About
I'm an applied mathematician whose main research interests are in
probability and its application to science and engineering. I use
mathematics in an effort to understand fundamental aspects of complex
systems found, for example, in technological and biological systems.
February 2014 
Cellular Barcoding and Inferring Lineage Pathways
There are many instances where one would wish to know the familial
relationships of cells, to be able identify those that came from
the same parent. For example, the purpose of a bonemarrow transplant
is to place new hematopoietic stem cells into to the recipient so
that their blood system can be rebuilt. Does each stem cell contribute
equally to this rebuilding? Does chance play a role? Are some stem
cells specialized? These are all questions that can only be tackled
if one can identify cells from the same progenitor.
Cellular barcoding, which
Ton N. Schumacher's lab. has been at the forefront of developing,
is an experimental method in which small pieces of nonfunctional
DNA into otherwise identical cells. Each small piece, a barcode,
can then be found in the progeny of that cell and so those in a
common family can be identified. This technique has led to several
highprofile results in the past year in everything from immunology,
cancer and blood system development, including several from Ton's
lab.
In a data analytics contribution to the Cellular Barcoding technique,
my colleagues
Leïla Perié,
Philip D. Hodgkin,
Shalin H. Naik,
Ton N. Schumacher,
Rob J. de Boer,
and I have published a
paper
in
Cell Reports
that develops a mathematical framework for the analysis of data
that comes from cellular barcoding experiments. The framework is
designed to draw inferences about the compatibility of potential
lineage pathways with the data. As an exemplar, we study data
from the blood system taken from one of these highprofile results,
published in
Nature by S. H. Naik, L. Perié, E. Swart, C. Gerlach, N.
van Rooij, R. J. de Boer and Ton N. Schumacher. The analysis suggests
the classical model of hematopoiesis is not consistent with the
data and, inspired by in vitro deductions from the 80s, we propose
an alternate lineage pathway that is consistent.
January 2014 
Integrated Random Walks and Large Busy Periods
Ever since an elegant paper by
Venkat Anantharam in 1989, it's been known that the way a random
walk becomes large, or how a big queue builds up, is by a piecewise
linear path. The question of how a large integrated random walk,
or how a large volume of work done during a busy period of a queue,
occurs was first tackled by
A. A. Borovkov
,
O. J. Boxma
and
Z. Palmowski
in a paper in 2003.
In a
paper
to appear in Stochastic Systems,
Sean Meyn
and I establish that the most likely path to a large busy period
is concave in general and follows an upside version of the scaled
cumulant generating function. Moreover, the path starts and ends in
the same fashion as the most likely path to a long queue as identified
by
Ayalvadi J. Ganesh
and
Neil O'Connell in 2002.
For 10 billion simulated paths with i.i.d. Gaussian increments,
below is a graph of the random walk that hits the highest height
and the prediction from Ganesh and O'Connell conditioned on the
height. Also plotted is the largest integrated random walk and our
prediction conditioned on the area under the curve. The predicted
paths start and end with the same slope, but diverge in between.
November 2013 
Guesswork, Wiretap and Erasure Channels
Devices such as doorcard readers transmit passwords over wireless
channels. Unintended receivers, eavesdroppers, are typically
distant and observe the communication over a noisy channel that
distorts it. How hard is it for the eavesdropper to fill in the
erased gaps and how does it depend on the properties of the
noisy channel?
Complementing earlier work with a distinct interpretation
of guesswork and wiretap channels by
Neri Merhav
and
Erdal Arikan,
as well as
Manjesh Kumar Hanawal
and
Rajesh Sundaresan,
this is a subject that with our collaborators, Flávio du Pin Calmon
and Muriel Médard
at MIT,
Mark Christiansen and I had a
paper on at this year's
Asilomar Conference on Signals, Systems &
Computers. The main observation is that the average noise
on the channel is not the determining factor in how difficult the task
is for the eavesdropper, but instead another average of the noise,
a moment, that is determined again by Rényi entropy.
October 2013 
Limits of Statistical Inference
A
paper, which was
driven by our collaborators, Flávio du Pin Calmon at MIT
and Mayank Varia, at the Lincoln Lab.,
was presented by Muriel Médard at this year's
Allerton conference Communication, Control, and Computing.
The work establishes bounds on how much can be inferred about a function
of a random variable's value, if only a noisy observation of the variable
is available.
September 2013 
Constraint Satisfaction and Rate Control
IEEE/ACM Transactions on Networking
papers are like buses in that you wait for a long time for one and
then two come at once. The work on
Decentralized Constraint Satisfaction that is mentioned below
has appeared in the August issue of the journal. The final
paper
from my exstudent
Kaidi Huang's doctoral thesis also appears in that issue. The
work, performed in collaboration with my Hamilton Institute colleague
David Malone, addresses a practical problem in wireless local
