# Elena Dimitrova

## Professor

**Email:** edimitro@calpoly.edu**Office Phone:** 805-756-1689**Office:** 25-342

**Education**

2006 Ph.D. in Mathematics, Virginia Tech, Blacksburg, Virginia

2003 M.S. in Mathematics, Virginia Tech, Blacksburg, Virginia

2001 B.A. in Computer Science, American University in Bulgaria, Blagoevgrad, Bulgaria

**Research ****Interests**

Algebraic design of experiments

Computational algebra

Discrete models of biochemical networks

Gröbner fans of zero-dimensional ideals

Polynomial maps over finite fields

Reverse-engineering methods

**About**

I am an Professor in the Department of Mathematics at Cal Poly, San Luis Obispo. My research involves theoretical development and practical application of algebraic models of biochemical networks. I also work in algebraic design of experiments with the goal of determining the optimal amount and type of experimental data needed for algebraic model construction. The models used in this work are time- and state-discrete dynamical systems, described by polynomial functions over a finite field.

I am also a senior researcher at The Southeast Center for Mathematics and Biology (SCMB) which is an NSF-Simons Research Center for Mathematics of Complex Biological Systems (MathBioSys), with a core mission of catalyzing new cross-disciplinary collaborations between biosystems experimentalists and interdisciplinary mathematicians. My project is in collaboration with Melissa Kemp.

Click here to learn more about our work.

## Current and Past Courses Taught

**List of Courses**

2020 - Winter: MATH 248 Methods of Proof in Mathematics

2019 - Fall: MATH 142 Calculus 2

2019 - Spring: Algebraic Biology at the African Institute for Mathematical Sciences

2018 - Fall: MATH (Abstract Algebra I)

2018 - Fall: MATH (Introduction to Proof)

2018 - Spring: MATH (Matrix Analysis)

2018 - Spring: MATH (Linear Algebra)

2017 - Spring: MATH Linear Algebra), Sections 1 & 2

2016 - Fall: MATH (Introduction to Proof), Sections 1 & 2

2016 - Spring: MATH (Introduction to Proof), Sections 1 & 2

2015 - Fall: MATH (Introduction to Proof), Sections 1 & 2

2015 - Spring: MATH (Linear Algebra)

2015 - Spring: MATH (Abstract Algebra)

2014 - Summer: MATH (Calculus of One Variable II)

2013 - Fall: MATH (Differential Equations), Sections 4, 6, and 7

2013 - Spring: MTHSC (Differential Equations), Sections 8 and 11

2012 - Summer: MTHSC (Calculus of One Variable I)

2012 - Summer: MTHSC (Calculus of One Variable II)

2012 - Spring + Summer: MTHSC (Introduction to Mathematical Models)

2012 - Spring + Summer: MTHSC (Abstract Algebra)

2011 - Fall: MTHSC (Introduction to Mathematical Models)

2011 - Fall: MTHSC (Abstract Algebra)

2011 - Summer: MTHSC (Elementary Statistical Inference)

2011 - Summer: MTHSC (Differential Equations)

2011 - Spring: MTHSC (Abstract Algebra)

2011 - Spring: MTHSC 208 (Differential Equations)

2010 - Summer: MTHSC (Elementary Statistical Inference)

2010 - Summer: MTHSC (Calculus of One Variable II)

2010 - Fall: MTHSC (Linear Algebra)

2010 - Fall: MTHSC (Discrete Mathematical Structures)

2010 - Spring: MTHSC (Discrete mathematical methods for modeling and simulation of biological systems)

2010 - Spring: MTHSC (Intro to Business Statistics)

2009- Fall: MTHSC (Intro to Business Statistics)

2009 - Summer: MTHSC (Abstract Algebra)

2009 - Spring: MTHSC (Abstract Algebra)

2008 - Fall: MTHSC (Intro to Business Statistics)

2008 - Fall: MTHSC (Matrix Analysis)

2008 - Summer: MTHSC (Computational Algebra)

2008 - Spring: MTHSC (Linear Algebra)

2008 - Spring: MTHSC (Matrix Analysis)

2007 - Fall: MTHSC (Intro to Business Statistics)

2007 - Fall: MTHSC (Matrix Analysis)

2007 - Spring: MTHSC (Intro to Business Statistics)

2006 - Fall: MTHSC (Statistical Methods I)

## Professional Distinctions

**List of Distinctions**

Southeast Center of Mathematics and Biology, NSF and Simons Foundation, PI on subaward, 2018-23.

