International
Congress of Mathematicians 2002 – Beijing
EIC-satellite
conference at Tsinghua University
Electronic
Information and Communication in Mathematics
Beijing,
Aug. 28-31, 2002
Mathematics
Subject Classification and related schemes in the OAI framework
Antonella De Robbio, Dario Maguolo
Mathematics Library – University Library System
University of Padova – ITALY
Alberto
Marini
Institute for Applied Mathematics and Information
Technology
National Research Council (CNR-IMATI), Milano - ITALY
Abstract
This paper aims to give a feeling of the roles that discipline-oriented
subject classifications can play in the Open Archive movement for the free
dissemination of information in research activities.
Mathematics, and Mathematics Subject Classification, will be the focuses
around which we will move to discover a variety of presentation modes,
protocols and tools for human and machine interoperability.
The Open Archives Initiative
(OAI) is intended to be the effective framework for such a play.
In the first part
of this paper, we start by describing
the most important subject classification schemes in mathematics and related
disciplines. Then we sketch the structure of discipline-oriented schemes in view of browsing
and we give an account of different browsing modalities, implemented in the
tools we produced and collected in The Scientific
Classifications Page. Finally we give an insight on the design,
implementation and use of a programming language for the generation of
hypertextual presentations of complex structured data.
In the second part, we list different strategies for e-print
communication in scientific research, up to the basic definitions of the Open
Archives Initiative.
A review of the functionalities actually implemented in OAI compatible archives managed by the EPrints software will lead us
to some
working hypotheses about the roles that subject classifications in
mathematics and related disciplines can play in the scenarios of the Open
Archives movement.
Contents
1 – Subject classification schemes
1.
Schemes for
mathematics
2.
Schemes for
computing, physics, control and information technology
3.
Schemes for
economics
4.
Discipline specific
and general schemes
2 – Classification schemes: from structure to browsing
1.
The common
structure of subject classification schemes
2. From structure to browsing
3.
H-volumes in The
Scientific Classifications Page
Towards a presentation generating language
3 – The OAI framework
1.
E-print
communication: tools and networking architectures
2.
The Open Archives
Initiative
3.
OAI compatible
refereed self-archives: the EPrints 2 software
4 – Conclusions
1 – Subject classification schemes
Subject classification schemes are primary tools for
the organization of knowledge and terminology in scientific disciplines.
They are produced mainly by professional societies, or
academic and research institutions, often to be employed in their own
bibliographic databases. Although many of the issuing bodies have national or
regional scope, subject classification schemes are generally international in
scope, and are intended to be a communication tool for the international
scientific community.
1.1 – Schemes for mathematics
Mathematics Subject Classification (MSC) [1] is developed by the editorial offices of the two world's most important
bibliographic databases for mathematical research:
·
MathSci, which is produced by the American Mathematical Society, and
·
Zentralblatt
MATH, which is produced by the European
Mathematical Society, the Fachinformationszentrum (FIZ) Karlsruhe, Germany and
other Editorial Units all over Europe.
MSC
covers all branches of pure and applied mathematics, including probability and
statistics, numerical analysis and computing, mathematical physics and
economics, systems theory and control, information and communication theory.
MSC underwent in time a number of revisions; the latest version came valid in
January 2000, so it is called MSC2000.
On the side of
mathematics education, the Zentralblatt
für Didaktik der Mathematik Classification Scheme [2]
is used for the bibliographic database MATHDI,
which is edited by the European Mathematical Society, FIZ
Karlsruhe, and Zentrum für Didaktik der Mathematik at Karlsruhe
Universit, in cooperation with Math Doc Cell (France)
1.2 – Schemes for computing, physics, control and
information technology
In
the field of computing, including hardware, software, networking, theory,
methodologies and applications, the most important tool is the Computing Classification System.[3]
It
is developed by the Association for Computing Machinery (USA) to classify items
in the directories Computing Reviews
and Guide to Computing Literature,
which are edited by the same body.
Section
68 Computer Science of MSC was
designed in rather tight matching with a great part of CCS.
