Quarkonia production in (ultra-)peripheral PbPb collisions at LHCb

Xiaolin Wang on behalf of the LHCb collaboration

<EMAIL_ADDRESS>
South China Normal University, Guangzhou, China

Presented at DIS2022: XXIX International Workshop on Deep-Inelastic Scattering
and Related Subjects, Santiago de Compostela, Spain, May 2-6 2022.

###### Abstract

The cross-sections of coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
and $\psi{(2S)}$ production in ultra-peripheral PbPb collisions at a nucleon-
nucleon centre-of-mass energy of $5.02\,\mathrm{TeV}$ are measured using a
data sample collected in 2018 at LHCb, and the differential cross-sections are
measured separately as a function of transverse momentum and rapidity. The
photo-production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons at
low transverse momentum is studied in peripheral PbPb collisions,
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates are reconstructed
through the prompt decay into $\mu^{+}\mu^{-}$ in the rapidity region of
$2.0<y<4.5$. These results significantly improve previous measurements and are
compared to the latest theoretical predictions.

##  1 Introduction

The LHCb detector is a single-arm forward spectrometer covering the unique
pseudorapidity range $2<\eta<5$ [1, 2], which could provide precise vertex
reconstruction, high particle momentum resolution and excellent particle
identification ability. The quarkonia production in (ultra-)peripheral
collisions is sensitive to the gluon parton distribution function in nuclear
at small-x, and coherent photo-production would provide an excellent
laboratory to study the nuclear shadowing effects and the initial state of
quark-gluon plasma with small-x at the LHC [3].

##  2 Study of charmonium production in ultra-peripheral PbPb collisions at
LHCb [4]

Ultra-peripheral collisions(UPCs) occur when the distance between the center
of two nuclei is larger than the sum of their radii [5]. The two ions interact
via their cloud of semi-real photons and photon-nuclear interactions dominate.
The basic process is electromagnetic and strong interactions are suppressed.
In UPCs, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$
mesons are produced from the colourless exchange of a photon from one nucleus
and a pomeron from the other. Coherent production occurs when the photon
interacts with a pomeron emitted by the entire nucleus, which is the process
we are going to study.

The charmonium candidates are reconstructed through the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$
and ${\psi{(2S)}}\rightarrow{\mu^{+}\mu^{-}}$ decay channels, using 2018 PbPb
data sample corresponding to an integrated luminosity of $228\pm
10\,\mathrm{\mu b}^{-1}$. The signal yields are extracted in two steps. First,
a fit on the dimuon invariant mass spectrum is needed to estimate the
charmonium and non-resonant background yields within the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ mass windows,
respectively. The mass distribution along with the dimuon mass fit is shown in
Fig 1.

Fig. 1: Dimuon mass distribution fit for signal candidates in the rapidity
range $2.0<y^{*}<4.5$.

Then fits to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ or $\psi{(2S)}$
$\ln(p_{\mathrm{T}}^{*2})$ distributions are performed to determine the
coherent production events from the yields in corresponding mass windows,
where the starred notation indicates that the observable is defined in the
nucleus-nucleus centre-of-mass frame. Figure 2 shows the fits to the
$\ln(p_{\mathrm{T}}^{*2})$ distributions of selected
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ candidates
within rapidity interval $2.0<y^{*}<4.5$. The shapes of coherent, incoherent
and $\psi{(2S)}$ feed-down components are taken from simulation, and the shape
of non-resonant background is taken from the mass window,
$3.2<m_{{\mu^{+}\mu^{-}}}<3.6\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, where
there is no signal component. The yields of the non-resonant background are
determined as the integral of the non-resonant component from the dimuon mass
fit in the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$
mass windows.

${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$

$\psi{(2S)}$

Fig. 2: The $\ln(p_{\mathrm{T}}^{*2})$ distribution fit of dimuon candidates
in the $2.0<y^{*}<4.5$ range for (left) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ candidates and (right) $\psi{(2S)}$ candidates.

The results of coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\psi{(2S)}$ differential cross-sections as a function of rapidity and their
ratio are calculated in five rapidity bins and shown in Fig. 3. The
differential production cross-sections as a function of transverse momentum
are also measured separately and shown in Fig. 4. We also compared the results
between experimental measurements and theoretical predictions [6, 7, 8, 9, 10,
11, 12, 13, 14, 15].

Fig. 3: Differential cross-section as a function $y^{*}$ for coherent
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ , $\psi{(2S)}$ production and
the ratio of coherent $\psi{(2S)}$ to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ production, compared to theoretical predictions. These models are
grouped as (red lines) perturbative-QCD calculations and (blue lines) colour-
glass-condensate models.

Fig. 4: Differential cross-section as a function of $p_{\mathrm{T}}^{*}$
within the rapidity range $2<y^{*}<4.5$ for coherent (left)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and (right) $\psi{(2S)}$
production compared to theoretical predictions.

Also, there are two previous results of coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production in PbPb UPCs by the
LHCb [16] and ALICE [17] experiments. Compared with above measurements, we see
this new result is slightly larger than the previous LHCb result by around
2$\sigma$ and more compatible with the ALICE measurement.

Fig. 5: Differential cross-sections as a function of rapidity for coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production compared to the
previous measurements by the LHCb [16] and ALICE [17]. The measurements are
shown as dots and squares, where the uncertainties represent total
uncertainties respectively. Then both results are compared to theoretical
predictions [8, 9, 10, 11, 12, 13, 6, 7, 15, 14].