Selection methods for algebraic design of experiments, NSF, 2017-20.

Data selection for unique model identification, NSF, 2014-17.

AWM-NSF Travel Grant, 2013

2011 Mathematical Sciences Faculty Teaching Award, Department of Mathematical Sciences, Clemson University

Developing discrete network models to discover transcriptional regulation of peach fruit color, University Research Grant Committee (URGC), 2011

Acquisition of Large-Memory, Many-Core Compute Node for Mathematical Science Research, NSF, 2010-2011

Project NExT (New Experiences in Teaching, a program of the MAA) Fellowship, 2006-2007

Invited Presentations

Dimitrova, E.S. Invited conference talk, “Network control through multistate canalization.” Third International Conference of Mathematics and Statistics, American University in Sharjah, United Arab Emirates, February 2020.

Dimitrova, E.S., “Unique Reduced Groebner Bases of Ideals of Points,” Discrete Math Days in the Northeast, University of New England, Biddeford, ME (May 5, 2018).

Dimitrova, E.S. “A discrete multiscale modeling perspective to the innate immune response to ischemic injury,” Joint Mathematics Meetings, San Diego, CA (January 2018).

Molecular Network Control Through Boolean Canalization, AMS Fall Southeastern Sectional Meeting, University of Central Florida, Orlando, Orlando, FL (September, 2017).

Vanishing ideals, CanaDAM 2017, Ryerson University, Toronto, ON, Canada (June 2017).

Unique Reduced Groebner Bases of Ideals of Points, Colloquium talk, Dartmouth College, Hanover, NH (October 2016).

Algebraic models for gene regulatory networks, Mathematical Biology and Ecology Seminar, Georgia Tech, Atlanta, GA (June 2016).

Properties and applications of vanishing ideals of points over finite fields, Meeting on Algebraic Geometry for Applications, Clemson University, Clemson, SC (April 2016).

Properties and applications of vanishing ideals of points over finite fields, Algebra and Discrete Mathematics Seminar and Graduate Student Combinatorics Conference, Clemson University, Clemson, SC (March 2016).

Control methods for Boolean networks, Eighth International Symposium on Biomathematics and Ecology: Education and Research (BEER 2015), Illinois State University, Normal, IL (October 2015).

A difference equation for tracking perturbations in systems of Boolean nested canalyzing functions. KNOWeSCAPE 2015, European Cooperation in Science and Technology, Mons, Belgium (September 2015).

Algebraic models in systems biology,” Department of Mathematics, University of Kentucky, Lexington, KY (December 2014).

Canalyzation in mathematical modeling, Keynote address, KNOWeSCAPE 2014, European Cooperation in Science and Technology, Thessaloniki, Greece (November 2014).

Canalization in modeling gene regulatory networks, Biomathematics and Ecology: Education and Research 2013 (BEER’13), Marymount University, Arlington, VA (October 2013).

Design of experiment for biological network inference, Conference on Applied Algebraic Geometry (AG13), Colorado State University, Fort Collins, CO (August 2013).

Data characterization and identification for network inference, Spring Central Sectional AMS Meeting, Iowa State University, Ames, IA (April 2013).

Modeling gene regulatory networks, Southern Methodist University, Department of Mathematics, Dallas, TX (April 2012).

Perturbation spread in Boolean networks, George Washington University, AMS special session on Dynamics of Complex Networks, Washington, DC (March 2012).

Modeling gene regulatory networks with canalyzing functions, Medical College of Georgia, Augusta, GA, (March 2011).

(with Layne, L.) Discrete models of biological networks, UC Santa Cruz, Department of Bioengineering, Santa Cruz, CA, (August 2010).

(with Layne, L.) Some properties of nested canalyzing and partially nested canalyzing functions, Department of Mathematics, UC Berkeley, Berkeley, CA (July 2010).

(with Mitra, I. and Jarrah, A.S.) Stochastic polynomial dynamical model of the yeast cell cycle, APS 2010 Meeting, Portland, OR (March 2010).

Probabilistic dynamical systems for reverse engineering of the yeast cell cycle network, AMS 2009 Central Section Meeting, Waco, TX (October 2009).