area networks: rate control. When transmitting packets, WiFi cards
must select a physicallayer rate at which to transmit. In principle,
the faster the rate, the less robust the transmission is to noise.
For the poorly engineered rates of standard WiFi, this is not strictly true
as Kaidi, David and I demonstrated in a
paper
published in
IEEE Transactions on Wireless Communications
in 2011. In the present work, we proposed a rate adaption scheme
based on opportunity cost and Bayesian decision making that was,
demonstrably thanks to hard work of Kaidi and David, implementable
on standard hardware and outperforms the standard algorithms.
July 2013  Information Theory, Guesswork & Computational Security
The late Kai Lai Chung purportedly said that there's only one theorem in
Information Theory: the Asymptotic Equipartition Property.
At the 2013
IEEE International Symposium on Information Theory,
Mark Christiansen presented a preliminary version of
a surprising
result that we established
in collaboration with our friends from M.I.T.,
Flávio du Pin Calmon
and
Muriel Médard. Namely, despite the fact that everything
within a Typical Set has, by construction, approximately equal
probability, it is exponentially easier as a function of word length to
guess a word chosen from a Typical Set than a naive application of the AEP
would have you deduce. This has ramifications for physical layer security.
January 2013  Guesswork & Information Theory
How hard is it to guess someone's password? More importantly, how
do you measure how hard it is to guess someone's password? It's a
question that has recieved less attention than one would suspect.
The recently deceased information theorist James Massey published
a fascinating one page paper at ISIT on this question in 1994 and
it is the topic of a
paper
that my student,
Mark Christiansen,
and I have had published in
IEEE Transactions on Information Theory.
Building on beautiful work of others,
which began with
Erdal Arikan
and included a contribution from my Hamilton Institute colleague
David Malone, that identified Rényi entropy as a key
player in the quantification of guesswork, in the article we provide
a direct estimate on the likelihood that it takes a given number
of guesses to guess a randomly selected object.
January 2013  Networking & Medium Access Control
There are two fundamental paradigms for sharing a resource such as
wireless medium. One can empower a centralized controller who gathers
everyone's requirements and sets out a schedule of who gets access
to the resource when. This system is used, for example, for speakers
at every conference and in cell phone networks. The alternate system
is to not be prescriptive, but to listen before speaking and when
the medium becomes silent, randomly interject. This is used, for
example, in human conversation as well as the method on WiFi networks.
Both of these systems have advantages and disadvantages. If one
knows exactly what who needs what resources and can agree on a
central party to adjudicate, the former is most efficient. If one
is uncertain about the number of users and their requirements,
the latter is more robust to this uncertainty, but suffers from
collisions  people talking over one another and thus wasting resources.
In a paper that has been published in the journal
Wireless Networks, written with my exstudent
Minyu Fang, and colleagues at the Hamilton Institute
David Malone
and
Douglas J. Leith,
we investigate a system that has the best of both worlds:
a decentralized stochastic algorithm is used to obtain a collisionfree
schedule.
October 2012  Constraint Satisfaction Problems
Is it possible to find a global solution to a problem, with everyone
only having local information and being unable to see
the global picture? That's the topic of a paper that my colleagues,
the French mathematician
Charles Bordenave
and
Douglas J. Leith, my Scottish engineering colleague from the
Hamilton Institute, address in a
paper
that has
been accepted for publication in
IEEE/ACM Transactions on Networking.
Two undergraduates, TCD's John Roche and NUIM's Tony Poole,
created java
applets
that illustrate how the proposed approach, which provably works,
solves problems. They also illustrate that, in this setting, it is
easier to agree to disagree than it is to find a consensus.
September 2012  Immunology & Cell Biology
My Australian immunology collaborator
Philip Hodgkin
and I had a
paper
published in Trends in Cell Biology.
It expands
on the hypothesis we employed in our earlier 2012 paper, published in
Science, to explain cell fate
diversity. Artwork based on the paper, illustrated by WEHI's
Jie H. S. Zhou, was used for the edition's cover:
January 2012  Immunology & Cellular Biology
With colleagues from the
Walter and Eliza Hall Institute of Medical Research
led by
Philip D. Hodgkin,
I had a
paper
published in
Science. The piece analyses data from
an experiment that took my Australian colleagues, particularly Mark Dowling and
John Markham, four years to perfect.
It enabled us to directly observe the times at which an important
class of cells in the immune system, the antibody secreting B lymphocytes,
make decisions on when and how to combat a pathogen.
Despite the data looking immensely complex,
it is consistent with a remarkably simple, holistic hypothesis.
Publications
Journal papers by subject:
Applied Probability;
Biology;
Networks.
Applied Probability

