Asymptotics of pooling design performance

1999 ◽  
Vol 36 (4) ◽  
pp. 951-964 ◽  
Author(s):  
J. K. Percus ◽  
O. E. Percus ◽  
W. J. Bruno ◽  
D. C. Torney
Keyword(s):  
Group Testing ◽  
Performance Criterion ◽  
Expected Number ◽  
Pooling Design ◽  
Pooling Designs ◽  
Parametric Control ◽  
Expected Performance ◽  
Qualitative Effect ◽  
Pooling Strategy ◽  
Asymptotic Forms

We analyse the expected performance of various group testing, or pooling, designs. The context is that of identifying characterized clones in a large collection of clones. Here we choose as performance criterion the expected number of unresolved ‘negative’ clones, and we aim to minimize this quantity. Technically, long inclusion–exclusion summations are encountered which, aside from being computationally demanding, give little inkling of the qualitative effect of parametric control on the pooling strategy. We show that readily-interpreted re-summation can be performed, leading to asymptotic forms and systematic corrections. We apply our results to randomized designs, illustrating how they might be implemented for approximating combinatorial formulae.

Asymptotics of pooling design performance

1999 ◽  
Vol 36 (04) ◽  
pp. 951-964
Author(s):  
J. K. Percus ◽  
O. E. Percus ◽  
W. J. Bruno ◽  
D. C. Torney
Keyword(s):  
Group Testing ◽  
Performance Criterion ◽  
Expected Number ◽  
Pooling Design ◽  
Pooling Designs ◽  
Parametric Control ◽  
Expected Performance ◽  
Qualitative Effect ◽  
Pooling Strategy ◽  
Asymptotic Forms

We analyse the expected performance of various group testing, or pooling, designs. The context is that of identifying characterized clones in a large collection of clones. Here we choose as performance criterion the expected number of unresolved ‘negative’ clones, and we aim to minimize this quantity. Technically, long inclusion–exclusion summations are encountered which, aside from being computationally demanding, give little inkling of the qualitative effect of parametric control on the pooling strategy. We show that readily-interpreted re-summation can be performed, leading to asymptotic forms and systematic corrections. We apply our results to randomized designs, illustrating how they might be implemented for approximating combinatorial formulae.

A Monotonicity Result for Inspecting Independent Items

1989 ◽  
Vol 3 (1) ◽  
pp. 135-140
Author(s):  
F.K. Hwang ◽  
S.G. Papastavridis
Keyword(s):  
Cost Function ◽  
Failure Probability ◽  
General Model ◽  
Group Testing ◽  
Probabilistic Algorithms ◽  
Expected Number ◽  
Monotonicity Result ◽  
Crucial Part

Recently, the conjecture that the expected number of tests is nondecreasing in the failure probability for binomial group testing has been proved. The proof has also been extended to three models of multiaccess systems. However, probabilistic algorithms are used as a crucial part of these proofs. In this paper, we give conceptually simpler new proofs without using probabilistic algorithms. We also extend the result to a more general model where the number of tests is replaced by a cost function.

scholarly journals A NEW CONSTRUCTION FOR POOLING DESIGNS

2011 ◽  
Vol 85 (1) ◽  
pp. 121-127
Author(s):  
FENGLIANG JIN ◽  
HOUCHUN ZHOU ◽  
JUAN XU
Keyword(s):  
Library Screening ◽  
Pooling Design ◽  
Pooling Designs ◽  
Disjunct Matrix ◽  
Helpful Tool ◽  
Dna Library ◽  
New Family ◽  
New Construction ◽  
Dna Library Screening ◽  
Disjunct Matrices

AbstractPooling designs are a very helpful tool for reducing the number of tests for DNA library screening. A disjunct matrix is usually used to represent the pooling design. In this paper, we construct a new family of disjunct matrices and prove that it has a good row to column ratio and error-tolerant property.

scholarly journals An Improvement Over the Information Lower Bound in Binomial Group Testing

1988 ◽  
Vol 2 (3) ◽  
pp. 313-320 ◽  
Author(s):  
Y.C. Yao
Keyword(s):  
Lower Bound ◽  
Group Testing ◽  
Expected Number ◽  
Testing Problem

The group-testing problem for a binomial set of items is considered. It is desired to classify all items as good or defective with a minimum expected number of group tests. An improvement over the information lower bound, via a weak concavity property, is made for the minimum expected number of group tests.

