Formulation and components of efficient coding.

<p>(A) A schematic plot of the efficient encoding transform. (B) Signal transformation in the auditory system. The cochlea turns the time-varying waveform into a time-frequency representation , as the population activities of the auditory nerves, which is the input to the efficient encoding system. Signal and noise pass through a series of brain nuclei such as cochlear nucleus, superior olive, inferior colliculus, etc. The current work proposes that the effective transform STRF of the spectrogram that is collectively realized by these nuclei is, in its linear form, the optimal filter implied by the efficient coding principle. The output is the activity of neurons in a higher nucleus. (C) Three steps of signal flow within the linear encoding step or STRF in (A) and (B). Note that these three steps are merely abstract algorithmic steps, rather than neural implementation processes for the effective transform or STRF.</p

Simulation of temporal receptive field TRF, when the spectral dimension is omitted.

<p>The same stimulus ensemble is used as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002123#pcbi-1002123-g003" target="_blank">Figure 3A</a>, except the factor in equation (12) to ensure translation invariance of correlation. (A;B) Demonstration of transforming an acausal temporal filter (A) to its causal minimum-phase counterpart (B) at a relatively high input SNR. (C) TRF for a relatively low input SNR.</p

The effect of signal-to-noise ratio (SNR) on gain and the spectral receptive field (SRF).

<p>Same stimulus ensemble as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002123#pcbi-1002123-g003" target="_blank">Figure 3A</a> except the overall SNR has been scaled by . (A) Gain control (red), signal (blue), and noise power (black) under high, medium and low SNR. (B) The corresponding SRFs of one output neuron (channel #120) in the three SNR cases.</p

The 2D STRFs/MTFs implied by efficient coding and found physiologically.

<p>(A) input power (equation (15), , ) in decorrelated channels. (B, C) MTF profile and the corresponding STRFs with two SNRs (scaled by 's). (D) and STRF as in B;C (when ) except with larger input correlations (, in equation (15)). (E;F) Modulation transfer functions (MTFs) and their properties at low and high input sound intensities averaged over 40 IC neurons from Lesica and Grothe <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002123#pcbi.1002123-Lesica1" target="_blank">[7]</a>. Here, is the spectral-temporal modulation frequency where the MTF peaks. Modulation frequencies in E and F are normalized by the same value across cells and intensities. Error bars in E indicate standard errors. The magnitude patterns of the MTFs for all neurons are normalized to peak value . Their average across neurons at each input intensity is then normalized to the same peak value and displayed in F.</p

Adaptation of gain and spectral filter kernel SRF to input correlations under high/low SNR.

<p>Same input ensemble as that in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002123#pcbi-1002123-g003" target="_blank">Figure 3A</a>, except that the smoothing parameter, and , are set for short and long range correlations, respectively. Analogous figure format as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002123#pcbi-1002123-g004" target="_blank">Figure 4</a>, with added illustrations of the adaptation to input correlations. The thick and thin curves correspond to quantities for inputs with large and small correlations respectively, blue/red curves plot signal power and gain respectively.</p

A schematic example of a typical spectro-temporal receptive field, plotted with a reversed abscissa.

<p>This STRF has one excitatory and three inhibitory regions, prefers frequency , and evokes response at a typical latency . Since the response at time is , an input stimulus exactly as depicted in this plot is most likely to elicit a large response at time , or indeed a spike.</p

Simulation of the efficient spectral kernel SRF, when the temporal dimension is omitted.

<p>(A) 250 samples of input spectra , each of which is smoothed Gaussian white noise in the frequency domain (equations (11–13), ). (B) Correlation between different frequency channels . Left: Correlation ; Right: an zoomed-in view, as vs . (C) Ten examples of eigenvectors of the correlation matrix in B; each is an independent component in . Smaller indices are associated with larger eigenvalues. (D) Gain profile (peaking at ), and signal and noise power in decorrelated channels. (E) Four examples (, , , and ) of spectral receptive fields ; each prefers input frequencies around .</p

Standard curves for RT-qPCR assays of <i>G6PDH</i> and <i>EF1</i> mRNA expression.

<p>Standard curve for <i>G6PDH</i> (a) was generated using <i>V</i>. <i>mali</i> cDNA serially (10⁹ to 10² fg/μL) diluted in host cDNA (10⁹ fg/μL). Standard curve for EF1 (b) was generated by <i>Malus × domestica</i> cv. Fuji cDNA diluted serially (10⁹ to 10² fg/μL) in water. A linear regression curve was calculated for use to quantify RNA levels from plant samples.</p

Primers for CALS1 and CALS2 used in this study.

<p>Primers for CALS1 and CALS2 used in this study.</p

Study on Interactions between the Major Apple Valsa Canker Pathogen <i>Valsa mali</i> and Its Biocontrol Agent <i>Saccharothrix yanglingensis</i> Hhs.015 Using RT-qPCR

<div><p>The mechanism of biocontrol agent <i>Saccharothrix yanglingensis</i> Hhs.015 action against <i>Valsa mali</i>, a major apple Valsa canker pathogen, was examined using a novel, sensitive (minimum detection limit 100 pg/μL) and reliably RT-qPCR technique. Prior to lesion formation, total concentration of <i>V</i>. <i>mali</i> in the bark showed a significant decrease (<i>p</i><0.05) after 24 h of Hhs.015 treatment. This was more pronounced at 48 and 96 h post treatment. After lesion formation, levels of <i>V</i>. <i>mali</i> remained constant at the boundary between infected and uninfected bark tissues, although the relative expansion rate of the lesion was significantly reduced (<i>p</i><0.05). Gene expression levels of endo-polygalacturonase, a marker for fungal pathogenicity, were sharply reduced while host induced resistance callose synthase levels increased significantly (<i>p</i><0.05) at the boundary bark at 9 d after Hhs.015 treatment. The results showed that biocontrol agent Hhs.015 prevented infection of <i>V</i>. <i>mali</i> by inhibiting pathogen growth, down-regulating pathogenicity factor expression and inducing a high level of host resistance.</p></div