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\title{Multi-word Expressions in English Scientific Writing}

%ET: mention diachrony in title?

% Author information can be set in various styles:
% For several authors from the same institution:
% \author{Author 1 \and ... \and Author n \\
%         Address line \\ ... \\ Address line}
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%         Author 1 \\ {\bf Author 2} \\ ... \\ {\bf Author n} \\
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\author{Diego Alves \\
  Saarland University, Germany \\
  \texttt{diego.alves@uni-saarland.de} \\\And
  Stefan Fischer \\
  Saarland University, Germany \\
  \texttt{stefan.fischer@uni-saarland.de} \\\AND
  Stefania Degaetano-Ortlieb \\
  Saarland University, Germany \\
  \texttt{s.degaetano@mx.uni-saarland.de} \\\And
  Elke Teich \\
  Saarland University, Germany \\
  \texttt{e.teich@mx.uni-saarland.de}
  }

\begin{document}
\maketitle
\begin{abstract}
%We trace the evolution of Multi-Word Expressions (MWEs) in scientific English from the mid-17th century to the present. 
Multi-Word Expressions (MWEs) %, ranging from idioms to phrasal verbs and compounds, 
play a pivotal role in language use overall and in register formation more specifically, e.g. encoding  domain-specific terminology. Our study focuses on the identification and categorization of MWEs used in English scientific writing, considering their formal characteristics as well as their developmental trajectory over time from the mid-17th century to the present. For this, we develop an approach combining three  different types of methods to identify MWEs (Universal Dependency annotation, Partitioner and the Academic Formulas List) and selected measures to characterize MWE properties (e.g., dispersion by Kullback-Leibler Divergence and several association measures). This allows us to inspect MWE types in a novel data-driven way regarding their functions and change over time in specialized discourse. 

%We show that while MWEs serving as field-specific terminology (e.g., noun-noun compounds) exhibit agility and productivity, others, such as expressions of stance, change at a slower rate and are less varied. %Using a corpus-driven approach, we address the identification and categorization of MWEs, analyzing their frequency, fixedness, and productivity across different periods.
\end{abstract}

\section{Introduction}
\label{sec:intro}

%ET: Problem addressed, goal of the paper
Regularity in language does not only concern structural aspects (syntax, morphology), but also the way we combine words. Some word combinations are perceived as patterns that are associated with specific  meanings or connotations, collectively referred to as multi-word expressions (MWEs). MWEs range from idioms that are formally fixed and have a figurative meaning (e.g., \textit{kick the bucket})  to compounds (\textit{bus ticket}) or phrasal verbs (\textit{take a ride}) that are typically compositional and often lexically fairly productive (cf. \citet{AvgustinovaIomdin2019}). 

MWEs are ubiquitous since they contribute to language efficiency by having  highly predictable transitions from one word to the next or, if highly conventionalized,  they can be retrieved from the lexicon rather than processed incrementally, thus giving them a processing advantage over other word sequences. Furthermore, MWEs play a crucial role in register formation as they provide conventional encodings of context-specific meanings.  For example, MWEs such as \textit{in no event} or \textit{said therein} are typical of legal language and rarely encountered elsewhere, while  
%in this paper`` or ``it is obvious'' 
%are typical of the scientific register, rarely encountered elsewhere; 
noun-noun and adjective-noun combinations such as \textit{iron oxide} or \textit{sulphuric acid} are a typical type of MWEs used in scientific language forming domain-specific %field-specific 
terminology.  
%MWEs are patterns in the sense of pattern grammar or construction grammar


In particular, we are interested in MWEs in scientific English from a diachronic perspective (mid 17th century to today). Scientific English develops into a recognizable register during the late modern period and becomes highly conventionalized in modern times. Overall, we want to better understand the process of register formation and whether  processing advantages might have an impact.  Specifically, we ask (i) what are the %specific 
MWEs used in scientific English, (ii) which specific \textit{types} of MWEs are used in the scientific domain, %typical of scientific writing, %(compared to other registers), 
and (iii) how to characterize the diachronic development of MWEs in this %the scientific 
domain, e.g., do specific MWEs trend in particular periods, do MWEs become more/less fixed and/or productive over time, thus contributing to conventionalization.  For instance, we expect that MWEs serving domain-specific %field-specific 
terminology (such as noun-noun compounds) will be quite agile and productive, while others, e.g., expressions of stance (e.g. \textit{it is interesting}) will change at a lower rate and be less varied. We  develop an approach to identify MWEs in scientific texts in order to be able to address these questions and better understand the role MWEs play in register formation. The scientific domain  is well-suited as it encompasses different types of MWEs ranging from scientific terms up to stylistic expressions. In this paper, we take a first step towards answering the above questions, focusing on the identification of MWEs and possibilities of categorization into types by applying dispersion and association measures to  our diachronic data set.  %address the first and second questions, presenting a corpus-driven  approach to the identification and categorization of MWEs. 

