Establishing propositional truth-value in counterfactual and real-world contexts during sentence comprehension: Differential sensitivity of the left and right inferior frontal gyri

What makes a proposition true or false has traditionally played an essential role in philosophical and linguistic theories of meaning. A comprehensive neurobiological theory of language must ultimately be able to explain the combined contributions of real-world truth-value and discourse context to sentence meaning. This fMRI study investigated the neural circuits that are sensitive to the propositional truth-value of sentences about counterfactual worlds, aiming to reveal differential hemispheric sensitivity of the inferior prefrontal gyri to counterfactual truth-value and real-world truth-value. Participants read true or false counterfactual conditional sentences (“If N.A.S.A. had not developed its Apollo Project, the first country to land on the moon would be Russia/America”) and real-world sentences (“Because N.A.S.A. developed its Apollo Project, the first country to land on the moon has been America/Russia”) that were matched on contextual constraint and truth-value. ROI analyses showed that whereas the left BA 47 showed similar activity increases to counterfactual false sentences and to real-world false sentences (compared to true sentences), the right BA 47 showed a larger increase for counterfactual false sentences. Moreover, whole-brain analyses revealed a distributed neural circuit for dealing with propositional truth-value. These results constitute the first evidence for hemispheric differences in processing counterfactual truth-value and real-world truth-value, and point toward additional right hemisphere involvement in counterfactual comprehension

Relative errors of approximations for <i>ETMRCA</i> (upper plot) and <i>ETBLT</i> (lower plot) proposed by Chen and Chen (2013) [16].

<p>Relative errors of approximations for <i>ETMRCA</i> (upper plot) and <i>ETBLT</i> (lower plot) proposed by Chen and Chen (2013) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0170701#pone.0170701.ref016" target="_blank">16</a>].</p

Influence of round-off errors on accuracy of computation of expected allele frequencies by using expressions Eqs (22)–(25).

<p>The plot shows upper bounds of maximum relative error for the scenario of exponential growth of population with different values of product parameter <i>ρ</i>, obtained by corrupting values of expected times <i>e</i>_<i>j</i> by Gaussian, relative error with standard deviation <i>σ</i> = 10⁻¹³.</p

Values of skewness coefficient <i>γ</i>(<i>T</i>_<i>k</i>) of probability distributions of times in the coalescence tree computed for different genealogy sizes, <i>n</i> = 100 (upper plot) and <i>n</i> = 1000 (lower plot) and for different scenarios of population size change constant (<i>ρ</i> = 0) and exponentially growing with <i>ρ</i> = 1, <i>ρ</i> = 10 and <i>ρ</i> = 100.

<p>Values of skewness coefficient <i>γ</i>(<i>T</i>_<i>k</i>) of probability distributions of times in the coalescence tree computed for different genealogy sizes, <i>n</i> = 100 (upper plot) and <i>n</i> = 1000 (lower plot) and for different scenarios of population size change constant (<i>ρ</i> = 0) and exponentially growing with <i>ρ</i> = 1, <i>ρ</i> = 10 and <i>ρ</i> = 100.</p

Log-likelihood curves for the exponential model of population growth for data on segregating sites from the mtDB database [25].

<p>Each segregating site from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0170701#pone.0170701.t002" target="_blank">Table 2</a> was treated as a separate SNP. The curve marked with asterisks shows the exact log likelihood function and the one marked with open circles is the approximate log likelihood function. The maximum of the exact log likelihood function is attained at and the maximum of the approximate log likelihood function is attained at .</p

Relative errors of expected allele frequencies <i>q</i>_<i>nb</i> versus allele type <i>b</i> for two values of genealogy size <i>n</i> = 1000 (upper plot) and <i>n</i> = 10000 (lower plot) for different values of the product parameter of the population growth <i>ρ</i> = 1, <i>ρ</i> = 10, <i>ρ</i> = 100 and <i>ρ</i> = 1000.

<p>Relative errors of expected allele frequencies <i>q</i>_<i>nb</i> versus allele type <i>b</i> for two values of genealogy size <i>n</i> = 1000 (upper plot) and <i>n</i> = 10000 (lower plot) for different values of the product parameter of the population growth <i>ρ</i> = 1, <i>ρ</i> = 10, <i>ρ</i> = 100 and <i>ρ</i> = 1000.</p

Statistics of segregating sites in mtDNA data from Human mtDNA database [22].

<p>Elements in <i>b</i> are possible numbers of copies of the rare allele, and elements in <i>c</i>_<i>k</i> are numbers of segregating sites in the sample that have the number of copies of the rare allele equal <i>b</i>.</p

Short fragment of MS including one ground truth Aurum peak m/z = 1690.766 Da from the spectrum T10761_Well A24_18836 and its GMM.

<p><b>(A)</b> MS fragment, <b>(B)</b> GMM decomposition, <b>(C)</b> GMM components. We additionally mark, by vertical lines m/z positions, black: true Aurum peak 1690.766, red: m/z estimate by using MS-GMM, blue: m/z estimate by using CWT algorithm.</p

Fragment of one virtual MS dataset (with 200 peaks, m/z range 2900–3300 Da).

<p>Comparison of MS-GMM and CWT. MS signal (black), GMM model components (red), peaks detected by CWT algorithm (blue asterisks). Positions of true peaks in the spectral signal are marked by circles symbols and detection status is depicted by colors: peak detected only by MS-GMM method (red), peak detected only by CWT method (blue), peak detected by both MS-GMM and CWT (black), peak not detected by any of algorithms (empty circle).</p

Performance indexes for the three peak detection algorithms applied for mean spectra in the simulated datasets.

<p><b>(A)</b> F1 score. <b>(B)</b> Sensitivity. <b>(C)</b> FDR. <b>(D)</b> No of detected peaks. Colors: MS-GMM—red, CWT—blue, CROM—green.</p