Highly Ranked Scholars and the influence of countries and regions in research fields, disciplines, and specialties

Abstract The scholarly influence of a country or region can be inferred from its number of exceptional scientists in specific research areas. Using the ScholarGPS database, we provide the first analysis of the number and geographical distribution of Highly Ranked ScholarsTM from a universe of over 30 million scholars in more than 200 countries. The associated influence of nations is reported for 14 broad fields of scholarly pursuit, two disciplines (Chemistry and Computer Science), and three specialties (Artificial Intelligence, Polymer, and Stem Cell). By comparing numbers of Highly Ranked Scholars for the last 5 years to lifetime information, we quantify the growth and decay of the influence of multiple countries and regions and identify those that are emerging in their influence. For the research areas considered here, the United States has the largest recent reduction in influence, whereas China, India, and Iran have increased their influence notably.


INTRODUCTION
Evaluation of research performance at a national level is necessary for countries to compare their strengths to those of competing nations in specific areas of engineering, technology, science, and medicine; identify research priorities; and develop an advanced workforce (Almeida, Borges et al., 2020;Chen, Chen et al., 2023;King, 2004;Sun & Cao, 2021).Quantitative assessment of the research activity of countries and regions has been reported frequently in the past, with input to the analyses usually consisting of some variation of publication and citation data.In this study we quantify the scholarly influence of countries and regions based on their numbers of Highly Ranked Scholars TM (HRS) in various research fields, disciplines, and specialties, and show how the influence has changed over time.King (2004) analyzed the scientific impact of 31 nations in each of five broad research areas (medical sciences, natural sciences, agricultural sciences, engineering and technology, and social sciences).The analysis covered two time periods (1993-1997 and 1997-2001) and was based on the number of publications produced by authors from each country; citations of the publications; and the number of publications placed in the top 1% of highly cited publications.Several trends were observed, such as a persistent performance gap between the United States and other countries.US leadership was attributed, in part, to perceived higher salaries paid by US institutions at the time.Later, Horta and Veloso (2007) carried out a similar analysis based on publications and citations in the same five research areas of interest to King (2004), as well as in 24 additional scientific areas for three 5-year time periods between 1988 and 2002.The main comparison was between the United States and 15 members of the European Union (EU-15) relevant to the time periods considered.The degree to which the United States or the EU led in research depended on the area of research, with the individual countries of the EU contributing nonuniformly to the overall EU performance.
The emergence of China and several other countries has been addressed in multiple studies.For example, Zhou and Leydesdorff (2006) compared publication and citation data for China to data associated with a group of seven other countries as well as two EU cohorts .Notably, the authors focused exclusively on the narrow topic of nanotechnology in an attempt to add precision and actionability relative to the evaluations of broader areas of research, such as conducted by King (2004) and Horta and Veloso (2007).Zhou and Leydesdorff concluded that China had become a leading nation in nanoscience and nanotechnology, and attributed the emergence of Chinese science to the rapid growth of China's economy and policies promoting the return of overseas scholars back to China.The authors also discussed the methodological challenges associated with properly categorizing research publications in highly focused yet interdisciplinary areas of research such as nanotechnology.
Multiple investigations have quantified national research performance using an array of inputs and analysis techniques (Aksnes, Sivertsen et al., 2017;Auranen & Nieminen, 2010;Fairclough & Thelwall, 2015;Guba & Tsivinskaya, 2023;Jacsó, 2009;Leydesdorff & Zhou, 2005;Rodríguez-Navarro, 2016).The assessments typically involved only several specified nations for comparison, clouding the potential discovery of emerging nations; considered only broad areas of research, limiting the ability of responsible individuals such as deans or chief technology officers to act on the assessments in a concrete manner; or in contrast, considered only a narrow area of research for comparison, diminishing the broader impact of the assessment.In general, the morass of conclusions drawn depend on which nations were included in (or excluded from) the analysis, which areas of research were considered (or omitted), the breadth (or granularity) of the research areas of interest, and the methodologies used to define and quantify research performance.
