<B>DKA</B>

David K. Arrowsmith (DKA), Professor
School of Mathematical Sciences
Queen Mary , University of London
Mile End Road, London E1 4NS, UK
E: d.k.arrowsmith@qmul.ac.uk

SENIOR QMUL/UL ROLES

Head of Group:Teaching & Scholarship Staff (2020-23).
Head of School of Physics and Astronomy, (2016-2019).
Deputy Head of the School of Mathematical Sciences, (2013-2015).
Head of the School of Mathematical Sciences, (2003-2011).
Director of Postgraduate Studies, School of Mathematical Sciences, (2001-03).
Director of Applied Mathematics, Mathematics Research Centre, (2000-2003).
Secretary to the University of London Mathematics Panel (1998-2001).
Director of the Mathematics Research Centre, (1996-99)
Director of Undergraduate Studies, School of Mathematical Sciences, (1993-96)
Secretary to the University of London Mathematics Panel (1998-2001).

ACADEMIC LEADERSHIP

Chair of the NE London Maths Hub (Elmhurst School), 2017-2021.
Member of an EPSRC Programme Grant Selection Panel, 2018.
Chair of an EPSRC CDT Prioritisation Panel, October 2017.
Chair of an EPSRC Mathematics Prioritisation Panel, September, 2015.
Education Secretary of the Institute of Mathematics and its Applications(IMA), January 2015-17.
Member of the OFQUAL Mathematics Subject Benchmark Committee, 2014.
Member of the Executive Committee of the Joint Mathematical Council, 2014-15.
Member of the EPSRC CDT Prioritisation Panels, March, 2013.
Chair of the EPSRC Mathematics Prioritisation Panel, December, 2012
Member of the EPSRC Strategic Advisory Team 2010-2014.
Chair of the Heads of the Departments of Mathematical Sciences(HoDoMS) 2010-2014.
HoDoMS representative on the LMS Research Committee 2011-2014.
Member of the IMA Higher Education Service Area ((HEdSA), 2011-2014. a Committee of the Institute of Mathematics and its Applications that works to promote mathematics education at tertiary level.
Fellow of the Institute of Mathematics and its Applications 2011- .

EU RESEARCH FUNDING (PI)

EC PATHFINDER PROGRAMME MANMADE (2007-2009): Diagnosing vulnerability, emergent phenomena, and volatility in man-made networks.
PI and COORDINATOR - DKA. Collaborating institutions: Collegium Budapest; Macedonian Academy of Sciences and Arts, Skopje; Queen Mary, University of London, Universita Carlo Cattaneo, Castellanza; Joint Research Centre, Ispra.
MANMADE website.

UK RESEARCH FUNDING (PI)

EPSRC PDRA (2010-2013): RESILIENCE, ADAPTABILITY and VULNERABILITY of COMPLEX ENERGY NETWORKS RAVEN. PI - DKA PR - R. Carvalho. Co-Is: W. Just (Mathematical Sciences,QMUL), R. Mondragon (Electronic Engineering, QMUL) . EPSRC (2011-2012): Data support for RAVEN project from impactQM . PI - DKA ,DKA PR - R. Carvalho. Co-Is: W. Just (Mathematical Sciences,QMUL), R. Mondragon (Electronic Engineering, QMUL) .
EPSRC PDRA (2002-05): SOURCES OF LONG RANGE DEPENDENCE IN INTERNET TRAFFIC and THEIR RELATIVE IMPORTANCE IN NETWORKS PI -DKA, Co-I - M. Dodson (York), J.M. Pitts (Electrical Engineering, QMUL).
BRITISH TELECOMS CASE SUPPORT (joint with Elec.Eng.QMUL). Funding for 2 research students Web Caching and Dynamical Modelling of Packet Traffic
MINISTRY of DEFENCE(1990-19993): PhD funding for project Control of Cellular Automata .
EPSRC PDRA(1994-97): CONTROL OF ENTRAINMENT, PI- DKA PDRA ( Dr A. Lansbury (UCL,Brunel), Dr R. Mondragon(QMUL).
Coordinator for an INTAS, proposal (1999) The Bogdanov map and weakly dissipative KAM Theory involving the University of Grenada (JHC Cartwright), Moscow State University (RI Bogdanov), QMUL(DKA) and UMIST (PA Glendinning).
EU JOINT RESEARCH CENTRE(Ispra) ITALY - funded PhD Research Student. ELSA Structural Mechanics Laboratory, Ispra, Italy.
Visit to EC Joint Research Centre, Ispra, Italy (October 1st - Dec 16th 2011).

