# History-enhanced ICT For Sustainability education: Learning together with
Business Computing students.
††thanks: The research was part-funded by the Royal Historical Society through
the award of a Jinty Nelson Teaching Fellowship 2023-24 to the research team.

Ian Brooks  School of Computing and Creative Technologies
University of the West of England
Bristol, UK
<EMAIL_ADDRESS>Laura Harrison  School of Arts
University of the West of England
Bristol, UK
<EMAIL_ADDRESS>Mark Reeves  School of Arts
University of the West of England
Bristol, UK
<EMAIL_ADDRESS>Martin Simpson  School of Arts
University of the West of England
Bristol, UK
<EMAIL_ADDRESS>Rose Wallis  School of Arts
University of the West of England
Bristol, UK
<EMAIL_ADDRESS>
###### Abstract

This research explores the use of History to enhance education in the field of
ICT For Sustainability (ICT4S) in response to a challenge from the ICT4S 2023
conference. No previous studies were found in ICT4S but the literature on
History and Education for Sustainable Development is reviewed. An ICT4S
lecturer collaborated with History lecturers to add an historic parallel to
each week’s teaching on a Sustainable Business and Computing unit for final
year undergraduate BSc Business Computing students. A list of the topics and
rationale is provided. Student perceptions were surveyed before and after the
teaching and semi-structured interviews carried out. A majority of students
saw relevance to their degree and career. There was an increase in the
proportion of students with interest in History. The paper explores the
lessons learned from the interdisciplinary collaboration, including topic
choice, format and perceived value. The project has enhanced the way we
approach our subjects as computing and history educators. We believe this is
the first empirical, survey-based study of the use of history to enhance ICT4S
education. The team will extend the research to a larger unit covering a wider
range of computing degrees.

###### Index Terms:

Sustainable Development, Social Implications of Technology, Humanities –
History, Education, Curriculum Development, ICT For Sustainability, ICT4S,
Education for Sustainable Development

##  I Introduction

What role can History play in the teaching of ICT For Sustainability (ICT4S)?
The question was raised in the ICT4S EDU educators workshop in June 2023. A
roundtable discussion surfaced the following questions and observations: What
would be the purpose of using History in ICT4S? To see the errors of the past
and not reproduce them. To question what is understood as progress. To learn
from past experiences looking for similarities and wisdom. To develop a theory
of change. To see how things could be different. To teach sufficiency. How to
engage Computer Science students with History? Using discussion and parallels.
Establishing the value of historical understanding to their career. To
recognise when they might be involved in developing exploitative systems (How
would I know if I was building a slave ship?). To use place-based examples
e.g. Bristol Slavery / Tobacco / Armaments. To use technical examples e.g.
history of automobiles and society, Industrial Revolution, Printing. To use
databases e.g. Slave Voyages [1], Legacies of British Slavery [2]. What
challenges might ICT4S educators face and how could these be addressed? Lack
of expertise, knowledge and vocabulary. Working with Historians,
Anthropologists, STS (Science and Technology) scholars. Some specific sources
and authors were mentioned [3, 4, 5, 6].

One of the authors of this paper participated in that workshop and had
observed on the basis of several years of teaching ICT4S [7] it appeared that
many students could benefit from a greater awareness of how society has been
different and how it has changed. In other words, a greater knowledge of
history might help students appreciate the nature of change needed toward a
more sustainable economy and society. This paper sets out initial findings of
a pilot on the use of History in ICT4S teaching in a UK university, the
University of the West of England. One of the authors designed and teaches the
unit Sustainable Business and Computing, a mandatory unit for 3rd year
undergraduate students on the BSc Business Computing programme. The unit is an
eleven-week taught course with three hours per week contact time, which has
been running every Autumn since 2020. The unit learning objectives are as
follows and an overview of the unit by week can be found in table 1.

  1. 1.

