# Richard B Sowers

**Professor**

Biomedical and Translational Sciences

Biomedical and Translational Sciences

(217) 333-6246

216C Transportation Building

## For More Information

## Education

- B.S. in Electrical Engineering, Drexel University, 1986.
- M.S. Electrical Engineering, University of Maryland at College Park, 1988.
- Ph.D. Applied Mathematics, University of Maryland at College Park, 1991.

## Academic Positions

- Professor, University of Illinois at Urbana-Champaign, Department of Industrial and Enterprise Systems Engineering, 2012-present.
- Professor, University of Illinois at Urbana-Champaign, Department of Statistics (courtesy), 2011-present.
- Professor, University of Illinois at Urbana-Champaign, Department of Mathematics, 2006-present.
- Associate Professor, University of Illinois at Urbana- Champaign, Department of Mathematics, 2001-2006.
- Assistant Professor, University of Illinois at Urbana- Champaign, Department of Mathematics, 1996-2001.
- Visiting Assistant Professor, Northwestern University, Department of Mathematics, 1994-1995 (with NSF Postdoctoral Fellowship).
- Visitor, University of Maryland, Department of Mathematics, 1993-1994 (with NSF Postdoctoral Fellowship).
- Research Assistant Professor (Postdoctoral), University of Southern California, Center for Applied Mathematical Sciences, 1991-1993.

## Other Professional Employment

- Research Principal, Office of Financial Research, 2012-present.

