Works (221)

Updated: August 23rd, 2023 21:19

2023 journal article

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

BULLETIN OF MATHEMATICAL BIOLOGY, 85(1).

By: S. Shao*, J. Canner*, R. Everett*, K. Bekele-Maxwell*, A. Kuerbis*, L. Stephenson n, J. Menda n, J. Morgenstern*, H. Banks n

author keywords: Ecological momentary assessment data; Generalized estimating equations; Generalized linear mixed models; Markov models; Generalized linear mixed-effects Markov models; Differential equations
MeSH headings : Humans; Ecological Momentary Assessment; Alcoholism; Mathematical Concepts; Models, Biological; Alcohol Drinking / psychology
UN Sustainable Development Goal Categories
2. Zero Hunger (OpenAlex)
Source: Web Of Science
Added: January 3, 2023

2022 journal article

Beyond body size-new traits for new heights in trait-based modelling of predator-prey dynamics

PLOS ONE, 17(7).

MeSH headings : Animals; Body Size; Food Chain; Herbivory; Insecta; Predatory Behavior
TL;DR: A dynamic food-web model incorporating microhabitat and non-consumptive predator effects in addition to body size is developed, and the value of iterative cycling between theory, data and experiment is demonstrated to hone current insights into how traits affect food- web dynamics. (via Semantic Scholar)
Source: Web Of Science
Added: March 6, 2023

2021 journal article

Inferring pore radius and density from ultrasonic attenuation using physics-based modeling

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 149(1), 340–347.

By: R. White n, O. Yousefian*, H. Banks n, A. Alexanderian n & M. Mueller

MeSH headings : Bone Density; Bone and Bones; Cortical Bone / diagnostic imaging; Porosity; Ultrasonics; Ultrasonography
TL;DR: This work validates the use of both the ISA and WT approximations to model ultrasonic wave attenuation in heterogeneous structures mimicking cortical bone, and illustrates the effectiveness of both models in inferring pore radius and density solely from ultrasonic attenuation data. (via Semantic Scholar)
UN Sustainable Development Goal Categories
5. Gender Equality (Web of Science)
Source: Web Of Science
Added: February 15, 2021

2020 journal article

Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 17(2), 1743–1756.

By: H. Banks*, J. Banks*, J. Catenacci*, M. Joyner* & J. Stark*

author keywords: plant-insect interactions; inverse problems; hypothesis testing and standard errors in dynamical models; aggregate data; Prohorov metric
MeSH headings : Animals; Aphids; Herbivory; Insecta; Pesticides; Population Dynamics
TL;DR: A population dynamics model is considered 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 and correctly model the data as aggregate data. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: January 13, 2020

2020 journal article

Lethal and sublethal effects of toxicants on bumble bee populations: a modelling approach

ECOTOXICOLOGY, 29(3), 237–245.

author keywords: Hymenoptera; Neonicitinoid; Delay differential equation
MeSH headings : Agriculture; Animals; Bees / physiology; Ecosystem; Environmental Monitoring; Hazardous Substances / toxicity; Neonicotinoids / toxicity; Pesticides / toxicity; Pollination
TL;DR: A delay differential equation (DDE) model is used, which requires fewer parameter estimations than agent-based models while affording the ability to explicitly describe the effect of larval incubation and colony history on population outcomes. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (Web of Science; OpenAlex)
Source: Web Of Science
Added: March 16, 2020

2020 journal article

Modelling the effects of field spatial scale and natural enemy colonization behaviour on pest suppression in diversified agroecosystems

AGRICULTURAL AND FOREST ENTOMOLOGY, 22(1), 30–40.

By: J. Banks*, A. Laubmeier n & H. Banks n

author keywords: Beetle; differential equation; diffusion; dispersal; habitat heterogeneity
TL;DR: This study addresses gaps in 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
2. Zero Hunger (Web of Science)
13. Climate Action (Web of Science)
15. Life on Land (Web of Science; OpenAlex)
Source: Web Of Science
Added: September 23, 2019

2019 journal article

ADAPTION OF AKAIKE INFORMATION CRITERION UNDER LEAST SQUARES FRAMEWORKS FOR COMPARISON OF STOCHASTIC MODELS

QUARTERLY OF APPLIED MATHEMATICS, 77(4), 831–859.

By: H. Banks n & M. Joyner*

author keywords: Continuous time Markov chain models; CTMC; stochastic differential equations; SDE; random differential equations; RDE; inverse problems; model comparison techniques; Akaike information criterion; AIC
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: October 21, 2019

2019 journal article

Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 16(3), 1082–1114.

author keywords: liver disease; zonation; computational inverse models; dispersion in flows; compartments-in-series models
MeSH headings : Adipose Tissue / metabolism; Food; Glucose / pharmacokinetics; Hepatocytes / metabolism; Humans; Insulin / metabolism; Lipid Metabolism; Lipolysis; Liver / blood supply; Liver / metabolism; Models, Biological; Non-alcoholic Fatty Liver Disease / metabolism; Non-alcoholic Fatty Liver Disease / pathology
TL;DR: This paper analyzes a "compartments-in-series" model of metabolic zonation in non-alcoholic fatty liver disease, focusing specifically at how the number of compartments and inclusion of dispersion in the flow affect simulation results. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: April 20, 2020

2019 journal article

Ecosystem function in predator-prey food webs-confronting dynamic models with empirical data

JOURNAL OF ANIMAL ECOLOGY, 88(2), 196–210.

author keywords: agricultural pests; allometry; body mass; conservation biological control; herbivore suppression; multitrophic functioning; predator-prey interactions; species traits
MeSH headings : Animals; Ecosystem; Food Chain; Models, Biological; Population Dynamics; Predatory Behavior; Sweden
TL;DR: It is demonstrated how in-depth model analysis can disentangle the likely drivers of function, such as the community's abundance and trait composition, and how trait-based parameterization must be refined and extended to include more traits than body size. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (Web of Science)
Source: Web Of Science
Added: March 4, 2019

2019 journal article

Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 16(6), 7299–7326.

author keywords: aggregate data; CAR T-cell therapy; cancer model; inverse problems; design of experiments
MeSH headings : Algorithms; Animals; Computer Simulation; Humans; Immunotherapy, Adoptive; Mice; Models, Theoretical; Neoplasm Transplantation; Neoplasms, Experimental / therapy; Population Dynamics; Probability; Receptors, Chimeric Antigen / chemistry; Reproducibility of Results; T-Lymphocytes / cytology
TL;DR: First elementary computations on the question how much data is needed for successful estimation of probability distributions are carried out on a class of CAR T-call cancer models in mice. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: October 14, 2019

2019 journal article

IMMUNOSUPPRESSANT TREATMENT DYNAMICS IN RENAL TRANSPLANT RECIPIENTS: AN ITERATIVE MODELING APPROACH

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 24(6), 2781–2797.

By: N. Murad, H. Tran*, H. Banks*, R. Everett* & E. Rosenberg*

author keywords: Inverse problem; infection dynamics; differential equations; renal transplantation; immunosuppression therapy; iterative modeling process; BKV
TL;DR: This work analyzes and improves the current mathematical model by modifying it to be more biologically realistic and amenable for designing an adaptive treatment strategy for renal transplant recipients infected by BK virus. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: April 22, 2019

2019 journal article

LOCAL SENSITIVITY VIA THE COMPLEX-STEP DERIVATIVE APPROXIMATION FOR 1D PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS

MATHEMATICAL CONTROL AND RELATED FIELDS, 9(4), 623–642.

By: H. Banks*, K. Bekele-Maxwell, L. Bociu*, M. Noorman & G. Guidiboni

author keywords: Sensitivity; poro-elastic; poro-visco-elastic; biological tissues; complex-step method
Sources: Web Of Science, ORCID
Added: December 2, 2019

2019 journal article

Modeling Zika Virus Transmission Dynamics: Parameter Estimates, Disease Characteristics, and Prevention

SCIENTIFIC REPORTS, 9.

By: M. Rahman*, K. Bekele-Maxwell*, L. Cates*, H. Banks* & N. Vaidya*

MeSH headings : Basic Reproduction Number / statistics & numerical data; Disease Outbreaks / statistics & numerical data; Humans; Islands / epidemiology; Models, Statistical; Polynesia / epidemiology; Prevalence; Time Factors; Zika Virus; Zika Virus Infection / blood; Zika Virus Infection / prevention & control; Zika Virus Infection / transmission
TL;DR: A method that utilizes a mathematical model of ZIKV dynamics and the complex-step derivative approximation technique to identify parameters that can be estimated from the available data and found that peak prevalence can be reduced to nearly 10% by reducing mosquito-to-human contact or increasing mosquito death by at least a factor of three of the base case. (via Semantic Scholar)
Source: Web Of Science
Added: August 12, 2019

2019 journal article

Population model for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) over a ten-year period

JOURNAL OF BIOLOGICAL DYNAMICS, 13(1), 422–446.

By: H. Banks*, J. Banks*, N. Cody*, M. Hoddle* & A. Meade*

author keywords: Population model; data fitting; inverse problems; weighted least squares; generalized least squares; biological control; Homalodisca vitripennis; Gonatocerus ashmeadi; Cosmocomoidea ashmeadi; density dependence
MeSH headings : Animals; Hemiptera / physiology; Models, Biological; Ovum / growth & development; Population Dynamics; Probability; Temperature; Uncertainty
TL;DR: 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 populations on unsprayed citrus, indicating that the observed population decrease may possibly be attributed to factors other than the abiotic effect of temperature. (via Semantic Scholar)
Source: Web Of Science
Added: June 4, 2019

2018 journal article

A MULTISCALE METHOD FOR COMPUTING EFFECTIVE PARAMETERS OF COMPOSITE ELECTROMAGNETIC MATERIALS WITH MEMORY EFFECTS

QUARTERLY OF APPLIED MATHEMATICS, 76(4), 713–738.

By: V. Bokil*, H. Banks n, D. Cioranescu* & G. Griso*

author keywords: Maxwell's equations; periodic unfolding; homogenization; dispersive media; auxiliary differential equation
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: November 26, 2018

2018 journal article

A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 26(6), 859–873.

By: H. Banks n, S. Kabanikhin, O. Krivorotko* & D. Yermolenko*

author keywords: Mathematical model of HIV dynamics; parameter specification problem; inverse problem; optimization approach; genetic algorithm; confidence intervals
TL;DR: A genetic algorithm for solving the least squares function minimization problem is implemented and investigated and the results of a numerical solution of the inverse problem are analyzed. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: December 17, 2018

2018 journal article

Estimating intratumoral heterogeneity from spatiotemporal data

JOURNAL OF MATHEMATICAL BIOLOGY, 77(6-7), 1999–2022.

By: E. Rutter n, H. Banks n & K. Flores n

author keywords: Glioblastoma multiforme; Random differential equation; Parameter estimation
MeSH headings : Antineoplastic Agents / therapeutic use; Brain Neoplasms / drug therapy; Brain Neoplasms / pathology; Cell Movement; Cell Proliferation; Computer Simulation; Glioblastoma / drug therapy; Glioblastoma / pathology; Humans; Mathematical Concepts; Models, Biological; Neoplasm Invasiveness / pathology; Phenotype; Probability; Spatio-Temporal Analysis; Tumor Burden / drug effects
TL;DR: The predicted effect of treatment, specifically, chemotherapy, when assuming such a heterogeneous population and compare with predictions from a homogeneous cell population model are examined. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: December 17, 2018

2018 journal article

From theory to experimental design-Quantifying a trait-based theory of predator-prey dynamics

PLoS One, 13(4).

By: A. Laubmeier, K. Wootton, J. Banks, R. Bommarco, A. Curtsdotter, T. Jonsson, T. Roslin, H. Banks

Source: NC State University Libraries
Added: August 6, 2018

2018 review

Improving the generation and selection of virtual populations in quantitative systems pharmacology models

[Review of ]. PROGRESS IN BIOPHYSICS & MOLECULAR BIOLOGY, 139, 15–22.