Tail asymptotics for busy periods.
Ken R. Duffy and
Sean P. Meyn.
Stochastic Systems, to appear.

Guesswork, large deviations and Shannon entropy.
Mark M. Christiansen
and
Ken R. Duffy.
IEEE Transactions on Information Theory, 59 (2), 796802, 2013.

Sample path large deviations of Poisson shot noise with heavy tail
semiexponential distributions.
Ken R. Duffy and
Giovanni Luca Torrisi.
Journal of Applied Probability, 48 (3), 688698, 2011.

Estimating Loynes' exponent.
Ken R. Duffy and
Sean P. Meyn.
Queueing Systems: Theory & Applications, 68 (34), 285293, 2011.

Sample path large deviations for order statistics.
Ken R. Duffy,
Claudio Macci
and
Giovanni Luca Torrisi.
Journal of Applied Probability, 48 (1), 238257, 2011.

On the large deviations of a class of modulated additive
processes.
Ken R. Duffy,
Claudio Macci
and
Giovanni Luca Torrisi.
ESAIM: Probability and Statistics, 2011 (15), 83109, 2011.

Most likely paths to error when estimating the mean of a reflected
random walk.
Ken R. Duffy and
Sean P. Meyn.
Performance Evaluation, 67 (12), 12901303, 2010.

Complexity analysis of a decentralised graph colouring algorithm.
Ken R. Duffy,
Neil O'Connell
and
Artem Sapozhnikov.
Information Processing Letters, 107 (2), 6063, 2008.

The large deviation principle for the on/off Weibull sojourn process.
Ken R. Duffy and
Artem Sapozhnikov.
Journal of Applied Probability, 45 (1), 107117, 2008.

Logarithmic asymptotics for a singleserver processing distinguishable sources.
Ken R. Duffy and
David Malone.
Mathematical Methods of Operations Research, 68 (3), 509537, 2008.

Loss aversion, large deviation preferences and optimal portfolio weights
for some classes of return processes.
Ken Duffy, Olena Lobunets and
Yuri Suhov.
Physica A,
378 (2), 408422, 2007.

Ambiguities in estimates of critical exponents for longrange dependent processes.
Ken Duffy,
Christopher King
and
David Malone.
Physica A, 377 (1), 4352, 2007.

Some remarks on LD plots for heavytailed traffic.
David Malone,
Ken Duffy and
Christopher King.
ACM SIGCOMM Computer Communications Review,
37 (1), 4142, 2007.