Based on our understanding of the literature, previous studies of national research performance have primarily used total publication counts and citations as indicators, without necessarily accounting for the records of exceptional individual scholars.Here, we employ artificial intelligence and machine learning to determine the number of HRS associated with individual countries and regions as a measure of national research performance.As will be elaborated upon below, these outstanding scholars are identified based on three indicators pertaining to their productivity as well as the impact and quality of their work.In addition, relatively few studies have accounted for the adverse distorting effects of including selfcitations (Pranckutė, 2021;Vîiu, 2016) or giving full credit to each author for publications and citations (Batista, Campiteli et al., 2006;Fire & Guestrin, 2019;Liu, Yu et al., 2021;Van Hooydonk, 1997;Zeng, Shen et al., 2017).Although various investigations have reported annual national research performance (e.g., Liu et al., 2021), few have used multiyear time periods (such as 5 years) to reduce the noise associated with annual evaluation of areas of research characterized by relatively small numbers of scholars such as in the individual specialties that will be considered here.
Previous investigations of scholarly performance have commonly utilized one of three databases: Scopus (https://beta.elsevier.com/products/scopus?trial=true, accessed July 20, 2023), Web of Science ( WoS; https://clarivate.com/products/scientific-and-academic-research/research-discovery-and-workflow-solutions/webofscience-platform/, accessed July 20, 2023) or Google Scholar (GS; https://scholar.google.com/,accessed July 20, 2023).Both Scopus and WoS categorize scholars into broad fields or disciplines, but do not assign them to more granular specialties.WoS classifies scholarly work into approximately 250 subject categories in Science, Social Sciences, and Arts and Humanities.Scopus classifies scholars into 27 broad fields and 176 subfields, but the association of scholars with fields and disciplines can be opaque, and a scholar might be assigned to multiple fields and disciplines.A recent Scopus feature (Discovery) allows users to search for scholars by keyword and provides a list of scholars ranked according to various sorting options.However, the metrics (citations and h-indices) used for ranking are relative to a scholar's overall output, rather than being associated directly with the keyword used in the search.Both WoS and Scopus regularly publish rankings of top scholars, typically based on citation counts or h-indices.In the case of WoS, Clarivate's rankings rely on citation counts.Scopus, in collaboration with other groups (Ioannidis, Baas et al., 2019), has published rankings for the top 2% of scientists using the Scopus database, based on both citation counts and the h-index.GS enables scholars to create profiles and share them publicly, but not all scholars have done so, making ranking of all scholars in any area of research problematic.Additionally, GS scholar rankings are based on the overall h-index and are therefore not relevant to specific fields, disciplines, or specialties.Both WoS and Scopus use journal-based classification techniques to associate publications with particular fields and disciplines, which can lead to errors when classifying an individual publication or scholar, as discussed by Milojević (2020).
In this study, a new and extensive database (ScholarGPS TM , described in more detail below) that harnesses the power of artificial intelligence and data mining technology is used to quantify every active, retired, and deceased scholar's research record using three indicators: productivity (number of publications); quality (number of citations); and impact (h-index).With this information, all scholars are then ranked to identify the HRS and the countries with which they are associated.This ranking process therefore permits an assessment of the scholarly influence (number of HRS) in each of over 200 countries and regions in hundreds of thousands of broad-to-narrowly focused research categories based on lifetime (all years available) publication, citation, and h-index information as well as corresponding data (publications, citations to those publications, and the corresponding h-index) for work only appearing in the last 5 years.
The ScholarGPS database considers scholars overall (all scholarly work in all fields); in each of 14 broad fields; in each of 177 disciplines that comprise the fields; and in each of over 350,000 specialties.To properly assign a level of scholarly influence to each country or region, the analysis is not restricted to the work of individuals in academia, but includes scholars from over 55,000 institutions worldwide, including universities, medical institutions, national laboratories, independent research organizations, the private sector, and industry.The methods can be extended to consider subsets of the preceding universe, such as to quantify university research activity pertinent to performance-based university research funding systems employed by various countries (Banal-Estañol, Jofre-Bonet et al., 2023).
In summary, shortcomings of the existing studies reported in the literature and deficiencies in other databases limit their usefulness in attempts to quantify and compare national research performance.In contrast, to our knowledge, the methods and analysis to be used here are novel in that they can be utilized to • associate all scholars with unique fields (including all fields), and disciplines, and multiple niche specialties from a menu of hundreds of thousands of specialties; • assess the performance of each scholar within their field, their discipline, and their specialties based on their productivity, impact, and quality; • compare the performance of all scholars within individual fields, disciplines, and specialties on both lifetime and last 5-year bases; • rank all scholars in each of the fields, disciplines, and specialties separately, to accommodate the vast differences in scholarly activity that characterize different areas of research; • identify the HRS in each field, discipline, and specialty; and • infer the scholarly influence of countries and regions based on the geographical distribution of HRS.