The remainder of the paper is organized as follows. In Section~\ref{sec:relw} we discuss related work on MWEs in computational linguistics/NLP. Sections~\ref{sec:meth} and~\ref{sec:res} presents our methods and results, including a preliminary diachronic analysis. We conclude with a summary and outlook (Section~\ref{sec:sum}).

\section{Related Work}
\label{sec:relw}

From a linguistic perspective, there are numerous corpus-based accounts of MWEs in different registers, including the scientific one (e.g. \citet{biberbarbieri2007,Hyland2008,Dilin2012}). Some of these descriptions include lists of MWEs used in academic texts that are freely available. We make use of one specific list \cite{simpson2010academic} in our own approach (Section~\ref{sec:meth}), but obviously such lists are always biased (time, corpus). Therefore, a sound, reusable computational method for identifying MWEs is needed, including analysis of their inherent properties (such as transparency, compositionality, fixedness; cf. also \citet{SchulteimWalde2019}).

From a computational point of view, MWEs have been considered ``a pain in the neck'' \cite{Sag-etal2002}  because they are not trivial to identify, let alone classify, by standard language models or NLP tools.
%Buerki, A. (2016). Formulaic sequences: a drop in the ocean of constructions or something more significant? European Journal of English Studies, 20:15–34.
Two formal criteria of MWEs are \textit{predictability} 
%To qualify for an MWE, a word combination must be fairly \textit{predictable} 
in a given context (e.g., register) and relative \textit{fixedness} of the elements within the expression. In combination with relative frequency,
well-established measures to assess MWE candidates are pointwise mutual information (PMI) and log-likelihood, commonly also applied to identify collocations (e.g., \citet{Evert2008,Ramisch-etal2010,Wahl2018,fabre:hal-02272435}).
%Fillmore, C. J., Kay, P., & O’Connor, M. C. 1988. Regularity and Idiomaticity in Grammatical Constructions: The Case of Let Alone. Language (64), 501–538.
%Traugott, Elizabeth Closs. 2019. Constructional pattern-development in language change. In Beatrix Busse & Ruth Moehlig-Falke (eds.), Patterns in Language and Linguistics, 125–156. Berlin, Boston: De Gruyter

Regarding the identification of MWEs using machine-learning methods, \citet{ramisch-etal-2023-survey} conducted a survey on existing MWE corpora and evaluation methods. They showed that most of the existing tools for this specific NLP task are based either on DiMSUM \cite{schneider2016semeval} or PARSEME \cite{savary:hal-01223349} corpora and that, due to the complexity of the task and differences between approaches, results are not always comparable. PARSEME acknowledges discontinuity, variability, nesting, and overlaps and has a fine-grained MWE classification, however, it considers only verbal MWEs. On the other hand,  DiMSUM corpus is annotated for most major MWE categories (i.e., nominal, verbal, adverbial, and functional), but does not include any category labels. Considering the scope of our study, the broader coverage of DiMSUM seems more relevant and aligned with our aims. The complexity of the automatic extraction of MWEs is noticeable in works such as \citet{tanner2023mwe} where state-of-the-art tools have F1-scores below 65.

Given the complexity of the task, different approaches focus on different aspects of MWEs, so we decided to combine the state-of-the-art approaches for a more comprehensive treatment. 

\section{Methods}
\label{sec:meth}

\subsection{Dataset}

As the main objective of this study is to investigate the role of MWEs in the development of English scientific writing, we decided to use the Royal Society Corpus (RSC) 6.0, a diachronic corpus of scientific English covering the period from 1665 until 1996. The RSC comprises 47 837 texts (295 895 749 tokens), mainly scientific articles covering a wide range of areas from both the mathematical and physical sciences and the biological sciences, and is based on the Philosophical Transactions and Proceedings of the Royal Society of London \citep{fischer2020royal}. 
%Table \ref{size_rsc} shows a detailed overview of the distribution of texts and tokens over time.

