Text mining arXiv: a look through
quantitative finance papers

Michele Leonardo Bianchia,111 The author thanks arXiv, ChatGPT, and Google
Scholar for use of their open access interoperability and Sabina Marchetti for
her comments and suggestions. This publication should not be reported as
representing the views of the Bank of Italy. The views expressed are those of
the author and do not necessarily reflect those of the Bank of Italy.

aFinancial Stability Directorate, Bank of Italy, Rome, Italy

This version: August 28, 2024

Abstract. This paper explores articles hosted on the arXiv preprint server
with the aim to uncover valuable insights hidden in this vast collection of
research. Employing text mining techniques and through the application of
natural language processing methods, we examine the contents of quantitative
finance papers posted in arXiv from 1997 to 2022. We extract and analyze
crucial information from the entire documents, including the references, to
understand the topics trends over time and to find out the most cited
researchers and journals on this domain. Additionally, we compare numerous
algorithms to perform topic modeling, including state-of-the-art approaches.

Key words: quantitative finance, text mining, natural language processing,
unsupervised clustering, topic modeling, research trends, named entity
recognition.

##  1 Introduction

Quantitative finance is a field of finance that studies mathematical and
statistical models and applies them to financial markets and investments, for
pricing, risk management, and portfolio allocation. These models are needed to
analyze financial data, to find the price of financial instruments and to
measure their risk (see Vogl (2022) and Bianchi et al. (2023)). Readers are
referred to Derman (2011) for an insightful exploration of the role of models
in finance and to Ippoliti (2021) for some philosophical remarks on
mathematics and finance.

The world of finance is always moving forward even in times of crisis.
Innovations in finance come from the development of new financial services,
products or technologies. Research trends in quantitative finance are driven
not only by innovations, but also by structural changes in financial markets
or by changes in regulation (Cesa (2017) and Carmona (2022)). When a
structural change occurs some models are not anymore able to explain the
phenomena observed in the market, consequently quants and researchers start
working on new models. Examples of such changes are when the implied
volatility smile appeared in 1987 (see Derman and Miller (2016)) or the
Euribor-OIS spread materialized in 2007 (see Bianchetti and Carlicchi (2012)).
Research activities driven by new products are, for instance, the development
of pricing models for interest rate and equity derivatives started in ’90s,
the structuring of credit products in the early 2000s, or the recent research
trend on cryptocurrencies. New technologies applied to finance are namely the
increasing role of big data and the advent of machine learning techniques.
Regulation have an impact on the development of new quantitative tools for
measuring, managing and monitoring financial risks (e.g. the Basel Accords).

In this paper we explore the arXiv preprint server, the dominant open-access
preprint repository for scholarly papers in the fields of physics,
mathematics, computer science, quantitative biology, quantitative finance,
statistics, electrical engineering and systems science, and economics. The
papers in arXiv are not peer-reviewed but there are advantages in submitting
to this repository, mainly to disseminate a paper without waiting for the peer
review and publishing process, which can be slow (see Huisman and Smits
(2017)). The arXiv collection provides a unique source of data to conduct
various studies, including bibliometric, trend, and citation network analyses
(see Clement et al. (2019)). It is a valuable resource for advancing
scientific knowledge and conducting research on research, often referred to as
meta-research. For example, Eger et al. (2019) and Viet and Kravets (2019)
perform trend detection on computer science papers stored in arXiv, Lin et al.
(2020) conduct a case study of computer science preprints submitted to arXiv
from 2008 to 2017 to quantify how many preprints have eventually been printed
in peer-reviewed venues, Tan et al. (2021) explore the images of around 1.5
million of papers held in the repository, Okamura (2022) investigates the
citations of more than 1.5 million preprints on arXiv to study the evolution
of collective attention on scientific knowledge, Bohara et al. (2023) train a
state-of-art classification approach, and Fatima et al. (2023) design an
algorithm to help researchers to perform systematic literature reviews.

We study all papers on quantitative finance, a small portion of the entire
arXiv containing more than two millions of works at the time of writing. The
choice is also motivated by our experience in this domain and by scientific
curiosity.

The code is run on a standard desktop environment, without recurring to a big
cluster. Scaling to a large number of papers may be not trivial. Dealing with
a large amount of data requires significant computing resources, including
processing power and memory, to manipulate and analyze the data efficiently.
It is not simple, and maybe even impossible, to explore more than two million
of papers with a standard desktop environment like ours.

The studies of papers on finance topics is not new in the literature. Burton
et al. (2020) review the history of a well-known journal in this field and
highlight its growth in terms of productivity and impact. The authors present
a bibliometric analysis and identify key contributors, themes, and co-
authorship patterns and suggest future research directions. Ali and Bashir
(2022) conduct a systematic literature review and a bibliometric analysis on
around 3,000 articles on asset pricing sourced from the top 50 finance and
economics journals, spanning a 47-year period from 1973 to 2020. As observed
by the authors, the exclusion of certain publications may potentially offer an
alternative perspective on the landscape of existing asset pricing research.
By using bibliometric and network analysis techniques, including the
Bibliometrix Tool of Aria and Cuccurullo (2017), Sharma et al. (2023)
investigate more than 4,000 papers on option pricing appeared from 1973 to
2019. They follow the procedure suggested by Donthu et al. (2021). Their study
aims to pinpoint high-quality research publications, to discern trends in
research, to evaluate the contributions of prominent researchers, to assess
contributions from different geographic regions and institutions, and,
ultimately, to examine the interconnectedness among these aspects. The works
of Burton et al. (2020), Ali and Bashir (2022) and Sharma et al. (2023) are
focused on asset pricing or on a specific journal, their corpus is obtained by
searching in the Scopus database some specific keywords, and the bibliometric
analysis relies on VOS viewer (see Van Eck and Waltman (2010)) and Gephi (see
Bastian et al. (2009)).

Our study explores all papers on quantitative finance collected in arXiv till
the end of 2022 (around 16,000) and it considers text mining techniques
implemented in Python to extract information directly from the portable
document format (pdf) files containing the full text of the papers, excluding
images, without relying on ad-hoc software or proprietary databases.
Westergaard et al. (2018) found that examining the full text of documents
significantly improved text mining compared to studies that only explored
information collected from abstracts.222 As a crosscheck, we conduct the
analysis on both abstracts and full texts. The analysis using the full text
data shows better results. Their finding highlights the importance of using
complete textual content for more comprehensive and accurate text mining and
analysis.

