Generalization of the small-world effect on a model approaching the Erd\H{o}s-R\'enyi random graph

The famous Watts-Strogatz (WS) small-world network model does not approach the Erd\H{o}s-R\'enyi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we discuss a simple alternative which was first introduced by Song and Wang, where instead of rewiring, edges are drawn between pairs of nodes with a distance-based connection probability. We show that this model is simpler to analyze, approaches the true ER random graph model in the completely randomized limit, and demonstrate that the WS model and the alternative model may yield different quantitative results using the example of a random walk temporal observable. An efficient sampling algorithm for the alternative model is proposed. Analytic results regarding the degree distribution, degree variance, number of two-stars per node, number of triangles per node, clustering coefficient, and random walk mixing time are presented. Subsequently, the small-world effect is illustrated by showing that the clustering coefficient decreases much slower than an upper bound on the message delivery time with increasing long-range connection probability which generalizes the small-world effect from informed searches to random search strategies. Due to its accessibility for analytic evaluations, we propose that this modified model should be used as an alternative reference model for studying the influence of small-world topologies on dynamic systems as well as a simple model to introduce numerous topics when teaching network science.Comment: 6 pages, 5 figure

The legal regulation of internal party democracy - a study of South Africa and Germany

This paper attempts to expand the knowledge on these issues and therefore seeks to get a deeper understanding on the legal regulation of internal party democracy, which is widely considered as one of the most controversial topics concerning party regulation. This will be done by carrying out a case study of two constitutional democracies that handle party regulation differently. Germany, known as 'heart land of party law', constitutes the example of a state in which the internal organisation and functioning of political parties is regulated by both the Basic Law (the German Constitution) and federal laws. South Africa will be provided as the contrast example of a state that lacks express provisions that regulate the internal organisation and functioning of political parties. This paper does therefore not seek to conduct a 'classical' comparative study as the legal framework of two countries will be examined which deal in different ways with internal party democracy. However, this research approach promises to create a more holistic - even though certainly not complete - image of the challenges of the legal regulation of internal party democracy

Deep Denoising for Hearing Aid Applications

Reduction of unwanted environmental noises is an important feature of today's hearing aids (HA), which is why noise reduction is nowadays included in almost every commercially available device. The majority of these algorithms, however, is restricted to the reduction of stationary noises. In this work, we propose a denoising approach based on a three hidden layer fully connected deep learning network that aims to predict a Wiener filtering gain with an asymmetric input context, enabling real-time applications with high constraints on signal delay. The approach is employing a hearing instrument-grade filter bank and complies with typical hearing aid demands, such as low latency and on-line processing. It can further be well integrated with other algorithms in an existing HA signal processing chain. We can show on a database of real world noise signals that our algorithm is able to outperform a state of the art baseline approach, both using objective metrics and subject tests.Comment: submitted to IWAENC 201

Application of Ewald's Method for Efficient Summation of Dyon Long-Range Potentials

We study a model of dyons for SU(2) Yang-Mills theory at finite temperature T < T_c, in particular its ability to generate a confining force between a static quark antiquark pair. The interaction between dyons corresponds to a long-range 1/r potential, which in naive treatments with a finite number of dyons typically gives rise to severe finite volume effects. To avoid such effects we apply the so-called Ewald method, which has its origin in solid state physics. The basic idea of Ewald's method is to consider a finite number of dyons inside a finite cubic volume and enforce periodicity of this volume. We explain the technicalities of Ewald's method and outline how the method can be applied to a wider class of 1/r^p long-range potentials.Comment: 8 pages, 4 figures, contribution to conference "Confinement X

Stability and convergence of the Ritz map in the maximum norm for nonconforming finite elements

In this report, we consider the Poisson problem on a domain with regular boundary and discretize it with isoparametric finite elements of order $k\geq1$. We study a (generalized) Ritz map and show stability and convergence of optimal order $k$ in $W^{1,\infty}$

Color in context: psychological context moderates the influence of red on approach- and avoidance-motivated behavior.

A basic premise of the recently proffered color-in-context model is that the influence of color on psychological functioning varies as a function of the psychological context in which color is perceived. Some research has examined the appetitive and aversive implications of viewing the color red in romance- and achievement-relevant contexts, respectively, but in all existing empirical work approach and avoidance behavior has been studied in separate tasks and separate experiments. Research is needed to directly test whether red influences the same behavior differently depending entirely on psychological context. The present experiment was designed to put this premise to direct test in romance- and achievement-relevant contexts within the same experimental paradigm involving walking behavior. Our results revealed that exposure to red (but not blue) indeed has differential implications for walking behavior as a function of the context in which the color is perceived. Red increased the speed with which participants walked to an ostensible interview about dating (a romance-relevant context), but decreased the speed with which they walked to an ostensible interview about intelligence (an achievement-relevant context). These results are the first direct evidence that the influence of red on psychological functioning in humans varies by psychological context. Our findings contribute to both the literature on color psychology and the broader, emerging literature on the influence of context on basic psychological processes

Maximum norm error estimates for an isoparametric finite element discretization of elliptic boundary value problems

In this paper, we consider an elliptic boundary value problem on a domain with regular boundary and discretize it with isoparametric finite elements of order $k\geq1$. We show optimal order of convergence of the isoparametric finite element solution in the $W^{1,\infty}$-norm. As an intermediate step, we derive stability and convergence estimates of optimal order $k$ for a (generalized) Ritz map

Optimal W1,∞^{1,∞}-estimates for an isoparametric finite element discretization of elliptic boundary value problems

In this paper, we consider an elliptic boundary value problem on a domain with regular boundary and discretize it with isoparametric finite elements of order $k\geq1$. We show optimal order of convergence of the isoparametric finite element solution in the $W^{1,\infty}$-norm. As an intermediate step, we derive stability and convergence estimates of optimal order $k$ for a (generalized) Ritz map