Related papers: Multi-stage Group Testing with (r,s)-regular desig…
Quality control is an essential operation in manufacturing, ensuring products meet the necessary standards of quality, safety, and reliability. Traditional methods, such as visual inspections, measurements, and statistical techniques, help…
Consider a very large (infinite) population of items, where each item independent from the others is defective with probability p, or good with probability q=1-p. The goal is to identify N good items as quickly as possible. The following…
We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the…
In industrial settings, surface defects on steel can significantly compromise its service life and elevate potential safety risks. Traditional defect detection methods predominantly rely on manual inspection, which suffers from low…
Consider a finite population of $N$ items, where item $i$ has a probability $p_i$ to be defective. The goal is to identify all items by means of group testing. This is the generalized group testing problem (hereafter GGTP). In the case of…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…
Given $d$ defective items in a population of $n$ items with $d \ll n$, in threshold group testing without gap, the outcome of a test on a subset of items is positive if the subset has at least $u$ defective items and negative otherwise,…
Recently, methodology was presented to facilitate the incorporation of interim analyses in stepped-wedge (SW) cluster randomised trials (CRTs). Here, we extend this previous discussion. We detail how the stopping boundaries, allocation…
In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main…
The group testing problem is concerned with identifying a small number $k \sim n^\theta$ for $\theta \in (0,1)$ of infected individuals in a large population of size $n$. At our disposal is a testing procedure that allows us to test groups…
Inspired by applications in testing for Covid-19, we consider a variant of two-stage group testing called "conservative" (or "trivial") two-stage testing, where every item declared to be defective must be definitively confirmed by being…
This paper proposes a novel generalization of group testing, called multi-group testing, which relaxes the notion of "testing subset" in group testing to "testing multi-set". The generalization aims to learn more information of each item to…
The motivation for this paper comes from the ongoing SARS-CoV-2 Pandemic. Its goal is to present a previously neglected approach to non-adaptive group testing and describes it in terms of residuated pairs on partially ordered sets. Our…
Addressing the reproducibility crisis in artificial intelligence through the validation of reported experimental results is a challenging task. It necessitates either the reimplementation of techniques or a meticulous assessment of papers…
Large scale disease screening is a complicated process in which high costs must be balanced against pressing public health needs. When the goal is screening for infectious disease, one approach is group testing in which samples are…
As an important way of assuring software quality, software testing generates and executes test cases to identify software failures. Many strategies have been proposed to guide test-case generation, such as source-code-based approaches and…
Group testing algorithms are very useful tools for DNA library screening. Building on recent work by Levenshtein (2003) and Tonchev (2008), we construct in this paper new infinite classes of combinatorial structures, the existence of which…
Unit testing verifies the presence of faults in individual software components. Previous research has been targeting the automatic generation of unit tests through the adoption of random or search-based algorithms. Despite their…
Adaptive designs have been proposed for clinical trials in which the nuisance parameters or alternative of interest are unknown or likely to be misspecified before the trial. Whereas most previous works on adaptive designs and mid-course…
We study the group testing problem with non-adaptive randomized algorithms. Several models have been discussed in the literature to determine how to randomly choose the tests. For a model ${\cal M}$, let $m_{\cal M}(n,d)$ be the minimum…