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<div id="header">
<h1 class="title toc-ignore">Formal definitions of field normalized
citation indicators and their implementation at KTH Royal Institute of
Technology</h1>
<h4 class="date">2023-09-20</h4>
</div>
<div id="TOC">
<ul>
<li><a href="#introduction" id="toc-introduction">Introduction</a></li>
<li><a href="#part-1-definitions" id="toc-part-1-definitions">Part 1
Definitions</a>
<ul>
<li><a href="#mean-field-normalized-citation-rate"
id="toc-mean-field-normalized-citation-rate">1.1 Mean field normalized
citation rate</a></li>
<li><a
href="#proportion-publication-among-the-10-most-frequently-cited-in-the-field"
id="toc-proportion-publication-among-the-10-most-frequently-cited-in-the-field">1.2.
Proportion publication among the 10 % most frequently cited in the
field</a></li>
<li><a href="#mean-field-normalized-journal-impact"
id="toc-mean-field-normalized-journal-impact">1.3 Mean field normalized
journal impact</a></li>
<li><a
href="#proportion-publications-in-the-20-most-frequently-cited-journals-in-the-field"
id="toc-proportion-publications-in-the-20-most-frequently-cited-journals-in-the-field">1.4
Proportion publications in the 20 % most frequently cited journals in
the field</a></li>
</ul></li>
<li><a
href="#part-2-implementation-at-kth-royal-institute-of-technology"
id="toc-part-2-implementation-at-kth-royal-institute-of-technology">Part
2 Implementation at KTH Royal Institute of Technology</a>
<ul>
<li><a href="#database-contents" id="toc-database-contents">2.1 Database
contents</a></li>
<li><a href="#document-types-included-in-calculations"
id="toc-document-types-included-in-calculations">2.2 Document types
included in calculations</a></li>
<li><a href="#citations-included" id="toc-citations-included">2.3
Citations included</a></li>
<li><a
href="#retroactive-changes-of-the-web-of-science-subject-category-assigned-to-journals"
id="toc-retroactive-changes-of-the-web-of-science-subject-category-assigned-to-journals">2.4
Retroactive changes of the Web of Science subject category assigned to
journals</a></li>
<li><a
href="#reclassification-of-journals-categorized-as-multidisciplinary-in-web-of-science"
id="toc-reclassification-of-journals-categorized-as-multidisciplinary-in-web-of-science">2.5
Reclassification of journals categorized as Multidisciplinary in Web of
Science</a></li>
<li><a
href="#exclusion-of-publication-fractions-with-low-field-reference-values"
id="toc-exclusion-of-publication-fractions-with-low-field-reference-values">2.6
Exclusion of publication fractions with low field reference
values</a></li>
</ul></li>
<li><a href="#references" id="toc-references">References</a></li>
</ul>
</div>
<div id="introduction" class="section level1">
<h1>Introduction</h1>
<p>This document describes the calculation of bibliometric indicators
based on field normalization in the bibliometric database at KTH
(Bibmet), which is based on Web of Science data. The indicators are
described in Part&nbsp:1 and aspects regarding implementation in the
KTH database are addressed in Part 2.</p>
<p>The following indicators are defined in this document:</p>
<ul>
<li><p>Mean field normalized citation rate (cf)</p></li>
<li><p>Proportion publication among the 10 % most frequently cited in
the field (ptop10%)</p></li>
<li><p>Mean field normalized journal impact (jcf)</p></li>
<li><p>Proportion publications in the 20 % most frequently cited
journals in the field (jtop20%)</p></li>
</ul>
</div>
<div id="part-1-definitions" class="section level1">
<h1>Part 1 Definitions</h1>
<p>This document treats the case, in which fractional counts are used in
the calculations of indicator values. In case whole counts should be
used in the calculations, <span class="math inline">\(a_i\)</span> in
the equation under subcase (1.1) below is set to unity.</p>
<p>Let <span class="math inline">\(A\)</span> be a unit of analysis, and
<span class="math inline">\(n\)</span> the number of publications for
<span class="math inline">\(A\)</span>. Let <span
class="math inline">\(r_i\)</span> be the number of authors of the <span
class="math inline">\(i\)</span>:th publication for <span
class="math inline">\(A\)</span>. Let <span
class="math inline">\(a_i\)</span> be the fraction <span
class="math inline">\(A\)</span> has of the <span
