Lawrence Udeigwe

Professor, Mathematics

Affiliate Research Faculty, Brain & Cognitive Sciences, Massachusetts Institute of Technology (MIT)

As an academic, Dr.Udeigwe enjoys devoting equal attention to both teaching and research, as well as being able to introduce his research materials in his courses with the goal of continuously improving mathematics pedagogy and, even, birthing new courses. His research areas include differential equations; dynamical systems, and computational neuroscience. At Manhattan College, he has introduced and created new courses in computational neuroscience and applied dynamical systems that he has taught to both graduate and undergraduate students. 

Dr. Udeigwe has received research grants from national agencies including the National Science Foundation (NSF) and the Department of Defense Army Research Office (ARO) to support his work on the homeostasis of synaptic plasticity during vision processing and memory formation.

Dr. Udeigwe is an Affiliate Research Faculty and a 21/22 MLK Visiting Associate Professor in Brain and Cognitive Sciences at Massachusetts Institute of Technology (MIT). He has served as Senior Fellow and Visiting Scholar at the Institute for Pure and Applied Mathematics (IPAM), Los Angeles, CA, where he was one of the core participants in the long-term program Mathematical Challenges and Opportunities for Autonomous Vehicles.

Outside of mathematics and science, Dr. Udeigwe is a jazz musician. He also explores the different ways in which mathematics and jazz can be interfaced.

Education

PHD, University of Pittsburgh, 2014
MA, University of Pittsburgh, 2008
MS,  University of Delaware, 2006
BS & BA, Duquesne University, 2004

Courses Taught

Math 096: Bridge Course for Business Students 
Math 100: Precalculus 
Math 158: Introduction to Mathematical Computations
Math 185: Calculus I 
Math 186: Calculus II 
Math 285: Calculus III 
Math 272: Linear Algebra 
Math 286: Differential Equations  
Math 386: Partial Differential Equations 
Math 387: Analysis I 
Math 491: Topics in Mathematics - Dynamical Systems 
Matg 511: Computational Methods for Analytics 
Matg 557: Machine Learning
Matg 630: Probability and Statistics for Analytics
Matg 692: Topics in Mathematics - Theory of Differential Equations
Matg 692: Topics in Mathematics - Dynamical Systems
Math 692: Topics in Mathematics - Theoretical Neuroscience
Matg 699: Research in Mathematics
  • Research
    Research Areas of Interest 
    • Differential Equations and Dynamical Systems
    • Mathematical and Computational Neuroscience
    • Mathematics Pedagogy
    Current Research Topics
    • Using differential equations and machine learning tools to understand synaptic plasticity and memory formation in the the brain.
    • Using artificial neural networks (ANN) in understanding the neuronal representations and computational mechanisms that underlie visual object recognition in primates.
    • How to apply results (from the above two topics) in amenable technologies such as autonomous vehicles.
  • Publications and Scholarly Activities
     
    Select Publications
    1. Udeigwe, L. C. Rate-Based Synaptic Plasticity Rules. Notices of the American Mathematical Society, Vol. 71, No. 9, 12 pages (2024). DOI: https://doi.org/10.1090/noti3023
    2. Udeigwe, L. C. An Analysis of the Cluster-Detecting Property of the BCM Neuron. Computing Open, Vol. 02, 2450002, 22 pages (2024). DOI: https://doi.org/10.1142/S2972370124500028
    3. Udeigwe, L. C. Interfacing Mathematics and Music: A Case for More Engagement. Notices of the American Mathematical Society, Vol. 73, No. 22 (2023), 309–313. DOI: https://doi.org/10.1090/noti2610
    4. Cirincione, A., Verrier, R., Bic, A., Olaiya, S., DiCarlo, J., Udeigwe, L., & Marques, T. (2022). Implementing Divisive Normalization in CNNs Improves Robustness to Common Image Corruptions. Open Reviews / NeurIPS. https://openreview.net/pdf?id=KAAbo44qhJV
    5. Udeigwe, L. C., et al. White Paper: Mathematical Challenges and Opportunities for Autonomous Vehicles. Institute for Pure and Applied Mathematics (IPAM), UCLA, Long Program (Fall 2020). https://www.ipam.ucla.edu/wp-content/uploads/2024/01/Whitepaper_AV2020.pdf
    6. Udeigwe, L. C., et al. Neuromatch Academy: A 3-Week, Online Summer School in Computational Neuroscience. Journal of Open Source Education, Vol. 5, No. 49, 118 (2022). https://doi.org/10.21105/jose.00118
    7. Bohling, M. E., & Udeigwe, L. C. (2022). The Spiking Neuron Model. In Goldwyn, E. E., Ganzell, S., & Wootton, A. (eds.), Mathematics Research for the Beginning Student, Volume 2. Foundations for Undergraduate Research in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-08564-2_5
    8. Udeigwe, L. C. Using Phase Portraits to Analyze Relationship Dynamics. SIMIODE, 2019. https://www.simiode.org/resources/6263
    9. Udeigwe, L. C., Munro, P. W., & Ermentrout, G. B. Emergent Dynamical Properties of the BCM Learning Rule. Journal of Mathematical Neuroscience, Vol. 7:2 (2017). https://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-017-0044-6
    10. Udeigwe, L. C., & Ermentrout, G. B. Waves and Patterns on Regular Graphs. SIAM Journal on Applied Dynamical Systems, Vol. 14(2), 1102–1129 (2015). https://epubs.siam.org/doi/abs/10.1137/140969488
    11. Udeigwe, L. C., Ermentrout, G. B., & Munro, P. W. Oscillation and Chaos in the Dynamics of the BCM Learning Rule. BMC Neuroscience, Vol. 14(1), 2013. https://doi.org/10.1186/1471-2202-14-S1-P61
    12. Smith, D. B., Udeigwe, L. C., & Rubin, J. Physical Interactions Between D1 and NMDA Receptors as a Possible Inhibitory Mechanism to Avoid Excessive NMDA Currents. BMC Neuroscience, Vol. 8(2), 2007. https://doi.org/10.1186/1471-2202-8-S2-P74


