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2022

  1. Vanja G. Svenda, Mark K Transtrum, Benjamin L. Francis, Andrija T. Saric, and Aleksandar M Stankovic
    IEEE Trans. Power Syst. 37 (1), 272-281 (2022).
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2021

  1. Katrina Pedersen, Mark K. Transtrum, Kent L. Gee, Shane V. Lympany, Michael M. James, and Alexandria R. Salton
    JASA Express Letters 1 (12), 122401 (2021).
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  2. Mylan R. Cook, Kent L. Gee, Mark K. Transtrum, Shane V. Lympany, and Matt Calton
    JASA Express Letters 1 (6), 063602 (2021).
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  3. Zachary Jones, Mylan R. Cook, Kent L. Gee, Mark K. Transtrum, Shane V. Lympany, Matthew F. Calton, and Michael M. James
    179th Meeting of the Acoustical Society of America, Acoustics Virtually Everywhere (December 2020). Proc. Meet. Acoust. 42 (1), 045007 (2021).
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  4. Andrija T. Sarić, Aleksandar A. Sarić, Mark K. Transtrum, and Aleksandar M. Stanković
    IEEE Trans. Power Syst. 36 (3), 2390-2402 (2021).
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  5. Andrija T. Sarić, Mark K. Transtrum, and Aleksandar M. Stanković
    IEEE Trans. Power Syst. 36 (3), 2222-2233 (2021).
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  6. Nathan S. Sitaraman, Michelle M. Kelley, Ryan D. Porter, Matthias U. Liepe, Tomás A. Arias, Jared Carlson, Alden R. Pack, Mark K. Transtrum, … (1 other authors)
    Phys. Rev. B 103 (11), 115106 (2021).
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  7. Jared Carlson, Alden Pack, Mark K. Transtrum, Jaeyel Lee, David N. Seidman, Danilo B. Liarte, … (6 other authors)
    Phys. Rev. B 103 (2), 024516 (2021).
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2020

  1. Eric Todd, Mylan R. Cook, Katrina Pedersen, David S. Woolworth, Brooks A. Butler, Xin Zhao, Colt Liu, Kent L. Gee, Mark K. Transtrum, … (1 other authors)
    178th Meeting of the Acoustical Society of America, (San Diego, CA, December 2019). Proc. Meet. Acoust. 39, 040003 (2020).
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  2. Aleksandar M. Stanković, Aleksandar A. Sarić, Andrija T. Sarić, and Mark K. Transtrum
    Electr. Power Syst. Res. 189, 106824 (2020).
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  3. Vanja G. Švenda, Aleksandar M. Stanković, Andrija T. Sarić, and Mark K. Transtrum
    Int. J. Electr. Power Energy Syst. 122, 106179 (2020).
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  4. Brooks A. Butler, Katrina Pedersen, Casie Maekawa, Kent L. Gee, Mark K. Transtrum, Michael M. James, and Alexandria R. Salton
    176th Meeting of Acoustical Society of America, 2018 Acoustics Week in Canada (Victoria, Canada, November 2018). Proc. Meet. Acoust. 35 (1), 055008 (2020).
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  5. Alex M. Stanković, Aleksandar A. Sarić, Andrija T. Sarić, and Mark K. Transtrum
    2020 IEEE Power & Energy Society General Meeting, (Montreal, Canada, August 2020).
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  6. Journal
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  7. V. G. Švenda, A. M. Stanković, A. T. Sarić, and M. K. Transtrum
    IET Gener. Transm. Distrib. 14 (11), 2111-2119 (2020).
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2019

  1. Network Reduction in Transient Stability Models using Partial Response Matching
    Benjamin L. Francis, Jacob R. Nuttall, Mark K. Transtrum, Andrija T. Sarić, and Aleksandar M. Stanković
    2019 North American Power Symposium (NAPS), (Wichita, Kansas, October 2019).
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  2. P. E. Paré, D. Grimsman, A. T. Wilson, M. K. Transtrum, and S. Warnick
    IEEE Trans. Autom. Control 64 (11), 4796-4802 (2019).
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  3. Katrina Pedersen, Mark K. Transtrum, Kent L. Gee, Brooks A. Butler, Michael M. James, and Alexandria R. Salton
    176th Meeting of Acoustical Society of America; 2018 Acoustics Week in Canada, (Victoria, Canada, November 2018). Proc. Meet. Acoust. 35 (1), 022002 (2019).
    Proceedings
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  4. Brooks A. Butler, Katrina Pedersen, Mylan R. Cook, Spencer G. Wadsworth, Eric Todd, Dallen Stark, Kent L. Gee, Mark K. Transtrum, … (1 other authors)
    176th Meeting of Acoustical Society of America; 2018 Acoustics Week in Canada, (Victoria, Canada, November 2018). Proc. Meet. Acoust. 35 (1), 055006 (2019).
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  5. Andrija T. Sarić, Mark K. Transtrum, and Aleksandar M. Stanković
    2019 IEEE Milan PowerTech, (Milan, Italy, June 2019).
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  6. Journal
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  7. Johnathon Rackham, Brittni Newbold, Steve Kotter, Dallin Smith, Dalton Griner, Roger Harrison, … Mark Transtrum, and Karine Chesnel (1 other authors)
    AIP Advances 9 (3), 035033 (2019).
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  8. Tracianne B. Neilsen, David F. Van Komen, Mark K. Transtrum, Makenzie B. Allen, and David P. Knobles
    Proc. Meet. Acoust. 35 (1), 055004 (2019).
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  9. Andrija T. Sarić, Mark T. Transtrum, and Aleksandar M. Stanković
    IEEE Trans. Power Syst. 34 (1), 360-370 (2019).
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2018

  1. Mark K. Transtrum, Benjamin L. Francis, Andrija T. Saric, and Aleksandar M. Stankovic
    2018 IEEE Power & Energy Society General Meeting (PESGM). (Portland, OR, August 2018).
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  2. Vanja G. Švenda, Alex M. Stanković, Andrija T. Sarić, and Mark K. Transtrum
    2018 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe). (Sarajevo, Bosnia-Herzegovina, October 2018).
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  3. Lee D. Hansen, Nieves Barros, Mark K. Transtrum, Jose A. Rodríguez-Añón, Jorge Proupín, Verónica Piñeiro, Ander Arias-González, and Nahia Gartzia
    Thermochim. Acta 670, 128-135 (2018).
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  4. Mark K. Transtrum, Benjamin L. Francis, Clifford C. Youn, Andrija T. Saric, and Aleksander M. Stankovic
    2018 North American Power Symposium (NAPS). (Fargo, ND, September 2018).
    Proceedings
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  5. C. Anthony Hunt, Ahmet Erdemir, William W. Lytton, Feilim Mac Gabhann, Edward A. Sander, Mark K. Transtrum, and Lealem Mulugeta
    Processes 6 (5), 56 (2018).
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  6. Jenny E. Jeong, Qinwei Zhuang, Mark K. Transtrum, Enlu Zhou, and Peng Qiu
    Quant. Biol. 6 (4), 287-306 (2018).
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  7. Lee D. Hansen, Mark K. Transtrum, and Colette F. Quinn
    Springer (2018)
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  8. Henry H. Mattingly, Mark K. Transtrum, Michael C. Abbott, and Benjamin B. Machta
    Proc. Natl. Acad. Sci. U. S. A. 115 (8), 1760-1765 (2018).
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  9. Marco Mason, Matteo Scampicchio, Colette F. Quinn, Mark K. Transtrum, Nicholas Baker, Lee D. Hansen, and Jason D. Kenealey
    J. Food Sci. 83 (2), 326-331 (2018).
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  10. Aleksandar M. Stanković, Vanja Švenda, Andrija T. Sarić, and Mark K. Transtrum
    Power & Energy Society General Meeting, IEEE (Chicago, IL, July 2017)
    Proceedings
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  11. D. B. Liarte, T. Arias, D. L. Hall, M. Liepe, J. P. Sethna, N. Sitaraman, A. Pack, and M. K. Transtrum
    18th International Conference on RF Superconductivity, (Lanzhou, China, 2017).
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  12. M. K. Transtrum, A. T. Saric, and A. M. Stankovic
    IEEE Trans. Power Syst. 33 (1), 440-450 (2018).
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2017

  1. Andrija T. Sarić, Mark K. Transtrum, and Aleksandar M. Stanković
    IET Gener. Transm. Distrib. 12 (6), 1294-1302 (2017).
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  2. Clifford C. Youn, Andrija T. Sarić, Mark K. Transtrum, and Aleksandar M. Stanković
    2017 IEEE Manchester PowerTech (Manchester, UK, June 2017).
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  3. Andrew D. Mathis, Bradley C. Naylor, Richard H. Carson, Eric Evans, Justin Harwell, Jared Knect, Eric Hexem, … Mark K. Transtrum, … (5 other authors)
    Mol. Cell. Proteomics 16 (2), 243-254 (2017).
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  4. Danilo B. Liarte, Sam Posen, Mark K. Transtrum, Gianluigi Catelani, Matthias Liepe, and James P. Sethna
    Supercond. Sci. Technol. 30 (3), 033002 (2017).
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2016

  1. Andrew White, Malachi Tolman, Howard D. Thames, Hubert Rodney Withers, Kathy A. Mason, and Mark K. Transtrum
    PLoS Comput. Biol. 12, 1-12 (2016).
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  2. Danilo B. Liarte, Mark K. Transtrum, and James P. Sethna
    Phys. Rev. B 94 (14), 144504 (2016).
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  3. Mark K. Transtrum , Andrija T. Saric, and Aleksandar M. Stankovic
    IEEE Trans. Power Syst. 32 (3), 2243-2253 (2016).
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  4. Andrija T. Sarić, Mark K. Transtrum, and Aleksandar M. Stanković
    IEEE Power in Energy and Society General Meeting, (Boston, MA, July 2016).
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  5. Mark K. Transtrum, Andrija T. Saric, and Alex M. Stankovic
    2016 Power Systems Computation Conference (PSCC), (Genova, Italy, June 2016).
    Proceedings
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  6. Journal
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  7. Lee D. Hansen, Mark K. Transtrum, Colette Quinn, and Neil Demarse
    Biochim. Biophys. Acta-Gen. Subj. 1860 (5), 957-966 (2016).
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2015