By: T. Rieger*, R. Allen*, L. Bystricky*, Y. Chen, G. Colopy*, Y. Cui*, A. Gonzalez*, Y. Liu* ...

author keywords: Global optimization; Acceptance rejection sampling; Mathematical modeling; Ordinary differential equations; Genetic algorithm; Metropolis-Hastings
MeSH headings : Algorithms; Models, Biological; Pharmacology / methods; Systems Biology / methods; Uncertainty; User-Computer Interface
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: January 14, 2019

2018 review

Information content in data sets: A review of methods for interrogation and model comparison

[Review of ]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 26(3), 423–452.

By: H. Banks n & M. Joyner*

author keywords: Information content; weighted least squares; sensitivity; model comparison techniques; Akaike Information Criterion
TL;DR: This review discusses methodology to ascertain the amount of information in given data sets with respect to determination of model parameters with desired levels of uncertainty in the context of least squares based inverse problem formulations. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2018 journal article

OPTIMAL DESIGN FOR DYNAMICAL MODELING OF PEST POPULATIONS

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 15(4), 993–1010.

By: H. Banks n, R. Everett*, N. Murad, R. White, J. Banks, B. Cass, J. Rosenheim n

author keywords: Dynamic modeling; pest management; optimal experimental design; constrained optimization; ecoinformatics
MeSH headings : Animals; Citrus / parasitology; Computer Simulation; Mathematical Concepts; Mites / pathogenicity; Models, Biological; Monte Carlo Method; Pest Control / methods; Pest Control / statistics & numerical data; Plant Diseases / parasitology; Plant Diseases / prevention & control; Population Dynamics
TL;DR: This work applies SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets, and suggests that a field researcher should collect at least 12 data points at the optimal times. (via Semantic Scholar)
UN Sustainable Development Goal Categories
2. Zero Hunger (OpenAlex)
Source: Web Of Science
Added: October 29, 2018

2018 journal article

Optimal control of immunosuppressants in renal transplant recipients susceptible to BKV infection

Optimal Control Applications and Methods, 40(2), 292–309.

By: N. Murad n, H. Tran n & H. Banks n

author keywords: BK virus; immunosuppression; Kalman filtering; optimal feedback control; receding horizon control; renal transplant
TL;DR: A feedback control formulation is designed to predict the optimal amount of immunosuppression required by renal transplant recipients in the context of infections caused by BK virus and concludes that, using the presented methodology, an individualized adaptive treatment schedule can be built for kidney transplant recipients. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, Crossref
Added: March 25, 2019

2018 journal article

RANDOM DELAY DIFFERENTIAL EQUATIONS AND INVERSE PROBLEMS FOR AGGREGATE DATA PROBLEMS

EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS, 6(4), 4–16.

By: H. Banks* & W. Thompson*

author keywords: Inverse problems; random delay differential equations; aggregate data; approximation and consistency of estimators
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: December 3, 2018

2018 journal article

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

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 144(2), 709–719.

By: O. Yousefian n, R. White n, Y. Karbalaeisadegh n, H. Banks n & M. Muller n

TL;DR: The sensitivity of the model to various parameter estimates depends on the micro-architectural parameters, pore diameter and pore density, so the ability to estimate model-sensitive parameters with a high degree of confidence is established. (via Semantic Scholar)
UN Sustainable Development Goal Categories
5. Gender Equality (Web of Science)
Source: Web Of Science
Added: October 16, 2018

2017 journal article

A dynamical modeling approach for analysis of longitudinal clinical trials in the presence of missing endpoints

APPLIED MATHEMATICS LETTERS, 63, 109–117.

By: H. Banks n, S. Hu n & E. Rosenberg n

author keywords: HIV; Hypothesis testing; Ordinary differential equation; Inverse problems
TL;DR: A validated mathematical model combined with an inverse problem approach is used to predict the values for the missing endpoints in a small randomized HIV clinical trial. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2017 journal article

A numerical scheme for the early steps of nucleation-aggregation models

JOURNAL OF MATHEMATICAL BIOLOGY, 74(1-2), 259–287.

By: H. Banks n, M. Doumic* & C. Kruse*

author keywords: Polymerization; Aggregation-fragmentation models; Finite volume schemes; Adaptive grid
MeSH headings : Computer Simulation; Kinetics; Models, Chemical; Polymers / chemistry
TL;DR: This article proposes 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2017 journal article

AIC under the framework of least squares estimation

APPLIED MATHEMATICS LETTERS, 74, 33–45.

By: H. Banks n & M. Joyner*

author keywords: Inverse problems; Akiake information content; Least squares estimation; Biological applications
TL;DR: The Akiake Information Criterion and its related model comparison indices are explained in the context of least squares (ordinary, weighted, iterative weighted or “generalized”, etc.) based inverse problem formulations. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2017 journal article

Continuous Structured Population Models for Daphnia magna

Bulletin of Mathematical Biology, 79(11), 2627–2648.

By: E. Rutter n, H. Banks n, G. LeBlanc n & K. Flores n

author keywords: Continuous structured population models; Inverse problems; Generalized least squares; Model selection; Information content; Residual plots
MeSH headings : Animals; Computer Simulation; Confidence Intervals; Daphnia / growth & development; Daphnia / physiology; Female; Fertility; Food; Least-Squares Analysis; Male; Mathematical Concepts; Models, Biological; Population Dynamics
TL;DR: The model is fit to experimental data using the generalized least-squares framework, and the authors use cross-validation and Akaike Information Criteria to select hyper-parameters and present the confidence intervals on parameter estimates. (via Semantic Scholar)
UN Sustainable Development Goal Categories
2. Zero Hunger (OpenAlex)
Source: Crossref
Added: July 20, 2019

2017 journal article

Dynamic Modeling of Problem Drinkers Undergoing Behavioral Treatment

BULLETIN OF MATHEMATICAL BIOLOGY, 79(6), 1254–1273.

By: H. Banks n, K. Bekele-Maxwell n, R. Everett n, L. Stephenson n, S. Shao* & J. Morgenstern*

author keywords: Mathematical psychology; Inverse problems; Iterative weighted least squares; Behavior change; Personalized medicine
MeSH headings : Alcohol Drinking; Alcoholism / therapy; Decision Making; Humans; Models, Theoretical
TL;DR: This work uses dynamical systems modeling to help understand how selected intra-personal factors interact to form mechanisms of behavior change in problem drinkers and suggests that this is a promising direction in research in alcohol use disorders as well as other behavioral sciences. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2017 journal article

Estimating the rate of prion aggregate amplification in yeast with a generation and structured population model

Inverse Problems in Science and Engineering, 26(2), 257–279.

author keywords: Structured population model; aggregate data; inverse problem; PDEs; prion; General biology and biomathematics
TL;DR: A mathematical and inverse problem formulation is developed to determine the amplification rate with prion aggregates from single-cell measurements observed in propagon amplification experiments, and 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 prions aggregates to amplify. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Crossref
Added: July 20, 2019

2017 journal article

Inverse problems and techniques with applications in the biological sciences

Inverse Problems in Science and Engineering, 26(2), 151–151.

By: H. Banks n & J. Burns*

TL;DR: 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. (via Semantic Scholar)
Source: Crossref
Added: August 28, 2020

2017 journal article

Mathematical and statistical model misspecifications in modelling immune response in renal transplant recipients

Inverse Problems in Science and Engineering, 26(2), 203–222.

By: H. Banks n, R. Everett n, S. Hu n, N. Murad n & H. Tran n

author keywords: Renal transplant; BK virus; polyomavirus nephropathy; inverse problems; pseudo measurement errors; difference-based methods; model misspecification; statistical error model; 62P10; 92B99; 62G99; 37N15
TL;DR: This work examines uncertainty in clinical data from a kidney transplant recipient infected with BK virus and investigates mathematical model and statistical model misspecifications in the context of least squares methodology. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Crossref, Web Of Science, ORCID
Added: November 11, 2019

2017 journal article

Modeling bumble bee population dynamics with delay differential equations

ECOLOGICAL MODELLING, 351, 14–23.

By: H. Banks n, J. Banks*, R. Bommarco*, A. Laubmeier n, N. Myers n, M. Rundlof*, K. Tillman n

author keywords: Population models; Delay differential equations; Non-linear; Non-autonomous; Spline approximations; Bombus terrestris; Reproduction
TL;DR: A delay differential equation model is proposed that describes multi-colony bumble bee population dynamics and ways in which resource limitation, pesticide exposure and other pressures can be reflected in the model are described. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (Web of Science)
Source: Web Of Science
Added: August 6, 2018

2017 journal article

Modelling populations of Lygus hesperus on cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice

JOURNAL OF BIOLOGICAL DYNAMICS, 11(1), 25–39.

By: H. Banks n, J. Banks*, J. Rosenheim* & K. Tillman n

author keywords: Inverse problem; ordinary least squares; generalized least squares; model selection; information content; bootstrapping; residual plots; linear splines; hemiptera; herbivory; pest suppression; pesticide
MeSH headings : Animals; California; Heteroptera / physiology; Models, Biological; Pesticides; Population Dynamics
TL;DR: The dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States, are explored and the statistical assumptions often haphazardly made in the process of parameter estimation are investigated. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2017 journal article

SENSITIVITY ANALYSIS IN PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS WITH RESPECT TO BOUNDARY DATA

QUARTERLY OF APPLIED MATHEMATICS, 75(4), 697–735.

By: H. Banks n, K. Bekele-Maxwell n, L. Bociu n, M. Noorman n & G. Guidoboni*

author keywords: Sensitivity; poro-elastic; poro-visco-elastic; biological tissues; complex-step method
TL;DR: Sensitivity analysis is the first step towards optimization and control problems associated with these models, which is the ultimate goal. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2017 journal article

SENSITIVITY VIA THE COMPLEX-STEP METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH NON-SMOOTH INITIAL DATA

QUARTERLY OF APPLIED MATHEMATICS, 75(2), 231–248.

By: H. Banks n, K. Bekele-Maxwell n, L. Bociu n & C. Wang n

author keywords: Inverse problems; sensitivity with respect to parameters; complex-step method; delay differential equations
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2017 journal article

Statistical error model comparison for logistic growth of green algae (Raphidocelis subcapitata)

Applied Mathematics Letters, 64, 213–222.

By: H. Banks n, E. Collins n, K. Flores n, P. Pershad n, M. Stemkovski n & L. Stephenson n

author keywords: Algae growth models; Parameter estimation; Uncertainty quantification; Asymptotic theory
TL;DR: A proportional error statistical model is suggested to be the most appropriate for logistic growth modeling of R. subcapitata continuous population growth. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, Crossref
Added: August 6, 2018

2016 journal article

AN ADAPTIVE FEEDBACK METHODOLOGY FOR DETERMINING INFORMATION CONTENT IN STABLE POPULATION STUDIES

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 13(4), 653–671.

By: H. Banks n, J. Banks, R. Everett* & J. Stark n

author keywords: Demographic data; inverse problem; ordinary least squares; information content; adaptive feedback
MeSH headings : Animals; Daphnia / physiology; Ecosystem; Life Tables; Models, Biological; Population Dynamics
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2016 journal article

Aggregate data and the Prohorov Metric Framework: Efficient gradient computation

APPLIED MATHEMATICS LETTERS, 56, 1–9.

By: H. Banks n & J. Catenacci n

author keywords: Inverse problems; Least squares estimation; Estimation of probability distributions; Splines; Prohorov metric
TL;DR: 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 are discussed. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2016 journal article

In celebration of the 60th birthday of Professor Alemdar Hasanoglu (Hasanov)

Journal of Inverse and Ill-Posed Problems, 24(2), 109–110.

By: V. Andreev, H. Banks, G. Dulikravich, B. Hofmann, S. Kabanikhin, F. Kuchuk, D. Lesnic, M. Nashed ...

Source: NC State University Libraries
Added: August 6, 2018

2016 chapter

Modelling Pesticide Treatment Effects on Lygus hesperus in Cotton Fields

In IFIP Advances in Information and Communication Technology (pp. 95–106).

