Bridging the gap between agent based models and continuous opinion dynamics

There is a rich literature on microscopic models for opinion dynamics; most of them fall into one of two categories - agent-based models or differential equation models - with a general understanding that the two are connected in certain scaling limits. In this paper we show rigorously this is indeed the case. In particular we show that DEMs can be obtained from ABMs by simultaneously rescaling time and the distance an agent updates their opinion after an interaction. This approach provides a pathway to analyse much more diverse modelling paradigms, for example: the motivation behind several possible multiplicative noise terms in stochastic differential equation models; the connection between selection noise and the mollification of the discontinuous bounded confidence interaction function; and how the method for selecting interacting pairs can determine the normalisation in the corresponding differential equation. Our computational experiments confirm our findings, showing excellent agreement of solutions to the two classes of models in a variety of settings

Single-Shot Electron Diffraction using a Cold Atom Electron Source

Cold atom electron sources are a promising alternative to traditional photocathode sources for use in ultrafast electron diffraction due to greatly reduced electron temperature at creation, and the potential for a corresponding increase in brightness. Here we demonstrate single-shot, nanosecond electron diffraction from monocrystalline gold using cold electron bunches generated in a cold atom electron source. The diffraction patterns have sufficient signal to allow registration of multiple single-shot images, generating an averaged image with significantly higher signal-to-noise ratio than obtained with unregistered averaging. Reflection high-energy electron diffraction (RHEED) was also demonstrated, showing that cold atom electron sources may be useful in resolving nanosecond dynamics of nanometre scale near-surface structures.Comment: This is an author-created, un-copyedited version of an article published in Journal of Physics B: Atomic, Molecular and Optical Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0953-4075/48/21/21400

Scenario Planning for Building Coastal Resilience in the Face of Sea Level Rise: The Case of Jacobs Avenue, Eureka, CA

This article examines issues surrounding flood control measures for the Jacobs Avenue community located in Eureka, California. This area of northern California is experiencing some of the most rapid rates of sea level rise recorded throughout the state. Researchers conducted interviews with stakeholders, developed geospatial analyses, and reviewed policy documents in order to understand the social, environmental, and political context related to sea level rise planning for Jacobs Avenue. From this information we developed a scenario-based set of management options to guide stakeholders in future decision-making regarding the fate of Jacobs Avenue. We explored the potential challenges and benefits of three possible scenarios: no action, levee improvement, and strategic retreat. Our analysis reveals that there are no easy solutions. Lack of funding and lack of a clear political path towards retreat make it extremely difficult for planners to take proactive steps that might ultimately contribute to increased safety, as well as economic and environmental benefits, for flood-vulnerable communities. The scenario framework developed in this paper can be a useful tool for a wide range of coastal communities, in particular those of geographically isolated northern California and southern Oregon

Scenario Planning for Building Coastal Resilience in the Face of Sea Level Rise: The Case of Jacobs Avenue, Eureka, CA

This article examines issues surrounding flood control measures for the Jacobs Avenue community located in Eureka, California. This area of northern California is experiencing some of the most rapid rates of sea level rise recorded throughout the state. Researchers conducted interviews with stakeholders, developed geospatial analyses, and reviewed policy documents in order to understand the social, environmental, and political context related to sea level rise planning for Jacobs Avenue. From this information we developed a scenario-based set of management options to guide stakeholders in future decision-making regarding the fate of Jacobs Avenue. We explored the potential challenges and benefits of three possible scenarios: no action, levee improvement, and strategic retreat. Our analysis reveals that there are no easy solutions. Lack of funding and lack of a clear political path towards retreat make it extremely difficult for planners to take proactive steps that might ultimately contribute to increased safety, as well as economic and environmental benefits, for flood-vulnerable communities. The scenario framework developed in this paper can be a useful tool for a wide range of coastal communities, in particular those of geographically isolated northern California and southern Oregon

Late-Time Spectral Observations of the Strongly Interacting Type Ia Supernova PTF11kx

PTF11kx was a Type Ia supernova (SN Ia) that showed time-variable absorption features, including saturated Ca II H&K lines that weakened and eventually went into emission. The strength of the emission component of H{\alpha} increased, implying that the SN was undergoing significant interaction with its circumstellar medium (CSM). These features were blueshifted slightly and showed a P-Cygni profile, likely indicating that the CSM was directly related to, and probably previously ejected by, the progenitor system itself. These and other observations led Dilday et al. (2012) to conclude that PTF11kx came from a symbiotic nova progenitor like RS Oph. In this work we extend the spectral coverage of PTF11kx to 124-680 rest-frame days past maximum brightness. These spectra of PTF11kx are dominated by H{\alpha} emission (with widths of ~2000 km/s), strong Ca II emission features (~10,000 km/s wide), and a blue "quasi-continuum" due to many overlapping narrow lines of Fe II. Emission from oxygen, He I, and Balmer lines higher than H{\alpha} is weak or completely absent at all epochs, leading to large observed H{\alpha}/H{\beta} intensity ratios. The broader (~2000 km/s) H{\alpha} emission appears to increase in strength with time for ~1 yr, but it subsequently decreases significantly along with the Ca II emission. Our latest spectrum also indicates the possibility of newly formed dust in the system as evidenced by a slight decrease in the red wing of H{\alpha}. During the same epochs, multiple narrow emission features from the CSM temporally vary in strength. The weakening of the H{\alpha} and Ca II emission at late times is possible evidence that the SN ejecta have overtaken the majority of the CSM and agrees with models of other strongly interacting SNe Ia. The varying narrow emission features, on the other hand, may indicate that the CSM is clumpy or consists of multiple thin shells.Comment: 12 pages, 7 figures, 1 table, re-submitted to Ap

Exploring the role of the potential surface in the behaviour of early warning signals

The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system’s potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up