, statisticians and clinicians are presented.}, number={1}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Adams, BM and Banks, HT and Davidian, M and Kwon, HD and Tran, HT and Wynne, SN and Rosenberg, ES}, year={2005}, month={Dec}, pages={10–49} }
 @article{ackleh_banks_deng_hu_2005, title={Parameter estimation in a coupled system of nonlinear size-structured populations}, volume={2}, DOI={10.3934/mbe.2005.2.289}, abstractNote={A least squares technique is developed for identifying unknown parameters in a coupled system of nonlinear size-structured populations. Convergence results for the parameter estimation technique are established. Ample numerical simulations and statistical evidence are provided to demonstrate the feasibility of this approach.}, number={2}, journal={Mathematical Biosciences and Engineering}, author={Ackleh, A. S. and Banks, H. T. and Deng, K. and Hu, S. H.}, year={2005}, pages={289–315} }
 @article{adams_banks_banks_stark_2005, title={Population dynamics models in plant-insect herbivore-pesticide interactions}, volume={196}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2004.09.001}, abstractNote={We consider several population dynamics models in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). We carry out parameter estimation computations along with statistical analysis to compare autonomous versus non-autonomous model dynamics. We conclude with a brief discussion of some not-so-subtle pitfalls that can arise when using quantitative measures of model fit-to-data to make biological inferences as well as offer a positive example of how one might combine a priori biological hypothesis and intuition with rather sophisticated (from a field biology viewpoint) mathematical methodologies to suggest synergisms.}, number={1}, journal={MATHEMATICAL BIOSCIENCES}, author={Adams, BM and Banks, HT and Banks, JE and Stark, JD}, year={2005}, month={Jul}, pages={39–64} }
 @article{banks_browning_2005, title={Time domain electromagnetic scattering using finite elements and perfectly matched layers}, volume={194}, ISSN={["0045-7825"]}, DOI={10.1016/j.cma.2004.06.013}, abstractNote={We consider a model for the interrogation of a planar Debye medium by a non-harmonic microwave pulse from an antenna source in free space, and we compute the reflected solution using finite elements in the spatial variables and finite differences in the time variable. Perfectly matched layers (PMLs) and an absorbing boundary condition are used to damp waves interacting with artificial boundaries imposed to allow finite computational domains. We present simulation results showing that numerical reflections from interfaces at PML boundaries can be controlled.}, number={2-5}, journal={COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, author={Banks, HT and Browning, BL}, year={2005}, pages={149–168} }
 @article{banks_gibson_2005, title={Well-posedness in Maxwell systems with distributions of polarization relaxation parameters}, volume={18}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2004.02.008}, abstractNote={We present existence, uniqueness and continuous dependence (with respect to probability distributions on polarization parameters) of solutions in Maxwell systems. This provides a theoretical and computational foundation for associated inverse problems.}, number={4}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, HT and Gibson, NL}, year={2005}, month={Apr}, pages={423–430} }
 @article{banks_potter_2005, title={Well-posedness results for a class of toxicokinetic models}, volume={14}, number={2}, journal={Dynamic Systems and Applications}, author={Banks, H. T. and Potter, L. K.}, year={2005}, pages={297–322} }
 @article{adams_banks_kwon_tran_2004, title={Dynamic multidrug therapies for HIV: Optimal and STI control approaches}, volume={1}, DOI={10.3934/mbe.2004.1.223}, abstractNote={We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug "cocktail " therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) in hibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI)in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.}, number={2}, journal={Mathematical Biosciences and Engineering}, author={Adams, B. M. and Banks, H. T. and Kwon, H. D. and Tran, Hien}, year={2004}, pages={223–241} }
 @article{banks_pinter_2004, title={High-frequency pulse propagation in nonlinear dielectric materials}, volume={5}, ISSN={["1468-1218"]}, DOI={10.1016/j.nonrwa.2003.10.002}, abstractNote={Abstract We consider a variational formulation based on Maxwell's equations for the propagation of high-frequency (gigahertz to terahertz) ultrashort input pulses in dielectric materials modeled by a linear Debye medium. We demonstrate computationally the emergence of Brillouin precursors in the material (water) and the fact that the peak of this transient is attenuated at a much slower rate than is the carrier frequency. In the 0.1– 1 THz regime the carrier frequency does not propagate in our calculations. Only the precursors enter the material, and this is in line with experiments reported by Pleshko and Palocz (Phys. Rev. Lett. 22 (1969) 1201). We also implement models that include nonlinearly forced Debye and nonlinear Debye polarization dynamics and demonstrate the importance of nonlinear effects, especially when the amplitude of the input signal is large. This is an important step in understanding high-frequency pulse propagation, and it has potential applications in the assessment of safety standards and in extending current imaging capabilities in both civilian and military uses.}, number={4}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, HT and Pinter, GA}, year={2004}, month={Sep}, pages={597–612} }
 @article{banks_cole_schlosser_tran_2004, title={Modeling and optimal regulation of erythropoiesis subject to benzene intoxication}, volume={1}, ISSN={["1547-1063"]}, DOI={10.3934/mbe.2004.1.15}, abstractNote={Benzene (C(6)H(6)) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans subjected to low exposures are uncertain. The exposure-dose- response relationship of benzene in humans is expected to be nonlinear because benzene undergoes a series of metabolic transformations, detoxifying and activating, resulting in various metabolites that exert toxic effects on the bone marrow. Since benzene is a known human leukemogen, the toxicity of benzene in the bone marrow is of most importance. And because blood cells are produced in the bone marrow, we investigated the effects of benzene on hematopoiesis (blood cell production and development). An age-structured model was used to examine the process of erythropoiesis, the development of red blood cells. This investigation proved the existence and uniqueness of the solution of the system of coupled partial and ordinary differential equations. In addition, we formulated an optimal control problem for the control of erythropoiesis and performed numerical simulations to compare the performance of the optimal feedback law and another feedback function based on the Hill function.}, number={1}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, HT and Cole, CE and Schlosser, PM and Tran, HT}, year={2004}, month={Jun}, pages={15–48} }
 @article{banks_medhin_pinter_2004, title={Nonlinear reptation in molecular based hysteresis models for polymers}, volume={62}, ISSN={["1552-4485"]}, DOI={10.1090/qam/2104273}, abstractNote={We extend the linear “stick-slip” models of Doi-Edwards and Johnson-Stacer to nonlinear tube reptation models. We then show that such models, when combined with probabilistic formulations allowing distributions of relaxation times, provide a good description of dynamic experiments with highly filled rubber in tensile deformations. A connection to other applications including dielectric polarization and reptation in other viscoelastic materials (e.g., living tissue) is noted.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, HT and Medhin, NG and Pinter, GA}, year={2004}, month={Dec}, pages={767–779} }