Objectives
In this study we report numbers of HRS for various countries associated with all fields, with elaboration in four large fields of science, medicine, and engineering; two sample disciplines within the four large fields; and three traditional as well as emerging interdisciplinary specialties.
Building on this information we will quantify levels of scholarly influence associated with individual countries and regions in these fields, disciplines, and specialties; trends in terms of the increasing or decreasing scholarly influence of nations; and countries and regions that are emerging in terms of their scholarly influence.The countries and regions in this study are not specified a priori but are identified quantitatively as part of the automated assessment and ranking process.

METHODS
This section introduces general concepts and describes the detailed methodologies used to achieve the objectives of the study.

General Concepts
The organization of fields, disciplines, and specialties used here is shown in Figure 1.The overall category includes all scholarly work, entailing more than 30 million scholars and over 140 million archival publications ( journal articles, conference papers, books, book chapters, and patents) compiled by ScholarGPS.Each of the 30 million scholars is assigned to one of the 14 fields and one of the 177 disciplines (except for cases explained in Section 3).As shown in Figure 1, each discipline is a subset of only one field (e.g., Cardiology is a subset of only Medicine; Chemistry is a subset of only Physical Sciences and Mathematics).Each publication is also assigned to one of over 350,000 unique specialties that are not tied to specific disciplines or fields; for example, a publication in the specialty of Artificial Intelligence might be affiliated with multiple fields or disciplines as discussed by Sachini, Sioumalas-Christodoulou et al. (2022).
After the publications and scholars are organized into the proper fields, disciplines, and specialties, all scholars are ranked relative to all other scholars (overall); scholars in the same field; scholars in the same discipline; and scholars in the same specialty using the ranking process described in the Section 2.2.The HRS are exceptional researchers in the top 0.05% of all scholars overall, or in a field, or in a discipline, or in a specialty.Ranking is based on either the totality of each scholar's work or only work published in the last 5 years.

Detailed Methodology
Highly Ranked Scholars and the countries with which they are affiliated are determined using ScholarGPS.This recently introduced database begins with the construction of a unique profile for each of approximately 30 million scholars.Each profile contains the scholar's publication, citation, and h-index information, as well as other information, such as their affiliation history, which is determined from the scholar's publications.Scholar ranking is based on either the totality of each scholar's work (lifetime basis as of December 30, 2021), or only work published in the last 5 years ( January 17, 2017 through December 30, 2021).The following methods, which are further described at www.scholargps.com,are used.
Raw publication metadata from various sources, including (but not limited to) Crossref, PubMed, Microsoft Academic Graph, and Unpaywall are collected.Preprocessing algorithms improve the data quality by eliminating publications deemed to be nonarchival or duplicates and managing publisher errors, which can take the form of metadata formatting mistakes, structural errors, and other inconsistencies.The improved data are then indexed for further analysis.
Only archival publications are included in the scholar rankings.In general, a publication that has a DOI, ISBN/ISSN, or a patent number, and has undergone a peer review process is considered archival.However, publications associated with a memoriam, commentary, celebration, book review, discussion, correction, rubuttal, and other peripheral matters are culled and not included.Open access repository publications that are not peerreviewed, such as those in arXiv, are also excluded.Publications with more than 30 authors are not included because it is impossible to accurately partition credit among the authors of such works.Any individual who has authored at least one archival publication is considered a scholar.Names of scholars are disambiguated as accurately as possible.To further improve the quality of the data, individuals can claim their scholar profiles and make corrections or merge multiple profiles that belong to them.Note that some authors are excluded from the rankings, such as those who have authored an excessive number of retractions, have published the same material in multiple venues, have demonstrated excessive plagiarism, or have published fraudulent data.Corrections for any perceived language bias (Beveridge & Bak, 2011;Ramírez-Castañeda, 2020;van Leeuwen, Moed et al., 2001;van Raan, van Leeuwen, & Visser, 2011) in the underlying data used by ScholarGPS are not attempted.
A manual evaluation of over 5,000 scholar profiles (including scholars with frequently encountered last names as well as those with unique last names) taken from various fields and disciplines was used to estimate the precision, PR, and recall, RC, relative to the assignment of publications to authors.Letting true positives, TP, be associated with publications that were correctly assigned to a scholar; false positives, FP, with publications incorrectly assigned to a scholar; and false negatives, FN, with publications that should have been assigned to a scholar but were not, we have The precision of the sample was 98.5% and the recall was 96%.In addition, disciplines and fields were correctly assigned to each publication with an accuracy of 95%.The country associated with each scholar is that which was listed by the scholar in their most recent publication.
As noted above, scholar rankings are conducted in four categories: overall (all fields), by field, by discipline, and by specialty.Four metrics are calculated across each of the categories: productivity (archival publication count), impact (citation count), quality (h-index), and the ScholarGPS Rank, which is the geometric mean of the product, impact, and quality rankings.Self-citations are excluded, as recommended by Vîiu (2016), and author publication and citation counts are weighted by the number of authors of each publication, as described by Van Hooydonk (1997).For example, if a publication has two authors, each is credited with 0.5 publications and half of the citations to the publication.The scholar's fractional h-index (Koltun & Hafner, 2021) is also calculated based on these weighted citation counts.
The ranking calculation proceeds as follows.The top percentage rank of a scholar within any of the four categories, based on any of the four metrics, is determined from knowledge of the total number of scholars in a category, N, the standard competition rank of the scholar in the category, R, and the number of scholars, F, who share rank R. Top percentage ranks by publication, TPR p , by citation, TPR c , and by h-index, TPR h are found using The ScholarGPS Rank, S, is the geometric mean of TPR p , TPR c , and TPR h : and the HRS of this study are defined as the exceptional scholars who have a ScholarGPS Rank of S ≤ 0.05%.Because scholar rankings are based on either the totality of each scholar's work