Using estimated entropy in a queueing system with dynamic routing.
Ken Duffy, Eugene A. Pechersky,
Yuri M. Suhov
and Nikita D. Vvedenskaya.
Markov Processes and Related Fields,
13 (12), 5784, 2007.

How to estimate a cumulative process's ratefunction.
Ken Duffy and Anthony P. Metcalfe.
Journal of Applied Probability 42 (4), 10441052, 2005.

The large deviations of estimating ratefunctions.
Ken Duffy and Anthony P. Metcalfe.
Journal of Applied Probability 42 (1), 267274, 2005.

Some useful functions for functional large deviations.
Ken Duffy and Mark RodgersLee.
Stochastics and Stochastics Reports 76 (3), 267279, 2004.

Logarithmic asymptotics for unserved messages at a FIFO.
Ken Duffy and
Wayne G. Sullivan.
Markov Processes and Related Fields 10 (1), 175189, 2004.

On Knuth's generalization of Banach's matchbox problem.
Ken Duffy and
W. M. B. Dukes.
Mathematical Proceedings of the Royal Irish Academy 104A, 107118,
2004.

Logarithmic asymptotics for the supremum of a stochastic process.
Ken Duffy, John T. Lewis and
Wayne G. Sullivan.
Annals of Applied Probability 13:2, 430445, 2003.

Distributionfree confidence intervals for measurements of
effective bandwidth.
Laszlo Gyorfi, Andras Racz, Ken Duffy, John T. Lewis
and Fergal Toomey.
Journal of Applied Probability 37:1, 224235, 2000.
Biology

Determining lineage pathways from cellular barcoding experiments.
Leïla Perié,
Philip D. Hodgkin,
Shalin H. Naik,
Ton N. Schumacher,
Rob J. de Boer
and Ken R. Duffy.
Cell Reports, 6 (4), 617624, 2014.

Intracellular competition for fates in the immune system.
Ken R. Duffy
and
Philip D. Hodgkin.
Trends in Cell Biology, 22 (9), 457464, 2012.
Art based on this paper, illustrated by WEHI's Jie H. S. Zhou, was
used for the
journal's cover.

Activationinduced B cell fates are selected by intracellular stochastic competition.
Ken R. Duffy,
Cameron J. Wellard,
John F. Markham,
Jie H. S. Zhou, Ross Holmberg,
Edwin D. Hawkins, Jhagvaral Hasbold, Mark R. Dowling
and
Philip D. Hodgkin.
Science, 335 (6066), 338341, 2012.

A minimum of two distinct heritable factors are required to explain
correlation structures in proliferating lymphocytes.
John F. Markham,
Cameron J. Wellard, Edwin D. Hawkins, Ken R. Duffy
and
Philip D. Hodgkin.
Journal of the Royal Society Interface, 7 (48), 10491059, 2010.
The data used in this study is available for
download
from the
Hodgkin Lab
at
WEHI.

On the impact of correlation between collaterally consanguineous cells
on lymphocyte population dynamics.
Ken R. Duffy and
Vijay G. Subramanian.
Journal of Mathematical Biology, 59 (2), 255285, 2009.

Determining the expected variability of immune responses using the Cyton Model.
Vijay G. Subramanian,
Ken R. Duffy,
Marian L. Turner
and
Philip D. Hodgkin.
Journal of Mathematical Biology, 56 (6), 861892, 2008.
Networks

Decentralized constraint satisfaction.
Ken R. Duffy,
Charles Bordenave
and
Douglas J. Leith.
IEEE/ACM Transactions on Networking, 21 (4), 12981308, 2013.
For a realtime illustration of how the algorithm solves problems, see the
applets
for two problem
classes: decentralized graph colouring and decentralized consensus
identification.

HRCA: 802.11 collisionaware rate control.
K. D. Huang,
Ken R. Duffy and
David Malone.
IEEE/ACM Transactions on Networking, 21 (4), 10211034, 2013.

Decentralised learning MACs for collisionfree
access in WLANs.
Minyu Fang,
David Malone,
Ken R. Duffy
and
Douglas J. Leith.
Wireless Networks, 19 (1), 8398, 2013.