The main objectives of our work are twofold. First, we explore the topics of
the quantitative finance papers collected in arXiv in order to describe the
evolution of topics over time. After having evaluated the performance of
various clustering algorithms, we investigate on which themes researchers have
focused their attention in the period from 1997 to 2022. Second, we try to
understand who are the most prominent authors and journals in this field. Both
analyses are performed with data mining techniques and without actually
reading the papers.

The remainder of the paper is organized as follows. First, we provide a brief
description of the data analyzed in this work (Section 2). Then, in Section 3
the preprocessing phase is discussed by offering further insights on the
papers analyzed in our work. In Section 4 we compare various clustering
algorithms and, after having selected the best performer, we explore, by
splitting our corpus in 30 clusters, the evolution of topics over time.
Finally, in Section 5 we describe an entity extraction process to investigate
authors and journals with the largest number of occurrences in the corpus
considered in this work. Section 6 concludes.

##  2 Data description

In this section we provide a description of the papers analyzed in this work.
As observed above, there are various domains in arXiv (i.e. physics,
mathematics, computer science, quantitative biology, quantitative finance,
statistics, electrical engineering and systems science, and economics) and
each domain has is own categories. The categories within the quantitative
finance domain are the following:

  * •

computational finance (q-fin.CP) includes Monte Carlo, PDE, lattice and other
numerical methods with applications to financial modeling;

  * •

economics (q-fin.EC) is an alias for econ.GN and it analyses micro and macro
economics, international economics, theory of the firm, labor economics, and
other economic topics outside finance;

  * •

general finance (q-fin.GN) is focused on the development of general
quantitative methodologies with applications in finance;

  * •

mathematical finance (q-fin.MF) examines mathematical and analytical methods
of finance, including stochastic, probabilistic and functional analysis,
algebraic, geometric and other methods;

  * •

portfolio management (q-fin.PM) deals with security selection and
optimization, capital allocation, investment strategies and performance
measurement;

  * •

pricing of securities (q-fin.PR) discusses valuation and hedging of financial
securities, their derivatives, and structured products;

  * •

risk management (q-fin.RM) is about risk measurement and management of
financial risks in trading, banking, insurance, corporate and other
applications;

  * •

statistical finance (q-fin.ST) includes statistical, econometric and
econophysics analyses with applications to financial markets and economic
data;

  * •

trading and market microstruture (q-fin.TR) studies market microstructure,
liquidity, exchange and auction design, automated trading, agent-based
modeling and market-making.

These categories are assigned by the authors when they submit their papers.
Even if it is possible to select multiple couples of domain-category belonging
to more than one domain, we select as reference category only the first
category within the quantitative finance domain. Figure 1 shows the numbers of
papers on quantitative finace submitted to arXiv between 1997 and 2022. The
increase in the last three years is mainly due to the q-fin.EC category.

Figure 1: Categories by year.

As observed in Section 1, the code is implemented in Python and it is run
under Ubuntu 22.04 on a desktop with an AMD Ryzen 5 5600g processor with 32GB
of RAM. As we will describe in the following, numerous packages are
considered.

As far as the collection process is concerned, we retrieve data from arXiv by
selecting all categories within quantitative finance (i.e. q-fin). We collect
articles metadata and pdf files for all articles from 1997 to 2022 for a total
of around 16,000 articles (18GB of data).

While the metadata are obtained through urllib.request and feedparser, the pdf
files are downloaded by means of the arxiv package. The metadata can be
collected by following the suggestions provided in the arXiv web-pages. They
are a fundamental input of the analysis and include the link to the paper main
web-page, from where it is possible to extract the paper identification code
(id, e.g. 2005.06390). The metadata contain information like authors names,
paper title, primary category, submission and last update dates, abstract, and
publication data when available (e.g. digital object identifier, DOI).
Subsequent updates of the papers can be stored in the repository and for this
reason there is the version number at the end of the paper id.

Since a paper could be assigned to multiple categories, a web-scraping tool
written in Python allows us to retrieve from the paper main web-page the list
of all categories of each single paper. We select from this list the subset of
categories within the quantitative finance domain. Thus we assign as reference
category of a paper the first category appearing in this subset. Starting from
this list, we are able to filter and analyze all papers in the nine categories
within q-fin.

The pdftotext package allows us to extract the text from pdf files. Each paper
becomes a single (long) string. As discussed in Section 3, the length of these
strings vary accross papers (see Figure 5), also because some documents are
not papers (e.g. there are both theses and books). As a first assessment of
the corpus, for each document we estimate the readability of the papers
through textstat. As shown in Figure 2 the Flesch reading ease score (see
DuBay (2004)) is on average equal to 65.7 (plain English), the lower and upper
quartile are 59.91 (fairly difficult to read, but not far from the plain
English) and 71.95 (fairly easy to read), respectively, and 99 per cent of the
papers are in the range from 40.28 (difficult to read) and 88.20 (easy to
read). There is only one paper with a negative value, but this is caused by
the text contained in the figures. All other papers are above 17.17, that is
above the extremely difficult to read level.

Figure 2: The Flesch reading ease score is reported. The vertical line
represents the median, the dashed line is the quantile of level 0.25 (0.75),
and the dotted line is the quantile of level 0.005 (0.995).

##  3 Text preprocessing

This section describes the text processing steps. The preprocessing phase is
performed with nltk:(1) we split the text in tokens; (2) we extract the
numbers representing years in the text;333 We assume these numbers have 4
digits. We do not explore this data in the empirical analysis. (3) we identify
all strings containing alphabet letters, and we refer to them as words even in
the case they do not belong to the English vocabulary; this step allows also
to remove some symbols which are not recognized as letters in text analysis.
Then, (4) we remove all stopwords and all words with lenght less than 3
characters; we also check whether there are words with more than 25 characters
(quite uncommon in English); (5) we conduct a lemmatization by means of a
part-of-speech tagger considering nouns, verbs, adjectives and adverbs; (6) we
check if the paper is written in English by means of the langdetect package
and we discard all non English papers. Both the extraction phase and the
preliminary text analysis is parallelized by means of the multiprocessing
package. We refer to the output of this first preprocessing phase as
lemmatized data.

Figure 3: Frequent words of the corpus and their percentage of appearance.

Figure 4: Bigrams and tri(four)grams word clouds based on frequency with
parameters min count equal to 250 and threshold equal to 10.