##  3 Study of J/$\psi$ photo-production in PbPb peripheral collisions at
$\sqrt{s_{NN}}=5\text{\,Te\kern-1.00006ptV}$[18]

In peripheral collisions, the impact parameter b is less than the sum of
radii, so there is not only photo-nuclear interaction but also hadronic
interaction. The photo-produced ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
is expected to have a very low transverse momentum of less than 300
$\text{\,Me\kern-1.00006ptV\\!/}c$, whereas the hadronic produced
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ typically have transverse
momentum of about 1-2 $\text{\,Ge\kern-1.00006ptV\\!/}c$. Thanks to the high
precision of the LHCb experiment, the very low $p_{\mathrm{T}}$ region can be
explored and the number of photo-produced
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ could be extracted, as shown in
Fig. 6.

Fig. 6: The $\ln(p_{\mathrm{T}}^{*2})$ distribution of dimuon candidates in
the $2.0<y^{*}<4.5$ range for (left) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ candidates and (right) $\psi{(2S)}$ candidates. The data are overlaid
with the result of the fit.

The differential photo-production yields of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ versus the rapidity, the number
of participants in the collision, and the double-differential
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ photo-production yields versus
transverse momentum as shown in Fig. 7, and are compared to theoretical
calculations. One scenario does not consider the destructive effect due to the
overlap between the two nuclei, whereas the other takes it into account. The
two theoretical curves do not show a significant difference because the
collisions are peripheral. This nuclear overlapping effect is expected to
increase at more central collisions. The trend between
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ photo-production measurements
and theoretical predictions are consistent in general.

Fig. 7: The results of the differential photo-production yields of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ versus the rapidity, the number
of participants in the collision and the double-differential
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ photo-production yields versus
transverse momentum.

##  4 Conclusion

The cross-sections of coherent J/$\psi$, $\psi$(2S) production, and their
ratio in UPCs are measured using the 2018 PbPb dataset. It is the first
coherent $\psi{(2S)}$ measurement in forward rapidity region for UPC at LHC
and the first time to measure the coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ production
cross-sections versus $p_{\mathrm{T}}$ distribution in PbPb UPCs. The
measurement of photo-produced ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mesons in peripheral PbPb collisions using the 2018 dataset is the first
result using PbPb hadronic collisions data by the LHCb and also the most
precise coherent photoproduced ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
measurement to date.

## References

  * [1] LHCb Collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [2] LHCb Collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [3] S. P. Jones, A. D. Martin, M. G. Ryskin, and T. Teubner, _Exclusive $J/\psi$ and $\Upsilon$ photoproduction and the low $x$ gluon_, J. Phys. G43 (2016) 035002, arXiv:1507.06942
  * [4] LHCb collaboration, _Study of coherent charmonium production in ultra-peripheral lead-lead collisions_ , arXiv:2206.08221
  * [5] C. A. Bertulani, S. R. Klein, and J. Nystrand, _Physics of ultra-peripheral nuclear collisions_ , Ann. Rev. Nucl. Part. Sci. 55 (2005) 271, arXiv:nucl-ex/0502005
  * [6] V. Guzey, E. Kryshen, and M. Zhalov, _Coherent photoproduction of vector mesons in ultraperipheral heavy ion collisions: Update for run2 at the CERN Large Hadron Collider_ , Phys. Rev. C93 (2016) 055206, arXiv:1602.01456
  * [7] V. Guzey, M. Strikman, and M. Zhalov, _Accessing transverse nucleon and gluon distributions in heavy nuclei using coherent vector meson photoproduction at high energies in ion ultraperipheral collisions_ , Phys. Rev. C95 (2017) 025204, arXiv:1611.05471
  * [8] V. P. Gonçalves and M. V. T. Machado, _Vector meson production in coherent hadronic interactions: an update on predictions for RHIC and LHC_ , Phys. Rev. C84 (2011) 011902, arXiv:1106.3036
  * [9] J. Cepila, J. G. Contreras, and M. Krelina, _Coherent and incoherent $\mathrm{J/}\psi$ photonuclear production in an energy-dependent hot-spot model_, Phys. Rev. C97 (2018) 024901, arXiv:1711.01855
  * [10] B. Z. Kopeliovich, M. Krelina, J. Nemchik, and I. K. Potashnikova, _Heavy quarkonium production in ultraperipheral nuclear collisions_ , arXiv:2008.05116
  * [11] V. P. Gonçalves et al., _Color dipole predictions for the exclusive vector meson photoproduction in $pp$, $p\mathrm{Pb}$, and $\mathrm{Pb}\mathrm{Pb}$ collisions at run2 LHC energies_, Phys. Rev. D96 (2017) 094027, arXiv:1710.10070
  * [12] V. P. Gonçalves and M. V. T. Machado, _The QCD pomeron in ultraperipheral heavy ion collisions: IV. Photonuclear production of vector mesons_ , Eur. Phys. J. C40 (2005) 519, arXiv:hep-ph/0501099
  * [13] H. Kowalski, L. Motyka, and G. Watt, _Exclusive diffractive processes at HERA within the dipole picture_ , Phys. Rev. D74 (2006) 074016, arXiv:hep-ph/0606272
  * [14] H. Mäntysaari and B. Schenke, _Probing subnucleon scale fluctuations in ultraperipheral heavy ion collisions_ , Phys. Lett. B772 (2017) 832, arXiv:1703.09256
  * [15] T. Lappi and H. Mäntysaari, _Diffractive vector meson production in ultraperipheral heavy ion collisions from the color glass condensate_ , PoS DIS2014 (2014) 069, arXiv:1406.2877
  * [16] LHCb collaboration, R. Aaij et al., _Study of coherent $J/\psi$ production in lead-lead collisions at $\sqrt{s_{NN}}=5TeV$_, arXiv:2107.03223
  * [17] ALICE collaboration, S. Acharya et al., _Coherent J/ $\psi$ photoproduction at forward rapidity in ultra-peripheral Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=5.02$ TeV_, Phys. Lett. B798 (2019) 134926, arXiv:1904.06272
  * [18] LHCb collaboration, R. Aaij et al., _$J/\psi$ photoproduction in Pb-Pb peripheral collisions at $\sqrt{s_{NN}}$= 5 TeV_, Phys. Rev. C 105 (2022) L032201, arXiv:2108.02681