Demonstrate a detailed knowledge and understanding of the concepts and
competing definitions of a sustainable business.

  2. 2.

Evaluate companies’ sustainability using the Global Reporting Initiative
framework.

  3. 3.

Analyse the negative impacts of ICT on sustainability.

  4. 4.

Discuss in detail case examples of the role of ICT in delivering
sustainability benefits.

The first six weeks introduce general concepts of sustainability, business
impacts and reporting. The remaining weeks focus on the sustainability impacts
of computing. The unit makes extensive use of the United Nations Sustainable
Development Goals as a framing of sustainability and the Hilty & Aebischer
(2015) Lifecycle – Enabling – Systemic (LES) model for ICT4S impacts [8].

Following the ICT4S EDU 2023 workshop, the unit leader collaborated with the
co-authors who are all Historians in the same university. We were introduced
through the University’s Knowledge Exchange for Sustainability Education
(KESE) group, which has a representative from every Department. The aim was to
explore in practice how History teaching could enhance the existing ICT4S
unit. Teaching ICT4S should help students to build a mental model of the
impacts of technology and a theory of change. An understanding of history may
help students develop a stock of examples of previous technology
implementation and models of the process of societal change.

###  I-A Positionality

The authors are all white British or American academic lecturers /
researchers. The team has a balanced proportion of gender representation. We
recognise the risk of a developed country bias in our work and selection of
historical cases. We welcome criticism from colleagues in countries
experiencing the legacies of colonialism and the opportunity to collaborate on
future iterations of this work.

##  II Background and Related Work

We reviewed the literature for sources which have relevance to the use of
History in teaching ICT4S. Below, we start with an overview of relevant
textbooks and literature from Science and Technology Studies, since it was
specifically mentioned by a participant in the ICT4S EDU workshop, and from
the History field. We then offer a review of the academic literature
specifically covering both History and Education for Sustainable Development
(ESD) based on keyword searching. Lastly we review the relevant professional
guidance applying to Higher Education in the UK.

The academic field of Science and Technology Studies (STS), or Science,
Technology and Society, includes topics which are broadly relevant to the
understanding of history and sustainability. Johnson and Wetmore (2021) is a
useful primer on STS and includes leading writers in the field such as Latour
[9]. The readings are likely to be useful in teaching STS specific units but
the book does not write about teaching STS or its use in ESD. Journals such as
Science, Technology and Society are also a valuable source. However, it has
only published one paper which mentions ESD, this is in the context of
discussing UNESCO’s Encyclopedia Life Support Systems (UNESCO-EOLSS) [10].
There are a number of papers which discuss the STS curriculum including [11]
which emphasises the connection with the History of Technology and the
importance of historical context. There are a number of well-established STS
programmes such as that offered by MIT [12]. So STS sources provide us with
useful context for History in ICT4S education but little which directly
addresses the topic.

History of Computing is a directly relevant sub-field and there are a range of
useful textbooks such as [13]. More recent papers have explored some of the
entanglements of computing with colonial slave economies, such as [14]
exploring the relationship of Babbage’s thinking with plantation operations.
The film Hidden Figures [15] brought a sustainability issue (gender and ethnic
bias) of History of Computing to a wider audience. The History of Computing
potentially provides us with content to include in ICT4S education but
students may already have been taught History of Computing as part of their
course. Also, the parallels for ICT4S may be relatively constrained compared
to a broader field of History.

The field of Environmental History is gaining increasing academic and public
interest, a recent example being [4]. Schama 2021 calls for a ‘deep
environmental history’ which ‘marries natural and human history’ [16, p 324]
and continues “of all our histories, that of the environment is perhaps the
one where past and future most hopefully seed each other.” [16, p 328].

