spring board of my latest research in topology of networks and
Adiabatic Quantum Computations
Research Highlights: I am currently involved in the following
Coarse geometry of
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
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.
highlight of this research is that, quite contrary to classical
networks that have a congestion core, quantum networks have an
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
Quantum control for selective excitation-encoded
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.
control: I would just let a
quotation from Murray Gell-Mann, 1969 Nobel Laureate in Physics, speak
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
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.
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.
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.
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.
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].
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.
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.
NSF United States-United Kingdom Advanced Studies Institute (ASI)
in Robust Control of Quantum Networks
The program was held June 23-July 07, 2019, in Wales,
Kingdom. The lecturing material and research slides are available upon
request. Contact E. Jonckheere at email@example.com to get URL of the
repository and the guest password.
My main extra curricular activity is teaching, not to engineering
students, but to student pilots. I am a FAA Certified Flight Instructor
(CFI), instructing both primary (for private pilot candidates),
advanced (for commercial pilot and Certified Flight
candidates). I have flown all kind of
aircraft, gliders, motor gliders, single-engine airplanes,
multi-engine airplanes, and a pure jet power airplane (Cessana
Citation). My instruction, however, is limited to
(SEL) airplanes. Furthermore, I am 1/4 owner of a Piper Dakota. In
academia, we like to "dirty our hands" and the situation is no
different in the aeronautical world: Here I
am--literally speaking--dirtying my hands holding the propeller of the
Piper Dakota during the cylinder compression check.