Related papers: Optimal Nested Test Plan for Combinatorial Quantit…
A method to compute the optimal success probability of discrimination of N arbitrary quantum states is presented, based on the decomposition of any N-outcome measurement into sequences of nested two-outcome ones. In this way the…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern…
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…
Group testing has its origin in the identification of syphilis in the US army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently,…
Choosing an optimal strategy for hierarchical group testing is an important problem for practitioners who are interested in disease screening with limited resources. For example, when screening for infectious diseases in large populations,…
In probabilistic nonadaptive group testing (PGT), we aim to characterize the number of pooled tests necessary to identify a random $k$-sparse vector of defectives with high probability. Recent work has shown that $n$ tests are necessary…
The goal of group testing is to identify a small number of defective items within a large population. In the non-adaptive setting, tests are designed in advance and represented by a measurement matrix $\mM$, where rows correspond to tests…
The principal goal of Group Testing (GT) is to identify a small subset of "defective" items from a large population, by grouping items into as few test pools as possible. The test outcome of a pool is positive if it contains at least one…
Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the…
Group testing enables to identify infected individuals in a population using a smaller number of tests than individual testing. To achieve this, group testing algorithms commonly assume knowledge of the number of infected individuals;…
We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that…
Motivated by testing for pathogenic diseases we consider a new nonadaptive group testing problem for which: (1) positives occur within a burst, capturing the fact that infected test subjects often come in clusters, and (2) that the test…
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
We have a large number of samples and we want to find the infected ones using as few number of tests as possible. We can use group testing which tells about a small group of people whether at least one of them is infected. Group testing is…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
We consider the nonadaptive group testing with N items, of which $K = \Theta(N^\theta)$ are defective. We study a test design in which each item appears in nearly the same number of tests. For each item, we independently pick L tests…
We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We…
Group testing techniques are widely used in resource-constrained settings, such as infectious-disease screening, blood safety, DNA library screening, and industrial inspection, where the efficient use of limited testing resources depends…
Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based…
We treat the statistical inference problems in which one needs to detect and estimate simultaneously using as small number of samples as possible. Conventional methods treat the detection and estimation subproblems separately, ignoring the…