The 802.11g 11 Mb/s rate is more robust than 6 Mb/s.
K. D. Huang,
David Malone
and Ken R. Duffy.
IEEE Transactions on Wireless Communications, 10 (4), 10151020, 2011.

On the validity of IEEE 802.11 MAC modeling hypotheses.
K. D. Huang,
Ken R. Duffy and
David Malone.
IEEE/ACM Transactions on Networking, 18 (6), 19351948, 2010.

Mean field Markov models of wireless local area networks.
Ken R. Duffy.
Markov Processes and Related Fields, 16 (2), 295328, 2010.

Logconvexity of rate region in 802.11e WLANs.
Douglas J. Leith,
Vijay G. Subramanian
and Ken R. Duffy.
IEEE Communications Letters, 14 (1), 5759, 2010.

Existence and uniqueness of fair rate allocations
in lossy wireless networks.
Vijay G. Subramanian,
Ken R. Duffy and
Douglas J. Leith.
IEEE Transactions on Wireless Communications, 8 (7), 34013406, 2009.

On a buffering hypothesis in 802.11 analytic models.
K. D. Huang
and Ken R. Duffy
IEEE Communications Letters, 13 (5), 312314, 2009.

Modeling the impact of buffering on 802.11.
Ken Duffy and Ayalvadi J. Ganesh.
IEEE Communications Letters, 11 (2), 219221, 2007.

Modeling the 802.11 distributed coordination function in
nonsaturated heterogeneous conditions.
David Malone,
Ken Duffy and
Douglas J. Leith.
IEEE/ACM Transactions on Networking, 15 (1), 159172, 2007.

Modeling 802.11 Mesh Networks.
Ken Duffy,
Douglas J. Leith,
Tianji Li
and
David Malone.
IEEE Communications Letters 10 (8), 635637, 2006.

Modeling the 802.11 distributed coordination function in
nonsaturated conditions.
Ken Duffy,
David Malone
and
Douglas J. Leith.
IEEE Communications Letters, 9 (8), 715717, 2005.
Conference papers

Guessing a password over a wireless channel (on the effect of noise
nonuniformity).
Mark M. Christiansen,
Ken R. Duffy,
Flávio du Pin Calmon
and
Muriel Médard
Asilomar Conference on Signals, Systems & Computers
36 November, California, USA.

Bounds on inference.
Flávio du Pin Calmon,
Mayank Varia,
Muriel Médard,
Mark M. Christiansen,
Ken R. Duffy and
Stefano Tessaro,
51st Allerton Conference on Communication, Control, and Computing,
24 October, Illinois, USA.

Brute force searching, the typical set and Guesswork.
Mark M. Christiansen,
Ken R. Duffy,
Flávio du Pin Calmon
and
Muriel Médard,
IEEE International Symposium on Information Theory,
712 July, 2013, Istanbul, Turkey.

Lists that are smaller than their parts: A coding approach
to tunable secrecy.
Flávio Calmon,
Muriel Médard,
Linda Zeger,
Joao Barros,
Mark M. Christiansen
and
Ken R. Duffy,
50th Annual Allerton Conference on Communication, Control, and Computing,
15 October 2012, Illinois, USA.

Modeling conservative updates in multihash approximate count sketches.
Giuseppe Bianchi,
Ken R. Duffy,
Douglas J. Leith
and
Seva Shneer.
24th International Teletraffic Congress,
47th September 2012, Krakow, Poland.

Investigating the validity of IEEE 802.11 MAC modeling hypotheses.
K. D. Huang,
Ken R. Duffy,
David Malone
and
Douglas J. Leith.
IEEE PIMRC
1518th September 2008, Cannes, France.

Improving fairness in multihop mesh networks using 802.11e.
Ken Duffy,
Douglas J. Leith,
Tianji Li
and
David Malone.
Resource Allocation in Wireless Networks,
3rd April 2006, Boston, USA.