# Employing distributional semantics to organize task-focused vocabulary
learning

Haemanth Santhi Ponnusamy Detmar Meurers
University of Tübingen, Germany
<EMAIL_ADDRESS>

###### Abstract

How can a learner systematically prepare for reading a book they are
interested in? In this paper, we explore how computational linguistic methods
such as distributional semantics, morphological clustering, and exercise
generation can be combined with graph-based learner models to answer this
question both conceptually and in practice. Based on the highly structured
learner model and concepts from network analysis, the learner is guided to
efficiently explore the targeted lexical space. They practice using multi-gap
learning activities generated from the book focused on words that are central
to the targeted lexical space. As such the approach offers a unique
combination of computational linguistic methods with concepts from network
analysis and the tutoring system domain to support learners in achieving their
individual, reading task-based learning goals.

##  1 Introduction

Learning vocabulary is a major component of foreign language learning. In the
school context, initially vocabulary learning is typically organized around
the words introduced by the text book. In addition to the incrementally
growing vocabulary lists, some textbooks also provide thematically organized
word banks. When other texts are read, the publisher or the teacher often
provides annotations for new vocabulary items that appear in the text. A wide
range of digital tools have been developed to support such vocabulary
learning, from digital versions of file cards to digital text editions
offering annotations.

While such applications serve the needs of the formal learning setting in the
initial foreign language learning phase, where the texts that are read are
primarily chosen to systematically introduce the language, later the selection
of texts to be read can in principle follow the individual interests of the
student or adult, which boosts the motivation to engage with the book. Linking
language learning to a functional goal that someone actually wants to achieve
using language is in line with the idea of Task-Based Language Teaching (TBLT)
as a prominent strand of foreign language education [Willis and Willis, 2013].

Naturally, not all authentic texts are accessible to every learner, but
linguistically-aware search engines, such as FLAIR [Chinkina and Meurers,
2016], make it possible to identify authentic texts that are at the right
reading level and are rich in the language constructions next on the
curriculum. Where the unknown vocabulary that the reader encounters in such a
setting goes beyond the around 2% of unknown words in a text that can be
present without substantial loss of comprehension [Schmitt et al., 2011], many
digital reading environments provide the option to look up a word in a
dictionary. Yet, frequently looking up words in such a context is cumbersome
and distracts the reader from the world of the book they are trying to engage
with. Relatedly, one of the key criteria of TBLT is that learners should rely
on their own resources to complete a task [Ellis, 2009]. But this naturally
can require pre-task activities preparing the learner to be able to
successfully tackle the task [Willis and Willis, 2013]. But how can a learner
systematically prepare for reading a text or book they are interested in
reading?

In this paper, we explore how computational linguistic methods such as
distributional semantics, morphological clustering, and exercise generation
can be combined with graph-based learner models to answer this question both
conceptually and in practice. On the practical side, we developed an
application that supports vocabulary learning as a pre-task activity for
reading a self-selected book. The conceptual goal is to automatically organize
the lexical semantic space of any given English book in the form of a graph
that makes it possible to sequence the vocabulary learning in a way
efficiently exploring the space and to visualize this graph for the users as
an open learner model [Bull and Kay, 2010] showing their growing mastery of
the book’s lexical space. Lexical learning is fostered and monitored through
automatically generated multi-gap activities [Zesch and Melamud, 2014] that
support learning and revision of words in the contexts in which they occur in
the book.

In section 2 we discuss how a book or other text chosen by the learner is
turned in to a graph encoding the lexical space that the learner needs to
engage with to read the book, and how words that are morphologically related
as word families [Bauer and Nation, 1993] are automatically identified and
compactly represented in the graph (2.1.1). In section 3 we then turn to the
use of the graph representation of the lexical semantic space of the book to
determine the reader’s learning path and represent their growing lexical
knowledge as spreading activation in the graph. In section 4, the conceptual
ideas are realized in an application. We discuss how the new learner cold-
start problem is avoided using a very quick word recognition task we
implemented, before discussing the content selection and activity generation
for practice and testing activities. Section 5 then provides a conceptual
evaluation of the approach and compares it with related with, before wrapping
up with a conclusion in section 6.

