Professor Henrik Jeldtoft Jensen  -  Complex Systems Science

Department of Mathematics  Imperial College London South Kensington campus London SW7 2AZ  Office: Electrical Engineering Building - EEE1201  Tel: +44 (0) 20 759 49853, Fax: +44(0) 20 7594 8517 Email: h.jensen@imperial.ac.uk                                                                                               For Imperial College Centre for Complexity Science  click here

Why do we do science?   For the same reason as Glenn Gould plays piano:    The purpose of art is not the release of     a momentary ejection of adrenaline but    rather the gradual, lifelong construction of     a state of wonder.                                          Glenn Gould   There are no such things as   applied sciences,   only applications of science.                                           Louis Pasteur     We shall not cease frome exploration   And the end of all our exploration   Will be to arrive where we started   And know the place for the first time.            T S Eliot                                                                                                                                            HJJ08

On the relationship between  painting and art   Mathematics is painting without the brush; painting is mathematics without the chalk. Talk presented at  INTERNATIONAL CONFERENCE EXCELLENCE: EDUCATION & HUMAN DEVELOPMENT, ATHENS, GREECE, 1 - 4, 2009                          Mathematics and Painting.  Article first published in             Interdisciplinary Science Reviews, 27, 45 (2002).   Music and painting         Two videos with    music composed by Eitan Altman    and paintings by Henrik Jeldtoft Jensen   Watercolour   and   Acrylic              Oxherding - HJJ08  An essay on the true emergent nature of time   Sindsvaesner og tidens egentlige natur   (in Danish)

Project on Improvisation in Classical Music        Collaborative project with Guildhall School of Music and Drama    For a presentation from King's College London's Weekend February 17-19,  2017  click here    For papers describing the research click here and here.    For a video talk click here.

Feza Gursey Institute and Imperial College International Summer School and Research Workshop on Complexity   Istanbul 5-10 September 2011           For more information click here                                                                                                                                                     Download my lectures a the school: Dynamics of Complex Systems and Music and the Brain

Complex Systems:   I lead the Centre for Complexity Science  (additional information here)   The Centre engages in a range of research into the applied and fundamental aspects of complexity science, where often the most interesting questions extend beyond the realms of idealised models and the simplifications arising within typical experiments. To access and begin to address such questions, theoretical investigations are often best carried out in close collaboration with researchers working on a variety of real systems. This is a common theme within the Centre; much of the research exploits the richness of real world data sets in order to study fundamental questions in complexity science. Many projects undertaken are collaborative in nature, and a diverse range of research is currently being undertaken within this framework, including: applying evolutionary dynamics to study economics and finance exploiting ideas from statistical mechanics to analyse the dynamics and structuring of social insects applying themes from self-organised criticality to analyse heart arrhythmia employing field theoretic methods to improve our understanding of the statistical mechanics of complex systems Ultimately, the focus is on maintaining a diverse set of research themes within the Centre which allow for extensive insight into real world data, and the opportunity to identify commonalities of theoretical and practical importance to fundamental complexity science.

Complexity, collective effects, and modelling of ecosystems:    formation, function, and instability        Paper in the Annals of the New York Academy of Sciences

For me statistical mechanics is about understanding why the whole is different from the sum of the parts: identifying and understanding emergent properties; understanding how the combined effect of simple interactions and many degrees of freedom creates the never ending complexity we observe in our surroundings. Obviously these general questions have to be studied through concrete cases. I am fortunate to work together with a number of graduate students, research assistants and colleagues on research projects including biology, neuroscience and statistical mechanics. The analysis of the emergence of structure in networks is a natural tool in this quest.

Tangled Nature: Ecology and Economics Evolutionary ecology is a prototype example of dynamics of complex systems. We have developed a simple individual based model which exhibit intermittency and is able to reproduce a range of ecological observables such as the species-area law and typical species abundance distributions.                                                                                                              Click here for an overview poster on the properties of the   Tangled Nature Model. Below are a few preprints           Review to appear in the proceeding of the 2006 ECMTB Dresden meeting           The Tangled nature model with inheritance and constraint: Evolutionary ecology restricted by a conserved resource  More recently we have developed the Tangled Nature approach to study economics            Entangled economy: An ecosystems approach to modeling systemic level dynamics and some reprints:            Diversity as a product of interspecial interactions          The species-area relationship and evolutio          Network properties, species abundance and evolution in a model of evolutionary ecology.          Tangled Nature: a model of evolutionary ecology. (J. Theo. Biol.)        Time dependent extinction rate and species abundance in the Tangled Nature model of biological evolution. (Phys. Rev. E.)           The Tangled Nature model as an evolving quasi-species model. (J. Phys. A) On selection of the mode of evolution         Origins of evolution: Non-acquired characters dominates over acquired characters in changing environment

Record dynamics: Intermittency and relaxation is very often encountered in complex systems. In a broad range of cases we have found that log-Poisson record dynamics is a good description of the observed dynamics. This has a number of very strong implications concerning the structure of the phase space as well as many consequences for the macroscopic temporal behaviour.         Evolution in Complex Systems (Complexity).         Intermittency, aging and extremal fluctuations.         Record dynamics and the observed temperature plateau in the magnetic creep-rate of type II superconductors.

