1,651 research outputs found
A Fast Approach to Creative Telescoping
In this note we reinvestigate the task of computing creative telescoping
relations in differential-difference operator algebras. Our approach is based
on an ansatz that explicitly includes the denominators of the delta parts. We
contribute several ideas of how to make an implementation of this approach
reasonably fast and provide such an implementation. A selection of examples
shows that it can be superior to existing methods by a large factor.Comment: 9 pages, 1 table, final version as it appeared in the journa
Empirical modelling principles to support learning in a cultural context
Much research on pedagogy stresses the need for a broad perspective on learning. Such a perspective might take account (for instance) of the experience that informs knowledge and understanding [Tur91], the situation in which the learning activity takes place [Lav88], and the influence of multiple intelligences [Gar83]. Educational technology appears to hold great promise in this connection. Computer-related technologies such as new media, the internet, virtual reality and brain-mediated communication afford access to a range of learning resources that grows ever wider in its scope and supports ever more sophisticated interactions.
Whether educational technology is fulfilling its potential in broadening the horizons for learning activity is more controversial. Though some see the successful development of radically new educational resources as merely a matter of time, investment and engineering, there are also many critics of the trends in computer-based learning who see little evidence of the greater degree of human engagement to which new technologies aspire [Tal95].
This paper reviews the potential application to educational technology of principles and tools for computer-based modelling that have been developed under the auspices of the Empirical Modelling (EM) project at Warwick [EMweb]. This theme was first addressed at length in a previous paper [Bey97], and is here revisited in the light of new practical developments in EM both in respect of tools and of model-building that has been targetted at education at various levels. Our central thesis is that the problems of educational technology stem from the limitations of current conceptual frameworks and tool support for the essential cognitive model building activity, and that tackling these problems requires a radical shift in philosophical perspective on the nature and role of empirical knowledge that has significant practical implications.
The paper is in two main sections. The first discusses the limitations of the classical computer science perspective where educational technology to support situated learning is concerned, and relates the learning activities that are most closely associated with a cultural context to the empiricist perspective on learning introduced in [Bey97]. The second outlines the principles of EM and describes and illustrates features of its practical application that are particularly well-suited to learning in a cultural setting
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Prym varieties and their moduli
We discuss the geometry of the moduli space of Prym varieties. The article is
based on series of lectures given in Bedlewo and Luminy. The first section of
the paper contains a detailed historical account of the lives of Friedrich Prym
and Friedrich Schottky.Comment: 35 pages, minor corrections and additions. To appear in
"Contributions to algebraic geometry" edited by P. Pragacz and published by
the EM
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