UK RESEARCH and EDUCATION FUNDING (Co-I)

EPSRC PDRA(Eng) (1998-2001) CHAOTIC CONTROL FOR FAST RESOURCE MANAGEMENT, PI - J.M. Pitts(Elec. Eng.,QMUL), Co-I: DKA.
HEFCE (2006-2009) More Maths Grads - University Hubs - Coventry, Leeds, QMUL PI - Michael Grove (B'ham). Co-I (QMUL)- DKA DKA Final Report here.

AUTHORED BOOKS on DYNAMICAL SYSTEMS

Information on Introduction to Dynamical Systems (CUP), DKA and C.M. Place 1990. (Also translated into German).
Dynamische Systeme: Mathematische Grundlagen und Anwendungen, DKA and C.M. Place, Spektrum Academischer VERlag Gmb H (Heidelberg), 1994.
Information on Dynamical Systems: Differential Equations, Maps and Chaotic Behaviour (Chapman & Hall), DKA and C.M. Place, 1992.
Information on Ordinary Differential Equations: A qualitative approach with applications (Chapman & Hall), DKA and C.M. Place, 1982. (Also translated into Russian).
A collage of books co-authored with Colin Place.

PUBLICATIONS

a listing of publications and preprints can be found within the School lists here

BROADER RESEARCH INTERESTS

Dynamical systems
- Normal Forms
- Bifurcation theory
Networks
- Infrastructure networks
- interconnectedness
- structure and resilience
Grid dynamics
- source sink flows
- introduction of renewable sources
- pricing and shaping of demand
Control of dynamical systems
- parametric and external forcing
- use of dynamical iteration to model packet transport in computer networks
- modelling and control of double impact oscillators
Chromatic polynomials and partition functions
- Walker problems on lattices
- Chromatic functions and associated structures on directed graphs

MOST RECENT PUBLICATIONS

Applied Dynamical Systems (ch. 6) LTCC Advanced Mathematics SeriesDynamical and Complex Systems, pp. 189-219 (2017)
Congestion dependencies in the European gas pipeline network during crises, IEEE Proc COMPENG2014, ( Complexity in Engineering) 978-1-4799-4079-0/14, L. Buzna, R. Carvalho, F. Bono, M. Masera, DKA.
Resilience of natural gas networks during conflicts, crises and disruptions, PLOS | one DOI:10.1371/journal.pone.0090265, (2014) R. Carvalho, L. Buzna, F. Bono, M. Masera, DKA, D. Helbing.
Review of Resilience of natural gas networks during conflicts, crises and disruptions, Journal of Energy Security, 2014
Acute Traumatic Coagulopathy has multiple important patterns of coagulation system derangement. Raza I, Khan S, Rourke C, Davenport R, Platton S, Carvalho R, Arrowsmith D, Brohi K. SHOCK . 40 34 - 34 (2013).
Fair sharing of resources in a supply network with constraints, Phys. Rev. E 85, 046101 (2012) R. Carvalho, L. Buzna, W. Just, D Helbing, DKA.
The emerging energy Web, M. Ajmone-Marsan, DKA, W. Breymann, O. Fritz, M. Masera, A. Mengolini, and A. Carbone, Eur. Phys. J. Special Topics 214, 547 - 569 (2012).
Generating functions and duality for non-crossing walks on a plane graph, DKA, F.M. Bhatti, J.W. Essam, J. Phys. A: Math. Theor. 45 (2012) 494008 (19pp)
Bose and Fermi Walk Configurations on Planar Graphs, DKA, F.M. Bhatti, J.W. Essam, J. Phys A: Math. Theor. 45 (2012). . Currently available here
An overview of research programmes and prospective technology in the development of more secure supply chains: The Case of Shipping Containers Report EUR 25298 (EN 2012) JRC Scientific and Policy Reports, E. Gutierrez (DG-JRC), W. van Heeswijk (DG-TAXUD), DKA (Queen Mary, University of London), EUR 25298 EN, ISBN 978-92-79-24168-0 (pdf),ISBN 978-92-79-24167-3 (print).
Maximal Fermi walk configurations on the directed square lattice and standard Young Tableaux, DKA, F.M. Bhatti and J. Essam J. Phys. A: Math. Theor. 43 145206 (2010).
Robustness of Trans-European Gas Networks: The Hot Backbone, R. Carvalho, L. Buzna,, Flavio Bono, E. Gutierrez, W. Just, DKA. Phys. Rev. E 78, 016110 (2009)