By: H. Banks n, J. Banks n, N. Murad n, J. Rosenheim* & K. Tillman n

TL;DR: This work addresses the question of whether data, as it is currently collected, can support time-dependent parameter estimates andfitting models to field data, and considers model selection for an appropriate mathematical model and corresponding statistical models. (via Semantic Scholar)
Source: Crossref
Added: February 24, 2020

2016 journal article

Modelling immune response to BK virus infection and donor kidney in renal transplant recipients

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 24(1), 127–152.

By: H. Banks n, S. Hu n, K. Link n, E. Rosenberg*, S. Mitsuma* & L. Rosario*

author keywords: renal transplant; human polyomavirus type 1 (BKV); mathematical model; inverse problem; sensitivity analysis; 62F12; 65L09; 92B05
TL;DR: 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 is developed and validated with bootstrapping techniques. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2016 journal article

On analytical and numerical approaches to division and label structured population models

APPLIED MATHEMATICS LETTERS, 60, 81–88.

By: H. Banks n, K. Flores n & S. Sindi*

author keywords: Division-structured population model; Heterogeneous cell populations; Protein dynamics
TL;DR: This work demonstrates 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2016 journal article

Parameter Estimation Using Unidentified Individual Data in Individual Based Models

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 11(6), 9–27.

By: H. Banks n, R. Baraldi n, J. Catenacci n & N. Myers

author keywords: pharmacokinetics; pharmacodynamics; physiological based pharmacokinetic modeling; inter-individual parameter variability; uncertainty quantification; random differential equations; distribution estimation; Prohorov metric framework; aggregate population data
TL;DR: This work proposes a novel method which accounts for inter-individual variability in experiments where only unidentified individual data is available, and results in more accurate quantification of the uncertainty attributed to inter- individual variability. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2016 journal article

Parameter Selection and Verification Techniques Based on Global Sens Analysis Illustrated for an HIV Model

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 4(1), 266–297.

By: M. Wentworth, R. Smith* & H. Banks*

author keywords: global sensitivity analysis; parameter selection; verificatio
TL;DR: This work considers parameter selection and verification techniques for models having one or more parameters that are noninfluential in the sense that they minimally impact model outputs, and focuses on global sensitivity analysis techniques based on Pearson correlation coefficient, Sobol indices, and Morris indices. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2016 article

Quantifying the degradation in thermally treated ceramic matrix composites

INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS, Vol. 52, pp. 3–24.

By: H. Banks n, J. Catenacci n & A. Criner*

author keywords: Ceramic matrix composites; prohorov metric; reflectance spectroscopy; uncertainty quantification
Source: Web Of Science
Added: August 6, 2018

2016 article

Statistical parameter estimation of dielectric materials using MCMC for nonlinear hierarchical models

INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS, Vol. 52, pp. 49–54.

By: F. Kojima* & H. Banks n

author keywords: Inverse problem; nondestructive evaluation; electromagnetic interrogation; polarization
Source: Web Of Science
Added: August 6, 2018

2016 journal article

Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems

Journal of Inverse and Ill-Posed Problems, 24(4), 413–433.

By: H. Banks, J. Catenacci & S. Hu

Source: NC State University Libraries
Added: August 6, 2018

2016 journal article

Validation of a mathematical model for green algae (Raphidocelis Subcapitata) growth and implications for a coupled dynamical system with Daphnia magna

Applied Sciences-Basel, 6(5).

Source: NC State University Libraries
Added: August 6, 2018

2015 journal article

Characterisation of Elastic and Acoustic Properties of an Agar-Based Tissue Mimicking Material

ANNALS OF BIOMEDICAL ENGINEERING, 43(10), 2587–2596.

By: M. Brewin*, M. Birch*, D. Mehta*, J. Reeves*, S. Shaw*, C. Kruse*, J. Whiteman*, S. Hu n ...

author keywords: Acoustic properties; Acoustic localisation; Coronary artery; Elastic moduli; Poisson's ratio; Shear modulus; Shear wave; Stenosis; Tissue mimicking material; Viscoelasticity
MeSH headings : Agar / chemistry; Animals; Biomimetic Materials / chemistry; Coronary Stenosis / diagnostic imaging; Coronary Stenosis / physiopathology; Elastic Modulus; Humans; Phantoms, Imaging; Ultrasonography
TL;DR: Measurements are reported for an agar-based tissue mimicking material of the shear wave propagation velocity, attenuation and viscoelastic constants, together with one dimensional quasi-static elastic moduli and Poisson’s ratio to provide baseline data required for the computational modelling of wave propagation in a phantom. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance

Journal of Inverse and Ill-Posed Problems, 23(5), 491–509.

By: H. Banks, J. Catenacci & S. Hu

Source: NC State University Libraries
Added: August 6, 2018

2015 journal article

Estimation of time-varying mortality rates using continuous models for Daphnia magna

APPLIED MATHEMATICS LETTERS, 44, 12–16.

By: K. Adoteye n, H. Banks n, K. Flores n & G. LeBlanc n

author keywords: Structured population model; Leslie matrix model; Sinko-Streifer model; Daphnia magna; Time-dependent mortality rate
TL;DR: It is found that a continuous differential equation model with a time-varying mortality rate was the most accurate model for describing the authors' experimental D. magna survival data. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2015 conference paper

Identification of thermal degradation using probabilistic models in reflectance spectroscopy

1650, 1898–1906.

By: A. Criner*, A. Cherry, A. Cooney, T. Katter*, H. Banks n, S. Hu n, J. Catenacci n

Event: 41ST ANNUAL REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION: Volume 34

Sources: Crossref, NC State University Libraries
Added: August 6, 2018

2015 journal article

Immuno-modulatory strategies for reduction of HIV reservoir cells

JOURNAL OF THEORETICAL BIOLOGY, 372, 146–158.

By: H. Banks n, K. Flores n, S. Hu n, E. Rosenberg*, M. Buzon*, X. Yu*, M. Lichterfeld*

author keywords: Immune response; Mathematical model; Inverse problem; Stability analysis
MeSH headings : Anti-HIV Agents / chemistry; CD4-Positive T-Lymphocytes / immunology; CD4-Positive T-Lymphocytes / virology; CD8-Positive T-Lymphocytes / immunology; CD8-Positive T-Lymphocytes / virology; Cell Proliferation; Computer Simulation; HIV Infections / immunology; HIV Infections / therapy; HIV-1; Homeostasis; Humans; Models, Biological; Viral Load; Virus Latency
TL;DR: The 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Information content in data sets for a nucleated-polymerization model

JOURNAL OF BIOLOGICAL DYNAMICS, 9(1), 172–197.

By: H. Banks n, M. Doumic*, C. Kruse*, S. Prigent* & H. Rezaei*

author keywords: inverse problems; polyglutamine and aggregation modelling; information content; sensitivity; uncertainty quantification; 65M32; 62P10; 64B10; 49Q12
MeSH headings : Algorithms; Amyloid / chemistry; Kinetics; Models, Biological; Models, Statistical; Peptides / chemistry; Polymerization; Sensitivity and Specificity
TL;DR: The methodology developed here may be of great help to experimentalists and it is concluded 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Model comparison tests to determine data information content

APPLIED MATHEMATICS LETTERS, 43, 10–18.

By: H. Banks n, J. Banks*, K. Link n, J. Rosenheim*, C. Ross n & K. Tillman n

author keywords: Ordinary least squares; Model comparison in inverse problems; Information content
TL;DR: In the context of inverse or parameter estimation problems, the use of statistically based model comparison tests is demonstrated in several examples of practical interest 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

OPTIMAL DESIGN FOR PARAMETER ESTIMATION IN EEG PROBLEMS IN A 3D MULTILAYERED DOMAIN

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 12(4), 739–760.

By: H. Banks n, D. Rubio, N. Saintier & M. Troparevsky n

author keywords: Electromagnetic inverse problems; optimal design in 3D EEG analysis; parameter estimation; asymptotic error analysis
MeSH headings : Algorithms; Animals; Brain / physiology; Brain Mapping / methods; Computer Simulation; Diagnosis, Computer-Assisted / methods; Electroencephalography / methods; Humans; Models, Neurological; Models, Statistical; Pattern Recognition, Automated / methods; Reproducibility of Results; Sensitivity and Specificity
TL;DR: This work considers 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Optimal design of non-equilibrium experiments for genetic network interrogation

APPLIED MATHEMATICS LETTERS, 40, 84–89.

By: K. Adoteye n, H. Banks n & K. Flores n

author keywords: Optimal experimental design; Inverse problem; Uncertainty analysis; Brome mosaic virus; Synthetic biology; Genetic networks
TL;DR: An optimal design algorithm is developed 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Optimal sampling frequency and timing of threatened tropical bird populations: A modeling approach

ECOLOGICAL MODELLING, 303, 70–77.

By: J. Banks*, H. Banks n, K. Rinnovatore n & C. Jackson*

author keywords: Arabuko-Sokoke Forest; Inverse problem; Kenya; Least squares optimization; Leslie matrix; Sheppardia gunningi
TL;DR: It is illustrated 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
14. Life Below Water (Web of Science)
15. Life on Land (Web of Science)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Statistical validation of structured population models for Daphnia magna

Mathematical Biosciences, 266, 73–84.

By: K. Adoteye n, H. Banks n, K. Cross n, S. Eytcheson n, K. Flores n, G. LeBlanc n, T. Nguyen n, C. Ross n ...

author keywords: Sensitivity analysis; Structured population model; Uncertainty quantification; Density-dependence; Multi-scale data; Daphnia magna
MeSH headings : Animals; Daphnia; Models, Statistical; Population Dynamics
TL;DR: This study develops structured population models that exemplify specific mechanisms and uses multi-scale experimental data in order to test their importance, and shows that fecundity and survival rates are affected by both time-varying density-independent factors and density-dependent factors. (via Semantic Scholar)
Sources: Web Of Science, ORCID, Crossref
Added: August 6, 2018

2015 journal article

UNCERTAINTY QUANTIFICATION IN MODELING HIV VIRAL MECHANICS

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 12(5), 937–964.

MeSH headings : Algorithms; Anti-HIV Agents / therapeutic use; CD4-Positive T-Lymphocytes / virology; Clinical Trials as Topic; HIV Infections / drug therapy; HIV Infections / physiopathology; HIV Infections / virology; HIV-1 / physiology; Humans; Least-Squares Analysis; Models, Biological; Models, Statistical; RNA, Viral / analysis; Reverse Transcriptase Inhibitors / therapeutic use; Uncertainty; Viral Load
TL;DR: An in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work is considered and Bootstrapping and asymptotic theory are compared in the context of confidence intervals for the resulting parameter estimates. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2014 journal article

DYNAMIC MODELING OF BEHAVIOR CHANGE

QUARTERLY OF APPLIED MATHEMATICS, 72(2), 209–251.

By: H. Banks*, K. Rehm, K. Sutton, C. Davis, L. Hail, A. Kuerbis, J. Morgenstern n

author keywords: Mathematical psychology; inverse problems; delay differential equations; behavior change; model comparison
TL;DR: This work presents a novel dynamical systems modeling approach to understand the processes governing an individual’s behavior in the context of problem drinking, and discusses the construction of an initial mathematical model for two starkly distinct individuals. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2014 conference paper

Decomposition of permittivity contributions from reflectance using mechanism models

2014 american control conference (acc), 367–372.

By: H. Banks, J. Catenacci, S. Hu & Z. Kenz

Source: NC State University Libraries
Added: August 6, 2018

2014 journal article

High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 98(2), 131–156.

By: H. Banks n, M. Birch*, M. Brewin*, S. Greenwald*, S. Hu n, Z. Kenz n, C. Kruse*, M. Maischak*, S. Shaw*, J. Whiteman*

author keywords: viscoelasticity; high order methods; discontinuous Galerkin finite element method; spectral element method; space-time finite elements
TL;DR: This work revisits a method for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation and applies this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2014 journal article

MODEL VALIDATION FOR A NONINVASIVE ARTERIAL STENOSIS DETECTION PROBLEM

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 11(3), 427–448.