Given its fair size and time coverage, the RSC is not only particularly relevant for diachronic linguistic analysis (e.g., \citet{feltgen2017frequency}; \citet{degaetano2018using}; \citet{degaetano2022toward}), but also for historical and cultural analysis (e.g., \citet{fyfe2015350}; \citet{moxham2018royal}).

%\begin{table}
%\small
%\centering
%\begin{tabular}{crr}
%\hline
%\textbf{Period} & \textbf{Texts} & \textbf{Tokens}\\
%\hline
%\ 1665--1699 & 1 325 & 2 582 856 \\
%\ 1700--1749 & 1 686 & 3 414 795 \\
%\ 1750--1799 & 1 819 & 6 342 489 \\
%\ 1800--1849 & 2 774 & 9 112 274 \\
%\ 1850--1899 & 6 754 & 36 993 412 \\
%\ 1900--1949 & 10 011 & 65 431 384 \\
%\ 1950--1996 & 23 468 & 172 018 539
%\\
%\hline
%\end{tabular}
%\caption{\label{size_rsc}
%Size of the Royal Society Corpus 6.0 over time
%}
%\end{table}

\subsection{Extraction of Multi-word Expressions}

To identify and extract MWEs from the RSC corpus, we combined three different approaches which are schematised in Figure \ref{fig:methodology}. The idea was to increase the number of identified MWEs, reducing biases related to the recall of each approach. From each method, we extract a list of MWEs which are, then, merged into the final RSC MWE list. For each method, MWEs are extracted in lowercase.  
Each method is described in detail in the subsections below.

\begin{figure*}[htbp]
  \centering
  \includegraphics[width=0.8\linewidth]{Figures/methodology_1.png}
  \caption{Methodology for extracting MWEs from the RSC corpus.}
  \label{fig:methodology}
\end{figure*}

\subsubsection{Universal Dependencies Method}

The Universal Dependencies\footnote{https://universaldependencies.org/} (UD) guidelines for the annotation of dependency relations \citep{de2021universal} include 5 dependency labels which concern MWEs: i) compound - combinations of tokens that morphosyntactically behave as single words. In English, we find most commonly nominal compounds written as separate words, for example, \textit{orange juice}; b) compound:prt - phrasal verbs (e.g., \textit{shut down} and \textit{find out}); c) flat - this relation combines elements of an expression where none of the immediate components can be identified as the sole head using standard substitution tests. For example: \textit{Hillary Clinton} and \textit{San Francisco}; d) flat:foreign - sequences of foreign words; and e) fixed - used for certain fixed grammaticalized expressions which tend to behave like function words (e.g., \textit{because of}, \textit{in spite of}, \textit{as well as}).

CoNNL-U is the standard format for texts containing morphosyntactic annotations following the UD guidelines. It is supported by state-of-the-art dependency parsers (e.g., Stanza) and can be easily queried for specific syntactic information. Thus, from a parsed corpus, it is possible to identify the word units composing the different types of MWE according to the UD framework.

The RSC 6.0 was parsed using Stanza tool \citep{qi2020stanza} and the combined model for the English language provided by the developers which was trained with different UD corpora. Then, we developed a Python script using pyconll library\footnote{https://github.com/pyconll/pyconll} to identify and count the MWEs in the RSC texts per year and merged the results in a unified list of UD MWEs concerning all RSC.

The UD method for extracting MWEs depends on the accuracy of the parser, thus, although Stanza is a state-of-the-art tool for dependency annotation, some errors are inevitable. A manual evaluation of 70 sentences (10 per 50-year period of the RSC) showed that the accuracy of the parser is equal or higher than 85\% for compound:prt, compound, and fixed MWEs, and equal to 75\% for flat ones. The scores are quite consistent throughout the different time periods\footnote{flat:foreign was not evaluated as this class is rare in the RSC and it did not appear in the evaluation set}.

Another bias related to the UD method concerns the fact that many MWEs are not captured as they are described syntactically with dependency relations different from the 5 ones described above (e.g., \textit{in terms of}, \textit{so far}, \textit{as so}). Therefore, this method alone is not enough for a global diachronic analysis of MWEs. 