## Research Interests

- Financial Networks
- Dynamics
- Stochastics

## Selected Articles in Journals

- Richard B. Sowers and Armand M. Makowski, Discrete-time filtering for linear systems with non-Gaussian initial conditions: asymptotic behavior of the difference between the MMSE and LMSE estimates,
*IEEE Transactions on Automatic Control*, AC-37, pp. 114-120, (1992). - Richard Sowers, Large deviations for the invariant measure of a reaction-diffusion equation with non-Gaussian perturbations,
*Probability Theory and Related Fields*, 92, pp. 393-421, (1992). - Richard B. Sowers, Large deviations for a reaction-diffusion equation with non-Gaussian perturbations,
*Annals of Probability*, 20, pp. 504-537, (1992). - Carl Mueller and Richard Sowers, Blowup for the heat equation with a noise term,
*Probability Theory and Related Fields*, 97, pp. 287-320, (1993). - Richard B. Sowers, Recent results on the short-time geometry of random heat kernels,
*Mathematical Research Letters*, 1, pp. 663-675, (1994). - R. B. Sowers, Multidimensional reaction-diffusion equations with white noise boundary perturbations,
*Annals of Probability*, 22, pp. 2071--2121 (1994) of Probability, 22, pp. 2071-2121, (1994). - Richard B. Sowers, Intermittency-type estimates for some nondegenerate PDE's,
*Annals of Probability,*23, pp. 1853-1874, (1995). - Carl Mueller and Richard B. Sowers, Random travelling waves for the KPP equation with noise,
*Journal of Functional Analysis,*128, pp. 439-498, (1995). - Richard B. Sowers, Short-Time Geometry of Random Heat Kernels,
*Memoirs of the American Mathematical Society,*132, 130pp., (1998). - Richard B. Sowers, Hydrodynamical limits and geometric measure theory: mean
curvature limits from a threshold voter model,
*Journal of Functional Analysis,*169, pp. 421-455, (1999). - Richard B. Sowers and Jang-Mei Wu, Thermal capacity estimates on the Allen-Cahn equation,
*Transactions of the American Mathematical Society,*6, pp. 2553-2567, (1999). - Mark I. Freidlin and Richard B. Sowers, A comparison of homogenization and large deviations,
with applications to wavefront propagation,
*Stochastic Process and Their Applications*82, pp. 23-52, (1999). - N. Sri Namachchivaya and Richard B. Sowers, Unified approach for noisy nonlinear Mathieu-type systems,
*Stochastics and Dynamics*, 1, pp. 405-450, (2001). - Richard B. Sowers, Hypoelliptic random heat kernels: a case study,
*Proceedings of the American Mathematical Society*, 129, pp. 2451-2460, (2001). - N. Sri Namachchivaya and Richard B. Sowers, Rigorous stochastic averaging at a center with additive noise,
*Meccanica,*37, pp. 85-114, (2002). - Richard B. Sowers, On the tangent flow of a stochastic differential
equation with fast drift,
*Transactions of the American Mathematical Society,*353, pp. 1321-1334, (2001). - Richard B. Sowers, Stochastic Averaging Near Long Heteroclinic Orbits,
*Stochastics and Dynamics,*7, pp. 187-228, (2007). - N. Sri Namachchivaya, Richard B. Sowers, and Lalit Vedula, Nonstandard reduction of noisy Duffing-van der Pol equation,
*Dynamical Systems: an International Journal,*16, pp. 223-245, (2001). - Richard B. Sowers, Stochastic averaging with a flattened Hamiltonian; a Markov process on a stratified space (a whiskered sphere),
*Transactions of the American Mathematical Society,*354, pp. 853-900, (2002). - Steven N. Evans and Richard B. Sowers, Pinching and twisting Markov processes,
*Annals of Probability,*31, pp. 486-527, (2003). - Richard B. Sowers, Stochastic averaging near a homoclinic orbit with multiplicative noise,
*Stochastics and Dynamics,*, pp. 299-391, (2003). - Richard B. Sowers, A Boundary Layer Theory for Diffusively Perturbed Transport around a Heteroclinic Cycle,
*Communications on Pure and Applied Mathematics*, 58, pp. 30-84, (2005). - Richard B. Sowers, Random Perturbations of Two-Dimensional Pseudoperiodic Flows,
*Illinois Journal of Mathematics,*50, pp. 853-959, (2006). - Jun H. Park, N. Sri Namachchivaya, and Richard B. Sowers, A Problem in Stochastic Averaging of Nonlinear Filtering,
*Stochastics and Dynamics,*8, pp. 543-560, (2008). - Richard B. Sowers, Random Perturbations of Canards,
*Journal of Theoretical Probability,*21, pp. 824-889, (2008). - Richard B. Sowers, Averaging of Stochastic Flows: Twist maps and Escape from Resonance,
*Stochastic Processes and Their Applications,*119, pp. 349-3582, (2009). - R. Sowers, Exact Pricing Asymptotics of Investment-Grade Tranches of Synthetic CDO's: A Large Homogeneous Pool,
*International Journal of Theoretical and Applied Finance,*3, pp. 367-403, (2010). - Kunwoo Kim, Carl Mueller, and Richard Sowers, A stochastic moving boundary value problem,
