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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. 

Hypergraphs are used to model higher-order interactions amongst agents and there exist many practically relevant instances of hypergraph datasets. To enable the efficient processing of hypergraph data, several hypergraph neural network plat- forms have been proposed for learning hypergraph properties and structure, with a special focus on node classification tasks. However, almost all existing methods use heuristic propagation rules and offer suboptimal performance on benchmark- ing datasets. We propose AllSet, a new hypergraph neural network paradigm that represents a highly general framework for (hyper)graph neural networks and for the first time implements hypergraph neural network layers as compositions of two multiset functions that can be efficiently learned for each task and each dataset. The proposed AllSet framework also for the first time integrates Deep Sets and Set Transformers with hypergraph neural networks for the purpose of learning mul- tiset functions and therefore allows for significant modeling flexibility and high expressive power. To evaluate the performance of AllSet, we conduct the most ex- tensive experiments to date involving ten known benchmarking datasets and three newly curated datasets that represent significant challenges for hypergraph node classification. The results demonstrate that our method has the unique ability to either match or outperform all other hypergraph neural networks across the tested datasets: As an example, the performance improvements over existing methods and a new method based on heterogeneous graph neural networks are close to 4% on the Yelp and Zoo datasets, and 3% on the Walmart dataset. Our AllSet network implementation is available online.