class="math inline">\(i\)</span>:th publication. We consider two
cases.</p>
<div id="a-is-an-organization." class="section level5">
<h5>(1) <span class="math inline">\(A\)</span> is an organization.</h5>
<p>We treat two subcases.</p>
<p>(1.1) <span class="math inline">\(a_i\)</span> is the <em>author</em>
fraction A has of the <span class="math inline">\(i\)</span>:th
publication and is defined as</p>
<p><span class="math display">\[ a_i = \sum_{j=1}^{m_i} \frac{1}{r_i
s_j} \]</span></p>
<p>where <span class="math inline">\(m_i\)</span> is the number of
authors affiliated to <span class="math inline">\(A\)</span> regarding
the <span class="math inline">\(i\)</span>:th publication and <span
class="math inline">\(s_j\)</span> the number of affiliations of the
<span class="math inline">\(j\)</span>:th of these <span
class="math inline">\(A\)</span> authors. Note that the right-hand side
is equal to <span class="math inline">\(m_i / r_i\)</span> when each
<span class="math inline">\(A\)</span> author has exactly one
affiliation.</p>
<p>(1.2) <span class="math inline">\(a_i\)</span> is the
<em>organization</em> fraction <span class="math inline">\(A\)</span>
has of the <span class="math inline">\(i\)</span>:th publication and is
defined as the number of occurrences of <span
class="math inline">\(A\)</span>’s name in the address field of the
<span class="math inline">\(i\)</span>:th publication divided by the
total number organization name occurrences in the address field in
question.</p>
</div>
<div id="a-is-an-individual-author." class="section level5">
<h5>(2) <span class="math inline">\(A\)</span> is an individual
author.</h5>
<p>In this case, <span class="math inline">\(a_i\)</span> is the
<em>author</em> fraction <span class="math inline">\(A\)</span> has of
the <span class="math inline">\(i\)</span>:th publication and is defined
as <span class="math inline">\(1/r_i\)</span>.</p>
</div>
<div id="mean-field-normalized-citation-rate" class="section level3">
<h3>1.1 Mean field normalized citation rate</h3>
<p>We define the <em>mean field normalized citation rate</em> for <span
class="math inline">\(A\)</span>, <span
class="math inline">\(mcf(A)\)</span>, as</p>
<p><span class="math display">\[ mcf(A) = \frac{\sum_{i=1}^n a_i
\bar{x}_i}{\sum_{i=1}^n a_i} \]</span> <span class="math display">\[
\bar{x}_i = \frac{1}{q_i} \sum_{i=1}^{q_i} \frac{c_i}{\mu_{iq}}
\]</span> <span class="math display">\[ \mu_{iq} =
\frac{\sum_{j=1}^{m_{iq}} c_j / F_j}{\sum_{j=1}^{m_{iq}} 1 / F_j}
\]</span></p>
<p>where <span class="math inline">\(q_i (c_i)\)</span> is the number of
subject categories (the citation rate) of the <span
class="math inline">\(i\)</span>:th publication for <span
class="math inline">\(A\)</span>, <span
class="math inline">\(m_{iq}\)</span> is the number of publications,
with the same publication year and of the same document type as the
<span class="math inline">\(i\)</span>:th publication for <span
class="math inline">\(A\)</span>, in the <span
class="math inline">\(q\)</span>:th subject category of the <span
class="math inline">\(i\)</span>:th publication of <span
class="math inline">\(A\)</span>, and <span
class="math inline">\(c_j\)</span> (<span
class="math inline">\(F_j\)</span>) the citation rate of the <span
class="math inline">\(j\)</span>:th of these publications (the number of
subject categories of the <span class="math inline">\(j\)</span>:th of
these publications). <span class="math inline">\(µ_{iq}\)</span> is the
<em>field reference value</em> that the citation rate of the <span
class="math inline">\(i\)</span>:th publication, <span
class="math inline">\(c_i\)</span>, is normalized against regarding the
<span class="math inline">\(q\)</span>:th subject category of the
publication, and the normalization gives rise to a <em>field normalized
citation rate</em> for the publication.</p>
</div>
<div
id="proportion-publication-among-the-10-most-frequently-cited-in-the-field"
class="section level3">
<h3>1.2. Proportion publication among the 10 % most frequently cited in
the field</h3>
<p>We define <em>ptop10%</em> for <span
class="math inline">\(A\)</span>, <span
class="math inline">\(ptop10\%(A)\)</span>, as</p>
<p><span class="math display">\[ ptop10\%(A) = \frac{\sum_{i=1}^n a_i
\sum_{q=1}^{q_i} b_{iq}}{\sum_{i=1}^n a_i}\]</span> <span
