Book project in the making: I have been working on this project for several years

1. From Large Scale to Small Scale Geometric Topology of Networks--Wireline, Wireless, Quantum, and Power

Research Highlights: I am currently involved in the following research areas

1. Coarse geometry of complex networks

   This research started as an attempt to interpret an internet graph as a simplicial complex and determine whether it could be the triangulation of a manifold (see, e.g., the work of Shmuel Weinberger). However, the visually obvious Gromov hyperbolic property of the Internet Service Provider (ISP) and other graphs allowed us to simplity the problem as a coarse geometry one. This led to the following results:

   • For wired network, existence of a congestion core as a result of least cost path routing in a Gromov negatively curved network
   • For wireless network: strong dependency of the capacity region on the Ollivier-Ricci curvature

2. Quantum Information Science and Technology: My foci of interest are the following:

   • Quantum networks: This is a spinoff of my earlier research on congestion in classical networks.

     • A highlight of this research is that, quite contrary to classical networks that have a congestion core, quantum networks have an "anti-core," that is, a spin that has a very low probability of receiving or transmitting a "spin down" excitation. This anti-core needs to be eliminated by control in such devices as quantum routers. 
     • Quantum control for selective excitation-encoded information information in quantum routers is highly nonclassical, in the sense that the error defined as (1-fidelity) is concordant with the sensitivity of the error to spin coupling and bias fiedl focusing uncertainties. In other words, in contradiction to classical robust control, the best controllers in terms of minimal error are also the least sensitivitive to uncertainties.

   • Decoherence control: I would just let a quotation from Murray Gell-Mann, 1969 Nobel Laureate in Physics, speak for itself:

     "Finally, the construction of quantum machines is likely to need major advances in our uses of feedback techniques, which differ qualitatively from their classical counterparts because of information-disturbance theorems that preclude gaining information about a quantum system without introducing projection noise into its evolution." [Source: the Santa-Fe Institute]

   • Adiabatic Quantum Computations

     • Differential topology explanation of the gap phenomenon: This is a spinoff of my earlier reseach on the differential topology of the numerical range. The Toeplitz-Hausdorff theorem says that the numerical range is convex with, generically, a smooth boundary curve. Less well known is the fact that the numerical range has, in addition to the boundary curve, other crtical value curves that are highly singular. The connection with adiabatic computation is that the minimum energy level is related to the smooth boundary curve while the first and higher excitation levels are related to the singular critical value curves. We further conjecture that the swallow tail singularity is a differential-topolological manifestation of tunneling.
     • Benchmark AQC scheduling of wireless networks: A hotly debated isue is whther there is, if not a quantum speed-up, at least a "quantum advantage." We found a quantum advantage in the sense that the gap expansion technique to have the minimum energy solution satisfy the interference constraints works much better in quantum annealing than in classical simulated annealing.

3. Smart Grid: I have five focis of interest:

   • Connection between line overloading and curvature of the bus model, embodied in a novel electrical betweenness centrality concept
   • Multi-agent cooperative voltage stability control
   • Detection of false data injection
   • PMU driven load modeling for voltage stability
   • PMU data analysis to anticipate imminent blackout

4. Biomedical signal processing: I have two focis of interest:

   • Surface electromyographic (sEMG) data processing as a mean to investigate coherence on the neuro-skeletal system
   • Electrocardiographic (ECG) signal processing: The beat-to-beat interval is viewed as a Poincare return time, from which such dynamical properties as mixing can be assessed
   • Mathematical oncology

Publications: For my older research projects, click here

1. Coarse geometry of complex networks

   

   

   

   
   
