scholarly journals Theoretical Bounds on Performance in Threshold Group Testing Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 637
Author(s):  
Jin-Taek Seong
Keyword(s):  
Channel Coding ◽  
Coding Theory ◽  
Large Population ◽  
Group Testing ◽  
Density Ratio ◽  
Upper And Lower Bounds ◽  
Probability Of Error ◽  
Group Matrix ◽  
Minimum Number ◽  
Threshold Group Testing

A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We aim to find lower and upper bounds for finding a set of defective samples in a large population. The decoding for the TGT scheme is exploited by minimization of the Hamming weight in channel coding theory and the probability of error is also defined. Then, we derive a new upper bound on the probability of error and extend a lower bound from conventional one to the TGT scheme. We show that the upper and lower bounds well match with each other at the optimal density ratio of the group matrix. In addition, we conclude that when the gaps between the two thresholds in the TGT framework increase, the group matrix with a high density should be used to achieve optimal performance.

Almost Safe Group Testing with Few Tests

1994 ◽  
Vol 3 (3) ◽  
pp. 411-419
Author(s):  
Andrzej Pelc
Keyword(s):  
Lower Bounds ◽  
Group Testing ◽  
Upper And Lower Bounds ◽  
Probability Functions ◽  
Minimum Number ◽  
Location Strategies

In group testing, sets of data undergo tests that reveal if a set contains faulty data. Assuming that data items are faulty with given probability and independently of one another, we investigate small families of tests that enable us to locate correctly all faulty data with probability converging to one as the amount of data grows. Upper and lower bounds on the minimum number of such tests are established for different probability functions, and respective location strategies are constructed.

scholarly journals Early detection of superspreaders by mass group pool testing can mitigate COVID-19 pandemic

2020 ◽  
Author(s):  
Maxim B Gongalsky
Keyword(s):  
New York ◽  
Early Detection ◽  
Group Testing ◽  
Scale Model ◽  
Rt Pcr ◽  
Infected People ◽  
Group Matrix ◽  
New Strategy ◽  
Mass Group ◽  
Log Normal

Background Most of epidemiological models applied for COVID-19 do not consider heterogeneity in infectiousness and impact of superspreaders, despite the broad viral loading distributions amongst COVID-19 positive people (1-1 000 000 per mL). Also, mass group testing is not used regardless to existing shortage of tests. I propose new strategy for early detection of superspreaders with reasonable number of RT-PCR tests, which can dramatically mitigate development COVID-19 pandemic and even turn it endemic. Methods I used stochastic social-epidemiological SEIAR model, where S-suspected, E-exposed, I-infectious, A-admitted (confirmed COVID-19 positive, who are admitted to hospital or completely isolated), R-recovered. The model was applied to real COVID-19 dynamics in London, Moscow and New York City. Findings Viral loading data measured by RT-PCR were fitted by broad log-normal distribution, which governed high importance of superspreaders. The proposed full scale model of a metropolis shows that top 10% spreaders (100+ higher viral loading than median infector) transmit 45% of new cases. Rapid isolation of superspreaders leads to 4-8 fold mitigation of pandemic depending on applied quarantine strength and amount of currently infected people. High viral loading allows efficient group matrix pool testing of population focused on detection of the superspreaders requiring remarkably small amount of tests. Interpretation The model and new testing strategy may prevent thousand or millions COVID-19 deaths requiring just about 5000 daily RT-PCR test for big 12 million city such as Moscow. Though applied to COVID-19 pandemic the results are universal and can be used for other infectious heterogenous epidemics. Funding No funding

scholarly journals A Generalized Channel Coding Theory for Distributed Communication

2015 ◽  
Vol 63 (4) ◽  
pp. 1043-1056 ◽  
Author(s):  
Jie Luo
Keyword(s):  
Channel Coding ◽  
Coding Theory ◽  
Distributed Communication

scholarly journals Group Testing-Based Robust Algorithm for Diagnosis of COVID-19

Diagnostics ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 396
Author(s):  
Jin-Taek Seong
Keyword(s):  
Large Population ◽  
Group Testing ◽  
Incidence Rates ◽  
Posteriori Probability ◽  
Iterative Detection ◽  
Robust Algorithm ◽  
A Posteriori Probability ◽  
Small Set ◽  
Diagnosis Method ◽  
Severe Infections

At the time of writing, the COVID-19 infection is spreading rapidly. Currently, there is no vaccine or treatment, and researchers around the world are attempting to fight the infection. In this paper, we consider a diagnosis method for COVID-19, which is characterized by a very rapid rate of infection and is widespread. A possible method for avoiding severe infections is to stop the spread of the infection in advance by the prompt and accurate diagnosis of COVID-19. To this end, we exploit a group testing (GT) scheme, which is used to find a small set of confirmed cases out of a large population. For the accurate detection of false positives and negatives, we propose a robust algorithm (RA) based on the maximum a posteriori probability (MAP). The key idea of the proposed RA is to exploit iterative detection to propagate beliefs to neighbor nodes by exchanging marginal probabilities between input and output nodes. As a result, we show that our proposed RA provides the benefit of being robust against noise in the GT schemes. In addition, we demonstrate the performance of our proposal with a number of tests and successfully find a set of infected samples in both noiseless and noisy GT schemes with different COVID-19 incidence rates.

