While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic Susceptible, Infected, Recovered (SIR) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona.
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Abstract Background Low-depth sequencing allows researchers to increase sample size at the expense of lower accuracy. To incorporate uncertainties while maintaining statistical power, we introduce to analyze population structure of low-depth sequencing data.
Results The method optimizes the choice of nonlinear transformations of dosages to maximize the Ky Fan norm of the covariance matrix. The transformation incorporates the uncertainty in calling between heterozygotes and the common homozygotes for loci having a rare allele and is more linear when both variants are common.
Conclusions We apply to samples from two indigenous Siberian populations and reveal hidden population structure accurately using only a single chromosome. The package is available on
https://github.com/yiwenstat/MCPCA_PopGen . -
null (Ed.)In the classical Steiner tree problem, given an undirected, connected graph G =( V , E ) with non-negative edge costs and a set of terminals T ⊆ V , the objective is to find a minimum-cost tree E &prime ⊆ E that spans the terminals. The problem is APX-hard; the best-known approximation algorithm has a ratio of ρ = ln (4)+ε < 1.39. In this article, we study a natural generalization, the multi-level Steiner tree (MLST) problem: Given a nested sequence of terminals T ℓ ⊂ … ⊂ T 1 ⊆ V , compute nested trees E ℓ ⊆ … ⊆ E 1 ⊆ E that span the corresponding terminal sets with minimum total cost. The MLST problem and variants thereof have been studied under various names, including Multi-level Network Design, Quality-of-Service Multicast tree, Grade-of-Service Steiner tree, and Multi-tier tree. Several approximation results are known. We first present two simple O (ℓ)-approximation heuristics. Based on these, we introduce a rudimentary composite algorithm that generalizes the above heuristics, and determine its approximation ratio by solving a linear program. We then present a method that guarantees the same approximation ratio using at most 2ℓ Steiner tree computations. We compare these heuristics experimentally on various instances of up to 500 vertices using three different network generation models. We also present several integer linear programming formulations for the MLST problem and compare their running times on these instances. To our knowledge, the composite algorithm achieves the best approximation ratio for up to ℓ = 100 levels, which is sufficient for most applications, such as network visualization or designing multi-level infrastructure.more » « less
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Influence of age at seizure onset on the acquisition of neurodevelopmental skills in an SCN8A cohortmore » « less
Abstract Objective To characterize a cohort of patients with
SCN 8A‐related epilepsy and to perform analyses to identify correlations involving the acquisition of neurodevelopmental skills.Methods We analyzed patient data (n = 91) submitted to an online registry tailored to characteristics of children with
SCN 8AII items. Spearman rank tests were utilized to test for correlations among a variety of aspects of seizures, medications, and neurodevelopmental progression.Results The 91 participants carried 71 missense variants (41 newly reported) and three truncating variants. Ages at seizure onset ranged from birth to >12 months of age (mean ± SD = 5 months 21 days ± 7 months 14 days). Multiple seizure types with multimodal onset times and developmental delay were observed as general features of this cohort. We found a positive correlation between a developmental score based upon percentage of acquired skills and the age at seizure onset, current seizure freedom, and initial febrile seizures. Analyses of cohort subgroups revealed clear distinctions between patients who had a single reported variant in
SCN 8ASCN 8ASignificance This is the first study of an
SCN 8A patient cohort of this size and for which correlations between age at seizure onset and neurodevelopment were investigated. Our correlation studies suggest that variants of uncertain significance should be considered in assessing children withSCN 8A‐related disorders. This study substantially improves the characterization of this patient population and our understanding of the neurodevelopmental effects associated with seizures forSCN 8A patients, and provides a clinical context at initial presentation that may be prognostic for developmental outcome.
