We consider the problem of non-adaptive noiseless group testing of N items of which K are defective. We describe four detection algorithms: the COMP algorithm of Chan et al.; two new algorithms, DD and SCOMP, which require stronger evidence to declare an item defective; and an essentially optimal but computationally difficult algorithm called SSS. By considering the asymptotic rate of these algorithms with Bernoulli designs we see that DD outperforms COMP, that DD is essentially optimal in regimes where K ≥ √ N , and that no algorithm with a nonadaptive Bernoulli design can perform as well as the best non-random adaptive designs when K > N 0.35 . In simulations, we see that DD and SCOMP far outperform COMP, with SCOMP very close to the optimal SSS, especially in cases with larger K. Contents
Abstract-We define capacity for group testing problems and deduce bounds for the capacity of a variety of noisy models, based on the capacity of equivalent noisy communication channels. For noiseless adaptive group testing we prove an informationtheoretic lower bound which tightens a bound of Chan et al. This can be combined with a performance analysis of a version of Hwang's adaptive group testing algorithm, in order to deduce the capacity of noiseless and erasure group testing models.
An m × n matrix A with column supports {Si} is k-separable if the disjunctions i∈K Si are all distinct over all sets K of cardinality k. While a simple counting bound shows that m > k log 2 n/k rows are required for a separable matrix to exist, in fact it is necessary for m to be about a factor of k more than this. In this paper, we consider a weaker definition of 'almost k-separability', which requires that the disjunctions are 'mostly distinct'. We show using a random construction that these matrices exist with m = O(k log n) rows, which is optimal for k = O(n 1−β ). Further, by calculating explicit constants, we show how almost separable matrices give new bounds on the rate of nonadaptive group testing.
In recent years, vitamin D has become the protagonist in many studies. From cardiology to oncology the spotlight was on this vitamin. While in the past it was considered for its important role in phospho-calcium metabolism and skeletal disorders; today by studying it better, thousands of scenarios and facets have opened up on this vitamin which is actually a hormone in all respects. There are authoritative studies that demonstrate its activity in vitro and in vivo on: carcinogenesis, inflammation, autoimmunity and endocrinopathies. Its role has been studied in type 1 and type 2 diabetes mellitus, in Hashimoto or Graves’ thyroiditis and even in adrenal gland diseases. In fact, there are several studies that demonstrate the possible correlations between vitamin D and: Addison’s disease, Cushing disease, hyperaldosteronism or adrenocortical tumors. Moreover, this fascinating hormone and adrenal gland even seem to be deeply connected by common genetic pathways. This review aimed to analyze the works that have tried to study the possible influence of vitamin D on adrenal diseases. In this review we analyze the works that have tried to study the possible influence of vita-min D on adrenal disease.
The workflow of data scientists normally involves potentially inefficient processes such as data mining, feature engineering and model selection. Recent research has focused on automating this workflow, partly or in its entirety, to improve productivity. We choose the former approach and in this paper share our experience in designing the client2vec: an internal library to rapidly build baselines for banking applications. Client2vec uses marginalized stacked denoising autoencoders on current account transactions data to create vector embeddings which represent the behaviors of our clients. These representations can then be used in, and optimized against, a variety of tasks such as client segmentation, profiling and targeting. Here we detail how we selected the algorithmic machinery of client2vec and the data it works on and present experimental results on several business cases.
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