An Improved Lower Bound on the Minimum Expected Number of Binomial Group Tests

1993 ◽  
Vol 7 (1) ◽  
pp. 121-124 ◽  
Author(s):  
Julia Abrahams
Keyword(s):  
Lower Bound ◽  
Group Testing ◽  
Huffman Coding ◽  
Expected Number ◽  
The Cost

The minimum expected number of binomial group tests is lower bounded by the cost of a particular Huffman coding problem whose solution is known. Thus, the information lower bound in binomial group testing is improved when the probability that each item is defective is small.

scholarly journals Cutting testing costs by the pooling design

2020 ◽  
Vol 68 (4) ◽  
pp. 743-759
Author(s):  
Dimitrije Čvokić
Keyword(s):  
Large Scale ◽  
Group Testing ◽  
Current Situation ◽  
Resource Usage ◽  
Pooling Design ◽  
Splitting Algorithm ◽  
The Matrix ◽  
Binary Splitting ◽  
Testing Algorithms ◽  
Group Testing Algorithms

Introduction/purpose: The purpose of group testing algorithms is to provide a more rational resource usage. Therefore, it is expected to improve the efficiency of large-scale COVID-19 screening as well. Methods: Two variants of non-adaptive group testing approaches are presented: Hwang's generalized binary-splitting algorithm and the matrix strategy. Results: The positive and negative sides of both approaches are discussed. Also, the estimations of the maximum number of tests are given. The matrix strategy is presented with a particular modification which reduces the corresponding estimation of the maximum number of tests and which does not affect the complexity of the procedure. This modification can be interesting from the applicability viewpoint. Conclusion: Taking into account the current situation, it makes sense to consider these methods in order to achieve some resource cuts in testing, thus making the epidemiological measures more efficient than they are now.

ASYMPTOTIC ANALYSIS OF OPTIMAL NESTED GROUP-TESTING PROCEDURES

2016 ◽  
Vol 30 (4) ◽  
pp. 547-552 ◽  
Author(s):  
Nabil Zaman ◽  
Nicholas Pippenger
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Group Testing ◽  
Fractional Part ◽  
Expected Number ◽  
Small Oscillations ◽  
Testing Procedures ◽  
Average Value ◽  
Positive Individual ◽  
Image Position

We analyze a construction for optimal nested group-testing procedures, and show that, when individuals are independently positive with probability p, the expected number of tests per positive individual, F*(p), has, as p→0, the asymptotic behavior $$F^{\ast}(p) = \log_2 {1\over p} + \log_2 \log 2 + 2 + f\left(\log_2 {1\over p} + \log_2 \log 2\right) + O(p),$$ where $$f(z) = 4\times 2^{-2^{1-\{z\}}} - \{z\} - 1,$$ and {z}=z−⌊z⌋ is the fractional part of z. The function f(z) is a periodic function (with period 1) that exhibits small oscillations (with magnitude <0.005) about an even smaller average value (<0.0005).

scholarly journals POOLING FOR SARS-COV-2 CONTROL IN CARE INSTITUTIONS

2020 ◽  
Author(s):  
Jorge J Cabrera ◽  
Sonia Rey ◽  
Sonia Pérez ◽  
Lucía Martínez-Lamas ◽  
Olaia Cores-Calvo ◽  
...  
Keyword(s):  
Scale Up ◽  
Average Delay ◽  
Global Rate ◽  
Local Experience ◽  
Expected Performance ◽  
Pooling Strategy ◽  
Low Prevalence ◽  
Small Clusters ◽  
Very High ◽  
Special Risk

ABSTRACTWorkers and residents in Care Homes are considered at special risk for the acquisition of SARS-CoV-2 infection, due to the infectivity and high mortality rate in the case of residents, compared to other containment areas. The aims of the present study, based in our local experience, were (a) to describe SARS-CoV-2 prevalence in institutionalized people in Galicia (Spain) during the Coronavirus pandemic and (b) to evaluate the expected performance of a pooling strategy using RT-PCR for the next rounds of screening of institutionalized people.Distribution of SARS-CoV-2 infection at Care Houses was uneven. As the virus circulation global rate was low in our area, the number of people at risk of acquiring the infection continues to be very high. In this work, we have successfully demonstrated that pooling of different groups of samples at low prevalence clusters, can be done with a small average delay on quantification cycle (Cq) values. A new surveillance system with guaranteed protection is required for small clusters, previously covered with individual testing. Our proposal for Care Houses, once prevalence zero is achieved, would include successive rounds of testing using a pooling solution for transmission control preserving testing resources. Scale-up of this method may be of utility to confront larger clusters to avoid the viral circulation and keeping them operative.

ERROR-TOLERANT TRIVIAL TWO-STAGE GROUP TESTING FOR COMPLEXES USING ALMOST SEPARABLE AND ALMOST DISJUNCT MATRICES

2009 ◽  
Vol 01 (02) ◽  
pp. 235-251 ◽  
Author(s):  
WEIWEI LANG ◽  
YUEXUAN WANG ◽  
JAMES YU ◽  
SUOGANG GAO ◽  
WEILI WU
Keyword(s):  
Fault Tolerant ◽  
Group Testing ◽  
Pooling Designs ◽  
Two Stage ◽  
Disjunct Matrix ◽  
Expected Values ◽  
Disjunct Matrices ◽  
Separable Matrix ◽  
The Given

In this paper, we define an α-almost (k; 2e + 1)-separable matrix and an α-almostke-disjunct matrix. Using their complements, we devise algorithms for fault-tolerant trivial two-stage group tests (pooling designs) for k-complexes. We derive the expected values for the given algorithms to identify all such positive complexes.

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