TEACHING

Dynamical Systems (MTH744), Semester A;. (2022-23)
Dynamical Systems (MTH744), Semester A. (2021-22)
Dynamical Systems (MTH744), Semester A., Communicating and Teaching Mathematics (MTH6110), Semester B (2020-21)
Dynamical Systems (MTH744), Semester B. (2019-20)
Metric Spaces(MTH6126), Semester A (2015-16).
Metric Spaces(MTH6126), Semester A (2014-15).
Metric Spaces(MTH6126), Semester A (2013-14).
MTH744 Dynamical Systems Lecture Notes (Autumn 2022) are here
Principal Fellowship of the HEA (submission failed).

RESEARCH TALKS and SEMINARS

Resilience of Infrastructure Networks, DKA George Boole Bicentenary Conference, University College Cork, (August 2015) .
Royal Institution Masterclass - INFINITY and beyond , given on 5th March, 2014 is here
EPSRC/DST Interaction Meeting in Applied Mathematics Sciences Research Challenges (Edinburgh, 2012), UK Mathematical Sciences Research Landscape with Energy relevance, DKA.
INFRASTRUCTURE NETWORKS DKA University of Catania, 2012 .
INFRASTRUCTURE NETWORKS DKA Manchester, May 2010 .
INFRASTRUCTURE NETWORKS DKA IWCSN, Bristol June 2009 .
Critical infrastructures in European Power Structures , DKA British Applied Mathematics Colloquium, Nottingham, UK, April 2009
Spectral and topological analysis of weighted networks , DKA, F. Bono, E. Gutierrez, K. Poljansek Control and Management of Risk, La Sapienza, Rome, July 2008 .
MANMADE,DIAGNOSING VULNERABILITY, EMERGENT PHENOMENA, and VOLATILITY in MANMADE NETWORKS DKA Control and Management of Risk, La Sapienza, Rome, July 2008 .
Modelling of Critical Infrastructures, DKA Bridging the Gaps, QMUL, June 2008
Optimal Networks, Congestion and Braess Paradox DKA and R.J. Mondragon, IWCSN - 2007 Guilin, CHINA.
MANMADE DKA, DKA*, F.Bono**, E. Gutierrez, NEST Pathfinder CRP Forum, European Conference on Complex Systems 2007 (ECCS '07), Dresden 6th October, 2007
MANMADE DKA, NEST Pathfinder ECCS06 Satellite Workshops, European Conference on Complex Systems 2006 (ECCS '06), Said Business School, University of Oxford 25-29 September 2006.
Background lecture notes , DKA and R.J. Mondragon . These notes are an expanded version of Data Traffic, Topology and Networks, DKA, R.J. Mondragon and M. Woolf, "Modelling in Complex Networks", eds Vattay and Kocarev Springer Verlag, 2005, 127-158 .
EPSRC WORKSHOP on COMPLEXITY, Bristol, July 2006. Lecture slides: Packet Traffic on Networks, DKA and R.J. Mondragon .
Communication models with distributed transmission rates and buffer sizes, DKA, Mario di Bernardo, Francesco Sorrentino, . IEEE Proceedings of Systems andCircuits, (Kos) May 2006 .
Congestion and Centrality in Data Networks, DKA and R.J. Mondragon, InternationalWorkshop on Complex Systems and Networks, City University of HongKong, May, 2005 .
Effects of variations of load distribution on network performance, DKA, Mario di Bernardo, Francesco Sorrentino, . IEEE Proceedings of Systems andCircuits, Kobe} May 2005, 3773-3776. .
The statistics of intermittency maps and dynamical modelling of packet traffic networks, DKA , M. Barenco, R.J. Mondragon, M. Woolf Conference-Nonlinear Dynamics and Complexity in Information and Communication Technology, University of Bologna, September 6-8, 2004 .
The statistics of intermittency maps and dynamical modelling of networks, DKA , M. Barenco, R.J. Mondragon, M. Woolf Sixteenth International Symposium onMathematical Theory of Networks and Systems (MTNS2004)Katholieke Universiteit Leuven, BelgiumJuly 5-9, 2004.
MODELLING OF TCP PACKET TRAFFIC IN A LARGE INTERACTIVE GROWTH NETWORK, DKA and M.WoolfProc. IEEE Systems and Circuits, Vancouver, 2004 V, 477-480. .
Special invited session: Nonlinear Dynamics forCoding Theory and Network Traffic in the IEEE Proceedings of Systems and Circuits (Bangkok, May, 2003)PAPER: INTERNET PACKET TRAFFIC CONGESTION, DKA, R.J. Mondragon, J.M.Pitts, M. Woolf Vol 3 pp746-749, and PRESENTATION: INTERNET PACKET TRAFFIC CONGESTION.
Theme lecture at the University of Sharjah(UAE) Mathematics Day, May 8th, 2003. Modelling internet packet traffic congestion in networks using chaotic maps
Conference paper for the ATCM 2002 Conference (Kuala Lumpur) Nonlinear Modelling of Packet Traffic , DKA and M.Woolf, Proc. 7th Asian Tech. Conf. in Mathematics, 34-43, 2002.
Plenary lecture at the ATCM 2002 Conference (Kuala Lumpur) Nonlinear Modelling of Packet Traffic