Thus, we analyze the frequency of the words across the whole corpus and we
remove all words appearing less than 25 times. We discard also some words
frequently used in writing papers on quantitative finance and which do not
help in understanding the topic of the paper. The list of these words
includes, for example, “proof” and “theorem”, verbs commonly used in
mathematical sentences (e.g.,“assume”,“satisfy”, and “define”), mathematical
functions (e.g. “min”, and “log”) and adverbs. The complete list is available
upon request. In Figure 3 the list of the top 100 most frequent words obtained
after this cleaning phase and their percentage of appearance is shown. The
word “model” is extremely frequent (one every 100 words). The word “http” is
also quite common, indicating that the papers full texts contain numerous
internet links.

After a first preprocessing phase, we conduct an $n$-gram analysis by
considering the Phrases model of the gensim package. We ignore all words and
bigrams with total collected count over the entire corpus lower than 250 and
set the score threshold equal to 10. We find the bigrams and then, to find
trigrams and fourgrams, we apply again the same model to the trasformed corpus
including bigrams. This approach allows us to have a better ex-post
understanding of the corpus which is full of $n$-grams (e.g. Monte Carlo
simulation, Eisenberg and Noe, or bank balance sheet). The wordclouds of the
main bigrams and trigrams (fourgrams) are depicted in Figure 4.

It should be noted that some topic modeling algorithms analized in Section 4
do not need text preprocessing. In those cases the input is just a single list
containing the whole paper text. While we refer to this latter input as raw
data, we define the output of the preprocessing as cleaned data.

Figure 5: Papers length, in terms of number of words, for raw, lemmatized and
cleaned data. The x-axis values are in thousands. The scale of x-axis varies
across the three datasets. The vertical line represents the median, the dashed
line is the quantile of level 0.25 (0.75), and the dotted line is the quantile
of level 0.01 (0.99).

In Figure 5 we show how the length of the papers varies over the three data
preprocessing phases. Starting from the raw data, containing all words and
symbols, after a preliminary cleaning step we obtain the lemmatized data and
then, after the last cleaning steps, the cleaned data. The number of words
varies from a median value of 8,824 words for the raw data to around 2,518
words for the cleaned ones.

##  4 Topics trend

Now we are in the position to perform a topics trend analysis. We employ a
topic modeling approach to identify the subjects discussed in the documents
examined in this study, and then we observe how these topics change over time.
Topic modeling refers to a class of statistical methods used to determine
which subjects are prevalent in a given corpus. In Section 4.1 we select the
best performing model among some selected approaches presented in the related
literature. We evaluate these approaches by assessing their ability to
accurately match the nine q-fin categories that researchers assign to their
work when submitting it to arXiv. Then in Section 4.2, after having split the
papers into 30 clusters, each one representing a specific topic, we discuss
the evolution of research trends over time.

###  4.1 Algorithms performance on full texts

Topic modeling algorithms are widely used in natural language processing and
text mining to uncover latent thematic structures in a collection of
documents. Different algorithms have been developed, each with its own
strengths and limitations (see Sethia et al. (2022)). The choice of a topic
modeling algorithm depends on specific factors, such as the desired level of
topic granularity and computational constraints. Some algorithms may require
substantial computational resources and large amounts of training data. Here,
we compare different algorithms by looking at some standard performance
measures.

Since is not simple to assess the performance of different topic modeling
algorithms (see Rüdiger et al. (2022)), we start by comparing the clusters
assigned by each algorithm on the entire corpus to the nine clusters defined
by the q-fin categories described in Section 2, that is the categories that
researchers assign to their work during the submission process to arXiv. By
exploiting a Bayesian optimization strategy, Terragni et al. (2021) present a
framework for training, analyzing, and comparing topic models where the
competitor models are trained by searching for their optimal hyperparameter
configuration, for a given metric and dataset. Here we consider a simpler
approach in which we compare the models by looking at some metrics. Evaluating
topic modeling algorithms typically involves the use of performance measures,
and it is important to note that different algorithms can yield varying
results across these metrics.

We consider the following models.

  * •

K-means. We perform a clustering analysis by considering the K-means algorithm
implemented in scikit-learn. This algorithm groups data points into K clusters
by minimizing the distance between data points and their cluster center. The
document word matrix is created through the CountVectorizer function, that
converts the corpus to a matrix of token counts. We ignore terms that have a
document frequency strictly higher than 75%. T

  * •

LDA. By considering the same document word matrix analyzed with the K-means
algorithm, we perform topic modeling with the latent Dirichlet allocation
(LDA). LDA is a well-known unsupervised learning algorithm. As observed in the
seminal work of Blei et al. (2003), the basic idea is that documents are
represented as random mixtures over latent topics, where each topic is
characterized by a distribution over words. We study two different
implementations of LDA (i.e. scikit-learn and gensim).

  * •

Word2Vec. We train a word embedding model (i.e. Word2Vec) and then we perform
a clustering analysis by considering again the K-means approach. An embedding
is a low-dimensional space into which high-dimensional vectors are projected.
Machine learning on large inputs like sparse vectors representing words is
easiser if embeddings are considered. Ideally, an embedding captures some of
the semantics of the input by placing semantically similar inputs close
together in the embedding space. The Word2Vec neural network introduces
distributed word representations that capture syntactic and semantic word
relationships (see Mikolov et al. (2013)). More in details, we generate
document vectors using the trained Word2Vec model, that is, we get numerical
vectors for each word in a document, and then the document vector is the
weighted average of the vectors. Thus, the K-means algorithm is applied to the
matrix representing the corpus. We consider the Word2Vec model implemented in
gensim.

  * •

Doc2Vec. We create a vectorised representation of each document through the
Doc2Vec model and then we perform a clustering analysis by considering the
K-means approach. The Doc2Vec extends Word2Vec and it can learn distributed
representations of varying lengths of text, from sentences to documents (see
Le and Mikolov (2014)). We consider the Doc2Vec model implemented in gensim.

  * •

Top2Vec. We study the Top2Vec model, an unsupervised learning algorithm that
finds topic vectors in a space of jointly embedded document and word vectors
(see Angelov (2020)). This algorithm directly detects topics by performing the
following steps. First, embedding vectors for documents and words are
generated. Second, a dimensionality reduction on the vectors is implemented.
Third, the vectors are clustered and topics are assigned. This algorithm is
implemented in an ad-hoc library named Top2Vec and it automatically provides
information on the number of topics, topic size, and words representing the
topics.