##  2 Constructing a graph for the lexical space of a book: a structured
domain model

Going beyond the benefits of interactivity and adaptivity of individualized
digital learning tools, supporting learner autonomy is known to be important
for boosting motivation and self-regulation skills [Godwin-Jones, 2019]. This
includes the choice of reading material a learner wants to engage with, where
the texts prepared by a teacher or publisher cannot reflect the interests of
individual students, the topics and genres they want to explore in the foreign
language. The freedom of choosing a text that the learner wants to engage with
also identifying a clear functional goal for learning vocabulary – learning
new words to enable us to read a text of interest, so that the interest in the
content coincides with the interest in further developing the language skills.
In that sense learning vocabulary becomes a pre-task activity in the spirit of
task-based language learning. Organizing vocabulary learning in this way also
helps turn the otherwise open-ended challenge of learning the lexical space of
a new language to the clearly delineated task of mastering a sub-space. This
functionally guided approach contrasts with the approach of other vocabulary
learning tools selecting random infrequent lexical items from the language to
be learned, which given their rare and often highly specialized nature are
likely to only be useful for impressing friends when playing foreign language
scrabble.

To make text-driven vocabulary learning work, we need to map the text selected
by the learner into a structured domain to support systematic and efficient
learning of the lexical space as used in the book. We distinguish the process
of structuring the vocabulary used in the book, independent of the learner’s
background, from the representation of the individual learner’s knowledge. The
former is tackled in this section and can be regarded as our domain model,
while the latter is a learner model that essentially is an overlay over the
domain model, and will be discussed in section 3.

Since vocabulary learning is about establishing form-meaning connections, in
principle the basic unit best suited for this would be word senses. At the
same time, full automatic word sense disambiguation is complex, error prone,
and often domain specific – and in the context of a given book, a given word
will often occur with the same meaning. We therefore limit ourselves to only
disambiguating homographs in terms of their part-of-speech, following ?).
Throughout our approach, we therefore use $<$word, POS$>$ pairs as basic
units. To POS annotate the book selected by the user, we use the Spacy NLP
tools (http://spacy.io). Given our focus on learning the characteristic
vocabulary of the book, we eliminate stop words as well as word-POS pairs
appearing less than five times in the given book.

###  2.1 Semantic and thematic relations

To structure the lexical space in terms of meaning, there are two related
options. Words can be _semantically related_ , for example, tiger, lion,
elephant, and crocodile all have the property of being wild animals, on from
the perspective of a WordNet, they are hyponyms of wild animal. On the other
hand, words can also be _thematically related_ , such as blackboard, teacher,
and chalk all belonging to a school theme. ?) highlights the benefits of the
semantic approach over the thematic approach from the perspective of a tutor.
As we are building a system that acts like a tutor tracking and fostering the
learner’s vocabulary knowledge, we decided to focus on semantic relatedness.

####  2.1.1 Word families

Complementing the lexical semantic relationships, words are also related to
each other through derivational and inflectional morphology. Many of these
morphological processes are semantically transparent. ?) proposed the idea of
grouping words into so-called _word families_ stating that “once the base word
or even a derived word is known, the recognition of other members of the
family requires little or no extra effort”. The creation of word families is
based on criteria involving frequency, regularity, productivity and
predictability of all the English affixes. ?) arranged the inflectional
affixes and common derivational affixes into the graded levels, as exemplified
on the left-hand side of Figure 1.

2 |  | develop
---
develops
developed
developing
| wood
---
wood’s
woods
wooded
| bright
---
brighter
brightest
3 |  | developable
---
undevelopable
developers(s)
undeveloped
| woody
---
woodiest
woodier
woodiness
| brightly
---
brightish
brightness
4 |  | development(s)
---
developmental
developmentally
|
5 |  | developmentwise
---
semideveloped
antidevelopment
wooden | brighten
6 |  | redeveloped
---
predevelopment
anti-wooden |

Figure 1: A word family example [Bauer and Nation, 1993] and an expanded
family node in our graph

We adopt the idea of word families to compactly represent morphologically
related words. The graph on the right side of Figure 1 exemplifies the word
family that becomes visible when selecting the lemma _dream_ in our graph
representation (where word families normally are shown in collapsed form and
represented by their underlying lemma). We currently collapse words belonging
to any of the levels into one word family, though in the future one could
chose to collapse only those levels that are semantically most transparently
connected.

###  2.2 Generating a lexical graph of word families and their semantic
relations

To structure the lexical space of the user selected book in terms of a
semantically related word graph, we start with a distributional semantic
vector representation of each word, which we obtain from the pre-trained model
of GloVe [Pennington et al., 2014] based on the co-occurrence statistics of
the the words form a large Common Crawl data-set (http://commoncrawl.org).

On this basis, the relationship score between the families are computed to be
the maximum of pair-wise cosine similarity score of all its members. Let
${F_{1}}$ be a family with ${m}$ members and ${F_{2}}$ be a family with ${n}$
members. The relationship score between the two family ${F_{1}}$ and ${F_{2}}$
is the maximum of cosine similarity score of all ${m\times n}$ pairs, as
spelled out in Figure 2.

$w_{12}=\max_{i\in F_{1};j\in F_{2}}\frac{V_{i}*V_{j}}{\|V_{i}\|\|V_{j}\|}$

where, ${w_{12}}$ is the cosine similarity between the families ${F_{1}}$ and
${F_{2}}$

Figure 2: Formula for computing relationship between families and a resulting
example

In this way, we create a fully connected network of word families, as
exemplified in the figure. The families with members that are closer in the
semantic vector space are connected with higher weights.

Following ?), the number of edges in the graph can be computed as
$e=\frac{n\times(n-1)}{2}$, where $e$ is the total number of edges and $n$ is
the number of nodes or families in the graph. The number of edges in the graph
thus grows exponentially as the number of node increases.

When inspecting graphs derived for sample texts, we observe the majority of
the connections are weak. To obtain a graph of semantic relationships that
meaningfully structure the vocabulary used in a book, we focus on stronger
relationship and eliminate edges with weights less than 0.3.

