Keith Briggs

Keith Briggs is a mathematician with interests in:

graph theory for network applications
stochastic processes for network applications
mathematical computing & computational mathematics
computer arithmetic - floating point and other models
computational number theory

and with software skills including C, C++, python, perl, TeX, bash, and linux generally.

Keith's non-professional interests include historical linguistics, onomastics, harpsichord playing, cycling, not driving, and not using a mobile phone. For further information see personal website.

qualifications

PhD in mathematics (University of Melbourne)
BSc (Hons) in mathematical physics (University of Adelaide)
BSc in physics (University of Adelaide)
Erdõs number=2

employment

senior mathematician, BT Research
visiting researcher, King's College Research Centre, Cambridge
postdoctoral researcher in biomathematics, University of Cambridge
mathematics tutor, King's College, Cambridge
research associate, Physics Department, University of Western Australia
associate lecturer, Applied Mathematics Department, University of Adelaide
research fellow, Mathematics Department, University of Melbourne
research associate, Mathematics Department, La Trobe University
tutor, Physics Department, University of Adelaide
tutor, Physics Department, Prifysgol Cymru Bangor

recent research highlights

Branch-and-bound optimization techniques for WAP channel assignment
Practical implementation of fast algorithms for various graph theory problems
Development of accurate statistical models for train delays
Fast optimal algorithms for channel assignment in wireless cities
Development of Bayesian language models for multilingual texts
Markov chain models of communications protocols (TCP, DCCP)
New algorithms for constructing Klein polyhedra in the theory of simultaneous Diophantine approximation
Explicit computation of the most badly-approximable irrational pair
Discovery of the simplest universal differential equation (roughly speaking, this means it has solutions arbitrarily close to any continuous function). The equation is y''''y'^2-3y'''y''y'+2(1-1/n2)y''^3=0
Development of the first practical software package for exact stochastic lazy real arithmetic
Derivation of the most precise known asymptotic expansions for the numbers of certain classes of graphs (labelled, planar, unicyclic etc.)
Extension of the counting series to world-record levels for certain classes of graphs (see here)
Development of very fast low-level algorithms for Monte-Carlo Markov chain simulations for graph theory models
Computations extending the construction of abundant numbers far beyond previously known values
Construction of distributed algorithms for the solutions of various graph-theory centrality problems
Development of symbolic (i.e. computer-algebra) algorithms for the analysis of Markov chain models arising in telecoms: TCP and wireless access points

previous research

exact real arithmetic
historical linguistic cladistics
simultaneous Diophantine approximation algorithms
statistics of internet round-trip times
Markov chain models of TCP
efficiency of small-world graphs
low-discrepancy sequences for image sampling
complexity of Boolean functions
parameter estimation in nonlinear dynamical systems models
universal scaling in nonlinear dynamical systems
biological effects of electromagnetic radiation
Potts models and self-avoiding walks in statistical mechanics
acoustics of baroque brass instruments
quaternion iteration theory
dense colloid simulations
classical relativistic radiation theory
My Ph.D. thesis: Feigenbaum scaling in discrete dynamical systems

other professional activities

student supervision - 4 PhD students supervised and approximately 8 MSc students
steering committee, MSc in Applied Numerical Computing, University of Manchester
MASI strategy committee, University of Leicester
Many Smith Institute (University of Oxford) meetings attended
Joint organizer (with Richard Clegg) of Mathematics of Networks conference series
CABDyN meeting, Oxford
Meeting on mathematics of networks, Martlesham
EPSRC Novel Computation cluster, Bristol, Bath and Oxford
advisory panel, MSc in mathematics of networks, University of York
advisory panel, eMathematics MSc, Brunel University
advisory panel, research program in long-range dependence, QMUL & York
complex systems thinktank, Smith Institute, Oxford
supervision of MSc and PhD students from Oxford, York and UMIST
member of American Mathematical Society and SIAM
contributor to Mathworld and Wikipedia on mathematics topics
contributor of software components to GNU scientific library, igraph, and networkx
referee for EPSRC, IEE, IEEE, AMS, Physical Review, Physics Letters etc. etc. etc.

papers

2006

Modelling train delays with q-exponential functions (with C. Beck) . Physica A378, 498
Properties of geometric random graph models for wireless network applications (with Linlin Song). Submitted to VTC2007
Optimal channel allocation for wireless cities (with Andrew Ainsworth). Submitted to VTC2007
Martlesham and Newbourne - a note on two obscure Suffolk names. Journal of the English Place-Name Society 38, 31-36 (2006)
Abundant numbers and the Riemann hypothesis. Exp. Math. 15, 251-6 (2006)
Implementing exact real arithmetic in C++, python, and C Theoretical computer science 351, 74-81 (2006)