*Illinois Journal of Mathematics,*54, pp. 927-962, (2010). - J. H. Park, R. B. Sowers, and N. Sri Namachchivaya, Dimensional
Reduction in Nonlinear Filtering,
*Nonlinearity,*23, pp. 305-324, (2010). - Konstantinos Spiliopoulos and Richard Sowers, Recovery rates in investment-grade pools of credit assets: A large deviations analysis,
*Stochastic Processes and their Applications,*121, pp. 2861-2898, (2011). - Jun H. Park, Boris Rozovskii, and Richard B. Sowers, Efficient nonlinear filtering of a singularly perturbed stochastic hybrid system,
*London Mathematical Society Journal of Computation and Mathematics,*14, pp. 254-270, (2011). - Kay Giesecke, Konstantinos Spiliopoulos, Richard B. Sowers, and Justin Sirignano, Large Portfolio Asymptotics for Loss From Default,
*Mathematical Finance*, (2012). - Andrei Kirilenko, Richard B. Sowers, and Xiangqian Meng, Multiscale Model of High-Frequency Trading,
*Algorithmic Finance*, 2, pp. 59-89, (2013). - Kunwoo Kim and Richard Sowers, Numerical Analysis of the Stochastic Moving Boundary Problem,
*Stochastic Analysis and Applications*, Volume 30, Issue 6, pp. 963-996, (2012). - Kunwoo Kim, Zhi Zheng, and Richard B. Sowers, A Stochastic Stefan Problem,
*Journal of Theoretical Probability,*25, pp. 1040-1080, (2012). - Kay Giesecke, Konstantinos Spiliopoulos, and Richard B. Sowers, Default Clustering in Large Portfolios: Typical Events,
*Annals of Applied Probability*, pp. 348-385, (2013). - Rui Song, Richard B. Sowers, and Jonathan Jones, The Topology of Central Counterparty Clearing Networks and Network Stability, Stochastic Models 30 16--47 (2014).
- Nitin Srivastava,
Peter Maneykowski, and Richard B. Sowers, Algorithmic geolocation of harvest in hand-picked agriculture,
*Natural Resource Modelling*, (2018). - Rava, Uma, Shanbhag, Uday, and Sowers, Richard B. On the inadequacy of VaR-based risk management: VaR, CVaR, and nonlinear interactions, Optimization Methods and Software 29, 877--897 (2014).
- Xiao Li, Michael D. Lipkin, and Richard B. Sowers, Dynamics of Bankrupt Stocks, SIAM J. Financial Mathematics 5, 323--257 (2014).
- Wang, R., Work, D.B., and Sowers, R., Multiple Model Particle Filter for Traffic Estimation and Incident Detection, IEEE Transactions on Intelligent Transportation Systems, 1-10 (2016).
- Jingnan Chen and Mark Flood and Richard B. Sowers. Measuring the Unmeasurable: An application of uncertainty quantification to Treasury bond portfolios,
*Quantitative Finance*, (2017) - Devasia Manuel and Richard B. Sowers Optimal Transport to Cold Chain
in Hand-Picked Agriculture,
*Natural Resource Modelling*, 30, (2017). - Daniel R. Carmody and Richard B. Sowers, Tradeoffs between Safety and Time: A Scale-Free Routing View,
*Transportation Research: Part C*, (2019) - Daniel Carmody and R Sowers, Topological Analysis of Traffic Pace via Persistent Homology,
*Journal of Physics: Complexity*, (2020) - Henry Schenck, R. Sowers, and Rui Song. Trading networks and Hodge theory,
*Journal of Physics Communications*, (2021) - Rachneet Kaur, Clara Schaye, Kevin Thompson, Daniel C. Yee, Rachel Zilz, R. S. Sreenivas, and Richard B. Sowers, Machine learning and price-based load scheduling for an optimal IoT control in the smart and frugal home,
*Energy and AI*, (2020) - Rachneet Kaur, Zizhang Chen; Robert Motl; Manuel Enrique Hernandez; Richard Sowers, Predicting Multiple Sclerosis from Gait Dynamics Using an Instrumented Treadmill – A Machine Learning Approach,
*IEEE Transactions on Biomedical Engineering*(2021) - Vaibhav Karve, Derrek Yager, Marzieh Abolhelm, Daniel B. Work, Richard B. Sowers, Seasonal Disorder in Urban Traffic Patterns: a Low Rank Analysis,
*Journal of Big Data Analytics in Transportation*(2021) - Hossein Nick Zinat Matin and Richard B. Sowers, Near-collision dynamics in a noisy car-following model,
*SIAM Journal on Applied Mathematics*(2022) - Rachneet Kaur, Robert Motl, Richard Sowers, and Manuel E. Hernandez, A Vision-Based Framework for Predicting Multiple Sclerosis and Parkinson’s Disease Gait Dysfunctions---A Deep Learning Approach,
*IEEE Journal of Biomedical and Health Informatics*(2022) - Rachneet Kaur, Joshua Levy, Robert W. Motl, Richard Sowers, Manuel E. Hernandez, Deep Learning for Multiple Sclerosis Differentiation Using Multi-Stride Dynamics in Gait,
*IEEE Transactions on Biomedical Engineering*(2023) - M. Singh, P. Prakash, R. Kaur, R. Sowers, J.R. Brasic, M. Hernandez, A Deep Learning Approach for Automatic and Objective Grading of the Motor Impairment Severity in Parkinson’s Disease for Use in Tele-Assessments,
*Sensors*(2023)

