Space-time duality for fractional diffusion

Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional derivatives in place of the usual integer order derivatives. They govern scaling limits of random walk models, with power law jumps leading to fractional derivatives in space, and power law waiting times between the jumps leading to fractional derivatives in time. The limit process is a stable L\'evy motion that models the jumps, subordinated to an inverse stable process that models the waiting times. Using duality, we relate the density of a spectrally negative stable process with index $1<\alpha<2$ to the density of the hitting time of a stable subordinator with index $1/\alpha$, and thereby unify some recent results in the literature. These results also provide a concrete interpretation of Zolotarev duality in terms of the fractional diffusion model.Comment: 16 page

Ethnicity, consanguinity, and genetic architecture of hypertrophic cardiomyopathy

AIMS: Hypertrophic cardiomyopathy (HCM) is characterized by phenotypic heterogeneity that is partly explained by the diversity of genetic variants contributing to disease. Accurate interpretation of these variants constitutes a major challenge for diagnosis and implementing precision medicine, especially in understudied populations. The aim is to define the genetic architecture of HCM in North African cohorts with high consanguinity using ancestry-matched cases and controls. METHODS AND RESULTS: Prospective Egyptian patients (n = 514) and controls (n = 400) underwent clinical phenotyping and genetic testing. Rare variants in 13 validated HCM genes were classified according to standard clinical guidelines and compared with a prospective HCM cohort of majority European ancestry (n = 684). A higher prevalence of homozygous variants was observed in Egyptian patients (4.1% vs. 0.1%, P = 2 × 10-7), with variants in the minor HCM genes MYL2, MYL3, and CSRP3 more likely to present in homozygosity than the major genes, suggesting these variants are less penetrant in heterozygosity. Biallelic variants in the recessive HCM gene TRIM63 were detected in 2.1% of patients (five-fold greater than European patients), highlighting the importance of recessive inheritance in consanguineous populations. Finally, rare variants in Egyptian HCM patients were less likely to be classified as (likely) pathogenic compared with Europeans (40.8% vs. 61.6%, P = 1.6 × 10-5) due to the underrepresentation of Middle Eastern populations in current reference resources. This proportion increased to 53.3% after incorporating methods that leverage new ancestry-matched controls presented here. CONCLUSION: Studying consanguineous populations reveals novel insights with relevance to genetic testing and our understanding of the genetic architecture of HCM

Disease-specific variant pathogenicity prediction significantly improves variant interpretation in inherited cardiac conditions

Funder: Science and Technology Development Fund; doi: https://doi.org/10.13039/Funder: Al-Alfi FoundationFunder: Magdi Yacoub Heart FoundationFunder: Rosetrees and Stoneygate Imperial College Research FellowshipFunder: National Health and Medical Research Council (Australia)Abstract: Purpose: Accurate discrimination of benign and pathogenic rare variation remains a priority for clinical genome interpretation. State-of-the-art machine learning variant prioritization tools are imprecise and ignore important parameters defining gene–disease relationships, e.g., distinct consequences of gain-of-function versus loss-of-function variants. We hypothesized that incorporating disease-specific information would improve tool performance. Methods: We developed a disease-specific variant classifier, CardioBoost, that estimates the probability of pathogenicity for rare missense variants in inherited cardiomyopathies and arrhythmias. We assessed CardioBoost’s ability to discriminate known pathogenic from benign variants, prioritize disease-associated variants, and stratify patient outcomes. Results: CardioBoost has high global discrimination accuracy (precision recall area under the curve [AUC] 0.91 for cardiomyopathies; 0.96 for arrhythmias), outperforming existing tools (4–24% improvement). CardioBoost obtains excellent accuracy (cardiomyopathies 90.2%; arrhythmias 91.9%) for variants classified with >90% confidence, and increases the proportion of variants classified with high confidence more than twofold compared with existing tools. Variants classified as disease-causing are associated with both disease status and clinical severity, including a 21% increased risk (95% confidence interval [CI] 11–29%) of severe adverse outcomes by age 60 in patients with hypertrophic cardiomyopathy. Conclusions: A disease-specific variant classifier outperforms state-of-the-art genome-wide tools for rare missense variants in inherited cardiac conditions (https://www.cardiodb.org/cardioboost/), highlighting broad opportunities for improved pathogenicity prediction through disease specificity

Disease-specific variant pathogenicity prediction significantly improves variant interpretation in inherited cardiac conditions

Funder: Science and Technology Development Fund; doi: https://doi.org/10.13039/Funder: Al-Alfi FoundationFunder: Magdi Yacoub Heart FoundationFunder: Rosetrees and Stoneygate Imperial College Research FellowshipFunder: National Health and Medical Research Council (Australia)Abstract: Purpose: Accurate discrimination of benign and pathogenic rare variation remains a priority for clinical genome interpretation. State-of-the-art machine learning variant prioritization tools are imprecise and ignore important parameters defining gene–disease relationships, e.g., distinct consequences of gain-of-function versus loss-of-function variants. We hypothesized that incorporating disease-specific information would improve tool performance. Methods: We developed a disease-specific variant classifier, CardioBoost, that estimates the probability of pathogenicity for rare missense variants in inherited cardiomyopathies and arrhythmias. We assessed CardioBoost’s ability to discriminate known pathogenic from benign variants, prioritize disease-associated variants, and stratify patient outcomes. Results: CardioBoost has high global discrimination accuracy (precision recall area under the curve [AUC] 0.91 for cardiomyopathies; 0.96 for arrhythmias), outperforming existing tools (4–24% improvement). CardioBoost obtains excellent accuracy (cardiomyopathies 90.2%; arrhythmias 91.9%) for variants classified with >90% confidence, and increases the proportion of variants classified with high confidence more than twofold compared with existing tools. Variants classified as disease-causing are associated with both disease status and clinical severity, including a 21% increased risk (95% confidence interval [CI] 11–29%) of severe adverse outcomes by age 60 in patients with hypertrophic cardiomyopathy. Conclusions: A disease-specific variant classifier outperforms state-of-the-art genome-wide tools for rare missense variants in inherited cardiac conditions (https://www.cardiodb.org/cardioboost/), highlighting broad opportunities for improved pathogenicity prediction through disease specificity