## About

I am currently an Associate Professor in the Department of Mathematics at UH Mānoa. Before moving to UH Mānoa I was a Visiting Scholar at the Coordinated Science Lab and Mathematics Department at the University of Illinois at Urbana-Champaign working with Yuliy Baryshnikov. I also held postdoctoral positions at Duke University Mathematics and Computer Science departments, where I worked with John Harer and Herbert Edelsbrunner, and at Georgia Institute of Technology, where I was a part of the Theoretical Ecology and Integrative Biology group of Joshua Weitz. I received my Ph.D. in Mathematical Sciences from New Jersey Institute of Technology and Rutgers University under the supervision of Denis Blackmore.

This Fall I am teaching MATH 242 (Calculus II) and MATH 649K (Topic: Applied Math). For previously taught courses take a look at the Teaching section.

You can contact me by sending me an email at .

## Research

I am interested in developing topological and geometric tools, with a rigorous theoretical foundation, for problems in science and engineering, in particular those that may benefit from non-standard data analysis. However, since such problems require techniques from many disciplines, I often venture out of the familiar realm and sample a variety of scientific areas. I am also attracted to problems from the broad area of dynamical systems, especially if they involve topological and geometric aspects. For the past couple of years, I have also been involved in the work on modeling the spread of the pandemic.

### Publications

- M. Chyba, T. Klotz, Y. Mileyko, and C. Shanbrom, A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation, 2023, URL for item titled A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigationhttps://arxiv.org/abs/2109.01738. In review.
- R. Carney, M. Chyba, V. Y. Fan, P. Kunwar, T. Lee, I. Macadangdang, and Y. Mileyko, Modeling variants of the COVID-19 virus in Hawai`i and the responses to forecasting, AIMS Mathematics, 8 (2023), pp. 4487–4523.
- S. Allred, M. Chyba, J. M. Hyman, Y. Mileyko, and B. Piccoli, The COVID-19 Pandemic Evolution in Hawai`i and New Jersey: A Lesson on Infection Transmissibility and the Role of Human Behavior, N. Bellomo and M. A. J. Chaplain, eds., Springer International Publishing, 2022, pp. 109–140.
- P. Kunwar, O. Markovichenko, M. Chyba, Y. Mileyko, A. Koniges, and T. Lee, A study of computational and conceptual complexities of compartment and agent based models, Networks and Heterogeneous Media, 17 (2022), pp. 359–384.
- M. Chyba, P. Kunwar, Y. Mileyko, A. Tong, W. Lau, and A. Koniges, COVID-19 heterogeneity in islands chain environment, PLOS ONE, 17 (2022), e0263866.
- Y. Mileyko, Another look at recovering local homology from samples of stratified sets, Journal of Applied and Computational Topology, 5 (2021), pp. 55–97.
- Y. Mileyko, Topological and geometric techniques for analyzing association data in ecology and biology, vol. 11 of AIMS Applied Mathematics Book Series, 2020, pp. 144–164.
- M. Chyba, Y. Mileyko, O. Markovichenko, R. Carney, and A. Koniges, Epidemiological Model of the Spread of COVID-19 in Hawaii's Challenging Fight Against the Disease, in GLOBAL HEALTH 2020 : The Ninth International Conference on Global Health Challenges, 2020, pp. 32–38.
- V. Kala, K. Guo, E. Swantek, A. Tong, M. Chyba, Y. Mileyko, C. Gray, T. Lee, and A. Koniges, Pandemics in Hawai'i: 1918 Influenza and COVID-19, in GLOBAL HEALTH 2020 : The Ninth International Conference on Global Health Challenges, 2020, pp. 26–31.
- N. A. Hynson, K. L. Frank, R. A. Alegado, A. S. Amend, M. Arif, G. M. Bennett, A. J. Jani, M. C. I. Medeiros, Y. Mileyko, C. E. Nelson, N. H. Nguyen, O. D. Nigro, S. Prisic, S. Shin, D. Takagi, S. T. Wilson, and J. Y. Yew, Synergy among Microbiota and Their Hosts: Leveraging the Hawaiian Archipelago and Local Collaborative Networks To Address Pressing Questions in Microbiome Research, mSystems, 3 (2018).
- M. Arnold, Y. Baryshnikov and Y. Mileyko, Typical representatives of free homotopy classes in a punctured plane, Journal of Topology and Analysis, (2017), pp. 1–37.
- Y. Mileyko, G. Reis, R. N. Smith, and M. Chyba, Energy-Efficient Control Strategies for Updating an Augmented Terrain-Based Navigation Map for Autonomous Underwater Navigation, in Proceedings of the 1st IEEE Conference on Control Technology and Applications (CCTA), August 2017, pp. 223–228.
- M. Chyba, J.-M. Coron, P. Gabriel, Y. Mileyko, and H. Rezaei, Optimization of prion assemblies fragmentation, in Proceedings of the 55th IEEE Conference on Decision and Control (CDC), 2016, pp. 1631–1636.
- M. Chyba, J.-M. Coron, P. Gabriel, Y. Mileyko, and H. Rezaei, Identification of the Fragmentation Role in the Amyloid Assembling Processes and Application to their Optimization, 2015, ch. 47, pp. 348–355.
- K. Turner, Y. Mileyko, S. Mukherjee, and J. Harer, Fréchet Means for Distributions of Persistence Diagrams, Discrete & Computational Geometry, 52 (2014), pp. 44–70.
- C. N. Topp, A. S. Iyer-Pascuzzi, J. T. Anderson, C.-R. Lee, P. R. Zurek, O. Symonova, Y. Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. T. Moore, J. Harer, H. Edelsbrunner, T. Mitchell-Olds, J. S. Weitz, and P. N. Benfey, 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture, Proceedings of the National Academy of Sciences, 110 (2013), pp. E1695–E1704.
- T. Galkovskyi, Y. Mileyko, A. Bucksch, B. Moore, O. Symonova, C. A. Price, C. N. Topp, A. S. Iyer-Pascuzzi, P. R. Zurek, S. Fang, J. Harer, P. N. Benfey, and J. S. Weitz, GiA Roots: software for the high throughput analysis of plant root system architecture, BMC plant biology, 12 (2012), pp. 116.
- Y. Mileyko, H. Edelsbrunner, C. A. Price, and J. S. Weitz, Hierarchical Ordering of Reticular Networks, PLoS ONE, 7 (2012), e36715.
- C. A. Price, O. Symonova, Y. Mileyko, T. Hilley, and J. S. Weitz, Leaf extraction and analysis framework graphical user interface: segmenting and analyzing the structure of leaf veins and areoles, Plant Physiology, 155 (2011), pp. 236–245.
- Y. Mileyko, S. Mukherjee and J. Harer, Probability measures on the space of persistence diagrams, Inverse Problems, 27 (2011), pp. 124007.
- D. Cohen-Steiner, H. Edelsbrunner, J. Harer, and Y. Mileyko, Lipschitz functions have Lₚ-stable persistence, Foundations of Computational Mathematics, 10 (2010), pp. 127–139.
- A. S. Iyer-Pascuzzi, O. Symonova, Y. Mileyko, Y. Hao, H. Belcher, J. Harer, J. S. Weitz, and P. N. Benfey, Imaging and analysis platform for automatic phenotyping and trait ranking of plant root systems, Plant Physiology, 152 (2010), pp. 1148–1157.
- Y. Mileyko and J. S. Weitz, Bifurcation analysis of gene regulatory circuits subject to copy number variation, SIAM Journal on Applied Dynamical Systems, 9 (2010), pp. 799–826.
- M.-L. Dequéant, S. Ahnert, H. Edelsbrunner, T. M. A. Fink, E. F. Glynn, G. Hattem, A. Kudlicki, Y. Mileyko, J. Morton, A. R. Mushegian, L. Pachter, M. Rowicka, A. Shiu, B. Sturmfels, and O. Pourquié, Comparison of Pattern Detection Methods in Microarray Time Series of the Segmentation Clock, PLoS ONE, 3 (2008), e2856.
- Y. Mileyko, R. I. Joh and J. S. Weitz, Small-scale copy number variation and large-scale changes in gene expression, Proceedings of the National Academy of Sciences, 105 (2008), pp. 16659–16664.
- J. S. Weitz, Y. Mileyko, R. I. Joh, and E. O. Voit, Collective decision making in bacterial viruses, Biophysical journal, 95 (2008), pp. 2673–2680.
- D. Attali, H. Edelsbrunner and Y. Mileyko, Weak witnesses for Delaunay triangulations of submanifolds, in Proceedings of the 2007 ACM symposium on Solid and physical modeling, 2007, ACM, pp. 143–150.
- D. Attali, H. Edelsbrunner, J. Harer, and Y. Mileyko, Alpha-Beta Witness Complexes, in Algorithms and Data Structures, vol. 4619, Springer Berlin Heidelberg, 2007, pp. 386–397.
- D. Blackmore and Y. Mileyko, Computational differential topology, Applied general topology, 8 (2007), pp. 35–92.
- D. Blackmore, Y. Mileyko, M. C. Leu, W. C. Regli, and W. Sun, Computational topology and swept volumes, in Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing, vol. 67, AMS, 2005, pp. 53–78.