The journal Environmental History has been published by Chicago University
Press since 1996, though its precursor Forest History Newsletter was started
in 1954, and brings together scholars and practitioners from the humanities,
sciences, and social sciences to ‘explore the changing relationships between
humans and the environment over time’. [17]

Recent work, such as All We Want is the Earth: Land, Labour and Movements
Beyond Environmentalism (2023) by Patrick Bresnihan and Naomi Millner,
examines the history of modern environmentalism with a focus on key
interventions made by feminist, anti-colonial, Indigenous, workers’ and
agrarian movements [18]. At a specific local level, Brownlee (2011) provides a
history of the environmental movement in Bristol [19].

Environmental history is a key feature of many undergraduate history courses,
and recent years has seen a proliferation of stand-alone MA programmes in
Environmental Humanities and Environmental History (Bristol, Durham,
Nottingham, Plymouth to name just a few).

Environmental History inevitably deals with the introduction of technologies
and their impact. Frankopan particularly mentions the development of
technology to extract and exploit coal, starting an age of fossil fuels[4].
“By 1850, some 18 million people in Britain used as much energy as 300 million
in China” [4, p 218]. There is also a section on weather modification
technology in the 1950s both for benefit for farmers and as a potential
weapon. Frankopan draws attention to a 1955 article “Can We Survive
Technology?” by Von Neumann on the topic, which stated “All experience shows
that even smaller technological changes than those now in the cards profoundly
transform political and social relationships” [20, p 519]. The technology of
the agricultural ‘green revolution’ is also questioned as it becomes clearer
that it has “significant impacts both on ecosystems and on health” [4, p 273].
However, specific coverage of ICT impacts is sparse. Frankopan does draw
attention to the way in which the digital age has boosted consumption and the
packaging and transportation of parcels [4, p 290].

Turning to a keyword-based literature review, a search for history and ICT4S
on SCOPUS returns only one paper [21] which situates “digital music within a
cultural history of industrialisation” but does not address questions of
education. SCOPUS was chosen as it provides coverage of a wide range of
disciplines and includes a large proportion of IEEE and ACM publications.

So broadening the search, the meta-discipline of ESD should also be useful to
our study. ESD addresses the teaching of sustainability across all disciplines
but for this case we are focused on its application in computing and in
history. A literature review using the search terms “history” AND education
for sustainable development finds 88 sources on SCOPUS (27 Dec 2023). 8 of
these are classified by SCOPUS as being in the Computer Science field. We
imported the SCOPUS data into the Parsifal literature review tool and used
this to coordinate a consistent team review of the literature. The following
is a summary of the themes we identified in this literature.

####  II-1 History IN ESD (16) or History OF ESD (40)

The majority of sources identified in this search were papers about the
history of ESD and its development as a pedagogical approach. There were only
16 papers which related to our interest in the use of History IN ESD. This
topic has attracted little research to date. The following themes were found
within this subset of 16 papers.

####  II-2 Environmental legacies of history

An interesting paper on Invasion Biology discussed teaching around the topic
of invasive species in South Africa. The paper recognises species “were
introduced for a particular use and then established self-sustaining and
expanding populations beyond the area of introduction, where they may have
both positive and negative impacts”[22] but doesn’t take the next step of
giving the historical context for those doing the introduction and their
‘particular use’ [22]. There are clearly teaching opportunities to use the
history of invasive species as an illustration of the development of the
modern world.

####  II-3 Disciplines which lend themselves to ESD teaching

Several papers research the academic fields which are particularly suited to
teaching ESD. These include History and Geography [23], Liberal education,
Civics [24] and Indigenous ways of knowing [25]. There was also a somewhat
inconclusive paper on the History discipline [26]. These are disciplines which
require a critical engagement with the processes of change and with primary
sources. They are described as supporting the “social conscience of their
students, and the promotion of the concept of active citizenship” [23, p 7].

####  II-4 Teaching Teachers

Four of the papers related to the training of teachers to deliver ESD. This
included curriculum mapping [27], interdisciplinary training [28], and
integration into initial teacher training [29]. [23] noted that a significant
obstacle is the integration of new content into an “overpopulated” curriculum.

