The proportion of failures of the Hasse norm principle

For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio

Applications of patching to quadratic forms and central simple algebras

This paper provides applications of patching to quadratic forms and central simple algebras over function fields of curves over henselian valued fields. In particular, we use a patching approach to reprove and generalize a recent result of Parimala and Suresh on the u-invariant of p-adic function fields, for p odd. The strategy relies on a local-global principle for homogeneous spaces for rational algebraic groups, combined with local computations.Comment: 48 pages; connectivity now required in the definition of rational group; beginning of Section 4 reorganized; other minor change

Concentration or representation : the struggle for popular sovereignty

There is a tension in the notion of popular sovereignty, and the notion of democracy associated with it, that is both older than our terms for these notions themselves and more fundamental than the apparently consensual way we tend to use them today. After a review of the competing conceptions of 'the people' that underlie two very different understandings of democracy, this article will defend what might be called a 'neo-Jacobin' commitment to popular sovereignty, understood as the formulation and imposition of a shared political will. A people's egalitarian capacity to concentrate both its collective intelligence and force, from this perspective, takes priority over concerns about how best to represent the full variety of positions and interests that differentiate and divide a community

Campana points of bounded height on vector group compactifications

We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. We call the points in these sets Campana points. Earlier work of Campana and subsequently Abramovich shows that there are several reasonable competing definitions for Campana points. We use a version that delineates well different types of behaviour of points as the weights on the boundary divisor vary. This prompts a Manin-type conjecture on Fano orbifolds for sets of Campana points that satisfy a klt (Kawamata log terminal) condition. By importing work of Chambert-Loir and Tschinkel to our set-up, we prove a log version of Manin's conjecture for klt Campana points on equivariant compactifications of vector groups.Comment: 52 pages; minor revision, changes in the definition of Campana point

Detection of Epileptogenic Cortical Malformations with Surface-Based MRI Morphometry

Magnetic resonance imaging has revolutionized the detection of structural abnormalities in patients with epilepsy. However, many focal abnormalities remain undetected in routine visual inspection. Here we use an automated, surface-based method for quantifying morphometric features related to epileptogenic cortical malformations to detect abnormal cortical thickness and blurred gray-white matter boundaries. Using MRI morphometry at 3T with surface-based spherical averaging techniques that precisely align anatomical structures between individual brains, we compared single patients with known lesions to a large normal control group to detect clusters of abnormal cortical thickness, gray-white matter contrast, local gyrification, sulcal depth, jacobian distance and curvature. To assess the effects of threshold and smoothing on detection sensitivity and specificity, we systematically varied these parameters with different thresholds and smoothing levels. To test the effectiveness of the technique to detect lesions of epileptogenic character, we compared the detected structural abnormalities to expert-tracings, intracranial EEG, pathology and surgical outcome in a homogeneous patient sample. With optimal parameters and by combining thickness and GWC, the surface-based detection method identified 92% of cortical lesions (sensitivity) with few false positives (96% specificity), successfully discriminating patients from controls 94% of the time. The detected structural abnormalities were related to the seizure onset zones, abnormal histology and positive outcome in all surgical patients. However, the method failed to adequately describe lesion extent in most cases. Automated surface-based MRI morphometry, if used with optimized parameters, may be a valuable additional clinical tool to improve the detection of subtle or previously occult malformations and therefore could improve identification of patients with intractable focal epilepsy who may benefit from surgery

Comparison of clinical rating scales in genetic frontotemporal dementia within the GENFI cohort

