On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

Interface issues in the ESCHER visual database editor

Presentation at the 1997 Dagstuhl Seminar "Evaluation of Multimedia Information Retrieval", Norbert Fuhr, Keith van Rijsbergen, Alan F. Smeaton (eds.), Dagstuhl Seminar Report 175, 14.04. - 18.04.97 (9716). - Abstract: This presentation will introduce ESCHER, a database editor which supports visualization in non-standard applications in engineering, science, tourism and the entertainment industry. It was originally based on the extended nested relational data model and is currently extended to include object-relational properties like inheritance, object types, integrity constraints and methods. It serves as a research platform into areas such as multimedia and visual information systems, QBE-like queries, computer-supported concurrent work (CSCW) and novel storage techniques. In its role as a Visual Information System, a database editor must support browsing and navigation. ESCHER provides this access to data by means of so called fingers. They generalize the cursor paradigm in graphical and text editors. On the graphical display, a finger is reflected by a colored area which corresponds to the object a finger is currently pointing at. In a table more than one finger may point to objects, one of which is the active finger and is used for navigating through the table. The talk will mostly concentrate on giving examples for this type of navigation and will discuss some of the architectural needs for fast object traversal and display. ESCHER is available as public domain software from our ftp site in Kassel. The portable C source can be easily compiled for any machine running UNIX and OSF/Motif, in particular our working environments IBM RS/6000 and Intel-based LINUX systems. A porting to Tcl/Tk is under way.

Audio-Visual Information Processing across different age groups

People possess different sensory modalities to detect, interpret, and efficiently act upon various events in a complex and dynamic environment (Fetsch, DeAngelis, & Angelaki, 2013). Much empirical work has been done to understand the interplay of modalities (e.g. audio-visual interactions, see Calvert, Spence, & Stein, 2004). On the one hand, integration of multimodal input as a functional principle of the brain enables the versatile and coherent perception of the environment (Lewkowicz & Ghazanfar, 2009). On the other hand, sensory integration does not necessarily mean that input from modalities is always weighted equally (Ernst, 2008). Rather, when two or more modalities are stimulated concurrently, one often finds one modality dominating over another. Study 1 and 2 of the dissertation addressed the developmental trajectory of sensory dominance. In both studies, 6-year-olds, 9-year-olds, and adults were tested in order to examine sensory (audio-visual) dominance across different age groups. In Study 3, sensory dominance was put into an applied context by examining verbal and visual overshadowing effects among 4- to 6-year olds performing a face recognition task. The results of Study 1 and Study 2 support default auditory dominance in young children as proposed by Napolitano and Sloutsky (2004) that persists up to 6 years of age. For 9-year-olds, results on privileged modality processing were inconsistent. Whereas visual dominance was revealed in Study 1, privileged auditory processing was revealed in Study 2. Among adults, a visual dominance was observed in Study 1, which has also been demonstrated in preceding studies (see Spence, Parise, & Chen, 2012). No sensory dominance was revealed in Study 2 for adults. Potential explanations are discussed. Study 3 referred to verbal and visual overshadowing effects in 4- to 6-year-olds. The aim was to examine whether verbalization (i.e., verbally describing a previously seen face), or visualization (i.e., drawing the seen face) might affect later face recognition. No effect of visualization on recognition accuracy was revealed. As opposed to a verbal overshadowing effect, a verbal facilitation effect occurred. Moreover, verbal intelligence was a significant predictor for recognition accuracy in the verbalization group but not in the control group. This suggests that strengthening verbal intelligence in children can pay off in non-verbal domains as well, which might have educational implications.