SOME FURTHER PAPERS and PUBLICATIONS

Time series analysis and long range correlations of Nordic spot electricity market data H. Erzgraber, F. Strozzi, J-M Zaldivar, H Touchette, E. Gutierrez, DKA, Physica A 2008 387, Issue 26, p. 6567-6574. PHYSA11614
Queues, Long-range Dependent Traffic and Non-linear Maps , Raul J. Mondragon (University of London), DKA (University of London) Bologna, 100055 NOLTA 2006.
Data Traffic, Topology and Networks, DKA, R.J. Mondragon, M. Woolf, "Modelling in Complex Networks", Springer Verlag, 2005.
DKA, R.J. Mondragon, J.M. Pitts and M. Woolf, Phase transitions in Packet Traffic on Regular Networks:a comparison of source types and topologies,Report 08, 2004/2005, Institut Mittag-Leffler, Stockholm
M. Woolf, DKA, S. Zhou, R.J. Mondragon and J.M. Pitts, Dynamical Modelling of TCP Packet Traffic on Scale-Free Networks, Report 07, 2004/2005, Institut Mittag-Leffler, Stockholm.
The Encyclopedia of Nonlinear Science (editor Alwyn Scott, Routledge, 2004) provides complete coverage at the introductory level of the field of nonlinear science, from intuitive descriptions to mathematical concepts over a wide range of subject matters. I have contributions on topology and symbolic dynamics.
E. Gutierrez and DKA, Control of a double impacting mechanical oscillator using displacement feedback, , International Journal of Bifurcation and Chaos, 14 No. 9 (2004), 3095-3113.
M. Barenco, DKA, The autocorrelation of double intermittency maps and the simulation of computer packet traffic , DYNAMICAL SYSTEMS,19(1) 2004, 61-74.
M. Woolf, DKA, R.J. Mondragon and J.M. Pitts, Optimization and phase transitions in a chaotic model of data traffic, Phys Rev E 66(4) 046106, 2002. See also Supplementary Figures.
R.J.Mondragon, J.M. Pitts and DKA, Minimising end-to-end delays in the presence of self-similar traffic, XVIII World Telecommunications Congress (Paris) ,September 2002.
End-to-end performance in real time IP networks with self-similar behaviour, J.M. Pitts, J.A. Schormans, M. Woolf, R.J. Mondragon, DKA), IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002, Orlando, USA (invited paper).
ERCIM News Online No. 50 Special theme: erciMATHEMATICS Nonlinear Modelling of Packet Traffic July 2002.
