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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Mathematical Modeling of the Processes of Interdisciplinary Collections Formation in the Digital Libraries Environment</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>Joint Supercomputer Center of the Russian Academy of Sciences - Branch of Federal State Institution “Scientific Research Institute for System Analysis of the Russian Academy of Sciences” (JSCC RAS - Branch of SRISA)</institution>
          ,
          <addr-line>119334, Moscow, Leninsky av., 32 a</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
      </contrib-group>
      <fpage>391</fpage>
      <lpage>398</lpage>
      <abstract>
        <p>The task of forming a digital space of scientific knowledge (DSSK) is analyzed in the paper. The difference of this concept from the general concept of the information space is considered. The DSSK is represented as numerous different accessible objects verified by the world scientific community. The form of structured representations in the digital space is the semantic network, in which the fundamental principles of the organization are the fundamental objects and the subsequent construction of their hierarchy, in particular, according to the principle of inheritance. The classification of the objects that make up the content of the DSSK is introduced. The concept of a hierarchical relationship between an object is defined. The use of the concepts of set theory in the construction of DSSK allows you to divide by information into levels of detail. The concept of levels of the objects hierarchy of digital space of scientific knowledge is introduced. The definitions of objects of various levels are given. The principles of working with objects of each level are formulated too. It is shown that with the help of the hierarchical structure of information presentation in the digital library environment, a user collection can be formed in the central processing center. Constructing a hierarchy which is a section with a high degree of detail, allows you to increase the efficiency of information search in the space of knowledge and information analysis.</p>
      </abstract>
      <kwd-group>
        <kwd>Semantic Network</kwd>
        <kwd>Information Space of Knowledge</kwd>
        <kwd>Electronic Library</kwd>
        <kwd>Levels of Detail</kwd>
        <kwd>Hierarchy of Information Objects</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>Information is at the forefront of the many areas of our lives. IT and computing
technologies penetration has expanded the possibilities for the capturing, analysis,
disseminating, processing and use of scientific information.</p>
      <p>Modern needments for professional information require the development of a
knowledge space, which is a digital environment in which information resources and
services from different fields of science, culture and education are integrated. A part
of the general knowledge space is the digital space of scientific knowledge (DSSK),
which differs from other components of the common space (in particular, such as
Wikipedia) in that the information objects represented in the DSSK are verified by the
world scientific community and are separated from information objects that are
ideological, religious and other scientifically controversial character [1].</p>
      <p>The flow of requests to the DSSK is often continuous, rapidly time-varying, not
always predictable and unlimited in the form of the request. The software that
processes such requests cannot afford to store and “review” the parameters of the request,
which often requires a quick response in real time. Requirements for the accuracy of
data retrieval in the DSSK (in contrast to the Search Engine) necessitate the
development of special methods for request processing queries with a sufficiently accurate
mapping of the query text to the metadata space describing certain objects of the
DSSK. DSSK metadata, on the other hand, includes not only sets of keywords, but
also more complex structures, for example, hierarchical classification systems.</p>
      <p>The form of a structured representation of the digital knowledge space is a
semantic network. The basic organization principle of this space is based on the
classification system of objects and the subsequent construction of their hierarchy, in
particular, according to the principle of inheritance: “macroeconomics” - section of the
“economy”, “poetry collection” – publication, etc.</p>
      <p>In accordance with this principle, objects are classified into a number of categories
or classes based on their common features.</p>
      <p>Most digital data collections are a diverse information network connecting objects
of various types. For example, an electronic publication (the type of the object is
“book”), in addition to plain text, contains additional information, such as the author
of the publication (the type of the object is “person”), year of publication, publishing
house, place of publication, etc. In turn, the object "person", in addition to a sequence
of characters that specify a surname, is associated with person’s biography, a field of
scientific interests ("subject matter"), etc. Thus, from the object “publication”, a
connection can be established with another “object” (“author”), with the text of this
publication, with the “subject of the object”, etc. In the general case, the DSSK should
support various types of relationships between its elements – both within the same
class of objects (in particular, a recursive hierarchical relationship) and between
objects of different classes.</p>
      <p>
        A significant number of studies have been devoted to the construction of thematic
hierarchies, a hierarchy of concepts, object models, etc., which provide hierarchical
organization of data at different levels of detail and have applications such as web
search and viewing tasks [
        <xref ref-type="bibr" rid="ref7">2, 3, 4</xref>
        ].