By: H. Banks n, S. Hu*, Z. Kenz*, C. Kruse, S. Shaw, J. Whiteman, M. Brewin, S. Greenwald, M. Birch n

author keywords: Viscoelastic model; sensitivity analysis; inverse problem; asymptotic theory
MeSH headings : Arterial Occlusive Diseases / diagnosis; Computational Biology; Confidence Intervals; Constriction, Pathologic / diagnosis; Finite Element Analysis; Hemodynamics; Humans; Least-Squares Analysis; Mathematical Concepts; Models, Cardiovascular; Models, Statistical; Phantoms, Imaging
TL;DR: 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 by using one-dimensional shear wave experimental data from novel acoustic phantoms to validate a corresponding viscoelastic mathematical model. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2014 conference paper

Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions

2014 american control conference (acc), 2753–2758.

Source: NC State University Libraries
Added: August 6, 2018

2013 journal article

A Comparison of Stochastic Systems with Different Types of Delays

STOCHASTIC ANALYSIS AND APPLICATIONS, 31(6), 913–955.

By: H. Banks n, J. Catenacci n & S. Hu n

author keywords: Fixed vs; random delays; Gamma distribution and the linear chain trick; Kurtz limit theorem; Markov Chain stochastic vs; deterministic approximations; Systems with delays
Source: Web Of Science
Added: August 6, 2018

2013 journal article

A novel statistical analysis and interpretation of flow cytometry data

JOURNAL OF BIOLOGICAL DYNAMICS, 7(1), 96–132.

By: H. Banks n, D. Kapraun n, W. Thompson n, C. Peligero*, J. Argilaguet* & A. Meyerhans*

author keywords: immunology; flow cytometry; cyton models; mathematical and statistical models; label dynamics; parameter estimation; cellular models
MeSH headings : CD4-Positive T-Lymphocytes / drug effects; CD4-Positive T-Lymphocytes / immunology; CD8-Positive T-Lymphocytes / drug effects; CD8-Positive T-Lymphocytes / immunology; Cell Proliferation / drug effects; Data Interpretation, Statistical; Flow Cytometry / statistics & numerical data; Fluoresceins; Fluorescent Dyes; Humans; Mathematical Concepts; Mitogens / pharmacology; Models, Immunological; Models, Statistical; Phytohemagglutinins / pharmacology; Succinimides
TL;DR: A 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Acoustic localisation of coronary artery stenosis: Wave propagation in soft tissue mimicking gels

Artery Research, 7(3-4), 124.

By: S. Greenwald*, H. Banks n, M. Birch*, M. Brewin*, S. Hu n, Z. Kenz n, C. Kruse*, D. Mehta* ...

TL;DR: Wave Propagation in Soft TISSUE MIMICKing Gel is presented, which proposes a new approach to wave-based reinforcement learning that combines reinforcement learning with discrete-time reinforcement learning. (via Semantic Scholar)
Source: Crossref
Added: February 24, 2020

2013 journal article

Experimental design for distributed parameter vector systems

Applied Mathematics Letters, 26(1), 10–14.

By: H. Banks* & K. Rehm*

author keywords: Optimal design; Inverse problems; Optimal selection of observables; Sampling points
TL;DR: 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 nonlinear partial differential systems is formulated. (via Semantic Scholar)
Source: Crossref
Added: February 24, 2020

2013 journal article

Experimental design for vector output systems

Inverse Problems in Science and Engineering, 22(4), 557–590.

By: H. Banks* & K. Rehm

author keywords: optimal design; inverse problems; optimal selection of observables and sampling times; HIV models; plant metabolism and growth
TL;DR: 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 is formulated. (via Semantic Scholar)
Source: Crossref
Added: August 28, 2020

2013 journal article

Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology

Journal of Inverse and Ill-Posed Problems, 21(1), 25–57.

By: H. Banks, S. Hu, Z. Kenz, C. Kruse, S. Shaw, J. Whiteman, M. Brewin, S. Greenwald, M. Birch

Source: NC State University Libraries
Added: August 6, 2018

2013 journal article

Parameter selection methods in inverse problem formulation

Mathematical Modeling and Validation in Physiology: Applications to the Cardiovascular and Respiratory Systems, 2064, 43–73.

By: H. Banks, A. Cintron-Arias & F. Kappel

Source: NC State University Libraries
Added: August 6, 2018

2013 journal article

Quantifying CFSE label decay in flow cytometry data

APPLIED MATHEMATICS LETTERS, 26(5), 571–577.

By: H. Banks n, A. Choi n, T. Huffman n, J. Nardini n, L. Poag n & W. Thompson n

author keywords: Carboxyfluorescein succinimidyl ester (CFSE); Ordinary differential equation models; Inverse problems; Exponential decay; Gompertz growth; Akiake Information
TL;DR: A series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester is used as a staining agent are developed. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Towards computational diagnosis of coronary artery disease

Artery Research, 7(3-4), 123–124.

By: S. Shaw*, J. Whiteman*, S. Greenwald*, C. Kruse*, H. Banks*, M. Birch*, Z. Kenz, J. Reeves*, S. Hu, M. Brewin*

TL;DR: The new cuff-based SphygmoCor technique used for evaluation of CBP parameters in a clinical environment is a convenient and accurate proxy for the previous tonometric technique regardless of patient age. (via Semantic Scholar)
Source: Crossref
Added: February 24, 2020

2012 journal article

A COMPARISON OF COMPUTATIONAL EFFICIENCIES OF STOCHASTIC ALGORITHMS IN TERMS OF TWO INFECTION MODELS

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 9(3), 487–526.

By: H. Banks n, S. Hu*, M. Joyner, A. Broido, B. Canter, K. Gayvert, K. Link n

author keywords: Dynamical models; continuous time Markov chain models; stochastic simulation algorithms; Gillespie; tau-leaping; bacterial and viral infection models
MeSH headings : Algorithms; Computer Simulation / statistics & numerical data; Enterococcus / drug effects; Gram-Positive Bacterial Infections / drug therapy; Gram-Positive Bacterial Infections / epidemiology; Gram-Positive Bacterial Infections / transmission; HIV Infections / epidemiology; HIV Infections / transmission; Humans; Models, Statistical; Population Dynamics; Vancomycin Resistance
TL;DR: The numerical results suggest that the SSA is the best choice due to its simplicity and accuracy for the simpler VRE model, and with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2012 journal article

A DIVISION-DEPENDENT COMPARTMENTAL MODEL FOR COMPUTING CELL NUMBERS IN CFSE-BASED LYMPHOCYTE PROLIFERATION ASSAYS

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 9(4), 699–736.

By: H. Banks n, W. Tompson, C. Peligero, S. Giest, J. Argilaguet & A. Meyerhans n

author keywords: Cell proliferation; cell division number; CFSE; label structured population dynamics; partial differential equations; inverse problems
MeSH headings : Animals; Cell Division / physiology; Cell Proliferation; Computer Simulation; Fluoresceins; Humans; Image Interpretation, Computer-Assisted / methods; Lymphocyte Count / methods; Lymphocytes / cytology; Lymphocytes / physiology; Microscopy, Fluorescence / methods; Models, Biological; Succinimides
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2012 journal article

A Monte Carlo based analysis of optimal design criteria

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 20(1), 1–37.

By: H. Banks n, K. Holm n & F. Kappel*

author keywords: Optimal design methods; least squares inverse problems; Fisher information matrix; D-optimal; E-optimal; SE-optimal; Monte Carlo analysis
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2012 book

A functional analysis framework for modeling, estimation, and control in science and engineering

By: H. Banks*

Source: NC State University Libraries
Added: August 6, 2018

2012 journal article

A review of selected techniques in inverse problem nonparametric probability distribution estimation

Journal of Inverse and Ill-Posed Problems, 20(4), 429–460.

By: H. Banks, Z. Kenz & W. Thompson

Source: NC State University Libraries
Added: August 6, 2018

2012 journal article

A zero-sum electromagnetic evader-interrogator differential game with uncertainty

APPLICABLE ANALYSIS, 91(4), 645–674.

By: H. Banks n & S. Hu n

author keywords: electromagnetic evasion pursuit; uncertainty; differential games; theory and approximation; backward Kolmogorov equations
Source: Web Of Science
Added: August 6, 2018

2012 journal article

Experimental design and inverse problems in plant biological modeling

Journal of Inverse and Ill-Posed Problems, 20(2), 169–191.

By: M. Avery, H. Banks, K. Basu, Y. Cheng, E. Eager, S. Khasawinah, L. Potter, K. Rehm

Source: NC State University Libraries
Added: August 6, 2018

2012 journal article

Mathematical Models of Dividing Cell Populations: Application to CFSE Data

Mathematical Modelling of Natural Phenomena, 7(5), 24–52.

By: H. Banks* & W. Clayton Thompson*

author keywords: cell proliferation; cell division number; CFSE; ordinary differential equations; cytons; label structured population dynamics; partial differential equations; inverse problems
TL;DR: 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 are presented. (via Semantic Scholar)
Source: Crossref
Added: February 24, 2020

2012 journal article

Modelling and optimal control of immune response of renal transplant recipients

JOURNAL OF BIOLOGICAL DYNAMICS, 6(2), 539–567.

By: H. Banks n, S. Hu n, T. Jang* & H. Kwon n

author keywords: renal transplant; human cytomegalovirus; mathematical model; optimal feedback control; state estimation; model predictive control
MeSH headings : Computer Simulation; Humans; Immunity / drug effects; Immunity / immunology; Immunosuppression Therapy; Immunosuppressive Agents / pharmacology; Infections / microbiology; Infections / virology; Kidney Transplantation / immunology; Models, Immunological; Transplantation Immunology / drug effects; Virus Activation / drug effects
TL;DR: 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, and a computational framework for designing adaptive optimal treatment regimes with partial observations and low-frequency sampling is developed. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2012 journal article

Preface. Distributed Parameter Systems in Immunology

Mathematical Modelling of Natural Phenomena, 7(5), 1–3.

By: H. Banks*, G. Bocharov*, Z. Grossman* & A. Meyerhans*

author keywords: mathematical model; distributed parameter systems; immunophysiological systems; virus infections
Source: Crossref
Added: February 24, 2020

2012 journal article

Propagation of Growth Uncertainty in a Physiologically Structured Population

Mathematical Modelling of Natural Phenomena, 7(5), 7–23.

By: H. Banks n & S. Hu n

Source: Crossref
Added: February 24, 2020

2012 journal article

Thermal based methods for damage detection and characterization in porous materials

Inverse Problems, 28(6), 065021.

By: H. Banks* & A. Criner*

UN Sustainable Development Goal Categories
Sources: Crossref, NC State University Libraries
Added: August 6, 2018

2011 review

A Brief Review of Elasticity and Viscoelasticity for Solids

[Review of ]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 3(1), 1–51.

By: H. Banks n, S. Hu n & Z. Kenz n

author keywords: Mathematical modeling; Eulerian and Lagrangian formulations in continuum mechanics; elasticity; viscoelasticity; computational simulations in soil; constitutive relationships
TL;DR: An overview of the subject for both elastic and viscoelastic materials is provided, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging, and some applications for these constitutive equations. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2011 journal article

A DETERMINISTIC METHODOLOGY FOR ESTIMATION OF PARAMETERS IN DYNAMIC MARKOV CHAIN MODELS

JOURNAL OF BIOLOGICAL SYSTEMS, 19(1), 71–100.

By: A. Ortiz*, H. Banks n, C. Castillo-Chavez*, G. Chowell* & X. Wang*

author keywords: Markov Chain Stochastic Models; Inverse Problems; Parameter Estimation; Parameter Selection; Large Population Sample Path Approximations
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2011 journal article

A new model for the estimation of cell proliferation dynamics using CFSE data

JOURNAL OF IMMUNOLOGICAL METHODS, 373(1-2), 143–160.

