@article{pambuccian_schacht_2022, title={The Case for the Irreducibility of Geometry to Algebra(dagger)}, volume={30}, ISSN={["1744-6406"]}, DOI={10.1093/philmat/nkab022}, abstractNote={ABSTRACT}, number={1}, journal={PHILOSOPHIA MATHEMATICA}, author={Pambuccian, Victor and Schacht, Celia}, year={2022}, month={Feb}, pages={1–31} }
 @article{pambuccian_schacht_2021, title={The Ubiquitous Axiom}, volume={76}, ISSN={["1420-9012"]}, DOI={10.1007/s00025-021-01424-3}, number={3}, journal={RESULTS IN MATHEMATICS}, author={Pambuccian, Victor and Schacht, Celia}, year={2021}, month={Aug} }
 @article{banks_meade_schacht_catenacci_thompson_abate-daga_enderling_2020, title={Parameter estimation using aggregate data}, volume={100}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2019.105999}, abstractNote={In biomedical/physiological/ecological experiments, it is common for measurements in time series data to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (often referred to as aggregate population data). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. As we show by examples, this assumption leads to an overconfidence in model parameter (means, variances) values and model based predictions. We discuss these issues 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.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. . T. and Meade, Annabel E. and Schacht, Celia and Catenacci, Jared and Thompson, W. Clayton and Abate-Daga, Daniel and Enderling, Heiko}, year={2020}, month={Feb} }
 @article{schacht_meade_banks_enderling_abate-daga_2019, title={Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model}, volume={16}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2019365}, abstractNote={In this effort we explain fundamental formulations for aggregate data inverse problems requiring estimation of probability distribution parameters. We use as a motivating example a class of CAR T-call cancer models in mice. After ascertaining results on model stability and sensitivity with respect to parameters, we carry out first elementary computations on the question how much data is needed for successful estimation of probability distributions.}, number={6}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Schacht, Celia and Meade, Annabel and Banks, H. T. and Enderling, Heiko and Abate-Daga, Daniel}, year={2019}, pages={7299–7326} }
 @article{pambuccian_schacht_2019, title={Lippmann's axiom and Lebesgue's axiom are equivalent to the Lotschnittaxiom}, volume={60}, ISSN={["2191-0383"]}, DOI={10.1007/s13366-019-00445-y}, number={4}, journal={BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY}, author={Pambuccian, Victor and Schacht, Celia}, year={2019}, month={Dec}, pages={733–748} }