  1. Sam Posen, Mark K. Transtrum, Gianluigi Catelani, Matthias U. Liepe, and James P. Sethna
    Phys. Rev. Applied 4, 044019 (2015).
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  2. Brian K. Mannakee, Aaron P. Ragsdale, Mark K. Transtrum, and Ryan N. Gutenkunst
    Uncertainty in Biology, Volume 17 of the series Studies in Mechanobiology, Tissue Engineering and Biomaterials
    Book/Chapter
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  3. Philip E. Paré, Alma T. Wilson, Mark K. Transtrum, and Sean C. Warnick
    American Control Conference, (Chicago, IL, July 2015), pp 1984-1989.
    Proceedings
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  4. Mark K. Transtrum, Benjamin B. Machta, Kevin S. Brown, Bryan C. Daniels, Christopher R. Myers, and James P. Sethna
    J. Chem. Phys. 143 (1), 010901 (2015).
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  5. Mark K. Transtrum, Lee D. Hansen, and Colette Quinn
    Methods 76, 194-200 (2015).
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2014

  1. Mark K. Transtrum and Peng Qiu
    Phys. Rev. Lett. 113, 098701 (2014).
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2013

  1. Benjamin B. Machta, Ricky Chachra, Mark K. Transtrum, and James P. Sethna
    Science 342 (6158), 604-607 (2013).
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  2. Tommy Sheu, Jessica Molkentine, Mark K. Transtrum, Thomas A. Buchholz, Hubert Rodney Withers, Howard D. Thames, and Kathy A. Mason
    Radiother. Oncol. 109 (1), 21-25 (2013).
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2012

  1. Ricky Chachra, Mark K. Transtrum, and James P. Sethna
    Phys. Rev. E 86 (2), 026712 (2012).
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  2. Journal
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2011

  1. Journal
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  2. Mark K. Transtrum, Gianluigi Catelani, and James P. Sethna
    Phys. Rev. B 83 (9), 094505 (2011).
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  3. Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna
    Phys. Rev. E 83 (3), 036701 (2011).
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  4. Mark K. Transtrum, Yanjiun Chen, Benjamin B. Machta, James P. Sethna, and Ryan Gutenkunst
    Read before The Royal Statistical Society at a meeting organized by the Research Section (October 2010). See discussion on page 199. J. Roy. Stat. Soc. B 73 (2), 123-214 (2011).
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2010

  1. Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna
    Phys. Rev. Lett. 104 (6), 060201 (2010).
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2009

  1. Chad Junkermeier, Mark Transtrum, and Manuel Berrondo
    Int. J. Quantum Chem. 109 (5), 982-998 (2009).
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2007

  1. Beyond the Quantum, (June 2006,Leiden, The Netherlands), 235-243.
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2006

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2005

  1. Journal
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Undergraduate Student Author

Graduate Student Author

Selected Publications

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BYU Authors: Mark K. Transtrum, published in 2016 Power Systems Computation Conference (PSCC), (Genova, Italy, June 2016).
The paper describes a new class of system identification procedures that are tailored to electric power systems with renewable sources. Our procedure builds on computational advances in differential geometry, and offers a new, global, intrinsic characterization of challenges frequently encountered in system identification of electric power systems. The approach also benefits from increased availability of high-quality measurements. While the proposed procedure is illustrated on renewable source IEEE 14-bus based example in a multi-machine benchmark power system, it is equally applicable to identification of other system components (for example, dynamic loads).
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BYU Authors: Mark K. Transtrum, published in PLoS Comput. Biol.
The inherent complexity of biological systems gives rise to complicated mechanistic models with a large number of parameters. On the other hand, the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. We use the Manifold Boundary Approximation Method (MBAM) as a tool for deriving simple phenomenological models from complicated mechanistic models. The resulting models are not black boxes, but remain expressed in terms of the microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of distinct systems exhibiting the same range of collective behavior, and identify the combinations of components that function as tunable control knobs for the behavior. We demonstrate the procedure for adaptation behavior exhibited by the EGFR pathway. From a 48 parameter mechanistic model, the system can be effectively described by a single adaptation parameter τ characterizing the ratio of time scales for the initial response and recovery time of the system which can in turn be expressed as a combination of microscopic reaction rates, Michaelis-Menten constants, and biochemical concentrations. The situation is not unlike modeling in physics in which microscopically complex processes can often be renormalized into simple phenomenological models with only a few effective parameters. The proposed method additionally provides a mechanistic explanation for non-universal features of the behavior.
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BYU Authors: Lee D. Hansen and Mark K. Transtrum, published in Biochim. Biophys. Acta-Gen. Subj.
Background

Isothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems, and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data.

Scope of Review

This article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions.

Major Conclusions

A complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error.

General Significance

Methods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences - Principles and Applications, edited by Fadi Bou-Abdallah.
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BYU Authors: Mark K. Transtrum, published in Phys. Rev. Applied
Determining the optimal arrangement of superconducting layers to withstand large-amplitude ac magnetic fields is important for certain applications such as superconducting radio-frequency cavities. In this paper, we evaluate the shielding potential of the superconducting-film–insulating-film–superconductor (SIS ′  ) structure, a configuration that could provide benefits in screening large ac magnetic fields. After establishing that, for high-frequency magnetic fields, flux penetration must be avoided, the superheating field of the structure is calculated in the London limit both numerically and, for thin films, analytically. For intermediate film thicknesses and realistic material parameters, we also solve numerically the Ginzburg-Landau equations. It is shown that a small enhancement of the superheating field is possible, on the order of a few percent, for the SIS′   structure relative to a bulk superconductor of the film material, if the materials and thicknesses are chosen appropriately.
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BYU Authors: Mark K. Transtrum, published in Uncertainty in Biology, Volume 17 of the series Studies in Mechanobiology, Tissue Engineering and Biomaterials
When modeling complex biological systems, exploring parameter space is critical, because parameter values are typically poorly known a priori. This exploration can be challenging, because parameter space often has high dimension and complex structure. Recent work, however, has revealed universal structure in parameter space of models for nonlinear systems. In particular, models are often sloppy, with strong parameter correlations and an exponential range of parameter sensitivities. Here we review the evidence for universal sloppiness and its implications for parameter fitting, model prediction, and experimental design. In principle, one can transform parameters to alleviate sloppiness, but a parameterization-independent information geometry perspective reveals deeper universal structure. We thus also review the recent insights offered by information geometry, particularly in regard to sloppiness and numerical methods.
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BYU Authors: Mark K. Transtrum and Sean C. Warnick, published in American Control Conference, (Chicago, IL, July 2015), pp 1984-1989.
This paper demonstrates that both Balanced Truncation and Balanced Singular Perturbation Approximations can be viewed as limiting approximations of the same parameterization of Linear Time Invariant (LTI) systems. First, we introduce a specific parameterization of LTI systems that distinguishes dynamic and structural parameters. Next, we apply the Model Boundary Approximation Method (MBAM) [1] to particular parameters to achieve different approximations. This unified view of these popular model reduction techniques, which themselves can result in quite different approximations, illustrates that each approximation corresponds to a particular boundary element on a manifold, the “model manifold,” which is associated with the specific choice of model parameterization and is embedded in a sample space of measured outputs.
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BYU Authors: Mark K. Transtrum, published in J. Chem. Phys.
Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are “sloppy,” i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher information matrix, which is interpreted as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. The manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.
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BYU Authors: Mark K. Transtrum and Lee D. Hansen, published in Methods

The purposes of this paper are (a) to examine the effect of calorimeter time constant (τ) on heat rate data from a single enzyme injection into substrate in an isothermal titration calorimeter (ITC), (b) to provide information that can be used to predict the optimum experimental conditions for determining the rate constant (k2), Michaelis constant (KM), and enthalpy change of the reaction (ΔRH), and (c) to describe methods for evaluating these parameters. We find that KM, k2 and ΔRH can be accurately estimated without correcting for the calorimeter time constant, τ, if (k2E/KM), where E is the total active enzyme concentration, is between 0.1/τ and 1/τ and the reaction goes to at least 99% completion. If experimental conditions are outside this domain and no correction is made for τ, errors in the inferred parameters quickly become unreasonable. A method for fitting single-injection data to the Michaelis–Menten or Briggs–Haldane model to simultaneously evaluate KM, k2, ΔRH, and τ is described and validated with experimental data. All four of these parameters can be accurately inferred provided the reaction time constant (k2E/KM) is larger than 1/τ and the data include enzyme saturated conditions.