 @article{banks_potter_2004, title={Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model}, volume={192}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2004.11.008}, abstractNote={Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.}, number={2}, journal={MATHEMATICAL BIOSCIENCES}, author={Banks, HT and Potter, LK}, year={2004}, month={Dec}, pages={193–225} }
 @article{banks_raye_2004, title={Well-posedness for a nonsmooth acoustic system}, volume={17}, DOI={10.1016/S0893-9659(04)00013-8}, number={3}, journal={Applied Mathematics Letters}, author={Banks, H. T. and Raye, J. K.}, year={2004}, pages={317–322} }
 @article{banks_raye_2004, title={Well-posedness for a nonsmooth acoustic system}, volume={17}, ISSN={0893-9659}, url={http://dx.doi.org/10.1016/S0893-9659(04)90069-9}, DOI={10.1016/S0893-9659(04)90069-9}, abstractNote={We consider an acoustic wave system with discontinuous coefficients and nonsmooth inputs. Existence, uniqueness, and continuous dependence on input data of weak solutions are established.}, number={3}, journal={Applied Mathematics Letters}, publisher={Elsevier BV}, author={Banks, H.T and Raye, J.K}, year={2004}, month={Mar}, pages={317–322} }
 @article{banks_furati_ito_luke_smith_2003, title={Acoustic attenuation employing variable wall admittance}, number={2003}, journal={Directions in mathematical systems theory and optimization  (Lecture notes in control and information sciences; 286)}, publisher={New York: Springer}, author={Banks, H. T. and Furati, K. M. and Ito, K. and Luke, N. S. and Smith, C. J.}, editor={A. Rantzer, C. I. ByrnesEditor}, year={2003}, pages={15–26} }
 @book{banks_castillo-chavez_2003, title={Bioterrorism: Mathematical modeling applications in homeland security}, ISBN={0898715490}, publisher={Philadelphia, PA: Society for Industrial and Applied Mathematics}, author={Banks, H. T. and Castillo-Chavez, C.}, year={2003} }
 @article{banks_bortz_holte_2003, title={Incorporation of variability into the modeling of viral delays in HIV infection dynamics}, volume={183}, ISSN={["1879-3134"]}, DOI={10.1016/S0025-5564(02)00218-3}, abstractNote={We consider classes of functional differential equation models which arise in attempts to describe temporal delays in HIV pathogenesis. In particular, we develop methods for incorporating arbitrary variability (i.e., general probability distributions) for these delays into systems that cannot readily be reduced to a finite number of coupled ordinary differential equations (as is done in the method of stages). We discuss modeling from first principles, introduce several classes of non-linear models (including discrete and distributed delays) and present a discussion of theoretical and computational approaches. We then use the resulting methodology to carry out simulations and perform parameter estimation calculations, fitting the models to a set of experimental data. Results obtained confirm the statistical significance of the presence of delays and the importance of including delays in validating mathematical models with experimental data. We also show that the models are quite sensitive to the mean of the distribution which describes the delay in viral production, whereas the variance of this distribution has relatively little impact.}, number={1}, journal={MATHEMATICAL BIOSCIENCES}, author={Banks, HT and Bortz, DM and Holte, SE}, year={2003}, month={May}, pages={63–91} }
 @article{banks_pinter_2003, title={Maxwell-systems with nonlinear polarization}, volume={4}, ISSN={["1468-1218"]}, DOI={10.1016/S1468-1218(02)00074-3}, abstractNote={We establish well-posedness results for a model describing the propagation of high-intensity electromagnetic waves in a nonlinear medium. The nonlinear material properties are represented by a nonlinear polarization in the form of a convolution. We also include some remarks on potential applications.}, number={3}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, HT and Pinter, GA}, year={2003}, month={Sep}, pages={483–501} }
 @article{banks_cole_furati_ito_pinter_2002, title={A computational model for sound field absorption by acoustic arrays}, volume={13}, DOI={10.1106/104538902028631}, number={4}, journal={Journal of Intelligent Material Systems and Structures}, author={Banks, H. T. and Cole, D. G. and Furati, K. M. and Ito, K. and Pinter, G. A.}, year={2002}, pages={231–240} }
 @article{ackleh_banks_deng_2002, title={A finite difference approximation for a coupled system of nonlinear size-structured populations}, volume={50}, ISSN={["1873-5215"]}, DOI={10.1016/S0362-546X(01)00780-5}, abstractNote={Production of red blood cells involves growth-factor mediated regulation of erythroid progenitor apoptosis and self-renewal. During severe anemia, characterized by a strong fall of the hematocrit followed by a recovery phase, these controls allow a fast recovery of the hematocrit and survival of the organism. Using a mathematical model of stress erythropoiesis and an ad hoc numerical method, we investigate the respective roles of anemia-inducing phenylhydrazine injections and physiological regulation on the organism’s recovery. By explicitly modeling the experimental protocol, we show that it mostly characterizes the fall of the hematocrit following the anemia and its severeness, while physiological process regulation mainly controls the recovery. We confront our model and our conclusions to similar experiments inducing anemia and show the model’s ability to reproduce several protocols of phenylhydrazine-induced anemia. In particular, we establish a link between phenylhydrazine effect and the severeness of the anemia.}, number={6}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Ackleh, AS and Banks, HT and Deng, K}, year={2002}, month={Sep}, pages={727–748} }
 @article{ackleh_banks_pinter_2002, title={A nonlinear beam equation}, volume={15}, ISSN={["0893-9659"]}, DOI={10.1016/S0893-9659(01)00147-1}, abstractNote={The existence and uniqueness of weak solutions to a nonlinear beam equation are established under relaxed assumptions (locally Lipschitz plus affine domination) on the nonlinearity in the stiffness constitutive law. The results provide alternatives to previous theories requiring rather stringent monotonicity assumptions. The techniques and arguments are applicable to a large class of nonlinear second-order (in time) partial differential equation systems.}, number={3}, journal={APPLIED MATHEMATICS LETTERS}, author={Ackleh, AS and Banks, HT and Pinter, GA}, year={2002}, month={Apr}, pages={381–387} }
 @article{banks_pinter_yeoh_2002, title={Analysis of bonded elastic blocks}, volume={36}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(02)00234-0}, abstractNote={We investigate the compression of rubber blocks bonded to rigid metal plates for several different geometries, namely, for rectangular and V-shaped blocks. We obtain reasonably simple solutions in series form relating the force and the displacement using the “pressure method” developed by Gent [1–3]. Our initial assumption concerning the incompressibility of the rubber is subsequently relaxed to “near incompressibility” to yield more accurate solutions. We demonstrate a very good agreement between the theoretical solutions and the results of linear finite element simulations.}, number={7-8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Pinter, GA and Yeoh, OH}, year={2002}, month={Nov}, pages={875–888} }
 @article{banks_bihari_2002, title={Analysis of thermal conductivity in composite adhesives}, volume={23}, ISSN={["0163-0563"]}, DOI={10.1081/NFA-120016266}, abstractNote={ABSTRACT In this work, we provide theoretical foundations for use in design of thermally conductive composite adhesives. For proof of concept, we consider a two dimensional model. We prove existence, uniqueness, and continuous dependence theorems for the model. We formulate a probability based parameter estimation problem for estimating thermal parameters and present numerical results. We derive sensitivity equations for our system and use these to investigate the sensitivity of composite silicones with respect to the thermal conductivity of both the base silicone polymer and the filler particles. Numerical results of this investigation are also presented.}, number={7-8}, journal={NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION}, author={Banks, HT and Bihari, KL}, year={2002}, pages={705–745} }