  * •

BERTopic. We study a BERTopic model, which is similar to Top2Vec in terms of
algorithmic structure and uses BERT as an embedder. As described in the
seminal work of Grootendorst (2022), from the clusters of documents, topic
representations are extracted using a custom class-based variation of term
frequency-inverse document frequency (TF-IDF). This is the main difference
with respect to Top2Vec. The algorithm is implemented in an ad-hoc library
named BERTopic. The main downside with working with large documents, as in our
case, is that information will be ignored if the documents are too long. A
limited number of tokens are treated and anything longer is cut off. Since we
are dealing with large documents, to work around this issue, we first split
each documents in chunks of 300 tokens, thus we fit the model on these chunks.
BERTopic does not allow one to directly select the number of topics, for this
reason on the first step we obtain a number of topics much larger than the
desired one. Since we obtain for each chunk the corresponding topic, we have
for each document a list of possibly different topics and the length of these
lists varies across documents (i.e. the length of a single list depends on the
length of the corresponding document). To cluster this list of lists of
topics, we consider each integer representing a topic as a word. Thus we use
the Word2Vec algorithm described above to find similarities between these list
of topics. Each topic label, that is the number representing the topic, is
treated as a string, and Word2Vec transforms it into a numerical vector. We
then apply K-means clustering to group these lists based on their similarity
in the vector space. The resulting clusters reveal relationships and patterns
among these lists and allow us to select the number of clusters we need for
our purposes.

In theory both BERTopic and Top2Vec should use raw data since these algorithms
rely on an embedding approach, and keeping the original structure of the text
is of paramount importance (see Egger and Yu (2022)). However, raw data
extracted from quantitative finance papers have a considerable amounts of
formulas, symbols and numbers that may affect the algorithms performance. For
this reason, we consider both raw and cleaned data. Additionally, for these
state-of-the-art algorithms the number of extracted topics tends be large, but
the algorithms offer the possibility to reduce the number of topics and of
outliers, that can be larger than expected. The parameters of a BERTopic model
have to be carefully chosen to avoid memory issues. Alternativelly, it is
possible to perform an online topic modeling, that is the model is trained
incrementally from a mini-batch of instances. This result in a less resource
demanding approach in terms of memory and CPU usage, but it generates less
rich and less comprehensive outputs and for these reasons we do not consider
this incremental approach here.

In Table 1 we report the following similarity measures between true and
predicted cluster labels: (1) the rand score (RS) is defined as the ratio
between the number of agreeing pairs and the number of pairs, and it ranges
between 0 and 1, where 1 stands for perfect match; (2) the adjusted rand score
(ARS), that is the rand score adjusted for chances, has a value close to 0 for
random labeling, independently of the number of clusters and samples, and
exactly 1 when the clusterings are identical (up to a permutation), however is
bounded below by -0.5 for especially discordant clusterings; (3) the mutual
info score (MI) is independent of the absolute values of the labels (i.e. a
permutation of the cluster labels does not change the value of the score); (4)
the normalized mutual information (NMI) is a normalization of the MI to scale
the results between 0 (no mutual information) and 1 (perfect correlation); (5)
cluster accuracy (CA) is based on the Hungarian algorithm to find the optimal
matching between true and predicted cluster labels; (6) to compute the purity
score (PS), each cluster is assigned to the class which is most frequent in
the cluster, and the similarity measure is obtained by counting the number of
correctly assigned papers and dividing by the number of observations. This
latter score increases as the number of clusters increases and for this
reason, it cannot be used as a trade off between the number of clusters and
clustering quality, that is to find the optimal number of clusters.

The measures presented in Table 1 demonstrates that the Doc2Vec approach, when
coupled with K-means clustering on cleaned data, outperforms other models.
This is evident from the higher MI and PS measures it achieves compared to its
competitors. Moreover, Doc2Vec exhibits practical advantages, as it is
straightforward to implement and significantly reduces computing time when
compared to more advanced techniques like BERTopic. Interpreting the results
of the Doc2Vec approach is simple, as it allows for the easy identification of
the most representative documents by retrieving the centroid vectors of each
cluster. The Word2Vec approach, when coupled with K-means clustering on
cleaned data, shows also a good performance.

|  RS |  ARS |  MI |  NMI |  CA |  PS
---|---|---|---|---|---|---
K-means |  0.570 |  0.029 |  0.232 |  0.136 |  0.271 |  0.297
LDA scikit-learn |  0.823 |  0.194 |  0.608 |  0.284 |  0.376 |  0.460
LDA gensim |  0.788 |  0.085 |  0.276 |  0.131 |  0.275 |  0.314
Word2Vec K-means |  0.832 |  0.200 |  0.613 |  0.283 |  0.371 |  0.427
Doc2Vec K-means |  0.831 |  0.220 |  0.699 |  0.325 |  0.388 |  0.490
Top2Vec raw |  0.810 |  0.195 |  0.501 |  0.239 |  0.365 |  0.404
Top2Vec cleaned |  0.811 |  0.206 |  0.530 |  0.387 |  0.253 |  0.416
BERTopic raw |  0.826 |  0.238 |  0.608 |  0.289 |  0.436 |  0.458
BERTopic cleaned |  0.821 |  0.239 |  0.574 |  0.276 |  0.398 |  0.429
Table 1: Algorithms performance. We report the rand score (RS), the adjusted
rand score (ARS), the mutual info score (MI), the normalized mutual info score
(NIM), the cluster accuracy (CA), and the purity score (PS).

It is worth noting that there are no significant differences in performance
measures when applying either the Top2Vec or BERTopic methods to raw or
cleaned data. This could be attributed to the fact that raw data contain
mathematical formulas that do not contribute substantial additional
information, even if, as shown in Figure 5, raw data have a larger number of
words. This finding indicating an equivalence between raw or cleaned data
could be also attributed to the relatively simple structure commonly found in
quantitative finance papers. It is important to note that these findings may
not generalize to papers or books with more intricate and complex text
structures and without formulas.

LDA implemented in scikit-learn has a better performance than the LDA
implementation in gensim. The plain K-means does not show satisfactory
results, even if the algorithm can be implement without a great effort.

Finally, as an overall assessment, it is important to highlight that the
performance metrics reported in Table 1 do not demonstrate particularly
impressive results. This could partly stem from the wide-ranging nature of
each q-fin category, encompassing numerous subtopics and arguments.
Conversely, some papers can be classified under multiple categories, as it is
not always obvious how to select a single definitive category for a given
work.

