The Rice-Shapiro theorem in Computable Topology

We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of effectively enumerable topological spaces where the Rice-Shapiro theorem does not hold. We propose two constructions that generate effectively enumerable topological spaces with particular properties from wn--families and computable trees without computable infinite paths. Using them we propose examples that give a flavor of this class

First Order Theories of Some Lattices of Open Sets

We show that the first order theory of the lattice of open sets in some natural topological spaces is $m$-equivalent to second order arithmetic. We also show that for many natural computable metric spaces and computable domains the first order theory of the lattice of effectively open sets is undecidable. Moreover, for several important spaces (e.g., $\mathbb{R}^n$, $n\geq1$, and the domain $P\omega$) this theory is $m$-equivalent to first order arithmetic

Genome-wide association study for frozen-thawed sperm motility in stallions across various horse breeds

Objective: The semen quality of stallions including sperm motility is an important target of selection as it has a high level of individual variability. However, effects of the molecular architecture of the genome on the mechanisms of sperm formation and their preservation after thawing have been poorly investigated. Here, we conducted a genome-wide association study (GWAS) for the sperm motility of cryopreserved semen in stallions of various breeds. Methods: Semen samples were collected from the stallions of 23 horse breeds. The following semen characteristics were examined: progressive motility (PM), progressive motility after freezing (FPM), and the difference between PM and FPM. The respective DNA samples from these stallions were genotyped using Axiom™ Equine Genotyping Array. Results: We performed a GWAS search for single nucleotide polymorphism (SNP) markers and potential genes related to motility properties of frozen-thawed semen in the stallions of various breeds. As a result of the GWAS analysis, two SNP markers, rs1141327473 and rs1149048772, were identified that were associated with preservation of the frozen-thawed stallion sperm motility, the relevant putative candidate genes being NME8, OR2AP1 and OR6C4. Potential implications of effects of these genes on sperm motility are herein discussed. Conclusion: The GWAS results enabled us to localize novel SNPs and candidate genes for sperm motility in stallions. Implications of the study for horse breeding and genetics are a better understanding of genomic regions and candidate genes underlying stallion sperm quality, and improvement in horse reproduction and breeding techniques. The identified markers and genes for sperm cryotolerance and the respective genomic regions are promising candidates for further studying the biological processes in the formation and function of the stallion reproductive system

AUTOSTABILITY OF CONSTRUCTIVE MODELS

The proposed sufficient condition of the autostability is the autostability criterion of the models of some classes, specifically, I-models, but is not the general criterion. The criterion of the recursive stability has been shown, the autostable I-models have been described completely. The correlations between classes of the models being uniformly stable at different formalizations of this concept have been determinedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

The finite Language for Computable Metric Spaces

In this paper we propose a model-theoretic characterisation of computable metric spaces and computability over them in a finite language

Towards Computability over Effectively Enumerable Topological Spaces

In this paper we study different approaches to computability over effectively enumerable topological spaces. We introduce and investigate the notions of computable function, strongly-computable function and weakly-computable function. Under natural assumptions on effectively enumerable topological spaces the notions of computability and weakly-computability coincide

Algorithmic Properties of Sigma--definability over Positive Predicate Structures

In this paper we propose a generalisation of the authors p results on semantical characterisation of $\Sigma$--definability. We prove that over every positive predicate structure a set is $\Sigma$-definable if and only if it is definable by a disjunction of a recursively enumerable set of existential formulas

Uniformity principle for Σ\Sigma-definability

The main goal of this research is to develop logical tools and techniques for effective reasoning about continuous data based on $\Sigma$-definability. In this article we invent the Uniformity Principleand prove it for $\Sigma$-definability over the real numbers extended by open predicates. Using the Uniformity Principle, we investigate different approaches to enrich the language of {Sigma}-formulas in such a way that simplifies reasoning about computable continuous data without enlarging the class of $\Sigma$-definable sets. In order to do reasoning about computability of certain continuous data we have to pick up an appropriate language of a structure representing these continuous data. We formulate several major conditions how to do that in a right direction. We also employ the Uniformity Principleto argue that our logical approach is a good way for formalization of computable continuous data in logical terms

The Rice-Shapiro theorem in Computable Topology

We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of effectively enumerable topological spaces where the Rice-Shapiro theorem does not hold. We propose two constructions that generate effectively enumerable topological spaces with particular properties from wn--families and computable trees without computable infinite paths. Using them we propose examples that give a flavor of this class