 @article{banks_begashaw_medhin_2002, title={Analytical and numerical treatment of a curved active constrained layer structure}, volume={11}, number={1}, journal={Dynamic Systems and Applications}, author={Banks, H. T. and Begashaw, N. and Medhin, N. G.}, year={2002}, pages={75–87} }
 @misc{yeoh_pinter_banks_2002, title={Compression of bonded rubber blocks}, volume={75}, ISSN={["1943-4804"]}, DOI={10.5254/1.3547682}, abstractNote={Abstract}, number={3}, journal={RUBBER CHEMISTRY AND TECHNOLOGY}, author={Yeoh, OH and Pinter, GA and Banks, HT}, year={2002}, pages={549–561} }
 @article{banks_kojima_2002, title={Identification of material damage in two-dimensional domains using the SQUID-based nondestructive evaluation system}, volume={18}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/18/6/324}, abstractNote={Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of material damage are considered. For electromagnetic nondestructive evaluation systems, observations of the magnetic flux from the front surface are used in a output least-squares approach. Parameter estimation techniques based on the method of mappings are discussed and approximation schemes are developed applying a finite-element Galerkin approach. Theoretical convergence results for computational techniques are given and results are applied to numerical experiments to demonstrate the efficacy of the proposed schemes.}, number={6}, journal={INVERSE PROBLEMS}, author={Banks, HT and Kojima, F}, year={2002}, month={Dec}, pages={1831–1855} }
 @article{banks_potter_2002, title={Model predictions and comparisons for three toxicokinetic models for the systemic transport of trichloroethylene}, volume={35}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(02)00067-5}, abstractNote={In this paper, we present and compare three physiologically based pharmacokinetic models for the systemic transport of trichloroethylene (TCE), a common environmental toxicant. Of particular interest is the disposition of TCE in the adipose tissue, where TCE is known to accumulate. The first two systemic models utilize standard ODE-based adipose compartments that assume rapid equilibrium and uniformity. The third model includes a PDE-based axial dispersion model that is designed to capture the heterogeneous physiology of adipose tissue and the expected transport of TCE there. Using numerical methods and model simulations, we compare the predicted concentration profiles of TCE in the adipose tissue for the three systemic models. Our results suggest that the dispersion-based adipose compartmental model is best able to capture the physiological heterogeneities of adipose tissue and their expected effects on TCE adipose concentrations.}, number={9-10}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Potter, LK}, year={2002}, month={May}, pages={1007–1032} }
 @article{albanese_banks_raye_2002, title={Nondestructive evaluation of materials using pulsed microwave interrogating signals and acoustic wave induced reflections}, volume={18}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/18/6/330}, abstractNote={A class of inverse problems is formulated for the estimation of material dielectric parameters using reflections of pulsed microwave interrogating signals from moving acoustic interfaces in the dielectric. A model for acoustic pressure dependence of material constitutive parameters in Maxwell’s equations is presented and analysed. Theoretical and computational findings for approximation and estimation are given.}, number={6}, journal={INVERSE PROBLEMS}, author={Albanese, RA and Banks, HT and Raye, JK}, year={2002}, month={Dec}, pages={1935–1958} }
 @article{albanese_banks_evans_potter_2002, title={Physiologically based pharmacokinetic models for the transport of trichloroethylene in adipose tissue}, volume={64}, ISSN={["1522-9602"]}, DOI={10.1006/bulm.2001.0268}, abstractNote={In this paper we present three physiologically based pharmacokinetic (PBPK) models for the systemic transport of trichloroethylene (TCE), with a focus on the adipose, or fat tissue. TCE is a widespread environmental contaminant, and has been shown to produce toxic effects in both animals and humans. A key characteristic of TCE is its tendency to accumulate in fat tissue, which has a major impact on the overall systemic disposition of TCE.Here we use PBPK models to predict the dynamics of TCE in the various tissues and organs, including the adipose tissue. The first model utilizes the standard ‘perfusion-limited’ compartmental model for the fat tissue, while the second model uses a ‘diffusion-limited’ model to describe the transport through the adipose tissue. Both of these ODE models are based on ‘well-mixed’ and rapid equilibrium assumptions, and do not take into account the specific and largely heterogeneous physiology of adipose tissue.The third model we discuss is a PBPK hybrid model with an axial-dispersion type model for the adipose tissue. This PDE-based model is designed to capture key physiological heterogeneities of fat tissue, including widely varying fat cell sizes, lipid distribution, and blood flow properties. Model simulations demonstrate that this model may be well-suited to predict the experimental behavior of TCE in adipose tissue using parameter estimation techniques.}, number={1}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Albanese, RA and Banks, HT and Evans, MV and Potter, LK}, year={2002}, month={Jan}, pages={97–131} }
 @article{banks_rosario_tran_2002, title={Proper orthogonal decomposition-based control of transverse beam vibrations: Experimental implementation}, volume={10}, ISSN={["1063-6536"]}, DOI={10.1109/TCST.2002.801793}, abstractNote={Linear quadratic Gaussian (LQG) compensator control of transverse vibrations was implemented on an aluminum cantilevered beam in a "smart structure" paradigm. The beam was mounted with two self-sensing self-actuating piezoceramic patches. The Euler-Bernoulli beam equation was discretized via a Galerkin type approximation (referred to as the full-order model). To reduce the size of the resulting finite-dimensional approximating system, the proper orthogonal decomposition (POD) was employed as a reduced basis method. A reduction of dimension from 34 to 2 was obtained through the model reduction technique. Feedback control based on the reduced order system was implemented in real time using a dSpace DS1103 control system. Experimental results indicate that POD-based control achieves comparable control attenuation with full-order model-based control.}, number={5}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Banks, HT and Rosario, RCH and Tran, HT}, year={2002}, month={Sep}, pages={717–726} }
