The challenge of non-Markovian energy balance models in climate.

We first review the way in which Hasselmann's paradigm, introduced in 1976 and recently honored with the Nobel Prize, can, like many key innovations in complexity science, be understood on several different levels. It can be seen as a way to add variability into the pioneering energy balance models (EBMs) of Budyko and Sellers. On a more abstract level, however, it used the original stochastic mathematical model of Brownian motion to provide a conceptual superstructure to link slow climate variability to fast weather fluctuations, in a context broader than EBMs, and led Hasselmann to posit a need for negative feedback in climate modeling.

Temperature variability implies greater economic damages from climate change.

A number of influential assessments of the economic cost of climate change rely on just a small number of coupled climate-economy models. A central feature of these assessments is their accounting of the economic cost of epistemic uncertainty-that part of our uncertainty stemming from our inability to precisely estimate key model parameters, such as the Equilibrium Climate Sensitivity. However, these models fail to account for the cost of aleatory uncertainty-the irreducible uncertainty that remains even when the true parameter values are known.

Storylines: an alternative approach to representing uncertainty in physical aspects of climate change.

As climate change research becomes increasingly applied, the need for actionable information is growing rapidly. A key aspect of this requirement is the representation of uncertainties. The conventional approach to representing uncertainty in physical aspects of climate change is probabilistic, based on ensembles of climate model simulations.

(A)phantasia and severely deficient autobiographical memory: Scientific and personal perspectives.

I address two interlinked aspects of the diversity in our experiences of memory and the mind's eye. I summarise the long-appreciated role of imagery in mathematics and the physical sciences, and contrast it with the evidence that some scientists have had limited or zero imagery. I then recount the story of how I became aware of my own lack of mental imagery, and the accompanying deficit in my episodic memory, how I have sought scientific understanding of these conditions, and how they have affected my life.

A dynamical systems explanation of the Hurst effect and atmospheric low-frequency variability.

The Hurst effect plays an important role in many areas such as physics, climate and finance. It describes the anomalous growth of range and constrains the behavior and predictability of these systems. The Hurst effect is frequently taken to be synonymous with Long-Range Dependence (LRD) and is typically assumed to be produced by a stationary stochastic process which has infinite memory.

Robustness of estimators of long-range dependence and self-similarity under non-Gaussianity.

Long-range dependence (LRD) and non-Gaussianity are ubiquitous in many natural systems such as ecosystems, biological systems and climate. However, it is not always appreciated that the two phenomena may occur together in natural systems and that self-similarity in a system can be a superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes.

Topological isomorphisms of human brain and financial market networks.

Although metaphorical and conceptual connections between the human brain and the financial markets have often been drawn, rigorous physical or mathematical underpinnings of this analogy remain largely unexplored. Here, we apply a statistical and graph theoretic approach to the study of two datasets - the time series of 90 stocks from the New York stock exchange over a 3-year period, and the fMRI-derived time series acquired from 90 brain regions over the course of a 10-min-long functional MRI scan of resting brain function in healthy volunteers. Despite the many obvious substantive differences between these two datasets, graphical analysis demonstrated striking commonalities in terms of global network topological properties.

Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer.

The study of animal foraging behaviour is of practical ecological importance, and exemplifies the wider scientific problem of optimizing search strategies. Lévy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails, such that clusters of short steps are connected by rare long steps. Lévy flights display fractal properties, have no typical scale, and occur in physical and chemical systems.

Application of computational mechanics to the analysis of natural data: an example in geomagnetism.

We discuss how the ideal formalism of computational mechanics can be adapted to apply to a noninfinite series of corrupted and correlated data, that is typical of most observed natural time series. Specifically, a simple filter that removes the corruption that creates rare unphysical causal states is demonstrated, and the concept of effective soficity is introduced. We believe that computational mechanics cannot be applied to a noisy and finite data series without invoking an argument based upon effective soficity.