In
the fields of theoretical, experimental and applied physics and astronomy we
have the Physics and Astronomy
Classification Scheme (PACS).[4]
Section 02 Mathematical methods in
physics of PACS closely resembles the top level codes for pure mathematics,
probability and statistics of MSC. PACS is prepared and revised, at least
biennially, by the American Institute of Physics.
A
version of PACS is established as Section
A of INSPEC Classification.[5]
INSPEC is a bibliographic information service provided by the Institution of
Electrical Engineers (UK). It covers physics, electrical engineering,
electronics, communications, control engineering, computers and computing, and
information technology.
INSPEC Classification has three other major sections:
·
Section B: Electrical & Electronic Engineering
·
Section C: Computer & Control
·
Section
D: Information Technology
1.3 – Schemes for
economics
The
fields of economics are increasingly involved in mathematical arguments, both
in theoretical and specific topics; and conversely, mathematical problems and
theories even more often arise from economic domains.
This can be seen by the place mathematical topics take
in the Journal of Economic Literature
Classification System,[6]
developed by the American Economics Association for its indexing journal and
for the corresponding EconLit
database.
Such topics are mostly located in the 62 Statistics, 90 Operations research, mathematical programming, and 91 Game theory, economics, social and
behavioral sciences sections of MSC2000.
1.4 – Discipline specific and
general schemes
Besides
these, many other subject classification schemes exist for use in any
scientific discipline or field of disciplines.
Yet other schemes are the general ones, not oriented to specific
disciplines, such as Dewey Decimal
Classification.[7]
2 – Classification
schemes: from structure to browsing
2.1 – The common
structure of
subject classification schemes
The structure of subject classification schemes, be they discipline
specific or general, is essentially the same: a relational system of categories, identified by alphanumerical
codes, whose meaning is specified by descriptions or scope notes in some
natural language (primarily, for current scientific research, English;
translations and multilingual editions are frequently made available).
Generally there is one main relation, which in most cases is
tree-shaped (monohierarchical, or, simply, hierarchical) and the categories are
called nodes. Sometimes, however, the
main relation is a more relaxed partial order, allowing nodes to be under more
than one node (so the relation is called multihierarchical).
Other
relations are considered as cross-references, allowing connections between
diverging paths of the main relation-
Subject classification
schemes vary in time through succeeding versions; one version keeps valid for
indexing and searching in a bibliographic database for a more or less long
period of years. Two
subsequent versions can be related by linking categories in the older and the
newer version which hold some correspondence in meaning,
even if the relation may not be one-one, or structure preserving, due to
splits, merges, reorganizations, deaths and births of topics, as represented in
the positions of the two versions.
For example, Mathematics Subject Classification has
5531 categories in a three-level hierarchy. The top level counts 63 nodes.
Cross-references, often equipped with explanatory text (“For …”) are of the
following types: see also – see mainly – see. Some notes for coordinate indexing (and searching) are
present.
Physics and Astronomy Classification Scheme has a four-level hierarchy. The top level counts 10 nodes, the second
level 66 nodes.
2.2 – From structure to browsing
Due to their
structural features, subject classifications are effective tools for browsing
and searching in bibliographic databases, catalogs and other kinds of metadata
repositories.
Moreover, subject classifications can set up knowledge organization
tools for lexical collections extracted from metadata or fulltext databases,
for terminologies, glossaries, dictionaries or encyclopedias, surveys, up to
distributed libraries of natively digital documents or digitalized paper
document. The set of descriptions of a classification scheme is itself a
primary terminological resource.
2.3 – H-volumes in The Scientific
Classifications Page
Different
modes in browsing subject classifications can be exploited by hypertextual
techniques.
We
managed to produce various tools to demonstrate some of these modes.
The Scientific Classifications Page [8]
collects such tools. It is presented both in English and in Italian language.
It includes the following sections:
·
The
Mathematics Classification Page
·
Mathematics
Subject Classification MSC and Dewey Decimal Classification DDC
·
Relating
Scientific Subject Classification
The tools we produced consist
of systems of syntactically simple but highly connected and coordinated HTML
pages, called h-volumes.
