Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts in the same volume. Part I is dedicated to information theory and the mathematical formalization of randomness based on Kolmogorov complexity. This last application goes back to the 60's and 70's with the work of Martin-L\"of, Schnorr, Chaitin, Levin, and has gained new impetus in the last years.Comment: 40 page

Kolmogorov complexity in perspective

We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented namely, the mathematical notion of randomness (which goes back to the 60's with the work of Martin-Lof, Schnorr, Chaitin, Levin), and classification, which is a recent idea with provocative implementation by Vitanyi and Cilibrasi.Comment: 37 page

Robustness in geometric modeling - an intuitionistic and tolerance-based approach

Journal ArticleAn intuitionistic geometry approach is taken to develop two tolerance-based methods for robust geometric computation. The so called analytic model method and the approximated model method are developed independently of a specific application or a geometric algorithm. Geometric robustness is formally defined. Geometric relations are computed based on tolerances defined for geometric objects. Dynamic tolerance updating rules are given to preserve properties of the geometric relations. The two methods differ in the definition of robustness and they use different tolerance updating rules, and hence, they preseve different properties and are suitable for different kinds of applications. To handle the possibly occuring ambiguities dynamic ambiguity handling methods are described as well

Rendering volumetric haptic shapes in mid-air using ultrasound

We present a method for creating three-dimensional haptic shapes in mid-air using focused ultrasound. This approach applies the principles of acoustic radiation force, whereby the non-linear effects of sound produce forces on the skin which are strong enough to generate tactile sensations. This mid-air haptic feedback eliminates the need for any attachment of actuators or contact with physical devices. The user perceives a discernible haptic shape when the corresponding acoustic interference pattern is generated above a precisely controlled two-dimensional phased array of ultrasound transducers. In this paper, we outline our algorithm for controlling the volumetric distribution of the acoustic radiation force field in the form of a three-dimensional shape. We demonstrate how we create this acoustic radiation force field and how we interact with it. We then describe our implementation of the system and provide evidence from both visual and technical evaluations of its ability to render different shapes. We conclude with a subjective user evaluation to examine users’ performance for different shapes