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BYU Authors: Mark K. Transtrum, published in Phys. Rev. Lett.
Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce “black boxes” disconnected from the microscopic physics. We propose a new approach by translating the model reduction problem for an arbitrary statistical model into a geometric problem of constructing a low-dimensional, submanifold approximation to a high-dimensional manifold. When models are overly complex, we use the observation that the model manifold is bounded with a hierarchy of widths and propose using the boundaries as submanifold approximations. We refer to this approach as the manifold boundary approximation method. We apply this method to several models, including a sum of exponentials, a dynamical systems model of protein signaling, and a generalized Ising model. By focusing on parameters rather than physical degrees of freedom, the approach unifies many other model reduction techniques, such as singular limits, equilibrium approximations, and the renormalization group, while expanding the domain of tractable models. The method produces a series of approximations that decrease the complexity of the model and reveal how microscopic parameters are systematically “compressed” into a few macroscopic degrees of freedom, effectively building a bridge between the microscopic and the macroscopic descriptions.
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BYU Authors: Mark K. Transtrum, published in Science
The microscopically complicated real world exhibits behavior that often yields to simple yet quantitatively accurate descriptions. Predictions are possible despite large uncertainties in microscopic parameters, both in physics and in multiparameter models in other areas of science. We connect the two by analyzing parameter sensitivities in a prototypical continuum theory (diffusion) and at a self-similar critical point (the Ising model). We trace the emergence of an effective theory for long-scale observables to a compression of the parameter space quantified by the eigenvalues of the Fisher Information Matrix. A similar compression appears ubiquitously in models taken from diverse areas of science, suggesting that the parameter space structure underlying effective continuum and universal theories in physics also permits predictive modeling more generally.
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BYU Authors: Mark K. Transtrum, published in Radiother. Oncol.
Purpose To test the appropriateness of the linear-quadratic (LQ) model to describe survival of jejunal crypt clonogens after split doses with variable (small 1–6Gy, large 8–13Gy) first dose, as a model of its appropriateness for both small and large fraction sizes. Methods C3Hf/KamLaw mice were exposed to whole body irradiation using 300kVp X-rays at a dose rate of 1.84Gy/min, and the number of viable jejunal crypts was determined using the microcolony assay. 14Gy total dose was split into unequal first and second fractions separated by 4h. Data were analyzed using the LQ model, the lethal potentially lethal (LPL) model, and a repair-saturation (RS) model. Results Cell kill was greater in the group receiving the larger fraction first, creating an asymmetry in the plot of survival vs size of first dose, as opposed to the prediction of the LQ model of a symmetric response. There was a significant difference in the estimated βs (higher β after larger first doses), but no significant difference in the αs, when large doses were given first vs small doses first. This difference results in underestimation (based on present data by approximately 8%) of isoeffect doses using LQ model parameters based on small fraction sizes. While the LPL model also predicted a symmetric response inconsistent with the data, the RS model results were consistent with the observed asymmetry. Conclusion The LQ model underestimates doses for isoeffective crypt-cell survival with large fraction sizes (in the present setting, >9Gy).
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BYU Authors: Mark K. Transtrum, published in Phys. Rev. E
We use an extension of the van der Pol oscillator as an example of a system with multiple time scales to study the susceptibility of its trajectory to polynomial perturbations in the dynamics. A striking feature of many nonlinear, multiparameter models is an apparently inherent insensitivity to large-magnitude variations in certain linear combinations of parameters. This phenomenon of "sloppiness" is quantified by calculating the eigenvalues of the Hessian matrix of the least-squares cost function. These typically span many orders of magnitude. The van der Pol system is no exception: Perturbations in its dynamics show that most directions in parameter space weakly affect the limit cycle, whereas only a few directions are stiff. With this study, we show that separating the time scales in the van der Pol system leads to a further separation of eigenvalues. Parameter combinations which perturb the slow manifold are stiffer and those which solely affect the jumps in the dynamics are sloppier.
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BYU Authors: Mark K Transtrum, published in BMC Bioinformatics
We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment selection can also allow one to restrict model predictions without constraining the parameters using many fewer experiments. We suggest that predicting model behaviors and inferring parameters represent two different approaches to model calibration with different requirements on data and experimental cost.
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BYU Authors: Mark K. Transtrum, published in Mol. BioSyst.
We explain that part of the reduction in the parameter uncertainties in the computations of Apgar et al. (Mol. Biosyst. 2010, 6, 1890–900) is due to a greatly increased number of effective data points.
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BYU Authors: Mark K. Transtrum, published in Phys. Rev. B
We study the superheating field of a bulk superconductor within Ginzburg-Landau theory, which is valid near the critical temperature. We calculate, as functions of the Ginzburg-Landau parameter., the superheating field H(sh) and the critical momentum k(c) characterizing the wavelength of the instability of the Meissner state to flux penetration. By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for an ordinary differential equation, we solve the problem numerically. We demonstrate agreement between the numerics and analytics, and show convergence to the known results at both small and large.. We discuss the implications of the results for superconducting rf cavities used in particle accelerators.
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BYU Authors: Mark K. Transtrum, published in Phys. Rev. E
Parameter estimation by nonlinear least-squares minimization is a common problem that has an elegant geometric interpretation: the possible parameter values of a model induce a manifold within the space of data predictions. The minimization problem is then to find the point on the manifold closest to the experimental data. We show that the model manifolds of a large class of models, known as sloppy models, have many universal features; they are characterized by a geometric series of widths, extrinsic curvatures, and parameter-effect curvatures, which we describe as a hyper-ribbon. A number of common difficulties in optimizing least-squares problems are due to this common geometric structure. First, algorithms tend to run into the boundaries of the model manifold, causing parameters to diverge or become unphysical before they have been optimized. We introduce the model graph as an extension of the model manifold to remedy this problem. We argue that appropriate priors can remove the boundaries and further improve the convergence rates. We show that typical fits will have many evaporated parameters unless the data are very accurately known. Second, "bare" model parameters are usually ill-suited to describing model behavior; cost contours in parameter space tend to form hierarchies of plateaus and long narrow canyons. Geometrically, we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter-effect curvature on the manifold. By constructing alternative coordinates based on geodesic motion, we show that these long narrow canyons are transformed in many cases into a single quadratic, isotropic basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting algorithms as an Euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph, respectively. By adding a geodesic acceleration adjustment to these algorithms, we alleviate the difficulties from parameter-effect curvature, improving both efficiency and success rates at finding good fits.
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BYU Authors: Mark K. Transtrum, published in J. Roy. Stat. Soc. B
The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.
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BYU Authors: Mark K. Transtrum, published in Phys. Rev. Lett.
Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to changes in parameters, and one is left to make adjustments by hand. We explain this difficulty by interpreting the fitting process as a generalized interpolation procedure. By considering the manifold of all model predictions in data space, we find that cross sections have a hierarchy of widths and are typically very narrow. Algorithms become stuck as they move near the boundaries. We observe that the model manifold, in addition to being tightly bounded, has low extrinsic curvature, leading to the use of geodesics in the fitting process. We improve the convergence of the Levenberg-Marquardt algorithm by adding geodesic acceleration to the usual step.
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BYU Authors: Chad Junkermeier, Mark Transtrum, and Manuel Berrondo, published in Int. J. Quantum Chem.
In this article, we introduce a simple analytic method for obtaining approximate solutions of the Schrodinger equation for a wide range of potentials in one- and two-dimensions. We define an operator, called the iteration operator, which will be used to solve for the lowest order state(s) of a system. The method is simple in that it does not require the computation of any integrals in order to obtain a solution. We use this method on several potentials which are well understood or even exactly solvable in order to demonstrate the strengths and weaknesses of this method. (C) 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 982-998, 2009
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BYU Authors: J. F. S. Van Huele and M. K. Transtrum, published in Beyond the Quantum, (June 2006,Leiden, The Netherlands), 235-243.
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BYU Authors: Mark K. Transtrum and Jean-François S. Van Huele, published in J. Phys. A
In this paper, we present a method for studying systems in the modified formulation of quantum mechanics known as Snyder space, proposed by Snyder (1947 Phys. Rev. 71 38-41). Snyder space predicts a modified commutation algebra for position and momentum operators. The method described in this paper introduces operators satisfying the canonical commutation relations and relates them to the position and momentum operators of Snyder space, effectively mapping a problem in Snyder space into a similar problem in standard quantum mechanics. The method is applied to the simple harmonic oscillator (SHO) in one and two dimensions as well as to the one-dimensional infinite square well. The energy spectra are calculated perturbatively for the SHO. We also find an exact spectrum for the one-dimensional infinite square well potential. These results are shown to agree with similar results found elsewhere in the literature.
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BYU Authors: Mark K. Transtrum and Jean-François S. Van Huele, published in J. Math. Phys.
We derive an expression for the commutator of functions of operators with constant commutations relations in terms of the partial derivatives of these functions. This result extends the well-known commutation relation between one operator and a function of another operator. We discuss the range of applicability of the formula with examples in quantum mechanics. (C) 2005 American Institute of Physics.
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BYU Authors: Mark K Transtrum, published in IEEE Trans. Power Syst.

This paper presents a procedure for estimating the systems state when considerable Information and Communication Technology (ICT) component outages occur, leaving entire system areas un-observable. For this task, a novel method for analyzing system observability is proposed based on the Manifold Boundary Ap-proximation Method (MBAM). By utilizing information geome-try, MBAM analyzes boundaries of models in data space, thus detecting unidentifiable system parameters and states based on available data. This approach extends local, matrix-based meth-ods to a global perspective, making it capable of detecting both structurally unidentifiable parameters as well as practically uni-dentifiable parameters (i.e., identifiable with low accuracy). Be-yond partitioning identifiable/unidentifiable states, MBAM also reduces the model to remove reference to the unidentifiable state variables. To test this procedure, cyber-physical system (CPS) simulation environments are constructed by co-simulating the physical and cyber system layers.

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BYU Authors: Katrina Pedersen, Mark K. Transtrum, and Kent L. Gee, published in JASA Express Letters

Modeling outdoor environmental sound levels is a challenging problem. This paper reports on a validation study of two continental-scale machine learning models using geospatial layers as inputs and the summer daytime A-weighted L-50 as a validation metric. The first model was developed by the National Park Service while the second was developed by the present authors. Validation errors greater than 20 dBA are observed. Large errors are attributed to limited acoustic training data. Validation environments are geospatially dissimilar to training sites, requiring models to extrapolate beyond their training sets. Results motivate further work in optimal data collection and uncertainty quantification.