By: H. Banks n, K. Sutton n, W. Thompson n, G. Bocharov*, M. Doumic*, T. Schenkel*, J. Argilaguet*, S. Giest*, C. Peligero*, A. Meyerhans*

author keywords: Cell proliferation; Cell division number; CFSE; Label structured population dynamics; Partial differential equations; Inverse problems
MeSH headings : Algorithms; Cell Division; Cell Proliferation; Flow Cytometry; Fluoresceins / metabolism; Fluorescent Dyes / metabolism; Humans; Kinetics; Leukocytes, Mononuclear / cytology; Leukocytes, Mononuclear / metabolism; Lymphocytes / cytology; Lymphocytes / metabolism; Models, Biological; Molecular Dynamics Simulation; Succinimides / metabolism
TL;DR: A significant revision of this PDE model is presented which improves the physiological understanding of several parameters and results in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2011 journal article

Comparison of optimal design methods in inverse problems

Inverse Problems, 27(7), 075002.

By: H. Banks n, K. Holm n & F. Kappel n

TL;DR: A new Prohorov metric-based theoretical framework is presented that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix and a new optimal design, SE-optimal design, is introduced in the context of general optimization problems over distributions of sampling times. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 6, 2018

2011 journal article

Dynamic evasion-interrogation games with uncertainty in the context of electromagetics

Numerical Mathematics: Theory, Methods and Applications, 4(3), 359–378.

By: H. Banks, S. Hu, K. Ito & S. Muccio

Source: NC State University Libraries
Added: August 6, 2018

2011 journal article

Estimation of Cell Proliferation Dynamics Using CFSE Data

BULLETIN OF MATHEMATICAL BIOLOGY, 73(1), 116–150.

By: H. Banks n, K. Sutton n, W. Thompson n, G. Bocharov*, D. Roose*, T. Schenkel*, A. Meyerhans*

author keywords: Cell proliferation; CFSE; Label structured population dynamics; Partial differential equations; Inverse problems
MeSH headings : Cell Proliferation; Flow Cytometry / methods; Flow Cytometry / statistics & numerical data; Fluoresceins; Fluorescent Dyes; Humans; In Vitro Techniques; Least-Squares Analysis; Mathematical Concepts; Models, Biological; Models, Statistical; Succinimides
TL;DR: 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, and should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2011 journal article

Host immune responses that promote initial HIV spread

JOURNAL OF THEORETICAL BIOLOGY, 289, 17–35.

By: K. Wendelsdorf*, G. Dean n, S. Hu n, S. Nordone n & H. Banks n

author keywords: HIV; Innate inflammatory response pathway; Regulatory response pathway; Mathematical model
MeSH headings : CD4-Positive T-Lymphocytes / immunology; Dendritic Cells / immunology; HIV / physiology; HIV Infections / immunology; HIV Infections / transmission; HIV Infections / virology; Humans; Inflammation / immunology; Inflammation / virology; Lymphocyte Activation / immunology; Models, Immunological; T-Lymphocytes, Regulatory / immunology; Virus Replication / immunology
TL;DR: A model of the host inflammatory response to virus as well as inherent nTreg-mediated regulation of Th1 recruitment and activation is created to identify mechanisms of the natural inflammatory response that are best targeted to inhibit viral spread without compromising initial antiviral activity. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2011 journal article

Parameter estimation for the heat equation on perforated domains

Journal of Inverse and Ill-Posed Problems, 19(6), 825–857.

By: H. Banks, D. Cioranescu, A. Criner & W. Winfree

Source: NC State University Libraries
Added: August 6, 2018

2011 journal article

Receding Horizon Control of HIV

OPTIMAL CONTROL APPLICATIONS & METHODS, 32(6), 681–699.

By: J. David n, H. Tran n & H. Banks n

author keywords: HIV model; Receding Horizon Control; extended Kalman filter; state estimator
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2010 journal article

A discrete events delay differential system model for transmission of Vancomycin-resistant enterococcus (VRE) in hospitals

Journal of Inverse and Ill-Posed Problems, 18(7), 787–821.

By: A. Ortiz, H. Banks, C. Castillo-Chavez, G. Chowell & X. Wang

Source: NC State University Libraries
Added: August 6, 2018

2010 journal article

DYNAMIC SOCIAL NETWORK MODELS INCORPORATING STOCHASTICITY AND DELAYS

QUARTERLY OF APPLIED MATHEMATICS, 68(4), 783–802.

By: H. Banks n, K. Rehm n & K. Sutton n

author keywords: Social networks; stochastic differential equations; delay differential equations; clustering
TL;DR: The work in Banks, Karr, Nguyen and Samuels (2008), which demonstrated a simple dynamical system framework in which to study social network behavior, is extended to include a discrete delay, which represents the time lag that is likely required for an agent to change his/her own characteristics after interacting with an agent possessing different characteristics. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Electromagnetic interrogation and the Doppler shift using the method of mappings

MATHEMATICAL AND COMPUTER MODELLING, 51(5-6), 389–399.

By: H. Banks n, S. Hu n & W. Thompson n

author keywords: Electromagnetic Doppler shift; Moving interfaces; Method of mappings; Finite elements
TL;DR: The method of mappings is employed to transform the problem to one of computing solutions of a Maxwell system with time dependent coefficients on a fixed reference domain, obtaining a problem that is eminently tractable with finite element or finite difference time domain methods. (via Semantic Scholar)
UN Sustainable Development Goal Categories
1. No Poverty (Web of Science)
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Generalized sensitivities and optimal experimental design

Journal of Inverse and Ill-Posed Problems, 18(1), 25–83.

By: H. Banks, S. Dediu, S. Ernstberger & F. Kappel

Source: NC State University Libraries
Added: August 6, 2018

2010 journal article

Label structured cell proliferation models

APPLIED MATHEMATICS LETTERS, 23(12), 1412–1415.

By: H. Banks n, F. Charles*, M. Jauffret, K. Sutton n & W. Thompson n

author keywords: Cell proliferation; Label structured population dynamics; Partial differential equations; Moving coordinate systems
TL;DR: 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 are presented and address overall label degradation. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping

MATHEMATICAL AND COMPUTER MODELLING, 52(9-10), 1610–1625.

By: H. Banks n, K. Holm n & D. Robbins n

author keywords: Parameter estimation; Bootstrapping; Asymptotic standard errors
TL;DR: This work computationally investigates two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems and considers both constant variance absolute error data and relative error which produces non-constant variance data in parameter estimation formulations. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Thermal-based damage detection in porous materials

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 18(6), 835–851.

By: H. Banks n, B. Boudreaux n, A. Criner n, K. Foster*, C. Uttal*, T. Vogel*, W. Winfree*

author keywords: thermal interrogation; material with porosity; random porosity; damage detection; computational methods
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Using inverse problem methods with surveillance data in pneumococcal vaccination

MATHEMATICAL AND COMPUTER MODELLING, 51(5-6), 369–388.

By: K. Sutton n, H. Banks n & C. Castillo-Chavez*

author keywords: Inverse problems; Surveillance data; Epidemiological models; Pneumococcal diseases; Age structure
TL;DR: It is demonstrated that relevant yet typically unknown parameters may be estimated, and it is shown 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2009 journal article

A comparison of probabilistic and stochastic formulations in modelling growth uncertainty and variability

Journal of Biological Dynamics, 3(2-3), 130–148.

By: H. Banks n, J. Davis n, S. Ernstberger n, S. Hu n, E. Artimovich, A. Dhar, C. Browdy*

MeSH headings : Animals; Decapoda / growth & development; Models, Biological; Population Dynamics; Probability; Stochastic Processes; Uncertainty
TL;DR: A theoretical analysis is presented that allows one to include comparable levels of uncertainty in the two distinct formulations in making comparisons of the two approaches for inclusion of uncertainty/variability in modelling growth in size-structured population models. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Source: Crossref
Added: February 24, 2020

2009 journal article

A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system

MATHEMATICAL AND COMPUTER MODELLING, 50(7-8), 959–974.

By: H. Banks n, K. Holm n, N. Wanner n, A. Cintron-Arias n, G. Kepler n & J. Wetherington*

author keywords: Compartmental model; Circulatory system; Drug delivery; Differential equations; Optimal dosing strategies; Sensitivity
TL;DR: A preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart using a compartmental mass balance approach and a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection is presented. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2009 journal article

A model for HCMV infection in immunosuppressed patients

MATHEMATICAL AND COMPUTER MODELLING, 49(7-8), 1653–1663.

By: G. Kepler*, H. Banksa, M. Davidian* & E. Rosenberg*

author keywords: HCMV; CMV; Herpes; Transplantation; Mathematical model; Immunosuppression
TL;DR: Simulations with the approximated parameter values demonstrates that the model is capable of describing primary, latent, and secondary (reactivated) HCMV infection. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2009 journal article

A sensitivity matrix based methodology for inverse problem formulation

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 17(6), 545–564.

By: A. Cintron-Arias*, H. Banks*, A. Capaldi* & A. Lloyd*

author keywords: Inverse problems; ordinary least squares; sensitivity matrix; Fisher Information matrix; parameter selection; standard errors
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Dispersive Media

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 25(4), 885–917.

By: H. Banks n, V. Bokil* & N. Gibson*

author keywords: Maxwell's equations; Debye; Lorentz; finite elements; FDTD; dissipation; dispersion
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Analysis of Viscoelastic Wall Properties in Ovine Arteries

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 56(2), 210–219.

By: D. Valdez-Jasso n, M. Haider n, H. Banks n, D. Santana*, Y. German*, R. Armentano*, M. Olufsen n

author keywords: Arterial wall properties; data analysis; mathematical modeling; mechanics; parameter estimation; viscoelasticity
MeSH headings : Algorithms; Animals; Arteries / physiology; Biomechanical Phenomena / physiology; Blood Pressure; Elasticity; Equipment Design; Male; Models, Cardiovascular; Nonlinear Dynamics; Sensitivity and Specificity; Sheep; Signal Processing, Computer-Assisted; Viscosity
TL;DR: Results reveal that elastic properties in both models vary across locations (smaller arteries are stiffer than larger arteries), and show that for all locations, the inclusion of viscoelastic behavior is important to capture pressure-area dynamics. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2009 journal article

Detection of arterial occlusions using viscoelastic wave propagation

Advances in Applied Mathematics & Mechanics, 1(1), 1–28.

By: H. Banks & J. Samuels

Source: NC State University Libraries
Added: August 6, 2018

2009 journal article

Estimation in time-delay modeling of insecticide-induced mortality

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 17(2), 101–125.

By: H. Banks*, J. Banks & S. Joyner*

author keywords: Inverse problems; ordinary and generalized least squares; delay-differential equation models; insect populations; insecticide exposure; time-varying mortality and maturation rates
TL;DR: Empirical efficacy of the methodology in the context of models for insect maturation and mortality due to insecticide exposure is demonstrated. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Experimental design and estimation of growth rate distributions in size-structured shrimp populations

Inverse Problems, 25(9), 095003.

By: H. Banks n, J. Davis n, S. Ernstberger n, S. Hu n, E. Artimovich* & A. Dhar*

TL;DR: 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
2. Zero Hunger (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: August 6, 2018

2009 book

Mathematical and experimental modeling of physical and biological processes

Boca Raton : CRC Press.

By: H. Banks & H. Tran

Source: NC State University Libraries
Added: August 6, 2018

2009 journal article

Public vaccination policy using an age-structured model of pneumococcal infection dynamics

Journal of Biological Dynamics, 4(2), 176–195.

By: K. Sutton n, H. Banks n & C. Castillo-Chavez*

MeSH headings : Adolescent; Adult; Age Factors; Aged; Aged, 80 and over; Child; Child, Preschool; Communicable Disease Control; Computer Simulation; Humans; Immunization Programs / methods; Infant; Infant, Newborn; Middle Aged; Models, Theoretical; Pneumococcal Infections / prevention & control; Pneumococcal Vaccines / immunology; Public Health; Public Policy; Streptococcus pneumoniae / metabolism; Vaccination
TL;DR: An age-structured SEIS-type model of pneumococcal diseases and their vaccination is introduced and the use of this framework in predicting the impact of vaccine strategies is discussed, with pneumitiscal diseases as an example. (via Semantic Scholar)
Source: Crossref
Added: January 5, 2021

2009 journal article

THE ESTIMATION OF THE EFFECTIVE REPRODUCTIVE NUMBER FROM DISEASE OUTBREAK DATA

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 6(2), 261–282.