We also observed that the node families of very frequently occurring verbs
tend to be very densely connected, and this impact of frequency on
distributional semantic measures has been discussed in the literature [Patel
et al., 1998, Weeds et al., 2004]. In order to control for this kind of over-
sensitivity of distributional semantic measures for highly frequent words, we
restrict the node degree to a maximum threshold, which based on experiments
with sample data we set to five. So for each node, only the five edges with
the highest weight are retained.

As a result of the method described in this section, we obtain a lexical graph
for the user-provided text that structures and compactly represents the
lexical space of the text in a graph-based domain model. This is the lexical
space that the user wants to explore and master enough to be able to read the
book. In terms of computational linguistic methods, on the one hand,
distributional semantics creates the overall structure of a meaning-connected
lexical space, on the hand, word families organize and collapse forms that are
related by morphological processes in the linguistic system.

###  2.3 Example generation of graphs for books

To test the graph construction, we chose three books as a sample to study the
characteristics of the vocabulary space created by our application: (a) Twenty
Thousand Leagues Under the Sea by Jules Verne, (b) Harry Potter and the
Sorcerer’s Stone by J. K. Rowling and (c) A Game of Thrones: A Song of Ice and
Fire by George R. R. Martin. Table 1

Book title |  Unique words |  Learning targets |  Graph nodes |  Graph edges |  Graph size
---|---|---|---|---|---
Twenty Thousand Leagues Under the Sea |  10k |  1.7k |  1.3k |  3.3k |  18 MB
Harry Potter and the Sorcerer’s Stone |  6.5k |  1.2k |  1k |  2.4k |  13 MB
A Game of Thrones: A Song of Ice and Fire |  14k |  3.7k |  2.5k |  5.6k |  35 MB
Table 1: Characteristics of the graphs derived for vocabulary space for three
books

indicates the size of the text and the graph created for each book. We see
that 15–25% of the words from the text qualifies as the lexical learning
targets. 20–30% of those collapse into a family encoded by a graph node. The
average connections a family has with other families is around 2.5. The
algorithm thus seems to work as expected for these sample books. Some example
word family clusters formed for these books at a threshold of similarity
scores greater than 0.7 are shown in Figure 3, with only the root nodes of
each family being displayed here.

Figure 3: Example family clusters from the graphs resulting for the sample
books

##  3 Representing the lexical knowledge of a learner: an open learner model

With a structured domain model established for the vocabulary space to be
explored by the user, we want to make use of it to efficiently guide the
learner to cover the space and track learning in a learner model. The learner
model is an overlay on the domain model that helps us track the learner’s
vocabulary knowledge in terms of a mastery score associated with each word
family. On the basis of the learner model, we then can propose the next set of
words to be practiced in a way that reduces the number of interaction required
to cover the vocabulary space. It also serves as an open learner model [Bull
and Kay, 2010] by allowing the user to view and explore the lexical space of
the book as a graph, with each node being colored according to the current
mastery score. In this section we discuss how this is achieved.

###  3.1 Central node selection for efficient exploration of the vocabulary
graph

Identifying the nodes that are more central than others is one of the vital
task in network analysis [Freeman, 1978, Bonacich, 1987, Borgatti, 2005,
Borgatti and Everett, 2006]. ?) formulated three major centrality measures for
a node in a network: (a) _degree centrality:_ Measure of strength of ties of
each nodes in the network, (b) _closeness centrality:_ Measure of closeness of
a node to all other nodes in the network, and (c) _betweenness centrality_ :
Measure of cardinality (number of elements) of a set S, the set of shortest
paths of other node pairs in the network that passes through a node.

The degree centrality measure is a greedy approach looking only at the
immediate neighbours to decide the central node, whereas the closeness
centrality measure accounts for the bigger picture of the entire network. So
closeness centrality seems best suited for our goal of efficient coverage of
the network, in our case: the graph representing the vocabulary of the given
book. However, closeness centrality cannot as such be applied to networks with
disconnected components – which is problematic since we may well obtain
networks with many disconnected components due to the pruning of weak links
discussed in the previous section. Fortunately, ?) proposes an improved
formula that also works for such graphs. Based on this metric, we choose the
top 20 words for a learning session.

Selecting the next words to be learned based on closeness centrality brings up
the problem that neighbors that are tightly bound to the central node are
likely have a similar closeness centrality score. So when selecting the words
to be practiced only based on closeness centrality, we would risk practicing
closely related lexical items rather than systematically introducing the
learner to the broader lexical space. In order to avoid this issue, we exclude
the immediate neighbours of a word that was selected from that learning
session. The resulting approach supports a more distributed selection of
words, as illustrated by Figure 4 showing an example with highlighted central
nodes selected for the next learning session.

Figure 4: A lexical graph for a book with highlighted central nodes selected
for the next learning session

###  3.2 Mastery scores and updating them in the graph to capture learning

Each node in the graph is associated with a mastery score ranging from 0 to 1,
with 1 indicating that the learner masters the word. We initialize the master
score of each node with 0.5 and interpret this as a middle ground, where the
model is uncertain about the learner’s knowledge about that word.

The mastery score is updated based on the learner responses in the learning
activities. To address this bottleneck that the system is tied to such a thin
stream of evidence about the learner’s lexical knowledge, we make use of the
fact that the learner model is based on a network of semantically related word
families. We use this to spread some activation from a word where the learner
has shown mastery to semantically closely related words to indicate that this
word is more likely to also be known.

