Dynamics of bootstrap percolation

Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed transition is characterized by power law avalanches, while the continuous transition is characterized by truncated avalanches in a related sequential bootstrap process. We explain this behavior on the basis of a through analytical and numerical study of the avalanche distributions on a Bethe lattice.Comment: Proceedings of the International Workshop and Conference on Statistical Physics Approaches to Multidisciplinary Problems, IIT Guwahati, India, 7-13 January 200

Bayes linear kinematics in the analysis of failure rates and failure time distributions

Collections of related Poisson or binomial counts arise, for example, from a number of different failures in similar machines or neighbouring time periods. A conventional Bayesian analysis requires a rather indirect prior specification and intensive numerical methods for posterior evaluations. An alternative approach using Bayes linear kinematics in which simple conjugate specifications for individual counts are linked through a Bayes linear belief structure is presented. Intensive numerical methods are not required. The use of transformations of the binomial and Poisson parameters is proposed. The approach is illustrated in two examples, one involving a Poisson count of failures, the other involving a binomial count in an analysis of failure times

The neural correlates of emotion regulation by implementation intentions

Several studies have investigated the neural basis of effortful emotion regulation (ER) but the neural basis of automatic ER has been less comprehensively explored. The present study investigated the neural basis of automatic ER supported by ‘implementation intentions’. 40 healthy participants underwent fMRI while viewing emotion-eliciting images and used either a previously-taught effortful ER strategy, in the form of a goal intention (e.g., try to take a detached perspective), or a more automatic ER strategy, in the form of an implementation intention (e.g., “If I see something disgusting, then I will think these are just pixels on the screen!”), to regulate their emotional response. Whereas goal intention ER strategies were associated with activation of brain areas previously reported to be involved in effortful ER (including dorsolateral prefrontal cortex), ER strategies based on an implementation intention strategy were associated with activation of right inferior frontal gyrus and ventro-parietal cortex, which may reflect the attentional control processes automatically captured by the cue for action contained within the implementation intention. Goal intentions were also associated with less effective modulation of left amygdala, supporting the increased efficacy of ER under implementation intention instructions, which showed coupling of orbitofrontal cortex and amygdala. The findings support previous behavioural studies in suggesting that forming an implementation intention enables people to enact goal-directed responses with less effort and more efficiency

Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model

The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is observed that the time-dependent solutions of the derived dynamical systems obtained by the perturbation analysis become systematically closer to the results obtained by Monte Carlo simulations as the order of a perturbation series is increased. This systematic perturbation analysis also clarifies the existence of a dynamical scaling law, which provides a implication for a universal relation between a size scale and a time scale near the nonergodic transition.Comment: 17 pages, 7 figures, v2; results have been refined, v3; A figure has been modified, v4; results have been more refine

Reducing MCPA herbicide pollution at catchment scale using an agri-environmental scheme

Publication history: Accepted - 16 May 2022; Published online - 20 May 2022.In river catchments used as drinking water sources, high pesticide concentrations in abstracted waters require an expensive treatment step prior to supply. The acid herbicide 2-methyl-4-chlorophenoxyacetic acid (MCPA) is particularly problematic as it is highly mobile in the soil-water environment following application. Here, an agri-environmental scheme (AES) was introduced to a large-scale catchment (384 km2) to potentially reduce the burden of pesticides in the water treatment process. The main measure offered was contractor application of glyphosate by weed wiping as a substitute for boom spraying of MCPA, supported by educational and advisory activities. A combined innovation applied in the assessment was, i) a full before-after-control-impact (BACI) framework over four peak application seasons (April to October 2018 to 2021) where a neighbouring catchment (386 km2) did not have an AES and, ii) an enhanced monitoring approach where river discharge and MCPA concentrations were measured synchronously in each catchment. During peak application periods the sample resolution was every 7 h, and daily during quiescent winter periods. This sampling approach enabled flow- and time-weighted concentrations to be established, and a detailed record of export loads. These loads were up to 0.242 kg km−2 yr−1, and over an order of magnitude higher than previously reported in the literature. Despite this, and accounting for inter-annual and seasonal variations in river discharges, the AES catchment indicated a reduction in both flow- and time-weighted MCPA concentration of up to 21% and 24%, respectively, compared to the control catchment. No pollution swapping was detected. Nevertheless, the percentage of MCPA occurrences above a 0.1 μg L−1 threshold did not reduce and so the need for treatment was not fully resolved. Although the work highlights the advantages of catchment management approaches for pollution reduction in source water catchments, it also indicates that maximising participation will be essential for future AES.This work was carried out as part of Source to Tap (IVA5018), a project supported by the European Union's INTERREG VA Programme, managed by the Special EU Programmes Body (SEUPB)

