Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

A comparison of two identification and tracking methods for polar lows

In this study, we compare two different cyclone-tracking algorithms to detect North Atlantic polar lows, which are very intense mesoscale cyclones. Both approaches include spatial filtering, detection, tracking and constraints specific to polar lows. The first method uses digital bandpass-filtered mean sea level pressure (MSLP) fieldsin the spatial range of 200�600 km and is especially designed for polar lows. The second method also uses a bandpass filter but is based on the discrete cosine transforms (DCT) and can be applied to MSLP and vorticity fields. The latter was originally designed for cyclones in general and has been adapted to polar lows for this study. Both algorithms are applied to the same regional climate model output fields from October 1993 to September 1995 produced from dynamical downscaling of the NCEP/NCAR reanalysis data. Comparisons between these two methods show that different filters lead to different numbers and locations of tracks. The DCT is more precise in scale separation than the digital filter and the results of this study suggest that it is more suited for the bandpass filtering of MSLP fields. The detection and tracking parts also influence the numbers of tracks although less critically. After a selection process that applies criteria to identify tracks of potential polar lows, differences between both methods are still visible though the major systems are identified in both.

Quantifying volcanic ash dispersal and impact of the Campanian Ignimbrite super-eruption

1] We apply a novel computational approach to assess, for the first time, volcanic ash dispersal during the Campanian Ignimbrite (Italy) super-eruption providing insights into eruption dynamics and the impact of this gigantic event. The method uses a 3D time-dependent computational ash dispersion model, a set of wind fields, and more than 100 thickness measurements of the CI tephra deposit. Results reveal that the CI eruption dispersed 250–300 km3 of ash over ∼3.7 million km2. The injection of such a large quantity of ash (and volatiles) into the atmosphere would have caused a volcanic winter during the Heinrich Event 4, the coldest and driest climatic episode of the Last Glacial period. Fluorine-bearing leachate from the volcanic ash and acid rain would have further affected food sources and severely impacted Late Middle-Early Upper Paleolithic groups in Southern and Eastern Europe

High leverage interventions: three cases of defensive action and their lessons for OR/MS today.

This paper has two aims. First, to present cases in which scientists developed a defensive system for their homeland: Blackett and the air defense of Britain in WWII, Forrester and the SAGE system for North America in the Cold War, and Archimedes’ work defending Syracuse during the Second Punic War. In each case the historical context and the individual’s other achievements are outlined, and a description of the contribution’s relationship to OR/MS is given. The second aim is to consider some of the features the cases share and examine them in terms of contemporary OR/MS methodology. Particular reference is made to a recent analysis of the field’s strengths and weaknesses. This allows both a critical appraisal of the field and a set of potential responses for strengthening it. Although a mixed set of lessons arise, the overall conclusion is that the cases are examples to build on and that OR/MS retains the ability to do high stakes work.

Conflict resolution in overlapping information fields for context-based activity design

Norms are a set of rules that govern the behaviour of human agent, and how human agent behaves in response to the given certain conditions. This paper investigates the overlapping of information fields (set of shared norms) in the Context State Transition Model, and how these overlapping fields may affect the choices and actions of human agent. This paper also includes discussion on the implementation of new conflict resolution strategies based on the situation specification. The reasoning about conflicting norms in multiple information fields is discussed in detail.)

The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Releasing of pheasants for shooting in the UK alters woodland invertebrate communities

The management of pheasants (Phasianus colchicus) in pens and their subsequent release within woodland for game shoots is widely practised in Britain. With the exception of ground flora and songbirds, the impacts on other taxa have not been well documented. We investigated the effects of pheasants on invertebrate abundance and community composition, using pitfall trapping. We compared release pens with control plots located in the same woods and in woods where no pheasant releasing had occurred for at least 25 years. Conditions for invertebrates within release pens were altered, with more annual plants and disturbance-tolerant perennials and a reduced leaf litter layer. No major differences in invertebrate abundance, or Carabidae or Staphylinidae richness, were found in spring at either the pen scale or the wood scale. However, pheasant release pens resulted in significant changes in the species composition of Carabidae, with shifts towards species typical of arable fields and grassland. Carabid species active in spring and those that are very large (N17.0 mm) declined at pheasant release densities higher than 1000 birds/ha. Both effects are likely to be due to predation by pheasants at the peak of release in July–August, operating separately on larvae and adults respectively. There was an overall increase in the abundance of detritivores, including Diplopoda, Oniscoidea, Gastropoda (snails), at higher release densities. Mean release density in our study was 1489 ± 126 birds/ha (range 174–3409, n = 37 pens) and we suggest that detrimental effects on specialist woodland invertebrates would be minimized if releasing was conducted at the recommended density of 700 birds/ha.