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BYU Authors: Mylan R. Cook, Kent L. Gee, and Mark K. Transtrum, published in JASA Express Letters

Outdoor acoustic data often include non-acoustic pressures caused by atmospheric turbulence, particularly below a few hundred Hz in frequency, even when using microphone windscreens. This paper describes a method for automatic wind-noise classification and reduction in spectral data without requiring measured wind speeds. The method finds individual frequency bands matching the characteristic decreasing spectral slope of wind noise. Uncontaminated data from several short-timescale spectra can be used to obtain a decontaminated long-timescale spectrum. This method is validated with field-test data and can be applied to large datasets to efficiently find and reduce the negative impact of wind noise contamination.

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BYU Authors: Zachary Jones, Mylan R. Cook, Kent L. Gee, and Mark K. Transtrum, published in Proc. Meet. Acoust.

Jones et al. [J. Acoust. Soc. Am. 146, 2912 (2019)] compared an elevated (1.5 m) acoustical measurement configuration that used a standard commercial windscreen for outdoor measurements with a ground-based configuration with a custom windscreen. That study showed that the ground-based measurement method yielded superior wind noise rejection, presumably due to the larger windscreen and lower wind speeds experienced near the ground. This study further examines those findings by attempting to decouple the effects of windscreens and microphone elevation using measurements at 1.5 m and near the ground with and without windscreens. Simultaneous wind speed measurements at 1.5 m and near the ground were also made for correlation purposes. Results show that the insertion of the custom windscreen reduces wind noise more than placing the microphone near the ground, and that the ground-based setup is again preferable for obtaining broadband outdoor acoustic measurements.

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BYU Authors: Mark K. Transtrum, published in IEEE Trans. Power Syst.

This paper describes a data-driven symbolic regression identification method tailored to power systems and demonstrated on different synchronous generator (SG) models. In this work, we extend the sparse identification of nonlinear dynamics (SINDy) modeling procedure to include the effects of exogenous signals (measurements), nonlinear trigonometric terms in the library of elements, equality, and boundary constraints of expected solution. We show that the resulting framework requires fairly little in terms of data, and is computationally efficient and robust to noise, making it a viable candidate for online identification in response to rapid system changes. The SINDy-based model identification is integrated with the manifold boundary approximation method (MBAM) for the reduction of the differential-algebraic equations (DAE)-based SG dynamic models (decrease in the number of states and parameters). The proposed procedure is illustrated on an SG example in a real-world 441-bus and 67-machine benchmark.

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BYU Authors: Mark K. Transtrum, published in IEEE Trans. Power Syst.

The paper describes a manifold learning-based algorithm for big data classification and reduction, as well as parameter identification in real-time operation of a power system. Both black-box and gray-box settings for SCADA- and PMU-based measurements are examined. Data classification is based on diffusion maps, where an improved data-informed metric construction for partition trees is used. Data classification and reduction is demonstrated on the measurement tensor example of calculated transient dynamics between two SCADA refreshing scans. Interpolation/extension schemes for state extension of restriction (from data to reduced space) and lifting (from reduced to data space) operators are proposed. The method is illustrated on the single-phase Motor D example from very detailed WECC load model, connected to the single bus of a real-world 441-bus power system.

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BYU Authors: Jared Carlson, Alden R. Pack, and Mark K. Transtrum, published in Phys. Rev. B

Although often ignored in first-principles studies of material behavior, electronic free energy can have a profound effect in systems with a high-temperature threshold for kinetics and a high Fermi-level density of states (DOS). Nb3Sn and many other members of the technologically important A15 class of superconductors meet these criteria. This is no coincidence: both electronic free energy and superconducting transition temperature Tc are closely linked to the electronic density of states at the Fermi level. Antisite defects are known to have an adverse effect on Tc in these materials because they disrupt the high Fermi-level density of states. We observe that this also locally reduces electronic free energy, giving rise to large temperature-dependent terms in antisite defect formation and interaction free energies. This work explores the effect of electronic free energy on antisite defect behavior in the case of Nb3Sn. Using ab initio techniques, we perform a comprehensive study of antisite defects in Nb3Sn, and find that their effect on the Fermi-level DOS plays a key role determining their thermodynamic behavior, their interactions, and their effect on superconductivity. Based on our findings, we calculate the A15 region of the Nb-Sn phase diagram and show that the phase boundaries depend critically the electronic free energy of antisite defects. In particular, we show that extended defects such as grain boundaries alter the local phase diagram by suppressing electronic free-energy effects, explaining experimental measurements of grain boundary antisite defect segregation. Finally, we quantify the effect of antisite defects on superconductivity with the first ab initio study of Tc in Nb3Sn as a function of composition, focusing on tin-rich compositions observed in segregation regions around grain boundaries. As tin-rich compositions are not observed in bulk, their properties cannot be directly measured experimentally; our calculations therefore enable quantitative Ginzburg-Landau simulations of grain boundary superconductivity in Nb3Sn. We discuss the implications of these results for developing new growth processes to improve the properties of Nb3Sn thin films.

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BYU Authors: Mark K. Transtrum, published in Phys. Rev. B

We study mechanisms of vortex nucleation in Nb3Sn superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy imaging and energy dispersive spectroscopy of some Nb3Sn cavities show Sn segregation at grain boundaries in Nb3Sn with Sn concentration as high as ∼35 at. % and widths ∼3 nm in chemical composition. Using ab initio calculations, we estimate the effect excess tin has on the local superconducting properties of the material. We model Sn segregation as a lowering of the local critical temperature. We then use time-dependent Ginzburg-Landau theory to understand the role of segregation on magnetic vortex nucleation. Our simulations indicate that the grain boundaries act as both nucleation sites for vortex penetration and pinning sites for vortices after nucleation. Depending on the magnitude of the applied field, vortices may remain pinned in the grain boundary or penetrate the grain itself. We estimate the superconducting losses due to vortices filling grain boundaries and compare with observed performance degradation with higher magnetic fields. We estimate that the quality factor may decrease by an order of magnitude (1010 to 109) at typical operating fields if 0.03% of the grain boundaries actively nucleate vortices. We additionally estimate the volume that would need to be filled with vortices to match experimental observations of cavity heating.

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BYU Authors: Eric Todd, Mylan R. Cook, Katrina Pedersen, Brooks A. Butler, Xin Zhao, Kent L. Gee, Mark K. Transtrum, and Sean Warnick, published in Proc. Meet. Acoust.

This paper describes the development of an automated classification algorithm for detecting instances of focused crowd involvement present in crowd cheering. The purpose of this classification system is for situations where crowds are to be rewarded for not just the loudness of cheering, but for a concentrated effort, such as in Mardi Gras parades to attract bead throws or during critical moments in sports matches. It is therefore essential to separate non-crowd noise, general crowd noise, and focused crowd cheering efforts from one another. The importance of various features—both spectral and low-level audio processing features—are investigated. Data from both parades and sporting events are used for comparison of noise from different venues. This research builds upon previous clustering analyses of crowd noise from collegiate basketball games, using hierarchical clustering as an unsupervised machine learning approach to identify low-level features related to focused crowd involvement. For Mardi Gras crowd data we use a continuous thresholding approach based on these key low-level features as a method of identifying instances where the crowd is particularly active and engaged.

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BYU Authors: Mark K. Transtrum, published in Electr. Power Syst. Res.

The paper explores interleaved and coordinated refinement of physicsand data-driven models in describing transient phenomena in large-scale power systems. We develop and study an integrated analytical and computational data-driven gray box environment needed to achieve this aim. Main ingredients include computational differential geometry-based model reduction, optimization-based compressed sensing, and a finite approximation of the Koopman operator. The proposed two-step procedure (the model reduction by differential geometric (information geometry) tools, and data refinement by the compressed sensing and Koopman theory based dynamics prediction) is illustrated on the multi-machine benchmark example of IEEE 14-bus system with renewable sources, where the results are shown for doubly-fed induction generator (DFIG) with local measurements in the connection point. The algorithm is directly applicable to identification of other dynamic components (for example, dynamic loads).

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BYU Authors: Mark K. Transtrum, published in Int. J. Electr. Power Energy Syst.

This paper proposes a probabilistic extension to flexible hybrid state estimation (FHSE) for cyber-physical systems (CPSs). The main goal of the algorithm is improvement of the system state tracking when realistic communications are taken into account, by optimizing information and communication technology (ICT) usage. These advancements result in: 1) coping with ICT outages and inevitable irregularities (delay, packet drop and bad measurements); 2) determining the optimized state estimation execution frequencies based on expected measurement refresh times. Additionally, information about CPSs is gathered from both the phasor measurement units (PMU) and SCADA-based measurements. This measurement transfer introduces two network observability types, which split the system into observable (White) and unobservable (Grey) areas, based on 1) deployed measuring instruments (MIs) and 2) received measurements. A two-step bad data detection (BDD) method is introduced for ICT irregularities and outages. The proposed algorithm benefits are shown on two IEEE test cases with time-varying load/generation: 14-bus and 300-bus.

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BYU Authors: Brooks A. Butler, Katrina Pedersen, Kent L. Gee, and Mark K. Transtrum, published in Proc. Meet. Acoust.

Outdoor ambient acoustical environments may be predicted through machine learning using geospatial features as inputs. However, collecting sufficient training data is an expensive process, particularly when attempting to improve the accuracy of models based on supervised learning methods over large, geospatially diverse regions. Unsupervised machine learning methods, such as K-Means clustering analysis, enable a statistical comparison between the geospatial diversity represented in the current training dataset versus the predictor locations. In this case, 117 geospatial features that represent the contiguous United States have been clustered using K-Means clustering. Results show that most geospatial clusters group themselves according to a relatively small number of prominent geospatial features. It is shown that the available acoustic training dataset has a relatively low geospatial diversity because most training data sites reside in a few clusters. This analysis informs the selection of new site locations for data collection that improve the statistical similarity of the training and input datasets.