Modeling 802.11e for data traffic parameter design.
Peter Clifford, Ken Duffy, John Foy,
Douglas J. Leith
and
David Malone.
WiOPT 2006, 2837,
3rd7th April 2006, Boston, USA.

Modelling 802.11 wireless links.
Ken Duffy,
David Malone
and
Douglas J. Leith.
IEEE Conference on Decision and Control,
6952  6957, 12th15th December 2005, Seville, Spain.

On improving voice capacity in 802.11 infrastructure networks.
Peter Clifford, Ken Duffy,
Douglas J. Leith
and
David Malone.
IEEE WirelessCom, 214  219,
13th16th June 2005, Maui, Hawaii, USA.

Modeling the 802.11 distributed coordination function with heterogeneous
finite load.
David Malone,
Ken Duffy and
Douglas J. Leith.
Resource Allocation in Wireless Networks,
3rd April 2005, Trento, Italy.
Book chapters
Other articles
Research Funding
Recent Funding

"Quantitative analysis of immune cell fate: stochastic competition
and censorship",
20131017, Science Foundation Ireland Investigator Grant.

"Quantitative T Cell Immunology",
20131017, European Union Marie Curie FP7 ITN,
coPI with 16 other institutions, including industry, with
coordinating coPI
Grant Lythe (Leeds).

"IndoEuropean Research Network in Mathematics for Health and Disease",
20132017, European Union Marie Curie FP7 IRSES,
coPI with five other institution,
coordinating coPI
Carmen MolinaParis (Leeds),

"Single cell lineage tracing to understand hematopoietic development and differentiation",
20122015, Human Frontier Science Program Research Grant
coPI with
Andrew Cohen (Drexel),
Philip Hodgkin (WEHI),
Shalin Naik (WEHI)
and
Ton Schumacher (NKI).

"FLAVIA: FLexible Architecture for Virtualizable future wireless Internet Access"
20102013, European Union Framework 7 Strep Grant,
collaborator, ten partner academic and industry grant
led by
Giuseppe Bianchi (U. Rome), and locally by
David Malone.

"Mathematical modelling of lymphocyte proliferation and differentiation
during an adaptive immune response",
2009, Science Foundation Ireland Shortterm Travel Fellowship
to visit
Philip Hodgkin.

"Using 802.11 medium access control layer measurements to
understand and improve network performance",
20072010, Science Foundation Ireland Research Frontiers Programme,
PI, with
David Malone as coPI.
Students
Current graduatestudents
Past graduatestudents

Kaidi Huang, Ph.D. (NUI Maynooth), 2010.

Minyu Fang, M.Sc. (NUI Maynooth), 2010.
 Anthony Paul Metcalfe, M.Sc. (University of Dublin), 2004.
 Mark RodgersLee, M.Sc. (University of Dublin), 2003.
Interns
 Conor Leonard, Mathematics (University College Cork), 2013.
 Brendan Williamson, Mathematics (Dublin City University), 2012.
 John Roche, Mathematics (University of Dublin), 2011.
 Tony Poole, Science (NUI Maynooth), 2011.
 Joshua Tobin, Mathematics (University of Dublin), 2010.
Scholarly Activity
Affiliations
Societies
Editorial Boards
Technical Programme Committees

Stochastic, statistical and computational approaches to immunology, 2013,
(ICMS).

25th International Teletraffic Congress, 2013,
(ITC 25).

11th International Conference on Artificial Immune Systems, 2012,
(ICARIS 2012).

ACM CoNEXT, 2012,
(CoNEXT 2012).

24th International Teletraffic Congress, 2012,
(ITC 24).
 1st International Workshop on Network Science, 2011,
(Hamilton InstituteNS1).

IEEE International Conference on Computer Communications and Networks, 2011,
(ICCCN 2011).

23rd International Teletraffic Congress, 2011,
(ITC 23).
 3rd International Workshop on Systems Biology, 2010,
(Hamilton InstituteSB3).

22nd International Teletraffic Congress, 2010,
(ITC 22).
 3rd International Workshop on Performance Analysis and Enhancement
of Wireless Networks, 2008,
(PAEWN 08).

