Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group, we explore synchronization patterns that emerge from the phase-shift invariance of the dynamical equations and symmetries in the nodes. We show that these nonstructural symmetries simplify stability calculations. We analyze a ring-network of phase-amplitude oscillators that exhibits a "decoupled" state in which physically-coupled nodes appear to act independently due to emergent cancellations in the equations of dynamical evolution. We establish that this state can be linearly stable for a ring of phase-amplitude oscillators, but not for a ring of phase-only oscillators that otherwise require explicit long-range, nonpairwise, or nonphase coupling. In short, amplitude-phase interactions are key to stable synchronization at a distance.

As states, cities, tribes, and private interests cope with climate damages and seek to increase preparedness and resilience, they will need to navigate myriad choices and options available to them. Making these choices in ways that identify pathways for climate action that support their development objectives will require constructive public dialogue, community participation, and flexible and ongoing access to science- and experience-based knowledge. In 2016, a Federal Advisory Committee (FAC) was convened to recommend how to conduct a sustained National Climate Assessment (NCA) to increase the relevance and usability of assessments for informing action. The FAC was disbanded in 2017, but members and additional experts reconvened to complete the report that is presented here. A key recommendation is establishing a new nonfederal ‘‘climate assessment consortium’’ to increase the role of state/local/tribal government and civil society in assessments. The expanded process would 1) focus on applied problems faced by practitioners, 2) organize sustained partnerships for collaborative learning across similar projects and case studies to identify effective tested practices, and 3) assess and improve knowledge-based methods for project implementation. Specific recommendations include evaluating climate models and data using user-defined metrics; improving benefit–cost assessment and supporting decision-making under uncertainty; and accelerating application of tools and methods such as citizen science, artificial intelligence, indicators, and geospatial analysis. The recommendations are the result of broad consultation and present an ambitious agenda for federal agencies, state/local/tribal jurisdictions, universities and the research sector, professional associations, nongovernmental and community-based organizations, and private-sector firms.

The Supernova / Acceleration Probe (SNAP) is a proposed space-based experiment designed to study the dark energy and alternative explanations of the acceleration of the Universe's expansion by performing a series of complementary systematics-controlled measurements. We describe a self-consistent reference mission design for building a Type Ia supernova Hubble diagram and for performing a wide-area weak gravitational lensing study. A 2-m wide-field telescope feeds a focal plane consisting of a 0.7 square-degree imager tiled with equal areas of optical CCDs and near infrared sensors, and a high-efficiency low-resolution integral field spectrograph. The SNAP mission will obtain high-signal-to-noise calibrated light-curves and spectra for several thousand supernovae at redshifts between z=0.1 and 1.7. A wide-field survey covering one thousand square degrees resolves ~100 galaxies per square arcminute. If we assume we live in a cosmological-constant-dominated Universe, the matter density, dark energy density, and flatness of space can all be measured with SNAP supernova and weak-lensing measurements to a systematics-limited accuracy of 1%. For a flat universe, the density-to-pressure ratio of dark energy can be similarly measured to 5% for the present value w0 and ~0.1 for the time variation w'. The large survey area, depth, spatial resolution, time-sampling, and nine-band optical to NIR photometry will support additional independent and/or complementary dark-energy measurement approaches as well as a broad range of auxiliary science programs. (Abridged)