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BYU Authors: Mark K. Transtrum, published in 2020 IEEE Power & Energy Society General Meeting, (Montreal, Canada, August 2020).

The paper describes a data-driven system identification method tailored to power systems and demonstrated on models of synchronous generators (SGs). In this work, we extend the recent sparse identification of nonlinear dynamics (SINDy) modeling procedure to include the effects of exogenous signals and nonlinear trigonometric terms in the library of elements. We show that the resulting framework requires fairly little in terms of data, and is computationally efficient and robust to noise, making it a viable candidate for online identification in response to rapid system changes. The proposed method also shows improved performance over linear data-driven modeling. While the proposed procedure is illustrated on a SG example in a multi-machine benchmark, it is directly applicable to the identification of other system components (e.g., dynamic loads) in large power systems.

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BYU Authors: Alden R. Pack, Jared Carlson, Spencer Wadsworth, and Mark K. Transtrum, published in Phys. Rev. B

We use time-dependent Ginzburg-Landau theory to study the nucleation of vortices in type-II superconductors in the presence of both geometric and material inhomogeneities. The superconducting Meissner state is metastable up to a critical magnetic field, known as the superheating field. For a uniform surface and homogeneous material, the superheating transition is driven by a nonlocal critical mode in which an array of vortices simultaneously penetrate the surface. In contrast, we show that even a small amount of disorder localizes the critical mode and can have a significant reduction in the effective superheating field for a particular sample. Vortices can be nucleated by either surface roughness or local variations in material parameters, such as 

T

c

. Our approach uses a finite-element method to simulate a cylindrical geometry in two dimensions and a film geometry in two and three dimensions. We combine saddle-node bifurcation analysis along with a fitting procedure to evaluate the superheating field and identify the unstable mode. We demonstrate agreement with previous results for homogeneous geometries and surface roughness and extend the analysis to include variations in material properties. Finally, we show that in three dimensions, surface divots not aligned with the applied field can increase the superheating field. We discuss implications for fabrication and performance of superconducting resonant frequency cavities in particle accelerators.

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BYU Authors: M. K. Transtrum, published in IET Gener. Transm. Distrib.

This study proposes a novel flexible hybrid state estimation (SE) algorithm when a realistic communication system with its irregularities is taken into account. This system is modelled by the Network Simulator 2 software tool, which is also used to calculate communication delays and packet drop probabilities. Within this setup, the system observability can be predicted, and the proposed SE can decide between using the static SE (SSE) or the discrete Kalman filter plus SSE-based measurements and time alignment (Forecasting-aided SE). Flexible hybrid SE (FHSE) incorporates both phasor measurement units and supervisory control and data acquisition-based measurements, with different time stamps. The proposed FHSE with detailed modelling of the communication system is motivated by: (i) well-known issues in SSE (time alignment of the measurements, frequent un-observability for fixed SE time stamps etc.); and (ii) the need to model a realistic communication system (calculated communication delays and packet drop probabilities are a part of the proposed FHSE). Application of the proposed algorithm is illustrated for examples with time-varying bus load/generation on two IEEE test cases: 14-bus and 300-bus.

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BYU Authors: Benjamin L. Francis, Jacob R. Nuttall, and Mark K. Transtrum, published in 2019 North American Power Symposium (NAPS), (Wichita, Kansas, October 2019).

We describe a method for simultaneously identifying and reducing dynamic power systems models in the form of differential-algebraic equations. Often, these models are large and complex, containing more parameters than can be identified from the available system measurements. We demonstrate our method on transient stability models, using the IEEE 14-bus test system.Ourapproachusestechniquesofinformationgeometryto remove unidentifiable parameters from the model. We examine the case of a networked system with 58 parameters using full observations throughout the network. We show that greater reduction can be achieved when only partial observations are available, including reduction of the network itself.

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BYU Authors: M. K. Transtrum, published in IEEE Trans. Autom. Control

Model Boundary Approximation Method as a Unifying Framework for Balanced Truncation and Singular Perturbation Approximation

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BYU Authors: Katrina Pedersen, Mark K. Transtrum, Kent L. Gee, and Brooks A. Butler, published in Proc. Meet. Acoust.
Outdoor ambient sound levels can be predicted from machine learning-based models derived from geospatial and acoustic training data. To improve modeling robustness, median predicted sound levels have been calculated from an ensemble of tuned models from different supervised machine learning modeling classes. The ensemble is used to predict ambient sound levels throughout the contiguous United States. The training data set consists of 607 unique sites, where various acoustic metrics, such as overall daytime L50 levels and one-third octave frequency band levels, have been obtained. Data for 117 geospatial features, which include metrics such as distance to the nearest road or airport, are used. The spread in the ensemble provides an estimate of the modeling accuracy. Results of an initial leave-one-out and leave-four-out validation study are presented.
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BYU Authors: Brooks A. Butler, Katrina Pedersen, Mylan R. Cook, Spencer G. Wadsworth, Eric Todd, Dallen Stark, Kent L. Gee, Mark K. Transtrum, and Sean Warnick, published in Proc. Meet. Acoust.
The relationship between crowd noise and crowd behavioral dynamics is a relatively unexplored field of research. Signal processing and machine learning (ML) may be useful in classifying and predicting crowd emotional state. This paper describes using both supervised and unsupervised ML methods to automatically differentiate between different types of crowd noise. Features used include A-weighted spectral levels, low-level audio signal parameters, and Mel-frequency cepstral coefficients. K-means clustering is used for the unsupervised approach with spectral levels, and six distinct clusters are found; four of these clusters correspond to different amounts of crowd involvement, while two correspond to different amounts of band or public announcement system noise. Random forests are used for the supervised approach, wherein validation and testing accuracies are found to be similar. These investigations are useful for differentiating between types of crowd noise, which is necessary for future work in automatically determining and classifying crowd emotional state.
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BYU Authors: Mark K. Transtrum, published in 2019 IEEE Milan PowerTech, (Milan, Italy, June 2019).

This paper describes a manifold learning algorithm for big data classification and parameter identification in real-time operation of power systems. We assume a black-box setting, where only SCADA-based measurements at the point of interest are available. Data classification is based on diffusion maps, where an improved data-informed metric construction for partition trees is used. Data reduction is demonstrated on an hourly measurement tensor example, collected from the power flow solutions calculated for daily load/generation profiles. Parameter identification is performed on the same example, generated via randomly selected input parameters. The proposed method is illustrated on the case of the static part (ZIP) of a detailed WECC load model, connected to a single bus of a real-world 441-bus power system.

