Stability of Normal Bundles of Space Curves

In this paper, we prove that the normal bundle of a general Brill-Noether space curve of degree $d$ and genus $g \geq 2$ is stable if and only if $(d,g) \not\in \{ (5,2), (6,4) \}$. When $g\leq1$ and the characteristic of the ground field is zero, it is classical that the normal bundle is strictly semistable. We show that this fails in characteristic $2$ for all rational curves of even degree

The normal bundle of a general canonical curve of genus at least 7 is semistable

No description supplie

The four sessions for the two different training groups (categorical and non-categorical) used different levels of audio-visual feedback.

<p>The four sessions for the two different training groups (categorical and non-categorical) used different levels of audio-visual feedback.</p

Participant performance in terms of percent of performance (targets reached; A) and time to target (reaction time; B) are shown for established categories with auditory and text cues (blue and white striped; EC–AT), established categories with only auditory cues (black; EC–A), and new categories (red; NC).

<p>While the time-to-target data did not show differences between training schemes, the percent correct performance showed significant differences across training groups: the EC-AT group performance was significantly higher than the EC-A and NC groups (both <i>p_adj</i> <0.002). There was a trend for an interaction between session and training group, suggesting that categorical vowel perception aided participants in utilizing and generalizing auditory feedback (third and fourth sessions). Error bars show ± 1 standard error.</p

Categorical (red) and non-categorical (dark blue) vowel targets are shown by their designated ellipses in the formant (F1–F2) plane.

<p>Categorical vowels were assigned exemplar words that were shown in the center of the ellipse or center of the screen for the established categories text cue (EC-AT) group, depending on the session, to cue the participant which vowel sound to produce. Solid ellipses designate the vowel targets trained and tested in the first three sessions, while the dashed ellipses designate novel (untrained) vowel targets participants had to generalize to in the final (fourth) session.</p

The sEMG signal used to control human-machine-interface operation was obtained from electrodes placed on the left and right orbicularis oris muscles of each participant, who then underwent training phases to become accustomed to controlling the synthesized vowel production caused by activating the left and right muscles.

<p>The sEMG signal used to control human-machine-interface operation was obtained from electrodes placed on the left and right orbicularis oris muscles of each participant, who then underwent training phases to become accustomed to controlling the synthesized vowel production caused by activating the left and right muscles.</p

Specifications for occupancy (Ψ) and detection probability (<i>P</i>) modeling using environmental DNA (eDNA) for the Black Warrior Waterdog (<i>Necturus alabamensis</i>) and Flattened Musk Turtle (<i>Sternotherus depressus</i>), with ΔAIC and model weights (<i>w</i>) for the ten most supported models and all other considered models combined.

<p>Models with ΔAIC ≤2 are denoted with *. Predictor abbreviations are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0165273#pone.0165273.t001" target="_blank">Table 1</a>.</p

Environmental DNA (eDNA) Detection Probability Is Influenced by Seasonal Activity of Organisms

<div><p>Environmental DNA (eDNA) holds great promise for conservation applications like the monitoring of invasive or imperiled species, yet this emerging technique requires ongoing testing in order to determine the contexts over which it is effective. For example, little research to date has evaluated how seasonality of organism behavior or activity may influence detection probability of eDNA. We applied eDNA to survey for two highly imperiled species endemic to the upper Black Warrior River basin in Alabama, US: the Black Warrior Waterdog (<i>Necturus alabamensis</i>) and the Flattened Musk Turtle (<i>Sternotherus depressus</i>). Importantly, these species have contrasting patterns of seasonal activity, with <i>N</i>. <i>alabamensis</i> more active in the cool season (October-April) and <i>S</i>. <i>depressus</i> more active in the warm season (May-September). We surveyed sites historically occupied by these species across cool and warm seasons over two years with replicated eDNA water samples, which were analyzed in the laboratory using species-specific quantitative PCR (qPCR) assays. We then used occupancy estimation with detection probability modeling to evaluate both the effects of landscape attributes on organism presence and season of sampling on detection probability of eDNA. Importantly, we found that season strongly affected eDNA detection probability for both species, with <i>N</i>. <i>alabamensis</i> having higher eDNA detection probabilities during the cool season and <i>S</i>. <i>depressus</i> have higher eDNA detection probabilities during the warm season. These results illustrate the influence of organismal behavior or activity on eDNA detection in the environment and identify an important role for basic natural history in designing eDNA monitoring programs.</p></div

Predictor variables for occupancy estimation using environmental DNA (eDNA) detections of the Black Warrior Waterdog (<i>Necturus alabamensis</i>) and Flattened Musk Turtle (<i>Sternotherus depressus</i>) given at three spatial scales: point, local riparian (100 m riparian buffer upstream and within 300 m radius of point), and watershed (entire upstream area from point).

<p>Predictor variables are given with abbreviations for reference in subsequent tables, brief descriptions with units, data sources with references, and the mean and range.</p

Two-way ANOVA results for performance (percent of targets reached by each participant in a session) and reaction time (RT).

<p>Two-way ANOVA results for performance (percent of targets reached by each participant in a session) and reaction time (RT).</p