Improvement in capture rate 〈<i>C</i>_<i>r</i>〉 due to motion noise <i>D</i>_<i>m</i> and the noise of the targets motion <i>D</i>_<i>p</i>.

<p>The ensemble average of the capture rate 〈<i>C</i>_<i>r</i>〉 as a function of <i>D</i>_<i>p</i> and <i>D</i>_<i>m</i> with internal neural noise <i>D</i>_<i>s</i> = 1 × 10⁻³ <b>(A)</b> and <i>D</i>_<i>s</i> = 5 × 10⁻³ <b>(B)</b>. The other parameters are <i>K</i> = 5, <i>g</i> = 10⁻², <i>b</i> = 0.24, <i>N</i> = 100, and <i>θ</i> = 1. The peak 〈<i>C</i>_<i>r</i>〉 is distributed roughly along the line <i>D</i>_<i>p</i> + <i>D</i>_<i>m</i> = 0.4 in (A) and <i>D</i>_<i>p</i> + <i>D</i>_<i>m</i> = 0.3 in (B). It is clear that the maximization of 〈<i>C</i>_<i>r</i>〉 requires a balance among <i>D</i>_<i>m</i>, <i>D</i>_<i>s</i>, and <i>D</i>_<i>p</i>. Numerical 〈<i>C</i>_<i>r</i>〉 are computed from 400 trials of a numerical simulation.</p

Behavioral SR of an agent driven by a simple non-neural PI controller.

<p><b>(A)</b> Improvement in the goal-reaching success rate due to additive motion noise. Numerical 〈<i>P</i>_<i>R</i>〉 are computed from 40 trials of a 500 s numerical simulation with <i>K</i>_<i>I</i> = 0.01 and <i>θ</i> = 0.1. Error bars in <b>(A)</b> indicate standard deviations. <b>(B1–B3)</b> Capture-rate improvement due to motion additive noise. Numerical 〈<i>C</i>_<i>r</i>〉 are computed from 1,000 trials. The parameters for <b>(B1–B3)</b> are <i>K</i>_<i>I</i> = 0.02 × 10⁻² and <i>θ</i> = 2.</p

Theoretical analysis of RSRI.

<p><b>(A)</b> Schematic model of a feedback-controlled Brownian particle agent. The agent has an end-effector of size <i>θ</i> used to reach a target moving along the pre-designed path <i>x</i>_<i>g</i>(<i>t</i>). For simplicity, we assume that <i>x</i>_<i>g</i>(<i>t</i>) is periodic. <b>(B,C,D)</b> Plot of theoretical 〈<i>P</i>_<i>R</i>〉 with contour lines versus the moving target frequency <i>f</i> and the agent motion noise intensity <i>D</i> computed using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0188298#pone.0188298.e006" target="_blank">Eq (5)</a> with <i>θ</i> = 0.01 <b>(B)</b>, <i>θ</i> = 0.1 <b>(C)</b>, and <i>θ</i> = 1 <b>(D)</b>. <b>(E)</b> <i>B</i> with respect to <i>f</i> and <i>A</i> = 0.1, 1, 2, 3 with <i>ϵ</i> = 1. Note that with <i>t</i> = 1/<i>f</i>, lim_{<i>f</i>→∞} <i>B</i> = <i>A</i> cos(1). <b>(F)</b> 〈<i>P</i>_<i>R</i>〉 with respect to <i>D</i> × 10 and <i>θ</i> = 0.2, 0.4, 0.5, 0.55, 0.65, 0.8, 1 with <i>A</i> = 0.1.</p

Emergent aperiodic control signal and asynchronous neural firing.

<p><b>(S1, R1)</b> The input signal to the motion actuator <b>(S1)</b> and the corresponding neural firing rate <i>R</i>(<i>t</i>) − <i>R</i>₀ <b>(R1)</b>, with <i>D</i>_<i>s</i> = 0 and <i>D</i>_<i>m</i> = 0. Note that the input signal to the actuator is totally deterministic, although it exhibits jittering. In addition, the corresponding neural spikes are synchronized (the even vertical lines represent bursts of spikes, not individual spikes.) <b>(S2, R2)</b> An aperiodic and stochastic control signal emerges with either <i>D</i>_<i>m</i> > 0 or <i>D</i>_<i>s</i> > 0 <b>(S2)</b>. The corresponding firing rate becomes asynchronous if <i>D</i>_<i>s</i> > 0 <b>(R2)</b>.</p

Motion error with respect to <i>D</i>_<i>s</i>.

<p> with <i>g</i> = 0.02, <i>D</i>_<i>b</i> = 0.1, and <i>D</i>_<i>s</i> = 0.05 for <b>(A)</b>, and <i>g</i> = 0.5, <i>D</i>_<i>b</i> = 0.1, and <i>D</i>_<i>s</i> = 0.005 for <b>(B)</b>. The error bars indicate standard deviations. Note that we could not find any significant improvements due to the presence of force noise <i>D</i>_<i>m</i>. Numerical is computed from 500 trials of a 500 s numerical simulation, and the error bars correspond to the standard error.</p

Neurophysical agent design and task setup.

