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Lower Density Selection Schemes via Small Universal Hitting Sets with Short Remaining Path Length.

ABSTRACT: Universal hitting sets (UHS) are sets of words that are unavoidable: every long enough sequence is hit by the set (i.e., it contains a word from the set). There is a tight relationship between UHS and minimizer schemes, where minimizer schemes with low density (i.e., efficient schemes) correspond to UHS of small size. Local schemes are a generalization of minimizer schemes that can be used as replacement for minimizer scheme with the possibility of being much more efficient. We establish the link between efficient local schemes and the minimum length of a string that must be hit by a UHS. We give bounds for the remaining path length of the Mykkeltveit UHS. In addition, we create a local scheme with the lowest known density that is only a log factor away from the theoretical lower bound.

SUBMITTER: Zheng H

PROVIDER: S-EPMC8066347 | biostudies-literature | 2021 Apr

REPOSITORIES: biostudies-literature

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Lower Density Selection Schemes via Small Universal Hitting Sets with Short Remaining Path Length.

Zheng Hongyu H Kingsford Carl C Marçais Guillaume G

Journal of computational biology : a journal of computational molecular cell biology 20201215 4

Universal hitting sets (UHS) are sets of words that are unavoidable: every long enough sequence is hit by the set (i.e., it contains a word from the set). There is a tight relationship between UHS and minimizer schemes, where minimizer schemes with low density (i.e., efficient schemes) correspond to UHS of small size. Local schemes are a generalization of minimizer schemes that can be used as replacement for minimizer scheme with the possibility of being much more efficient. We establish the lin ...[more]

PMID: 33325773

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Project description:BackgroundUniversal Health Coverage (UHC) is a common health policy objective outlined in the Sustainable Development Goals. With provincial governments taking the initiative, Pakistan has implemented and extended UHC program amid a complex public health landscape. In this context, we assess Pakistan's progress toward achieving UHC at the national and subnational level.MethodsWe use data from the Demographic and Health Surveys and the Household Integrated Economic Survey to construct a UHC index at the national and subnational level for 2007, 2013, and 2018. Furthermore, we use Concentration Index (CI) and CI decomposition methodologies to assess the primary drivers of inequality in accessing medical services. Logistic regression and Sartori's two-step model are applied to examine the key determinants of catastrophic health expenditure (CHE).ResultsOur analysis underscores Pakistan's steady progress toward UHC, while revealing significant provincial disparities in UHC progress. Provinces with lower poverty rate achieve higher UHC index, which highlights the synergy of poverty alleviation and UHC expansion. Among the examined indicators, child immunization remains a key weakness that one third of the children are not fully vaccinated and one sixth of these not-fully-vaccinated children have never received any vaccination. Socioeconomic status emerges as a main contributor to disparities in accessing medical services, albeit with a declining trend over time. Household socioeconomic status is negatively correlated with CHE incidence, indicating that wealthier households are less susceptible to CHE. For individuals experiencing CHE, medicine expenditure takes the highest share of their health spending, registering a staggering 70% in 2018.ConclusionPakistan's progress toward UHC aligns closely with its economic development trajectory and policy efforts in expanding UHC program. However, economic underdevelopment and provincial disparities persist as significant hurdles on Pakistan's journey toward UHC. We suggest continued efforts in UHC program expansion with a focus on policy consistency and fiscal support, combined with targeted interventions to alleviate poverty in the underdeveloped provinces.

Dataset Information

Lower Density Selection Schemes via Small Universal Hitting Sets with Short Remaining Path Length.

Publications

Lower Density Selection Schemes via Small Universal Hitting Sets with Short Remaining Path Length.

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