Quantitative Science Studies
or only on work published in the last 5 years, an individual who is an HRS on the lifetime (last 5-year) basis is often not an HRS on the last 5-year (lifetime) basis.Profiles of individual HRS overall, in each field, in each discipline, and in specialties are available at www .scholargps.com.

RESULTS AND DISCUSSION
The total numbers of scholars and HRS in each field are reported in Table 1 on both lifetime and last 5-year bases.The four fields (Medicine, Engineering and Computer Science, Physical Sciences and Mathematics, and Life Sciences) that have traditionally utilized the publication venues included in Section 2 ( journal articles, conference papers, books, book chapters, and patents) to disseminate scholarly work comprise 71% of the HRS that have been assigned to fields over the last 5 years.Researchers in these fields publish predominantly in English (Liu, 2017).In contrast, Education, Dentistry, and Law have small numbers of scholars, and collectively represent 2.6% of the total HRS over the same time period.Other areas of scholarly work with small numbers of scholars who often publish in non-English languages, such as Literature and History in the Arts & Humanities (Liu, 2017), will not be assessed here.Note that the number of HRS overall (the total number of HRS for the last 5 years is N 5,tot = 7,467; the total on the lifetime basis is N ∞,tot = 14,465) both exceed the sum of HRS in each of the 14 fields as listed in Table 1 because it is not possible to assign every HRS to a field.Such is the case when, for example, an HRS has authored many interdisciplinary patents.Quantitative Science Studies 470 HRS and the influence of countries and regions

Overall (All Fields) Trends
The 10 countries or regions that were found to have the largest numbers of HRS on either the last 5-year or lifetime basis are identified in Figure 2. As is evident, the United States and Canada, along with various countries in Europe and Japan have fewer HRS over the last 5 years than over their lifetime.In contrast, China and Hong Kong, India, and Iran show relatively large increases in their HRS numbers in the last 5 years.Australia has little change in its number of HRS.
The data used to generate Figure 2 are provided in Table 2, along with the percentage of HRS associated with each of the countries or regions.As is evident in the table, the United States is associated with 58.4% of the HRS on a lifetime basis, and 27.4% of the HRS based on the last 5 years.In contrast, China has increased its share of HRS from 1.4% on a lifetime basis to 20.9% for the last 5 years.Other countries that have experienced large increases in their numbers of HRS include Iran (N 5 = 176, N ∞ = 13) and India (N 5 = 172, N ∞ = 35), which now claim the seventh and eighth largest numbers of HRS based on data for the last 5 years.
It is reasonable to assume that the most influential scholars are those who are highly ranked after the culling process described in Section 2 has been completed, and that geographical redistribution of the HRS reflects an increasing or decreasing level of scholarly influence of individual countries and regions.Hence, the scholarly influence of country or region i for the last 5 years may be quantified as where N 5,tot is the total number of HRS over all countries and regions.Similarly, the scholarly influence of country or region i on a lifetime basis is The countries and regions with the largest change in scholarly influence, |I 5,i − I ∞,i |, are reported in Figure 3.China and Hong Kong, Iran, India, Australia, South Korea, and

