Island tameness is a widely documented phenomenon in which island species, particularly those that have evolved with no or few natural predators, show a greatly reduced behavioral response when faced with unfamiliar predators. This insufficient anti-predator response has led to widespread population declines among many island species exposed to novel predators, and has become a serious conserva...

Let M = ⟨ , < + ⋯ ⟩ $\mathcal {M}=\langle M, <, +, \dots \rangle$ be an o-minimal expansion of ordered group, and P ⊆ $P\subseteq M$ a dense set such that certain tameness conditions hold. We introduce the notion product cone in ∼ $\widetilde{\mathcal {M}}=\langle \mathcal {M}, P\rangle$ prove: if {M}$ expands real closed field, then {M}}$ admits decomposition. If is linear, it does not. In par...

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

The program-over-monoid model of computation originates with Barrington's proof that the captures complexity class $\mathsf{NC^1}$. Here we make progress in understanding subtleties model. First, identify a new tameness condition on monoids entails natural characterization regular languages recognizable by programs over from class. Second, prove known as $\mathbf{DA}$ satisfies and hence recogn...

Given a real analytic set X in a complex manifold and a positive integer d, denote by Ad the set of points p in X at which there exists a germ of a complex analytic set of dimension d contained in X. It is proved that Ad is a closed semianalytic subset of X.

Background: The genetic and molecular mechanisms of tameness are largely unknown. A line of silver foxes (Vulpes vulpes) selected for non-aggressive behavior has been used in Russia since the 1960's to study the effect of domestication. We have previously compared descendants of these selected (S) animals with a group of non-selected (NS) silver foxes kept under identical conditions, and showed...

In the first part of this paper, we give a new analytical proof theorem C. Sabbah on integrable deformations meromorphic connections $\mathbb P^1$ with coalescing irregular singularities Poincar\'e rank 1, and generalizing previous result B. Malgrange. second as an application, prove that any semisimple formal Frobenius manifold (over C$), unit Euler field, is completion analytic pointed germ D...

We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about φ-types for φ NIP. In particular, we show that if M is a countable model, then an M -invariant φ-type is Borel definable. Also the space of M invariant φ-types is a Rosenthal compactum, which implies a number of topological tameness properties. Shelah introduced the indepen...