Valuetools workshop on interdisciplinary systems approach in performance
evaluation and design of computer and communication systems, 2007,
(InterPerf 2007).
 1st Hamilton Institute Workshop on Applied Probability, 2007,
(Hamilton InstituteAP1).
Oddities
I have had the unusual honour of having acknowledgments in at least
thirteen diverse places.

Christopher Fuchs thanks me for teaching him about magnalium in his
article "On the Quantumness of a Hilbert Space",
Quantum Information,
Statistics, Probability: Dedicated to Alexander S. Holevo on the Occasion
of His 60th Birthday,
edited by O. Hirota (Rinton Press, Princeton, NJ, 2004).

In their O'Reilly book IPv6 Network Administration, the authors,
Niall Murphy and
David Malone, say the following:
"Ken Duffy managed to resist the temptation to edit our manuscript,
and we can only admire his restraint."

My academic grandnephew,
Stephen Wills
thanks me for facilitating corrections to his paper
"On the generators of operator Markovian cocycles",
Markov Processes and Related Fields 13 (2007), 191211.

In his CUP Monograph Control Techniques for Complex Networks,
Sean Meyn thanks me for graphs generated by
code that I wrote while attending
a meeting organized by
Serguei Foss,
Takis Konstantopoulos
and
Stan Zachary.

In their article "Large deviation results on some estimators for
stationary Gaussian processes", Statistics 44 (2), 129144, 2010,
Claudio Macci and
Lea Petrella
thank me for illustrating to them
results from the literature on semiexponential distributions.

In their article "A singlecell pedigree analysis of alternative
stochastic lymphocyte fates", Proceedings of the National Academy
of Sciences
11, 106(32), 1345713462, 2009,
E. D. Hawkins, J. F. Markham, L. P. McGuinness and
P. D. Hodgkin
thank me, along with others,
for critical reading of the manuscript and helpful suggestions.

In the article "The effect of correlations on the population dynamics of
lymphocytes", Journal of Theoretical Biology,
264 (2), 443449
2010, by C. Wellard, J. Markham, E.D. Hawkins, P.D. Hodgkin, Cameron
thanks me for discussions.

In the article "On Thresholds for Robust GoodnessofFit Tests",
presented at the
IEEE Information Theory Workshop, 2010
by
Jayakrishnan Unnikrishnan,
Sean P. Meyn
and
Venugopal V. Veeravalli,
the authors thank me for for initial discussions that
motivated the problem studied in the paper.

In the article
"Large Deviations Of MaxWeight Scheduling Policies On Convex Rate Regions",
Mathematics of Operations Research
35(4), 881910, 2010, my colleague
Vijay G. Subramanian
is overly kind in thanking me for suggestions that helped expand its scope.

In the article "Many Sources Large Deviations of MaxWeight Scheduling",
IEEE Transactions on Information Theory 57(4),
21512168, 2011,
Vijay G. Subramanian
T. Javidi
and
S. Kittipiyakul
thank me,
Ruth Williams,
Milan Matejdes
and the reviewers for
"tremendously helpful suggestions". I don't know what Ruth, Milan
and the reviewers said, but in my case you're overly generous.

In the article "How neurons migrate: a dynamic insilico model of neuronal
migration in the developing cortex" by
Yaki Setty, ChihChun Chen, Maria Secrier,
Nikita Skoblov,
Dimitris Kalamatianos
and
Stephen Emmott
BMC Systems Biology 5:154, the authors
thank me for proofreading duties.

In "A model for studying the hemostatic consumption or destruction
of platelets" by
Mark R. Dowling, Emma C. Josefsson, Katya J. Henley,
Benjamin T. Kile
and
Philip Hodgkin, PLoS One 2013, the authors kindly
thank me for discussions.

In "Measuring pulsed interference in 802.11 links",
Brad W. Zarikoff and
Douglas J. Leith
in
IEEE/ACM Transactions on Networking thank myself
and
G. Bianchi, for comments.