Let $r$ be the learner response for a learning activity involving a word from
the family ${F_{i}}$. Then the update to its mastery ${m_{i}}$ is updated
using $\Delta m_{i}=m_{i}*\alpha*r$. The update to the mastery score of its
immediate neighbours is weighted based on the similarity score between the
families $\Delta m_{j}=m_{j}*(\beta*r*w_{ij})$ where ${m_{j}}$ is the mastery
score of ${F_{j}}$, a neighbouring family of ${F_{i}}$ attached with a edge
weight of ${w_{ij}}$. ${\alpha}$ and ${\beta}$ are tune-able parameters for
the magnitude of an update. ${r\in\\{-1,+1\\}}$ indicate the polarity of the
learner’s response, $+1$ for the learner responding correctly and $-1$ an
incorrect response.

Figure 5 provides a close-up view of the graph with enlarged nodes
highlighting the nodes selected for a learning activities.

Figure 5: A close-up view of a learner model showing nodes selected for
practice

The figure also illustrates the color representation of the mastery level and
the spreading activation to neighboring nodes. Initially all nodes are grey,
corresponding to mastery level of 0.5 that has not yet been touched during
learning. The closer the level gets to 1, the more green the node appears, and
the closer to 0, the more red. A node the user has sometimes shown mastery for
and sometimes not so that it returns to the 0.5 level is shown in yellow.

While the colored visualization of the lexical space serves as an open learner
model allowing learners to inspect the current state of their knowledge in
relation to the lexical demands of the book, the mastery level also plays a
role in the selection of the next words to be practiced. Words with a mastery
level over 0.8 are no longer selected. In the future, we plan to add a
component that takes into account memory decay and the so-called spacing
effect [Sense et al., 2016] to optimize when a word is selected again.

##  4 Putting it all together in an application

###  4.1 A warm start for the learner model

Given that we are targeting learners beyond the beginner stage, it is
important to determine their vocabulary knowledge to avoid a cold start of the
learner model. We do not want to start from a blank slate since that requires
many interactions with the system until the learner model reflects the
learner’s lexical competence – a time during which the system cannot optimally
select the words to be learned next.

To avoid this cold start problem, we implemented a short web-based vocabulary
Yes/No test, which has long been used for vocabulary estimation [Sims, 1929,
Tilley, 1936, Goulden et al., 1990].The participants are provided with a
checklist of words and the user has to select whether they know the word or
not. While there is a rich literature on the test and various adjustments have
been proposed to counter its weaknesses as a competence diagnostic [Meara and
Buxton, 1987, Beeckmans et al., 2001, Huibregtse et al., 2002, Mochida and
Harrington, 2006], for our goal of allowing learners to quickly initialize
their learner model, it is very well suited.

The words included in the test are selected from the graph using the same
central node selection approach we introduced in section 3.1, and the
mechanism spreading activation to related nodes discussed in section 3.2
allows the system to make additional use of the information from the fast
initial test.

###  4.2 Activity generation: practicing and testing in the target context

Content creation for vocabulary learning activities typically is a task
requiring human effort so that adapting the material to individual learners’
language competence and interests is beyond the reach of traditional methods.
To overcome this limitation, we generate activities based on the target text
for which the user wants to acquire the vocabulary. While there are multiple
activity types one could consider, we implemented multi-gap activities [Zesch
and Melamud, 2014], given that they make it possible for the learner to engage
with a word using several sentence contexts drawn from the targeted book.
Given the frequency threshold used in constructing the domain model graph,
there are at least five sentence for each word in the book. We rank sentences
to determine which sentences are best out of context. Fortunately this issue
has been addressed in lexicography, where authentic sentences are used in
dictionaries to illustrate word usage. ?) developed GDEX, a method to identify
sentences that are well-suited to illustrate word meaning within a single
sentence context. GDEX considers factors such as the sentence length, use of
rare words and anaphora, target word occurrence in main clauses, sentence
completeness, and target word collocations towards the end of sentences.
Sentence length and rare word usage are the highly weighted features. We
adapted GDEX for our purpose of ranking sentences for vocabulary learning
activities and customized the rare word feature to reflect the individual
learner’s vocabulary knowledge as recorded in the learner model.

Learning and testing in the system is conducted in sessions. Each session
consists of the top 20 central nodes from the learner model that are below the
mastery score threshold. Multi-gap activities consisting of three to four
sentences in which the target word chosen from the central node word family
occurs are used for both learning and testing. The sentences are initially
shown with the occurrences replaced by a blank. For each activity four lexical
options are provided, the target word and three distractors chosen from the
vocabulary space of the book as discussed below. Figure 6 shows an example
activity targeting the word family _scowl_ in a learning session for the book
”A Game of Thrones: A Song of Ice and Fire”, after the correct word was
selected by the learner.

Figure 6: An example activity

In the learning mode, the learners are provided with learning aid such as
dictionary look-up, translations, and word usage examples from within and
outside the targeted book. The mastery scores in the learner model are not
updated during training mode. In the testing mode, no such support is provided
and the master score for the target family and its neighbours are updated
based on the user responses.