class="math display">\[ b_{iq} = \frac{1}{q_i} \frac{\max(y_{iq}^{c_i+1}
- max(0.9, y_{iq}^{c_i}), 0)}{y_{iq}^{c_i+1} - y_{iq}^{ci}}
\]</span></p>
<p>where <span class="math inline">\(q_i\)</span> (<span
class="math inline">\(c_i\)</span>) is the number of subject categories
(the citation rate) of the <span class="math inline">\(i\)</span>:th
publication for <span class="math inline">\(A\)</span>, <span
class="math inline">\(y_{iq}^{c_i}\)</span> (<span
class="math inline">\(y_{iq}^{c_i+1}\)</span>) the proportion of
publications with the same publication year and of the same document
type as the <span class="math inline">\(i\)</span>:th publication for A,
and belonging to the <span class="math inline">\(q\)</span>:th subject
category of this publication with less than <span
class="math inline">\(c_i\)</span> (<span
class="math inline">\(c_i+1\)</span>) citations.<a href="#fn1"
class="footnote-ref" id="fnref1"><sup>1</sup></a> <span
class="math inline">\(\max(y_{iq}^{c_i+1} - max(0.9, y_{iq}^{c_i}), 0) /
(y_{iq}^{c_i+1} - y_{iq}^{ci})\)</span> is the fraction of the <span
class="math inline">\(i\)</span>:th publication assigned to the 10 %
most cited publications. Observe that this fraction is weighted by <span
class="math inline">\(1/q_i\)</span>, i.e., by the fraction of the
publication that belongs to the <span
class="math inline">\(q\)</span>:th subject category. The approach to
assign fractions of publications to the (for instance) 10 % most cited
publications is described and discussed by Waltman and Schreiber
(2013).</p>
</div>
<div id="mean-field-normalized-journal-impact" class="section level3">
<h3>1.3 Mean field normalized journal impact</h3>
<p>We define the <em>mean field normalized journal impact</em> for <span
class="math inline">\(A\)</span>, <span
class="math inline">\(mjcf(A)\)</span>, as</p>
<p><span class="math display">\[ mjcf(A) = \frac{\sum_{i=1}^n a_i\
jcf_i}{\sum_{i=1}^{n} a_i} \]</span> <span class="math display">\[ jcf_i
= \frac{\sum_{j=1}^{p_i} \bar{x}_j}{p_i} \]</span> <span
class="math display">\[ \bar{x}_j = \frac{1}{F_{ij}} \sum_{q=1}^{F_{ij}}
\frac{c_j}{\mu_{jq}} \]</span> <span class="math display">\[ \mu_{jq} =
\frac{\sum_{k=1}^{m_{jq}} c_k / F_k}{\sum_{k=1}^{m_{jq}} 1 / F_k}
\]</span> where <span class="math inline">\(jcf_i\)</span> is the
<em>mean field normalized citation rate of the journal</em>, say <span
class="math inline">\(J_i\)</span>, of the <span
class="math inline">\(i\)</span>:th publication, <span
class="math inline">\(p_i\)</span> the number of publications in <span
class="math inline">\(J_i\)</span>, <span
class="math inline">\(c_j\)</span> the citation rate of the <span
class="math inline">\(j\)</span>:th publication in <span
class="math inline">\(J_i\)</span>, say <span
class="math inline">\(P_j\)</span>, <span
class="math inline">\(F_{ij}\)</span> the number of subject categories
of <span class="math inline">\(p_j\)</span>, <span
class="math inline">\(m_{jq}\)</span> the number of publications, with
the same publication year and of the same document type as <span
class="math inline">\(P_j\)</span>, in the <span
class="math inline">\(q\)</span>:th subject category of <span
class="math inline">\(P_j\)</span>, and <span
class="math inline">\(c_k\)</span> (<span
class="math inline">\(F_k\)</span>) the citation rate (the number of
subject categories) of the <span class="math inline">\(k\)</span>:th of
these publications. <span class="math inline">\(\mu_{jq}\)</span> is the
field reference value that the citation rate of <span
class="math inline">\(P_j\)</span>, <span
class="math inline">\(c_j\)</span>, is normalized against regarding the
<span class="math inline">\(q\)</span>:th subject category of <span
class="math inline">\(P_j\)</span>, and the normalization gives rise to
a field normalized citation rate for <span
class="math inline">\(P_j\)</span> (cf. the definition of mean field
normalized citation rate above). If <span
class="math inline">\(J_i\)</span> is a non-multidisciplinary journal,
<span class="math inline">\(F_{ij} = F_{i(j+1)} (j = 0, 1, ...,\ p_i -
1)\)</span>, since the number of subject categories of a publication in
<span class="math inline">\(J_i\)</span> is then equal to the number of
subject categories of <span class="math inline">\(J_i\)</span>. (Cf.