## Articles in Conference Proceedings

- Hossein N.Z. Matin and Richard B. Sowers, Approximating the Transition Probability Function Corresponding to the Solution of Stochastic Optimal Velocity Dynamical Model, in
*2021 American Control Conference*, pp. 3326--3332. - Siwen Wang, Ryu Okubo, Gekai Liao, Conrad Ku, Richard Sowers, and Manuel E. Hernandez, Designing a closed loop system to achieve real-time evaluation and manipulation of state anxiety while walking in virtual reality, in
*2021 10th International IEEE/EMBS Conference On Neural Engineering* - Yang Hu, Alka Bishnoi, Rachneet Kaur, Richard Sowers and Manuel E. Hernandez, Exploration of Machine Learning to Identify Community Dwelling Older Adults with Balance Dysfunction Using Short Duration Accelerometer Data", in
*2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC)* - Hossein Nick Zinat Matin and Richard B. Sowers, Nonlinear Optimal Velocity Car Following Dynamics (II): Rate of Convergence In the Presence of Fast Perturbation,
*2020 American Control Conference*, Denver, 2020. - Hossein Nick Zinat Matin and Richard B. Sowers, Nonlinear Optimal Velocity Car Following Dynamics (I): Approximation in Presence of Deterministic and Stochastic Perturbations,
*2020 American Control Conference*, Denver, 2020. - Rachneet Kaur, Maxim Korolkov, Manuel E. Hernandez, and Richard Sowers}, Automatic Identification of Brain Independent Components in Electroencephalography Data Collected while Standing in a Virtually Immersive Environment - A Deep Learning-Based Approach, in
*2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC)* - Rachneet Kaur, Rongyi Sun, Liran Ziegelman, Richard Sowers, and Manuel E. Hernandez, Using Virtual Reality to Examine the Neural and Physiological Anxiety-Related Responses to Balance-Demanding Target-Reaching Leaning Tasks, in
*2019 IEEE-RAS 19th International Conference on Humanoid Robots (Humanoids)* - Rachneet Kaur, Sanjana Menon, Xiaomiao Zhang, Richard Sowers, Manuel Hernandez, Exploring Characteristic Features in Gait Patterns for Predicting Multiple Sclerosis,
*2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)*. - Rongyi Sun, Rachneet Kaur, Liran Ziegelman, Shuo Yang, Richard Sowers, and Manuel E. Hernandez, Using Virtual Reality to Examine the Correlation between Balance Function and Anxiety in Stance, in
*2019 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)* - Rachneet Kaur, Rongyi Sun, Liran Ziegelman, Richard Sowers, Manuel Hernandez, Using Virtual Reality to Examine the Neural and Physiological Responses to Height and Perturbations in Quiet Standing,
*2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)* - Yu Wu, Gabriel Shindnes, Vaibhav Karve, Derrek Yager, Daniel B. Work, Arnab Chakraborty, and Richard B. Sowers, Congestion Barcodes: Exploring the Topology of Urban Congestion Using Persistent Homology,
*2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC)* - Rachneet Kaur, Xun Lin, Alexander Layton, Manuel Hernandez, Richard Sowers}, Virtual Reality, Visual Cliffs, and Movement Disorders,
*2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)* - Vikram Ramavarapu, Richard Sowers and Ramavarapu Sreenivas, A Smart Power Outlet for Electric Devices That Can Benefit from Real-Time
Pricing,
*2017 International Conference on Control, Electronics, Renewable Energy and Communications (ICCREC)*(2017)

## Recent Courses Taught

- ASRM 406 - Lin Algebra & Financial Apps
- ASRM 499 (ASRM 595) - Deep Learning for Fin & Ins
- ASRM 510 - Financial Mathematics
- IE 434 - Deep Learning: Math/Appl.
- IE 498 DL1 (IE 498 DL2) - Deep Learning Math & Appl
- IE 525 - Stochastic Calculus
- IE 525 - Stochastics & Numerics in Fin
- IE 526 - Stochastic Calculus in Finance
- IE 534 (CS 547) - Deep Learning
- MATH 492 - Alexa
- MATH 492 - Conflict-Related Displacement
- MATH 492 - Undergraduate Research in Math
- MATH 492 - Virtual Reality, Visual Cliffs
- MATH 597 - Reading Course
- SE 261 - Business Side of Engineering
- TE 401 D - Develop Breakthrough Projects