Distractor generation is a critical part of multi-gap learning activities. If
the distractors are randomly selected or heterogeneous in linguistic
characteristics such as POS, this can make it easy to choose the right option
for the given sentence contexts. We instead are interested in distractors that
require more cognitive effort to discriminate, actively engaging the learner
with the different sentence contexts. We base the distractor selection on the
learner model. As this graph is built to encode semantically-related words
near each other, many of the immediate neighbours are (near) synonyms so that
there is a substantial danger of them fitting the gaps. By experimenting with
different node distances, we found that choosing second neighbours as
distractors that have the same POS as the target word works best. We are also
considering combining the distractor generation based on the learner model
with other distractor generation strategies discussed by ?).

##  5 Conceptual Evaluation and Related Work

Given the nature of the approach we presented, the evaluation and comparison
with related work has to evaluate conceptual advances and put them into
context. Our approach can be characterized by the following aspects: First,
the user can select what they want to learn the vocabulary for; they pick the
text of the book they want to be able to read, i.e., the functional task goal.
Second, the system automatically creates a domain model graph representing the
lexical semantic space to be learned. Third, a learner model is created as an
overlay of the domain model graph and records the mastery of the concepts by
the learner, with updates to the learner model spreading activation through
the graph to indirectly activate related concepts as a way to avoid explicit
interaction for every word. Fourth, it determines in which order the words can
be learned in such a way that the lexical space is efficiently explored,
prioritizing the words that are central nodes. Fifth, the system compactly
represents word families to allow the visualization and open learner model to
be concise and usable with minimal number of interactions. Sixth, the system
supports learning of the words using multi-gap activities using sentences
drawn from the authentic context of the book to be learned.

Putting this approach into context of the related work on vocabulary learning,
there is a large number of applications designed to support vocabulary
learning – though, as we will see, the above characteristics clearly seem to
set our approach apart from what is offered in this domain.

Foreign language textbooks systematically provide a list of vocabulary items
per chapter and there are many specialized or general file card applications
for memorizing these sentences including _Phase-6.de_ , _Quizlet.com_ , or
_Ankiweb.net_. Other applications offer more language-related functionality.

_Lextutor_ (https://lextutor.ca) is a website offering a collection of tools
to learn vocabulary using lexical resources such as frequency-based vocabulary
lists and corpus data. _List learn_ supports learners in choosing words from
frequency-based word lists and work with corpus concordances. _Grouplex_ lets
the learner select from a 2k crowd-sourced word list and practice them in
fill-in-the-blank activities, with hints based on dictionary definition and
POS tags. _Flash_ employs cards showing words on one side and lexical support
on the other. Apart from word meaning and usage, _MorphoLex_ supports learning
regular inflectional and derivational affixes based on the word family levels
of ?). Other lextutor tools target reading texts with support from
concordances and dictionaries. _Resource assisted reading_ lets the user
choose a pre-processed book, but _Hyper text_ allows the learner to upload
their own text. While lextutor offers a variety of tools and corpus resources,
none of them offer personalized learning, performance tracking, or structured
vocabulary spaces.

_Memrise.com_ is a flashcard based de-contextualized commercial vocabulary
learning application focused on beginners, with learning units grouped by
theme with little freedom for the learner to choose contents of interest.
_Duolingo.com_ is a strictly guided application supporting the users to learn
foreign language using various learning activities offering some gamification
elements but no personalized vocabulary learning for texts or domains of
personal interest. _Vocabulary.com_ is a gamified free vocabulary list
learning application that lets learners choose from collections and the
literature to practice the words in multiple choice questions activities to
choose the correct meaning phrase for the given word usage. The literature
only is a source of vocabulary though, it is not used as testing context or
learning goal, and the vocabulary domain is not semantically structured or to
construct a structured learner model. _Cabuu.app_ supports learning of
vocabulary lists scanned from books by associating each item with gestures.

Overall, while there is a rich landscape of applications supporting vocabulary
learning, the six characteristics of the method presented in this paper set
our approach apart – especially the use of distributional semantic methods to
create a graph representation for any book or text the user wants to read, to
efficiently organize and individually support and track the learning in this
lexical space.

##  6 Conclusion

In this paper, we discussed the methodological basis and realization of a tool
allowing the learner to systematically learn the lexical material needed to be
able to read a book they are interested in. Automatically structuring the
lexical space and sequencing the learning is achieved through distributional
semantic methods, the automatic identification of word families, and concepts
from network analysis. The graph-based domain model that is automatically
derived from the given book serves as the foundation of a learner model
supporting the selection of an efficient learning path through the lexical
space to be acquired. Multi-gap activities are automatically generated from
the targeted book and used for practice and testing activities.

In addition to self-guided learning for people interested in reading specific
books, which may be particularly useful in the context of so-called intensive
reading programs, the approach is particularly well-suited for the English for
Specific Purposes context, where both the language and the particular content
domain are of direct importance. Given this kind of integration of language
and content learning, a similar affinity exists to so-called Content and
Language Integrated Learning [Coyle et al., 2010].