####  II-5 Local history as a significant lever

A frequent theme is the power of rooting ESD in local history and local lived
experiences [25]. Amongst other approaches, [30] describes the use of old
postcards of the local area for students to research local historical change.
[29] uses family trees as the focus for historical change, particularly
emphasising the female stories. [31] explores local stories and [32] recounts
ESD using history at World Heritage Sites. [33] described the particular
effectiveness of Kominkans (community learning centre) in Okayama, as a non-
formal setting for ESD and for connection to the history of local geographical
features.

####  II-6 Learning from past failures

Two papers specifically mentioned the use of past failures as a spur to
learning – from past local disasters [34] and from sports corruption [35].

####  II-7 Models

There was no common model across the papers. [33] describes their Quintuple
helix model (QHM), [28] uses a ‘Big History’ model from [36] to situate events
in the long sweep of time. [29] uses a feminist methodology with the example
of researching female members in family tree.

####  II-8 Computer Science field

SCOPUS identified eight sources as from the Computer Science subject area.
Only two of these related to use of History IN ESD. [35] used sports websites
as a source of histories of corruption in sports as a foundation for ESD in
anti-corruption. [23] appears to be included because their study of teachers
included 8.6% in a Technology subject but there is no specific analysis
relating to Computer Science.

###  II-A Professional Guidance

As staff in UK Higher Education, we follow the professional guidance of the
Quality Assurance Agency for Higher Education (QAA). The relevant subject
benchmarks in this case are History (2022) [37], Computing (2022) [38] and
Education for Sustainable Development (2021) [39]. Discussion of the relevant
guidance follows.

####  II-A1 QAA Subject Benchmark: History 2022

[37]

The History subject benchmark contains no explicit discussion of the history
of technology or computing. It does discuss the use of ICT for delivering
online history teaching and for assessment e.g. creation of digital history
projects. The benchmark identifies the need for History students to be
proficient in “retrieval, selection, interpretation, analysis and synthesis of
information from extensive datasets, both analogue and digital” [37, p 7].

The benchmark includes three paragraphs on the topic of Sustainability and the
contribution History can make to sustainability and achieving the UN
Sustainable Development Goals (SDGs). There is specific mention of the
contribution of Environmental History but also acknowledgement of public
history, cultural history and economic history. The benchmark includes the
following assertion about the subject:

“history prepares students to meet sustainability needs and challenges through
its inherent attention to issues of change, continuity and causation; its
demand for multi-perspectivity and multi-factorial understanding of events,
issues and problems; its appreciation of the relationships between economic,
political, cultural, social and environmental factors and systems; its ability
to observe processes taking place in more than one place and more than one
time; and its acknowledgement that there are rarely simple answers to
problems.” [37, p 6].

These are clearly attributes which would be beneficial for computing students
learning about ICT4S.

It is worth noting that the Royal Historical Society, the Institute of
Historical Research (IHR) and History UK do not currently have explicit
policies on ESD / sustainability. The Historical Association, the UK national
charity for history, which offers support, resources and events for teachers
(primarily primary & secondary) has done some work in this area, and supports
‘Teaching for Sustainable Futures’, an online professional development
programme for teachers run by the Centre for Climate Change and Sustainability
Education at University College London.

####  II-A2 QAA Benchmark Statement on Computing (2022)

[38]

