Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

Large datasets are increasingly common and are often difficult to interpret. Principal component analysis (PCA) is a technique for reducing the dimensionality of such datasets, increasing interpretability but at the same time minimizing information loss. It does so by creating new uncorrelated variables that successively maximize variance. Finding such new variables, the principal components, reduces to solving an eigenvalue/eigenvector problem, and the new variables are defined by the dataset at hand, not a priori , hence making PCA an adaptive data analysis technique. It is adaptive in another sense too, since variants of the technique have been developed that are tailored to various different data types and structures. This article will begin by introducing the basic ideas of PCA, discussing what it can and cannot do. It will then describe some variants of PCA and their application.

The human imprint on the global environment has now become so large and active that it rivals some of the great forces of Nature in its impact on the functioning of the Earth system. Although global-scale human influence on the environment has been recognized since the 1800s, the termAnthropocene, introduced about a decade ago, has only recently become widely, but informally, used in the global change research community. However, the term has yet to be accepted formally as a new geological epoch or era in Earth history. In this paper, we put forward the case for formally recognizing the Anthropocene as a new epoch in Earth history, arguing that the advent of the Industrial Revolution around 1800 provides a logical start date for the new epoch. We then explore recent trends in the evolution of the Anthropocene as humanity proceeds into the twenty-first century, focusing on the profound changes to our relationship with the rest of the living world and on early attempts and proposals for managing our relationship with the large geophysical cycles that drive the Earth’s climate system.

Recent coordinated efforts, in which numerous climate models have been run for a common set of experiments, have produced large datasets of projections of future climate for various scenarios. Those multi-model ensembles sample initial condition, parameter as well as structural uncertainties in the model design, and they have prompted a variety of approaches to quantify uncertainty in future climate in a probabilistic way. This paper outlines the motivation for using multi-model ensembles, reviews the methodologies published so far and compares their results for regional temperature projections. The challenges in interpreting multi-model results, caused by the lack of verification of climate projections, the problem of model dependence, bias and tuning as well as the difficulty in making sense of an ‘ensemble of opportunity’, are discussed in detail.

Man and nature both exploit the remarkable properties of cellular solids, by which we mean foams, meshes and microlattices. To the non-scientist, their image is that of soft, compliant, things: cushions, packaging and padding. To the food scientist they are familiar as bread, cake and desserts of the best kind: meringue, mousse and sponge. To those who study nature they are the structural materials of their subject: wood, coral, cancellous bone. And to the engineer they are of vast importance in building lightweight structures, for energy management, for thermal insulation, filtration and much more.

When a solid is converted into a material with a foam-like structure, the single-valued properties of the solid are extended. By properties we mean stiffness, strength, thermal conductivity and diffusivity, electrical resistivity and so forth. And the extension is vast—the properties can be changed by a factor of 1000 or more. Perhaps the most important concept in analysing the mechanical behaviour is that of the distinction between astretch- and abending-dominated structure. The first is exceptionally stiff and strong for a given mass; the second is compliant and, although not strong, it absorbs energy well when compressed. This paper summarizes a little of the way in which the mechanical properties of cellular solids are analysed and illustrates the range of properties offered by alternative configurations.

Computational thinking will influence everyone in every field of endeavour. This vision poses a new educational challenge for our society, especially for our children. In thinking about computing, we need to be attuned to the three drivers of our field: science, technology and society. Accelerating technological advances and monumental societal demands force us to revisit the most basic scientific questions of computing.

This paper examines the main approaches and challenges in the design and implementation of underwater wireless sensor networks. We summarize key applications and the main phenomena related to acoustic propagation, and discuss how they affect the design and operation of communication systems and networking protocols at various layers. We also provide an overview of communications hardware, testbeds and simulation tools available to the research community.