Standing on the shoulders of giants: an examination of the interdisciplinary foundation of relationship marketing

In the 20th century, the scholarly study of human relationships both grew dramatically and simultaneously fragmented into various disciplines and subdisciplines. Although diversity of thought is generally considered helpful for the evolution of scientific fields, the value accrued from interdisciplinary discourse depends on the ability of scholars to integrate multiple perspectives and synthesize foundational works in a systematic manner. The goal of this study is to synthesize foundational theories from social and behavioral sciences that have contributed to an understanding of relationship marketing. In seeking to provide a holistic understanding of the field, we incorporate contributions from the disciplines of marketing, management, psychology, and sociology. In building on our analysis, we synthesize our findings into a conceptual model that examines the systematic dimensions of relationship marketing. The article concludes by identifying key themes for contributors to the Journal of Relationship Marketing to consider going forward.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

New perspectives on the Northern Hemisphere winter storm tracks

The aim of this paper is to explore the use of both an Eulerian and system-centered method of storm track diagnosis applied to a wide range of meteorological fields at multiple levels to provide a range of perspectives on the Northern Hemisphere winter transient motions and to give new insight into the storm track organization and behavior. The data used are primarily from the European Centre for Medium-Range Weather Forecasts reanalyses project extended with operational analyses to the period 1979-2000. This is supplemented by data from the National Centers for Environmental Prediction and Goddard Earth Observing System 1 reanalyses. The range of fields explored include the usual mean sea level pressure and the lower- and upper-tropospheric height, meridional wind, vorticity, and temperature, as well as the potential vorticity (PV) on a 330-K isentropic surface (PV330) and potential temperature on a PV = 2 PVU surface (theta(PV2)). As well as reporting the primary analysis based on feature tracking, the standard Eulerian 2-6-day bandpass filtered variance analysis is also reported and contrasted with the tracking diagnostics. To enable the feature points to be identified as extrema for all the chosen fields, a planetary wave background structure is removed at each data time. The bandpass filtered variance derived from the different fields yield a rich picture of the nature and comparative magnitudes of the North Pacific and Atlantic storm tracks, and of the Siberian and Mediterranean candidates for storm tracks. The feature tracking allows the cyclonic and anticyclonic activities to be considered seperately. The analysis indicates that anticyclonic features are generally much weaker with less coherence than the cyclonic systems. Cyclones and features associated with them are shown to have much greater coherence and give tracking diagnostics that create a vivid storm track picture that includes the aspects highlighted by the variances as well as highlighting aspects that are not readily available from Eulerian studies. In particular, the upper-tropospheric features as shown by negative theta(PV2), for example, occur in a band spiraling around the hemisphere from the subtropical North Atlantic eastward to the high latitudes of the same ocean basin. Lower-troposphere storm tracks occupy more limited longitudinal sectors, with many of the individual storms possibly triggered from the upper-tropospheric disturbances in the spiral band of activity.

Teleconnections between Ethiopian summer rainfall and sea surface temperature: part I. Observation and modelling

In this study, the oceanic regions that are associated with anomalous Ethiopian summer rains were identified and the teleconnection mechanisms that give rise to these associations have been investigated. Because of the complexities of rainfall climate in the horn of Africa, Ethiopia has been subdivided into six homogeneous rainfall zones and the influence of SST anomalies was analysed separately for each zone. The investigation made use of composite analysis and modelling experiments. Two sets of composites of atmospheric fields were generated, one based on excess/deficit rainfall anomalies and the other based on warm/cold SST anomalies in specific oceanic regions. The aim of the composite analysis was to determine the link between SST and rainfall in terms of large scale features. The modelling experiments were intended to explore the causality of these linkage. The results show that the equatorial Pacific, the midlatitude northwest Pacific and the Gulf of Guinea all exert an influence on the summer rainfall in various part of the country. The results demonstrate that different mechanisms linked to sea surface temperature control variations in rainfall in different parts of Ethiopia. This has important consequences for seasonal forecasting models which are based on statistical correlations between SST and seasonal rainfall totals. It is clear that such statistical models should take account of the local variations in teleconnections.