###  4.2 Empirical study

Figure 6: Topics trend by year across the sample of around 16,000 papers in
the q-fin categories. Figure 7: We show the topics clusters projected on the
2-dimensional space through the standard t-distributed stochastic neighbor
embedding (t-SNE) algorithm. The numbers represent the topics reported in
Table LABEL:table:Topics.

As shown in Section 4.1, the best performing model is Doc2Vec with K-means
clustering applied on cleaned data. This model is considered to have a better
understanding of the topics discussed in the quantitative finance papers
analized in this work. To obtain the desired number of topics we perform again
a K-means clustering analysis. To extract the most representative documents,
we retrieve the centroid vectors of each cluster. These centroids represent
the average position of all document embeddings assigned to a particular
cluster. For each cluster centroid, we find the nearest neighbors among the
original Doc2Vec embeddings. These nearest neighbors are the documents that
are closest to the centroid in the embedding space and can be considered as
the main documents of that cluster. Thus we select for each cluster the 20
most representative documents and we find a label for the topic on the basis
of the documents titles. Note that the underlying meanings of the topics are
subject to human interpretation. However, also this phase is automated by
asking the topic to ChatGPT (GPT-3.5) after having provided the list of 20
titles (see Ebinezer (2023)).

Given the size of our sample, a reduction down to 30 topics can be considered
a good compromise for a topic analysis. The selected number of topics strikes
a good balance between ensuring a sufficient quantity of documents for each
topic and maintaining the desired level of granularity. This approach allows
us to extract meaningful insights from the data while avoiding an excessive
division of content that could affect our ability to identify overarching
trends and patterns. As shown in Figure 6, most of the topics have an
increasing trend (topic 28 seems to be the only exception). This is also
motivated by the growth in the number of papers shown in Figure 1. For each
topic, the list of 20 titles is the input for the question we ask to the
ChatGPT chatbot. The topics label (i.e. the ChatGPT reply to the question)
together with the title of the most representative paper are reported in Table
LABEL:table:Topics.

It is interesting to observe that topics related to decentralized finance and
blockchain technology (2) and stock price prediction with deep learning and
news sentiment analysis (20) show a remarkable increase. This is also true for
health, policy, and social impact studies, represented by the topic 16, and
diverse perspectives in education, innovation, and economic development (0).
Both topics are oriented towards economics. These topics trends depend also by
the introduction in 2014 of the q-fin.EC category within the arXiv
quantitative finance papers. Classical quantitative finance subjects like
portfolio optimization techniques and strategies (6), stochastic volatility
modeling and option pricing (7), game theory and strategic decision-making
(19) high-order numerical methods for option pricing in finance (23) as well
as, new themes appeared in the literature in the last years, like deep
reinforcement learning in stock trading and portfolio management (4) and
environmental and economic impacts of mobility technologies (25) have
attracted the interest of researchers in the analized period. The
representativeness of topic 28 is limited, mainly because the number of papers
in this cluster is low, and one could merge it with another cluster (i.e. 8).

It is clear that some topics are more related to economics than to finance.
This also depends on the presence of the q-fin.EC category. For articles in
this category there is not always a flawless alignment with quantitative
finance.

To visualize the clusters, in Figure 7 the documents vectors are projected in
the 2-dimensional space through the standard t-distributed stochastic neighbor
embedding (t-SNE) algorithm. The larger the distance between topics, the more
distinct the papers in those topics are in the original high-dimensional
space. Conversely, it is also possible to have a better view on how close are
topics each other (e.g. 8 and 28). It appears that the most specialized or
narrowly-focused topics tend to occupy peripheral positions, while themes that
are more aligned with economics are positioned closer to the center.

##  5 Extracting authors and journals

In this section we extract the author surnames by means of the spacy package.
More in details, starting from the raw data, we perform a named-entities
recognition. Since this approach extract both first names and surnames, we
remove all first names by checking if these names are included in a list of
about 67,000 first names. It should be noted that the number of occurence of
the surname of the author in a paper strongly depends on the citation style.
Surnames are always reported in the references, but they do not necessary
appear in the main text of a paper. Additionally, even if the author-date
style is widely used (i.e. the citation in the text consists of the authors
name and year of publication), the surname of the first author appears more
frequently (e.g. Bianchi is more probable than Tassinari, even if Bianchi and
Tassinari are coauthors of the same papers, together with other coauthors).

The algorithm is able to find the names and surnames occuring in the text.
These are included in the PERSON entity types. The first 100 authors by number
of occurences in the corpus are selected. In order to have additional
information on these authors, we obtain topics, number of citations, h-index
and i10-index from Google Scholar (see Table LABEL:table:Authors). It should
be noted that not all authors are registered in Google Scholar, even if they
made a significant contribution to the field (e.g. Markowitz) or there are
authors with the same surname and belonging to the same research field (see
also Figure 3 in Sharma et al. (2023)). This is the case for some researchers
we find in our corpus (e.g. Zhou, Bayraktar and Chakrabarti). For these last
authors is not simple to find a perfect match in Google Scholar even if their
number of occurrences is generally high.444 For the reasons described above we
exclude from Table LABEL:table:Authors the following researcher: Zhou,
Markowitz, Peng, Jacod, Merton, Guo, Lo, Follmer, Yor, Almgren, Embrechts,
Bayraktar, Artzner, Weber, Jarrow, Feng, Samuelson, Tang, Chakrabarti,
Glasserman, Tsallis, Leung, Sato, Zariphopoulou, Kramkov, Karoui, Cizeau, Cao
and Christensen.