 @article{banks_joyner_wincheski_winfree_2002, title={Real time computational algorithms for eddy-current-based damage detection}, volume={18}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/18/3/318}, abstractNote={In the field of nondestructive evaluation, new and improved techniques are constantly being sought to facilitate the detection of hidden corrosion and flaws in structures such as aeroplanes and pipelines. In this paper, we explore the feasibility of detecting such damage by application of an eddy-current-based technique coupled with reduced order modelling. We begin by developing a model for a specific eddy current method in which we make some simplifying assumptions reducing the three-dimensional problem to a two-dimensional problem (we do this for proof of concept). Theoretical results are then presented which establish the existence and uniqueness of solutions as well as continuous dependence of the solutions on the parameters which represent the damage. We further discuss theoretical issues concerning the least squares parameter estimation problem used in identifying the geometry of the damage. To solve the identification problem, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. In constructing these computational methods, we employ reduced order proper orthogonal decomposition (POD) techniques. This approach permits one to create a set of basis elements spanning a data set consisting of either numerical simulations or experimental data. We discuss two different algorithms for forming the POD approximations, a POD/Galerkin technique and a POD/interpolation technique. Finally, results of the inverse problem associated with damage detection are given using both simulated data with relative noise added as well as experimental data obtained using a giant magnetoresistive sensor. The experimental results are based on successfully using experimental data to form the POD basis elements (instead of numerical simulations), thus illustrating the effectiveness of this method on a wide range of applications. In both instances the methods are found to be efficient and robust. Moreover, the methods were fast; our findings demonstrate a significant reduction in computational time.}, number={3}, journal={INVERSE PROBLEMS}, author={Banks, HT and Joyner, ML and Wincheski, B and Winfree, WP}, year={2002}, month={Jun}, pages={795–823} }
 @article{banks_beeler_kepler_tran_2002, title={Reduced order modeling and control of thin film growth in an HPCVD reactor}, volume={62}, ISSN={["1095-712X"]}, DOI={10.1137/S0036139901383280}, abstractNote={This paper describes the development of a reduced order model-based feedback control methodology for regulation of the growth of thin films in a high-pressure chemical vapor deposition (HPCVD) reactor. Precise control of the film thickness and composition is highly desirable, making real-time control of the deposition process very important. The source vapor species transport is modeled by the standard gas dynamics partial differential equations, with species decomposition reactions, reduced down to a small number of ordinary differential equations through use of the proper orthogonal decomposition technique. This system is coupled with a reduced order model of the surface reactions involved in the source vapor decomposition and film growth on the substrate. Also modeled is the real-time observation technique used to obtain a partial measurement of the deposition process.The utilization of reduced order models greatly simplifies the mathematical formulation of the physical process so that it can be solved...}, number={4}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Banks, HT and Beeler, SC and Kepler, GM and Tran, HT}, year={2002}, month={Apr}, pages={1251–1280} }
 @article{banks_raye_2002, title={Well-posedness for systems representing electromagnetic/acoustic wavefront interaction}, volume={8}, ISSN={["1262-3377"]}, DOI={10.1051/cocv:2002019}, abstractNote={In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.}, journal={ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS}, author={Banks, HT and Raye, JK}, year={2002}, month={Jun}, pages={105–125} }
 @article{ackleh_banks_pinter_2002, title={Well-posedness results for models of elastomers}, volume={268}, ISSN={["0022-247X"]}, DOI={10.1006/jmaa.2000.7281}, abstractNote={Existence and uniqueness of weak solutions are shown for different models of the dynamic behavior of elastomers. The models are based on a nonlinear stress-strain relationship (satisfying a locally Lipschitz and affine domination property) and incorporate hysteretic effects as well. The results provide alternatives to previous theories that required monotonicity assumptions on the nonlinearities. Results with a nonlinear constitutive law and nonlinear internal dynamics are presented for the first time.}, number={2}, journal={JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, author={Ackleh, AS and Banks, HT and Pinter, GA}, year={2002}, month={Apr}, pages={440–456} }
 @article{kepler_tran_banks_2001, title={Compensator control for chemical vapor deposition film growth using reduced-order design models}, volume={14}, ISSN={["1558-2345"]}, DOI={10.1109/66.939820}, abstractNote={We present a summary of investigations on the use of proper orthogonal decomposition techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapor deposition (HPCVD) reactor. These investigations incorporate multiple species and controls, gas phase reactions, and time dependent tracking signals that are consistent with pulsed vapor reactant inputs. Numerical implementation of the model-based feedback control uses a reduced-order state estimator, based on partial state observations of the fluxes of reactants at the substrate center, which can be achieved with current sensing technology. We demonstrate that the reduced-order state estimator or compensator system is capable of substantial control authority when applied to the full system.}, number={3}, journal={IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING}, author={Kepler, GM and Tran, HT and Banks, HT}, year={2001}, month={Aug}, pages={231–241} }
 @article{banks_rosario_2001, title={Convergence of approximations in feedback control of structures}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00229-6}, abstractNote={Convergence of linear quadratic regulator (LQR) problems in structures is discussed. The abstract formulation of the system using a variational framework based on sesquilinear forms is considered. Since convergence theorems require uniform stabilizability of the finite-dimensional approximating system, we present a detailed proof of a fundamental lemma due to Banks and Ito [1] which can be used to easily verify this condition for many applications. Existing results for the well posedness of the infinite-dimensional system and convergence of Galerkin approximations are summarized.}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Rosario, RCH}, year={2001}, pages={65–78} }
 @article{ly_ito_banks_jolly_reitich_2001, title={Dynamic simulation of the temporal response of microstructure formation in magnetorheological fluids}, volume={15}, ISSN={["0217-9792"]}, DOI={10.1142/s0217979201005416}, abstractNote={ Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as two-dimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of the composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development [Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997]. As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes. }, number={6-7}, journal={INTERNATIONAL JOURNAL OF MODERN PHYSICS B}, author={Ly, HV and Ito, K and Banks, HT and Jolly, MR and Reitich, F}, year={2001}, month={Mar}, pages={894–903} }
 @article{petzold_ascher_banks_crowley_gander_greengard_heath_lumsdaine_moler_oden_et al._2001, title={Graduate education in computational science and engineering}, volume={43}, number={1}, journal={SIAM Review}, author={Petzold, L. R. and Ascher, U. and Banks, H. T. and Crowley, J. and Gander, W. and Greengard, L. and Heath, M. and Lumsdaine, A. and Moler, C. and Oden, T. and et al.}, year={2001}, pages={163–177} }
 @article{banks_bihari_2001, title={Modelling and estimating uncertainty in parameter estimation}, volume={17}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/17/1/308}, abstractNote={In this paper we discuss questions related to reliability or variability of estimated parameters in deterministic least-squares problems. By viewing the parameters for the inverse problem as realizations for a random variable we are able to use standard results from probability theory to formulate a tractable probabilistic framework to treat this uncertainty. We discuss method stability and approximate problems and are able to show convergence of solutions of the approximate problems to those of the original problem. The efficacy of our approach is demonstrated in numerical examples involving estimation of constant parameters in differential equations.}, number={1}, journal={INVERSE PROBLEMS}, author={Banks, HT and Bihari, KL}, year={2001}, month={Feb}, pages={95–111} }
