A fast pattern matching scheme termed matching by tone mapping (MTM) is introduced which allows matching under nonlinear tone mappings. We show that, when tone mapping is approximated by a piecewise constant/linear function, a fast computational scheme is possible requiring computational time similar to the fast implementation of normalized cross correlation (NCC). In fact, the MTM measure can be viewed as a generalization of the NCC for nonlinear mappings and actually reduces to NCC when mappings are restricted to be linear. We empirically show that the MTM is highly discriminative and robust to noise with comparable performance capability to that of the well performing mutual information, but on par with NCC in terms of computation time.

Inter-individual variation in regulatory circuits controlling gene expression is a powerful source of functional information. The study of associations among genetic variants and gene expression provides important insights about cell circuitry but cannot specify whether and when potential variants dynamically alter their genetic effect during the course of response. Here we develop a computational procedure that captures temporal changes in genetic effects, and apply it to analyze transcription during inhibition of the TOR signaling pathway in segregating yeast cells. We found a high-order coordination of gene modules: sets of genes co-associated with the same genetic variant and sharing a common temporal genetic effect pattern. The temporal genetic effects of some modules represented a single state-transitioning pattern; for example, at 10-30 minutes following stimulation, genetic effects in the phosphate utilization module attained a characteristic transition to a new steady state. In contrast, another module showed an impulse pattern of genetic effects; for example, in the poor nitrogen sources utilization module, a spike up of a genetic effect at 10-20 minutes following stimulation reflected inter-individual variation in the timing (rather than magnitude) of response. Our analysis suggests that the same mechanism typically leads to both inter-individual variation and the temporal genetic effect pattern in a module. Our methodology provides a quantitative genetic approach to studying the molecular mechanisms that shape dynamic changes in transcriptional responses.

We propose a fast pattern matching scheme termed Matching by Tone Mapping (MTM) which allows matching under non-linear tone mappings. We show that, when tone mapping is approximated by a piecewise constant function, a fast computational scheme is possible requiring computational time similar to the fast implementation of Normalized Cross Correlation (NCC). In fact, the MTM measure can be viewed as a generalization of the NCC for non-linear mappings and actually reduces to NCC when mappings are restricted to be linear. The MTM is shown to be invariant to non-linear tone mappings, and is empirically shown to be highly discriminative and robust to noise.