Mutual Dimension

We define the lower and upper mutual dimensions $mdim(x:y)$ and $Mdim(x:y)$ between any two points $x$ and $y$ in Euclidean space. Intuitively these are the lower and upper densities of the algorithmic information shared by $x$ and $y$. We show that these quantities satisfy the main desiderata for a satisfactory measure of mutual algorithmic information. Our main theorem, the data processing inequality for mutual dimension, says that, if $f:\mathbb{R}^m \rightarrow \mathbb{R}^n$ is computable and Lipschitz, then the inequalities $mdim(f(x):y) \leq mdim(x:y)$ and $Mdim(f(x):y) \leq Mdim(x:y)$ hold for all $x \in \mathbb{R}^m$ and $y \in \mathbb{R}^t$. We use this inequality and related inequalities that we prove in like fashion to establish conditions under which various classes of computable functions on Euclidean space preserve or otherwise transform mutual dimensions between points.Comment: This article is 29 pages and has been submitted to ACM Transactions on Computation Theory. A preliminary version of part of this material was reported at the 2013 Symposium on Theoretical Aspects of Computer Science in Kiel, German

Mutual Savings Banks

Aim The aim of the thesis is to explain the factors that affect the auditor's recommendation concerning audit services to customers who are not subject to mandatory auditing. Background and problem In 2010 mandatory auditing for small companies was abolished. It is common for the auditor to provide recommendations re-garding whether or not a customer should chose to retain the audit. The question is which factors can explain the auditor's recommendation. Method and empirics This thesis uses a deductive approach with inductive elements and a combination of qualitative and quantitative data is used. The qualitative data consists of a pilot study and the quantitative data consists of a questionnaire survey. The analysis of the empirical data was performed using regression analysis. Theory This thesis applies an eclectic approach where the starting point is legitimacy, institutional theory, professional theory and decision making theory to develop a model. Results and conclusions The notion of the recommendation as well as the extent of the recommendations can be explained by factors related to the auditor's agency affiliation and the auditor's personal qualities.Syfte Studiens syfte är att förklara vilka faktorer som påverkar revisorns rekommendation om revisionstjänster till kunder som inte omfattas av revisionsplikt. Bakgrund och problem År 2010 avskaffades revisionsplikten för mindre bolag. Vid valet om att behålla eller avskaffa revisionen är det vanligt att revisorn rekommenderar kunden om hur bolaget ska välja. Frågan är vilka faktorer som kan förklara revisorns rekommendation. Metod och analys Studien har en deduktiv ansats med induktiva inslag samt an-vänder en kombination av kvalitativ och kvantitativ data. Den kvalitativa datan består utav en pilotstudie och den kvantitativa datan utav en enkätundersökning. Regressionsanalyser genom-fördes vid analys av den empiriska datan. Teori Studien tillämpar ett eklektiskt angreppssätt där utgångspunkten är legitimitet, institutionell teori, professionsteori och beslutsteori som används för att utveckla en modell. Resultat och slutsats Både uppfattning om rekommendation samt omfattningen av rekommendationer kan förklaras av faktorer kopplade till dels revisorns byråtillhörighet och dels revisorns personliga egenskaper

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Deception and Mutual Trust: A Reply to Strudler

Alan Strudler has written a stimulating and provocative article about deception in negotiation. He presents his views, in part, in contrast with our earlier work on the Mutual Trust Perspective. We believe that Strudler is wrong in his account of the ethics of deception in negotiation and in his quick dismissal of the Mutual Trust Perspective. Though his mistakes may be informative, his views are potentially harmful to business practice. In this paper, we present arguments against Strudler's position and attempt to salvage the Mutual-Trust Perspective from his attack. Strudler's work reaffirms the need for a more pragmatic approach to business ethics. We close the paper with a renewed call for more constructive and practical approaches to business ethics research.Signaling; Negotiations; Business Ethics; Private Information

Mutual exclusion

Almost all computers today operate as part of a network, where they assist people in coordinating actions. Sometimes what appears to be a single computer is actually a network of cooperating computers; e.g., some supercomputers consist of many processors operating in parallel and exchanging synchronization signals. One of the most fundamental requirements in all these systems is that certain operations be indivisible: the steps of one must not be interleaved with the steps of another. Two approaches were designed to implement this requirement, one based on central locks and the other on distributed order tickets. Practicing scientists and engineers need to come to be familiar with these methods

Distribution of Mutual Information

The mutual information of two random variables i and j with joint probabilities t_ij is commonly used in learning Bayesian nets as well as in many other fields. The chances t_ij are usually estimated by the empirical sampling frequency n_ij/n leading to a point estimate I(n_ij/n) for the mutual information. To answer questions like "is I(n_ij/n) consistent with zero?" or "what is the probability that the true mutual information is much larger than the point estimate?" one has to go beyond the point estimate. In the Bayesian framework one can answer these questions by utilizing a (second order) prior distribution p(t) comprising prior information about t. From the prior p(t) one can compute the posterior p(t|n), from which the distribution p(I|n) of the mutual information can be calculated. We derive reliable and quickly computable approximations for p(I|n). We concentrate on the mean, variance, skewness, and kurtosis, and non-informative priors. For the mean we also give an exact expression. Numerical issues and the range of validity are discussed.Comment: 8 page