2005

Asymptotic expansions for enumerating connected labelled graphs. Submitted to Elec J Combinatorics, 2005 Aug 16
A distributed algorithm for graph centers (with Linlin Song). Submitted to IEEE Trans Par Dist Sys, 2005 July 26
Phylogenetic analysis of Chinese dialects (with Gesine Reinert, in preparation)
Connectivity of graphs - a tutorial survey (in preparation)
Analysis and simulation of internet round-trip times
Some explicit badly approximable pairs
Another universal differential equation
Scaling in a map of the two-torus
Computing TCP equilibrium sensitivity with Markov chains

2004

Review of Hypercomplex iterations by Dang, Kauffman and Sandin. Mathematical Intelligencer, Spring 2004 page 74
Gaussian multi-level FM for high-bandwidth satellite communications, (with Mike Fitch) WTC04
Traffic models for wireless services, Eurescom report 2004

2003

Some explicit badly approximable pairs Journal of Number Theory, 103, 71.

2002

Another universal differential equation submitted to Electronic journal of the qualitiative theory of differential equations
Analytical solution to Matthews' and Blakeslee's critical dislocation formation thickness of epitaxially grown thin films (with A. Braun) Journal of Crystal Growth, 241, 231-234

2001

On Furtwängler's algorithm for simultaneous Diophantine approximation

2000

Scaling in a map of the two-torus (with Gonzalo Alvarez) Experimental Mathematics, 9, 301-307
Master equation solution of a plant disease model (with N. Stollenwerk), Physics Letters A274, 84-91
Solution of a stochastic disease model via spheroidal functions (with N. Stollenwerk), poster, Dynamics Days 99 Comp

1999

The effects of sub-Milankovitch forcing on initiation of Northern Hemisphere glaciation (with A. Kleczkowski, K. Willis, and C. A. Gilligan). Science 285 , 568-571.
Essentially singular solutions of Feigenbaum-type functional equations (book chapter: M. T. Batchelor and L. T. Wille (eds.) Statistical Physics on the Eve of the Twenty-First Century, pages 65-77, World Scientific 1999)

1998

Analytic solutions of the Cvitanovic'-Feigenbaum and Feigenbaum-Kadanoff-Shenker equations (with T. Dixon and G. Szekeres) Int J Bif Chaos 8, 347-357 (1998) MR lookup

1997

Hydrodynamic interactions and some new periodic structures in three particle sediments (with I. K. Snook and E. R. Smith) Physica A 240 547-559
On the universality of singular circle maps (with T. W. Dixon and B. G. Kenny) Phys. Lett. A231 359-366

1996

Iteration of quaternion functions (with S. P. Bedding) American Mathematical Monthly 103, 654-664

1995

A torus map based on Jacobi's sn Computers and Graphics 19, 451
Formal power series solution of functional equations MapleTech^? 2, no. 2, 48-51
Two-body solutions of the Lorentz-Dirac equation In Confronting the Infinite, A. L. Carey (ed.) World Scientific
Formal solution of functional equations via algorithmic differentiation Aust Math Soc Gazette 22, 64
Iteration of quaternion maps (with S. P. Bedding) International Journal of Bifurcation and Chaos 5, 877
Nonlinear dynamics of charged particles interacting with combined ac-dc electromagnetic fields (with C. J. Thompson, P. Farrell, A. Fleming, B. Hocking, K. Joyner, V. Anderson and A. Wood). Physica A220, 471-8

1994

How to stabilize a fixed point ACM SIGNUM Newsletter 29, no. 2, 2
Series study of the Potts model II (with I. G. Enting and A. J. Guttmann) J. Phys. A27, 1503-1523
Corrections to universal scaling in real maps Phys. Lett. A191, 108-112

1993

Self-avoiding walks on quasilattices International Journal of Modern Physics B7, 1569

1992

Fitting ordinary differential equations to chaotic time series (with E. and M. Baake and H. Bock). Phys. Rev. A45 5524
Biological effects of electromagnetic radiation, Proceedings of the Mathematics in Industry Study Group, Melbourne 1992

1991

Feigenvalues for Mandelsets. (with G. R. W. Quispel and C. Thompson). J. Phys. A24 3363-3368
Positive-definiteness of the mobility tensor in dense colloid simulations. (with E. R. Smith, I. K. Snook and W. van Megen). Phys. Lett. A154, 149-153
A precise calculation of the Feigenbaum constants Mathematics of Computation 57, 435-439