BACKGROUND: Therapeutic trials are now underway in genetic forms of frontotemporal dementia (FTD) but clinical outcome measures are limited. The two most commonly used measures, the Clinical Dementia Rating (CDR)+National Alzheimer’s Disease Coordinating Center (NACC) Frontotemporal Lobar Degeneration (FTLD) and the FTD Rating Scale (FRS), have yet to be compared in detail in the genetic forms of FTD. METHODS: The CDR+NACC FTLD and FRS were assessed cross-sectionally in 725 consecutively recruited participants from the Genetic FTD Initiative: 457 mutation carriers (77 microtubule-associated protein tau (MAPT), 187 GRN, 193 C9orf72) and 268 family members without mutations (non-carrier control group). 231 mutation carriers (51 MAPT, 92 GRN, 88 C9orf72) and 145 non-carriers had available longitudinal data at a follow-up time point. RESULTS: Cross-sectionally, the mean FRS score was lower in all genetic groups compared with controls: GRN mutation carriers mean 83.4 (SD 27.0), MAPT mutation carriers 78.2 (28.8), C9orf72 mutation carriers 71.0 (34.0), controls 96.2 (7.7), p<0.001 for all comparisons, while the mean CDR+NACC FTLD Sum of Boxes was significantly higher in all genetic groups: GRN mutation carriers mean 2.6 (5.2), MAPT mutation carriers 3.2 (5.6), C9orf72 mutation carriers 4.2 (6.2), controls 0.2 (0.6), p<0.001 for all comparisons. Mean FRS score decreased and CDR+NACC FTLD Sum of Boxes increased with increasing disease severity within each individual genetic group. FRS and CDR+NACC FTLD Sum of Boxes scores were strongly negatively correlated across all mutation carriers (r_{s} =−0.77, p<0.001) and within each genetic group (r_{s} =−0.67 to −0.81, p<0.001 in each group). Nonetheless, discrepancies in disease staging were seen between the scales, and with each scale and clinician-judged symptomatic status. Longitudinally, annualised change in both FRS and CDR+NACC FTLD Sum of Boxes scores initially increased with disease severity level before decreasing in those with the most severe disease: controls −0.1 (6.0) for FRS, −0.1 (0.4) for CDR+NACC FTLD Sum of Boxes, asymptomatic mutation carriers −0.5 (8.2), 0.2 (0.9), prodromal disease −2.3 (9.9), 0.6 (2.7), mild disease −10.2 (18.6), 3.0 (4.1), moderate disease −9.6 (16.6), 4.4 (4.0), severe disease −2.7 (8.3), 1.7 (3.3). Sample sizes were calculated for a trial of prodromal mutation carriers: over 180 participants per arm would be needed to detect a moderate sized effect (30%) for both outcome measures, with sample sizes lower for the FRS. CONCLUSIONS: Both the FRS and CDR+NACC FTLD measure disease severity in genetic FTD mutation carriers throughout the timeline of their disease, although the FRS may be preferable as an outcome measure. However, neither address a number of key symptoms in the FTD spectrum, for example, motor and neuropsychiatric deficits, which future scales will need to incorporate

Relations between C9orf72 expansion size in blood, age at onset, age at collection and transmission across generations in patients and presymptomatic carriers

A (GGGGCC) n repeat expansion in C9orf72 gene is the major cause of frontotemporal dementia (FTD) and amyotrophic lateral sclerosis (ALS). The relations between the repeats size and the age at disease onset (AO) or the clinical phenotype (FTD vs. ALS) were investigated in 125 FTD, ALS, and presymptomatic carriers. Positive correlations were found between repeats number and the AO (p &lt; 10 e−4 ) but our results suggested that the association was mainly driven by age at collection (p &lt; 10 e−4 ). A weaker association was observed with clinical presentation (p = 0.02), which became nonsignificant after adjustment for the age at collection in each group. Importantly, repeats number variably expanded or contracted over time in carriers with multiple blood samples, as well as through generations in parent-offspring pairs, conversely to what occurs in several expansion diseases with anticipation at the molecular level. Finally, this study establishes that measure of repeats number in lymphocytes is not a reliable biomarker predictive of the AO or disease outcome in C9orf72 long expansion carriers

Cognitive composites for genetic frontotemporal dementia: GENFI-Cog

Background Clinical endpoints for upcoming therapeutic trials in frontotemporal dementia (FTD) are increasingly urgent. Cognitive composite scores are often used as endpoints but are lacking in genetic FTD. We aimed to create cognitive composite scores for genetic frontotemporal dementia (FTD) as well as recommendations for recruitment and duration in clinical trial design. Methods A standardized neuropsychological test battery covering six cognitive domains was completed by 69 C9orf72, 41 GRN, and 28 MAPT mutation carriers with CDR® plus NACC-FTLD ≥ 0.5 and 275 controls. Logistic regression was used to identify the combination of tests that distinguished best between each mutation carrier group and controls. The composite scores were calculated from the weighted averages of test scores in the models based on the regression coefficients. Sample size estimates were calculated for individual cognitive tests and composites in a theoretical trial aimed at preventing progression from a prodromal stage (CDR® plus NACC-FTLD 0.5) to a fully symptomatic stage (CDR® plus NACC-FTLD ≥ 1). Time-to-event analysis was performed to determine how quickly mutation carriers progressed from CDR® plus NACC-FTLD = 0.5 to ≥ 1 (and therefore how long a trial would need to be). Results The results from the logistic regression analyses resulted in different composite scores for each mutation carrier group (i.e. C9orf72, GRN, and MAPT). The estimated sample size to detect a treatment effect was lower for composite scores than for most individual tests. A Kaplan-Meier curve showed that after 3 years, ~ 50% of individuals had converted from CDR® plus NACC-FTLD 0.5 to ≥ 1, which means that the estimated effect size needs to be halved in sample size calculations as only half of the mutation carriers would be expected to progress from CDR® plus NACC FTLD 0.5 to ≥ 1 without treatment over that time period. Discussion We created gene-specific cognitive composite scores for C9orf72, GRN, and MAPT mutation carriers, which resulted in substantially lower estimated sample sizes to detect a treatment effect than the individual cognitive tests. The GENFI-Cog composites have potential as cognitive endpoints for upcoming clinical trials. The results from this study provide recommendations for estimating sample size and trial duration