Epistasis can be defined as the statistical interaction of genes during the expression of a phenotype. It is believed that it plays a fundamental role in gene expression, as individual genetic variants have reported a very small increase in disease risk in previous Genome-Wide Association Studies. The most successful approach to epistasis detection is the exhaustive method, although its exponential time complexity requires a highly parallel implementation in order to be used. This work presents Fiuncho, a program that exploits all levels of parallelism present in x86_64 CPU clusters in order to mitigate the complexity of this approach. It supports epistasis interactions of any order, and when compared with other exhaustive methods, it is on average 242, 7 and 3 times faster than MDR, BitEpi and MPI3SNP, respectively.
The interaction among different genes when expressing a particular phenotype is known as epistasis. High-order epistasis, when more than two loci are involved, is an active research area because it could be the cause of many complex traits. The most common abstraction for specifying an epistasis interaction is through a penetrance table, which captures the probability of expressing the studied phenotype given a particular genotype.Although it is very common for simulators to use penetrance tables, most of them do not allow the user to generate them directly, or present limitations for high-order interac- tions and/or realistic prevalence and heritability values. In this work, we present PyToxo, a Python tool for generating penetrance tables from any-order epistasis models. PyToxo allows to work with more appropriate scenarios than other state-of-the-art tools. Addi- tionally, it also improves in terms of accuracy, speed and ease of use, being available as a library, through a CLI or through a cross-platform GUI.
We consider a very general family of Hilbert spaces of analytic functions in the unit disk which satisfy only a minimum number of requirements and whose reproducing kernels have the usual natural form. Under such assumptions, we obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric (equivalently, unitary) on such a space. The result reveals a dichotomy identifying a specific family of weighted Hardy spaces as the only ones that support non-trivial operators of this kind.
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