By: A. Cintron-Arias n, C. Castillo-Chavez*, L. Bettencourt*, A. Lloyd* & H. Banks n

author keywords: effective reproductive number; basic reproduction ratio; reproduction number; R; R(t); R-0; parameter estimation; generalized least squares; residual plots
MeSH headings : Algorithms; Biometry / methods; Communicable Diseases / epidemiology; Disease Outbreaks / statistics & numerical data; Disease Transmission, Infectious / statistics & numerical data; Humans; Prevalence; Proportional Hazards Models
TL;DR: A single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t) are considered and the estimation of the underlying SIR parameters with a generalized least squares estimation technique is discussed. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Viscoelastic models for passive arterial wall dynamics

Advances in Applied Mathematics & Mechanics, 1(2), 151–165.

By: D. Valdez-Jasso, H. Banks, M. Haider, D. Bia, Y. Zocalo, R. Armentano, M. Olufsen

Source: NC State University Libraries
Added: August 6, 2018

2009 journal article

Well-posedness of inverse problems for systems with time dependent parameters

Arabian Journal for Science and Engineering, 34(1D), 39–58.

By: H. Banks & M. Pedersen

Source: NC State University Libraries
Added: August 6, 2018

2008 review

A brief review of some approaches to hysteresis in viscoelastic polymers

[Review of ]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 69(3), 807–815.

By: H. Banks n

author keywords: stress-strain laws; hysteresis; viseoelasticity; polymers; internal variables
Source: Web Of Science
Added: August 6, 2018

2008 journal article

A molecular based model for polymer viscoelasticity: Intra- and inter-molecular variability

APPLIED MATHEMATICAL MODELLING, 32(12), 2753–2767.

By: H. Banks n, J. Hood n & N. Medhin n

author keywords: molecular chain bead models; polymer viscoelasticity; variable and distributed relaxation times
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2008 journal article

A stick-slip/Rouse hybrid model for viscoelasticity in polymers

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 9(5), 2128–2149.

By: H. Banks n, J. Hood n, N. Medhin n & J. Samuels n

author keywords: viscoelasticity; stick-slip-Rouse model; parameter estimation
TL;DR: The model that is developed here treats PC molecule as entrapped within a constraining tube, which is comprised of both CC and PC molecules, and yields an explicit system of stress-strain equations for the system permitting simple calculations of complex stress–strain relations. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2008 journal article

Dynamic models for insect mortality due to exposure to insecticides

MATHEMATICAL AND COMPUTER MODELLING, 48(1-2), 316–332.

By: H. Banks n, J. Banks*, S. Joyner n & J. Stark*

author keywords: differential equation models; insect populations; insecticide exposure; time-varying mortality rates
TL;DR: It is shown that ordinary differential equation models for insecticide induced sublethal damage and delayed death in insect populations provide excellent fits to experimental data for populations subjected to numerous levels of insecticide exposure. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2008 journal article

Estimation of invasive pneumococcal disease dynamics parameters and the impact of conjugate vaccination in Australia

Mathematical Biosciences and Engineering, 5(1), 175–204.

By: K. Sutton, H. Banks & C. Castillo-Chavez

MeSH headings : Australia / epidemiology; Computer Simulation; Creutzfeldt-Jakob Syndrome / epidemiology; Creutzfeldt-Jakob Syndrome / prevention & control; Disease Outbreaks / prevention & control; Disease Outbreaks / statistics & numerical data; Humans; Incidence; Models, Biological; Pneumococcal Infections / epidemiology; Pneumococcal Infections / prevention & control; Population Surveillance / methods; Prevalence; Risk Assessment / methods; Risk Factors; Vaccines, Conjugate / therapeutic use
TL;DR: The results presented here suggest the state of these infections may be changing in response to the programs, and warrants close quantitative monitoring. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (OpenAlex)
Source: NC State University Libraries
Added: August 6, 2018

2008 journal article

Modeling of viscoelastic shear: A nonlinear stick-slip formulation

Dynamic Systems and Applications, 17(2), 383–405.

By: H. Banks, N. Medhin & G. Pinter

Source: NC State University Libraries
Added: August 6, 2018

2008 journal article

Modelling HIV immune response and validation with clinical data

Journal of Biological Dynamics, 2(4), 357–385.

By: H. Banks n, M. Davidian n, S. Hu n, G. Kepler n & E. Rosenberg n

MeSH headings : CD4-Positive T-Lymphocytes / immunology; CD4-Positive T-Lymphocytes / virology; HIV / immunology; HIV Antigens / immunology; HIV Infections / drug therapy; HIV Infections / immunology; HIV Infections / virology; Humans; Immunity / immunology; Models, Immunological; Reproducibility of Results; Viral Load / immunology; Viremia / immunology; Virus Activation / immunology
TL;DR: 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, and it is shown that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower viral load is not possible for these patients. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (OpenAlex)
Sources: Crossref, ORCID
Added: January 23, 2020

2008 journal article

Modelling of propagating shear waves in biotissue employing an internal variable approach to dissipation

Communications in Computational Physics, 3(3), 603–640.

By: H. Banks & N. Luke

Source: NC State University Libraries
Added: August 6, 2018

2008 journal article

QUANTIFYING UNCERTAINTY IN THE ESTIMATION OF PROBABILITY DISTRIBUTIONS

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 5(4), 647–667.

By: H. Banks n & J. Davis n

author keywords: approximation; asymptotic standard error theory; confidence bands; parameter estimation; probability distributions; size-structured populations
MeSH headings : Models, Statistical; Probability; Uncertainty
TL;DR: A computational framework for quantification of uncertainty associated with the estimated parameters is given and sample numerical findings are presented. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2008 journal article

Sensitivity to noise variance in a social network dynamics model

QUARTERLY OF APPLIED MATHEMATICS, 66(2), 233–247.

By: H. Banks n, A. Karr*, H. Nguyen n & J. Samuels n

UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2008 journal article

Time-varying vital rates in ecotoxicology: Selective pesticides and aphid population dynamics

ECOLOGICAL MODELLING, 210(1-2), 155–160.

By: J. Banks*, L. Dick n, H. Banks n & J. Stark*

author keywords: ecotoxicology; partial differential equation; Sinko-Streifer; sublethal effects; inverse problem; parameter estimates; Aphididae; risk assessment
TL;DR: This work shows that constant-parameter versions of commonly used population dynamics models do not adequately capture the population dynamics of aphids subjected to a selective pesticide, and suggests that a simple modification of the differential equation model with time-varying mortality rates provides a highly accurate fit to aphid population data. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2007 article

A comparison of approximation methods for the estimation of probability distributions on parameters

APPLIED NUMERICAL MATHEMATICS, Vol. 57, pp. 753–777.

By: H. Banks n & J. Davis n

Source: Web Of Science
Added: August 6, 2018

2007 journal article

A dynamic model for induced reactivation of latent virus

JOURNAL OF THEORETICAL BIOLOGY, 244(3), 451–462.

By: G. Kepler n, H. Nguyen n, J. Webster-Cyriaque* & H. Banks n

author keywords: reactivation of latent virus; mathematical model; KSHV; Herpes virus
MeSH headings : Butyrates / pharmacology; Cell Cycle; Cell Death; Cell Line, Tumor; DNA Replication; DNA, Viral / physiology; Herpesvirus 8, Human / physiology; Humans; Lymphoma / pathology; Lymphoma / virology; Models, Biological; Models, Statistical; Virus Activation; Virus Latency / drug effects
TL;DR: A deterministic mathematical model is developed to describe reactivation of latent virus by chemical inducers and 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2007 journal article

Estimation and prediction with HIV-treatment interruption data

BULLETIN OF MATHEMATICAL BIOLOGY, 69(2), 563–584.

By: B. Adams n, H. Banks n, M. Davidian n & E. Rosenberg*

author keywords: HIV models; treatment interruptions; censored data; parameter estimation; prediction
MeSH headings : Antiretroviral Therapy, Highly Active / methods; CD4 Lymphocyte Count; Cohort Studies; Data Interpretation, Statistical; Drug Administration Schedule; HIV Infections / drug therapy; HIV Infections / immunology; HIV-1; Humans; Longitudinal Studies; Models, Biological; Predictive Value of Tests; Viral Load
TL;DR: This work uses a nonlinear dynamical mathematical model in attempts to fit individual patient data for HIV patients undergoing treatment interruptions using a statistically-based censored data method and inverse problem techniques to estimate dynamic parameters. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2007 journal article

Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides

BULLETIN OF MATHEMATICAL BIOLOGY, 69(7), 2139–2180.

By: H. Banks n, J. Banks*, L. Dick n & J. Stark*

author keywords: population models; Leslie; Sinko-Streifer; McKendrick-VonForester; time-dependent parameters
MeSH headings : Age Factors; Algorithms; Animals; Aphids / growth & development; Computer Simulation; Confidence Intervals; Fertility / drug effects; Insecta / growth & development; Models, Biological; Pest Control / methods; Pesticides / toxicity; Population Density; Population Dynamics; Population Growth; Survival Analysis; Time Factors; Vicia faba / growth & development
TL;DR: This continuous model is used to estimate time-dependent mortality parameters in an ordinary least-squares technique and results from tests for statistical significance of added parameters are presented. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2007 journal article

Monotone approximation for a nonlinear size and class age structured epidemic model

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 8(3), 834–852.

By: H. Banks n, V. Bokil n & S. Hu n

author keywords: size and class age structured models; well-posedness; monotone approximations; comparison principle
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2007 journal article

Multiscale Considerations in Modeling of Nonlinear Elastomers

International Journal for Computational Methods in Engineering Science and Mechanics, 8(2), 53–62.

By: H. Banks n, N. Medhin n & G. Pinter*

author keywords: Nonlinear Partial Differential Equations; Computational Methods; Viscoelasticity; Hysteresis; Molecular Dynamics; Multiscale Modeling
TL;DR: A survey of results from an extended project focused on the understanding of the dynamic behavior of elastomers or filled rubbers, with particular emphasis are the nonlinear and hysteretic aspects of dynamic deformations. (via Semantic Scholar)
Source: Crossref
Added: February 24, 2020

2007 journal article

Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 37(2), 177–218.

By: H. Banks n, B. Lewis* & H. Tran n

author keywords: nonlinear feedback control; nonlinear compensator; state-dependent Riccati equations
TL;DR: This paper addresses the effectiveness and potential of the SDRE technique for the design of nonlinear compensator-based feedback controllers and the asymptotic convergence of the estimator and the compensated system. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2007 journal article

Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space

Mathematical Biosciences and Engineering, 4(3), 403–430.

By: H. Banks n, S. Dediu n & H. Nguyen n

MeSH headings : Algorithms; Computer Simulation; Models, Biological; Sensitivity and Specificity
TL;DR: A theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space is developed and schemes that approximate the measures in the Prohorov sense are illustrated. (via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018

2007 journal article

Stochastic and deterministic models for agricultural production networks

Mathematical Biosciences and Engineering, 4(3), 373–402.

By: P. Bai*, H. Banks n, S. Dediu n, A. Govan n, M. Last, A. Lloyd n, H. Nguyen*, M. Olufsen n, G. Rempala*, B. Slenning n

Contributors: P. Bai*, H. Banks n, S. Dediu n, A. Govan n, M. Last, A. Lloyd n, H. Nguyen*, M. Olufsen n, G. Rempala*, B. Slenning n

MeSH headings : Animal Husbandry / methods; Animal Husbandry / organization & administration; Animals; Animals, Domestic; Computer Simulation; Models, Biological; Models, Organizational; Models, Statistical; Stochastic Processes; Swine / growth & development
TL;DR: An approach to modeling the impact of disturbances in an agricultural production network and its approximate deterministic model for averages over sample paths of the stochastic system are presented. (via Semantic Scholar)
UN Sustainable Development Goal Categories
2. Zero Hunger (OpenAlex)
Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2007 article

Time delay systems with distribution dependent dynamics

ANNUAL REVIEWS IN CONTROL, Vol. 31, pp. 17–26.

