We examine the notion of structures and functions in the Ershov difference hierarchy, and of equivalence structures in particular. A equivalence structure A = (A,E) has universe A = ω and an equivalence relation E. The equivalence class [a] of a ∈ A is {b ∈ A : aEb} and the character K of A is {〈k, n〉 ∈ (ω − {0}) : A has at least n classes of size k}. It is known that for any character K, there...

background: the cells of mammalian female reproductive tract have been widely used for in vitro fertilization (ivf). this study was designed to study the effects of oviductal epithelial cells (oecs) and their conditioned medium during ivf on subsequent embryonic development and the relative abundance of zygote arrest 1 (zar1) transcript in ovine zygotes. methods: the in vitro matured ovine oocy...

background and aims: understanding β-cell function at the molecular level will likely facilitate the development of β-cells manufacture techniques. the aim of the present study was to investigate the pancreatic and duodenal homeobox 1 (pdx-1) gene expression into dtz-stained cellular clusters originating from emberyonal carcinoma cells. methods: this implemental -fundamental study was accomplis...

Recently, there has been a growing interest in understanding the complexity of common analytic equivalence relations between separable Banach spaces via the notion of Borel reducibility in descriptive set theory (see [Bos] [FG] [FLR] [FR1] [FR2] [Me]). In general, the notion of Borel reducibility yields a hierarchy (though not linear) among equivalence relations in terms of their relative compl...

We study further CCZ-equivalence of (n,m)-functions. We prove that for Boolean functions (that is, for m = 1), CCZ-equivalence coincides with EA-equivalence. On the contrary, we show that for (n,m)functions, CCZ-equivalence is strictly more general than EAequivalence when n ≥ 5 and m is greater or equal to the smallest positive divisor of n different from 1. Our result on Boolean functions allo...

background: the seladin-1 (selective alzheimer disease indicator-1), also known as dhcr24, is a gene found to be down-regulated in brain region affected by alzheimer disease (ad). whereas, hair follicle stem cells (hfsc), which are affected in with neurogenic potential, it might to hypothesize that this multipotent cell compartment is the predominant source of seladin-1. our aim was to evaluate...

This entry provides formulae for counting the number of equivalence relations and partial equivalence relations over a finite carrier set with given cardinality. To count the number of equivalence relations, we provide bijections between equivalence relations and set partitions [4], and then transfer the main results of the two AFP entries, Cardinality of Set Partitions [1] and Spivey’s General...

ion-side and Display-side behaviours of an interactor. Interactors are characterised by the behaviour they exhibit when observed from the abstraction or the display sides. The abstraction-side behaviour of the interactor is observed by interaction at gates Gaout and Gainp. The display-side behaviour is observed at gates Gdinp and Gdout. They are described by the pseudo-LOTOS expressions: A P = ...