On the limits of top-down control of visual selection

In the present study, observers viewed displays in which two equally salient color singletons were simultaneously present. Before each trial, observers received a word cue (e.g., the word red, or green) or a symbolic cue (a circle colored red or green) telling them which color singleton to select on the upcoming trial. Even though many theories of visual search predict that observers should be able to selectively attend the target color singleton, the results of the present study show that observers could not select the target singleton without interference from the irrelevant color singleton. The results indicate that the irrelevant color singleton captured attention. Only when the color of the target singleton remained the same from one trial to the next was selection perfect—an effect that is thought to be the result of passive automatic intertrial priming. The results of the present study demonstrate the limits of top-down attentional control

Optimising and Communicating Options for the Control of Invasive Plant Disease When There Is Epidemiological Uncertainty

<div><p>Although local eradication is routinely attempted following introduction of disease into a new region, failure is commonplace. Epidemiological principles governing the design of successful control are not well-understood. We analyse factors underlying the effectiveness of reactive eradication of localised outbreaks of invading plant disease, using citrus canker in Florida as a case study, although our results are largely generic, and apply to other plant pathogens (as we show via our second case study, citrus greening). We demonstrate how to optimise control via removal of hosts surrounding detected infection (i.e. localised culling) using a spatially-explicit, stochastic epidemiological model. We show how to define optimal culling strategies that take account of stochasticity in disease spread, and how the effectiveness of disease control depends on epidemiological parameters determining pathogen infectivity, symptom emergence and spread, the initial level of infection, and the logistics and implementation of detection and control. We also consider how optimal culling strategies are conditioned on the levels of risk acceptance/aversion of decision makers, and show how to extend the analyses to account for potential larger-scale impacts of a small-scale outbreak. Control of local outbreaks by culling can be very effective, particularly when started quickly, but the optimum strategy and its performance are strongly dependent on epidemiological parameters (particularly those controlling dispersal and the extent of any cryptic infection, i.e. infectious hosts prior to symptoms), the logistics of detection and control, and the level of local and global risk that is deemed to be acceptable. A version of the model we developed to illustrate our methodology and results to an audience of stakeholders, including policy makers, regulators and growers, is available online as an interactive, user-friendly interface at <a href="http://www.webidemics.com/" target="_blank">http://www.webidemics.com/</a>. This version of our model allows the complex epidemiological principles that underlie our results to be communicated to a non-specialist audience.</p></div

Definition of symbols and default values of parameters (based on values from [11,12,24,25,29,30]).

<p>Definition of symbols and default values of parameters (based on values from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref011" target="_blank">11</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref012" target="_blank">12</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref024" target="_blank">24</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref025" target="_blank">25</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref029" target="_blank">29</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref030" target="_blank">30</a>]).</p

Local vs. global control.

<p>(a) Epidemic time (τ_<i>E</i>); i.e. the time for the epidemic to be controlled, as a function of the cull radius <i>L</i>. The black dots on the x-axis mark <i>L</i> = 159m, the cull radius at which the median epidemic impact (κ_<i>E</i>) is minimised, and <i>L</i> = 63m, the radius at which the median epidemic time (τ_<i>E</i>) is maximised. (b) Normalised epidemic cost (</p><p></p><p></p><p></p><p><mo>ψ</mo><mi>E</mi></p>= ​​(1-η) <p></p><p><mi>κ</mi><mo>^</mo></p><mi>E</mi><p></p> + η <p></p><p><mi>τ</mi><mo>^</mo></p><mi>E</mi><p></p><p></p><p></p><p></p>) for a number of values of the weighting factor, η. <p></p><p></p><p></p><p></p><p><mi>κ</mi><mo>^</mo></p><mi>E</mi><p></p><p></p><p></p><p></p> and <p></p><p></p><p></p><p></p><p><mi>τ</mi><mo>^</mo></p><mi>E</mi><p></p><p></p><p></p><p></p> are the epidemic impact and epidemic time normalised according to their maximum values over all cull radii considered, whereas η controls the relative weighting given to potential global impacts of the epidemic outside the area of immediate interest. The inset shows the value of <i>L</i> at which the minimum Ψ_<i>E</i> is obtained as a function of η. As global impacts are increasingly weighted (<i>η</i> → 1), the optimum cull radius increases, despite the increased number of local removals that would then result. (c) Area under the disease progress curve (<i>A</i>_<i>E</i>) as a function of cull radius, <i>L</i>. The inset shows the logarithm of <i>A</i>_<i>E</i> as <i>L</i> is changed. (d) The probability of escape, <i>p</i>_<i>E</i>, as function of the cull radius, <i>L</i>, for different values of the connectivity parameter λ. (e) Normalised epidemic cost (<p></p><p></p><p></p><p><mi>ζ</mi><mi>E</mi></p>= <mo>​</mo><mo>​</mo>(1-<mi>δ</mi>) <p></p><p><mi>κ</mi><mo>^</mo></p><mi>E</mi><p></p> + <mi>δ</mi> <p></p><p><mi>p</mi><mo>^</mo></p><mi>E</mi><p></p><p></p><p></p><p></p>) in which the probability of escape rather than the time until eradication is included, for a number of values of the weighting factor, δ, and for fixed connectivity parameter λ = 10^-5 d^-1. The inset shows the value of <i>L</i> at which the optimum ζ_<i>E</i> is obtained for 0 ≤ δ ≤ 1. (f) Robustness to the value of λ. The inset to panel (e) is repeated for a number of values of λ; as potential global impacts are increasingly weighted (<i>δ</i> → 1), the optimal cull radius again becomes larger, for each value of λ we consider.<p></p

The epidemiological model.