Parameter estimation for a drought-related gene network in rice, SAMSI Transition Workshop: Algebraic Methods in Systems Biology and Statistics, Research Triangle, NC (June 2009).

Discovering gene networks in rice, SIAM Chapter at Virginia Tech, Blacksburg, VA (April 2009).

(with Jarrah, A.S.) Probabilistic polynomial systems for the reverse engineering of stochastic gene regulatory networks, Joint Meeting of the American Mathematical Society and Shanghai Mathematical Society, Fudan University, Shanghai, China (December 2008).

Conjecturing variable dependencies in biochemical networks, Visitors Day, Virginia Tech, Blacksburg, VA (March 2007).

Using the Groebner fan of an ideal for polynomial model selection, AMS Spring Southeastern Section Meeting, Special Session on Applicable Algebra, Davidson College, Davidson, NC (March 2007).

Using the Gröbner fan of an ideal for polynomial model selection, Computational Mathematics Seminar, Department of Mathematical Sciences, Clemson University (February 2007).

Inferring dependencies in biochemical networks, Third SC-INBRE Bioinformatics Research Symposium, Clemson University (January 2007).

Polynomial models for systems biology: a combinatorial method for model selection, Bioinformatics Seminar, Clemson University (November 2006).

(with Layne, L.) Term order effect on polynomial models for systems biology, National EPSCoR Conference, Lexington, KY (November 2006).

Using the Gröbner fan of an ideal for polynomial model selection, ADM Seminar, Mathematical Sciences, Clemson University (October 2006).

Experimental data preprocessing for reverse engineering, Mathematical Biology, Institute for Advanced Study / Park City Mathematics Institute, Park City, UT (July 2005).

Discretization of biological data, 1st Annual Faculty Retreat of Virginia Bioinformatics Institute, Homestead Resort, VA (May 2005).

Time series discretization for reverse engineering of gene networks, Bulgarian Academy of Science, Sofia, Bulgaria (January 2005).

Time series discretization for reverse engineering of gene networks, SIAM Student Chapter at Virginia Tech, Blacksburg, VA (November 2004).

A graph-theoretic method for the discretization of gene expression measurements, SACNAS National Conference, Austin, TX, (October 2004).

(with Stigler, B. and Laubenbacher, R.) Continuous and discrete modeling of biological systems, Mathematical Methods in Bioinformatics, Pre-conference Mathematics Institute Session, Austin, TX (October 2004).

(with Yordanov, O.) Statistics on low-dimensional chaotic flows, Summer School in Bifurcation and Chaos, Pamplona, Spain (June 2000).

Contributed Presentations

Conjecturing variable dependencies in biochemical networks, First Year Graduate Student Seminar, Department of Mathematical Sciences, Clemson University (February 2010).

Groebner basics, First Year Graduate Student Seminar, Department of Mathematical Sciences, Clemson University (April 2009).

Conjecturing variable dependencies in biochemical networks, First Year Graduate Student Seminar, Department of Mathematical Sciences, Clemson University (February 2008).

A computational algebra method for biochemical network modeling, Joint Mathematics Meetings, San Diego, CA (January 2008).

A Groebner fan method for biochemical network modeling, International Symposium on Symbolic and Algebraic Computation, University of Waterloo, Ontario, Canada, (July 2007).

(with Stigler, B.) Applications of the Gröbner fan to gene network reconstruction, East Coast Computer Algebra Day, Shepherdstown, WV (May 2008).

Mathematical modeling of biochemical networks, Workshop for Young Researchers in Mathematical Biology, MBI, The Ohio State University, Columbus, OH (March 2007).

Modeling of gene networks, First Year Graduate Student Seminar, Department of Mathematical Sciences, Clemson University (March 2007).

Time series discretization for reverse engineering of gene networks, Workshop for Young Researchers in Mathematical Biology, MBI, The Ohio State University, Columbus, OH (March 2006).

## Publications

**List of Publications**

(with Phillipson, K., Hoenecker, M., Hu, J., Liang, Q.) (2019). Gröbner bases of convex neural code ideals. To appear in the Symposium Proceedings of 2019 AWM Research Symposium (PDF).