The algorithm is also able to find the most cited journals, included in the
ORG entity types: Journal of Finance (4490 occurences)∗, Mathematical Finance
(3785), Journal of Financial Economics (3325)∗, Physica A (3137)∗,
Quantitative Finance (3044), Econometrica (2473)∗, Journal of Econometrics
(1971), American Economic Review (1878), Insurance Mathematics and Economics
(1667), Review of Financial Studies (2636)∗, Journal of Banking and Finance
(1542)∗, Physical Review (1538), Journal of Economic Dynamics (1289), Energy
(1267), Operations Research (1242), The Quarterly Journal of Economics
(1238)∗, Journal of the American Statistical Association (1204), Management
Science (1160), European Journal of Operational Research (1066), Quantum
(1043), IEEE Transactions (996), Journal of Political Economy (990), Journal
of Economic Theory (977), Energy Economics (946), International Journal of
Theoretical and Applied Finance (946), SIAM Journal on Financial Mathematics
(888), Science (865), Expert Systems with Applications (845), Applied
Mathematical Finance (743), Finance and Stochastics (736), Mathematics of
Operations Research (652), PLoS (602), The Annals of Applied Probability
(593), Stochastic Processes and their Applications (525), Energy Policy (520),
Internationl Journal of Forecasting (520), The European Physical Journal
(514), Journal of Empirical Finance (510), Journal of Risk (509). We consider
only journals with more than 500 occurrences and we esclude publishing houses.
The journals with the asterisk symbol are identified with more than one name.
It should be noted that some well-known journals are slightly below 500
occurences. Furthermore, it is worth noting that papers with a strong
mathematical focus tend to receive significantly fewer citations compared to
papers that lean more towards economics or finance.

It is important to acknowledge that while the arXiv repository serves as a
valuable resource for scholarly papers, it may not encompass the entirety of
the quantitative finance research landscape. While the repository strives to
be inclusive and comprehensive, there may be variations in the representation
of scholars from different countries. Some scholars may have a relatively
higher presence due to their active participation in submitting their research
to arXiv. The platform content is reliant on authors voluntarily submitting
their work, which introduces the possibility of selection bias. As a result,
some authors and their contributions may not be represented. Therefore, our
analysis and conclusions should be interpreted within the context of the
available arXiv data, recognizing that there may be additional research and
authors in the field of quantitative finance who have chosen alternative
avenues for publishing their work. The same observation is true for the
findings described in Section 4.2.

It is possible that influential scholars may not be as consistently
represented or that, for various reasons, they have not regularly submitted
their work to arXiv (see also Metelko and Maver (2023)). In the study of
Sharma et al. (2023), focused on option pricing, some well-known authors are
cited but they do not appear among the first 100 authors in our analysis. This
discrepancy could be influenced by factors such as publication preferences,
possible copyright issues, or institutional practices that may vary across
different academic communities.

As a final remark, in our view, researchers in quantitative finance should
consider submitting their work to arXiv due to the potential benefits it
offers (see also Mishkin et al. (2020)). The delay between arXiv posting and
journal publication, which can sometimes be more than a year, underscores the
importance of submitting preprints to the repository. By doing so, researchers
can help the community to understand research trends in their field more
promptly, while also accelerating the dissemination of their own findings.
This approach aligns with the findings of Wang et al. (2020), who show that
rapid and open dissemination through preprints helps scholarly and scientific
communication, enhancing the reception of findings in the field. In the
meanwhile, as a possible alternative to gain a comprehensive understanding of
the entire landscape, future studies may consider incorporating other
reputable academic databases and journals to ensure a more holistic
exploration of quantitative finance research and its authors. Network
approaches would also help to identify cliques and highly connected groups of
authors. Insights from network clusters could further improve the
understanding of the textual data investigated in this work.

##  6 Conclusions

In this study, we explore the field of quantitative finance through an
analysis of papers in the arXiv repository. Our objectives are twofold: first,
we investigate the evolution of topics over time, second, we identify
prominent authors and journals in this domain. By employing data mining
techniques, we achieve these goals without reading the papers individually.

The preprocessing phase, when needed, ensures the suitability of the data for
subsequent analyses. Topic modeling helps in gaining insights and
understanding the main themes and trends within our large dataset. By applying
topic modeling algorithms, we identify the best performer and examine the
temporal evolution of quantitative finance topics. This analysis reveals the
changing research trends and highlights the emergence and decline of various
topics over time.

Furthermore, we conduct an entity extraction process to identify influential
authors and journals in the field. Through quantifying authors and journals
occurrences, we shed light on the researchers who have made notable
contributions to quantitative finance.

Our study demonstrates the power of data mining techniques in uncovering
insights from a large-scale preprint repository. Our work not only showcases
the power of data mining but also highlights the continued growth and dynamism
of quantitative finance as a discipline. The techniques explored in this work
can assist researchers in exploring and identifying novel research topics,
discovering connections between different research areas, and staying up-to-
date with the latest developments in the field. Furthermore, our methodology
may serve as a roadmap for future studies on broader datasets or in other
scientific domains utilizing text mining techniques. Although scaling to a
larger number of papers may pose challenges, our approach provides valuable
insights.

Finally, we believe that quantitative finance researchers should consider
sharing their work on arXiv to potentially accelerate the dissemination and
impact of their findings and to enhance the community understanding of
research trends.