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BYU Authors: Benjamin L. Francis and Mark K. Transtrum, published in Phys. Rev. E
In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases, models are sloppy, that is, exhibit an exponential hierarchy of parameter sensitivities. We propose a parameter classification scheme based on how the sensitivities scale at long observation times. We show that for oscillatory models, either with a limit cycle or a strange attractor, sensitivities can become arbitrarily large, which implies a high effective dimensionality on the model manifold. Sloppy models with a single fixed point have model manifolds with low effective dimensionality, previously described as a “hyper-ribbon.” In contrast, models with high effective dimensionality translate into multimodal fitting problems. We define a measure of curvature on the model manifold which we call the winding frequency that estimates the density of local minima in the model's parameter space. We then show how alternative choices of fitting metrics can “unwind” the model manifold and give low winding frequencies. This prescription translates the model manifold from one of high effective dimensionality into the hyper-ribbon structures observed elsewhere. This translation opens the door for applications of sloppy model analysis and model reduction methods developed for models with low effective dimensionality.
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BYU Authors: Johnathon Rackham, Brittni Newbold, Steve Kotter, Dallin Smith, Dalton Griner, Roger Harrison, Mark Transtrum, and Karine Chesnel, published in AIP Advances
Magnetic nanoparticles are increasingly used in nanotechnologies and biomedical applications, such as drug targeting, MRI, bio-separation. Magnetite (Fe3O4) nanoparticles stand to be effective in these roles due to the non-toxic nature of magnetite and its ease of manufacture. To be more effective in these applications, a greater understanding of the magnetic behavior of a collection of magnetite nanoparticles is needed. This research seeks to discover the local magnetic ordering of ensembles of magnetite nanoparticles occurring under various external fields. To complete this study, we use x-ray resonant magnetic scattering (XRMS). Here we discuss the modeling of the magnetic scattering data using a one-dimensional chain of nanoparticles with a mix of ferromagnetic, anti-ferromagnetic, and random orders. By fitting the model to the experimental data, we extracted information about the magnetic correlations in the nanoparticle assembly.
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BYU Authors: Tracianne B. Neilsen, David F. Van Komen, Mark K. Transtrum, and Makenzie B. Allen, published in Proc. Meet. Acoust.
Optimal experimental design focuses on selecting experiments that minimize the statistical uncertainty in inferred parameter or predictions. In traditional optimizations, the experiment consists of input data, model parameters, and cost function. For machine learning and deep learning, the features, labels, and loss function define the experiment. One tool for optimal experimental design is the Fisher information, which gives an estimate of the relative uncertainty in and correlation among the model parameters based on the local curvature of the cost function. Using the Fisher information allows for rapid assessment of many different experimental conditions. In machine learning, the Fisher information can provide guidance as to which types of input features and labels maximize the gradients in the search space. This approach has been applied, for example, to systems biology models of biochemical reaction networks [Transtrum and Qiu, BMC Bioinformatics 13(1), 181 (2012)]. Preliminary application of the Fisher information to optimize experimental design for source localization in an uncertain ocean environment is a step towards finding an efficient machine learning algorithm that produces results with the least uncertainty in the quantities of interest.
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BYU Authors: Mark T. Transtrum, published in IEEE Trans. Power Syst.
The paper describes an algorithm for parameter identification of a dynamic equivalent for an external subsystem, based solely on the available online measurements in boundary buses and branches. Static equivalent part is represented by equivalent impedances from boundary buses (ones that separate the internal and external subsystems), and calculated using the modified (minimum loss) REI (Radial, Equivalent and Independent) method. Parameter identification of Synchronous Generator (SG)-based equivalent (for predominantly production external areas), Dynamic Load (DL)-based equivalent (for predominantly load external areas) or (SG+DL)-based equivalent (for mixed external areas) in fictitious buses is performed by Levenberg-Marquardt Weighted Least-Square (WLS) nonlinear optimization, which minimizes the variances between available online measurements and transient responses of the reduced power system. The IEEE 14-bus and 441-bus real-world test systems are used to illustrate and test the proposed power system equivalent derivation technique.
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BYU Authors: Mark K. Transtrum and Benjamin L. Francis, published in 2018 IEEE Power & Energy Society General Meeting (PESGM). (Portland, OR, August 2018).
The paper describes a global identification procedure for dynamic power system models in the form of differential and algebraic equations. Power system models have a number of features that makes their improvement challenging - they are multi-level, multi-user and multi-physics. Not surprisingly, they are nonlinear and time varying, both in terms of states (memory variables) and parameters, and discrete structures, such as graphs, are strongly blended with continuous dynamics, resulting in network dynamics. The transient stability models are used as a prototypical example. Our method is based on information geometry, and uses advances in computational differential geometry to characterize high-dimensional manifolds in the space of measurements. In the case of network parameters, a comparison is presented with circuit-theoretic techniques. The results are illustrated on the case of IEEE 14-bus test system with 58 parameters in our realization.
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BYU Authors: Mark K. Transtrum, published in 2018 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe). (Sarajevo, Bosnia-Herzegovina, October 2018).
The paper explores the effects of sensor behavior and communication system (CS) irregularities on power system state estimation (SE). CS are modeled in Network Simulator 2 (NS-2), allowing the quantification of irregularities, including delays and dropped packets. The overall information is obtained combining SCADA measurements with phasor measurement unit (PMU) derived data, where time stamping (based on GPS or an equivalent local clock) for all measurements is assumed. To fully analyze the effects of irregularities, a detailed analysis of sensitivities to different communication system parameters is provided as well. Using the co-simulation environment PiccSIM, a SE with these irregularities is quantified for CS parameter variation, with detailed models of power and communication flows.
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BYU Authors: Mark K. Transtrum, published in Thermochim. Acta
The relation between soil organic matter dynamics and temperature is an important research topic, poorly understood yet. This study focuses on the effect of temperature on the heat rate of soil organic matter decomposition using different soil types, by simulating an extreme heat wave with a calorimeter. Heat rates were measured with an automated step-scan of temperature upward at 20, 30, 40, 50, and 60 degrees C, and downward at 40 and 20 degrees C to monitor how soil recovers after the heat wave. The results show enzyme-catalyzed bioprocesses are not the only reactions in soil mineralization. Other reactions can be distinguished from the shape of the curve of the heat rate versus temperature. These reactions coexist at normal environmental temperatures, and their relative contribution to soil organic matter mineralization rates varies with soil type.
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BYU Authors: Mark K. Transtrum and Benjamin L. Francis, published in 2018 North American Power Symposium (NAPS). (Fargo, ND, September 2018).
This paper describes a geometric approach to parameter identifiability analysis in models of power systems dynamics. When a model of a power system is to be compared with measurements taken at discrete times, it can be interpreted as a mapping from parameter space into a data or prediction space. Generically, model mappings can be interpreted as manifolds with dimensionality equal to the number of structurally identifiable parameters. Empirically it is observed that model mappings often correspond to bounded manifolds. We propose a new definition of practical identifiability based the topological definition of a manifold with boundary. In many ways, our proposed definition extends the properties of structural identifiability. We construct numerical approximations to geodesics on the model manifold and use the results, combined with insights derived from the mathematical form of the equations, to identify combinations of practically identifiable and unidentifiable parameters. We give several examples of application to dynamic power systems models.
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BYU Authors: Mark K. Transtrum, published in Processes
Developing and improving mechanism-oriented computational models to better explain biological phenomena is a dynamic and expanding frontier. As the complexity of targeted phenomena has increased, so too has the diversity in methods and terminologies, often at the expense of clarity, which can make reproduction challenging, even problematic. To encourage improved semantic and methodological clarity, we describe the spectrum of Mechanism-oriented Models being used to develop explanations of biological phenomena. We cluster explanations of phenomena into three broad groups. We then expand them into seven workflow-related model types having distinguishable features. We name each type and illustrate with examples drawn from the literature. These model types may contribute to the foundation of an ontology of mechanism-based biomedical simulation research. We show that the different model types manifest and exert their scientific usefulness by enhancing and extending different forms and degrees of explanation. The process starts with knowledge about the phenomenon and continues with explanatory and mathematical descriptions. Those descriptions are transformed into software and used to perform experimental explorations by running and examining simulation output. The credibility of inferences is thus linked to having easy access to the scientific and technical provenance from each workflow stage.
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BYU Authors: Mark K. Transtrum, published in Quant. Biol.

Background: In systems biology, the dynamics of biological networks are often modeled with ordinary differential equations (ODEs) that encode interacting components in the systems, resulting in highly complex models. In contrast, the amount of experimentally available data is almost always limited, and insufficient to constrain the parameters. In this situation, parameter estimation is a very challenging problem. To address this challenge, two intuitive approaches are to perform experimental design to generate more data, and to perform model reduction to simplify the model. Experimental design and model reduction have been traditionally viewed as two distinct areas, and an extensive literature and excellent reviews exist on each of the two areas. Intriguingly, however, the intrinsic connections between the two areas have not been recognized.

Results: Experimental design and model reduction are deeply related, and can be considered as one unified framework. There are two recent methods that can tackle both areas, one based on model manifold and the other based on profile likelihood. We use a simple sum-of-two-exponentials example to discuss the concepts and algorithmic details of both methods, and provide Matlab-based code and implementation which are useful resources for the dissemination and adoption of experimental design and model reduction in the biology community.

Conclusions: From a geometric perspective, we consider the experimental data as a point in a high-dimensional data space and the mathematical model as a manifold living in this space. Parameter estimation can be viewed as a projection of the data point onto the manifold. By examining the singularity around the projected point on the manifold, we can perform both experimental design and model reduction. Experimental design identifies new experiments that expand the manifold and remove the singularity, whereas model reduction identifies the nearest boundary, which is the nearest singularity that suggests an appropriate form of a reduced model. This geometric interpretation represents one step toward the convergence of experimental design and model reduction as a unified framework.

 

