Beyond Natural Numbers: Negative Number Representation in Parietal Cortex

Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference <4) or far apart (difference >6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation

Better together: novel methods for measuring and modeling development of executive function diversity while accounting for unity

IntroductionExecutive functions (EFs) are linked to positive outcomes across the lifespan. Yet, methodological challenges have prevented precise understanding of the developmental trajectory of their organization.MethodsWe introduce novel methods to address challenges for both measuring and modeling EFs using an accelerated longitudinal design with a large, diverse sample of students in middle childhood (N = 1,286; ages 8 to 14). We used eight adaptive assessments hypothesized to measure three EFs, working memory, context monitoring, and interference resolution. We deployed adaptive assessments to equate EF challenge across ages and a data-driven, network analytic approach to reveal the evolving diversity of EFs while simultaneously accounting for their unity.Results and discussionUsing this methodological paradigm shift brought new precision and clarity to the development of these EFs, showing these eight tasks are organized into three stable components by age 10, but refinement of composition of these components continues through at least age 14

A systematic review of clinical trials of pharmacological interventions for acute ischaemic stroke (1955-2008) that were completed, but not published in full

<p>Abstract</p> <p>Background</p> <p>We assessed the prevalence, and potential impact of, trials of pharmacological agents for acute stroke that were completed but not published in full. Failure to publish trial data is to be deprecated as it sets aside the altruism of participants' consent to be exposed to the risks of experimental interventions, potentially biases the assessment of the effects of therapies, and may lead to premature discontinuation of research into promising treatments.</p> <p>Methods</p> <p>We searched the Cochrane Stroke Group's Specialised Register of Trials in June 2008 for completed trials of pharmacological interventions for acute ischaemic stroke, and searched MEDLINE and EMBASE (January 2007 - March 2009) for references to recent full publications. We assessed trial completion status from trial reports, online trials registers and correspondence with experts.</p> <p>Results</p> <p>We identified 940 trials. Of these, 125 (19.6%, 95% confidence interval 16.5-22.6) were completed but not published in full by the point prevalence date. They included 16,058 participants (16 trials had over 300 participants each) and tested 89 different interventions. Twenty-two trials with a total of 4,251 participants reported the number of deaths. In these trials, 636/4251 (15.0%) died.</p> <p>Conclusions</p> <p>Our data suggest that, at the point prevalence date, a substantial body of evidence that was of relevance both to clinical practice in acute stroke and future research in the field was not published in full. Over 16,000 patients had given informed consent and were exposed to the risks of therapy. Responsibility for non-publication lies with investigators, but pharmaceutical companies, research ethics committees, journals and governments can all encourage the timely publication of trial data.</p

Ramucirumab plus docetaxel versus placebo plus docetaxel in patients with locally advanced or metastatic urothelial carcinoma after platinum-based therapy (RANGE): a randomised, double-blind, phase 3 trial

Few treatments with a distinct mechanism of action are available for patients with platinum-refractory advanced or metastatic urothelial carcinoma. We assessed the efficacy and safety of treatment with docetaxel plus either ramucirumab-a human IgG1 VEGFR-2 antagonist-or placebo in this patient population

Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples

Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts

Probing the neural basis rational numbers: the role of inhibitory control and magnitude representations

Rational numbers, such as fractions, decimals and percentages, are a persistent challenge in the mathematics curriculum. An underappreciated source of rational number difficulties are whole number properties that apply to some, but not all, rational numbers. I contend that mastery of rational numbers involves refining and expanding whole number representations. Behavioral evidence for the role inhibitory control and magnitude-based processing of rational numbers support this hypothesis, although more attention is needed to task and stimuli selection, especially among fractions. In the brain, there is scant evidence on the role of inhibitory control in rational number processing, but surprisingly good correspondence, in the parietal lobe, between the handful of neuroimaging studies of rational numbers and the accumulated whole number literature. Decimals and discrete nonsymbolic representations are fruitful domains for probing the neural basis role of whole number interference in rational number processing

Adults Systematically Underestimate Decimals and Whole Number Exposure Induces Further Magnitude-Based Underestimation

Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected stimuli to investigate how equivalent decimals (e.g., 0.8 and 0.80 on a 0-1 number line) and proportionally equivalent whole numbers (e.g., 80 on a 0-100 number line) are estimated. We find that young adults (N = 88, Mage = 20.22 Years, SD = 1.65, 57 female) have a linear response pattern for both decimals and whole numbers, but that double-digit decimals (e.g., 0.08, 0.82, 0.80) are systematically underestimated relative to proportionally equivalent whole numbers (e.g., 8, 82, 80). Moreover, decimal string length worsens the underestimation, such that single- digit decimals (e.g., 0.8) are perceived as smaller than their equivalent double-digit decimals (e.g., 0.80). Finally, we find that exposing participants to whole number stimuli before decimal stimuli induces magnitude-based underestimation, that is, greater underestimation for larger decimals. Together, these results suggest a small but persistent underestimation bias for decimals less than one, and further that decimal magnitude estimation is fragile and subject to greater underestimation when exposed to whole numbers