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Table 2: For each topic we report the label extracted from ChatGPT and the title of the most representative paper. number | label | title of the most representative paper
---|---|---
0 | diverse perspectives in education, innovation, and economic development | Perspectives in public and university sector co-operation in the change of higher education model in Hungary, in light of China’s experience
1 | modeling financial market dynamics | Comment on: Thermal model for adaptive competition in a market
2 | decentralized finance and blockchain technology | Understanding the maker protocol
3 | correlation analysis in financial markets and networks | Random matrix theory and cross-correlations in global financial indices and local stock market indices
4 | deep reinforcement learning in stock trading and portfolio management | Practical deep reinforcement learning approach for stock trading optimal market making by reinforcement learning
5 | optimal trading and portfolio liquidation strategies in financial markets | An FBSDE approach to market impact games with stochastic parameters
6 | portfolio optimization techniques and strategies | Seven sins in portfolio optimization
7 | stochastic volatility modeling and option pricing | On the uniqueness of classical solutions of Cauchy problems
8 | asset pricing, investment, and arbitrage in financial markets | Characterization of arbitrage-free markets
9 | network analysis of financial contagion and systemic risk | Clearing algorithms and network centrality
10 | counterparty risk and valuation adjustments in financial derivatives | Collateral margining in arbitrage-free counterparty valuation adjustment including re-hypotecation and netting
11 | quantum models in finance and option pricing | Sornette-Ide model for markets: Trader expectations as imaginary part
12 | valuation and risk management in annuity and insurance products | A policyholder’s utility indifference valuation model for the guaranteed annuity option
13 | optimal dividend strategies in stochastic control and risk management | Optimal dividends problem with a terminal value for spectrally positive Levy processes
14 | risk measures and utility maximization under model uncertainty |  On the C-property and $w^{*}$-representations of risk measures
15 | economic complexity, networks, and trade patterns | Economic complexity and growth: Can value-added exports better explain the link?
16 | health, policy, and social impact studies | Ramadan and infants health outcomes
17 | statistical analysis of financial markets and volatility | Volatility distribution in the S&P500 Stock Index
18 | renewable energy economics and electricity market dynamics | On wholesale electricity prices and market values in a carbon-neutral energy system
19 | game theory and strategic decision-making | Simultaneous auctions for complementary goods
20 | stock price prediction with deep learning and news sentiment analysis | Stock Prediction: a method based on extraction of news features and recurrent neural networks
21 | kinetic wealth exchange models in economics | Gibbs versus non-Gibbs distributions in money dynamics
22 | market order flow and price impact | Order flow and price formation
23 | high-order numerical methods for option pricing in finance | High-order compact finite difference scheme for option pricing in stochastic volatility with contemporaneous jump models
24 | optimal investment and consumption in financial models with constraints | Recursive utility optimization with concave coefficients
25 | environmental and economic impacts of mobility technologies | A review on energy, environmental, and sustainability implications of connected and automated vehicles
26 | advanced risk measures in financial modeling | Generating unfavourable VaR scenarios with patchwork copulas
27 | Bayesian models for financial tail risk forecasting | A semi-parametric realized joint value-at-risk and expected shortfall regression framework
28 | pricing and modeling options in stochastic volatility models with jumps | Semi-analytical pricing of barrier options in the time-dependent Heston model
29 | economic growth and market dynamics | Uncovering volatility dynamics in daily REIT returns
Table 3: Number of authors occurrences and Google Scholar metrics as of May 2023. author_id | occurences | name | topics | citations | h-index | i10-index
---|---|---|---|---|---|---
mG07_6k | 4505.0 | Ioannis Karatzas | [’stochastic analysis’, ’stochastic control’, ’mathematical finance’] | 35724 | 60 | 127
58amEmw | 4441.0 | Jean-Philippe Bouchaud | [’statistical mechanics’, ’disordered systems’, ’random matrices’, ’quantitative finance’, ’agent based models’] | 49794 | 105 | 351
ahLm1v0 | 3256.0 | Walter Schachermayer | [] | 15891 | 56 | 124
HGsSmMA | 3135.0 | Didier Sornette | [’cooperation’, ’organization’, ’patterns’, ’prediction’] | 53371 | 112 | 587
CqFCQVE | 2794.0 | Alexander Schied | [’probability theory’, ’stochastic processes’, ’mathematical finance’] | 16780 | 35 | 71
2QOp9_M | 2457.0 | Peter Carr | [’financial engineering’, ’quantitative finance’, ’mathematical finance’, ’derivatives’, ’volatility’] | 24060 | 62 | 117
mVF1X_U | 2371.0 | Freddy Delbaen | [’mathematik’, ’ökonomie’] | 25557 | 50 | 90
ElAtiUs | 2258.0 | Darrell Duffie | [’finance’, ’central banking’] | 58442 | 88 | 142
fq7BQos | 2042.0 | Dilip B. Madan | [’mathematical finance’, ’general equilibrium theory’] | 25131 | 55 | 156
8abFiFM | 1774.0 | Robert Engle | [’finance and econometrics’] | 189678 | 118 | 229
GU9HgNA | 1743.0 | Quanquan Gu | [’statistical machine learning’, ’nonconvex optimization’, ’deep learning theory’, ’reinforcement learning’, ’ai for science’] | 14915 | 56 | 161
Q7N-rCk | 1672.0 | Rosario Nunzio Mantegna | [’econophysics’, ’statistical physics’, ’complex systems’, ’financial markets’, ’information filtering’] | 28269 | 67 | 139
QsYYhSE | 1629.0 | Søren Johansen | [’matamatical statistics’, ’econometrics’] | 97728 | 65 | 132
vZA2pjw | 1627.0 | Benoît B. Mandelbrot | [’mathematics’, ’fractals’, ’economics’, ’information theory’, ’fluid dynamics’] | 142895 | 96 | 319
Lf1kf1Q | 1505.0 | Mario Coccia | [’evolution of technology’, ’scientific change’, ’social dynamics’, ’complex adaptive systems’, ’environment & covid-19’] | 19376 | 106 | 228
