@article{banks_dediu_ernstberger_kappel_2010, title={Generalized sensitivities and optimal experimental design}, volume={18}, number={1}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Dediu, S. and Ernstberger, S. L. and Kappel, F.}, year={2010}, pages={25–83} }
@article{banks_dediu_nguyen_2007, title={Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space}, volume={4}, DOI={10.3934/mbe.2007.4.403}, abstractNote={We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.}, number={3}, journal={Mathematical Biosciences and Engineering}, author={Banks, H. T. and Dediu, S. and Nguyen, H. K.}, year={2007}, pages={403–430} }
@article{bai_banks_dediu_govan_last_lloyd_nguyen_olufsen_rempala_slenning_2007, title={Stochastic and deterministic models for agricultural production networks}, volume={4}, url={https://publons.com/publon/12886434/}, DOI={10.3934/mbe.2007.4.373}, abstractNote={An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.}, number={3}, journal={Mathematical Biosciences and Engineering}, author={Bai, P. and Banks, H. T. and Dediu, S. and Govan, A. Y. and Last, M. and Lloyd, Alun and Nguyen, H. K. and Olufsen, M. S. and Rempala, G. and Slenning, B. D.}, year={2007}, pages={373–402} }
@article{banks_dediu_nguyen_2007, title={Time delay systems with distribution dependent dynamics}, volume={31}, ISSN={["1367-5788"]}, DOI={10.1016/j.arcontrol.2007.02.002}, abstractNote={General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measures for computational purposes is surveyed.}, number={1}, journal={ANNUAL REVIEWS IN CONTROL}, author={Banks, H. T. and Dediu, Sava and Nguyen, Hoan K.}, year={2007}, pages={17–26} }
@article{dediu_mclaughlin_2006, title={Recovering inhomogeneities in a waveguide using eigensystem decomposition}, volume={22}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/22/4/007}, abstractNote={We present an eigensystem decomposition method to recover weak inhomogeneities in a waveguide from knowledge of the far-field scattered acoustic fields. Due to the particular geometry of the waveguide, which supports only a finite number of propagating modes, the problem of recovering inhomogeneities in a waveguide has a different set of challenges than the corresponding problem in free space. Our method takes advantage of the spectral properties of the far-field matrix, and by using its eigenvalues and its eigenvectors we obtain a representation of the linearized solution to the inverse problem in terms of products of fields which are linear combinations of the propagating modes of the waveguide with weights given by the eigenvectors of the far-field matrix. The problem of finding the unknown inhomogeneity reduces to a problem of determining some coefficients in a finite system of linear equations, whose coefficients depend on the background medium and the eigenvalues and the eigenvectors of the far-field matrix. By numerically implementing our inverse algorithm we reconstructed the inhomogeneities present in the waveguide. We show that (1) even with as few as seven propagating modes we obtain a good recovery of the size and shape of the inhomogeneity; (2) multiple inhomogeneities can be well recovered and, as expected, (3) the recovery improves when the number of propagating modes increases.}, number={4}, journal={INVERSE PROBLEMS}, author={Dediu, Sava and McLaughlin, Joyce R.}, year={2006}, month={Aug}, pages={1227–1246} }