Quantitative Science Studies
Singapore have seen the most noteworthy recent increases in their influence.In contrast, the United States and Canada, along with several European countries, Israel, and Japan have experienced the largest recent declines in scholarly influence on an overall (all fields) basis.

Field Trends
It was evident in Figure 2 that the United States has the largest number of overall HRS on either a lifetime or last 5-year basis, whereas it was shown in Figure 3 that China and the United States experienced the largest increase and decrease in scholarly influence, respectively.The approach taken for all fields can also be applied to individual fields, and trends associated with fields having the largest numbers of HRS (Engineering and Computer Science, Life Sciences, Medicine, and Physical Sciences and Mathematics), are reported in Figures 4 and 5.Note that the disciplines comprising each of the preceding four fields are identified in Table 3; the disciplines of Chemistry (in Physical Sciences and Mathematics) and Computer Science (in Engineering and Computer Science) will be considered in more detail shortly.
Analysis of the Life Sciences (Figure 4     Countries and regions experiencing the largest increase or decrease in scholarly influence for the four largest fields are reported in Figure 5. Regardless of the field, the most notable decreases have occurred primarily in the United States, Canada, Japan, and European countries.Israel has also experienced a large decline in the Life Sciences (Figure 5 It can be noted from Figure 4 that the difference in the numbers of HRS between the r = 1 and r = 2 countries in the four largest fields is smaller for the last 5 years than on the lifetime basis.To quantify how the gap between the top two countries has closed for each of the 14 fields, the following parameter is used to calculate the relative change in the gap separating the two top-ranked countries in each field: The numerator in the first term on the right-hand side is the difference between the number of HRS in the r = 1 country and the number of HRS in the r = 2 country based on data for the last 5 years.The denominator in this term is the same as the numerator, but on a lifetime basis.The second term on the right-hand side is the ratio of the summed (over all ∼200 countries and regions) lifetime number of HRS in the field to the HRS totals for the last 5 years; this term facilitates both field-to-field comparisons and comparisons of the lifetime and last 5-year information.Note that G = 1 would correspond to lifetime and last 5-year gaps that are identical on a relative basis; there are no fields with G ≥ 1. Decreased gaps between the r = 1 and r = 2 countries correspond to G < 1, with smaller values of G corresponding to gaps that have closed the most in recent years.
Values of G for all 14 fields are shown in Figure 6.The United States has retained the top (r = 1) ranking in the fields to the right (the r = 2 country is identified above each bar) and is relatively firmly ensconced in the top position in Public Health and Medicine, with G = 0.848 and 0.765 respectively.Alternatively, China (the r = 1 country is shown above each bar in the left portion of the figure) has assumed strong leadership in the Physical Sciences and Mathematics with G = 0.335 and, to a lesser extent, in Engineering and Computer Science with G = 0.156.The United Kingdom has a modest lead in Education (G = 0.100 based on data for the last 5 years) and is tied with the United States in Law (G = 0 in the figure reflects the tie).Switzerland is tied with the United States in Dentistry (G = 0).

