We first show that the projection image of a discrete definable set is again for an arbitrary definably complete locally o-minimal structure. This fact together with results in previous paper implies tame dimension theory and decomposition theorem into good-shaped subsets called quasi-special submanifolds. Using this fact, latter part paper, we investigate expansions ordered groups when restric...

Grossberg and VanDieren have started a program to develop a stability theory for tame classes (see [GrVa1]). We name some variants of tameness (Definitions 1.4 and 1.7) and prove the following. Theorem 0.1. Let K be an AEC with Löwenheim-Skolem number ≤ κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then, K is Galois-stable in κ for all n < ω. ...

Domesticated species exhibit a suite of behavioral, endocrinological, and morphological changes referred to as "domestication syndrome." These changes may include a reduction in reactivity of the hypothalamic-pituitary-adrenal (HPA) axis and specifically reduced adrenocorticotropic hormone release from the anterior pituitary. To investigate the biological mechanisms targeted during domesticatio...

Grossberg and VanDieren have started a program to develop a stability theory for tame classes (see [GrVa1]). We name some variants of tameness (Definitions 1.4 and 1.7) and prove the following. Theorem 0.1. Let K be an AEC with Löwenheim-Skolem number ≤ κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then, K is Galois-stable in κ for all n < ω. ...

In experimental neurological models of brain injury, behavioral manipulations before and after the insult can have a major impact on molecular, anatomical, and functional outcome. Investigators using animals for preclinical research should keep in mind that people with brain injury have lived in, and will continue to live in, an environment that is far more complex than that of the typical labo...

Most of the text algorithms build data structures on words, mainly trees, as digital trees (tries) or binary search trees (bst). The mechanism which produces symbols of the words (one symbol at each unit time) is called a source, in information theory contexts. The probabilistic behaviour of the trees built on words emitted by the same source depends on two factors: the algorithmic properties o...

There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. Towards this end, the development of the theory of groups of finite Morley rank has achieved a good theory of Sylow 2-subgroups. It is now common practice to divide the Cherlin-Zilber conjecture into different cases depending on the nature of the...

Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The fir...

Given a semianalytic set S in Cn and a point p ∈ S, there is a unique smallest complex-analytic germ Xp which contains Sp, called the holomorphic closure of Sp. We show that if S is semialgebraic then Xp is a Nash germ, for every p, and S admits a semialgebraic filtration by the holomorphic closure dimension. As a consequence, every semialgebraic subset of a complex vector space admits a semial...