Multiple Representation

In a number of recent papers Sonis, Hewings and coworkers have extended spacial path analysis to a block structural context capable of analysing the relationship between direct blocks of influence, such as intra and interregional trade coefficients or demographic-economic interactions, and full model multipliers. The approach makes use of a definition of the direct coefficients block partitioned matrix in terms of simpler matrices each of which is made up of null blocks except for one block column. In the current paper, the underlying technique is extended by making use of an even simpler matrix construction - an "almost null" matrix, defined as null in all partitioned blocks except one. An arbitrary n x n block partitioned direct coefficients matrix can be represented as a sum of n-squared almost null matrices. Properties of almost null matrices are exploited to enable analytically manageable expressions for the Leontief inverse to be written entirely in terms of the almo...

The sustainable management and continuation of virtual 3D city models puts specific demands on 3D geodatabases. These demands result from the need to manage three different dimensions of multiple representation: Levels-of-detail, concurrent planning versions, and history over time. In this paper we propose a concept for the integration of all three aspects in the framework of spatial relational database management

Code It! fosters mathematics learning environments where pre-algebra students use handheld technologies to confidently and enjoyably explore and learn about functions. The resources we developed---server-based and handheld software and paper-based student and teacher texts---were packaged as a 20-session unit on code making and breaking and designed to boost students' understanding of mathematical functions and their facility with the multiple representations of tables, graphs and symbols. We field tested the wireless system with two teachers and 120 middle school students during a five week summer school, and conducted studies on the features and function of the technology as a learning and teaching resource. We report on project development and research, focusing on what we learned about the strengths and difficulties of wireless handheld technology in the mathematic classroom, and the emerging social engineering that helped students overcome the technological constraints.

Code It! fosters mathematics learning environments where pre-algebra students use handheld technologies to explore and learn about functions. The resources developed—server-based and handheld software and paper-based student and teacher texts—were packaged as a ...

IfJ is an indefinite signature matrix, then there exists aJ contractive holomorphic matrix valued functionW(z) in the open unit disc which can be expressed as a left Blaschke-Potapov product:W(z)=B (l)(z), but not as a right Blaschke-Potapov product:W(z)=E(z)B (r)(z), whereB (r)(z) is a right Blaschke-Potapov product andE(z) is a so called Arov singular matrix function. In factB (l)(z) may be chosen to obtain any Arov singular matrix functionE(z) in the second representation. This phenomenon and multiplicative representations of Arov singular functions are discussed.

This paper investigates representations of performance and the role of the archive. Notions of record and archive are critically investigated, raising questions about applying traditional archival definitions to the performing arts. Defining the nature of performances is at the root of all difficulties regarding their representation. Performances are live events, so for many people the idea of recording them for posterity is inappropriate. The challenge of creating and curating representations of an ephemeral art form are explored and performance-specific concepts of record and archive are posited. An open model of archives, encouraging multiple representations and allowing for creative reuse and reinterpretation to keep the spirit of the performance alive, is envisaged as the future of the performing arts archive.

Multimedia learning environments usually combine multiple forms of representations like texts, pictures, animations, tables or formulas. However, knowledge acquisition from multiple representations requires the integration of these sources in order to construct a coherent mental representation. The present paper therefore outlines a first theoretical framework for the process of coherence formation within cognitive load theory. Despite the benefits of dealing

Groupware Task Analysis is a task analysis method that deals with the context of use of a system in the broadest sense. The task world is seen from three viewpoints that deal with different aspects of the world. The processes of GTA and their background are described in detail. In addition a task analysis tool EUTERPE is described. EUTERPE is based on GTA and allows capturing of the task models and provides some basic analysis primitives.

Elementary school children, some of whom were nonnative speakers of English, learned to add and subtract integers in a discovery-based multimedia game either with or without verbal guidance in English or optionally in Spanish (Groups G—verbal guidance and No-G—no verbal ...

This paper describes a sonar-based mapping and navigation system for autonomous mobile robots operating in unknown and unstructured surroundings. The system uses sonar range data to build a multileveled description of the robot's environment. Sonar maps are represented in the system along several dimensions: the Abstraction axis, the Geographical axis, and the Resolution axis. Various kinds of problem-solving activities can be performed and different levels of performance can be achieved by operating with these multiple representations of maps. The major modules of the Dolphin system are described and related to the various mapping representations used. Results from actual runs are presented and further research is mentioned. The system is also situated within the wider context of developing an advanced software architecture for autonomous mobile robots.