Statistical Mechanics of epedemics:              We have studied the fluctuations in sizes of         Measles Outbreak in a Population with Declining Vaccine Uptake  SCIENCE 301, 804 (2003)                 additional material:  click here         and used lattice models in the study        On the critical behaviour of simple epidemics,                                             Proc. Rol. Soc. Lond. B  264, 1639 (1997). pdf

Population dynamics and evolutionary dynamics: Investigations of how the microscopic behaviour of the individuals in a population affects the behaviour of the whole.  Through the eyes of statistical physics, our main emphasis has been on the phase transitions that occur in our model as the population becomes extinct. Of particular interest is our recent study of the nature of the extinction transition in fractal dimensions between one and two. Aside from this largely theoretical approach, we also examine how the model could be used for ecological purposes, particularly in the conservation of species. Allee Effects and Extinction in a Lattice Model. Change in order of phase transition on fractal lattices. Phase transitions in a lattice population model. The clustering in type space and its relation to neutral and non-neutral models. Understanding clustering in type space using field theoretic techniques. Neutral Evolution in a Biological Population as Diffusion in Phenotype Space: Reproduction with Local Mutation but without Selection.

Modelling in creativity and music cognition using a complexity science approach: We explore patterns in brain activity that are a result of a musician's playing. The focus in particular is to elucidate what happens when creative leaps and ingenuity occur during this playing - EEG recordings are analysed. Together with Conductor Richard Dickens and J Bhattacharya, Goldsmith.

Brain scales          We analyse the spatial and temporal scales of the brain by use of fMRI.

 
Additional interests: Kids, books, music, philosophy, painting,.... 
 
 

List of publications:    Click here to see Publication List                                         HJJ08

Some lectures:     Emergence of complex structure through co-evolution:     The Tangled Nature model of evoultionary ecology      (Key note lecture at the French Complex systems Societry Meeting,        Paris 25-27 Nov. 2009)      Slides  (8.5MB)     On the relation between painting and mathematics.     (Key note lecture at the conference on Excellence: Education & Human Development,       Athens, 1-4 July 2009. )      Slides (39.1MB)    Tangled Nature: a model of evolutionary ecology.      Slides  (2.9MB)     Dynamics of complex systems: The record dynamics.     Slides  (2.2MB)      Subtle relations:       prime numbers, complex functions, energy levels and Riemann.       Slides  (1.0MB)    Self-Organised Criticality:what does it mean and is it important.      Slides (1.1MB)     Godel's  Proof.     An introduction to the back ground, the structure of the proof and its consequences.    Slides (1.0MB)

 
 

Some selected publications:
 

Complex systems:  Self-Organized Criticality, H.J. Jensen, Cambridge University Press. 1998.           Buy online from  Cambridge University Press or from  Amazon.com   Anisotropy and universality: the Oslo model, the rice pile experiment  and the quenched Edwards-Wilkinson equation,         G. Pruessner and H.J. Jensen, Phys. Rev. Lett. 91, 244303 (2003). pdf    A solvable non-conservative model of Self-Organised Criticality,          G. Pruessner and H.J. Jensen, Europhys. Lett. 58, 250 (2002). pdf    Universal fluctuations in correlated systems,        S.T. Bramwell, K. Christensen, J.-Y. Fortin, P.C.W. Holdsworth,         H.J. Jensen, S. Lise, J. Lopez, M. Nicodemi, J.-F. Pinton, M. Sellito,        Phys. Rev. Lett. 84 , 3744 (2000).  pdf

Biology: Emergence of species and punctuated equilibrium in the Tangled Nature model of biological evolution.         H.J. Jensen, Physica A: 340,  697-704 (2004). pdf Darwinian selection in a locally unstable Boolean Network.         D. Eriksson and H.J. Jensen, J Stat. Mech.: Theor. Exp. P09001 (2004).pdf   Nonequlibrium Roughening transition in a Simple Model of Fungal Growth in 1+1 Dimensions,      J.M. Lopez and H.J. Jensen, Phys. Rev. Lett. 81 , 1734 (1998). pdf   A Genric Model of Morphological Changes in Growing Colonies of Fungi,      J.M. Lopez and H.J. Jensen,  Phys. Rev. E. 65, 021903 (2002). pdf

Vortex dynamics:     Time dependent phenomena in transport properties and I-V characteristics of a model for driven vortex matter.          M. Nicodemi and H.J. Jensen, J. Phys.: Cond. Mat. 16, 6789 (2004). pdf Creep of superconducting vortices in the limit of vanishing temperature A finger print off equilibrium dynamcs,      M. Nicodemi and H.J. Jensen,  Phys. Rev. Lett. 86, 4378 (2001). pdf Aging and memory phenomena in magnetic and transport properties of vortex matter,      M. Nicodemi and H.J. Jensen, J. Phys. A 34, 8425 (2001). pdf Off equilibrium glassy properties of vortex creep in superconductors,        H.J. Jensen and M. Nicodemi, Europhysics Lett. 54, 566 (2001). pdf

Other topics: Mathematics and painting.        H.J. Jensen, Interdisciplinary Science Review 27, 45 (2002). pdf Turner                              Mathematical Moddeling of Species formation.         K. Christensen and H.J. Jensen, Science Progress 83, 93 (2000).  pdf                                                                    HJJ03