   1. J. Sia, E. Jonckheere, and P. Bogdan, "Ollivier-Ricci curvature-based method to community detection in complex networks," Nature Scientific Reports, published online 05 July 2019. doi:10.1038/s41598-019-46079-x
   2. R. Banirazi, E. Jonckheere, and B. Krishnamachari, "Heat-Diffusion: Pareto optimal dynamic routing for time-varying wireless networks," IEEE/ACM Transactions on Networking, volume 28, No. 4, pp. 1520-1533, August 2020.
   3. P. Ghosh, He Ren, R. Banirazi, B. Krishnamachari and E. Jonckheere, "Empirical evaluation of the Heat-Diffusion collection protocol for wireless sensor networks," Computer Networks (COMNET), volume 127, pp. 217-232, 2017. Available at arXiv:1609.03289v1
   4. C. Wang, E. Jonckheere and R. Banirazi, "Interference constrained network performance control based on curvature control", American Control Conference 2016, Boston, USA, July 6-8, 2016, pp. 6036-6041.
   5. R. Banirazi, E. Jonckheere, and B. Krishnamachari, "Dirichlet's Principle on Multiclass Multihop Wireless Networks: Minimum Cost Routing Subject to Stability", ACM International Conference on Modeling, Analysis and Simulation of Wireless and Mobile Systems, Montreal, Canada, September 21-26, 2014, pp. 31-40.
   6. R. Banirazi, E. Jonckheere, and B. Krishnamachari, "Minimum delay in class of throughput-optimal control policies on wireless networks", American Control Conference (ACC 2014), Portland, OR, June 04-06, 2014, pp. 2668-2675
   7. C. Wang, E. Jonckheere and R. Banirazi, "Wireless network capacity versus Ollivier-Ricci curvature under Heat-Diffusion (HD) protocol", American Control Conference (ACC 2014), Portland, OR, June 04-06, 2014, pp. 3536-3541
   8. R. Banirazi, E. Jonckheere, and B. Krishnamachari, "Heat Diffusion: Optimal dynamic routing for multiclass multihop wireless networks", INFOCOM 2014, Toronto, Canada, April 27-May-02, 2014; pp. 325-333.
   9. R. Banirazi, E. Jonckheere, and B. Krishnamachari, "Heat diffusion algorithm for resource allocation and routing in multihop wireless networks", GLOBECOM, Anaheim, California, USA, December 3-7, 2012, pp. 5915-5920, Session WN16: Routing and Multicasting.
   10. E. Jonckheere, F. Ariaei, and P. Lohsoonthorn, "Scaled Gromov four-point condition for network graph curvature computation", Internet Mathematics, Vol. 7, No. 3, pp. 137-177, August 2011, DOI: 10.1080/15427951.2011.601233.
   11. Edmond Jonckheere, Mingji Lou, Francis Bonahon, and Yuliy Baryshnikov, "Euclidean versus hyperbolic congestion in idealized versus experimental networks", Internet Mathematics, Vol. 7, No.1, pp. 1-27, March 2011.
   12. M. Lou, E. Jonckheere, Y. Baryshnikov, F. Bonahon, and B. Krishnamachari, "Load Balancing by Network Curvature Control", International Journal of Computers, Communications and Control (IJCCC), Vol. 6, No.1, pp. 134-149, March 2011. ISSN 1841-9836.
   13. E. Jonckheere, P. Lohsoonthorn, and F. Bonahon, "Scaled Gromov hyperbolic graphs", Journal of Graph Theory, Vol. 57, pp. 157-180, 2008. DOI10.1002/jgt.20275.
   14. F. Ariaei, M. Lou, E. Jonckheere, B. Krishnamachari, and M. Zuniga, "Curvature of indoor sensor network: Clustering coefficient", EURASIP Journal on Wireless Communications and Networking, Vol. 2008, article ID 2131185, doi: 10.1155/2008/213185.
   15. E. A. Jonckheere, P. Lohsoonthorn and F. Ariaei, "Upper bound on scaled Gromov-hyperbolic delta", Applied Mathematics and Computations, Volume 192, pp. 191-204, 2007.

2. Quantum Information Sciences and Technology

   

   

   

   

   