Koshy-Chenthittayil S., Dimitrova E. (2020) From Chaos to Permanence Using Control Theory (Research). In: Acu B., Danielli D., Lewicka M., Pati A., Saraswathy RV, Teboh-Ewungkem M. (eds) Advances in Mathematical Sciences. Association for Women in Mathematics Series, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-42687-3_6

(with Ha, S., Hoops, S., Altarawy, D, Ansariola, M., Deb, D., Glazebrook, J., Hillmer, R., Hosamadine, H., Katagiri, E., McDowell, J., McGraw, M., Setubal, J., Tyler, B.M., Laubenbacher, R.) PlantSimLab - A Modeling and Simulation Web Tool for Plant Biologists. BMC Bioinformatics 20, 508 (PDF).

(with He, Q, Stigler, B., Zhang, A.) Geometric characterization of data sets with unique marked reduced Groebner bases. Bulletin of Mathematical Biology, 81:2691–2705.

(with Caromile, L.A., Laubenbacher, R., Shapiro, L.) The innate immune response to ischemic injury: a multiscale modeling perspective. BMC Systems Biology, 12:50.

(with He, Q., Robbiano, L., Stigler, B.) Small Gröbner fans of ideals of points. Journal of Applied Algebra, April 2017.

Discrete-Time Dynamical Systems. In “Handbook of Discrete and Combinatorial Mathematics,” 2nd Ed, Ed. Douglas Shier. CRC Press.

(with Laubenbacher, R.) Boolean models in immunology. In “System Immunology: An Introduction to Modeling Methods for Scientists,” Eds. Das, J. and Jayaprakash, C. Taylor & Francis Group.

(with Murrugarra, D) Molecular network control through Boolean canalization. EURASIP Journal on Bioinformatics and Systems Biology, 2015:9.

(with Matache, D. and Yordanov, O.) A difference equation for tracking perturbations in systems of Boolean nested canalyzing functions. Physical Review Letters E, 91(6), 062812.

(with Le Pape, S., Hannaert, P., Konovalov, A.,Volmer, R., Ron, D., Thuillier, R., Hauet, H.) Polynomial algebra as a tool to identify potential therapeutic targets: an application to ischemia-reperfusion injury. FEBS Letters, 588(17), pp. 3062-7.

(with Stigler, B.) Data Identification and Characterization for Improving Gene Network Inference. Bulleting of Mathematical Biology, October 2014 (PDF).

(with Stigler, B.) Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering. In Mathematical Concepts and Methods in Modern Biology, Eds. Hodge, T. and Robeva, R. Elsevier.

(with Layne, L. and Macauley, M.) Nested canalyzing depth and network stability. Bulletin of Mathematical Biology. 74(2), pp. 422-433 (PDF).

(with A. Jarrah and I. Mitra) Probabilistic polynomial dynamical systems for reverse engineering of gene regulatory networks. EURASIP J. on Bioinformatics and Systems Biology. 2011:1, pp. 1-33 (PDF).

(with L.D. Garcia-Puente, F. Hinkelmann, A. Jarrah, R. Laubenbacher, B. Stigler, M. Stillman, P. Vera-Licona) Parameter Estimation for Boolean Models of Biological Networks (PDF). Journal of Theoretical Computer Science, 412(2011), pp. 2816-2826.

Estimating the relative volumes of the cones in a Groebner fan (PDF). Special issue of Mathematics in Computer Science: Advances in Combinatorial Algorithms II,

3(4), pp. 457-466.

(with M.P. Vera Licona, J. McGee, and R. Laubenbacher) Discretization of Time Series Data. Journal of Computational Biology 17, pp. 1-17 (PDF).

(with R. Laubenbacher, A. Jarrah, B. Stigler, P. Vera-Licona) System Identification for Discrete Polynomial Models of Gene Regulatory Networks (PDF). 15th IFAC Symposium on System Identification (SYSID 2009), Volume 15, Part 1, pp. 11-17.

(with A. Zardecki) Forecasting Polynomial Dynamics (PDF). Applied Mathematics and Computation, 204(1), pp. 233-239.

(with A. Jarrah, R. Laubenbacher, and B. Stigler) A Groebner Fan Method for Biochemical Network Modeling. ISSAC Proceedings: 122-126 (PDF).

Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics. Virginia Tech Digital Library and Archives. Ph.D. Dissertation. 2006.

(with O. Yordanov) Statistics of Some Low-dimensional Chaotic Flows (PDF). International Journal of Bifurcation and Chaos, 11(10), pp. 2675-2682.