    Theses

    1. L.C. Udeigwe, Dynamical systems of the BCM learning rule: emergent properties and application to clustering (PhD dissertation). University of Pittsburgh, 2014 http://d-scholarship-dev.library.pitt.edu/22655/
    2. L.C. Udeigwe. Identification of objects in an acoustic waveguide: Numerical results and an introduction to an alternate approach via the method of images (Masters thesis). University of Delaware, 2006 https://udspace.udel.edu/handle/19716/27435

    Select presentations

    1. Modeling Recovery from Amblyopia: Mathematical Explorations with Synaptic Plasticity as Basis.
      Joint Mathematics Meetings (JMM), San Francisco, CA. January 5, 2024.
    2. Using Student Projects for General Public Education.
      Joint Mathematics Meetings (JMM), San Francisco, CA. January 4, 2024.
    3. Framing Ethics Through General Public Education.
      Joint Mathematics Meetings (JMM), San Francisco, CA. January 3, 2024.
    4. Implementing Divisive Normalization in CNNs.
      Mathematical Challenges and Opportunities for Autonomous Vehicles Reunion Conference, UCLA Lake Arrowhead Conference Center. June 15, 2023.
    5. Elements of Theory in Neuroscience.
      I Can’t Believe It’s Not Better: Understanding Deep Learning Through Empirical Falsification, NeurIPS 2022, New Orleans, LA. December 3, 2022.
    6. On the Elements of Theory in Neuroscience.
      Massachusetts Institute of Technology (MIT), Cambridge, MA. April 28, 2022.
    7. Two Theoretical Spaces: Neuroscience & DEIJ.
      Massachusetts Institute of Technology (MIT), Cambridge, MA. March 17, 2022.
    8. Modeling the Transmission and Control Dynamics of COVID-19.
      Manhattan College, Riverdale, NY. February 17, 2021.
    9. Using a Sensory Neuron to Learn a Dataset.
      United States Military Academy, West Point, NY. February 5, 2020.
    10. A Single-Neuron Data Classification Algorithm.
      MAA New York Sectional Meeting. May 4, 2019.
    11. An Unsupervised Clustering Algorithm Based on Sensory Neuronal Selectivity.
      Lafayette College, Easton, PA. April 17, 2019.
    12. A Single-Neuron Data Classification Algorithm.
      Manhattan College, Department of Mathematics Seminar Series, Riverdale, NY. April 11, 2018.
    13. Synaptic Plasticity as a Function of Homeostatic Time-Scales.
      Sense to Synapse Conference, New York, NY. April 7–8, 2017.
    14. The Effect of Homeostatic Time-Scale Adjustment of the BCM Learning Rule.
      Sense to Synapse Conference, Rockefeller University, New York, NY. 2016.
    15. The Perceptron: Overview, Convergence Theorem, Self-Supervision.
      Manhattan College, Department of Mathematics Seminar Series, Riverdale, NY. April 13, 2016.
    16. Oscillators and Patterns on a Sphere.
      Manhattan College, Department of Mathematics Seminar Series, Riverdale, NY. April 22, 2015.
    17. Emerging Dynamics of Cortical Neuronal Selectivity.
      (with G.B. Ermentrout and P.W. Munro) Temporal Dynamics of Learning Center, USDC, Annual Spring Retreat, La Jolla, CA. February 6, 2014.
    18. Dynamics of Cortical Plasticity: Oscillatory, Toroidal, and Chaotic Properties of the BCM Learning Model.
      (with G.B. Ermentrout and P.W. Munro) Complex Biological Systems Seminar, University of Pittsburgh, Pittsburgh, PA. October 10, 2013.
    19. Exploring the Dynamics of the BCM Learning Rule.
      (with G.B. Ermentrout and P.W. Munro) Temporal Dynamics of Learning Center, USDC, Annual Fall Retreat, La Jolla, CA. August 26, 2013.
    20. Oscillatory and Chaotic Dynamics of the BCM Learning Rule.
      (with G.B. Ermentrout and P.W. Munro) Annual Computational Neuroscience Meeting, Paris, France. July 17, 2013.
    21. Non-Synchronous Oscillations on Graphs.
      (with G.B. Ermentrout) SIAM Conference on Applications of Dynamical Systems. May 24, 2011.
    22. Coupled Neural Oscillators on the Surface of a Sphere.
      (with G.B. Ermentrout) Complex Biological Systems Seminar, University of Pittsburgh, Pittsburgh, PA. September 14, 2010.
    23. Application of Non-Synchronous Oscillations on Graphs.
      (with G.B. Ermentrout) SIAM Conference on the Life Sciences, Pittsburgh, PA. July 14, 2010.

