In this study, we aim to understand the origins of human intuitions about Euclidean geometry by simulating geometric concepts acquisition with unsupervised learning in hierarchical generative models. Specifically, we build a deep neural network that learns a hierarchical generative model of sensory inputs. The results show that hidden layer activities can support the categorization of different...

A virtual haptic-audio drawing program prototype designed for visuallyimpaired children has been gradually developed in a design-evaluation loop involvingusers in four stages. Three qualitative evaluations focused on recognizing drawnshapes and creating drawings have been conducted together with a reference group of5 visually impaired children. Additionally, one formal pilot tes...

Intuition is often regarded as essential in the learning of geometry, but questions remain about how we might effectively develop students’ such skills. This paper provides some results from analyses of innovative geometry teaching in the early part of the 20 century, a time when significant efforts were being made to improve the teaching and learning of geometry. As examples, we examine the ta...

In this paper we present a novel procedure for contour-based recognition of partially occluded three-dimensional objects. In our approach we use images of real and rendered objects whose contours have been deformed by a restricted change of the viewpoint. The preparatory part consists of contour extraction, preprocessing, local structure analysis and feature extraction. Themain part deals with ...

With the wide-spread availability of advanced digital cameras dermoscopy has become nowadays a standard technique to help the doctors taking diagnosis for many types of skin lesions. Further, computer-assisted techniques and image processing methods can be used for image filtering and for feature extraction and pattern recognition in the selected images. Apart from standard approaches based on ...

The sphere and circumscribing cylinder engraved on Archimedes’ tombstone commemorate his landmark discovery that their volumes and surface areas are related by the same constant ratio 2/3. He discovered the volume relation and many other geometrical results by mechanical balancing. In particular, he found the volume of a cylindrical wedge by introducing the special balancing shown in Figures 1a...

We investigate in a series of laboratory experiments how costs and benefits of linguistic communication affect the emergence of simple languages in a coordination task when no common language is available in the beginning. The experiment involved pairwise computerized communication between 152 subjects involved in at least 60 rounds. The subjects had to develop a common code referring to items ...

Maurits Cornelis Escher (1898-1972) is a famous Dutch artist known – amongst others – for his prints of impossible figures and impossible worlds. Many of his works illustrate mathematical and geometrical concepts such as perspective and limits. Works by Escher have motivated scientists over the years to discover the mathematical foundations of his work, ultimately leading to applications that a...

We present a novel theoretical approach to understanding the complex dynamics of glass-forming liquids, granular packings and amorphous solids. This theory, which is an elaboration of the free volume and inherent structure approaches, allows one to retrieve the thermodynamical properties of these systems from studies of geometrical and topological properties of local, static configurations alon...

The effects of sex and stress hormones on classical fear conditioning have been subject of recent experimental studies. A correlation approach between basal cortisol concentrations and neuronal activation in fear-related structures seems to be a promising alternative approach in order to foster our understanding of how cortisol influences emotional learning. In this functional magnetic resonanc...