<p><b>(A, B)</b> Two different numerical simulation setups for studying behavioral NIO. In setup (A), we study the NIO when a neurophysical agent tracks along a static predesigned path. In setup (B), we study the NIO that occurs when the agent captures randomly moving (i.e., noisy) targets. In the second paradigm, we consider not only the additive neural and force noises internal to the subject agent, but also the motion noise of the moving target.</p

Motion change due to the presence of neural and force noises.

<p><b>(A, B)</b> 〈<i>d</i>_<i>e</i>〉 and with the parameters <i>T</i> = 10, <i>K</i> = 10, <i>g</i> = 0.02. <b>(C)</b> 〈<i>d</i>_<i>e</i>〉 with <i>D</i>_<i>m</i> = 0.01 and 〈<i>e</i>_<i>m</i>〉, with <i>D</i>_<i>m</i> = 0.05 as a function of <i>D</i>_<i>s</i>. <b>(D)</b> 〈<i>ρ</i>〉 and 〈<i>N</i>_<i>o</i>〉 as a function of <i>D</i>_<i>s</i>. <b>(E, F)</b> The change in motion trajectory due to the presence of neural and motion noises, with <i>T</i> = 10, <i>K</i> = 10, and <i>g</i> ≪ 1 [<b>(E)</b>] and <i>g</i> ≫ 0 [<b>(F)</b>]. The inset is an enlargement of the respective areas inside the rectangles. Note that the bias variability <i>D</i>_<i>b</i> ≫ 0 leads to high pooling ability and reduces the oscillatory motion, but obscures the neuronal SR effect. Furthermore, the motion accuracy achieved due to neuronal SR (with <i>D</i>_<i>b</i> ∼ 0 and <i>D</i>_<i>s</i> > 0) is higher than it is in the noiseless system with high motor pooling ability (with <i>D</i>_<i>b</i> ≫ 0 and <i>D</i>_<i>s</i> = 0) <b>(G)</b>. Numerical 〈<i>d</i>_<i>e</i>〉, , 〈<i>ρ</i>〉, and 〈<i>N</i>_<i>o</i>〉 are computed from 500 trials of a 500 s numerical simulation.</p

The goal-reaching success rate 〈<i>P</i>_<i>R</i>〉 as a function of motion noise <i>D</i>_<i>m</i> and neural noise <i>D</i>_<i>s</i>.

<p>The task parameters are <i>T</i> = 10, <i>K</i> = 0.5 − 1.5 in panels <b>(A–C)</b>, and <i>T</i> = 5, <i>K</i> = 2 − 5 in panels <b>(D–F)</b>. Additive motion noise improves reaching success rate when <i>K</i> is not sufficient to produce a 100% goal-reaching success rate (this is shown in panels <b>(A), (B), (D), and (E)</b>). As shown in panels <b>(C)</b> and <b>(F)</b>, if <i>K</i> is large enough to realize a 100% success rate, the <i>P</i>_<i>R</i> monotonically decreases with <i>D</i>_<i>m</i>. Numerical 〈<i>P</i>_<i>R</i>〉 are computed from 100 trials of a 500 s numerical simulation with <i>θ</i> = 0.1 and <i>N</i> = 100, and the error bars correspond to the standard error.</p

Capture rate modification by threshold size <i>θ</i>.

<p>The parameters are <i>D</i>_<i>s</i> = 1 × 10⁻³, <i>K</i> = 5, <i>b</i> = 0.24, <i>N</i> = 100, and <i>g</i> = 0.01. The rate of improvement in capture rate is dependent on the size of the geometric threshold <i>θ</i>. Numerical 〈<i>C</i>_<i>r</i>〉 are computed from 100 trials of a 500 s numerical simulation, and error bars indicate standard errors and are within the symbols.</p

Networks analysis of visuo-tactile integration and connectivity.

<p><b>A</b> Connectivity circle linking the visual and tactile maps (resp. green and red) to the bimodal map (blue). The graph describes the dense connectivity of synaptic links starting from the visual and tactile maps and converging to the multimodal map. The colored links correspond to localized visuo-tactile stimuli on the nose (green/red links) and on the right eye (cyan/magenta links), see the patterns on the upper figure. The links show the correct spatial correspondance between the neurons of the two maps. <b>B</b> Weights density distribution from the visual and tactile maps to the bimodal map relative to their strength. These histograms show that the neurons from both modalities have only few strong connections from each others. This suggest a bijection between the neurons of each map. <b>C</b> Normalized distance error between linked visual and tactile neurons. When looking at the pairwise neurons of the two maps (red histogram in <b>B</b> for weights ), the spatial distortion between the neurons from the two maps is weak: vision neurons coding one location on the eyes receptive fields are strongly linked to the tactile neurons coding the same region on the face.</p