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref13">5</xref>
        ], the NetClus algorithm was described, which allows one to establish
relationships between multi-type objects to create high-quality network clusters. The
NetClus algorithm allows reordering attribute objects in each newly defined network
cluster.
      </p>
      <p>In this paper, we consider the DSSK in the aspect of theory of sets, which allows
us to approach the issues of constructing space and working with it from a new point
of view.</p>
      <p>Сonfiguration of DSSK
Let Ω – set containing all the elements of a digital scientific space located in some
(possibly distributed, storage). Ω includes, in turn, two sets. The first of them
(denoted by  ) consists of digital images of real-world objects (digitized publications,
archival documents, photographs, etc.) and objects created exclusively in the digital
environment (electronic publications, 3D models, multimedia materials, etc.). All
objects are being numbered in some way. Numbering should uniquely identify the
object and provide the ability to retrieve it from storage.</p>
      <p>The second set (denoted by  ) includes metadata containing multidimensional
characteristics of the objects of the first set, ensuring their selection by requests to DSSK
and presentation to users.</p>
      <p>The set  consists of elements   ,, where  =1…N (N is the total number of objects
reflected in Ω). These elements are objects of the following types:
 text files (recognized digitized printed or handwritten documents) or
documents originally generated in electronic form;
 static images (unrecognized digitized documents, digitized or originally
digitally generated photos);
 digital or digitized audio recordings;
 digital or digitized video/film materials;
 3D models of various objects;
 multimedia installations (digital models of natural processes and technical
devices, educational materials, virtual tours, etc.).</p>
      <p>If the elements of the set  are being represented by a simple collection of pairs
“object – its number”, then the set  in general, is a rather complex facet-hierarchical
structure. Each of its elements is represented not only by a specific meaning and
reference to an element of the set  (which is the case in traditional bibliographic
information retrieval systems), but may include an indication of links with other elements.
Thus, by elements of the set  we mean a structure that includes the semantic value of
object characteristics, an indication to one or more elements of the set 
corresponding this characteristic, and an indication ti relations with other structures, which are
also elements of set  .</p>
      <p>The constituent elements of set  can be indices of classification systems (such as
State Classifier of Scientific and Technical Information, UDC, etc.) documents
metadata such as individual characteristics of a person (surname and name, date and
place of birth, etc.), names of events, their text descriptions, temporal and
geographical characteristics of objects, etc.</p>
      <p>In order to ensure the accuracy of searching for objects in the DSSK, set  must
include a number of non-overlapping sets characterizing various aspects of
information about the elements of the set  . Obviously, there can be myriad such
partitions, but we will restrict ourselves to considering the “intuitive minimum”, but
covering a wide range of characteristics of objects, a data set including classes such as
“what (who), where, when”, supplemented by the “subject” class and formal
characteristics specific to the DSSK, allocated to the subsets  1 (types of objects listed
above) and  2 (conditions for providing users with various objects of the set  ).
The subset  1 of the set  ( 1:  1 ⊂  ) consists of 6 elements, which are the
characteristics of the elements of the metadata set, which we call the representation types of
a digital object. Namely:
  11 – text view with the ability to search for a fragment of text;
  12 – static image;
  13 – 3D object;
  14 – audio document;
  15 – video document;
  16 – is a multimedia object.</p>
      <p>The subset  2 of the set  ( 2:  2 ⊂  ) consists of elements that determine the
conditions for the provision of a digital object to the user. The introduction of this subset is
due to various legislative requirements for the public presentation of an object.