 @article{banks_choi_durso_ito_2001, title={Nonlinear exothermic contributions to radio-frequency bonding of adhesives}, volume={2}, ISSN={["1468-1218"]}, DOI={10.1016/S0362-546X(00)00110-3}, number={3}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, HT and Choi, MG and Durso, SR and Ito, K}, year={2001}, month={Sep}, pages={357–386} }
 @article{lee_reitich_jolly_banks_2001, title={Piecewise linear model for field-responsive fluids}, volume={37}, ISSN={["1941-0069"]}, DOI={10.1109/20.914377}, abstractNote={The Frohlich-Kennelly model provides a constitutive law for saturation that is field dependent and has been widely used for studying nonlinear properties for a variety of electric and magnetic applications. Under the Frohlich-Kennelly model, saturation begins to occupy the entire conducting domain even at low-moderate applied fields, in this paper, we first present a new nonlinear constitutive law for field-responsive fluids that depends on the local fields and allows regions where the fields have not reached a critical value to remain unsaturated. We then study numerically the nonlinear saturated model and compare the results to the Frohlich-Kennelly model and experiments performed at the Lord Corporation, Cary, NC.}, number={1}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Lee, CH and Reitich, F and Jolly, MR and Banks, HT}, year={2001}, month={Jan}, pages={558–560} }
 @article{banks_musante_raye_2001, title={Predictions for a distributed parameter model describing the hepatic processing of 2,3,7,8-TCDD}, volume={33}, ISSN={["1872-9479"]}, DOI={10.1016/S0895-7177(00)00228-4}, abstractNote={A distributed parameter model describing spatially-dependent hepatic processing of the chemical compound 2,3,7,8-tetrachlorodibenzo- p -dioxin (TCDD or dioxin) has previously been reported [1]. The mathematical system consists of coupled nonlinear partial and ordinary differential equations with delays. In this paper, we investigate the qualitative behavior of the system over a six-hour time period following a subcutaneous injection. A brief summary of the model is also given.}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Musante, CJ and Raye, JK}, year={2001}, pages={49–64} }
 @article{banks_2001, title={Remarks on uncertainty assessment and management in modeling and computation}, volume={33}, ISSN={["1872-9479"]}, DOI={10.1016/S0895-7177(00)00227-2}, abstractNote={We discuss questions related to uncertainty in scientific computations for mathematical models. A computationally tractable probabilistic framework to treat uncertainty in the estimation of parameters or inverse problems is given. The theory is illustrated by a simple computational example for the estimation of constant parameters in differential equations by treating the parameters as random variables.}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT}, year={2001}, pages={39–47} }
 @article{simon_reitich_jolly_ito_banks_2001, title={The effective magnetic properties of magnetorheological fluids}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00244-2}, abstractNote={Magnetorheological (MR) fluids represent a class of smart materials whose rheological properties change in response to the application of a magnetic field. These fluids typically consist of small (μm) magnetizable particles dispersed in a nonmagnetic carrier fluid that generally contains additives such as surfactants and antiwear agents [1]. Due to such additives, there is an outer nonmagnetic layer on the particles that keeps them from touching. The goal of this paper is to study the effective magnetic behavior of an MR composite as a function of the interparticle distance. To this end, we present and employ a model for the effective magnetic properties of MR fluids with periodic microstructure that is based on the theory of homogenization. Finally, we discuss an interpolating formula for the effective permeability of MR fluids as an extension of the work of Keller [2] and Doyle [3].}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Simon, TM and Reitich, F and Jolly, MR and Ito, K and Banks, HT}, year={2001}, pages={273–284} }
 @article{banks_musante_raye_2000, title={Approximation methods for inverse problems governed by nonlinear parabolic systems}, volume={21}, ISSN={["0163-0563"]}, DOI={10.1080/01630560008816986}, abstractNote={We present a rigorous theoretical framework for approximation of nonlinear parabolic systems with delays in the context of inverse least squares problems. Convergence of approximate optimal parameters and that of forward solutions in the context of semidiscrete Galerkin schemes are given. Sample numerical results demonstrating the convergence are given for a model of dioxin uptake and elimination in a distributed liver model that is a special case of the general theoretical framework.}, number={7-8}, journal={NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION}, author={Banks, HT and Musante, CJ and Raye, JK}, year={2000}, pages={791–816} }
 @article{beeler_tran_banks_2000, title={Feedback control methodologies for nonlinear systems}, volume={107}, ISSN={["0022-3239"]}, DOI={10.1023/A:1004607114958}, abstractNote={A number of computational methods have been proposed in the literature to design and synthesize feedback controls when the plant is modeled by nonlinear dynamics. However, it is not immediately clear which is the best method for a given problem; this may depend on the nature of the nonlinearities, size of the system, whether the amount of control used or time needed for the method is a concern, and other factors. In this paper, a comprehensive comparison study of five methods for the synthesis of nonlinear control systems is carried out. The performance of the methods on several test problems are studied, and some recommendations are made as to which feedback control method is best to use under various conditions.}, number={1}, journal={JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS}, author={Beeler, SC and Tran, HT and Banks, HT}, year={2000}, month={Oct}, pages={1–33} }
 @article{banks_joyner_wincheski_winfree_2000, title={Nondestructive evaluation using a reduced-order computational methodology}, volume={16}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/16/4/304}, abstractNote={This paper uses eddy current based techniques and reduced-order modelling to explore the feasibility of detecting subsurface damage in structures such as air foils and pipelines. To identify the geometry of the damage, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore, our computational methods are based on the reduced-order Karhunen-Loeve or proper orthogonal decomposition techniques. For proof of concept, we implement the methodology on a 2D problem and find the methods to be efficient and robust even with data containing 10% relative noise. Furthermore, the methods are fast: our findings suggest we can reduce the computational time on average by a factor of 3000.}, number={4}, journal={INVERSE PROBLEMS}, author={Banks, HT and Joyner, ML and Wincheski, B and Winfree, WP}, year={2000}, month={Aug}, pages={929–945} }