<p>(a) Transitions between compartments: (S)usceptible, (E)xposed, (C)ryptic or (D)etectable, (I)nfected and (R)emoved. (b) Markov chain model for environmental conditions; a transition occurs every <i>T</i>_<i>w</i> units of time.</p

Effect of epidemiological and logistic factors on control.

<p>(a),(c),(e) and (g): Responses of median epidemic impact (κ_<i>E</i>) to cull radius (<i>L</i>) for different values of probability of detection, <i>p</i> (a), the average cryptic period, 1/<i>σ</i> (c), the interval between successive surveys, <i>T</i>_<i>s</i> (e) and the notice period before culling, <i>T</i>_<i>c</i> (g). (b), (d), (f) and (h): How the performance of the optimum control strategy is affected by changes in <i>p</i> (b), 1/<i>σ</i> (d), <i>T</i>_<i>s</i> (f) and <i>T</i>_<i>c</i> (h). Insets show the response of the optimum cull radius <i>L</i>. Default parameter values were used for all parameters except that being scanned over: these are marked with black dots on the x-axis in (b), (d), (f) and (h).</p

Stochasticity and the effectiveness of a single control scenario as presented via the Webidemics interface.

<p>(a) Successful control, with fewer than 10% of hosts removed before the pathogen was eradicated after 790 days. (b) A larger and more long-lasting epidemic, with ~90% removal before eradication at 4300 days. Parameters controlling pathogen epidemiology and the control intervention were the same for both runs (default values; <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.t001" target="_blank">Table 1</a>). (c) Histograms summarising the final state in an ensemble of 500 runs (of which the individual simulation runs shown in (a) and (b) were part); note the variability in the number of healthy hosts unaffected by disease or control by the time of eradication.</p

The online front-end (available at http://www.webidemics.com/).

<p>(a) A single realisation. (b) An ensemble of realisations. (c) Parameter selection. The time axis of the graph in the single realisation view colour codes environmental conditions (suitable for transmission is red, unsuitable is blue).</p

Optimal control when there is uncertainty.

<p>(a) Epidemic impact κ_<i>E</i> (total number of hosts lost to disease or control) as a function of the cull radius, <i>L</i>. The optimum value of <i>L</i> depends on the percentile of the distribution of κ_<i>E</i> that is being optimised (e.g. the optimum <i>L</i> would be 159m if the objective were to minimise median κ_<i>E</i>, whereas it would be 194m if minimising κ_<i>E</i> on the 95^th percentile). The shape of the distribution of κ_<i>E</i> varies with <i>L</i> (insets A to F; distributions renormalized to the same height by scaling all distributions relative to the largest value in each). (b) Risk of failure. Given a notion of “acceptable risk” (i.e. a value of Ω, the threshold κ_<i>E</i> as a percentage of the total population), the probability of failing to achieve κ_<i>E</i> < Ω is shown. Dotted line marks radii with < 10% risk of failure for Ω = 20% (range 122m < <i>L</i> < 329m). (c) Effect of the initial level of infection, E₀, on the response of median κ_<i>E</i> to <i>L</i> (dots show minimum median κ_<i>E</i> for each E₀). (d) and (e) Effect of the scale of dispersal (<i>α</i>) and rate of infection (<i>β</i>) on the optimal <i>L</i> (shown in d) and median κ_<i>E</i> at optimal <i>L</i> to optimise median κ_<i>E</i> (shown in e). The white dots on (d) and (e) indicate the default values of <i>α</i> and <i>β</i>; the white squares show the values of <i>α</i> and <i>β</i> fitted by Cook <i>et al</i>. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref024" target="_blank">24</a>] (and used in the studies of Parnell <i>et al</i>. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref011" target="_blank">11</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref012" target="_blank">12</a>]) <i>cf</i>. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.s003" target="_blank">S3 Text</a>.</p

The underlying model and typical results without control.

<p>(a) The compartmental structure of the (S)usceptible, (E)xposed, (I)nfected, (R)emoved model. (b) Spread of disease in a typical grove when there is no control, showing the number of asymptomatic plants within the central grove () as a function of time, , starting with 1% of hosts (i.e. 17 plants) exposed to the pathogen at , and sampling parameters randomly on each run independently from the joint posterior parameter distribution obtained in model fitting. The density of shading shows the distribution of at each value of (1000 independent simulations). Breaks between different colours are at the and percentiles, with the percentile marked by the black curve. (c) Snapshots of disease spread from the single realisation shown by the red curve in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003753#pcbi-1003753-g001" target="_blank">Figure 1(b)</a>; green corresponds to healthy trees (S), blue to trees that have been infected but are not yet infectious (E), and red to trees that are able to infect other trees (I). Since there is no control, no trees enter the (R)emoved compartment.</p