configuration, 138Alternating Register Automata, 25Alternating Tree Register Automata,115ancestor relation ( , ≺), 57ARA, 25ARA(guess, spread), 25ARA(guess, spread, <), 32ATRA, 115ATRA(guess, spread), 115attrXPath, 63Aut, 79Aut , 79

We prove that every simplicial automorphism of the free splitting graph of a free group Fn is induced by an outer automorphism of Fn for n ≥ 3. In this note we consider the graph Gn of free splittings of the free group Fn of rank n ≥ 3. Loosely speaking, Gn is the graph whose vertices are non-trivial free splittings of Fn up to conjugacy, and where two vertices are adjacent if they are represen...

Generic automorphisms are a common theme when one works with auto-morphism groups of countable structures. They play a pivotal role in reconstruction results. In these notes we shall define and explain a notion of generic, due to John Truss, which is highly relevant to reconstruction. The idea is that a generic automorphism acts on the elements of the structure in the least special way, that is...

1 The Setup {s:setup} The starting point is: a group G, a Cartan involution θ, and another involution σ of finite order, commuting with θ. It is natural to consider the coset σK = {σ ◦ int(k) | k ∈ K} ⊂ Aut(G). Every element of this coset commutes with θ. We’re mainly interested when σ is an involution, especially the case σ = θ. Now fix a pinning P = (H,B, {Xα}), and write δ, ǫ ∈ Aut(G) for th...

Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...

We investigate the minimality property of the group of homeomor-phisms AUT(C) of some compact set C: In particular we show that for C = 0;1] n the corresponding group is minimal ii n = 1: Also we prove the minimality of AUT(D 1); where D 1 is a Cantor cube with a countable weight. These results partially answer the general question raised by Prodanov and Stojanov ((2]) , Dierolf et.al. ((3]) an...

Given an integer $g \geq 0$ and a weight vector $w \in \mathbb{Q}^n \cap (0, 1]^n$ satisfying $2g - 2 +\sum w\_i > 0$, let $\Delta\_{g, w}$ denote the moduli space of $n$-marked, $w$-stable tropical curves genus $g$ volume one. We calculate automorphism group $\operatorname{Aut}(\Delta\_{g, w})$ for 1$ arbitrary $w$, we $\operatorname{Aut}(\Delta\_{0, when $w$ is heavy/light. In both these case...

The purpose of this study was to evaluate sympathetic skin response (SSR) and heart rate variability (HRV) in determining autonomic nervous system (ANS) involvement in patients with Parkinson disease (PD). Forty-eight idiopathic PD patients and 30 healthy controls participated in this study. SSR, HRV, Unified Parkinson's Disease Rating Scale (UPDRS) III, the Scales for outcomes in Parkinson's D...