\subsubsection{Partitioner}

Partitioner 0.1.2\footnote{https://pypi.org/project/partitioner/} is a Python module that performs tokenization with generalisations into MWE segmentation using a supervised machine learning algorithm \citep{williams2016boundary}. It was presented by \citet{tanner2023mwe} as one of the state-of-the-art tools for MWE extraction (evaluated using the DiMSUM corpus).

We applied the partitioner method to the RSC texts and, as was the case of the UD method, extracted the ensemble of MWEs in the RSC and also identified the MWEs occurring each year.

The partitioner memory overhead comes from the English Wikipedia data set, thus, it may also fail in identifying certain MWEs from the earlier periods of the RSC. Moreover, although it is a state-of-the-art tool (with better recall than the others listed by \citet{tanner2023mwe}), it is clear that it is not possible to identify all MWEs in our corpus.

\subsubsection{Academic Formulas List}

The third approach that we selected regarding MWE identification in the RSC concerns the Academic Formulas List (AFL), which is a list of the most common formulaic sequences in academic English. It is composed of a core list of 207 formulaic expressions found in written and spoken academic language, a specific list of 200 expressions from written corpora, and another one (also with 200 expressions) based on spoken academic English texts \citep{simpson2010academic}. The AFL multi-word expressions were identified by the authors with a special measure of usefulness called the formula teaching worth (FTW), which combines frequency and mutual information measures.

Using a Python script, we identified and counted all AFL MWEs in the RSC. In total, 506 out of the 607 MWEs in the AFL occur in our corpus. As expected, most of the AFL expressions that do not appear in the RSC concern the ones from the AFL spoken list (e.g., \textit{I'll talk about}, \textit{gonna talk about}, \textit{let's look at}).

\subsubsection{Merged MWEs}

Once we identified and counted the MWEs in the RSC with the three methods, we merged the lists to create our final set of MWEs. 

Since UD MWEs are grammatically motivated and AFL MWEs were selected using specific measures, we kept all the elements from these lists. However, regarding the partitioner method, we consider only the MWEs with frequency (in the whole corpus) $>$3, following the threshold defined by \citet{gries2022multi}. The aim is to avoid, in our final list, syntagmas such as a determiner followed by a noun as well as other sequence of tokens which are not MWEs as they are not grammatically motivated like flat and compound structures and are not frequent in the text to be considered a collostructure. Moreover, we decided to exclude MWEs composed only of numbers.

Regarding the frequency values, if the MWE appeared in more than one list, we considered its frequency to be the highest number when comparing values from the different approaches.  

\subsection{Dimensions of Information}

Several measures are described in the literature to characterize MWE properties. \citet{gries2022multi} defined eight different ones which he used to identify MWEs in the Brown corpus \citep{francis1979brown} using a multi-dimensional strategy based on an information-theoretic approach.

In our case, MWEs were extracted using automatic methods, thus, our aim regarding dimensions of information is to use these metrics to describe the multi-word units identified in the RSC. Besides the MWE frequency provided by the scripts of the three approaches, we also calculated, for each MWE, its dispersion and association values across years. 

\subsubsection{Dispersion}

The dispersion measure assesses the spread of an MWE within a corpus. It is defined by \citet{gries2022multi} as a normalized version of the Kullback–Leibler divergence (KLD), which is a unidirectional measure quantifying how much in percent of a word’s total occurrences in each corpus part diverges from the corpus part sizes in percent. Dispersion values vary from 0 to 1, the higher that number, the more heterogeneously distributed the MWE is. In this study, dispersion for each MWE was calculated across time by subdividing the RSC per year.

Thus, with the frequency of each MWE and the size of each corpus part (number of tokens) per year, it was possible to calculate the normalized dispersion values of all MWEs of our merged list. 

\subsubsection{Association}

The Association measures of bi-grams are defined as (i) the degree to which the first token attracts the second one, and (ii) the degree to which the second token of the MWE attracts the first. For n-grams with $n>2$, we calculate as many association measures as necessary to describe the whole MWE, considering the whole left context. For example, for the MWE \textit{in spite of}, we calculate: a) association of \textit{in} and \textit{spite}; b) Association of \textit{spite} and \textit{in}; c) association of \textit{in spite} and \textit{of}; and c) association of \textit{of} and \textit{in spite}.

