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. We show how to account for this second source of uncertainty in a physically well-founded and tractable way, and we demonstrate that even modest variability implies trillions of dollars of previously unaccounted for economic damages.

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. In the face of deep uncertainties, the known limitations of this approach are becoming increasingly apparent. An alternative is thus emerging which may be called a 'storyline' approach. We define a storyline as a physically self-consistent unfolding of past events, or of plausible future events or pathways. No a priori probability of the storyline is assessed; emphasis is placed instead on understanding the driving factors involved, and the plausibility of those factors. We introduce a typology of four reasons for using storylines to represent uncertainty in physical aspects of climate change: (i) improving risk awareness by framing risk in an event-oriented rather than a probabilistic manner, which corresponds more directly to how people perceive and respond to risk; (ii) strengthening decision-making by allowing one to work backward from a particular vulnerability or decision point, combining climate change information with other relevant factors to address compound risk and develop appropriate stress tests; (iii) providing a physical basis for partitioning uncertainty, thereby allowing the use of more credible regional models in a conditioned manner and (iv) exploring the boundaries of plausibility, thereby guarding against false precision and surprise. Storylines also offer a powerful way of linking physical with human aspects of climate change.

(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. However, infinite memory appears to be at odds with the Markovian nature of most physical laws while the stationarity assumption lacks robustness. Here we use Lorenz's paradigmatic chaotic model to show that regime behavior can also cause the Hurst effect. By giving an alternative, parsimonious, explanation using nonstationary Markovian dynamics, our results question the common belief that the Hurst effect necessarily implies a stationary infinite memory process. We also demonstrate that our results can explain atmospheric variability without the infinite memory previously thought necessary and are consistent with climate model simulations.

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. The risk assessment of systems with these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. Two paradigmatic models are discussed that can simultaneously account for LRD and non-Gaussianity: autoregressive fractional integrated moving average (ARFIMA) and linear fractional stable motion (LFSM). Statistical properties of estimators for LRD and self-similarity are critically assessed. It is found that the most popular estimators can be biased in the presence of important features of many natural systems like trends and multiplicative noise. Also the LRD and non-Gaussianity of two typical natural time series are discussed.

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. Both the human brain and the market networks were non-random, small-world, modular, hierarchical systems with fat-tailed degree distributions indicating the presence of highly connected hubs. These properties could not be trivially explained by the univariate time series statistics of stock price returns. This degree of topological isomorphism suggests that brains and markets can be regarded broadly as members of the same family of networks. The two systems, however, were not topologically identical. The financial market was more efficient and more modular - more highly optimized for information processing - than the brain networks; but also less robust to systemic disintegration as a result of hub deletion. We conclude that the conceptual connections between brains and markets are not merely metaphorical; rather these two information processing systems can be rigorously compared in the same mathematical language and turn out often to share important topological properties in common to some degree. There will be interesting scientific arbitrage opportunities in further work at the graph-theoretically mediated interface between systems neuroscience and the statistical physics of financial markets.

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. An attempt to demonstrate their existence in a natural biological system presented evidence that wandering albatrosses perform Lévy flights when searching for prey on the ocean surface. This well known finding was followed by similar inferences about the search strategies of deer and bumblebees. These pioneering studies have triggered much theoretical work in physics (for example, refs 11, 12), as well as empirical ecological analyses regarding reindeer, microzooplankton, grey seals, spider monkeys and fishing boats. Here we analyse a new, high-resolution data set of wandering albatross flights, and find no evidence for Lévy flight behaviour. Instead we find that flight times are gamma distributed, with an exponential decay for the longest flights. We re-analyse the original albatross data using additional information, and conclude that the extremely long flights, essential for demonstrating Lévy flight behaviour, were spurious. Furthermore, we propose a widely applicable method to test for power-law distributions using likelihood and Akaike weights. We apply this to the four original deer and bumblebee data sets, finding that none exhibits evidence of Lévy flights, and that the original graphical approach is insufficient. Such a graphical approach has been adopted to conclude Lévy flight movement for other organisms, and to propose Lévy flight analysis as a potential real-time ecosystem monitoring tool. Our results question the strength of the empirical evidence for biological Lévy flights.

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. A related distinction between noise and unresolved structure is also defined: Noise can only be eliminated by increasing the length of the time series, whereas the resolution of previously unresolved structure only requires the finite memory of the analysis to be increased. The benefits of these concepts are demonstrated in a simulated times series by (a) the effective elimination of white noise corruption from a periodic signal using the expletive filter and (b) the appearance of an effectively sofic region in the statistical complexity of a biased Poisson switch time series that is insensitive to changes in the word length (memory) used in the analysis. The new algorithm is then applied to an analysis of a real geomagnetic time series measured at Halley, Antarctica. Two principal components in the structure are detected that are interpreted as the diurnal variation due to the rotation of the Earth-based station under an electrical current pattern that is fixed with respect to the Sun-Earth axis and the random occurrence of a signature likely to be that of the magnetic substorm. In conclusion, some useful terminology for the discussion of model construction in general is introduced.