 @article{kepler_tran_banks_2000, title={Reduced order model compensator control of species transport in a CVD reactor}, volume={21}, ISSN={["0143-2087"]}, DOI={10.1002/1099-1514(200007/08)21:4<143::AID-OCA671>3.0.CO;2-Y}, abstractNote={We propose the use of proper orthogonal decomposition (POD) techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapour deposition (HPCVD) reactor. In this paper, we present a proof-of-concept computational implementation of this method with a simplified growth example for III–V layers in which we implement Dirichlet boundary control of a dilute Group III reactant transported by convection and diffusion to an absorbing substrate with no reactions. We implement the model-based feedback control using a reduced order state estimator based on observations of the flux of reactant at the substrate centre. This is precisely the type of measurements available with current sensing technology. We demonstrate that the reduced order state estimator or compensator system is capable of substantial control authority when applied to a high-order system. In principle, these ideas can be extended to more general HPCVD control situations by including multiple species with gas-phase reactions and surface reactions. Copyright © 2000 John Wiley & Sons, Ltd.}, number={4}, journal={OPTIMAL CONTROL APPLICATIONS & METHODS}, author={Kepler, GM and Tran, HT and Banks, HT}, year={2000}, pages={143–160} }
 @article{banks_rosario_smith_2000, title={Reduced-order model feedback control design: Numerical implementation in a thin shell model}, volume={45}, ISSN={["0018-9286"]}, DOI={10.1109/9.867024}, abstractNote={Reduced-order models employing the Lagrange and popular proper orthogonal decomposition (POD) reduced-basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actuators. Donnell-Mushtari equations, modified to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functions constructed from Fourier polynomials tensored with cubic splines are employed in the Galerkin expansion of the full-order model. Reduced-basis elements are then formed from full order approximations of the exogenously excited shell taken at different time instances. Numerical examples illustrating the features of the reduced-basis methods are presented. As a first step toward investigating the behavior of the methods when implemented in physical systems, the use of reduced-order model feedback control gains in the full order model is considered and numerical examples are presented.}, number={7}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Banks, HT and Rosario, RCH and Smith, RC}, year={2000}, month={Jul}, pages={1312–1324} }
 @article{banks_pinter_1999, title={Approximation results for parameter estimation in a class of abstract nonlinear hyperbolic systems}, volume={12}, ISSN={["0893-9659"]}, DOI={10.1016/S0893-9659(99)00091-9}, abstractNote={In this paper, we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. These systems include as a special case those modeling a large class of nonlinear elastomers.}, number={6}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, HT and Pinter, GA}, year={1999}, month={Aug}, pages={129–133} }
 @article{simon_ito_banks_reitich_jolly_1999, title={Estimation of the effective permeability in magnetorheological fluids}, volume={10}, ISSN={["1045-389X"]}, DOI={10.1106/6KW6-7V12-NRQ3-BW6V}, abstractNote={ Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose Theological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in a nonpermeable carrier fluid. The essential characteristic of MR fluids is that they may be continuously and reversibly varied from a state of free flowing liquids in the absence of an applied magnetic field to that of stiff semi-solids in a moderate field. Understanding the magnetic properties of MR fluids is crucial to the design of MR fluid-based devices and it also provides valuable insight into the character of the microstructure responsible for their field-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however, due to the highly nonlinear and strongly spatially variable nature of the magnetization of the constituents. In this paper we propose a model for this behavior that is based on the mathematical theory of homogenization. We derive effective equations that govern the magnetic response of (periodically arranged) particle-chains through magnetic saturation. Comparisons of numerical results for these equations with experimental data show good agreement which suggests that our approach could be useful in the design of improved MR fluids. }, number={11}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Simon, TM and Ito, K and Banks, HT and Reitich, F and Jolly, MR}, year={1999}, month={Nov}, pages={872–879} }
 @article{banks_pinter_potter_gaitens_yanyo_1999, title={Modeling of nonlinear hysteresis in elastomers under uniaxial tension}, volume={10}, ISSN={["1045-389X"]}, DOI={10.1106/8M8M-F8DQ-GJ2V-PGK1}, abstractNote={As a fundamental component of an overall program in modeling smart material damping devices, we consider inactive host material models for moderate to highly filled rubbers undergoing uniaxial tensile deformations. Beginning from a neo-Hookean strain energy function formulation for nonlinear extension, we develop general constitutive models for both quasi-static and dynamic deformations of a viscoelastic rod. The constitutive laws are nonlinear and contain hysteresis through a Boltzmann superposition integral term. The resulting integropartial differential equations models are shown to be equivalent to the usual Lagrangian dynamic distributed parameter models coupled with linear ordinary differential equations for internal variables (internal strains). Comprehensive well-posedness results (existence, uniqueness and continuous dependence) are summarized in a discussion of theoretical aspects of the systems. The models are validated with experiments designed and carried out explicitly for this study. In particular, quasi-static Instron experimental data are used in a least squares inverse problem formulation to estimate nonlinear elastic and nonlinear viscoelastic contributions to the general stress-strain constitutive laws proposed. It is shown that the models provide an excellent prediction of nested hysteresis loops manifested in the data. These models are then used as initial estimates in determining the nonlinear hysteretic constitutive laws for the dynamic experiments. It is shown that in cases of more highly filled rubbers, multiple internal variable models lead to best fits to the data.}, number={2}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Banks, HT and Pinter, GA and Potter, LK and Gaitens, MJ and Yanyo, LC}, year={1999}, month={Feb}, pages={116–134} }
 @article{bachmann_banks_hopfner_kepler_lesure_mccall_scroggs_1999, title={Optimal design of a high pressure organometallic chemical vapor deposition reactor}, volume={29}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(99)00071-0}, abstractNote={A team composed of material scientists, physicists, and applied mathematicians have used computer simulations as a fundamental design tool in developing a new prototype High Pressure Organometallic Chemical Vapor Deposition (HPOMCVD) reactor for use in thin film crystal growth. Early design of the HPOMCVD reactor dramatically evolved long before any physical reactor was built. This effort offers a strong endorsement of such multidisciplinary, computationally based modeling teams in the design of new products in areas of emerging technologies where heretofore extensive and costly experimental design was the central paradigm.}, number={8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Bachmann, KJ and Banks, HT and Hopfner, C and Kepler, GM and LeSure, S and McCall, SD and Scroggs, JS}, year={1999}, month={Apr}, pages={65–80} }
 @article{banks_zia_1999, title={Pointwise convergence of approximation schemes for parameter estimation in parabolic equations}, volume={12}, ISSN={["0893-9659"]}, DOI={10.1016/S0893-9659(99)00097-X}, abstractNote={A finite element-based approximation scheme is presented for parameter estimation problems for parabolic PDEs on a two-dimensional domain. Pointwise convergence results relating the approximating subspaces to the full infinite-dimensional state space are discussed.}, number={7}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, HT and Zia, LL}, year={1999}, month={Oct}, pages={27–30} }