Associations measures are also obtained using normalized KLD as described by \citet{gries2022multi}. Thus, for each MWE from the merged list, we calculated the different association values considering the whole corpus and also for each 50-year period of the RSC.%described in Table~\ref{size_rsc}.

\section{Results}
\label{sec:res}


\subsection{Extraction of MWEs}

We present in Table~\ref{mwe_per_method} the details of the RSC MWE list in terms of the number of MWE types per class of MWE: (i) UD MWEs correspond to MWEs identified only with the UD method as well as the ones identified by both UD and partitioner approaches; (ii) Other MWEs are the partitioner MWEs which do not appear in the UD list; and (iii) AFL MWEs are the MWEs provided by the AFL approach.    

\begin{table}[ht]
\centering
\begin{tabular}{lr}
\hline
\textbf{Method} & \textbf{MWE} \\
\hline
\ UD & 3 147 597 \\
\ Other & 181 659 \\
\ AFL & 506 \\
\hline
\ \textbf{Total} & 3 329 762 \\
\hline
\end{tabular}
\caption{\label{mwe_per_method}
Number of MWE types of each extraction approach and for the RSC MWE merged list. 
}
\end{table}

It is possible to notice that the majority of the RSC MWEs (94\%) come from the UD method. This is due to our decision to keep even the MWEs extracted via this method with a frequency $<3$. Moreover, most MWEs in our list (69\%) appear only once in the whole corpus.

Table~\ref{UD_mwe} presents the distribution of the number of MWE types regarding UD MWEs in terms of dependency relation.

\begin{table}
\centering
\begin{tabular}{lrr}
\hline
\textbf{UD MWE} & \textbf{MWE} & \textbf{\%} \\
\hline
\ compound & 2 523 696 & 80.2 \\
\ flat & 604 057 & 19.2 \\
\ compound:prt & 16 337 & 0.5 \\
\ fixed & 3 107 & 0.1 \\
\ flat:foreign & 400 & 0.0 \\
\hline
\end{tabular}
\caption{\label{UD_mwe}
Distribution of UD MWEs in terms of dependency relation. 
}
\end{table}

%\begin{table*}
%\centering
%\begin{tabular}{lccc}
%\hline
%\textbf{UD MWE} & \textbf{MWE} & \textbf{\%} & \textbf{Hapax} \\
%\hline
%\ compound & 2 523 696 & 75.8 & 1 831 261 (73\%) \\
%\ compound:prt & 16 337 & 0.5 & 8 528 (52\%) \\
%\ flat & 604 057 & 18.1 & 452 030 (75\%) \\
%\ flat:foreign & 400 & 0.0 & 392 (98\%) \\
%\ fixed & 3 107 & 0.1 & 1 757 (57\%) \\
%\hline
%\end{tabular}
%\caption{\label{UD_mwe}
%Distribution of UD MWEs in terms of dependency relation. 
%}
%\end{table*}


Compound and flat are the UD MWE classes with the highest number of MWE types in the RSC, however, they have a high number of types that occur only once in the corpus (hapax percentage higher than 70\%). Most of these MWEs correspond to specific entities that are only mentioned in the precise context of specific articles (e.g., \textit{oligocene regime}; \textit{wavelength translators}; \textit{Prince Joseph Oscar}) and did not become part of  scientific terminology. The flat:foreign class is essentially composed of hapaxes, thus, of lesser interest for our study. The flat:foreign MWEs with a frequency $>1$ (8 in total) concern mostly parsing errors (e.g., \textit{J. McLean}, \textit{complete collection}, \textit{rb 27}).

Figure \ref{fig:freq} presents the relative frequency of each MWE class per year in the RSC. It is possible to notice a clear tendency of increasing the usage of compounds in scientific English (as observed previously by \citet{degaetano2018using}), with a more pronounced slope from the second half of the nineteenth century. Moreover, flat MWEs seem to become increasingly more common specially in the second half of the twentieth century.

\begin{figure*}[htbp]
  \centering
  \includegraphics[width=1\linewidth]{Figures/freq.png}
  \caption{Relative frequency of the different classes of MWE per year in the RSC.}
  \label{fig:freq}
\end{figure*}

Furthermore, applying the Mann-Kendall trend test to each class \citep{hussain2019pymannkendall}, with the exception of phrasal verbs (i.e., compound:prt), all the other classes present an overall increasing tendency (p-value below 0.05) even though, in some cases, decreasing periods are observed.

