Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Memory-based Embodied Cognition: a computational architecture

At its most fundamental, cognition as displayed by biological agents (such as humans) may be said to consist of the manipulation and utilisation of memory. Recent discussions in the field of cognitive robotics have emphasised the role of embodiment and the necessity of a value or motivation for autonomous behaviour. This work proposes a computational architecture – the Memory-Based Cognitive (MBC) architecture – based upon these considerations for the autonomous development of control of a simple mobile robot. This novel architecture will permit the exploration of theoretical issues in cognitive robotics and animal cognition. Furthermore, the biological inspiration of the architecture is anticipated to result in a mobile robot controller which displays adaptive behaviour in unknown environments.

Can knowledge of the state of the stratosphere be used to improve statistical forecasts of the troposphere?

Recent analysis of the Arctic Oscillation (AO) in the stratosphere and troposphere has suggested that predictability of the state of the tropospheric AO may be obtained from the state of the stratospheric AO. However, much of this research has been of a purely qualitative nature. We present a more thorough statistical analysis of a long AO amplitude dataset which seeks to establish the magnitude of such a link. A relationship between the AO in the lower stratosphere and on the 1000 hPa surface on a 10-45 day time-scale is revealed. The relationship accounts for 5% of the variance of the 1000 hPa time series at its peak value and is significant at the 5% level. Over a similar time-scale the 1000 hPa time series accounts for 1% of itself and is not significant at the 5% level. Further investigation of the relationship reveals that it is only present during the winter season and in particular during February and March. It is also demonstrated that using stratospheric AO amplitude data as a predictor in a simple statistical model results in a gain of skill of 5% over a troposphere-only statistical model. This gain in skill is not repeated if an unrelated time series is included as a predictor in the model. Copyright © 2003 Royal Meteorological Society

Embodied social capital and geographic perspectives: performing the habitus

This paper reopens debates of geographic theorizations and conceptualizations of social capital. I argue that human geographers have tended to underplay the analytic value of social capital, by equating the concept with dominant policy interpretations. It is contended that geographers could more explicitly contribute to pervasive critical social science accounts. With this in mind, an embodied perspective of social capital is constructed. This synthesizes Bourdieu's capitals and performative theorizations of identity, to progress the concept of social capital in four key ways. First, this theorization more fully reconnects embodied differences to broader socioeconomic processes. Second, an exploration of how embodied social differences can emerge directly from the political-economy and/or via broader operations of power is facilitated. Third, a path is charted through the endurance of embodied inequalities and the potential for social transformation. Finally, embodied social capital can advance social science conceptualizations of the spatiality of social capital, by illuminating the importance of broader sociospatial contexts and relations to the embodiment of social capital within individuals.

Strategy clusters and sources of knowledge in French L2 listening comprehension

This article reports on an exploratory investigation into the listening strategies of lower-intermediate learners of French as an L2, including the sources of knowledge they employed in order to comprehend spoken French. Data from 14 learners were analysed to investigate whether employment of strategies in general and sources of knowledge in particular varied according to the underlying linguistic knowledge of the student. While low linguistic knowledge learners were less likely to deploy effectively certain strategies or strategy clusters, high linguistic knowledge levels were not always associated with effective strategy use. Similarly, while there was an association between linguistic knowledge and learners’ ability to draw on more than one source of knowledge in a facilitative manner, there was also evidence that learners tended to over-rely on linguistic knowledge where other sources, such as world knowledge, would have proved facilitative. We conclude by arguing for a fresh approach to listening pedagogy and research, including strategy instruction, bottom-up skill development and a consideration of the role of linguistic knowledge in strategy use.

What's in a name? Lexical knowledge drives infants' visual preferences in the absence of referential input

Seventeen-month-old infants were presented with pairs of images, in silence or with the non-directive auditory stimulus 'look!'. The images had been chosen so that one image depicted an item whose name was known to the infant, and the other image depicted an image whose name was not known to the infant. Infants looked longer at images for which they had names than at images for which they did not have names, despite the absence of any referential input. The experiment controlled for the familiarity of the objects depicted: in each trial, image pairs presented to infants had previously been judged by caregivers to be of roughly equal familiarity. From a theoretical perspective, the results indicate that objects with names are of intrinsic interest to the infant. The possible causal direction for this linkage is discussed and it is concluded that the results are consistent with Whorfian linguistic determinism, although other construals are possible. From a methodological perspective, the results have implications for the use of preferential looking as an index of early word comprehension.

Negative correlations between control performance and verbalizable knowledge: indicators for implicit learning in process control tasks?

Negative correlations between task performance in dynamic control tasks and verbalizable knowledge, as assessed by a post-task questionnaire, have been interpreted as dissociations that indicate two antagonistic modes of learning, one being “explicit”, the other “implicit”. This paper views the control tasks as finite-state automata and offers an alternative interpretation of these negative correlations. It is argued that “good controllers” observe fewer different state transitions and, consequently, can answer fewer post-task questions about system transitions than can “bad controllers”. Two experiments demonstrate the validity of the argument by showing the predicted negative relationship between control performance and the number of explored state transitions, and the predicted positive relationship between the number of explored state transitions and questionnaire scores. However, the experiments also elucidate important boundary conditions for the critical effects. We discuss the implications of these findings, and of other problems arising from the process control paradigm, for conclusions about implicit versus explicit learning processes.

Modeling the user knowledge by belief networks

This paper describes the user modeling component of EPIAIM, a consultation system for data analysis in epidemiology. The component is aimed at representing knowledge of concepts in the domain, so that their explanations can be adapted to user needs. The first part of the paper describes two studies aimed at analysing user requirements. The first one is a questionnaire study which examines the respondents' familiarity with concepts. The second one is an analysis of concept descriptions in textbooks and from expert epidemiologists, which examines how discourse strategies are tailored to the level of experience of the expected audience. The second part of the paper describes how the results of these studies have been used to design the user modeling component of EPIAIM. This module works in a two-step approach. In the first step, a few trigger questions allow the activation of a stereotype that includes a "body" and an "inference component". The body is the representation of the body of knowledge that a class of users is expected to know, along with the probability that the knowledge is known. In the inference component, the learning process of concepts is represented as a belief network. Hence, in the second step the belief network is used to refine the initial default information in the stereotype's body. This is done by asking a few questions on those concepts where it is uncertain whether or not they are known to the user, and propagating this new evidence to revise the whole situation. The system has been implemented on a workstation under UNIX. An example of functioning is presented, and advantages and limitations of the approach are discussed.

Implicit and explicit knowledge bases in artificial grammar learning

Two experiments examined the claim for distinct implicit and explicit learning modes in the artificial grammar-learning task (Reber, 1967, 1989). Subjects initially attempted to memorize strings of letters generated by a finite-state grammar and then classified new grammatical and nongrammatical strings. Experiment 1 showed that subjects' assessment of isolated parts of strings was sufficient to account for their classification performance but that the rules elicited in free report were not sufficient. Experiment 2 showed that performing a concurrent random number generation task under different priorities interfered with free report and classification performance equally. Furthermore, giving different groups of subjects incidental or intentional learning instructions did not affect classification or free report.