Elements of the set  2 will be called the conditions for the provision of the object.
Namely:
  21 – the object is in the free access;
  24 – the object is in limited access, free of charge for a certain group of
users (for example, a paid subscription to full-text scientific publications for
employees of a certain institution) and inaccessible to other users;
  23– the object is in limited access free of charge for a certain group and
commercial for other users (for example, a digital model of a museum
exhibit may be available for free viewing to museum visitors, and remote viewing
provides a certain fee.
  24 – the object is commercially available, i.e. the user needs to pay access
to this resource.</p>
      <p>The subset  3 of the set  ( 3:  3 ⊂  ) contains the main characteristics of the object
necessary for its identification during the search (“what” or “who”, “where”, “when”).</p>
      <p>Note that the subsets  1,  2 and  3 of the set  do not intersect each other.</p>
      <p>The subset  4 contains elements of the class “subjects”, it can have a rather
complex structure containing indices and names of elements of various classification
systems (strictly hierarchical type State Rubricator of Scientific and Technical
Information [7], facetted type UDC [8, 9], etc.), keywords and terms, thesauruses, etc.
As an element of the set  3 belonging to the class “what”, to act as an obligatory
element is the name of a specific object, which can be supplemented by elements that
specify the type of object within a given view, such as a book, article, archive
document, etc., as well as unstructured explanations containing this or that information
about the object. For example, a collection of photos of Moscow of the 30s can be
supplemented by a detailed article on the architecture of the city of that time,
presented in the form of hypertext.</p>
      <p>As an element of the “where” class of the set  3, various implementations can be
made that are related directly to the geographical location of the object (for example,
for a person the place of birth, for a museum object - the place of its initial discovery,
for an event - the country or city where it occurred, etc.). Elements that are belonged
to class "where" may be represent as organizations described, in turn, by its metadata
(for example, the person’s place of work, the place of storage of a museum item, a
publishing house for a printed document, etc.). For example, the collection of herbaria
A.N.</p>
      <p>Petunnikova</p>
      <p>[http://www.gbmt.ru/ru/about/fund/fondovaya-kollektsiyagerbariy/, http://e-heritage.ru/ras/view/person/general.html?id=49901007], contains
information about geographic location of the collection elements.</p>
      <p>The print materials year of publication, or year of the person birth, etc. may act as
an element of the “when” class of the set  3.
3</p>
    </sec>
    <sec id="sec-2">
      <title>The Collections Generation of the Set</title>
    </sec>
    <sec id="sec-3">
      <title>Elements</title>
      <p>If the user’s requests to the DSSK include only elements of the set  , then the task of
selecting and presenting documents is reduced to the formation of the sampling
conditions, consisting of query terms connected each other by Boolean operators. Data
search in space  is carried out by comparing its elements with query elements (let's
call it linear search). The result of the search is the addresses of the corresponding
elements of the set  , by which these elements are retrieved from the store and
provided to the user in accordance with the conditions reflected in the set  2.</p>
      <p>However, in practice, often the user needs to create a collection of elements of the
set Α for requests that do not explicitly formulate in terms of the set  . For example, it
is necessary to form a user's collection of the "Silver Age" poets works reflected in
the digital library (DL) of 20th century publications. During the formation of the DL
elements the “Silver Age” was not indicated as a temporary characteristic. It is also
not present in any of the classification systems that could be used in the database
creation. In accordance with a query in terms of “Silver Age poets” its result will be an
empty subset of the elements of the set  . At the same time it is obvious that among
the elements of the set  there are objects that meet the requirements for this
collection. To detect them it is necessary to construct a mapping of the user query to the set
 and then implement a linear search for the query, including the corresponding
ele</p>
      <p>Note that the properties of objects of the space Ω are transferred to all objects of
the subsets of this set, which avoids a significant part of the duplication of
informents of the set  .
mation [10, 11].