By: H. Banks n, S. Dediu n & H. Nguyen n

author keywords: inverse dynamics problem; probability distribution function; sensitivity analysis; biomedical systems
TL;DR: 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2007 journal article

Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection

DRUG AND ALCOHOL DEPENDENCE, 88, S41–S51.

By: E. Rosenberg n, M. Davidian n & H. Banks n

author keywords: STI; CD4; HIV dynamics; drug resistance; viral load
MeSH headings : CD4 Antigens / immunology; HIV Infections / drug therapy; HIV Infections / immunology; Humans; Models, Theoretical
TL;DR: It is argued that the most promising STI strategies are adaptive treatment strategies, which involve cycles of treatment withdrawal and re-initiation and 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. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2007 article

Viscoelasticity in polymers: Phenomenological to molecular mathematical modeling

Banks, H. T., Luke, N. S., & Samuels, J. R., Jr. (2007, July). NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Vol. 23, pp. 817–831.

By: H. Banks n, N. Luke n & J. Samuels n

author keywords: viscoelastic polymers; constitutive models; biotissue; stenosis; shear wave propagation
TL;DR: A new constitutive model that combines the virtual stick‐slip continuum “molecular‐based” ideas of Johnson and Stacer with the Rouse bead chain ideas is reported and a two‐dimensional version of a model that accounts for stenosis‐driven shear wave propagation in biotissue is reported. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2006 journal article

A state-dependent Riccati equation-based estimator approach for HIV feedback control

OPTIMAL CONTROL APPLICATIONS & METHODS, 27(2), 93–121.

By: H. Banks n, H. Kwon*, J. Toivanen n & H. Tran n

author keywords: multidrug therapies; feedback control; estimator; HIV model; SDRE
TL;DR: By anticipation of and response to the disease progression, the dynamic multidrug strategy reduces the viral load, increases the CD4+ T‐cell count and improves the immune response. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2006 journal article

Determination of interrogating frequencies to maximize electromagnetic backscatter from objects with material coatings

Communications in Computational Physics, 1(2), 362–382.

By: H. Banks, K. Ito & J. Toivanen

Source: NC State University Libraries
Added: August 6, 2018

2006 journal article

Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters

QUARTERLY OF APPLIED MATHEMATICS, 64(4), 749–795.

By: H. Banks n & N. Gibson n

author keywords: electromagnetic interrogation; pulsed antenna source microwaves; inverse problems; complex dielectric materials; distributions of relaxation parameters and mechanisms
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Homogenization of periodically varying coefficients in electromagnetic materials

JOURNAL OF SCIENTIFIC COMPUTING, 28(2-3), 191–221.

By: H. Banks n, V. Bokil n, D. Cioranescu*, N. Gibson n, G. Griso* & B. Miara*

author keywords: Homogenization; Maxwell's equations; debye dielectric materials; pulsed antenna source microwaves
TL;DR: The periodic unfolding method for simulating the electromagnetic field in a composite material exhibiting heterogeneous microstructures which are described by spatially periodic parameters is employed. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Material surface design to counter electromagnetic interrogation of targets

SIAM JOURNAL ON APPLIED MATHEMATICS, 66(3), 1027–1049.

By: H. Banks*, K. Ito*, G. Kepler* & J. Toivanen*

author keywords: electromagnetic; inverse scattering; attenuation
TL;DR: F 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Sensitivity of dynamical systems to Banach space parameters

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 323(1), 146–161.

By: H. Banks* & H. Nguyen*

author keywords: sensitivity equations; delay differential equations; approximation
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Void detection in foam with knit lines using THz pulse interrogation

MATHEMATICAL AND COMPUTER MODELLING, 44(9-10), 807–815.

By: H. Banks n & N. Gibson n

author keywords: terahertz electromagnetic waves; heterogeneous materials; numerical simulations
TL;DR: This work describes its 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2005 journal article

A computational and statistical framework for multidimensional domain acoustooptic material interrogation

QUARTERLY OF APPLIED MATHEMATICS, 63(1), 156–200.

By: H. Banks n & V. Bokil n

author keywords: electromagnetic-acoustic interaction; Debye dielectric materials; pulsed antenna source microwaves; inverse problems; FDTD; statistical inference
Source: Web Of Science
Added: August 6, 2018

2005 journal article

A hierarchical Bayesian approach for parameter estimation in HIV models

INVERSE PROBLEMS, 21(6), 1803–1822.

By: H. Banks n, S. Grove n, S. Hu n & Y. Ma*

UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2005 journal article

A parameter sensitivity methodology in the context of HIV delay equation models

JOURNAL OF MATHEMATICAL BIOLOGY, 50(6), 607–625.

By: H. Banks n & D. Bortz*

author keywords: sensitivity analysis; parameter sensitivity methodology; HIV Models
MeSH headings : Computer Simulation; HIV / growth & development; HIV Infections / virology; Humans; Models, Biological; Virus Replication
TL;DR: A sensitivity methodology for nonlinear delay systems arising in one class of cellular HIV infection models is presented and theoretical foundations for a typical sensitivity investigation and illustrative computations are given. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2005 article

A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue

MULTISCALE MODELING & SIMULATION, Vol. 3, pp. 395–412.

By: H. Banks* & G. Pinter

author keywords: multiscale modeling; hysteresis; wave propagation; biotissues; probability measures; Prohorov metric
TL;DR: A theoretical framework for treating hysteresis as multiscale phenomena which must be averaged across distributions of internal variables is presented, which entail probability measure-dependent partial differential equations for which well-posedness is established. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Gap detection with electromagnetic terahertz signals

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 6(2), 381–416.

By: H. Banks n, N. Gibson* & W. Winfree*

author keywords: electromagnetic interrogation; dielectrics; terahertz; nonlinear optimization
Source: Web Of Science
Added: August 6, 2018

2005 journal article

HIV dynamics: Modeling, data analysis, and optimal treatment protocols

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 184(1), 10–49.

By: B. Adams n, H. Banks n, M. Davidian n, H. Kwon n, H. Tran n, S. Wynne n, E. Rosenberg*

author keywords: HIV models; parameter estimation; data and model reduction; structured treatment interruptions; optimal control
TL;DR: An overview of some concepts and methodologies useful in modeling HIV pathogenesis including parameter estimation, data reduction and representation, and optimal control relative to STI are presented. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2005 journal article

Parameter estimation in a coupled system of nonlinear size-structured populations

Mathematical Biosciences and Engineering, 2(2), 289–315.

By: A. Ackleh*, H. Banks*, K. Deng & S. Hu n

TL;DR: A least squares technique is developed for identifying unknown parameters in a coupled system of nonlinear size-structured populations and convergence results for the parameter estimation technique are established. (via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018

2005 journal article

Population dynamics models in plant-insect herbivore-pesticide interactions

MATHEMATICAL BIOSCIENCES, 196(1), 39–64.

By: B. Adams n, H. Banks n, J. Banks* & J. Stark*

author keywords: plant-insect interactions; inverse problems; hypothesis testing; standard errors in dynamical models
MeSH headings : Animals; Aphids / physiology; Brassica / drug effects; Brassica / parasitology; Brassica / physiology; Insecta / physiology; Insecticides / pharmacology; Mathematics; Models, Biological; Plant Diseases / parasitology; Plant Physiological Phenomena; Plants / drug effects; Plants / parasitology; Population Dynamics
TL;DR: This work considers several population dynamics models in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types and three levels of insecticide spray to compare autonomous versus non-autonomous model dynamics. (via Semantic Scholar)
UN Sustainable Development Goal Categories
2. Zero Hunger (Web of Science)
13. Climate Action (Web of Science)
15. Life on Land (Web of Science)
Source: Web Of Science
Added: August 6, 2018

2005 article

Time domain electromagnetic scattering using finite elements and perfectly matched layers

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol. 194, pp. 149–168.

By: H. Banks n & B. Browning n

author keywords: scattering; Debye; perfectly matched layers; absorbing boundary condition
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Well-posedness in Maxwell systems with distributions of polarization relaxation parameters

APPLIED MATHEMATICS LETTERS, 18(4), 423–430.

By: H. Banks n & N. Gibson n

author keywords: well-posedness; Maxwell's equations with polarization; relaxation parameters
TL;DR: This work presents existence, uniqueness and continuous dependence (with respect to probability distributions on polarization parameters) of solutions in Maxwell systems and provides a theoretical and computational foundation for associated inverse problems. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Well-posedness results for a class of toxicokinetic models

Dynamic Systems and Applications, 14(2), 297–322.

By: H. Banks & L. Potter

Source: NC State University Libraries
Added: August 6, 2018

2004 journal article

Dynamic multidrug therapies for HIV: Optimal and STI control approaches

Mathematical Biosciences and Engineering, 1(2), 223–241.

By: B. Adams n, H. Banks*, H. Kwon* & H. Tran n

TL;DR: A dynamic mathematical model is formulated that describes the interaction of the immune system with the human immunodeficiency virus and that permits drug "cocktail" therapies and supports a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (OpenAlex)
Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2004 journal article

High-frequency pulse propagation in nonlinear dielectric materials

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 5(4), 597–612.

By: H. Banks* & G. Pinter*

author keywords: Maxwell's equations; nonlinear dielectrics; terahertz pulse propagation
Source: Web Of Science
Added: August 6, 2018

2004 journal article

Modeling and optimal regulation of erythropoiesis subject to benzene intoxication

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 1(1), 15–48.

By: H. Banks n, C. Cole*, P. Schlosser n & H. Tran n

author keywords: hematopoiesis; age-structured model; existence and uniqueness; optimal control
TL;DR: This investigation proved the existence and uniqueness of the solution of the system of coupled partial and ordinary differential equations, 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. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2004 journal article

Nonlinear reptation in molecular based hysteresis models for polymers

QUARTERLY OF APPLIED MATHEMATICS, 62(4), 767–779.

By: H. Banks n, N. Medhin n & G. Pinter n

author keywords: viscoelastic; hysteresis; polymers; molecular models; relaxation times; probability; distributions; uncertainty
Source: Web Of Science
Added: August 6, 2018

2004 journal article

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

MATHEMATICAL BIOSCIENCES, 192(2), 193–225.

By: H. Banks n & L. Potter*

author keywords: parameter estimation; biological modeling; population variability; model uncertainty; toxicokinetics; trichloroethylene
MeSH headings : Animals; Environmental Pollutants / pharmacokinetics; Environmental Pollutants / toxicity; Humans; Mathematics; Models, Biological; Models, Statistical; Pharmacokinetics; Trichloroethylene / pharmacokinetics; Trichloroethylene / toxicity
TL;DR: 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2004 journal article

Well-posedness for a nonsmooth acoustic system

Applied Mathematics Letters, 17(3), 317–322.

By: H. Banks & J. Raye

Source: NC State University Libraries
Added: August 6, 2018

2004 journal article

Well-posedness for a nonsmooth acoustic system

Applied Mathematics Letters, 17(3), 317–322.

By: H. Banks n & J. Raye n

author keywords: well-posedness; wave equations; acoustics
TL;DR: An acoustic wave system with discontinuous coefficients and nonsmooth inputs is considered and existence, uniqueness, and continuous dependence on input data of weak solutions are established. (via Semantic Scholar)
Source: Crossref
Added: February 24, 2020

2003 journal article

Acoustic attenuation employing variable wall admittance

Directions in Mathematical Systems Theory and Optimization (Lecture Notes in Control and Information Sciences; 286), (2003), 15–26.

By: H. Banks, K. Furati, K. Ito, N. Luke & C. Smith

Ed(s): C. A. Rantzer

Source: NC State University Libraries
Added: August 6, 2018

2003 book

Bioterrorism: Mathematical modeling applications in homeland security

Philadelphia, PA: Society for Industrial and Applied Mathematics.

By: H. Banks & C. Castillo-Chavez

Source: NC State University Libraries
Added: August 6, 2018

2003 journal article

Incorporation of variability into the modeling of viral delays in HIV infection dynamics

MATHEMATICAL BIOSCIENCES, 183(1), 63–91.