   1. S. G. Schirmer, F. Langbein, C. A. Weidner, and E. Jonckheere, "Robust control performance for open quantum systems," IEEE Transactions on Automatic Control, May 2021, submitted.
   2. E. Jonckheere, S. Shermer, and F. Langbein, "Effect of quantum mechanical global phase factor on error versus sensitivity limitation in quantum routing," full version of CDC 2019 paper, 2019.
   3. E. Jonckheere, S. Schirmer, and F. langbein, "Efect of quantum mechanical global phase factor on error versus sensitivity limitation in quantum routing," 58th IEEE Conference on Control and Decision (CDC), Nice France, December 11-13, pp. 1339-1344.
   4. S. Schimrer, E. Jonckheere, S. O'Neil and F. Langbein, "Emergence of classicality under decoherence in near steady-state robust quantum transport," IEEE Transactions on Control Systems Technology, under revision, January 2020.
   5. S. Schirmer, E. Jonckheere, S. O'Neil, and F. C. Langbein, "Robustness of energy landscape control for spin networks under decoherence," 2018 IEEE Conference on Decision and Control, Miami Beach, Florida, Dec. 17-19, 2018, pp. 6608-6613.
   6. Chi Wang and Edmond Jonckheere, "Simulated versus reduced noise quantum annealing in maximum independent set solution to wireless network scheduling,"  Quantum Information Processing, 18:6, January 2019. https://doi.org/10.1007/s11128-018-2117-1.
   7. S. Schirmer, E. Jonckheere and F. Langbein, "Design of feedback control laws for spintronics networks," IEEE Transactions on Automatic Control, volume 63, number 8, pp. 2523-2536, August 2018. 
   8. E. Jonckheere, S. Schirmer and F. Langbein, "Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers," International Journal of Robust and Nonlinear Control, volume 28, number 6, pp. 2383-2403, April 2018. arXiv:1612.02784 [math.OC]
   9. E. Jonckheere, S. Schirmer and F. Langbein, "Structured singular value analysis for spintronics network information transfer control," IEEE Transactions on Automatic Control, volume 62, number 12, pp. 6568-6574, December 2017.
   10. P. Bogdan, E. Jonckheere and S. Schirmer, "Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond Thermalization and Many-Body-Localization," Chaos, Solitons & Fractals, volume 103, pp. 622-631, October 2017.  arXiv:1608.08192 [quant-ph]
   11. Chi Wang, Edmond Jonckheere and Todd Brun, "Differential geometric treewidth estimation in adiabatic quantum computation," Quantum Information Processing, July 19, 2016. doi:10.1007/s11128-016-1394-9
   12. C. Wang, H. Chen, and E. Jonckheere, "Quantum versus simulated annealing in wireless interference network optimization", Nature Scientific Reports, 6, Article number: 25797 (2016). Supplemental material.
   13. F. C. Langbein, S. Schirmer, E. Jonckheere, "Time optimal information transfer in spintronics networks", The 54th IEEE Conference on Decision and Control, Osaka, Japan, December 15-18, 2015, pp. 6454-6459
   14. D. D'Alessandro, E. Jonckheere, and R. Romano, "Control of open quantum systems in a Bosonic bath", The 54th IEEE Conference on Decision and Control, Osaka, Japan, Dec. 15-18, 2015, pp. 6460-6465.
   15. E. Jonckheere, A. Shabani and A. T. Rezakhani, "Indirect control invariance of Decoherence-Splitting Maniforld (DSM)", The 53rd IEEE Conference on Decision and Control, Los Angeles, CA, December 15-17, 2014, pp. 5794-5801
   16. D. D'Alessandro, E. Jonckheere, and R. Romano, "On the control of open quantum systems in the weak coupling limit", The 21st International Symposium on the Mathematical Theory of Networks and Systems, Groningen, the Netherlands, July 7-11, 2014. pp. 1677-1684
   17. E. Jonckheere, S. Schirmer, and F. Langbein, "Information transfer fidelity in spin networks and ring-based quantum routers", Quantum Information Processing (QINP) , Volume 14, Issue 12, pp. 4751-4785, December 2015. (arXiv:submit/1359959 [quant-ph] 24 Sep 2015.)
   18. E. Jonckheere, F. C. Langbein and S. Schirmer, "Quantum networks: Anti-core of spin chains", Quantum Information Processing Journal (QINP), volume 13, pp. 1607-1637, 2014
   19. C. Wang, E. Jonckheere, T. Brun, "Ollivier-Ricci curvature and fast approximation to tree-width in embeddability of QUBO problems", 6th International Symposium on Communications, Control, and Signal Processing (ISCCSP), Athens, Greece, May 21-23, 2014
   20. E. Jonckheere, A. T. Rezakhani, F. Ahmad, "Differential topology of adiabatically controlled quantum processes", Quantum Information Processing (QINP), Vol. 12, No. 3, pp. 1515-1538, 2013.
   21. E. Jonckheere, F. C. Langbein and S. G. Schirmer, "Curvature of quantum rings", Proceedings of the 5th International Symposium on Communications, Control and Signal Processing (ISCCSP 2012), Rome, Italy, May 2-4, 2012.
   22. E. Jonckheere, S. Schirmer and F. Langbein, "Geometry and curvature of spin network", 2011 IEEE Multi-Conference on Systems and Control, Denver, CO, September 2011. Available at arXiv:1102.3208v1 [quant-ph].

