Word images in symmetric and classical groups of Lie type are dense

Let $w\in\mathbf F_k$ be a non-trivial word and denote by $w(G)\subseteq G$ the image of the associated word map $w\colon G^k\to G$. Let $G$ be one of the finite groups ${\rm S}_n,{\rm GL}_n(q),{\rm Sp}_{2m}(q),{\rm GO}_{2m}^\pm(q),{\rm GO}_{2m+1}(q),{\rm GU}_n(q)$ ($q$ a prime power, $n\geq 2$, $m\geq 1$), or the unitary group ${\rm U}_n$ over $\mathbb C$. Let $d_G$ be the normalized Hamming distance resp. the normalized rank metric on $G$ when $G$ is a symmetric group resp. one of the other classical groups and write $n(G)$ for the permutation resp. Lie rank of $G$. For $\varepsilon>0$, we prove that there exists an integer $N(\varepsilon,w)$ such that $w(G)$ is $\varepsilon$-dense in $G$ with respect to the metric $d_G$ if $n(G)\geq N(\varepsilon,w)$. This confirms metric versions of a conjectures by Shalev and Larsen. Equivalently, we prove that any non-trivial word map is surjective on a metric ultraproduct of groups $G$ from above such that $n(G)\to\infty$ along the ultrafilter. As a consequence of our methods, we also obtain an alternative proof of the result of Hui-Larsen-Shalev that $w_1({\rm SU}_n)w_2({\rm SU}_n)={\rm SU}_n$ for non-trivial words $w_1,w_2\in\mathbf F_k$ and $n$ sufficiently large.Comment: 28 pages, no figure

Observation Centric Sensor Data Model

Management of sensor data requires metadata to understand the semantics of observations. While e-science researchers have high demands on metadata, they are selective in entering metadata. The claim in this paper is to focus on the essentials, i.e., the actual observations being described by location, time, owner, instrument, and measurement. The applicability of this approach is demonstrated in two very different case studies

The Liouville property and random walks on topological groups

We study harmonic functions and Poisson boundaries for Borel probability measures on general (i.e., not necessarily locally compact) topological groups, and we prove that a second-countable topological group is amenable if and only if it admits a fully supported, regular Borel probability measure with trivial Poisson boundary. This generalizes work of Kaimanovich--Vershik and Rosenblatt, confirms a general topological version of Furstenberg's conjecture, and entails a characterization of the amenability of isometry groups in terms of the Liouville property for induced actions. Moreover, our result has non-trivial consequences concerning Liouville actions of discrete groups on countable setsComment: 24 pages, no figures; v2: referee report taken into account, Proposition 4.2 generalized, minor error in the statement of Lemma 4.5 corrected, some references and background material added, 26 pages, final version to appear in Commentarii Mathematici Helvetic

Corruption and the Shadow Economy: A Structural Equation Model Approach

The relationship between corruption and the shadow economy is not clear. Theoretically, they either substitute or complement each other – exhibiting either a negative or positive relationship. This paper – using a structural equation model with two latent variables – extracts information on various dimensions of corruption and the shadow economy to contribute to the debate on their relationship. It presents empirical evidence of a positive relationship between the shadow economy and corruption. The results show that the shadow economy influences corruption more than corruption influences the shadow economy.shadow economy, corruption, SEM models

MIMIC Models, Cointegration and Error Correction: An Application to the French Shadow Economy

The analysis of economic loss attributed to the shadow economy has attracted much attention in recent years by both academics and policy makers. Often, multiple indicators multiple causes (MIMIC) models are applied to time series data estimating the size and development of the shadow economy for a particular country. This type of model derives information about the relationship between cause and indicator variables and a latent variable, here the shadow economy, from covariance structures. As most macroeconomic variables do not satisfy stationarity, long run information is lost when employing first differences. Arguably, this shortcoming is rooted in the lack of an appropriate MIMIC model which considers cointegration among variables. This paper develops a MIMIC model which estimates the cointegration equilibrium relationship and the error correction short run dynamics, thereby retaining information for the long run. Using France as our example, we demonstrate that this approach allows researchers to obtain more accurate estimates about the size and development of the shadow economy.shadow economy, tax burden, regulation, unemployment, cointegration, error correction models, MIMIC models

Monetary Commitment, Institutional Constraints and Inflation: Empirical Evidence for OECD Countries since the 1970s

Central bank independence (CBI) is a very important precondition for price stability. However, the empirical evidence for a correlation between both is relatively weak. In this paper, this weakness is countered with a) an extended measure of monetary commitment, which includes well-known criteria for CBI and external criteria such as convertibility and exchange rate regimes and b) the argument that monetary commitment can grant price stability best if it is backed by an adequate assignment of economic policy. An empirical assessment with data from four decades confirms the crucial role of monetary commitment for price stability.central bank independence, price stability, monetary commitment

MIMIC Models, Cointegration and Error Correction: An Application to the French Shadow Economy

The analysis of economic loss attributed to the shadow economy has attracted much attention in recent years by both academics and policy makers. Often, multiple indicators multiple causes (MIMIC) models are applied to time series data estimating the size and development of the shadow economy for a particular country. This type of model derives information about the relationship between cause and indicator variables and a latent variable, here the shadow economy, from covariance structures. As most macroeconomic variables do not satisfy stationarity, long run information is lost when employing first differences. Arguably, this shortcoming is rooted in the lack of an appropriate MIMIC model which considers cointegration among variables. This paper develops a MIMIC model which estimates the cointegration equilibrium relationship and the error correction short run dynamics, thereby retaining information for the long run. Using France as our example, we demonstrate that this approach allows researchers to obtain more accurate estimates about the size and development of the shadow economy.shadow economy, tax burden, regulation, unemployment, cointegration, error correction models, MIMIC models

Model Based Sensor System for Temperature Measurement in R744 Air Conditioning Systems

The goal is the development of a novel principle for the temperature acquisition of refrigerants in CO2 air conditioning systems. The new approach is based on measuring the temperature inside a pressure sensor, which is also needed in the system. On the basis of simulative investigations of different mounting conditions functional relations between measured and medium temperature will be derived.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838