    Research Technical Reports (with undergraduate students) 

    1. Artiom Bic, Andrew Cirincione, Lawrence Udeigwe. A Mathematical Investigation of Inhibition Stabilized Networks. The Manhattan Scientist, In press
    2. Parul Rai, Maxwell Bohling, Lawrence Udeigwe. Investigating the Activity of Coupled Neurons. The Manhattan Scientist, In press
    3. Andrew Cirincione, Maxwell Bohling, Lawrence Udeigwe. A Numerical Investigation of the Wilson-Cowan Model. The Manhattan Scientist, In press
    4.  Michael Rozycki, Lawrence Udeigwe Computing Direction of Maximal Skew in a Dataset. The Manhattan Scientist, Series B Volume 6, 2019
    5.  Michael Campliglia, Lawrence Udeigwe Single Neuron Cluster Detection using BCM and Oja Learning Rules. The Manhattan Scientist, Series B Volume 6, 2019
    6. Sebastian Pena, Lawrence Udeigwe, Igor Aizenberg. Using Laterally Inhibiting Neurons to Detect Clusters. The Manhattan Scientist, Series B Volume 6, 2019
    7. Nico Colon, Alex Gonzalez, Lawrence Udeigwe. Image recognition using autoencoding in multilayer neural networks and multi-value neurons. The Manhattan Scientist, Series B Volume 4, Fall 2017 
    8. Nico Colon, Alex Gonzalez, Lawrence Udeigwe, Igor Aizenberg. Image recognition using analysis of discrete Fourier transform by multilayer neural networks with multi-valued neurons. The Manhattan Scientist, Series B Volume 4, Fall 2017 
  • Professional Experience and Memberships
    Experience:
    • Director of Mathematics Graduate Programs, Manhattan College, Riverdale, NY [2022 - 2023]
    • Affiliate Research Faculty in Brain and Cognitive Sciences, Massachusetts Institute of Technology (MIT), Cambridge, MA [2022 - Present].
    • Dr Martin Luther King Jr. Visiting Associate Professor of Brain and Cognitive Sciences, Massachusetts Institute of Technology (MIT), Cambridge, MA [2021 - 2022].
    • Senior Fellow & Visiting Scholar, Institute for Pure & Applied Mathematics (IPAM), Los Angeles, CA [2020]
    • Associate Professor of Mathematics, Manhattan College, Riverdale, NY [2020 - present]
    • Assistant Professor of Mathematics, Manhattan College, Riverdale, NY [2016 - 2020]
    • Visiting Assistant Professor of Mathematics, Manhattan College, Riverdale, NY [2014 - 2016]
    • Adjunct Instructor of Mathematice, Community College of Allegheny County, Pittsburgh, PA [2012 - 2014]
    • Instructor of Mathematice, Pennsylvania State University, Fayette [2009 - 2012]
    Membership:
    • Sigma Xi [2016 - present]
    • Mathematical Association of America [2004 - present]
    • Organization for Computational Neuroscience [2012 - present]
    • Society of Industrial and Applied Mathematician [2004 - present]
  • Honors, Awards, and Grants
    Awards & Honors
    • MIT Brain & Cognitive Sciences Award for Excellence in Graduate Teaching, 2023
    • Honoree, Mathematically Gifted & Black, 2023
    • Nominee, University of Delaware Teaching Excellence Award, 2005
    Grants & Funding
    • U.S. Department of Defense, Army Research Office, 2021 — $371,000
    • NSF (via IPAM) Course Buyout, 2020 — $18,000
    • NSF (via IPAM) Travel Grant, 2020 — $1,600
    • NSF (via IPAM) Travel Grant, 2019 — $1,388
    • SIMIODE Content Development Grant, 2019 — $1,200
    • MC Jasper Scholar Grant for Faculty, 2019 — $1,500
    • MC Summer Grant for Faculty, 2019 — $3,000
    • MC Faculty Development Plan Award, Fall 2017 – Spring 2020
    • Organization for Computational Neuroscience Travel Grant, 2013 — $1,000
    Scholarships
    • University of Pittsburgh, Full Tuition Scholarship, Fall 2006 – Fall 2008; Fall 2011 – Spring 2014
    • University of Delaware, Full Tuition Scholarship, Fall 2004 – Fall 2006