H-volumes can amount even to
thousands of files, written in plain HTML with simple JavaScript routines; in
our working environment they are generated by a pool of standard C programs,
starting from ASCII files, which present lists of records without redundancies
and glossaries concerning attribute values.
H-volumes can be employed to display any kind of structured information set, such as directories, biographical collections, metadata collections, databases, glossaries, dictionaries, encyclopedias, etc.
The actual production
of h-volumes starts from ASCII files obtained by manipulating existing data
sets and texts, in particular available Web pages. This preparation activity is worked out partly by hand
(i.e. using interactively some flexible source editor), partly making use of
text processing procedures developed contextually to the development of
procedures for HTML page generation.
Let’s now turn to see the sections of The Scientific Classifications Page in
some detail.
The Mathematics Classification Page
The Mathematics Classification Page collects six hypertextual frame presentations of the
latest version of Mathematics Subject Classification, MSC2000.
From an ASCII file containing the whole MSC2000, a
simple frame presentation was obtained. From the same file a double view
presentation was obtained too.
The former process, generating a simple frame
presentation, was worked out on a file containing an Italian translation of
MSC2000, while, by processing the two files in combination, we obtained a
simple frame presentation, which displays interleaved English and Italian
texts.
From a file resulting from a comparison of MSC2000
with the 1991 version, we obtained a simple frame presentation which includes
changes from MSC 1991:
Finally, from the combination of the first ASCII file
with a file which contained data about subject-specific pages of relevant
Websites, we obtained a simple frame presentation, with guide pages linking to
those subject-specific pages of Websites.
[Fig. 1]
This is an example of simple
frame presentation.
The
top frame is a sort of Table of Contents, which gives access to different
slicings of the scheme: single list presentations of the classification
categories at level 1 and 1-2, and an indexed set of list presentations which
covers the whole scheme. For the latter, the top frame displays the list of the
first 2 digits of the codes of the 63 level 1 categories; each item in the list
points to a page which is displayed in the frame below, containing a list
presentation of the subtree below the indicated level 1 category.
In
this way, the long list of all the classification categories is divided into a
number of sublists, so you can browse the classification scheme by transferring
only files of moderate size.
On
the other hand, double or multiple view presentations can be exploited to
navigate through transversal links either inside one version of a classification
scheme or among more schemes or versions: you can move to and from parallel views of them.
[Fig. 2]
Here is an example of double
view presentation, showing connections between categories from the Dewey
Decimal Classification, 21st edition, and MSC2000.
The double view presentation included in
The Mathematics Classification Page is actually a duplicated simple frame
presentation of the whole tree of MSC2000 in English which allows walking
through cross references while keeping vision of the contexts of both endpoints
of the selected cross references.
Mathematics Subject Classification MSC and Dewey Decimal
Classification DDC
The Mathematics Subject Classification MSC and
Dewey Decimal Classification DDC section of The Scientific Classifications Page includes two English language
presentations:
·
the just shown page of connections between
categories from the Dewey Decimal Classification, 21st edition, and
MSC2000
·
a KWIC list h-volume for the combined set of
descriptions of:
- a revision proposal for
the 510 DDC section, Mathematics, presented in January 2001
- MSC2000
The
sections E - N of the ZDM classification, encoded as 97E - 97N in the MSC
style.
[Fig. 3]
KWIC list h-volumes (as in Fig. 3) are devised
for discovering textual similarities among subject descriptions in one or more
classification schemes or versions, in order to obtain suggestions about possible affinities of
contents.
A KWIC list (KWIC shortens KeyWords In Context)
presents every description through its circular permutations, beginning with a
significant word or phrase; the overall list is ordered along the list of
significant words.
By a method similar to that employed for simple frame presentation, long ordered list, as generally a KWIC list is, can be endowed with some sort of distributor allowing to reach quickly determined points or sections of the long sequence. A distributor can be built with pointers to initial letters, initial words of paged sections, sublists dealing with particular categories of entities. The list of permuted descriptions, subdivided into smaller manageable lists, is displayed on the right, while the distributor appears in the left frame.
