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Register a new userA framework for generalized group testing with inhibitors and its potential application in neuroscience
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Added by
Thach V. Bui
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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The main goal of group testing with inhibitors (GTI) is to efficiently identify a small number of defective items and inhibitor items in a large set of items. A test on a subset of items is positive if the subset satisfies some specific properties. Inhibitor items cancel the effects of defective items, which often make the outcome of a test containing defective items negative. Different GTI models can be formulated by considering how specific properties have different cancellation effects. This work introduces generalized GTI (GGTI) in which a new type of items is added, i.e., hybrid items. A hybrid item plays the roles of both defectives items and inhibitor items. Since the number of instances of GGTI is large (more than 7 million), we introduce a framework for classifying all types of items non-adaptively, i.e., all tests are designed in advance. We then explain how GGTI can be used to classify neurons in neuroscience. Finally, we show how to realize our proposed scheme in practice.
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Identification of up to $d$ defective items and up to $h$ inhibitors in a set of $n$ items is the main task of non-adaptive group testing with inhibitors. To efficiently reduce the cost of this Herculean task, a subset of the $n$ items is formed and then tested. This is called textit{group testing}. A test outcome on a subset of items is positive if the subset contains at least one defective item and no inhibitors, and negative otherwise. We present two decoding schemes for efficiently identifying the defective items and the inhibitors in the presence of $e$ erroneous outcomes in time $mathsf{poly}(d, h, e, log_2{n})$, which is sublinear to the number of items $n$. This decoding complexity significantly improves the state-of-the-art schemes in which the decoding time is linear to the number of items $n$, i.e., $mathsf{poly}(d, h, e, n)$. Moreover, each column of the measurement matrices associated with the proposed schemes can be nonrandomly generated in polynomial order of the number of rows. As a result, one can save space for storing them. Simulation results confirm our theoretical analysis. When the number of items is sufficiently large, the decoding time in our proposed scheme is smallest in comparison with existing work. In addition, when some erroneous outcomes are allowed, the number of tests in the proposed scheme is often smaller than the number of tests in existing work.
The goal of combinatorial group testing is to efficiently identify up to $d$ defective items in a large population of $n$ items, where $d ll n$. Defective items satisfy certain properties while the remaining items in the population do not. To efficiently identify defective items, a subset of items is pooled and then tested. In this work, we consider complex group testing (CmplxGT) in which a set of defective items consists of subsets of positive items (called textit{positive complexes}). CmplxGT is classified into two categories: classical CmplxGT (CCmplxGT) and generalized CmplxGT (GCmplxGT). In CCmplxGT, the outcome of a test on a subset of items is positive if the subset contains at least one positive complex, and negative otherwise. In GCmplxGT, the outcome of a test on a subset of items is positive if the subset has a certain number of items of some positive complex, and negative otherwise. For CCmplxGT, we present a scheme that efficiently identifies all positive complexes in time $t times mathrm{poly}(d, ln{n})$ in the presence of erroneous outcomes, where $t$ is a predefined parameter. As $d ll n$, this is significantly better than the currently best time of $mathrm{poly}(t) times O(n ln{n})$. Moreover, in specific cases, the number of tests in our proposed scheme is smaller than previous work. For GCmplxGT, we present a scheme that efficiently identifies all positive complexes. These schemes are directly applicable in various areas such as complex disease genetics, molecular biology, and learning a hidden graph.
We consider an efficiently decodable non-adaptive group testing (NAGT) problem that meets theoretical bounds. The problem is to find a few specific items (at most $d$) satisfying certain characteristics in a colossal number of $N$ items as quickly as possible. Those $d$ specific items are called textit{defective items}. The idea of NAGT is to pool a group of items, which is called textit{a test}, then run a test on them. If the test outcome is textit{positive}, there exists at least one defective item in the test, and if it is textit{negative}, there exists no defective items. Formally, a binary $t times N$ measurement matrix $mathcal{M} = (m_{ij})$ is the representation for $t$ tests where row $i$ stands for test $i$ and $m_{ij} = 1$ if and only if item $j$ belongs to test $i$. There are three main objectives in NAGT: minimize the number of tests $t$, construct matrix $mathcal{M}$, and identify defective items as quickly as possible. In this paper, we present a strongly explicit construction of $mathcal{M}$ for when the number of defective items is at most 2, with the number of tests $t simeq 16 log{N} = O(log{N})$. In particular, we need only $K simeq N times 16log{N} = O(Nlog{N})$ bits to construct such matrices, which is optimal. Furthermore, given these $K$ bits, any entry in the matrix can be constructed in time $O left(ln{N}/ ln{ln{N}} right)$. Moreover, $mathcal{M}$ can be decoded with high probability in time $Oleft( frac{ln^2{N}}{ln^2{ln{N}}} right)$. When the number of defective items is greater than 2, we present a scheme that can identify at least $(1-epsilon)d$ defective items with $t simeq 32 C(epsilon) d log{N} = O(d log{N})$ in time $O left( d frac{ln^2{N}}{ln^2{ln{N}}} right)$ for any close-to-zero $epsilon$, where $C(epsilon)$ is a constant that depends only on $epsilon$.
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in connected communities: each individual participates in one or more communities, and the infection probability of each individual depends on the communities (s)he participates in. Use cases include students who participate in several classes, and workers who share common spaces. Group testing reduces the number of tests needed to identify the infected individuals by pooling diagnostic samples and testing them together. We show that making testing algorithms aware of the community structure, can significantly reduce the number of tests needed both for adaptive and non-adaptive group testing.
We will discuss superimposed codes and non-adaptive group testing designs arising from the potentialities of compressed genotyping models in molecular biology. The given paper was motivated by the 30th anniversary of Dyachkov-Rykov recurrent upper bound on the rate of superimposed codes published in 1982. We were also inspired by recent results obtained for non-adaptive threshold group testing which develop the theory of superimposed codes
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