The Rank of Tree-Automatic Linear Orderings

We generalise Delhomm\'e's result that each tree-automatic ordinal is strictly below \omega^\omega^\omega{} by showing that any tree-automatic linear ordering has FC-rank strictly below \omega^\omega. We further investigate a restricted form of tree-automaticity and prove that every linear ordering which admits a tree-automatic presentation of branching complexity at most k has FC-rank strictly below \omega^k.Comment: 20 pages, 3 figure

Ehrenfeucht-Fraisse Games on Omega-Terms

Fragments of first-order logic over words can often be characterized in terms of finite monoids or finite semigroups. Usually these algebraic descriptions yield decidability of the question whether a given regular language is definable in a particular fragment. An effective algebraic characterization can be obtained from identities of so-called omega-terms. In order to show that a given fragment satisfies some identity of omega-terms, one can use Ehrenfeucht-Fraisse games on word instances of the omega-terms. The resulting proofs often require a significant amount of book-keeping with respect to the constants involved. In this paper we introduce Ehrenfeucht-Fraisse games on omega-terms. To this end we assign a labeled linear order to every omega-term. Our main theorem shows that a given fragment satisfies some identity of omega-terms if and only if Duplicator has a winning strategy for the game on the resulting linear orders. This allows to avoid the book-keeping. As an application of our main result, we show that one can decide in exponential time whether all aperiodic monoids satisfy some given identity of omega-terms, thereby improving a result of McCammond (Int. J. Algebra Comput., 2001)

Word Automaticity of Tree Automatic Scattered Linear Orderings Is Decidable

A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific simple trees and a structure is word automatic if it is encodable using only these trees. The question naturally arises whether a given tree automatic structure is already word automatic. We prove that this problem is decidable for tree automatic scattered linear orderings. Moreover, we show that in case of a positive answer a word automatic presentation is computable from the tree automatic presentation.Comment: 19 pages, 2 figure

Sensitivity of the synaptic membrane Na+/Ca2+ exchanger and the expressed NCX1 isoform to reactive oxygen species

AbstractTwo plasma membrane proteins, the Na+/Ca2+ exchanger (NCX) and the Ca2+-ATPase, are major regulators of free intraneuronal Ca2+ levels as they are responsible for extrusion of Ca2+ from the intracellular to the extracellular medium. Because disruption of cellular Ca2+ regulation plays a role in damage occurring under conditions of oxidative stress, studies were conducted to assess the sensitivity of the NCX to reactive oxygen species (ROS). Exchanger activity in brain synaptic plasma membranes and in transfected CHO-K1 cells was inhibited following brief exposure to the peroxyl radical generating azo initiator 2,2′-azobis(2-amidinopropane)dihydrochloride (AAPH) and to peroxynitrite. Incubation with hydrogen peroxide did not alter NCX activity, even at 800 μM concentration. In CHO-K1 cells transiently transfected with the NCX1 isoform of the exchanger, AAPH treatment decreased the maximal transport capacity (Vmax), whereas the Kact remained unchanged. Peroxynitrite led to an increase in Kact with no change in Vmax. Loss of activity following exposure to either AAPH or peroxynitrite was associated with the formation of high molecular weight aggregates of NCX, and AAPH also caused fragmentation of the exchanger protein. These findings suggest that the NCX is sensitive to biologically relevant ROS and could be involved in the loss of Ca2+ homeostasis observed under oxidative stress

Quantenautomaten und das Cut-Point-Theorem für beschränkte erkennbare Potenzreihen

Der Inhalt dieser Arbeit sind jedoch nicht Quantencomputer im Allgemeinen, sondern hauptsächlich Quantenautomaten. Dies führt zu den Begriffen der „endlichen Quantenautomaten“ und der „quantenregulären“ oder „quantenerkennbaren Sprachen“, die Hauptgegenstand der vorliegenden Arbeit sind

The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy

For two given $\omega$-terms $\alpha$ and $\beta$, the word problem for $\omega$-terms over a variety $\boldsymbol{\mathrm{V}}$ asks whether $\alpha=\beta$ in all monoids in $\boldsymbol{\mathrm{V}}$. We show that the word problem for $\omega$-terms over each level of the Trotter-Weil Hierarchy is decidable. More precisely, for every fixed variety in the Trotter-Weil Hierarchy, our approach yields an algorithm in nondeterministic logarithmic space (NL). In addition, we provide deterministic polynomial time algorithms which are more efficient than straightforward translations of the NL-algorithms. As an application of our results, we show that separability by the so-called corners of the Trotter-Weil Hierarchy is witnessed by $\omega$-terms (this property is also known as $\omega$-reducibility). In particular, the separation problem for the corners of the Trotter-Weil Hierarchy is decidable

Altered vascular smooth muscle function in the ApoE knockout mouse during the progression of atherosclerosis

Objectives: Relaxation of vascular smooth muscle (VSM) requires re-uptake of cytosolic Ca2+ into the sarcoplasmic reticulum (SR) via the Sarco/Endoplasmic Reticulum Ca2+ ATPase (SERCA), or extrusion via the Plasma Membrane Ca2+ ATPase (PMCA) or sodium Ca2+ exchanger (NCX). Peroxynitrite, a reactive species formed in vascular inflammatory diseases, upregulates SERCA activity to induce relaxation but, chronically, can contribute to atherogenesis and altered vascular function by escalating endoplasmic reticulum stress. Our objectives were to determine if peroxynitrite-induced relaxation and Ca2+ handling processes within vascular smooth muscle cells were altered as atherosclerosis develops.<p></p> Methods: Aortae from control and ApoE−/− mice were studied histologically, functionally and for protein expression levels of SERCA and PMCA. Ca2+ responses were assessed in dissociated aortic smooth muscle cells in the presence and absence of extracellular Ca2+.<p></p> Results: Relaxation to peroxynitrite was concentration-dependent and endothelium-independent. The abilities of the SERCA blocker thapsigargin and the PMCA inhibitor carboxyeosin to block this relaxation were altered during fat feeding and plaque progression. SERCA levels were progressively reduced, while PMCA expression was upregulated. In ApoE−/− VSM cells, increases in cytosolic Ca2+ [Ca2+]c in response to SERCA blockade were reduced, while SERCA-independent Ca2+ clearance was faster compared to control.<p></p> Conclusion: As atherosclerosis develops in the ApoE−/− mouse, expression and function of Ca2+ handling proteins are altered. Up-regulation of Ca2+ removal via PMCA may offer a potential compensatory mechanism to help normalise the dysfunctional relaxation observed during disease progression

On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids

This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic are investigated for this class of monoids. The first main result shows that for any consistent combination of these properties and their negations, there is a homogeneous monoid with exactly this combination of properties. We then introduce the new concept of abstract Rees-commensurability (an analogue of the notion of abstract commensurability for groups) in order to extend this result to show that the same statement holds even if one restricts attention to the class of n-ary homogeneous monoids (where every side of every relation has fixed length n). We then introduce a new encoding technique that allows us to extend the result partially to the class of n-ary multihomogenous monoids