Section 2.5 below)</p>
</div>
<div
id="proportion-publications-in-the-20-most-frequently-cited-journals-in-the-field"
class="section level3">
<h3>1.4 Proportion publications in the 20 % most frequently cited
journals in the field</h3>
<p>We define the <em>proportion publications in the 20 % most frequently
cited journals in the field</em> for <span
class="math inline">\(A\)</span>, <span
class="math inline">\(jtop20\%(A)\)</span>, as</p>
<p><span class="math display">\[ jtop20\%(A) = \frac{\sum_{i=1}^n a_i
\sum_{q=1}^{F_i} b'_{iq}}{\sum_{i=1}^n a_i} \]</span> <span
class="math display">\[ b'_{iq} = \frac{1}{F_i} \frac{(max(min(0.2,
y_{iq}^{r_{iq}}) - y_{iq}^{r_{iq}-1}, 0)}{y_{iq}^{r_{iq}} -
y_{iq}^{r_{iq}-1}} \]</span> where <span
class="math inline">\(F_i\)</span> is the number of subject categories
of the journal, say <span class="math inline">\(J_i\)</span>, of the
<span class="math inline">\(i\)</span>:th publication of <span
class="math inline">\(A\)</span>, <span
class="math inline">\(r_{iq}\)</span> the rank of <span
class="math inline">\(J_i\)</span> in the ranking of the journals in the
<span class="math inline">\(q\)</span>:th subject category of <span
class="math inline">\(J_i\)</span>, where the journals are ranked
descending after their mean field normalized citation rates<a
href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a>, <span
class="math inline">\(y_{iq}^{r_{iq}}\)</span> (<span
class="math inline">\(y_{iq}^{r_{iq}-1}\)</span>) the proportion
publications appearing in the journals in the <span
class="math inline">\(q\)</span>:th subject category of <span
class="math inline">\(J_i\)</span> with a rank less than or equal to
<span class="math inline">\(r_{iq}\)</span> (<span
class="math inline">\(r_{iq}-1\)</span>).<a href="#fn3"
class="footnote-ref" id="fnref3"><sup>3</sup></a> The rightmost factor
in <span class="math inline">\(b'_{iq}\)</span> is the fraction of
<span class="math inline">\(J_i\)</span> with which <span
class="math inline">\(J_i\)</span> is assigned to the 20 % most
frequently cited journals in the <span
class="math inline">\(q\)</span>:th subject category of <span
class="math inline">\(J_i\)</span>. Observe that this fraction is
weighted by <span class="math inline">\(1/F_i\)</span>, i.e., by the
fraction of <span class="math inline">\(J_i\)</span> that belongs to the
<span class="math inline">\(q\)</span>:th subject category. The approach
to assign fractions of journals to the (for instance) 20 % most cited
journals is basically the same as the assignment approach used in the
definition of <em>ptop10%</em> (Section 1.2).</p>
</div>
</div>
<div id="part-2-implementation-at-kth-royal-institute-of-technology"
class="section level1">
<h1>Part 2 Implementation at KTH Royal Institute of Technology</h1>
<div id="database-contents" class="section level3">
<h3>2.1 Database contents</h3>
<p>The bibliometric database at KTH (Bibmet) contains the following
indexes:</p>
<ul>
<li>Science Citation Index Expended (SCIE)</li>
<li>Social Sciences Citation Index (SSCI)</li>
<li>Arts & Humanities Citation Index (AHCI)</li>
<li>Conference Proceedings Citation Index - Sciences (CPCI-S)</li>
<li>Conference Proceedings Citation Index - Social Sciences &
Humanities (CPCI -SSH)).</li>
</ul>
<p>SCIE, SSCI, AHCI from 1980 and CPCI-S and CPCI-SSH from 1990.</p>
</div>
<div id="document-types-included-in-calculations"
class="section level3">
<h3>2.2 Document types included in calculations</h3>
<p>In Bibmet, calculations are made for all combinations of document
types, publication years and Web of Science categories. However, the
default presentation of field normalized citation indicators concern
only articles and reviews. The reason for excluding other document types
is the risk for anomalies caused by a low number of publications in the
reference groups and question marks regarding data quality and citation
matching (this especially applies to proceedings papers).</p>
</div>
<div id="citations-included" class="section level3">