 @article{banks_zou_1999, title={Regularity and approximation of systems arising in electromagnetic interrogation of dielectric materials}, volume={20}, ISSN={["0163-0563"]}, DOI={10.1080/01630569908816914}, abstractNote={In this paper we are concerned with a mathematical model which describes the electromagnetic interrogation of dielectric materials. We address the well-posedness of the system and regularity of solutions. Then we propose a semi-discrete finite element scheme for approximating the system and prove weak convergence under very mild regularity assumptions on the solutions of the original system. We also establish that the solution has higher regularity in time even though the input source may be a windowed signal of distributional type. This regularity is then utilized to show the strong convergence of the finite element solution.}, number={7-8}, journal={NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION}, author={Banks, HT and Zou, J}, year={1999}, pages={609–627} }
 @article{banks_1999, title={Remarks on well-posedness theorems for damped second-order systems}, volume={12}, ISSN={["0893-9659"]}, DOI={10.1016/S0893-9659(99)00073-7}, abstractNote={We consider an operator theoretic formulation for distributed damped second-order (in time) forced linear elastic systems. A brief summary of previous well-posedness results is presented along with new results which allow relaxed spatial regularity (which is important in smart material systems applications) on the forcing or input function. Extensions to nonlinear systems are also indicated. The results are presented in a variational format for easy development of finite element approximation methods.}, number={6}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, HT}, year={1999}, month={Aug}, pages={21–24} }
 @article{ly_reitich_jolly_banks_ito_1999, title={Simulations of particle dynamics in magnetorheological fluids}, volume={155}, ISSN={["1090-2716"]}, DOI={10.1006/jcph.1999.6335}, abstractNote={We present particle dynamics simulations for the response of magnetorheological (MR) fluids upon application of a magnetic field. The particles motion is considered to be governed by magnetic, hydrodynamic, and repulsive interactions. Fluid-particle interactions are accounted for via Stokes' drag while inter-particle repulsions are modeled through approximate hard-sphere rejections. In accordance with their greater significance, on the other hand (linear) magnetic interactions are fully simulated. The time evolution is considered to be magnetically quasi-static and magnetostatic forces are derived from the solution of (steady) Maxwell's equations, recomputed at each instant in time. For this we use a potential theoretic formulation where the boundary integral equations are solved with a fast multipole approach. We show that the resulting numerical codes can be effectively used to study a number of experimental observables such as effective magnetic permeabilities and response time-scales which are of crucial importance in the design of MR fluids.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ly, HV and Reitich, E and Jolly, MR and Banks, HT and Ito, K}, year={1999}, month={Oct}, pages={160–177} }
 @article{banks_musante_1999, title={Well-posedness for a class of abstract nonlinear parabolic systems with time delay}, volume={35}, ISSN={["0362-546X"]}, DOI={10.1016/S0362-546X(98)00053-4}, number={5}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Banks, HT and Musante, CJ}, year={1999}, month={Mar}, pages={629–648} }
 @article{banks_musante_tran_1998, title={A dispersion model for the hepatic uptake and elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin}, volume={28}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(98)00077-6}, abstractNote={A convection-dispersion model for the uptake and elimination of 2,3,7,8-tetrachlorodibenzo- p -dioxin (TCDD) in the liver is presented. The model is adapted from the general dispersion model of Roberts and Rowland and includes the dynamics of TCDD interaction with two intracellular proteins, the Ah receptor and cytochrome P450 IA2. A “well-mixed” compartment was added to describe the venous blood concentration of TCDD. The result is a nonlinear system of seven coupled partial and ordinary differential equations with time delays.}, number={1}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Musante, CJ and Tran, HT}, year={1998}, month={Jul}, pages={9–29} }
 @article{banks_emeric_1998, title={Detection of non-symmetrical damage in smart plate-like structures}, volume={9}, ISSN={["1045-389X"]}, DOI={10.1177/1045389x9800901005}, abstractNote={ A two-dimensional model for in-plane vibrations of a cantilever plate with a nonsymmetrical damage is used in the context of defect identification in materials with piezoelectric ceramic patches bonded to their surface. These patches can act both as actuators and sensors in a selfanalyzing fashion, which is a characteristic of smart materials. A Galerkin method is used to approximate the dynamic response of these structures. The natural frequency shifts due to the damage are estimated numerically and compared to experimental data obtained from tests on cantilever aluminum plate-like structures damaged at different locations with defects of different depths. The damage location and extent are determined by an enhanced least square identification method. Efficacy of the frequency shift based algorithms is demonstrated using experimental data. }, number={10}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Banks, HT and Emeric, PR}, year={1998}, month={Oct}, pages={818–828} }
 @article{banks_luo_bergman_inman_1998, title={On the existence of normal modes of damped discrete-continuous systems}, volume={65}, ISSN={["0021-8936"]}, DOI={10.1115/1.2791942}, abstractNote={In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a finite number of concentrated masses, elastic supports, and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately defined Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satisfied, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.}, number={4}, journal={JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME}, author={Banks, HT and Luo, ZH and Bergman, LA and Inman, DJ}, year={1998}, month={Dec}, pages={980–989} }
 @article{banks_durso_goodhart_joyner_1998, title={On the radio-frequency inputs in dipolar heating of adhesives}, volume={33}, DOI={10.1080/08327823.1998.11688380}, abstractNote={The form of the radio-frequency (RF) or dielectric input expression in the heat equation which arises in the modeling of the curing of epoxy adhesives in bonding of composites was considered. Two standard derivations of a commonly used expression for the RF heating source term were reviewed. In this context difficulties involving the associated inherent polarization assumption and asymptotic behavior of dielectric parameters as a function of the frequency of the RF signal were discussed. These difficulties cast doubt on the validity of the standard RF expression. Two standard polarization models (Debye and Lorentz) then were used to demonstrate how one can systematically derive general RF heating expressions which do not suffer the inconsistencies that arise in the standard RF expression.}, number={4}, journal={Journal of Microwave Power and Electromagnetic Energy}, author={Banks, H. T. and Durso, S. R. and Goodhart, M. A. and Joyner, M. L.}, year={1998}, pages={231–242} }
