## Regularities in Firm Dynamics: The Basic of the Complex Economy

Firm Dynamics is a field defined in mathematical economics and econophysics. The research question of my work is rather simple: what are the regularities of company performance? How a company evolves over time and what is the relevance to the macroeconomy. In this study, I use empirical evidence rather than hypothesis to draw a big picture of company activities in the economy. With data from Amadeus, Compustat and Company House, covering 20M companies in EU and US, the conclusion is drawn from empirical data in an unprecedented level of resolution. To analyse the detail, I further developed a high-resolution probability estimator which enables me to recover the true empirical distribution at the best...

Read More## Self-Organised Criticality

Self-Organised Criticality describes the tendency of some non-equilibrium systems to display scale-invariant, intermittent behaviour. As the name suggests, these systems seem to organise themselves to a classical critical point, where they experience all features of a second order phase transition. The key characteristics of these systems are: slow drive (separation of time scales), strong interaction, non-linear relaxation and thresholds, displaying bursts of activities (avalanches) whose distribution is self-similar (power laws) and only cut off by the system size. All scaling in such systems is finite size (and finite time) scaling. Our research into self-organised criticality (SOC) is three pronged: The basic principles of SOC (field theory, scaling, mapping to established critical phenomena). Numerical investigation of SOC using large scale computer simulations. Applying the concepts of SOC to understand natural...

Read More## Synchronisation by time delay

Synchronisation is a very widespread phenomenon observed in flashing fireflies, applauding audiences and the neuronal network of the brain. Hitherto, one major branch of research has focussed on the exchange of instantaneous, sudden pulses which are exchanged when an oscillator reaches a threshold, triggering sudden, discontinuous relaxations. A second branch focussed on smooth interaction that vanishes in the synchronised state, best known as the Kuramoto Model. We changed this setup, studying smooth, continuous interaction that never disappears. At first, very basic considerations suggest that such a system cannot synchronise. Numerics, however, seems to suggest otherwise. It turns out that this clash is caused by an effective time delay built into the numerics: Time delay causes synchronisation on a time scale that is inversely proportional to the time lag. On a more technical level, if the Kuramoto Model is $latex \dot{\theta}_{1,2}=\omega + J \sin(\theta_2-\theta_1)$ then we study, for example, $latex \dot{\theta}_{1,2}=\omega + J (\sin(\theta_{2,1}(t-\delta t)-\sin(\theta_{1,2}(t-\delta...

Read More## Paul Expert’s research

i) The brain function, is it critical? ii) Structure and function of complex networks, from a statistical to a homological description. iii) Application of network theory tools to brain function. iv) The economy, does it SOC?

Read More## Tim Evans’ Research

Tim Evans’ main interest is in the behaviour of many body systems both in and out of equilibrium. Currently he is interested in ideas falling under the broad area of complex systems. In particular the properties of Complex Networks, such as the “six degrees of separation”, intrigue me. This is both from a theoretical perspective and in terms of applications to practical problems such as bibliometrics or cultural transmission, part of an interest in sociophysics in general. For instance Tim has an ongoing project in Archaeology. Tim is also interested in Quantum Field theory in general. His early research was on the many-body problems where the underlying dynamics is described by quantum field theory, a topic known as Thermal Field Theory or Finite Temperature Field Theory. Initially this was in the context of relativistic particle physics which is important for applications such as cosmology and quark gluon plasmas. Later Tim became interested in parallel problems in condensed matter physics, where lab based experiments can be performed. Tim is also interested in general issues with quantum field theory which led to work on multiplicative anomalies and in turn their implications for zeta-function renormalisation in...

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