\subsection{Dimensions of Information}

\subsubsection{Dispersion and Association overview}

As previously mentioned, we focus our analysis on two specific dimensions of information: dispersion and association. Thus, to have a graphic overview of the distribution of the different classes of MWEs identified in the RSC according to these metrics, we plotted the graphs presented in Figure \ref{fig_disp_assoc}.

Each graph represents the MWEs of the specific class in red, and in black, the other ones. To improve the visualisation, we plot only the types with a frequency $>10$. For dispersion, each type has one value, while for association, the number depends on the number of words composing the MWE. Therefore, what is plotted corresponds to the mean of the different association values\footnote{If the paper is accepted, we will share via GitHub all the graphs in HTML format with the following information for each plotted MWE: class, dispersion, association values, and mean association value.}.

%\begin{figure*}[htbp]
%  \centering
%  \begin{tabular}{cc}
%  \textbf{AFL} & \textbf{Other MWE}  \\
%  \includegraphics[clip,scale=.5]{Figures/AFL_graph.png} &
%  \includegraphics[clip,scale=.5]{Figures/other_mwe.png} \\
%  \textbf{Compound} & \textbf{Compound:prt} \\ 
%  \includegraphics[clip,scale=.5]{Figures/compound.png} &
%  \includegraphics[clip,scale=.5]{Figures/compound_prt_graph.png} \\
%  \textbf{Flat} & \textbf{Fixed} \\ 
%  \includegraphics[clip,scale=.5]{Figures/flat_graph.png} &
%  \includegraphics[clip,scale=.5]{Figures/fixed_graph.png} \\
%  \end{tabular}
%  \caption{Distribution of the RSC MWE in terms of Dispersion and Association. Each graph presents in red the class of MWE specified in its title.}
%  \label{fig_disp_assoc}
%\end{figure*}


\begin{figure*}[htbp]
  \centering
  \begin{tabular}{ccc}
    \textbf{AFL} & \textbf{Other MWE} & \textbf{Compound} \\
    \includegraphics[clip,scale=.32]{Figures/AFL_graph.png} &
    \includegraphics[clip,scale=.32]{Figures/other_mwe.png} &
    \includegraphics[clip,scale=.32]{Figures/compound.png} \\

    \textbf{Compound:prt} & \textbf{Flat} & \textbf{Fixed} \\ 
    \includegraphics[clip,scale=.32]{Figures/compound_prt_graph.png} &
    \includegraphics[clip,scale=.32]{Figures/flat_graph.png} &
    \includegraphics[clip,scale=.32]{Figures/fixed_graph.png} \\
  \end{tabular}
  \caption{Distribution of the RSC MWEs in terms of Dispersion and Association. Each graph presents in red the class of MWE specified in its title.}
  \label{fig_disp_assoc}
\end{figure*}


As expected, the different classes of MWEs behave differently in terms of distribution regarding dispersion and association metrics. 

Most AFL MWEs are positioned in the lower left quadrant, thus indicating that these units are fairly well distributed within the RSC but with low mean association values. This is due to the fact that most of the AFL MWEs are composed of words that appear in many other contexts (e.g., \textit{that is the}, \textit{it is important}, \textit{on the other}). The AFL elements with a mean association value around 0.5 are the ones where at least one word is more usually present in that specific construction (e.g., \textit{in accordance with}). Few AFL MWEs are positioned in the upper left quadrant (i.e.; not homogeneously dispersed in the RSC) and usually concern MWEs with personal pronouns (mostly \textit{I} and \textit{you}).       

Compound and flat classes are the ones with the highest number of MWE types. In both cases, most of the MWEs are positioned in the upper quadrants of the graphs. However, compound MWEs have a better distribution in terms of dispersion in these quadrants. For these two classes, the elements in the upper right quadrant usually correspond to very specific scientific terms such as name of species (e.g., \textit{Ambystoma mexicanum}), while the MWEs in the upper left side are composed of words that are more generic (e.g., \textit{Mr Baker}, \textit{Dr Davies}, \textit{phase modulation}). The compound and flat MWEs in the lower right quadrant are very frequent terms that are quite homogeneously dispersed in the RSC, for example: \textit{Royal Society}, \textit{New York}, \textit{refractive index}, \textit{differential equations}, \textit{standard deviation}. The scientific terms in the lower quadrants correspond to broad concepts usually applied in different fields.   