3. Smart Grid

   

   

   1. L. Shalalfeh, P. Bogdan, and E. Jonckheere, "Fractional dynamics of PMU data," IEEE Transactions on Smart Grid, vol. 12, no. 3, pp. 2578-2588, May 2021.
   2. Zhongtao Luo and Edmond A. Jonckheere, "Nonlinearity design with power-law tails for correlation detection in impulsive noise," IEEE Access, volume 8, pp. 40667-40679, February 2020.
   3. L. Shalalfeh, P. Bogdan, and E. Jonckheere, "PMU visibility graph," 2020 IEEE PES Innovative Smart Grid Technologies Conference, Washington, DC, February 17-20, 2020.
   4. E. Jonckheere and E. Grippo and R. Banirazi, ``Curvature, entropy, congestion management and the power grid," The Third IEEE Conference on Control Technology and Applications (CCTA), Hong Kong, China, August 19-21, 2019, pp. 535-542.
   5. E. Jonckheere, R. Banirazi, and E. Grippo, "Congestion management for cost-effective power grid load balancing using FACTS and energy storage devices allocated via grid curvature means," American Control Conference, Philadelphia, PA, July 10-12, 2019, pp. 3909-3915.
   6. E. Jonckheere and E. Grippo, ``Ollivier-Ricci curvature appraoch to cost-effective power grid congestion management," Chinese Control and Decision Conference (CCDC), Nanchang, China, June 3-5, 2019, pp. 2118-2123.
   7. L. Shalalfeh, P. Bogdan, and E. Jonckheere, "Fractional dynamics of PMU data,"IEEE Transactions on Smart Grid, under revision, August 2020.
   8. J. Sia, E. Jonckheere, L. Shalalfeh and P. Bogdan, "PMU Change Point Detection of imminent voltage collapse and stealthy attacks," IEEE CDC, Miami Beach, FL, Dec. 2018, pp. 6812-6817. 
   9. L. Shalalfeh, P. Bogdan and E. Jonckheere, "Modeling of PMU data using ARFIMA models," Clemson University Power System Conference, Paper Session T-M II: Phasor Measurement Units (PMUs), Charleston, SC, September 2018.
   10. L. Shalalfeh, P. Bogdan and E. Jonckheere, "Kendall's tau of frequency Hurst exponent as blackout proximity margin," IEEE International Conference on Smart Grid Communications, Sydney, Australia, November 06-09, 2016, 978-1-5090-4075-9/16
   11. L. Shalalfeh and E. Jonckheere, "Load aggregation effect in the power grid," IEEE Conference on Decision and Control (CDC), Las Vegas, NV, Dec. 2016, pp. 5793-5798. 
   12. L. Shalalfeh, P. Bogdan, and E. Jonckheere, "Evidence of long-range dependence in power grid", Power and Energy Society General Meeting (PESGM), Boston, USA, July 17-21, 2016, 6 pages, 978-1-5990-41688/16.
   13. L. Shalalfeh and E. Jonckheere, "The Existence of a Voltage Collapse Solution in the Static-Dynamic Gap", American Control Conference, Boston, MA, July, 2016, pp. 4126-4131.
   14. H. Sedghi and E. Jonckheere, "Statistical Structure Learning to Secure Data Integrity in Smart Grid", IEEE Transactions on Smart Grid, vol 6, no. 4, pp.1924-1933, 2015
   15. H. Sedghi and E. Jonckheere, "On the Conditional Mutual Information in the Gaussian–Markov Structured Grids", in Information and Control in Networks, Como, Giacomo and Bernhardsson, Bo and Rantzer, Anders, Editors, Lecture Notes in Control and Information Sciences, volume 450, Springer International Publishing, pp. 277-297, 2014.
   16. H. Sedghi and E. Jonckheere, "Statistical structure learning of Smart Grid for detection of False Data Injection", IEEE Power & Energy Society General Meeting, Vancouver, BC, Canada, July 21-25, 2013.
   17. R. Banirazi and E. Jonckheere, "Geometry of power flow in negatively curved power grids: Toward a smart transmission system", 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, December 15-17, 2010, pp. 6259-6264.