By: H. Banks n, D. Bortz* & S. Holte*

author keywords: HIV pathogenesis; eclipse phase; variability; non-linear delay equations
MeSH headings : Computer Simulation; HIV / physiology; HIV Infections / virology; Humans; Models, Biological; Nonlinear Dynamics; Numerical Analysis, Computer-Assisted; Probability; Virus Replication
TL;DR: Methods for incorporating arbitrary variability for temporal delays in HIV pathogenesis into systems that cannot readily be reduced to a finite number of coupled ordinary differential equations are developed. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2003 journal article

Maxwell-systems with nonlinear polarization

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 4(3), 483–501.

By: H. Banks n & G. Pinter*

UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2002 journal article

A computational model for sound field absorption by acoustic arrays

Journal of Intelligent Material Systems and Structures, 13(4), 231–240.

By: H. Banks, D. Cole, K. Furati, K. Ito & G. Pinter

Source: NC State University Libraries
Added: August 6, 2018

2002 journal article

A finite difference approximation for a coupled system of nonlinear size-structured populations

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 50(6), 727–748.

By: A. Ackleh*, H. Banks n & K. Deng*

author keywords: coupled system of size-structured populations; existence-uniqueness; finite difference approximation; competition; extinction; survival
Source: Web Of Science
Added: August 6, 2018

2002 journal article

A nonlinear beam equation

APPLIED MATHEMATICS LETTERS, 15(3), 381–387.

By: A. Ackleh*, H. Banks n & G. Pinter n

author keywords: well posedness; locally Lipschitz nonlinear elastic systems
TL;DR: Existence and uniqueness of weak solutions to a nonlinear beam equation is established under relaxed assumptions (locally Lipschitz plus affine domination) on the nonlinearity in the stiffness constitutive law. (via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Analysis of bonded elastic blocks

MATHEMATICAL AND COMPUTER MODELLING, 36(7-8), 875–888.

By: H. Banks n, G. Pinter* & O. Yeoh*

author keywords: elasticity; compression; incompressibility; near incompressibility; partial differential equations; finite element simulations
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Analysis of thermal conductivity in composite adhesives

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 23(7-8), 705–745.

By: H. Banks n & K. Bihari n

author keywords: thermal conductivity; composite adhesives; well-posedness; inverse problems; sensitivity equations
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Analytical and numerical treatment of a curved active constrained layer structure

Dynamic Systems and Applications, 11(1), 75–87.

By: H. Banks, N. Begashaw & N. Medhin

Source: NC State University Libraries
Added: August 6, 2018

2002 review

Compression of bonded rubber blocks

[Review of ]. RUBBER CHEMISTRY AND TECHNOLOGY, 75(3), 549–561.

By: O. Yeoh*, G. Pinter* & H. Banks n

UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Identification of material damage in two-dimensional domains using the SQUID-based nondestructive evaluation system

INVERSE PROBLEMS, 18(6), 1831–1855.

By: H. Banks n & F. Kojima*

Source: Web Of Science
Added: August 6, 2018

2002 journal article

Model predictions and comparisons for three toxicokinetic models for the systemic transport of trichloroethylene

MATHEMATICAL AND COMPUTER MODELLING, 35(9-10), 1007–1032.

By: H. Banks n & L. Potter n

author keywords: PBPK modeling; TCE adipose tissue; PDE systems; dispersion
TL;DR: Three physiologically based pharmacokinetic models for the systemic transport of trichloroethylene (TCE) are presented and it is suggested 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Nondestructive evaluation of materials using pulsed microwave interrogating signals and acoustic wave induced reflections

INVERSE PROBLEMS, 18(6), 1935–1958.

By: R. Albanese*, H. Banks n & J. Raye n

Source: Web Of Science
Added: August 6, 2018

2002 journal article

Physiologically based pharmacokinetic models for the transport of trichloroethylene in adipose tissue

BULLETIN OF MATHEMATICAL BIOLOGY, 64(1), 97–131.

By: R. Albanese, H. Banks n, M. Evans* & L. Potter*

MeSH headings : Adipose Tissue / metabolism; Animals; Computer Simulation; Humans; Models, Biological; Rats; Rats, Sprague-Dawley; Trichloroethylene / pharmacokinetics
TL;DR: Three physiologically based pharmacokinetic (PBPK) models for the systemic transport of trichloroethylene (TCE), with a focus on the adipose, or fat tissue, are presented. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Proper orthogonal decomposition-based control of transverse beam vibrations: Experimental implementation

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, 10(5), 717–726.

By: H. Banks n, R. Rosario n & H. Tran n

author keywords: Euler-Bernoulli beam equation; feedback control; linear quadratic Gaussian (LQG); proper orthogonal decomposition (POD); reduced order model
TL;DR: Linear quadratic Gaussian compensator control of transverse vibrations was implemented on an aluminum cantilevered beam in a "smart structure" paradigm and experimental results indicate that POD-based control achieves comparable control attenuation with full-order model- based control. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2002 journal article

Real time computational algorithms for eddy-current-based damage detection

INVERSE PROBLEMS, 18(3), 795–823.

By: H. Banks n, M. Joyner n, B. Wincheski* & W. Winfree*

Source: Web Of Science
Added: August 6, 2018

2002 journal article

Reduced order modeling and control of thin film growth in an HPCVD reactor

SIAM JOURNAL ON APPLIED MATHEMATICS, 62(4), 1251–1280.

By: H. Banks*, S. Beeler, G. Kepler* & H. Tran*

author keywords: chemical vapor deposition; reduced order model; nonlinear feedback tracking control; nonlinear compensator; state-dependent Riccati equations
TL;DR: 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. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2002 journal article

Well-posedness for systems representing electromagnetic/acoustic wavefront interaction

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 8, 105–125.

By: H. Banks n & J. Raye n

author keywords: electromagnetic interrogation; acoustic wave reflectors; existence and uniqueness
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Well-posedness results for models of elastomers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 268(2), 440–456.

By: A. Ackleh*, H. Banks n & G. Pinter n

UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2001 journal article

Compensator control for chemical vapor deposition film growth using reduced-order design models

IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, 14(3), 231–241.

By: G. Kepler n, H. Tran n & H. Banks n

author keywords: compensators; CVD; feedback control; reduced order
Sources: Web Of Science, ORCID
Added: August 6, 2018

2001 article

Convergence of approximations in feedback control of structures

MATHEMATICAL AND COMPUTER MODELLING, Vol. 33, pp. 65–78.

By: H. Banks n & R. Rosario n

author keywords: feedback control; approximation; LQR; control convergence
Source: Web Of Science
Added: August 6, 2018

2001 article

Dynamic simulation of the temporal response of microstructure formation in magnetorheological fluids

Ly, H. V., Ito, K., Banks, H. T., Jolly, M. R., & Reitich, F. (2001, March 20). INTERNATIONAL JOURNAL OF MODERN PHYSICS B, Vol. 15, pp. 894–903.

By: H. Ly n, K. Ito n, H. Banks n, M. Jolly* & F. Reitich*

Source: Web Of Science
Added: August 6, 2018

2001 journal article

Graduate education in computational science and engineering

SIAM Review, 43(1), 163–177.

By: L. Petzold, U. Ascher, H. Banks, J. Crowley, W. Gander, L. Greengard, M. Heath, A. Lumsdaine ...

Source: NC State University Libraries
Added: August 6, 2018

2001 journal article

Modelling and estimating uncertainty in parameter estimation

INVERSE PROBLEMS, 17(1), 95–111.

By: H. Banks n & K. Bihari n

UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2001 journal article

Nonlinear exothermic contributions to radio-frequency bonding of adhesives

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2(3), 357–386.

By: H. Banks n, M. Choi n, . Durso* & K. Ito n

author keywords: radio-frequency electromagnetic bonding; nonlinear thermal processes; operator splitting; existence and uniqueness
Source: Web Of Science
Added: August 6, 2018

2001 journal article

Piecewise linear model for field-responsive fluids

IEEE TRANSACTIONS ON MAGNETICS, 37(1), 558–560.

By: C. Lee*, F. Reitich*, M. Jolly* & H. Banks n

author keywords: field-responsive fluids; Frohlich-Kennelly; nonlinear saturation; piecewise linear models
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2001 article

Predictions for a distributed parameter model describing the hepatic processing of 2,3,7,8-TCDD

MATHEMATICAL AND COMPUTER MODELLING, Vol. 33, pp. 49–64.

By: H. Banks n, C. Musante n & J. Raye n

author keywords: distributed parameter models; pharmacokinetic models; 2,3,7,8-tetrachlorodibenzopdioxin; liver transport models; delay equations
Source: Web Of Science
Added: August 6, 2018

2001 article

Remarks on uncertainty assessment and management in modeling and computation

MATHEMATICAL AND COMPUTER MODELLING, Vol. 33, pp. 39–47.

By: H. Banks n

author keywords: computational uncertainty; inverse problems; probability distributions
TL;DR: A computationally tractable probabilistic framework to treat uncertainty in the estimation of parameters or inverse problems is given and a simple computational example for the estimationof constant parameters in differential equations by treating the parameters as random variables is illustrated. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2001 article

The effective magnetic properties of magnetorheological fluids

MATHEMATICAL AND COMPUTER MODELLING, Vol. 33, pp. 273–284.

By: T. Simon n, F. Reitich*, M. Jolly*, K. Ito n & H. Banks n

author keywords: magnetorheological fluids; homogenization; effective properties
Source: Web Of Science
Added: August 6, 2018

2000 journal article

Approximation methods for inverse problems governed by nonlinear parabolic systems

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 21(7-8), 791–816.

By: H. Banks*, C. Musante & J. Raye*

author keywords: inverse problems; nonlinear parabolic systems; approximation techniques; least squares optimization; computational methods
TL;DR: A rigorous theoretical framework for approximation of nonlinear parabolic systems with delays in the context of inverse least squares problems is presented and sample numerical results demonstrating the convergence are given. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2000 journal article

Feedback control methodologies for nonlinear systems

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 107(1), 1–33.

By: S. Beeler n, H. Tran n & H. Banks n

author keywords: nonlinear optimal feedback control; Hamilton-Jacobi-Bellman equation; state-dependent Riccati equation; interpolation of open-loop controls
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2000 journal article

Nondestructive evaluation using a reduced-order computational methodology

INVERSE PROBLEMS, 16(4), 929–945.

By: H. Banks n, M. Joyner n, B. Wincheski* & W. Winfree*

TL;DR: 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 and finds the methods to be efficient and robust even with data containing 10% relative noise. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2000 journal article

Reduced order model compensator control of species transport in a CVD reactor

OPTIMAL CONTROL APPLICATIONS & METHODS, 21(4), 143–160.

By: G. Kepler n, H. Tran n & H. Banks n

author keywords: linear quadratic control; proper orthogonal decomposition; reduced order model; chemical vapour deposition; Dirichlet boundary control
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2000 journal article

Reduced-order model feedback control design: Numerical implementation in a thin shell model

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 45(7), 1312–1324.

By: H. Banks n, R. Rosario n & R. Smith n

author keywords: LQR feedback control; proper orthogonal decomposition; reduced-basis computational methods; thin shell dynamics
TL;DR: 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. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

1999 journal article

Approximation results for parameter estimation in a class of abstract nonlinear hyperbolic systems

APPLIED MATHEMATICS LETTERS, 12(6), 129–133.

By: H. Banks n & G. Pinter n

author keywords: nonlinear hyperbolic systems; parameter estimation; approximation
TL;DR: An approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems, including as a special case those modeling a large class of nonlinear elastomers. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Estimation of the effective permeability in magnetorheological fluids

JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, 10(11), 872–879.

By: T. Simon, K. Ito*, H. Banks n, F. Reitich* & M. Jolly*

UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Modeling of nonlinear hysteresis in elastomers under uniaxial tension

JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, 10(2), 116–134.

By: H. Banks*, G. Pinter, L. Potter n, M. Gaitens & L. Yanyo*

UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Optimal design of a high pressure organometallic chemical vapor deposition reactor

MATHEMATICAL AND COMPUTER MODELLING, 29(8), 65–80.

By: <