Displaying **all 18** works

Sorted by most recent date added to the index first, which may not be the same as publication date order.

2020 chapter

Central-upwind scheme for a non-hydrostatic Saint-Venant system

In *Hyperbolic problems: theory, numerics, applications* (Vol. 10, pp. 25–41). Am. Inst. Math. Sci. (AIMS), Springfield, MO.

Source: ORCID

Added: September 19, 2023

2020 journal article

Operator splitting based central-upwind schemes for shallow water equations with moving bottom topography

*Communications in Mathematical Sciences*, *18*(8), 2149–2168.

Source: ORCID

Added: April 28, 2021

2020 journal article

Biologically-informed neural networks guide mechanistic modeling from sparse experimental data

*PLOS COMPUTATIONAL BIOLOGY*, *16*(12).

MeSH headings : Computer Simulation; Machine Learning; Neural Networks, Computer; Nonlinear Dynamics

TL;DR:
BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE).
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: January 4, 2021

2020 article

Radiation Source Localization Using Surrogate Models Constructed from 3-D Monte Carlo Transport Physics Simulations

*NUCLEAR TECHNOLOGY*.

author keywords: Radiation detection; inverse problem; Bayesian inference; MCNP; surrogate modeling

TL;DR:
The Monte Carlo N-Particle code is employed to provide high-fidelity simulations of radiation transport within an urban domain to develop efficient and accurate surrogate models of the detector responses that provide an efficient framework for Bayesian inference and experimental design.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

11. Sustainable Cities and Communities
(OpenAlex)

Source: ORCID

Added: October 25, 2020

2020 journal article

Learning Equations from Biological Data with Limited Time Samples

*BULLETIN OF MATHEMATICAL BIOLOGY*, *82*(9).

author keywords: Equation learning; Numerical differentiation; Sparse regression; Model selection; Partial differential equations; Parameter estimation; Population dynamics; Glioblastoma multiforme

MeSH headings : Computational Biology / methods; Glioblastoma; Humans; Learning; Mathematical Concepts; Models, Biological; Nonlinear Dynamics

TL;DR:
This work presents an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data and highlights how these results are informative for data-driven modeling-based tumor invasion predictions.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: September 28, 2020

2020 journal article

AN FE-FD METHOD FOR ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *42*(4), B1041–B1066.

author keywords: anisotropic elliptic interface problem; finite element and finite difference method; maximum principle preserving scheme; normal derivative computation; scaling technique; error analysis

TL;DR:
Anisotropic elliptic interface problems are important but hard to solve either analytically or numerically, so there is limited literature on numerical methods based on structured meshes.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: September 28, 2020

2020 review

A tutorial review of mathematical techniques for quantifying tumor heterogeneity

[Review of ]. *MATHEMATICAL BIOSCIENCES AND ENGINEERING*, *17*(4), 3660–3709.

author keywords: cancer heterogeneity; mathematical oncology; tumor growth; glioblastoma multiforme; virtual populations; nonlinear mixed effects; spatiotemporal data; Bayesian estimation; generative; adversarial networks; non-parametric estimation; variational autoencoders; machine learning

MeSH headings : Bayes Theorem; Humans; Machine Learning; Models, Theoretical; Neoplasms; Precision Medicine

TL;DR:
Several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data are reviewed, including virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 3, 2020

2020 journal article

Method of Difference Potentials for Evolution Equations with Lacunas

*COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS*, *60*(4), 711–722.

author keywords: method of difference potentials; Huygens principle; lacunas; wave equation

Sources: Web Of Science, NC State University Libraries

Added: June 29, 2020

2020 journal article

STATISTICAL CHARACTERIZATION OF SCATTERING DELAY IN SYNTHETIC APERTURE RADAR IMAGING

*INVERSE PROBLEMS AND IMAGING*, *14*(3), 511–533.

author keywords: SAR imaging; scattering delay; speckle; confidence level; Monte-Carlo

TL;DR:
A maximum likelihood based approach for discriminating between the instantaneous and delayed targets in SAR images that takes into account the difference in thresholds for different target contrasts without making any assumptions about the statistics of those contrasts.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

10. Reduced Inequalities
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: April 14, 2020

2020 journal article

Learning partial differential equations for biological transport models from noisy spatio-temporal data

author keywords: numerical differentiation; equation learning; sparse regression; partial differential equations; parameter estimation; biological transport

TL;DR:
It is shown that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.
(via Semantic Scholar)

Source: Web Of Science

Added: March 30, 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

Variance-based sensitivity analysis for time-dependent processes

*RELIABILITY ENGINEERING & SYSTEM SAFETY*, *196*.

author keywords: Global sensitivity analysis; Sobol' Indices; Karhunen-Loeve expansion; Time-dependent processes; Surrogate models; Polynomial chaos; Uncertainty quantification

TL;DR:
A variance-based method is developed that leverages the correlation structure of the problems under study and employs surrogate models to accelerate the computations and analyzes errors resulting from fixing unimportant uncertain parameters to their nominal values through a priori estimates.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, ORCID

Added: March 16, 2020

2020 journal article

Mesh independence of the generalized Davidson algorithm

*Journal of Computational Physics*, *409*, 109322.

author keywords: Generalized Davidson algorithm; Mesh independence; Neutron transport; Electronic structure computations

TL;DR:
Conditions under which the generalized Davidson algorithm for eigenvalue computations is mesh-independent are given, which means that the iteration statistics of a sequence of discretizations of a problem in a Banach space converge the statistics for the infinite-dimensional problem.
(via Semantic Scholar)

Source: ORCID

Added: February 21, 2020

2020 journal article

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

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

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

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: January 13, 2020

2020 journal article

Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System

*COMMUNICATIONS IN COMPUTATIONAL PHYSICS*, *27*(2), 480–502.

Sources: Web Of Science, ORCID

Added: December 30, 2019

2020 journal article

Parameter estimation using aggregate data

*APPLIED MATHEMATICS LETTERS*, *100*.

author keywords: Uncertainty quantification; Parameter estimation; CAR T cancer therapy

TL;DR:
These issues are discussed in the context of a mathematical model to determine T-cell behavior with cancer chimeric antigen receptor (CAR) therapies where during the collection of data cancerous mice are sacrificed at each measurement time.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: November 25, 2019

2020 journal article

How to obtain an accurate gradient for interface problems?

*Journal of Computational Physics*, *405*, 109070.

author keywords: Accuracy of derivatives; Elliptic interface problems; Discontinuous coefficient; Discrete Green functions; IIM

TL;DR:
New strategies based on IIM are proposed for elliptic interface problems to compute the gradient at grid points both regular and irregular, and at the interface from each side of the interface, to validate the numerical methods and analysis.
(via Semantic Scholar)

Source: ORCID

Added: November 1, 2019

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.

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

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