Sub-linear Time Stochastic Threshold Group Testing via Sparse-Graph Codes

2018 ◽  
Author(s):  
Amirhossein Reisizadeh ◽  
Pedro Abdalla ◽  
Ramtin Pedarsani
Keyword(s):  
Linear Time ◽  
Group Testing ◽  
Sparse Graph ◽  
Graph Codes ◽  
Threshold Group Testing

scholarly journals Efficiently Decodable Non-Adaptive Threshold Group Testing

2019 ◽  
Vol 65 (9) ◽  
pp. 5519-5528 ◽  
Author(s):  
Thach V. Bui ◽  
Minoru Kuribayashi ◽  
Mahdi Cheraghchi ◽  
Isao Echizen
Keyword(s):  
Group Testing ◽  
Adaptive Threshold ◽  
Threshold Group Testing

2-Distance chromatic number of some graph products

2020 ◽  
Vol 12 (02) ◽  
pp. 2050021
Author(s):  
Ghazale Ghazi ◽  
Freydoon Rahbarnia ◽  
Mostafa Tavakoli
Keyword(s):  
Chromatic Number ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Graph Products ◽  
Lexicographic Product ◽  
Graph Product ◽  
Minimum Number

This paper studies the 2-distance chromatic number of some graph product. A coloring of [Formula: see text] is 2-distance if any two vertices at distance at most two from each other get different colors. The minimum number of colors in the 2-distance coloring of [Formula: see text] is the 2-distance chromatic number and denoted by [Formula: see text]. In this paper, we obtain some upper and lower bounds for the 2-distance chromatic number of the rooted product, generalized rooted product, hierarchical product and we determine exact value for the 2-distance chromatic number of the lexicographic product.

scholarly journals TESTING EMBEDDABILITY BETWEEN METRIC SPACES

2009 ◽  
Vol 20 (02) ◽  
pp. 313-329
Author(s):  
CHING-LUEH CHANG ◽  
YUH-DAUH LYUU ◽  
YEN-WU TI
Keyword(s):  
Metric Space ◽  
Upper Bound ◽  
Metric Spaces ◽  
Graph Isomorphism ◽  
Upper And Lower Bounds ◽  
Wrong Answer ◽  
Probability Of Error ◽  
Finite Metric Space ◽  
Finite Metric Spaces ◽  
Special Case

Let L ≥ 1, ε > 0 be real numbers, (M, d) be a finite metric space and (N, ρ) be a metric space. A query to a metric space consists of a pair of points and asks for the distance between these points. We study the number of queries to metric spaces (M, d) and (N, ρ) needed to decide whether (M, d) is L-bilipschitz embeddable into (N, ρ) or ∊-far from being L-bilipschitz embeddable into N, ρ). When (M, d) is ∊-far from being L-bilipschitz embeddable into (N, ρ), we allow an o(1) probability of error (i.e., returning the wrong answer "L-bilipschitz embeddable"). However, no error is allowed when (M, d) is L-bilipschitz embeddable into (N, ρ). That is, algorithms with only one-sided errors are studied in this paper. When |M| ≤ |N| are both finite, we give an upper bound of [Formula: see text] on the number of queries for determining with one-sided error whether (M, d) is L-bilipschitz embeddable into (N, ρ) or ∊-far from being L-bilipschitz embeddable into (N, ρ). For the special case of finite |M| = |N|, the above upper bound evaluates to [Formula: see text]. We also prove a lower bound of Ω(|N|3/2) for the special case when |M| = |N| are finite and L = 1, which coincides with testing isometry between finite metric spaces. For finite |M| = |N|, the upper and lower bounds thus match up to a multiplicative factor of at most [Formula: see text], which depends only sublogarithmically in |N|. We also investigate the case when (N, ρ) is not necessarily finite. Our results are based on techniques developed in an earlier work on testing graph isomorphism.

Stochastic threshold group testing

2013 ◽  
Author(s):  
C. L. Chan ◽  
S. Cai ◽  
M. Bakshi ◽  
S. Jaggi ◽  
V. Saligrama
Keyword(s):  
Group Testing ◽  
Threshold Group Testing
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