 @article{bachmann_sukidi_hopfner_harris_dietz_tran_beeler_ito_banks_1998, title={Real-time monitoring of steady-state pulsed chemical beam epitaxy by p-polarized reflectance}, volume={183}, ISSN={["0022-0248"]}, DOI={10.1016/s0022-0248(97)00410-7}, abstractNote={The structure in the p-polarized reflectance (PR) intensity Rp4(t) - observed under conditions of pulsed chemical beam epitaxy (PCBE) - is modeled on the basis of the four-layer stack: ambient/surface reaction layer (SRL)/epilayer/substrate. Linearization of the PR intensity with regard to the phase factor associated with the SRL results in a good approximation that can be expressed as Rp4 = Rp3 + ΔRp.Rp3 is the reflectivity of the three-layer stack ambient-epilayer-substrate. ΔRp describes the properties of the SRL. An explicit relation is derived between ΔRp(t) and the time-dependent surface concentrations ch(t) (h = 1, 2, …, N) of the constituents of the SRL, which holds for conditions of submonolayer coverage of the surface by source vapor molecules. Under conditions of low temperature PCBE at high flux, the SRL is expected to exhibit nonideal behavior, mandating replacement of the surface concentrations by activities. Also, in this case, the thickness of the SRL must be represented in terms of partial molar volumina Vh. Since the relation between ΔRp(t) and the activities of reactants, intermediates and products of the chemical reactions driving heteroepitaxial growth is non-linear, the extraction of kinetic parameters from the measured time dependence of the PR signal generally requires numerical modeling.}, number={3}, journal={JOURNAL OF CRYSTAL GROWTH}, author={Bachmann, KJ and Sukidi, N and Hopfner, C and Harris, C and Dietz, N and Tran, HT and Beeler, S and Ito, K and Banks, HT}, year={1998}, month={Jan}, pages={323–337} }
 @article{banks_demetriou_smith_1998, title={Utilization of coupling effects in compensator design for structural acoustic systems}, volume={103}, ISSN={["0001-4966"]}, DOI={10.1121/1.421205}, abstractNote={The quantification and utilization of coupling effects in a prototypical structural acoustic system are examined in this paper. In typical systems, the coupling mechanisms are manifested in two ways. The first leads to the transfer of energy from an ambient field to an adjacent structure and is often responsible for exogenous structural excitation. The second involves the transfer of energy from the vibrating structure to an adjacent field. This is the source of structure-borne noise and is ultimately the mechanism through which structural actuators are utilized to attenuate noise. The examples presented here demonstrate that in fully coupled systems, both mechanisms should be incorporated to accurately model system dynamics. The examples also illustrate advantages and limitations of compensators which utilize the accurate modeling of the structural coupling.}, number={2}, journal={JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA}, author={Banks, HT and Demetriou, MA and Smith, RC}, year={1998}, month={Feb}, pages={872–887} }
 @article{banks_zhang_1997, title={Computational methods for a curved beam with piezoceramic patches}, volume={8}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X9700800307}, abstractNote={We develop a computational scheme to approximate the solutions of a mathematical model that describes the vibrations of a curved beam structure. The physical model also includes pairs of piezoceramic patches that can be viewed either as passive devices, changing only the structural properties of the beam, or as active devices used to control vibrations of the beam. As part of our numerical experiments, we compare schemes with a method that employs hybrid B-spline basis elements and a method that employs just one family of B-spline basis elements. We calculate the first four fundamental frequencies and mode shapes of the structure, and we simulate patch-activated vibrations. Finally, we devote a section to investigation of locking phenomena which have been reported for some shell problems.}, number={3}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Banks, HT and Zhang, Y}, year={1997}, month={Mar}, pages={260–278} }
 @article{banks_smith_brown_silcox_metcalf_1997, title={Experimental confirmation of a PDE-based approach to design of feedback controls}, volume={35}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012995285909}, abstractNote={Issues regarding the experimental implementation of PDE-based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete-time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady-state vibrations through these techniques are presented.}, number={4}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Banks, HT and Smith, RC and Brown, DE and Silcox, RJ and Metcalf, VL}, year={1997}, month={Jul}, pages={1263–1296} }
 @article{banks_kurdila_webb_1997, title={Identification of hysteretic control influence operators representing smart actuators part I: Formulation}, volume={3}, ISSN={["1024-123X"]}, DOI={10.1155/S1024123X97000586}, abstractNote={A large class of emerging actuation devices and materials exhibit strong hysteresis characteristics during their routine operation. For example, when piezoceramic actuators are operated under the influence of strong electric fields, it is known that the resulting input–output behavior is hysteretic. Likewise, when shape memory alloys are resistively heated to induce phase transformations, the input–output response at the structural level is also known to be strongly hysteretic. This paper investigates the mathematical issues that arise in identifying a class of hysteresis operators that have been employed for modeling both piezoceramic actuation and shape memory alloy actuation. Specifically, the identification of a class of distributed hysteresis operators that arise in the control influence operator of a class of second order evolution equations is investigated. In Part I of this paper we introduce distributed,hysteretic control influence operators derived from smoothed Preisach operators and generalized hysteresis operators derived from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hysteretic control influence operator can be expressed as an ouput least square minimization over probability measures defined on a compact subset of a closed half-plane. In Part II of this paper, consistent and convergent approximation methods for identification of the measure characterizing the hysteresis are derived.}, number={4}, journal={MATHEMATICAL PROBLEMS IN ENGINEERING}, author={Banks, HT and Kurdila, AJ and Webb, G}, year={1997}, pages={287–328} }
 @article{banks_kurdila_webb_1997, title={Identification of hysteretic control influence operators representing smart actuators, Part II: Convergent approximations}, volume={8}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X9700800606}, abstractNote={ In a previous paper, the authors investigated the lower semicontinuity properties of two generalizations of the classical Preisach operator: the smoothed Preisach operator and the Krasnoselskii/Pokrovskii (KP) integral hysteresis operators. In particular, it was demonstrated that the output least squares identification problem for the KP operator is well-posed over compact subsets of the Preisach plane. The identification of the hysteretic control influence operator was shown to be equivalent to the identification of a measure in the space of probability measures taken with the weak* topology. In this paper, a consistent and convergent approximation scheme is introduced for this class of integral hysteresis operator. The Galerkin approximation scheme is shown to be function space parameter convergent. A numerical example is presented that illustrates aspects of the theory derived in this paper. }, number={6}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Banks, HT and Kurdila, AJ and Webb, G}, year={1997}, month={Jun}, pages={536–550} }
 @article{banks_emeric_plancke_1997, title={Modeling of nonsymmetrical damage in plate-like structures}, volume={26}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(97)00131-3}, abstractNote={A two-dimensional model for in-plane vibrations of a damped linear elastic Hookean partially clamped plate-like structure with a nonsymmetrical damage is proposed. The model includes both active and passive contributions of piezoelectric ceramic patches bonded to the surface of the structure. Both strong and weak formulations of the equations of motion are presented. The problem is then formulated as a second-order equation in time. The existence, uniqueness of the solutions, and continuity with respect to the data are discussed.}, number={3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Emeric, P and Plancke, L}, year={1997}, month={Aug}, pages={55–65} }