Phrasal verbs (compound:prt) present a particular behaviour. Usually, the association value of its preposition in regard to the verb is very low as this element can appear in a large variety of other contexts. Thus, it explains the fact that most compound:prt MWEs are positioned in the left quadrants. More specifically, the vast majority of these MWEs are not well dispersed in the RSC, thus, the upper left quadrant is the most populated one with this class. Some specific phrasal verbs which are common in the scientific language are better distributed in our corpus, such as: \textit{carried out}, \textit{pointed out}, \textit{depend on}. Phrasal verbs with mean association values close to 0.5 are the ones for which the verb is not encountered in other contexts in the RSC (e.g., \textit{churned up}, \textit{smoothes out}, \textit{budded off}).

Regarding fixed MWEs, we observe a cluster of elements on the left upper side and many others spread over the left lower quadrant. The MWEs in the upper side correspond to unusual terms (frequency below 50) such as \textit{according with}, \textit{one other}, \textit{without than}, while the ones in the lower part of the graph occur more frequently (more than 100 occurrences). Moreover, some fixed MWEs that are homogeneously distributed in the RSC have a mean association value closer to 0.5, indicating that at least one of its units is strongly attracted to the other words forming the MWE. This is the case for \textit{due to}, \textit{less than}, \textit{rather than}, etc.

Finally, the MWEs from the ``Other MWE'' class (extracted using the partitioner tool) are mostly present on the left upper and lower parts of the graph. A qualitative analysis of these terms shows that some of them correspond to nominal phrases composed of an adjective and a noun (e.g., \textit{electrical stimulation}, \textit{practical applications}). Also, many of-genitive examples can be identified as ``Other MWE'' such as \textit{University of Bristol} and \textit{Department of Chemistry}. We also notice many cases of discourse markers such as \textit{at first sight}, \textit{for example}, etc. 

\subsubsection{Diachronic Analysis of Association Values}

To analyse the diachronic evolution of MWEs in scientific English, we focus on the examination of the mean association values throughout the 50-year periods. As described in Section 3.3.2, for each period, we calculated the association metrics for each MWE present in the sub-corpus as well as its mean value.

Our aim is to check whether the identified MWEs became more or less fixed in time, a phenomenon that can indicate possible conventionalization processes in this specific register of the English language. Therefore, we used the Mann-Kendall trend test\footnote{pymannkendall 1.4.3 Python module available at: https://pypi.org/project/pymannkendall/} which is suited to the analysis of time series data regarding increasing or decreasing trends \citep{hussain2019pymannkendall}.

As we are interested in diachronic trends, only MWEs that appear in at least 2 periods were examined (316 390 out of 3 329 762). Thus, we applied the original Mann-Kendall test proposed by the pymannkendall module to these MWEs and extracted the following results: i) trend: increasing or decreasing (if p-value < 0.05) and no trend (if p-value > 0.05) and ii) slope: value representing the rate of change (positive for increasing values of mean association and negative when decreasing).

Table~\ref{diachronic_association} presents the results for each class of MWE in the RSC with detailed information regarding the number of MWEs with increasing and decreasing trends as well as the number of elements where no trend was observed. Overall, it is possible to observe that, for all classes of MWEs, the number of elements presenting no statistically valid trend is higher than in the cases where an increase or decrease is attested. Moreover, considering the percentage of MWEs with an increasing or decreasing tendency, AFL is the class with the highest number of MWEs where changes have occurred (34\%), Fixed and Compound:prt classes present changes for 5 to 8\%, and for the other classes, the percentage is below 1\%. 

\begin{table*}
\centering
\begin{tabular}{lcccccc}
\hline
\textbf{Trend} & \textbf{Compound} & \textbf{Compound:prt} & \textbf{Flat} & \textbf{Fixed} & \textbf{AFL} & \textbf{Other MWE}\\
\hline
\ Increasing & 60 & 15 & 20 & 7 & \textbf{149} & 61 \\
\ Decreasing & \textbf{437} & \textbf{181} & \textbf{84} & \textbf{40} & 13 & \textbf{365} \\
\ No trend & 128 007 & 3 895 & 18 781 & 630 & 309 & 48 146 \\
\hline
\ Total & 128 504 & 4 091 & 18 885 & 677 & 471 & 48 572 \\
\hline
\end{tabular}
\caption{\label{diachronic_association}
Mean Association values trends for each class of MWEs in the RSC. In bold are highlighted the highest values comparing increasing and decreasing trends.
}
\end{table*}

