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Contact Information

Education

• PhD in Mathematics, minor in Electrical Engineering, August 2012, University of Nebraska-Lincoln
  • Thesis: Equivalence and duality for rank-metric and matrix codes

    Advisor: Dr. Judy Walker

• M.S. Mathematics, August 2008, University of Nebraska-Lincoln
• Budapest Semesters in Mathematics, Fall 2005, The Technical University of Budapest
• B.A. Mathematics and Psychology, May 2005, Swarthmore College

Professional/Academic Experience

• 2012 鈥� Present, Professor, University of Northern Colorado
• July 2015 to Dec 2015, Research Associate, Pennsylvania State University
• 2006 鈥� 2012, Graduate Teaching Assistant, University of Nebraska-Lincoln

Research/Areas of Interest

Mathematical Neuroscience

• Theory of neural networks
  • ()
• Neural coding

Algebraic Coding Theory

• Applications of matrix codes to network coding
• Graph-based decoding algorithms for LDPC and polar codes

Publications/Creative Works

This work has been funded by NSF DMS-1951599 (2020 鈥� 2024) and NIH R01 EB022862 (2016 鈥� 2021).    

Pre-prints/Submitted: 

C. Curto, C. Langdon, K. Morrison. Robust motifs of threshold鈥恖inear networks. Available at. 

C. Langdon, K. Morrison*, C. Curto*. Combinatorial geometry of threshold-linear networks. (* equal last authors) Available at 

J. Bolkema, K. Morrison, J. L. Walker. The Tensor-Like Join: A Graph-Theoretic Approach to Polar Codes.  

Published/Accepted:  

K. Morrison, A. Degeratu, V. Itskov, C. Curto. Diversity of emergent dynamics in competitive threshold-linear networks.SIAM Journal of Applied Dynamical Systems, 23(1), 2024.

C. Curto, J. Geneson, K. Morrison. Stable fixed points of combinatorial threshold-linear networks. Advances in Applied Mathematics, 154, 2023.

C. Curto and K. Morrison. Graph rules for recurrent network dynamics. Notices of the American Mathematical Society, 70(4), 2023.

C. Parmelee, J. Londono Alvarez, C. Curto*, K. Morrison*. Sequence generation in inhibition-dominated neural networks. The Dynamical Systems Web Magazine, October, 2022. (* equal last authors)

C. Parmelee, J. Londono Alvarez, C. Curto*, K. Morrison*. Sequential attractors in combinatorial threshold-linear networks. SIAM Journal of Applied Dynamical Systems, 21(2), 2022. (* equal last authors)

D. Egas Santander, S. Ebli, A. Patania, N. Sanderson, F. Burtscher, K. Morrison*, C. Curto*. Nerve theorems for fixed points of neural networks. In Research in Computational Topology 2, Assoc. Women Math. Ser. 30, E. Gasparovic, V. Robins, and K. Turner, eds., Springer, Cham, 2022.  (* equal last authors)

C. Parmelee, S. Moore, K. Morrison*, C. Curto*. Core motifs predict dynamic attractors in combinatorial threshold-linear networks. PLOS ONE, 17(3): e0264456, 2022. (* equal last authors)

C. Curto and K. Morrison. Relating network connectivity to dynamics: opportunities and challenges for theoretical neuroscience. Current Opinion in Neurobiology, Vol 58, 11-20, 2019.

C. Curto, E. Gross, J. Jeffries, K. Morrison*, Z. Rosen, A. Shiu, N. Youngs. Algebraic signatures of convex and non-convex codes. J. of Pure and Appl. Algebra, Vol. 223, No. 9, 3919-3940, 2019. (* corresponding author)

C. Curto, J. Geneson, K. Morrison. Fixed points of competitive threshold-linear networks. Neural Computation, Vol 33, No. 1, 94-155, 2019.

K. Morrison and C. Curto. Predicting neural network dynamics via graphical analysis. Book chapter in Algebraic and Combinatorial Computational Biology. R. Robeva, M. Macaulay (Eds) 2018.

A.M. Burzynski, S.W. Anderson, K. Morrison, M.R. Patrick, T. Orr, W. Thelen, Lava lake thermal pattern classification using self-organizing maps and relationships to eruption processes at K墨lauea Volcano, Hawai'i. Chapter in Field Volcanology: A Tribute to the Distinguished Career of Don Swanson. M.P. Poland, M. O. Garcia, V. E. Camp, A. Grunder (Eds) 2018.

C. Curto, E. Gross, J. Jeffries, K. Morrison, M. Omar, Z. Rosen, A. Shiu, N. Youngs. What makes a neural code convex?  SIAM J. Appl. Algebra Geometry, Vol 1, 222-238, 2017.

C. Curto, K. Morrison. Pattern completion in threshold-linear networks. Neural Computation,  Vol 28, 2825-2852, 2016.

G. Karakok, K. Morrison, C. Craviotto. Lessons Learned from a Math Teachers鈥� Circle. Association for Women in Mathematics Series: Mathematics Education, Vol. 7, Jacqueline Dewar et al. (Eds), 2016.

K. Morrison. Enumeration of Equivalence Classes of Self-Dual Matrix Codes.Advances in Mathematics of Communication. Vol 9, No. 4, 415-436, 2015.

H. Gluesing-Luerssen, K. Morrison, C. Troha. Cyclic Orbit Codes and Stabilizer Subfields. Advances in Mathematics of Communication. Vol 9, No. 2, 177-197, 2015.

H. Gluesing-Luerssen, K. Morrison, C. Troha. On the Cardinality and Distance of Cyclic Orbit Codes based on Stabilizer Subfields. Proceedings of the 21^st International Symposium on Mathematical Theory of Networks and Systems. July 7-11, 2014.

K. Morrison. Equivalence for rank-metric and matrix codes and automorphism groups of Gabidulin codes.IEEE Transactions on Information Theory. Vol 60, Issue 11, pp. 1-12, 2014.

C. Curto, V. Itskov, K. Morrison, Z. Roth, J. L. Walker. Combinatorial neural codes from a mathematical coding theory perspective. Neural Computation. Vol 25, pp. 1891-1925, 2013.

F. Hunt, K. Morrison, C. Dabrowski. Spectral Based Methods that Streamline the Search for Failure Scenarios in Large-Scale Distributed Systems.Proceedings of the IASTED International Conference on Applied Simulation and Modeling, June 22-24th, 2011.

N. Axvig, K. Morrison, E. Psota, D. Dreher, L. C. P茅rez, J. L. Walker. Analysis of connections between pseudocodewords. IEEE Transactions on Information Theory. Vol 55, Issue 9, pp. 4099-4107, 2009.

N. Axvig, K. Morrison, E. Psota, D. Dreher, L. C. P茅rez, J. L. Walker. Towards universal cover decoding. In Proceedings of International Symposium on Information Theory and Its Applications. December 2008.

N. Axvig, K. Morrison, E. Psota, D. Dreher, L. C. P茅rez, J. L. Walker. Average min-sum decoding of LDPC codes. In Proceedings of Internat鈥檒 Symposium on Turbo Codes and Related Topics. September 2008.

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