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We propose a novel group testing method, termed semiquantitative group testing (SQGT), motivated by a class of problems arising in genome screening experiments. The SQGT is a (possibly) nonbinary pooling scheme that may be viewed as a concatenation of an adder channel and an integer-valued quantizer. In its full generality, SQGT may be viewed as a unifying… (More)

We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are “symmetric” while the outputs are drawn from a ternary alphabet. Using an information-theoretic approach, we derive sufficient and necessary conditions for… (More)

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model applies to a number of biological testing scenarios, where the subjects are assumed to be ordered based on their arrival times and where the probability of being… (More)

We propose a novel group testing method, termed semi-quantitative group testing, motivated by a class of problems arising in genome screening experiments. Semi-quantitative group testing (SQGT) is a (possibly) non-binary pooling scheme that may be viewed as a concatenation of an adder channel and an integer-valued quantizer. In its full generality, SQGT can… (More)

—We consider the problem of noiseless and noisy low-rank tensor completion from a set of random linear measurements. In our derivations, we assume that the entries of the tensor belong to a finite field of arbitrary size and that reconstruction is based on a rank minimization framework. The derived results show that the smallest number of measurements… (More)

We introduce a novel algorithm for inference of causal gene interactions, termed CaSPIAN (Causal Subspace Pursuit for Inference and Analysis of Networks), which is based on coupling compressive sensing and Granger causality techniques. The core of the approach is to discover sparse linear dependencies between shifted time series of gene expressions using a… (More)

—Metagenomics is an emerging field of molecular biology concerned with analyzing the genomes of environmental samples comprising many different diverse organisms. Given the nature of metagenomic data, one usually has to sequence the genomic material of all organisms in a batch, leading to a mix of reads coming from different DNA sequences. In deep… (More)

MOTIVATION
Cancer genomes exhibit a large number of different alterations that affect many genes in a diverse manner. An improved understanding of the generative mechanisms behind the mutation rules and their influence on gene community behavior is of great importance for the study of cancer.
RESULTS
To expand our capability to analyze combinatorial… (More)

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including dynamic testing with diminishing relative rates of defectives. We consider both nonadaptive and semi-adaptive identification… (More)

We present a new family of codes for non-uniformly quantized adder channels. Quantized adder channels are generalizations of group testing models, which were studied under the name of semi-quantitative group testing. We describe non-binary group testing schemes in which the test matrices are generated by concatenating scaled disjunct codebooks, with the… (More)