1987-1990

An improved method for estimating Liapunov exponents of chaotic time series. Phys. Lett. A151, 27-32
How to calculate the Feigenbaum constants on your PC. Aust. Math. Soc. Gazette 16, 89
The Billiard Equations Mathematical Gazette 72, 217
On the radiation from a rotating dipole Aust. J. Phys 41, 629
An exact solution of the relativistic two-body problem with scalar interaction J. Phys. A21, 1831
An exact two-body solution of the Lorentz-Dirac equation Phys. Rev. A37, 977
Simple experiments in chaotic dynamics Am. J. Phys 55 , 1083

talks and seminars given recently

MSc projects at BT University of York 2007 Jan 31
Some graph theory applications to communications networks University of Sheffield 2006 Nov 02
Some hard graph problems in telecoms University of Warwick Complexity Forum 2006 Oct 31
BICS seminar pdf slides University of Bath 2006 Jun 12
The work of George Szekeres on functional equations QMUL 2006 Jan 10
Exponential random graphs Mathematical & Psychological Sciences, Unilever Corporate Research, Sharnbrook, 2005 Nov 22
Exponential random graphs MoN4, QMUL 2005 Jul 22
Enumeration of labelled graphs LSE 2005 Apr 28
RH and abundant numbers University of York 2005 Mar 01
BT Research & Mixing time University of York 2005 Feb 28
Optimization MRC meeting 2005 Feb 17
Bayesian processing of multilingual documents Cavendish Lab 2005 Feb 15
Planar graphs CRG 2005 Feb 07
Exponential random graphs CRG 2005 Feb 07
Bayesian text processing CRG 2005 Jan 24
Some experimental approaches to Diophantine approximation problems QMUL seminar 2005 Jan 11
Mathematics of Networks 3rd Meeting, Imperial College 2004 Dec 20
Mixing time of random walks on networks PICT seminar, BT 2004 Dec 16
Maximum entropy traffic matrix estimation CRG meeting, BT 2004 Dec 03
Mixing time of random walks on networks CRG meeting, BT 2004 Nov 29
Connectivity of random graphs University of Manchester 2004 Nov 19
Connectivity of random graphs Complex Adaptive Systems Group Seminar, Oxford 2004 Oct 12
Wireless traffic models, Porto 2004 Sep 16
Probability of connectedness of labelled graphs BT CRG 2004 Sep 06
Delayed iteration BT CRG 2004 Jul 05
Combinatorial graph theory and connectivity Maths of Networks, 2004 Jul 02
Some issues in mathematical computing BT Exact 2004 Jun 25
Optimization for power control BT Exact 2004 Jun 03
Bayesian spam filtering BT Exact PICT seminar 2004 Apr 29
Traffic models for new wireless services Eurescom, Heidelberg, 2004 Mar 30
Exact real arithmetic University of Kent, 2004 Feb 10
Combinatorial graph theory BT Exact 2004 Jan 19
Statistics of continued fractions York winter dynamics day, 2003 Dec 19
Asynchronous distributed algorithms Bristol Uni Engineering Maths Dept 2003 Dec 02
DCCP BT Exact 2003 Nov 17
TeraLab Open Day 2003
EPSRC Novel computation meeting, Bristol University 2003 Sep 26
Discrete Green's function on graphs BT Exact CRG 2003 Sep 23
How to count without counting BT Exact Tempura 2003 Sep 04
Modelling internet round-trip time data University of York 2003 Jul 18
Graph eigenvalues and connectivity BT Exact 2003 Jul 07
The Durand-Flajolet algorithm BT Exact 2003 Jun 09
Connectivity of nodes TeraTalk, BT Exact 2003 May 15
Valiant's theory of the learnable BTexact 2003 Apr 14
Exact real arithmetic Oxford University, Computer Lab 2003 Mar 06
Distributed algorithms BTexact 2002 Oct 22
Exact real arithmetic Cambridge University, Cavendish Lab, 2002 Nov 20
Modelling TCP with Markov chains Budapest Technical University 2002 Jun 17
Simultaneous Diophantine approximation and linearization of C^2 maps Manchester 2000 Nov 30

software developed and released as open-source

very_nauty - graph theory software for clique and chromatic number
mpfs - stochastic lazy exact floating-point arithmetic
graphlib - low-level graph library
fps - formal power series library
xrc - exact real arithmetic in C
Ode - command line ode solver
pipemath - shell pipeline data analysis
try_iroot.c - algorithm to find the floor of nth root of a positive integer with all-integer arithmetic
try_vitter_fast_sampling.c - C version of Vitter's fast algorithm to randomly select n out of N objects
LambertW.c - C code for Lambert W function, principal branch
LambertW.py - python code for Lambert W function, principal branch
LambertW1.c - C code for Lambert W function, -1 branch

major BT internal reports from the last few years

Modelling and simulating wireless cities - the issues (2006)
Connectivity of random graphs (2005)
Optimization for global resource allocation on networks (2005)
Cross-layer optimization for wireless networks (2005)
Mathematical issues in mobile wireless networks (2004)
Traffic models for wireless networks, Eurescom report (2003)
Efficient network topologies (2002)
Analysis and simulation of internet round-trip times (2001)