Quantitative Science Studies 475
HRS and the influence of countries and regions Multiple countries and regions have made impressive gains in their HRS numbers in the various fields in recent years, often in conjunction with modest (or even nonexistent) lifetime HRS numbers.To discover the countries that have emerged impressively, the following parameter is introduced and calculated for each country/region: Here, the numerator of the first term inside the brackets is the difference between the number of HRS associated with the r = 1 country and country i for the last 5 years.The denominator is the same difference, but on a lifetime basis.The second term inside the brackets facilitates field-to-field comparisons as well as comparisons of the 5-year and lifetime records.Equation 8 is applied to every country, i = 1, 2, 3, …, ∼200 in each field, except for the r = 1 country associated with either the lifetime or last 5-year data (for these countries, the value of E i is of little relevance).Large values of E i are associated with countries that have emerged most notably in the field in that they have closed the gap between themselves and the r = 1 country over the last 5 years, relative to the gap that exists on a lifetime basis.
Countries associated with the largest value of E in each field are identified above the bars in Figure 7 and their ranking, r, for the last 5 years is shown in parentheses.Several trends can be inferred from the values of r and E. First, countries ranked r = 2 based on the last 5 years and having a large value of E in a field (e.g.,China in the Arts and Humanities with N 5 = 20, N ∞ = 1, E = 0.983, or the United Kingdom in Business and Management with N 5 = 16, N ∞ = 13, E = 0.968) could soon achieve the top r = 1 ranking in the field because their HRS numbers have increased substantially on a relative basis according to data for the last 5 years and the gap separating them from the r = 1 country is small.Second, countries ranked r = 2 and having a small value of E in a field (e.g., Germany in Medicine with N 5 = 97, N ∞ = 111, E = 0.609) have increased their HRS numbers in the field on a relative basis but have more slowly approached the r = 1 ranking in the field.In these fields, the r = 1 country (e.g., the United States in Medicine with N 5 = 713, N ∞ = 1,687) more firmly occupies the top position.Third, countries associated with r > 2 in the last 5-year time period in a field and having a large value of E in the to their lifetime record, and have impressive upward momentum as they approach and perhaps soon overtake countries of current higher rank.

Discipline Trends
Analysis of the 177 disciplines proceeds as for the 14 fields.Here, we report results for Chemistry (N 5,tot = 371, N ∞,tot = 802) and Computer Science (N 5,tot = 235, N ∞,tot = 367) to consider a discipline with a longer history (Chemistry) than the other.
As evident in Figure 8 The geographical distribution of HRS in Computer Science, presented in Figure 8(c), has changed remarkably according to the data for the last 5 years compared to lifetime information.This notable redistribution might be due to • the relatively short history of Computer Science leading to a higher efflux of HRS from a small number of countries in which the discipline was initially concentrated; • the smaller numbers of HRS in Computer Science compared to the fields or to Chemistry making geographical redistribution more sensitive to changes in HRS numbers; • a perceived higher mobility of HRS in disciplines such as Computer Science that require little physical infrastructure to conduct research; and • the priorities included in the research plans of various nations (e.g., Sun & Cao, 2021).

Specialty Trends
Over 350,000 specialties have been identified with the ScholarGPS platform, making comprehensive comparisons difficult.Therefore, trends associated with an established specialty (Polymer: N 5,tot = 146, N ∞,tot = 343), and two more recently emerging specialties (Artificial We conclude by considering two relatively new specialties previously identified to be of national strategic priority (Sun & Cao, 2021).As was noted for Computer Science (Figures 8(c  As evident upon close inspection of Figure 10(a), the United States has retained its r = 1 ranking over the last 5 years in Artificial Intelligence (N 5 = 14, N ∞ = 49), but shares the recent top position with China (N 5 = 14, N ∞ = 1), which has increased its scholarly influence dramatically in recent times (Figure 10(b)).The relative change in the gap between the r = 1 (China and the United States) countries and the r = 3 country (United Kingdom) is G = 0.319.Singapore (N 5 = 5, N ∞ = 0, E = 0.722), India, (N 5 = 4, N ∞ = 0, E = 0.691), Saudi Arabia (N 5 = 3, N ∞ = 0, E = 0.660), and Iran, as well as Vietnam (N 5 = 2, N ∞ = 0, E = 0.629) have increased their influence relative to other countries most remarkably over the last 5 years.In sharp contrast, and as evident from Figure 10(a), Israel (N 5 = 0, N ∞ = 5), France (N 5 = 0, N ∞ = 3), and Netherlands (N 5 = 0, N ∞ = 3) no longer have any HRS based on data for the last 5 years.
For all the fields, disciplines, and specialties discussed so far, China and the United States occupy either the r = 1 or r = 2 last 5-year ranking in terms of the number of HRS.This is of course not always the case, as evident in Figure 10(c 14, E = 0.291).In addition to Iran and China, Poland (N 5 = 3, N ∞ = 0, E = 0.338), and Serbia (N 5 = 3, N ∞ = 0, E = 0.338) have increased their scholarly influence impressively, as evident in Figure 10(d).In contrast, Australia (N 5 = 0, N ∞ = 4) no longer has any HRS based on the last 5-year data, whereas Israel (N 5 = 1, N ∞ = 5) and Sweden (N 5 = 1, N ∞ = 5) are left with only one HRS based on the last 5 years of information.

