Elucidating the genotype–phenotype map by automatic enumeration and analysis of the phenotypic repertoire
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Abstract Background: The gap between genotype and phenotype is filled by complex biochemical systems most of which are poorly understood. Because these systems are complex, it is widely appreciated that quantitative understanding can only be achieved with the aid of mathematical models. However, formulating models and measuring or estimating their numerous rate constants and binding constants is daunting. Here we present a strategy for automating difficult aspects of the process. Methods: The strategy, based on a system design space methodology, is applied to a class of 16 designs for a synthetic gene oscillator that includes seven designs previously formulated on the basis of experimentally measured and estimated parameters. Results: Our strategy provides four important innovations by automating: (1) enumeration of the repertoire of qualitatively distinct phenotypes for a system; (2) generation of parameter values for any particular phenotype; (3) simultaneous realization of parameter values for several phenotypes to aid visualization of transitions from one phenotype to another, in critical cases from functional to dysfunctional; and (4) identification of ensembles of phenotypes whose expression can be phased to achieve a specific sequence of functions for rationally engineering synthetic constructs. Our strategy, applied to the 16 designs, reproduced previous results and identified two additional designs capable of sustained oscillations that were previously missed. Conclusions: Starting with a system’s relatively fixed aspects, its architectural features, our method enables automated analysis of nonlinear biochemical systems from a global perspective, without first specifying parameter values. The examples presented demonstrate the efficiency and power of this automated strategy.Keywords:
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TRT Turkish folk music repertoire is used as a common repertoire in the performance of Turkish folk instruments. Among these Turkish folk instruments, the baglama is one of the main instruments that stand out in Turkish folk music. In baglama performance, it is known that works belonging to different musical genres or new works composed for the baglama are used, as well as the use of the THM repertoire to a large extent. It can be said that this is due to the ability of the baglama to easily adapt to different types of music and types of performance, and to have a large performance capacity that baglama players today reach. Therefore, given the level of performance that the baglama, which has a rich performing infrastructure, has reached today, there is a need for an instrumental repertoire based on instrument performance. In the study, the existing instrumental repertoire used in baglama performance was evaluated from various angles. The main results of the study are that the baglama has a very rich performing infrastructure, there are alternative or new/innovative repertoire works next to the existing THM repertoire, baglama performers are already entering the repertoire areas of different musical genres due to the need for instrumental repertoire.
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In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions and also r.e. sets and studied their properties. Based on this reducibility we introduce an equivalence relation "Enumeration Order Equivalency". We have reached some properties of it. In subsequent, we have introduced another concept named "type-2 Enumeration Order Equivalency" and studied its properties too.
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Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WilfPlus , which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decompositions, and the insertion encoding.
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Abstract Using properties of ${\cal K}$ -pairs of sets, we show that every nonzero enumeration degree a bounds a nontrivial initial segment of enumeration degrees whose nonzero elements have all the same jump as a . Some consequences of this fact are derived, that hold in the local structure of the enumeration degrees, including: There is an initial segment of enumeration degrees, whose nonzero elements are all high; there is a nonsplitting high enumeration degree; every noncappable enumeration degree is high; every nonzero low enumeration degree can be capped by degrees of any possible local jump (i.e., any jump that can be realized by enumeration degrees of the local structure); every enumeration degree that bounds a nonzero element of strictly smaller jump, is bounding; every low enumeration degree below a non low enumeration degree a can be capped below a .
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In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
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We exhibit finite injury constructions of a high Σ02 enumeration degree incomparable with all intermediate Δ02 enumeration degrees, as also of both an upwards properly Σ02 high and a low non-cuppable Σ02 enumeration degree.We also outline how to apply the same methods to prove that, for every Σ02 enumeration degree b there exists a non-cuppable degree a such that b' ≤a' and a" ≤ b", thus showing that there exist non-cuppable Σ02 enumeration degrees at every possible level of the high/low jump hierarchy.
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