4. Biomedical signal processing

   1. R. Martin del Campo and E. Jonckheere, "Detection of Rhythmic Synchronized Double Neuronal Discharges", in the proceedings of the 40th International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC'18), Honolulu, Hawaii, USA. July 16-21, 2018.
   2. R. Martin del Campo Vera and E. Jonckheere, "Neuronal Rhythmicity and its Rate Variability", University of Southern California, Ming Hsieh Dept. of Electrical Engineering, Technical Report, March, 2018.
   3. R. Martin del Campo and E. Jonckheere, "Stationary versus Bifurcation regime for Standing Wave Central Pattern Generator", Biomedical Signal Processing and Control (BSPC), vol. 32, pp. 57-68, 2017.
   4. F. Ariaei, E. Jonckheere, R. Berger. "Mixing Dynamics of Heart Rate Variability", Cardiology Research and Clinical Developments, Nova Publications, 2015, Chap. 6, pp. 131-142
   5. R. Martin del Campo and E. Jonckheere, "Stationary regime for Standing Wave Central Pattern Generator", 3rd IEEE Global SIP 2015 -- Symposium on Signal Processing and Mathematical Modeling of Biological Processes with Applications to Cyber-Physical Systems for Precise Medicine. Orlando, Florida, USA. December 14-16, 2015, pp. 913-917
   6. R. Martin del Campo and E. Jonckheere, "Stationary versus Bifurcation regime for Standing Wave Central Pattern Generator", University of Southern California, Ming Hsieh Dept. of Electrical Engineering, Technical Report, June, 2015.
   7. E. Jonckheere, P. Lohsoonthorn, V. Mahajan, S. Musuvathy, and M. Stefanovic, "On a standing wave Central Pattern Generator and the coherence problem", Biomedical Signal Processing and Control, Vol. 5, No. 4, pp. 336-347, 2010.

5. Machine Learning

   1. E. Jonckheere, H. Krovi, and A. A. Rompokos, "Nonconvex optimization on data manifold by accelerated curvature transport," 59th IEEE Conference on Decision and Control, Jeju Island, Korea, Dec. 8-11, 2020, to appear. 
   2. H. Sedghi, A. Anandkumar, and E. Jonckheere, "Multi-step stochastic ADMM in higher dimensions: Applications to sparse optimization and noisy matrix decomposition", Advances in Neural Information Processing Systems, 27 (NIPS 2014), Convention and Exhibition Center, Montreal, Quebec, Canada, December 8-11, 2014, Thu87.

6. Gene Expression, Cell biology, Mathematical Oncology

   1. Mahboobeh Ghorbani, Edmond A.Jonckheere, and Paul Bogdan, “Gene expression is not random: Scaling, long-range cross-dependence, and fractal characteristics of gene regulatory networks," Frontiers in Physiology, volume 9, pages 1446, October 2018. https://www.frontiersin.org/article/10.3389/fphys.2018.01446
   2. P. Macklin, H. Frieboes, J. Sparks, A. Ghaffarizadeh, S. Friedman, E. Juarez, E. Jonckheere, and S. Mumenthaler, ``Progress towards computational 3-D multicellular systems biology," in Systems Biology of Tumor Microenvironment, Quantitative Modeling and Simulations, Advances in Experimental Medicine and Biology, volume 936, Springer, Katarzyna A. Rejniak, Editor, pp. 225-246, 2016.
   3. E. F. Juarez, R. Lau, S. H. Friedman, A. Ghaffarizadeh, E. Jonckheere, D. B. Agus, S. M. Munenthaler, and P. Macklin, ``Quantifying difference in cell line population dynamics using CellPD," BMC Systems Biology,  volume 10:92, 21 Sept. 2016. DOI: 10.1186/s12918-016-0337-5.