The neural correlates of regulating another person's emotions: an exploratory fMRI study

Studies investigating the neurophysiological basis of intrapersonal emotion regulation (control of one's own emotional experience) report that the frontal cortex exerts a modulatory effect on limbic structures such as the amygdala and insula. However, no imaging study to date has examined the neurophysiological processes involved in interpersonal emotion regulation, where the goal is explicitly to regulate another person's emotion. Twenty healthy participants (10 males) underwent fMRI while regulating their own or another person's emotions. Intrapersonal and interpersonal emotion regulation tasks recruited an overlapping network of brain regions including bilateral lateral frontal cortex, pre-supplementary motor area, and left temporo-parietal junction. Activations unique to the interpersonal condition suggest that both affective (emotional simulation) and cognitive (mentalizing) aspects of empathy may be involved in the process of interpersonal emotion regulation. These findings provide an initial insight into the neural correlates of regulating another person's emotions and may be relevant to understanding mental health issues that involve problems with social interaction

Local structural studies of Ba1−x_{1-x}Kx_xFe2_2As2_2 using atomic pair distribution function analysis

Systematic local structural studies of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system are undertaken at room temperature using atomic pair distribution function (PDF) analysis. The local structure of the Ba$_{1-x}$K$_x$Fe$_2$As$_2$ is found to be well described by the long-range structure extracted from the diffraction experiments, but with anisotropic atomic vibrations of the constituent atoms ($U_{11}$ = $U_{22} \ne U_{33}$). The crystal unit cell parameters, the FeAs$_4$ tetrahedral angle and the pnictogen height above the Fe-plane are seen to show systematic evolution with K doping, underlining the importance of the structural changes, in addition to the charge doping, in determining the properties of Ba$_{1-x}$K$_x$Fe$_2$As$_2$

Cross sections for ionization and excitation in the two-photon transitions of CO B-X(0,0)

High-resolution spectroscopy of CO B-X is being performed to measure cross sections for the processes of two-photon absorption and ionization that underlie two methods often used for sensitive detection of CO in flames, namely, two-photon LIF and 2+1 resonance-enhanced multiphoton ionization (REMPI) via B(v=0). The use of multiphoton excitation is, for even LIF diagnostics, a practical necessity since the allowed one-photon transitions from CO X(v=0) begin at 152 nm. Two 230-nm photons, however, promotes transitions within B{l_arrow}X(0,0); detection in LIF then proceeds by collecting blue to green fluorescence in the Angstrom bands (B{r_arrow}A). In 2+1 REMPI, the ions (or electrons) are monitored as produced by a third ionizing photon at 230 nm that connects B(v=0) to the continuum. The signals acquired with either technique depend on the two-photon excitation rate and also on the ionization rate - a gain in REMPI signal from increased ionization is a loss to LIF in the manner of quenching. The authors have found no direct measurement of the ionization cross section of CO-B in the literature, in that all reported cross sections are extracted from measured trends of REMPI or fluorescence signals versus laser. A rate-equation analysis of a multi-level system was the usual model, with cross sections for intensity, two-photon absorption and ionization varied for best match with the measured trends. Further, only one such study, that of Looney et al., has offered a cross section for the photo-ionization of CO-B at 230 nm

Evaluation of elicitation methods to quantify Bayes linear models

The Bayes linear methodology allows decision makers to express their subjective beliefs and adjust these beliefs as observations are made. It is similar in spirit to probabilistic Bayesian approaches, but differs as it uses expectation as its primitive. While substantial work has been carried out in Bayes linear analysis, both in terms of theory development and application, there is little published material on the elicitation of structured expert judgement to quantify models. This paper investigates different methods that could be used by analysts when creating an elicitation process. The theoretical underpinnings of the elicitation methods developed are explored and an evaluation of their use is presented. This work was motivated by, and is a precursor to, an industrial application of Bayes linear modelling of the reliability of defence systems. An illustrative example demonstrates how the methods can be used in practice