## References

  * [Bauer and Nation, 1993]  Laurie Bauer and Paul Nation.  1993\.  Word families.  International journal of Lexicography, 6(4):253–279.
  * [Beeckmans et al., 2001]  Renaud Beeckmans, June Eyckmans, Vera Janssens, Michel Dufranne, and Hans Van de Velde.  2001\.  Examining the yes/no vocabulary test: Some methodological issues in theory and practice.  Language Testing, 18(3):235–274.
  * [Bonacich, 1987]  Phillip Bonacich.  1987\.  Power and centrality: A family of measures.  American journal of sociology, 92(5):1170–1182.
  * [Borgatti and Everett, 2006]  Stephen P Borgatti and Martin G Everett.  2006\.  A graph-theoretic perspective on centrality.  Social networks, 28(4):466–484.
  * [Borgatti, 2005]  Stephen P Borgatti.  2005\.  Centrality and network flow.  Social networks, 27(1):55–71.
  * [Bull and Kay, 2010]  Susan Bull and Judy Kay.  2010\.  Open learner models.  In Advances in intelligent tutoring systems, pages 301–322. Springer.
  * [Chinkina and Meurers, 2016]  Maria Chinkina and Detmar Meurers.  2016\.  Linguistically-aware information retrieval: Providing input enrichment for second language learners.  In Proceedings of the 11th Workshop on Innovative Use of NLP for Building Educational Applications (BEA), pages 188–198, San Diego, CA. ACL.
  * [Coyle et al., 2010]  Do Coyle, Philip Hood, and David Marsh.  2010\.  Content and language integrated learning.  Ernst Klett Sprachen.
  * [D’Angelo and West, 1997]  John P D’Angelo and Douglas B West.  1997\.  Mathematical thinking.  Problem Solving and Proofs.
  * [Ellis, 2009]  Rod Ellis.  2009\.  Task-based language teaching: Sorting out the misunderstandings.  International journal of applied linguistics, 19(3):221–246.
  * [Freeman, 1978]  Linton C Freeman.  1978\.  Centrality in social networks conceptual clarification.  Social networks, 1(3):215–239.
  * [Gholami and Khezrlou, 2014]  Javad Gholami and Sima Khezrlou.  2014\.  Semantic and thematic list learning of second language vocabulary.  CATESOL Journal, 25(1):151–162.
  * [Godwin-Jones, 2019]  Robert Godwin-Jones.  2019\.  Riding the digital wilds: Learner autonomy and informal language learning.  Language Learning & Technology, 23(1):8–25.
  * [Goulden et al., 1990]  Robin Goulden, Paul Nation, and John Read.  1990\.  How large can a receptive vocabulary be?  Applied linguistics, 11(4):341–363.
  * [Huibregtse et al., 2002]  Ineke Huibregtse, Wilfried Admiraal, and Paul Meara.  2002\.  Scores on a yes-no vocabulary test: Correction for guessing and response style.  Language testing, 19(3):227–245.
  * [Kilgarriff et al., 2008]  Adam Kilgarriff, Milos Husák, Katy McAdam, Michael Rundell, and Pavel Rychlỳ.  2008\.  Gdex: Automatically finding good dictionary examples in a corpus.  In Proceedings of the XIII EURALEX international congress, pages 425–432. Universitat Pompeu Fabra Barcelona, Spain.
  * [Meara and Buxton, 1987]  Paul Meara and Barbara Buxton.  1987\.  An alternative to multiple choice vocabulary tests.  Language testing, 4(2):142–154.
  * [Mochida and Harrington, 2006]  kira Mochida and Michael Harrington.  2006\.  The yes/no test as a measure of receptive vocabulary knowledge.  Language Testing, 23(1):73–98.
  * [Patel et al., 1998]  Malti Patel, John A Bullinaria, and Joseph P Levy.  1998\.  Extracting semantic representations from large text corpora.  In 4th Neural Computation and Psychology Workshop, London, 9–11 April 1997, pages 199–212. Springer.
  * [Pennington et al., 2014]  Jeffrey Pennington, Richard Socher, and Christopher D Manning.  2014\.  Glove: Global vectors for word representation.  In Proceedings of the 2014 conference on empirical methods in natural language processing (EMNLP), pages 1532–1543.
  * [Schmitt et al., 2011]  Norbert Schmitt, Xiangying Jiang, and William Grabe.  2011\.  The percentage of words known in a text and reading comprehension.  The Modern Language Journal, 95(1):26–43.
  * [Sense et al., 2016]  Florian Sense, Friederike Behrens, Rob R. Meijer, and Hedderik van Rijn.  2016\.  An individual’s rate of forgetting is stable over time but differs across materials.  Topics in Cognitive Science, 8(1):305–321.
  * [Sims, 1929]  Verner Martin Sims.  1929\.  The reliability and validity of four types of vocabulary tests.  The Journal of Educational Research, 20(2):91–96.
  * [Tilley, 1936]  Harvey C Tilley.  1936\.  A technique for determining the relative difficulty of word meanings among elementary school children.  The Journal of Experimental Education, 5(1):61–64.
  * [Wasserman et al., 1994]  Stanley Wasserman, Katherine Faust, et al.  1994\.  Social network analysis: Methods and applications, volume 8.  Cambridge university press.
  * [Weeds et al., 2004]  Julie Weeds, David Weir, and Diana McCarthy.  2004\.  Characterising measures of lexical distributional similarity.  In Proceedings of the 20th international conference on Computational Linguistics, page 1015. Association for Computational Linguistics.
  * [Wilks and Stevenson, 1998]  Yorick Wilks and Mark Stevenson.  1998\.  The grammar of sense: Using part-of-speech tags as a first step in semantic disambiguation.  Natural Language Engineering, 4(2):135–143.
  * [Willis and Willis, 2013]  Jane Willis and David Willis.  2013\.  Doing task-based teaching-Oxford handbooks for language teachers.  Oxford University Press.
  * [Zesch and Melamud, 2014]  Torsten Zesch and Oren Melamud.  2014\.  Automatic generation of challenging distractors using context-sensitive inference rules.  In Proceedings of the Ninth Workshop on Innovative Use of NLP for Building Educational Applications, pages 143–148, Baltimore, Maryland, June. Association for Computational Linguistics.