4</p>
    </sec>
    <sec id="sec-4">
      <title>Building a Hierarchy of Digital Objects Representation in a Digital Library Environment</title>
      <p>Let the set  be the set of “the object’s characteristics”. The characteristic of the
object (  , where  = 1 … ∞) is understood as a given parameter, according to which the
objects of the set Α will be combined into a user collection. For example, some
research area or object type (mineral, silver age poets, minerals mentioned in silver age
poetry, etc.) could be such parameter. I.e.  = ⋃∞  .</p>
      <p>Applying some mapping   to the elements of the sets  and  , we can obtain the
so-called collection that is the subset of one or more types objects integrated by a
given parameters:   ( ( ),  ).</p>
      <p>Applying the map   to the set  , we obtain the subset  (  ) by which we can
select the objects corresponding to it from the set A. We call the class of these objects
the user collection  (  ). The collection of subsets  corresponding to some common
characteristic  ( ) is called the class set  ( ). The concepts and definitions
described above make it possible to build a hierarchy of the representation of digital
library environment objects which allows to formalize of a general approach to the
formation of user collections conversely.</p>
      <p>The hierarchy levels of user collections are determined by the structure of
userdefined object mapping properties to subsets  . In general:</p>
      <p>(  ) =  1( ) ∪  3( ) ∪  4( )
The first level of the hierarchy (narrow-focus collections) includes collections for
which the subset  3( ) is not empty; the second level (theme-specific collections)
includes collections for which  3( ) is empty and  1( ) and  4( ) are not empty;
the third level (thematic collections) includes collections for which  1( ) and  3( )
are empty and not empty  4( ).
5</p>
    </sec>
    <sec id="sec-5">
      <title>Conclusion</title>
      <p>The creating of such a hierarchy allows to optimize the process of formation and
maintenance of information funds of digital libraries and also allows the user to
choose from the whole set of interconnected resources of the digital library those
information objects that are united by one or more features [11–16].</p>
      <p>Using the hierarchical structure of the information representation of objects in the
environment of the digital library, a user collection can be formed in the DSSK.</p>
      <p>Thus the task of collections creation according to a prescribed criterion is reduced
to the following steps (Figure 1):
1. A correspondence analysis of the elements of this collection attribute to the
elements of the set  ;
2. Separation the collection attributes into two subsets. The first subset contains
the elements of the set  in explicit form (for example, the type of an object,
typical objects, etc.). The second subset doesn't contains the elements of the
set  in explicit form;
3. The implementation of the algorithm for mapping the characteristics of the
collection to the set  .</p>
      <p>As an example of the implementation of the algorithm for mapping the collection
to a set of metadata, let us consider the formation of materials collection related to the
“Silver Age” poets in the environment of the Digital Library “Scientific Heritage of
Russia” (DL SHR). Such collection should include information about the authors and
all documents related to them (including bibliography and full texts of their works).</p>
      <p>At the first stage, the years of publication are determined. I.e. the parameter of the
request “Silver Age” is translated into the “language” of metadata. After that, a
selection is made of all objects included in the DL SHR for a given span of time. Next,
from the found data array, persons are selected that correspond to such metadata
elements as the “author”, which, in turn, are associated with publications that have a
“publication type” metadata element with the value “poetry”. As a result, we get a list
of the names of the poets of the Silver Age.</p>
      <p>Then, of all the objects obtained in the first stage, all materials are selected
according to the “author” parameter.</p>
      <p>Thus, a collection of all DL SHR objects associated with the “Silver Age” poets
will be obtained (including archival documents, photo documents, etc.).</p>
      <p>The research is carried out by JSCC RAS – branch of SRISA within supported by
Russian Foundation for Basic Research (projects 18-07-00893 and 18-00-00372).</p>
    </sec>
  </body>
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