CONCLUSIONS
Using a recently introduced database, ScholarGPS, we have developed the first quantitative assessment of the scholarly influence of nations determined by the geographical distribution and redistribution of exceptional scholars (HRS) in specific fields, disciplines, and specialties.Consideration of the HRS geographical distributions on both lifetime and last 5-year bases demonstrates how HRS have been redistributed geographically over time.
In all 14 fields, as well as in the two disciplines (Chemistry and Computer Science), and three niche specialties (Artificial Intelligence, Polymer, and Stem Cell) considered here, the leadership position of the United States has either eroded or has been eliminated entirely based on the comparison of lifetime and last 5-year data.The emergence of China is readily apparent, as is that of India and Iran.Other rising countries have been identified quantitatively by including all countries and regions in the assessment and ranking process and utilizing novel parameters that quantify the gap, G, separating the top two countries in each category and the emergence, E i , of countries that may not be currently ranked at or near the top in the category of interest.It has been shown that HRS redistribution has occurred to different degrees across the various fields, disciplines, and specialties.Analysis of other disciplines and specialties can be made with the methods introduced and used in this study.
Multiple factors might contribute to the geographical redistribution of HRS as discussed and implied in the literature (Chen et al., 2023;Goodall, 2009;King, 2004;Reymert, Vabø et al., 2022;Shi, Liu, & Wang, 2023;Zastrow, 2020;Zhou & Leydesdorff, 2006), such as: • dramatic recent increases in the economic strength of certain nations; • national initiatives to repatriate or attract scholars from other countries in key areas of strategic importance; • the mobility of scholars who require little physical infrastructure to perform research; • establishment of focused initiatives to improve the research stature of a country's top universities and research institutions; • tactical redirection of national research funding from applied research to more basic research; • focused initiation of new graduate and professional programs and universities in certain countries; • easier access to information compared to years past; and • questionable trends in some countries involving the appointment of leaders of knowledge-based institutions who have unremarkable or nonexistent personal research records.
The methods introduced here might provide important data to assist future identification of the root causes of HRS redistribution and the associated shifts in national scholarly influence, and help reveal how these causes vary across the hundreds of thousands of fields, disciplines, and specialties of scholarly endeavor.

Figure 2 .
Figure 2. Top countries and regions with the most HRS (lifetime and last 5 years) for all fields (overall).Numbers are shown for the top 10 countries and regions of either category (last 5 years, N 5 , or lifetime, N ∞ ).Countries and regions are shown in order of decreasing N 5 + N ∞ .

Figure 3 .
Figure 3. Countries/regions with the largest increase or decrease in scholarly influence for all fields (overall).
(a)) and Medicine (Figure 4(b)) again reveals that the top-ranked country (r = 1), the United States, has retained its lead over the second-ranked (r = 2) country in the last 5 years, but by a reduced margin relative to the lifetime lead.In general, the United States and Canada, several European countries, and Japan have experienced reductions in the numbers of HRS in both Life Sciences (Figure 4(a)) and Medicine (Figure 4(b)), although Italy, Netherlands, and Spain have increased HRS numbers recently in the Life Sciences.Italy and Spain have also increased their numbers of HRS in Medicine.The strong performance of India and China in the Life Sciences (Figure 4(a)) and China in Medicine (Figure 4(b)), as shown by HRS data for the last 5 years, is evident.

Figure 4 .
Figure 4. Top countries and regions with the most HRS (lifetime and last 5 years) for the four largest fields.Numbers are shown for the top 10 countries and regions of either category (last 5 years, N 5 , or lifetime, N ∞ ).Countries and regions are shown in order of decreasing N 5 + N ∞ .