KWIC lists may not be intended for the
end user, rather as a help in establishing structured connections within or
among classification schemes. This activity, although can greatly benefit from
automated techniques, requires an amount of field specific knowledge which
can’t be automated, at least with the current technologies. The connections so
discovered can be subsequently displayed through multiple view presentations of
the involved classification schemes.
Relating Scientific Subject Classifications
The Relating
Scientific Subject Classifications section of The Scientific Classifications Page contains a set of English
language presentations (in one case bilingual):
·
a double view presentation, showing connections between categories from
the ACM Computing Classification System (1998), and MSC2000
·
separate KWIC lists of descriptions of MSC2000,
of PACS 2001, of ACM Computing Classification System (1998)
·
combined KWIC list of descriptions of MSC2000
and PACS 2001, and of MSC2000 and ACM Computing Classification System (1998).
2.4 – Towards a presentation
generating language
The h-volumes we produced are not intended to be taken
as ultimate references, but as prototypes capable to clarify the real problems
to face for the production of more complete and professional h-volumes and to
test their effectiveness as documentation tools.
In fact, the development of such prototypes brought to
the specification of parametrization mechanisms, data structures and processing
modes which induced to define a programming language oriented to the
manipulation of hypertextual presentations and to displays of mathematical
structures.
The
definition and the implementation of an experimental language called TAMP (Text
Analysis Manipulation and Presentation) was actually started up.
TAMP is aimed to the analysis of text files of
specified format (TeX, HTML, XML, etc.), the organization of specific knowledge
bases endowed with links to other Internet resources and their presentation
through HTML pages.
The
language is implemented by means of a single C program, called YP, reading and
generating only plain ASCII files. The first input file, characterized by the
extension .ypg, is the source file of the program to execute. Many other
specific files pointed out in the program are read and written.
Such
files contain either data or sources of specific programs, dedicated to
generate HTML files or other publishable files (e.g. TeX files), to prepare
intermediate files, e.g., lists following defined orderings and collecting
items provided by partial unordered files (in particular files extracted from
Web pages), or to control manipulations of some types (actually few) of
mathematical structures starting from relatively simple expressions of basic
ones in order to produce readable presentations of significant structures,
possibly in a good consulting context.
The
implementation is only at a “less than 1 version” and is poor in many respects,
but has some peculiarities that allowed the production of practical Web pages
and whose developments seem worthy of investigation.
The
language can control many data types: the basic ones are integers (but not yet
real numbers) and strings; it controls aggregates of basic data as sequences,
tables and sequences of sequences. Moreover it's possible to manipulate some
specific presentation structures (indexing KWIC lists, glossaries, etc.) and
the representations of specific mathematical structures (permutations,
partitions, graphs, trees, paths in combinatorial plane, etc.).
While a good choice of operators on basic data types and their
aggregates is provided, only few operators acting on specific structures are implemented.
On the other hand the implementing program YP has good extensibility features:
the data types are parameterized, simple schemes allow the introduction of
identifiers and general functional characteristics of new operators and their
actions can be implemented in routines whose collocation and role are not
difficult to tune with the characteristics of existing operators.
Among richer data types the language provides some
kinds of constructors, composite entities targeted to build presentation structures.
A typical example is given by the so called KWIC engine: its definition
requires to specify the fields of a flat file, the catalogued routines charged
to distinguish and accept these fields, the catalogued routines commissioned to
build the different fields of final KWIC items and the parameters required by
some routines. Specific statements allow to activate the
constructors giving the possibility to choose for them parameters such as
schemes controlling files to be generated and prefixes of their names.
An
important characteristic of the language is the possibility to define automata
at different levels of generality. The automata of the more general type can be
defined by a specific rich jargon opening the possibility to determine
effective models of acceptors, transducers, text analysers and text generators,
typically through successive refinements.
Moreover, the translator of the proposed language can be used with a versatile preprocessor allowing substitutions, inclusions, selections and iterations of good reach: its control structures can act on variables concerning strings, integers and files. This preprocessor limits the actual major language drawback, i.e. lack of modularity. A group of statements that would be natural to encapsulate in a module can be recorded in a file endowed with dummy strings: this file can be included in other source files, either in the main one or in a file that can be included similarly.