% AFL - 34
%Fixed - 7
%Flat - 0.6
%Other MWE - 0.9
%Compound:prt - 5
%Compound - 0.4

\begin{table*}
\centering
\begin{tabular}{lll}
\hline
\textbf{MWE Class} & \textbf{Increasing Trend} & \textbf{Decreasing Trend} \\
\hline
\ compound & \textit{North Carolina}, \textit{University College}, & \textit{os ilium}, \textit{radius vector}, \\ 
\ & \textit{Great Britain} & \textit{os sacrum} \\
\ compound:prt & \textit{depend upon}, \textit{carry out}, \textit{break down} & \textit{set down}, \textit{taken out}, \textit{let loose} \\
\ flat & \textit{St. Petersburgh}, \textit{red deer}, \textit{J. D.}  & \textit{Dr. Johnson}, \textit{Thomas Barker}, \\
\ & & \textit{James Stirling} \\
\ fixed & \textit{of course}, \textit{no doubt}, \textit{whether or not} &  \textit{as if}, \textit{some other}, \textit{it is} \\
\ AFL & \textit{should be noted}, \textit{the other hand}, & \textit{of the same}, \textit{and if you}, \\
\ & \textit{on the other hand} & \textit{a kind of} \\
\ Other MWE & \textit{prime minister}, \textit{at first sight}, \textit{give rise} & \textit{at variance}, \textit{inmost recesses}, \\
\ & & \textit{in all likelihood} \\
\hline
\end{tabular}
\caption{\label{trend_ex}
Top-3 MWEs per class with increasing and decreasing trends in terms of mean association value. 
}
\end{table*}

Besides having the highest percentage of statistically valid trends, AFL is the only class for which the amount of MWEs with an increasing trend is higher than the decreasing one. As previously explained, AFL MWEs were identified in corpora of academic English using specific metrics, therefore, they correspond to formulaic expressions specific to this register, similar to RSC. 

Table~\ref{trend_ex} presents, for each class, the three MWEs with the highest rate of increase and decrease of the mean value of association measures. These results show that, in the evolution of scientific writing, specific lexical groups regarding this domain became more fixed, thus, indicating a conventionalization process. For the other classes, changes are less significant and the predominance of decreasing trends can be due to the MWEs' semantic characteristics. Compound, flat, and some Other MWEs usually refer to entities, thus related to the evolution of research topics and their terminology. On the other hand, the decrease observed in phrasal verbs and fixed MWEs could be related to a tendency of standardisation in terms of lexical choices, with some specific elements from these classes being preferred over the others. 

\section{Conclusions and Future Work}
\label{sec:sum}
We presented a multifaceted approach to identify MWEs in scientific English for  analysing their evolution from the mid-17th century. Our approach uniquely combines three distinct methods:\ (1) Universal Dependency annotation, which was key in uncovering syntactic structures of MWEs, (2) Partitioner, segmenting texts to detect MWEs effectively, and  (3) the Academic Formulas List, which further enriched our analysis by providing a benchmark for MWEs used in the scientific context. Our methodology went beyond identification; we used tools like Kullback-Leibler Divergence for dispersion analysis and various association measures to characterise MWEs (cf.\ \citet{gries2022multi}). This revealed their dynamic nature and evolving roles in scientific discourse. Some MWEs adapted over time, reflecting changes in scientific language, while others remained consistent, signifying their entrenched role in scientific communication.

Our findings not only enhance understanding of MWEs in scientific English but also pave the way for future linguistic research, particularly in language evolution and specialized registers. We currently work on integrating MWEs in word embeddings to classify them semantically and model their temporal dynamics in terms of productivity. Also, we intend to compute surprisal of MWEs to link up with processing explanations (e.g. \citet{SIYANOVACHANTURIA2017111,bhattasali-etal-2020-modeling}).

\section*{Acknowledgements}

This research is funded by \textit{Deutsche Forschungsgemeinschaft} (DFG, German Research Foundation) – Project-ID 232722074 – SFB 1102.

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