The 2015 Nobel Prize for Physics was shared by Takaaki Kajita and Arthur B. McDonald. These papers are the text of the address given in conjunction with the award.

The 2015 Nobel Prize for Physics was shared by Takaaki Kajita and Arthur B. McDonald. These papers are the text of the address given in conjunction with the award.

Symmetry-protected phases of matter have been at the forefront of condensed matter physics in recent years. Bosonic symmetry-protected phases have been interpreted in terms of anomalies and group cohomology. The present article aims to develop an analogous description of fermionic symmetry-protected phases, such as the topological insulators that have been seen experimentally in 2 or 3 space dimensions. The relevant mathematical concepts include the Atiyah-Singer index theorem and the Atiyah-Patodi-Singer eta invariant.

The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra. The concept has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc. The inclusion of nonlinearity has led to a number of new phenomena for which no counterparts exist in traditional dissipative systems. Several examples of nonlinear parity-time symmetric systems in different physical disciplines are presented and their implications discussed.

It is of societal importance to advance the understanding of emerging patterns of biodiversity from biological and ecological systems. The neutral theory offers a statistical-mechanical framework that relates key biological properties at the individual scale with macroecological properties at the community scale. This article surveys the quantitative aspects of neutral theory and its extensions for physicists who are interested in what important problems remain unresolved for studying ecological systems.

Everyday matter is made of the lightest up and down quarks. The strange quark is the third lightest of all quarks. Strangeness, a property of particles associated with the number of strange quarks, preceded the theory and discovery of the quark by about two decades. Recent experimental and theoretical developments in the field of strangeness in nuclei are reviewed. Topics include the production of strange particles, properties of hypernuclei, and strange dense matter.

In recent years an increasing amount of attention has been devoted to quantum materials with topological characteristics that are robust against disorder and other perturbations. In this context it was discovered that topological materials can be classified with respect to their dimension and symmetry properties. This review provides an overview of the classification schemes of both fully gapped and gapless topological materials and gives a pedagogical introduction into the field of topological band theory.

Complex networks range from subcellular biological networks to the Internet. Our ability to control these systems deeply challenges our understanding. Control also may well be a guiding principle in their design. This article reviews the emerging science of the control of complex networks.

Green plants harvest the energy of the Sun in the leaves by converting light energy into chemical energy in the bonds of sugar molecules, using water from the soil and carbon dioxide from the air. This review provides an overview of the vascular anatomy of plants and the physical models that describe the long-distance transport of water and minerals from root to leaf, and, in particular, of sugars from the leaves to the entire body of the plant sustaining growth and communication throughout even the tallest tree.

In the standard model of particle physics, the strong and weak interaction eigenstates of the three generations of quarks differ and are related by the unitary Cabibbo-Kobayashi-Maskawa matrix. This article reviews measurements of the decays of the mesons containing a bottom quark into final states with leptons. These measurements provide determinations of the matrix elements and other observables, and offer constraints on the standard model as well as pointers to possible new physics.

This review article contains the 2014 self-consistent set of values of the constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA). The CODATA values are based on a least-squares adjustment that that takes into account all data available up to the end of 2014. Details of the data selection and methodology are described.