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BYU Authors: Lee D. Hansen and Mark K. Transtrum, published in Springer (2018)
This Brief describes the calibration of titration calorimeters (ITCs) and calculation of stoichiometry, equilibrium constants, enthalpy changes, and rate constants for reactions in solution.  A framework/methodology for model development for analysis of ITC data is presented together with methods for assessing the uncertainties in determined parameters and test data sets. This book appeals to beginners, as well as to researchers and professionals in the field.
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BYU Authors: Mark K. Transtrum, published in Proc. Natl. Acad. Sci. U. S. A.
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter space. Thus, it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there are sufficient data to tightly constrain any number of parameters, this reduces to the Jeffreys prior. However, we argue that this limit is pathological when applied to the hyperribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.
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BYU Authors: Mark K. Transtrum, Nicholas Baker, Lee D. Hansen, and Jason D. Kenealey, published in J. Food Sci.
The aim of this work is to develop calorimetric methods for characterizing the activity and stability of membrane immobilized enzymes. Invertase immobilized on a nylon-6 nanofiber membrane is used as a test case. The stability of both immobilized and free invertase activity was measured by spectrophotometry and isothermal titration calorimetry (ITC). Differential scanning calorimetry was used to measure the thermal stability of the structure and areal concentration of invertase on the membrane. This is the 1st demonstration that ITC can be used to determine activity and stability of an enzyme immobilized on a membrane. ITC and spectrophotometry show maximum activity of free and immobilized invertase at pH 4.5 and 45 to 55 °C. ITC determination of the activity as a function of temperature over an 8-h period shows a similar decline of activity of both free and immobilized invertase at 55 °C.
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BYU Authors: Mark K. Transtrum, published in Power & Energy Society General Meeting, IEEE (Chicago, IL, July 2017)
The paper proposes a power system state estimation algorithm in the presence of irregular sensor sampling and random communication delays. Our state estimator incorporates Phasor Measurement Units (PMU) and SCADA measurements. We use an Extended Kalman filter based algorithm for time alignment of measurements and state variables. Time stamps are assumed for PMU, SCADA and state estimation. Application of the proposed algorithm is illustrated for hourly/daily load/generation variations on two test examples: 14-bus and 118-bus.
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BYU Authors: A. Pack and M. K. Transtrum, published in 18th International Conference on RF Superconductivity, (Lanzhou, China, 2017).
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BYU Authors: M. K. Transtrum, published in IEEE Trans. Power Syst.
The paper describes a new class of system identification procedures that are tailored to electric power systems, in particular to synchronous generators (SGs) and other dynamic components. Our procedure builds on computational advances in differential geometry, and offers a new, global characterization of challenges frequently encountered in system identification of electric power systems. The approach also benefits from increasing availability of high-quality measurements. While the proposed procedure is illustrated on SG example in a multi-machine benchmark (IEEE 14-bus and real-world 441-bus power systems), it is equally applicable to identification of other system components, such as loads.
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BYU Authors: Mark K. Transtrum, published in IET Gener. Transm. Distrib.
This study describes a new class of system identification procedures, tailored to electric power systems with renewable resources. The procedure described here builds on computational advances in differential geometry, and offers a new, global, and intrinsic characterisation of challenges in data-derived identification of electric power systems. The approach benefits from increased availability of high-quality measurements. The procedure is illustrated on the multi-machine benchmark example of IEEE 14-bus system with renewable resources, but it is equally applicable to identification of other components and systems (e.g. dynamic loads). The authors consider doubly-fed induction generators (DFIG) operating in a wind farm with system level proportional–integral controllers.
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BYU Authors: Mark K. Transtrum, published in 2017 IEEE Manchester PowerTech (Manchester, UK, June 2017).
Load modeling has been extensively studied in power systems. The problem is intrinsically hard, as a simple description is sought for a large collection of heterogeneous physical devices. One aspect of model simplification has to do with the number of parameters needed to describe a dynamic load. With the rich tapestry of methods proposed in the literature as a backdrop, this paper introduces a new approach to simplify the load models and estimate the parameters. Our method is based on information geometry which combines information theory with computational differential geometry to derive global estimation results and shed a new light on difficulties commonly encountered when fitting widely used models to the measurement data. The results are compared with the literature using simulations on the IEEE 14 bus benchmark system.
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BYU Authors: Andrew D. Mathis, Bradley C. Naylor, Richard H. Carson, Eric Evans, Justin Harwell, Jared Knect, Eric Hexem, Mark K. Transtrum, Benjamin T. Bikman, and John C. Price, published in Mol. Cell. Proteomics
Control of protein homeostasis is fundamental to the health and longevity of all organisms. Because the rate of protein synthesis by ribosomes is a central control point in this process, regulation and maintenance of ribosome function could have amplified importance in the overall regulatory circuit. Indeed, ribosomal defects are commonly associated with loss of protein homeostasis, aging and disease, whereas improved protein homeostasis, implying optimal ribosomal function, is associated with disease resistance and increased lifespan. To maintain a high quality ribosome population within the cell, dysfunctional ribosomes are targeted for autophagic degradation. It is not known if complete degradation is the only mechanism for eukaryotic ribosome maintenance or if they might also be repaired by replacement of defective components. We used stable-isotope feeding and protein mass-spectrometry to measure the kinetics of turnover of ribosomal RNA (rRNA) and 71 ribosomal proteins (r-proteins) in mice. The results indicate that exchange of individual proteins and whole ribosome degradation both contribute to ribosome maintenance in vivo. In general, peripheral r-proteins and those with more direct roles in peptide-bond formation are replaced multiple times during the lifespan of the assembled structure, presumably by exchange with a free cytoplasmic pool, whereas the majority of r-proteins are stably incorporated for the lifetime of the ribosome. Dietary signals impact the rates of both new ribosome assembly and component exchange. Signal-specific modulation of ribosomal repair and degradation could provide a mechanistic link in the frequently observed associations among diminished rates of protein synthesis, increased autophagy, and greater longevity. 
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BYU Authors: Mark K. Transtrum, published in Supercond. Sci. Technol.
Theoretical limits to the performance of superconductors in high magnetic fields parallel to their surfaces are of key relevance to current and future accelerating cavities, especially those made of new higher- T c materials such as Nb 3 Sn, NbN, and MgB 2 . Indeed, beyond the so-called superheating field ##IMG## [http://ej.iop.org/images/0953-2048/30/3/033002/sustaa4f2bieqn1.gif] {${H}_{\mathrm{sh}}$} , flux will spontaneously penetrate even a perfect superconducting surface and ruin the performance. We present intuitive arguments and simple estimates for ##IMG## [http://ej.iop.org/images/0953-2048/30/3/033002/sustaa4f2bieqn2.gif] {${H}_{\mathrm{sh}}$} , and combine them with our previous rigorous calculations, which we summarize. We briefly discuss experimental measurements of the superheating field, comparing to our estimates. We explore the effects of materials anisotropy and the danger of disorder in nucleating vortex entry. Will we need to control surface orientation in the layered compound MgB 2 ? Can we estimate theoretically whether dirt and defects make these new materials fundamentally more challenging to optimize than niobium? Finally, we discuss and analyze recent proposals to use thin superconducting layers or laminates to enhance the performance of superconducting cavities. Flux entering a laminate can lead to so-called pancake vortices; we consider the physics of the dislocation motion and potential re-annihilation or stabilization of these vortices after their entry.
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BYU Authors: Andrew White, Malachi Tolman, and Mark K. Transtrum, published in PLoS Comput. Biol.

We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physical mechanisms that must be included to explain system behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which mechanisms are relevant/irrelevant vary among experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will have a large systematic error and fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model’s discrepancy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the discrepancy in the model renders it less predictive than it was in the sloppy regime where systematic error is small. We introduce the concept of a sloppy system–a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is better approached by considering a hierarchy of models of varying detail rather than focusing on parameter estimation in a single model.

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BYU Authors: Mark K. Transtrum, published in Phys. Rev. B
We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for κ=λ/ξ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-gap model for MgB2 suggests high anisotropy of the superheating field near zero temperature. On the other hand, within Ginzburg-Landau theory for a single gap, we see that the superheating field shows significant anisotropy only when the crystal anisotropy is large and the Ginzburg-Landau parameter κ is small. We then conclude that only small anisotropies in the superheating field are expected for typical unconventional superconductors near the critical temperature. Using a generalized form of Ginzburg Landau theory, we do a quantitative calculation for the anisotropic superheating field by mapping the problem to the isotropic case, and present a phase diagram in terms of anisotropy and κ, showing type I, type II, or mixed behavior (within Ginzburg-Landau theory), and regions where each asymptotic solution is expected. We estimate anisotropies for a number of different materials, and discuss the importance of these results for radio-frequency cavities for particle accelerators.
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BYU Authors: Mark K. Transtrum , published in IEEE Trans. Power Syst.
The paper describes a new model reduction procedure tailored to power systems. It uses measurement data to devise a family of reduced order nonlinear models while retaining physical interpretability of parameters and equations. The Manifold Boundary Approximation Method (MBAM) uses the Fisher Information Matrix calculated from measurements to identify the least relevant parameter combination in the original model. Next, it numerically constructs a geodesic on the corresponding statistical manifold originating from the initial parameters in the least relevant parameter direction until a manifold boundary is found. MBAM then identifies a limiting approximation in the mathematical form of the model and removes one parameter combination. The simplified model is recalibrated by fitting its behavior to that of the original model, and the process is repeated as appropriate. MBAM is demonstrated on the example of a synchronous generator (SG), which has been treated extensively in the literature. Implications of the proposed model reduction procedure on large power system models are illustrated on a 441-bus, 72-SG dynamical model.
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BYU Authors: Mark K. Transtrum, published in IEEE Power in Energy and Society General Meeting, (Boston, MA, July 2016).
The paper describes a REI-based procedure for estimating parameters of a dynamic model from measurements in the boundary buses/branches. Parameter identification of equivalent synchronous generators in fictitious buses is performed by Weighted Least Square (WLS) nonlinear optimization to minimize the difference between online measurements and transient responses of reduced power system.

