University of East Anglia

Zilber constructed an exponential field B, which is conjecturally isomorphic to the complex exponential field. He did so by giving axioms in an infinitary logic, and showing there is exactly one model of those axioms. Following a suggestion of Zilber, I will give a different list of axioms satisfied by B which, under a number-theoretic conjecture known as CIT, describe its complete first-order theory

We apply the novel method of potential analysis to study climatic records. The method comprises (i) derivation of the number of climate states from time series, (ii) derivation of the potential coefficients. Dynamically

monitoring patterns of potential analysis yields indications of possible bifurcations and transitions of the system.

The method is tested on artificial data and then applied to various climatic records [1,2]. It can be applied to a wide range of stochastic systems where time series of sufficient length and temporal resolution are available and transitions or bifurcations are surmised. A recent application of the method in a model of globally coupled bistable systems [3] confirms its general applicability for studying time series in statistical physics.

[1] Livina et al, Climate of the Past, 2010.

[2] Livina et al, Climate Dynamics (submitted)

[3] Vaz Martins et al, Phys. Rev. E, 2010