<h3>2.3 Citations included</h3>
<p>Citations from all records in the database are included in the
calculations. The indicators are calculated both with self-citations
included and excluded. The default presentation is made with
self-citations excluded, since the intention when calculating citation
indicators is to see what impact a publication has had on other
researchers than those who wrote the publication. Furthermore, one
should avoid giving incentives to systematic self-quotation.</p>
</div>
<div
id="retroactive-changes-of-the-web-of-science-subject-category-assigned-to-journals"
class="section level3">
<h3>2.4 Retroactive changes of the Web of Science subject category
assigned to journals</h3>
<p>If a journal is reclassified from one Web of Science subject category
to another by Clarivate, no retroactive changes are made in the
delivered raw data. However, in Web of Science changes the
classification retroactively. Changes of the classification affect the
field reference values and consequently the outcome of the calculations
described in this document. For Bibmet to be consistent with Web of
Science, retroactive changes of the Web of Science subject categories
assigned to journals are made in Bibmet.</p>
</div>
<div
id="reclassification-of-journals-categorized-as-multidisciplinary-in-web-of-science"
class="section level3">
<h3>2.5 Reclassification of journals categorized as Multidisciplinary in
Web of Science</h3>
<p>Some journals are classified by Clarivate as multidisciplinary. When
field normalization is applied the classification of these journals into
the same category can results in skewed field reference values for this
field. By reclassifying publications in journals within the
multidisciplinary subject category the publications are instead compared
to other publications within the same subject field. The Swedish
Research Council has developed and applied a methodology for
reclassification of publications within the multidisciplinary Web of
Science subject category into other categories based on citations
(Gunnarsson, Fröberg, Jacobsson, & Karlsson, 2011). It enables a
higher degree of like-to-like comparison. A very similar method is used
at KTH.</p>
</div>
<div
id="exclusion-of-publication-fractions-with-low-field-reference-values"
class="section level3">
<h3>2.6 Exclusion of publication fractions with low field reference
values</h3>
<p>For all the four indicators defined in Part 1, publication fractions
with field reference values less than 0.5 are excluded.<a href="#fn4"
class="footnote-ref" id="fnref4"><sup>4</sup></a></p>
<div id="example-2.1-mcf-and-ptop10." class="section level5">
<h5><strong>Example 2.1</strong> (<em>mcf</em> and
<em>ptop10%</em>).</h5>
<p>Assume that the <span class="math inline">\(i\)</span>:th publication
of <span class="math inline">\(A\)</span>, say <span
class="math inline">\(P_i\)</span>, belongs to three subject categories
and that exactly one of these categories has a field reference value
less than 0.5. Then, under Section 1.1, <span
class="math inline">\(a_i\)</span> in the denominator and <span
class="math inline">\(\bar{x}_i\)</span> in the numerator are multiplied
by <span class="math inline">\(2/3\)</span>, and <span
class="math inline">\(q_i\)</span> is equal to 2 (and not to 3). Thus,
the sum of <span class="math inline">\(\bar{x}_i\)</span> concerns two
field normalized citation rates for <span
class="math inline">\(P_i\)</span>, and the sum is multiplied by <span
class="math inline">\(1/2\)</span> (and not by <span
class="math inline">\(1/3\)</span>).</p>
<p>For the equation under Section 1.2, under the assumptions given,
<span class="math inline">\(a_i\)</span> in the denominator and the
rightmost sum in the numerator are multiplied by <span
class="math inline">\(2/3\)</span>, and <span
class="math inline">\(q_i\)</span> is equal to 2 (and not to 3). Thus,
the sum concerns two ratios, both of which are weighted by <span
class="math inline">\(1/2\)</span> (and not by <span
class="math inline">\(1/3\)</span>).</p>