3 – The OAI framework
3.1 – E-print communication: tools and
networking architectures
Scientific
research relies heavily on the rapid dissemination of results. So the slow
formal process of submitting papers to journals has been augmented by other,
more rapid, dissemination methods.
Originally dissemination involved printed documents,
such as technical reports and informal conference papers.
Then researchers started taking advantage of the
Internet, putting papers on ftp sites and later on various web sites. But these
resources were fragmented. Searching through them resulted to be very
difficult, and there was no guarantee that information would be archived at the
end of a research project.
Different strategies for scientific research communication via e-prints
were have been developed in time, which involve:
·
small specialized archives
centralized archives such as arXIv [9] for physics and related disciplines, mathematics, nonlinear sciences, computer science; and CogPrints [10] for cognitive science, artificial intelligence, computational linguistics and neuroscience
single or networked institutional archives, such as NCSTRL [11] and the ERCIM Technical Reference Digital Library [12] for computer science and mathematics
·
distributed
networks connected by some interoperability protocol, such as RePEc [13]
for economics, and DoIS [14]
for library and information science
·
umbrella servers,
such as MPRESS [15] for
mathematics
·
servers connected
to groups of journals or sponsored by commercial publishers, etc.
Web search
and cash engines like Researchindex (formerly Citeseer),[16]
provide a solution which has been appreciated especially by people in the
computing area. E-prints posted in personal homepages without any specific care
about metadata are harvested and cashed; the service is comprehensive with
reference linking.
3.2 – The Open Archives Initiative
The Open Archives Initiative (OAI) [17]
is an international effort to develop interoperability standards for
disseminating content over the Web. OAI stresses the separation of being a data provider (i.e., publisher) and
being a service provider (i.e., interface
for search, browsing, reference linking). On the other hand, nothing prevents
the same system to embody and integrate both functions. It is even possible for
individual researchers to develop personal open archives, which can be accessed
to build tailored personal web sites and other services, as well as harvested
into department archives.
The base concept of the OAI is metadata
harvesting, which is realized in the OAI Protocol for Metadata Harvesting. [18]
So it no longer matters where papers
are archived; the papers in all registered OAI-compliant archives can be
harvested using the OAI protocol into one global "virtual archive" by
Open Archives service providers.
3.3 – OAI compatible refereed
self-archives: the EPrints 2 software
EPrints [19]
is a free (General Public License) software for managing e-prints archives,
developed at the Electronics and Computer Science Department of the University
of Southampton (UK).
It is aimed at organizations and communities rather
than individuals. It provides an interface for system administrators, for
archive editors to process submissions, for authors to deposit papers, and for
users to access papers by searching or browsing metadata.
The system comes configured to run an institutional
pre-prints archive, but can be reconfigured with utterly different metadata
fields and content.
Any version of EPrints is fully interoperable with the
current OAI Protocol for Metadata
Harvesting.
4 – Conclusions
Our work has been directed to the definition of text
processing methodologies for the development of hypertextual presentations of
complex documentation structures. Such presentation modalities can enrich the
browsing functionalities of archives and service providers in the OAI framework, allowing a full network of
bridges among specific subject areas to guide advanced research communication
activities.
In particular, we are investigating the possibility of
providing the EPrints software with tools modeled on the experimental ones we
produced for the Scientific Classification
Page.
Centering with Mathematics Subject Classification,
bridges can be launched and passed through inside mathematics and among the
disciplines that live and develop with mathematics.
This is equivalent to say that bridges can be launched all over the world of
scientific and technological knowledge, if we are aware of the dynamics that
mathematical disciplines are ever more moving in modeling and computing
activities for every field of human knowledge.
References
Antonella De Robbio, Dario Maguolo, Alberto Marini
Scientific and General Subject Classifications in the Digital World
High Energy Physics
Libraries Webzine, Issue 5, November 2001
http://doc.cern.ch/heplw/5/papers/4/
Alberto Marini
Text Processing for Presentation and Manipulation of Mathematical Resources
Paper presented at the
Workshop “Electronic Media in Mathematics”, Coimbra (Portugal),
September 13-15 2001
http://www.mat.uc.pt/EMM/index.html