Figure 5 .
Figure 5. Countries and regions with the largest increase or decrease in influence for the four largest fields.
Science.Significant recent decreases in numbers of HRS have also been experienced by Canada, Japan, and several European countries in both the Physical Sciences and Mathematics as well as in Engineering and Computer Science.In contrast, India and Iran show increases in their numbers of HRS in recent years in the Physical Sciences and Mathematics (Figure4(c)) and in Engineering and Computer Science (Figure 4(d)).Australia, Hong Kong, South Korea, and Singapore have also added to their HRS numbers based on data for the last 5 years in Engineering and Computer Science (Figure 4(d)).The last 5-year performance of Iran in Engineering and Computer Science (Figure 4(d)) is remarkable.
(a)), the Physical Sciences and Mathematics (Figure 5(b)), and Engineering and Computer Science (Figure 5(d)).In contrast, China has gained the most scholarly influence in these three fields; India and Iran have also increased their influence remarkably for these fields.Moreover, Australia, Italy, Spain, and Netherlands have performed well recently in the Life Sciences (Figure 5(a)) as have Italy, China, Australia, and several European countries in Medicine (Figure 5(b)).In addition to China, India, and Iran, impressive advances in the Physical Sciences and Mathematics are associated with Saudi Arabia, Pakistan, South Africa, and Spain (Figure 5(c)).In addition to China, Iran, and India, increases in scholarly influence have been made by Australia, Singapore, South Korea, and Saudi Arabia in Engineering and Computer Science (Figure 5(d)).

Figure 6 .
Figure 6.Field leadership gap in each field.Differences in the relative numbers of HRS separating the top two countries based on data for the last 5 years compared to lifetime information.Large gaps between the top two countries are represented by large bars.

Figure 7 .
Figure 7. Emerging countries (and their last 5-year ranking in the field) with the largest relative increases in the numbers of HRS (last 5 years versus lifetime) for each field.Longer bars are associated with countries that have more significantly narrowed the gap between themselves and the top country in the field in recent years.

Figure 8 .
Figure 8. Top countries and regions with the most highly ranked scholars (lifetime and last 5 years) and countries and regions with the largest increase or decrease in scholarly influence for Chemistry and Computer Science.(a), (c): Numbers for the top eight countries and regions of either category (last 5 years, N 5 , or lifetime, N ∞ ) are shown in order of decreasing N 5 + N ∞ .(b), (d): Countries and regions with the largest increase or decrease in scholarly influence. )

Figure 9 .
Figure 9. Top countries and regions with the most HRS (lifetime and last 5 years) and countries and regions with the largest increase or decrease in scholarly influence for Polymer.(a) Numbers for the top eight countries and regions of either category (last 5 years, N 5 , or lifetime, N ∞ ) are shown in order of decreasing N 5 + N ∞ .(b) Countries and regions with the largest increase or decrease in scholarly influence.
Figure 10.Top countries and regions with the most highly ranked scholars (lifetime and last 5 years) and countries and regions with the largest increase or decrease in scholarly influence for Artificial Intelligence and Stem Cell.(a), (c): Numbers for the top eight countries and regions of either category (last 5 years, N 5 , or lifetime, N ∞ ) are shown in order of decreasing N 5 + N ∞ .(b), (d): Countries and regions with the largest increase or reduction in scholarly influence.

Table 1 .
Total number of scholars and total number of HRS on either the lifetime or last 5-year basis for all fields, and for each of the 14 fields (source: ScholarGPS.com)

Table 2 .
Number of HRS on either the lifetime or last 5-year basis overall (all fields) for the top 10 countries or regions with the most HRS (on either the lifetime or last 5-year basis).The percentage of highly ranked scholars associated with each country is included (source: ScholarGPS.com)

Table 3 .
The disciplines comprising the fields of Engineering and Computer Science, Life Sciences, Medicine, and Physical Sciences and Mathematics (source: ScholarGPS.com) Orthopaedic Surgery, Otolaryngology, Pathology, Pediatrics, Physical Medicine and Rehabilitation, Psychiatry, Pulmonology, Radiology, Rheumatology, Sports Medicine, Surgery, Urology Physical Sciences & Mathematics Astronomy, Atmospheric Sciences, Chemistry, Earth and Planetary Sciences, Mathematics, Oceanography and Limnology, Physics, Statistics