</div>
<div id="example-2.2-mjcf-and-jtop20." class="section level5">
<h5><strong>Example 2.2</strong> (<em>mjcf</em> and
<em>jtop20%</em>).</h5>
<p>Assume that the journal <span class="math inline">\(J_i\)</span> of
the <span class="math inline">\(i\)</span>:th <span
class="math inline">\(A\)</span> publication belongs to four subject
categories. Assume that for the <span
class="math inline">\(j\)</span>:th publication in <span
class="math inline">\(J_i\)</span>, say <span
class="math inline">\(P_j\)</span>, published a given year and of a
given document type, two of the four subject categories have a field
reference value less than 0.5. For the equations in Section 2.3, <span
class="math inline">\(2/4\)</span> is subtracted from the denominator of
<span class="math inline">\(jcf_i\)</span>, and <span
class="math inline">\(\bar{x}_j\)</span> in its numerator is multiplied
by <span class="math inline">\(2/4\)</span>. <span
class="math inline">\(F_{ij}\)</span> is equal to 2 (and not to 4).
Thus, the sum of <span class="math inline">\(\bar{x}_j\)</span> concerns
two field normalized citation rates for <span
class="math inline">\(P_j\)</span>, and the sum is multiplied by <span
class="math inline">\(1/2\)</span> (and not by <span
class="math inline">\(1/4\)</span>).</p>
<p>For <em>jtop20%</em> (Section 1.4), under the assumptions given, two
of the four rankings in which <span class="math inline">\(J_i\)</span>
occurs are such that <span class="math inline">\(P_j\)</span> does not
contribute to the mean field normalized citation rates of <span
class="math inline">\(J_i\)</span> in the rankings.</p>
</div>
</div>
</div>
<div id="references" class="section level1">
<h1>References</h1>
<p>Gunnarsson, M., Fröberg, J., Jacobsson, C., & Karlsson, S.
(2011). <em>Subject classification of publications in the ISI database
based on references and citations</em> (No. 4).</p>
<p>Waltman, L., & Schreiber, M. (2013). On the calculation of
percentile-based bibliometric indicators. <em>Journal of the American
Society for Information Science and Technology, 64</em>(2), 372-379.</p>
</div>
<div class="footnotes footnotes-end-of-document">
<hr />
<ol>
<li id="fn1"><p>Weights are used for the citation distributions at
stake. Each citation value in a given distribution is assigned the
weight <span class="math inline">\(1/k\)</span>, where <span
class="math inline">\(k\)</span> is the number of subject categories of
the corresponding publication. The weight is the fraction with which the
publication contributes to each of its subject categories. The
proportion publications with less than <span
class="math inline">\(c\)</span> citations is then the sum of the
weights for the citation values that are less than <span
class="math inline">\(c\)</span>, divided by the sum of weights for all
the citation values in the distribution.<a href="#fnref1"
class="footnote-back">↩︎</a></p></li>
<li id="fn2"><p>Note that for a given journal in the ranking, these
rates may vary across the different rankings, corresponding to different
subject categories, in which the journal occurs.<a href="#fnref2"
class="footnote-back">↩︎</a></p></li>
<li id="fn3"><p>A non-multidisciplinary journal in the ranking
contributes, if each of its publications has a field reference value,
with respect to the <span class="math inline">\(q\)</span>:th subject
category of <span class="math inline">\(J_i\)</span>, greater than or
equal to 0.5 (see Section 2.6), with <span
class="math inline">\((1/k)m\)</span> publications to the ranking, where
<span class="math inline">\(k\)</span> is the number of subject
categories of the journal and <span class="math inline">\(m\)</span> the
number of publications of the journal.<a href="#fnref3"
class="footnote-back">↩︎</a></p></li>
<li id="fn4"><p>Such field reference values might give rise to very
large field normalized citation rates in spite of few citations.<a
href="#fnref4" class="footnote-back">↩︎</a></p></li>
</ol>
</div>
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