## Teaching

#### Fall 2023

- MATH242Calculus IIMATH649KTopics: Applied Math
#### Fall 2022

- MATH311Introduction to Linear Algebra
#### Spring 2022

- MATH302Introduction to Differential Equations IMATH100Survey of Mathematics
#### Fall 2021

- MATH622Topology II
#### Spring 2021

- MATH601Applied Dynamical Systems
#### Fall 2020

- MATH302Introduction to Differential Equations I
#### Spring 2020

- MATH252AAccelerated Calculus II
#### Fall 2019

- MATH302Introduction to Differential Equations IMATH251AAccelerated Calculus I
#### Spring 2019

- MATH601Applied Dynamical SystemsMATH216Applied Calculus II
#### Fall 2018

- MATH302Introduction to Differential Equations I
#### Spring 2018

- MATH407Numerical AnalysisMATH215Applied Calculus I
#### Fall 2017

- MATH302Introduction to Differential Equations I
#### Spring 2017

- MATH601Applied Dynamical SystemsMATH216Applied Calculus II
#### Fall 2016

- MATH100Survey of Mathematics
#### Spring 2016

- MATH321Introduction to Advanced MathamaticsMATH215Applied Calculus I
#### Fall 2015

- MATH490Mathematical Biology SeminarMATH449Topics in Undergraduate Mathematics
#### Spring 2015

- MATH432Principles of Analysis IIMATH304Mathematical Modeling I: Deterministic Models
#### Fall 2014

- MATH631Theory of Functions of Real Variable
#### Spring 2014

- MATH480Senior SeminarMATH302Introduction to Differential Equations I
#### Fall 2013

- MATH302Introduction to Differential Equations I