Controlling self-similar traffic and shaping techniques, R..J. Mondragon, DKA and J.M. Pitts), Nonlinear Control in the Year 2000, Lecture Notes in Control and Information Sciences 259, Springer-Verlag(Berlin), 2001, 2 149-61.
Chaotic maps for traffic modelling and queueing performance analysis, R.J. Mondragon, DKA, J.M. Pitts, Performance Evaluation 43 , 2001 223-240.
R.J. Mondragon, DKA, J.M. Pitts, Chaotic Maps for traffic modelling and queueing performance analysis, Performance Evaluation 43(2), 2001, 223-240.
Traffic Modelling and Queueing Performance using Chaotic Maps, Proc. Nonlinear Dynamics of Electronics (eds Setti et al), World Sci. 2000, 56-60.
C.M. Place, DKA, Control of Transient Chaos in Tent Maps near Crisis, I Fixed points, Phys Rev E abstract Phys Rev E, 61(2), 2000, 1357-1368.
C.M. Place, DKA, Control of Transient Chaos in Tent Maps near Crisis, II Periodic Orbits, Phys Rev E abstract Phys Rev E, 61(2), 2000, 1369-1381.
R. Carretero-Gonz\'alez, F. Vivaldi, DKA One-dimensional dynamics for travelling fronts in coupled map lattices and Phys Rev E abstract Phys Rev E, 61 (2), 2000, 1329-1336.
R.J.Mondragon, J.M. Pitts, DKAChaotic Maps for Traffic Modelling and Queueing Performance Analysis Electronic Letters36 2000, 184-186.
J.W. Essam, DKA, Chromatic polynomials and mod-q flows on Directed Graphs and Their Applications Proceedings, Centre de Researches Mathematiques , Montreal, 23(12), 1999, 1-20.

VISITORS

Makoto Katori (Chuo University, Tokyo) visited Queen Mary (March-August 2001) and All Souls, University of Oxford (September, 2001-February, 2002). An overview paper entitled "Flow polynomials, Schur Polynomials and Discrete Orthogonal Polynomials'', M. Katori, DKA, J.W. Essam was produced connecting properties of friendly walkers, Young tableaux, random matrices, and the Bender-Knuth formula.
Dr F.M. Bhatti (Lahore University of Management Sciences) visited QMUL (July 2009 and 2010) and Professor J.W. Essam (RHUL), under the London Mathematical Society (Scheme 5).

OTHER PUBLICATIONS

London Taught Course Centre (LTCC) 2009, - (Lecture notes for classes 1-5 on Basic Dynamical Systems: Intermittency and Auto-correlation.)
The Applied mathematics publication lists are here.
If you prefer something a little more congenial, try PURPLE GOLD: Niche Grape Growing Networks in Orange, an M.Sc. Thesis by Matthew Arrowsmith, University of Sydney, 2002!