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Abstract Background: Results: To address these issues, we introduce a novel adaptive semi-quantitative group testing (SQGT) scheme to e ciently screen populations via two-stage qPCR testing. The SQGT method quantizes cycle threshold (Ct) values into multiple bins, leveraging the information from the rst stage of screening to improve the detection sensitivity. Dynamic Ct threshold adjustments mitigate dilution e ects and enhance test accuracy. Comparisons with traditional binary outcome GT methods show that SQGT reduces the number of tests by 24% on the only complete real-world qPCR group testing dataset from Israel, while maintaining a negligible false negative rate. Conclusion: In conclusion, our adaptive SQGT approach, utilizing qPCR data and dynamic threshold adjustments, o ers a promising solution for e cient population screening. With a reduction in the number of tests and minimal false negatives, SQGT holds potential to enhance disease control and testing strategies on a global scale. Keywords: Group testing, Pooled testing, Semiquantitative group testing, qPCR, Ct values, Viral load, COVID-19 

Abstract BackgroundPathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease control and transmission prevention. Group testing is a well-established method for reducing the number of tests needed to screen large populations when the disease prevalence is low. However, it does not fully utilize the quantitative information provided by qPCR methods, nor is it able to accommodate a wide range of pathogen loads. ResultsTo address these issues, we introduce a novel adaptive semi-quantitative group testing (SQGT) scheme to efficiently screen populations via two-stage qPCR testing. The SQGT method quantizes cycle threshold (Ct) values into multiple bins, leveraging the information from the first stage of screening to improve the detection sensitivity. DynamicCtthreshold adjustments mitigate dilution effects and enhance test accuracy. Comparisons with traditional binary outcome GT methods show that SQGT reduces the number of tests by 24% on the only complete real-world qPCR group testing dataset from Israel, while maintaining a negligible false negative rate. ConclusionIn conclusion, our adaptive SQGT approach, utilizing qPCR data and dynamic threshold adjustments, offers a promising solution for efficient population screening. With a reduction in the number of tests and minimal false negatives, SQGT holds potential to enhance disease control and testing strategies on a global scale. 

Dictionary learning (DL), implemented via matrix factorization (MF), is commonly used in computational biology to tackle ubiquitous clustering problems. The method is favored due to its conceptual simplicity and relatively low computational complexity. However, DL algorithms produce results that lack interpretability in terms of real biological data. Additionally, they are not optimized for graph-structured data and hence often fail to handle them in a scalable manner. In order to address these limitations, we propose a novel DL algorithm calledonline convex network dictionary learning(online cvxNDL). Unlike classical DL algorithms, online cvxNDL is implemented via MF and designed to handle extremely large datasets by virtue of its online nature. Importantly, it enables the interpretation of dictionary elements, which serve as cluster representatives, through convex combinations of real measurements. Moreover, the algorithm can be applied to data with a network structure by incorporating specialized subnetwork sampling techniques. To demonstrate the utility of our approach, we apply cvxNDL on 3D-genome RNAPII ChIA-Drop data with the goal of identifying important long-range interaction patterns (long-range dictionary elements). ChIA-Drop probes higher-order interactions, and produces data in the form of hypergraphs whose nodes represent genomic fragments. The hyperedges represent observed physical contacts. Our hypergraph model analysis has the objective of creating an interpretable dictionary of long-range interaction patterns that accurately represent global chromatin physical contact maps. Through the use of dictionary information, one can also associate the contact maps with RNA transcripts and infer cellular functions. To accomplish the task at hand, we focus on RNAPII-enriched ChIA-Drop data fromDrosophila MelanogasterS2 cell lines. Our results offer two key insights. First, we demonstrate that online cvxNDL retains the accuracy of classical DL (MF) methods while simultaneously ensuring unique interpretability and scalability. Second, we identify distinct collections of proximal and distal interaction patterns involving chromatin elements shared by related processes across different chromosomes, as well as patterns unique to specific chromosomes. To associate the dictionary elements with biological properties of the corresponding chromatin regions, we employ Gene Ontology (GO) enrichment analysis and perform multiple RNA coexpression studies. 

We consider the problem of determining the mutational support and distribution of the SARS-CoV-2 viral genome in the small-sample regime. The mutational support refers to the unknown number of sites that may eventually mutate in the SARS-CoV-2 genome while mutational distribution refers to the distribution of point mutations in the viral genome across a population. The mutational support may be used to assess the virulence of the virus and guide primer selection for real-time RT-PCR testing. Estimating the distribution of mutations in the genome of different subpopulations while accounting for the unseen may also aid in discovering new variants. To estimate the mutational support in the small-sample regime, we use GISAID sequencing data and our state-of-the-art polynomial estimation techniques based on new weighted and regularized Chebyshev approximation methods.