In 2001, Hui and Neuhoff proposed auniformquantizerwithoverloadfor the quantization of scalar signals and derived the asymptotically optimal size of the quantization bins in the high-bitrate limit. The purpose of the present paper is to prove a quantitatively more precise version of this result which, at the same time, is valid for a more general, quite natural class of probability distributions that requires only little regularity and includes, for instance, positive Lipschitz-continuous functions of unit integral.

In distributed virtual environments, hosts typically have to react to events within a time span which is less than the network latency. As a consequence, hosts do routinely take actions although the system is in an inconsistent state. This has a noticeable influence on the perceived quality of these actions and their effect on the application. We argue that the level of this influence depends on the degree of inconsistency. In this paper, we tackle two fundamental questions: How does the degree of inconsistency influence the perceived quality of the users' actions? How can the degree of inconsistency be quantified? We propose a benchmark test for comparing different consistency algorithms with each other which consists of two measures of inconsistency and a sample scenario. For two different consistency algorithms, we compare the results of our benchmark test with the results of a user evaluation test and a simple yield measure.

Machine-readable semantic annotation of scientific knowledge is becoming increasingly important to manage and access the knowledge contained in an increasing number of scientific publications. At the same time, automated extraction of knowledge from natural language texts is a major technical challenge remaining largely unsolved. Scientific texts in general and mathematical texts in particular, are characterized by the use of complex language constructs with the intent to transfer knowledge. To a large extent, mathematical texts possess a strict internal structuring and can be separated into text elements such as definitions, theorems etc. These text elements are principal carriers of mathematical information. In addition, these elements show a characteristic linguistic structuring well suited for natural language processing techniques. In this paper we present mArachna, a system for extracting mathematical relations from texts and integrating them into a knowledge base. In response to user queries, parts of the knowledge base are visualized using OWL. In particular, mArachna aims to provide an overview of single fields of mathematics, as well as showing intra-field relations between mathematical objects and concepts