Theses, Captstones, and Dissertations

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In 1952 Hodgkin and Huxley formulated the fundamental biophysical model of how neurons integrate input and fire electric spikes. With 25 parameters and 4 dynamical variables, the model is quite complex. Using information theory, we analyze the model complexity and demonstrate that it is unnecessarily complex for many neural modeling tasks. Using the manifold boundary approximation method of model reduction, we perform a series of parameter reductions on the original 25-parameter model and create a series of spiking Hodgin-Huxley models, each with decreasing parameter number. We analyze the physical meaning of some key approximations uncovered by our systematic reduction methods, which are "blind" to the real physical processes the model is intended to capture. We then evaluate the behavior of the most greatly reduced 14-parameter model under different experimental conditions, including networks of neurons. We also discuss new questions that have arisen as a result of our work
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Using a finite element method, we numerically solve the time-dependent Ginzburg-Landau equations of superconductivity to explore vortex nucleation in type II superconductors. We consider a cylindrical geometry and simulate the transition from a superconducting state to a mixed state. Using saddle-node bifurcation theory we evaluate the superheating field for a cylinder. We explore how surface roughness and thermal fluctuations influence vortex nucleation. This allows us to simulate material inhomogeneities that may lead to instabilities in superconducting resonant frequency cavities used in particle accelerators.
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Many-parameter models of complex systems are ubiquitous, yet often difficult to interpret. To gain insight, these models are often simplified, sacrificing some of their global considerations as well as versatility. The task of finding a model that balances these features is of particular interest in statistical mechanics. Our group addresses the problem through a novel approach—the Manifold Boundary Approximation Method (MBAM). As the central step to this approach, we interpret models geometrically as manifolds. Many model manifolds have a set of boundary cells arranged in a hierarchy of dimension. Each of these boundary cells is itself a manifold which corresponds to a simpler version of the original model, with fewer parameters. Thus, a complete picture of all the manifold’s boundary cells—the boundary complex—yields a corresponding family of simplified models. It also characterizes the relationships among the extreme behaviors of the original model, as well as relationships among minimal models that relate subsets of these extreme behaviors. This global picture of the boundary complex for a model is termed the model’s manifold topology. Beginning in the context of statistical mechanics, this thesis defines a class of models— Superficially Determined Lattice (SDL) models—whose manifold topologies can be ascertained algorithmically. This thesis presents two algorithms. Given an SDL model, the Reconstruction Algorithm determines its manifold topology from minimal information. Given a model and desired extreme behaviors, the Minimal Model Algorithm finds the simplified model (with fewest parameters) that interpolates between all of the behaviors.
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Adaptation is an important biological function that can be achieved through networks of enzyme reactions. These networks can be modelled by systems of coupled differential equations. There has been recent interest in identifying what aspect of a network allows it to achieve adaptation. We ask what design principles are necessary for a network to adapt to an external stimulus. We use an information geometric approach that begins with a fully connected network and uses automated model reduction to remove unnecessary combinations of components, effectively constructing and tuning the network to the simplest form that still can achieve adaptation. We interpret the simplified network and combinations of parameters that arise in our model reduction to identify minimal mechanisms of adaptation in enzyme networks, and we consider the applications of these methods to other fields.
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Fitting non-linear models to data is a notoriously difficult problem. The standard algorithm, known as Levenberg-Marquardt (LM), is a gradient search algorithm based on a trust region approach that interpolates between gradient decent and the Gauss-Newton methods. Algorithms (including LM) often get lost in parameter space and take an unreasonable amount of time to converge, especially for models with many parameters. The computational challenge and bottleneck is calculating the derivatives of the model with respect to each parameter to construct the so-called Jacobian matrix. We explore methods for improving the efficiency of LM by approximating the Jacobian using partial-rank updates. We construct an update method that reduces the computational cost of the standard Levenberg-Marquardt routine by a factor of .64 on average for a set of test problems.
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We numerically study the time-dependent Ginzburg-Landau equations of superconductivity using a Galerkin method implemented in FEniCS, an automated differential equation solver. We consider geometries for both a bulk material (line from zero to infinity) and a film (half-line), corresponding to mixed and Neumann boundary conditions respectively. We simulate quenching by switching on an external magnetic field, allowing the material to approach a steady state, and then switching on a greater field. Our solutions exhibit the Meissner effect, convergence to the steady state solution, and quenching of superconductors.
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Neurons are complex physical systems with many interacting components. The foundational model of neural behavior is the Hodgkin-Huxley model. It models the cell membrane as a capacitor and protein ion channels as voltage-dependent resistors. The membrane voltage responds to an applied current and is calculated as a system of differential equations using standard circuit analysis. The Hodgkin-Huxley model involves four dynamical variables and 26 parameters; however, previous work explicitly constructing a reduced-order approximation showed that many of these parameters are irrelevant. A more realistic model from Buchholtz et al. expands on the model of Hodgkin-Huxley and involves 14 dynamical variables and 68 parameters. We implement the Buchholtz model in the Julia programming language and conduct a “sloppy model” analysis of the parameters. We show that this model is sloppy, meaning the importance of parameters used to explain the model behavior is exponentially distributed. Most of this behavior can be explained by a reduced number of combinations of parameters, suggesting that the model can be approximated by a low-order, reduced model. This work lays the foundation for a future parameter reduction analysis to find a simplified version of the Buchholtz model.
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Time delays are an inherent part of real-world systems. Besides the resulting slowing of the system, these time delays alter the dynamics and often cause destabilization. It has been shown that a system that possesses the property of intrinsic stability (a stronger form of global stability) maintains its stability when subject to any time-varying time delays, e.g., constant, periodic, stochastic, etc. Here, we begin to examine the effects and uses of adding stochastic time varying time delays to certain gradient-based optimizers. These optimizers include the well-known gradient descent and the Adam Optimizer, where the latter is commonly used in neural networks for deep learning. We show that time delays in the Adam optimizer can significantly improve the optimizer's performance on certain objective functions. We also explore the conditions under which gradient descent is intrinsically stable. Finally, to cover a wider range of loss functions, we investigate a new property of gradient descent, termed almost intrinsic stability which describes the systems' ability to get arbitrarily close to being intrinsically stable. We then use this definition to numerically examine conditions under which an almost intrinsically stable, and hence the gradient descent system, can maintain its stability when exposed to stochastic time delays bounded by a given maximum delay.
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Streptococcus pneumoniae causes over 150,000 cases of pneumonia annually in the United States alone. We present a meta-analysis of publicly available raw sequence data representing host transcriptomes before and during pneumococcus infection and carriage. We divide studies into infection and carriage samples to further investigate the differences of these models. Using computational methods, we identify the differentially expressed genes and intracellular signaling pathways that change in human and mouse cells during infection and carriage with this bacteria to test if a general infection or carriage model in mice could adequately represent these model states in humans. We found no overlapping significant signaling pathways between the mouse and human studies in either model, indicating that the mouse infection model is not specific enough to direct therapeutics for human infection. These results also suggest that there is no clear and general connection between host infection and carriage models of pneumococcus between mouse and human samples appearing in transcriptomics. Our findings are relevant to understanding the underlying mechanism of how this pathogen causes disease and how we can better combat its effects through the development of improved prophylactics and/or therapeutics.
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Superconducting resonance cavities are used in particle accelerators to accelerate beams of charged particles to near light speed. The fundamental limit to performance in these cavities is the maximum induced magnetic field that the superconductors can expel due to the Meissner effect. Traditionally, cavities have been made from Niobium; however, current technology has nearly reached the theoretical limit of performance for Niobium-based cavities. To overcome these limitations, Nb3Sn is being explored as a potential next-generation material. In actual development of Nb3Sn cavities, material defects arise that may limit performance. Time-dependent Ginzburg-Landau simulate deficiencies to explore if they cause detrimental effects to cavity performance. This research focuses on small ‘island’ regions containing deficits of Sn. These islands have been observed below the surface in real Nb3Sn cavities after fabrication. This research shows that these islands may affect performance if they are near the surface but become irrelevant when they are located more than a penetration depth below the interface.
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Interatomic models (IMs) are used in molecular modeling to predict material properties of interest. The development of an IM can take several months to years and relies on expert intuition, and yet these potentials are usually only valid for a particular application of interest. Extending existing IMs to new applications is an active area of research. Quantifying the uncertainty of an IM can tell us how much we can trust the predictions it makes. I discuss here two methods for analyzing uncertainty: Fisher Information Matrix (FIM) and Markov Chain Monte Carlo (MCMC). Using MCMC methods, I sample from the posterior distribution of the parameters when trained on data. I demonstrate this method on Lennard-Jones and Morse potentials fit to triclinic crystal configurations from the OpenKIM database. In particular, IMs are often sloppy, i.e., have likelihood surfaces with long, narrow canyons and broad, flat plateaus. I will be comparing the benefits and drawbacks of the two methods.
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Predictive models are key to understanding the behavior of physical systems. Effective models can facilitate understanding of a complicated system. Ineffective models may have a large number of parameters, leading to the phenomenon of sloppiness, characterized by large uncertainties in estimating parameter values from data. Sloppiness has previously been observed in many fields, including power systems, chemical kinetics, and systems biology. We observe that the Hodgkin- Huxley model, a canonical model of the action potential in the giant squid axon, is a sloppy model. We describe the Manifold Boundary Approximation Method (MBAM), a technique for general model reduction. We use MBAM to construct minimal versions of the Hodgkin-Huxley model of the action potential for two example behaviors. These minimal models can better inform large- scale simulation of neurons in addition to lending important insight into biologically conserved characteristics of the neuron.
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In this dissertation, I consider the problem of model reduction in both oscillatory and networked systems. Previously, the Manifold Boundary Approximation Method (MBAM) has been demonstrated as a data-driven tool for reducing the parametric complexity of so-called sloppy models. To be effective, MBAM requires the model manifold to have low curvature. I show that oscillatory models are characterized by model manifolds with high curvature in one or more directions. I propose methods for transforming the model manifolds of these models into ones with low curvature and demonstrate on a couple of test systems. I demonstrate MBAM as a tool for data-driven network reduction on a small model from power systems. I derive multiple effective networks for the model, each tailored to a specific choice of system observations. I find several important types of parameter reductions, including network reductions, which can be used in large power systems models. Finally, I consider the problem of piecemeal reduction of large systems. When a large system is split into pieces that are to be reduced separately using MBAM, there is no guarantee that the reduced pieces will be compatible for reassembly. I propose a strategy for reducing a system piecemeal while guaranteeing that the reduced pieces will be compatible. I demonstrate the reduction strategy on a small resistor network.
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We computationally explore the dynamics of superconductivity near the superheating field in two ways. First, we use a finite element method to solve the time-dependent Ginzburg-Landau equations of superconductivity. We present a novel way to evaluate the superheating field Hsh and the critical mode that leads to vortex nucleation using saddle-node bifurcation theory. We simulate how surface roughness, grain boundaries, and islands of deficient Sn change those results in 2 and 3 spatial dimensions. We study how AC magnetic fields and heat waves impact vortex movement. Second, we use automatic differentiation to abstract away the details of deriving the equations of motion and stability for Ginzburg-Landau and Eilenberger theory. We present calculations of Hsh and the critical wavenumber using linear stability analysis.
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Superconducting Radio Frequency (SRF) cavities are important components of particle accelerators. SRF cavity performance is limited by a maximum allowed applied magnetic field, known as the superheating field ($H_{\rm sh}$) at which magnetic vortices spontaneously enter the material and cause the superconducting material to quench. Previous work has calculated the theoretical maximum field a superconductor can withstand. However, this calculation assumed a perfectly smooth surface with no material inhomogeneities or surface roughness. Real world cavities are polycrystalline (typically Nb or Nb$_3$Sn) and exhibit surface defects near grain boundaries. Cavity preparation methods also lead to material inhomogeneities. I use the time-dependent Ginzburg-Landau theory and finite element methods to model the role of surface defects and material inhomogeneities in magnetic vortex nucleation. Results show the amount by which Hsh is reduced depends on the concentration of impurities as well as the physical dimensions of the defect. Reducing the size of grain boundaries and material inhomogeneities found therein has the potential to significantly increase SRF cavity performance.