9HXRjPk | 1444.0 | Damir Filipovic | [’quantitative finance’, ’quantitative risk management’] | 6910 | 39 | 73
6_INHZI | 1389.0 | Fabrizio Lillo | [’quantitative finance’, ’statistical mechanics’, ’data science’] | 10900 | 51 | 121
mGpnlA8 | 1218.0 | Touzi Nizar | [’stochastic control’, ’mathematical finance’, ’monte carlo methods’] | 11831 | 56 | 120
rp-3Yoo | 1187.0 | Barry Williams | [’banks and banking’, ’bank risk’, ’multinational’, ’banking’] | 2342 | 17 | 23
MZNxzRY | 1161.0 | Huyên Pham | [’mathematical finance’, ’stochastic control’, ’numerical probabilities’] | 9967 | 54 | 135
3HhvEUc | 1147.0 | Yuri Kabanov | [’mathematical finance’, ’mathematics’] | 6297 | 38 | 77
-YEPo1E | 1143.0 | Wing-Keung Wong | [’financial economics’, ’econometrics’, ’investment theory’, ’risk management’, ’operational research’] | 14440 | 65 | 274
GyPrRgc | 1138.0 | Swarn Chatterjee | [’financial planning’, ’wealth management’, ’financial literacy’, ’household finance’, ’behavioral finance’] | 2719 | 28 | 54
RZid9X8 | 1075.0 | Guido Caldarelli | [’network theory’, ’network science’, ’statistical physics’, ’complex systems’] | 24165 | 71 | 191
ImhakoA | 1075.0 | Daniel Kahneman | [] | 519507 | 158 | 369
zO_tShM | 1050.0 | Marek Rutkowski | [’mathematical finance’, ’stochastic processes’] | 7559 | 30 | 67
7NJ7Ax8 | 1039.0 | Patrick Cheridito | [] | 5400 | 34 | 59
nyfza90 | 1019.0 | Volker Schmidt | [’virtual materials testing’, ’statistical learning’, ’image analysis’, ’spatial stochastic modeling’, ’monte carlo simulation’] | 11896 | 52 | 230
x4vtSxI | 1017.0 | Rene Carmona | [’stochastic analysis’, ’financial mathematics’, ’financial engineering’] | 17474 | 59 | 139
kukA0Lc | 999.0 | Yoshua Bengio | [’machine learning’, ’deep learning’, ’artificial intelligence’] | 656874 | 222 | 763
vQ0_nz8 | 989.0 | Emmanuel Bacry | [’self-similarity’, ’multifractal’, ’stochastic modeling’, ’statistical finance’, ’financial time-series modelization’] | 11937 | 47 | 69
1XwLUrc | 980.0 | Jim Gatheral | [’volatility modeling’, ’market microstructure’, ’algorithmic trading’] | 6126 | 30 | 42
3HwRbiQ | 955.0 | Jerome Friedman | [] | 283058 | 95 | 197
e2Xowj0 | 900.0 | Neil Shephard | [’econometrics’, ’economics’, ’statistics’, ’financial econometrics’, ’finance’] | 42035 | 69 | 140
pEnxwCM | 887.0 | Victor M. Yakovenko | [’condensed matter theory’, ’econophysics’] | 8891 | 44 | 101
a11vssU | 845.0 | Constantinos Kardaras | [’stochastic analysis’, ’probability’, ’mathematical finance’] | 1557 | 20 | 31
79htA7g | 838.0 | Bent Flyvbjerg | [’project management’, ’management’, ’infrastructure’, ’planning’, ’cities’] | 73264 | 70 | 152
zH1qBSo | 834.0 | Albert Shiryaev | [’probability theory’] | 35521 | 59 | 163
QVb4LGI | 815.0 | Andrey Itkin | [’mathematical finance’, ’computational finance’, ’derivatives’, ’quantitative finance’, ’machine learning’] | 709 | 14 | 19
Zuhod6s | 813.0 | Yong Deng | [’uncertainty’, ’deng entropy’, ’information volume’, ’random permutation set’, ’chaos and fractal’] | 23189 | 81 | 335
bWlZ3-Y | 810.0 | Eric Jacquier | [] | 4458 | 19 | 25
GKthQJQ | 804.0 | Peter K. Friz | [’rough path theory’, ’stochastic analysis’, ’pdes’, ’finance’] | 5678 | 39 | 82
2qTa_4U | 794.0 | Francis Diebold | [’economics’, ’econometrics’, ’time series’, ’statistics’] | 76159 | 97 | 175
utY1nTo | 794.0 | Matteo Marsili | [’statistical mechanics’, ’stochastic processes’, ’collective phenomena in socio-economic systems’, ’networks’, ’complex systems’] | 10093 | 50 | 139
ZpG_cJw | 783.0 | Robert Tibshirani | [’statistics’, ’data science’, ’machine learning’] | 460493 | 172 | 525
65wdZxA | 780.0 | Damiano Brigo | [’probability’, ’mathematical finance’, ’stochastic analysis’, ’signal processing’, ’differential geometry and statistics’] | 9663 | 42 | 114
bxJe87s | 780.0 | Marco Frittelli | [’financial mathematics’, ’mathematical finance’, ’probability’] | 3795 | 24 | 33
aVju7cI | 771.0 | Monique Jeanblanc | [’mathématiques financières’] | 10256 | 51 | 110
-iOn6uI | 769.0 | Aurélien Alfonsi | [] | 2731 | 22 | 30
P_LECrk | 750.0 | Tomasz R. Bielecki | [’mathematical finance’, ’stochastic processes’, ’stochastic control’, ’stochastic analysis’, ’probability’] | 6901 | 39 | 89
5sQ0Fag | 729.0 | Ajit Singh | [] | 21592 | 60 | 360
6quAJUE | 706.0 | Josef Teichmann | [’mathematical finance’, ’machine learning in finance’, ’rough analysis’] | 3019 | 30 | 67
58amEmw | 705.0 | Jean-Philippe Bouchaud | [’statistical mechanics’, ’disordered systems’, ’random matrices’, ’quantitative finance’, ’agent based models’] | 49794 | 105 | 351
JicYPdA | 691.0 | Geoffrey Hinton | [’machine learning’, ’psychology’, ’artificial intelligence’, ’cognitive science’, ’computer science’] | 687453 | 180 | 436
i2MC67A | 679.0 | J.F. Muzy | [’multifractal analysis’, ’econophysics’, ’turbulence’] | 13417 | 55 | 83
K9yGky8 | 678.0 | Andreas Kyprianou | [’probability theory’, ’applied mathematics’] | 7946 | 44 | 99
aCSds20 | 670.0 | Xavier Gabaix | [’economics’, ’finance’] | 30926 | 56 | 75
G-WPCrM | 667.0 | Diego Garlaschelli | [’network theory’, ’econophysics’, ’sociophysics’, ’statistical physics’] | 7394 | 41 | 73
YTCnA4E | 664.0 | Eduardo Schwartz | [’finance’] | 44652 | 81 | 141
A0ISJPU | 664.0 | Steven Shreve | [’probability’, ’financial mathematics’] | 35605 | 42 | 70
fFFOHec | 660.0 | Alexander McNeil | [] | 24473 | 41 | 60
dYwbc9s | 659.0 | Guido Imbens | [’causal inference’, ’econometrics’] | 90765 | 95 | 169
OQK4DDY | 657.0 | Peter Forsyth | [’scientific computing’, ’computational finance’, ’numerical solution of pdes’] | 10617 | 58 | 143
c1wQ9_k | 655.0 | Daojian Zeng | [’natural language processing’] | 4877 | 13 | 17
Vs7kOf4 | 645.0 | Marcel Nutz | [’optimal transport’, ’mathematical finance’, ’game theory’] | 2339 | 30 | 43
vjc1kF0 | 640.0 | Francesca Biagini | [’financial and insurance mathematics’, ’stochastic calculus’, ’probability’] | 2598 | 20 | 42
zGJKZpk | 629.0 | Marianne Bertrand | [] | 64693 | 66 | 119
nEfnJZM | 628.0 | Vadim Linetsky | [’mathematical finance’, ’financial economics’] | 5260 | 39 | 63
Bekg2Qo | 621.0 | Joel Shapiro | [’financial intermediation’, ’regulation of financial institutions’, ’corporate governance’, ’industrial organization’] | 3449 | 15 | 16
KDhGvNQ | 611.0 | Johanna Ziegel | [’statistical forecasting’, ’risk measures’, ’postitive definite functions’, ’stereology’, ’copulas’] | 2088 | 19 | 31
r5PHkCs | 610.0 | Thomas Guhr | [’theoretical physics’] | 8395 | 39 | 104