The Computing benchmark has little explicit discussion of history beyond
“ensuring that case studies used as exemplars or as assessments are drawn from
a diverse range, highlighting global perspectives, featuring diverse cultures
and communities, showcasing the historical and cultural integration of
computing and the diverse people who do computing”. There is a page in the
benchmark devoted to sustainability and ESD. There is also a useful appendix
with two and a half pages of examples of ESD approaches. The sustainability
section states that Computing courses should lead to students developing “core
personal and professional competencies to address the key societal challenges
highlighted by the United Nations Sustainable Development Goals for 2030 in
their future working lives” [38, p 6]. Computing graduates will have an
“appreciation of domain-relevant issues related to sustainable development and
the emergent manner by which these issues might be addressed” [38, p 7].
“Emergent manner” implies a surprisingly reactive approach to sustainability
when an attention to history might enable more robust anticipation of issues.
Besides this, there are also tools available to foster awareness of
sustainability issues e.g. SusAF [40]. Outside of the page and appendix on
sustainability the subject benchmark has relatively little mention of the
topic, indeed amongst the six course outcome categories detailed,
sustainability is only mentioned in one – Professional Practice - which lists
“equality, diversity and inclusion (EDI) and sustainability” amongst a range
of other factors.

####  II-A3 QAA Education for Sustainable Development Guidance 2021

[39]

This guidance states that ESD student skills include “Use historical knowledge
and an understanding of the consequences of past actions to envision how
futures may be shaped” [39, p 25]. The ESD guidance applies as a cross-cutting
issue across all subjects, so it follows that we should be teaching Computing
students so that they acquire this history-oriented skill despite it not being
explicitly mentioned in the Computing subject benchmark.

####  II-A4 The Office for Standards in Education, Children’s Services and
Skills (Ofsted)

, which is responsible for the inspection of school standards in England,
draws attention to the significance of students developing ‘knowledge and
cultural capital’ that “that pupils need to be educated citizens” [41, p 250].
Teaching History can be an important component of acquiring that cultural
capital as discussed in [42].

###  II-B Research Questions

In the light of the ICT4S 2023 challenge and the sparse literature, we set out
the following research questions for our interdisciplinary collaboration to
make a contribution to knowledge concerning use of History in ICT4S education:

RQ1: What historical parallels can be used to enhance the teaching of ICT4S?

RQ2: What relevance do students see in the addition of History to ICT4S
teaching?

##  III Methods

In this section we set out the methods used to undertake the research which
included the recording of online videos, identification of resources for
students and in-class discussion. The impact was evaluated with pre- and post-
surveys, and semi-structured interviews with students. The research plan,
participant information sheets, consent form, survey instrument and semi-
structured interview plan were all submitted to the university’s ethics
committee and approved before the research started. Explicit consent was
obtained from all participants. The surveys, semi-structured interview
questions and participant information sheet are available on Zenodo
https://zenodo.org/doi/10.5281/zenodo.11073804. The following sections set out
the methods used to address each of the research questions.

###  III-A RQ1: What historical parallels can be used to enhance the teaching
of ICT4S?

The ICT4S lecturer provided a summary of the topics taught each week on the
existing Sustainable Business and Computing unit. The Historians proposed
historical parallel topics for each week. These were drawn from the
Historians’ existing areas of specialism in order to reduce the potential
burden of developing new content. After one iteration the list was agreed. The
final topics are listed in Table 1 along with a brief discussion of the reason
for selecting each topic. The first week was an in-person talk from the team
of Historians introducing themselves and the relevance of History to
sustainability. For weeks 2 – 10 individual Historians recorded a 10-15 minute
video introducing students to the specific topic and its relevance to
sustainability. The videos were made available to students via Panopto, the
university’s internal video platform, a few days before the timetabled
lecture. In addition, links were provided to additional readings and sources
on the topic, which were made available via Blackboard the university’s
virtual learning environment. These resources and links are included in the
Zenodo package [43]. Access statistics were set to record the number of
accesses made to the videos and materials. Each week an email announcement was
sent to students with a link to that week’s video and materials. Week 7 had an
additional in-person question session with one of the Historians. The content
was not mandatory for students on the unit and was not part of the assessment
as this was a research project.

The effectiveness of the combined, videos plus in-class, intervention was
tested in a survey of students at the start and end of the unit by an
unprompted recall question about the historical topics students recalled. It
was also tested in semi-structured interviews with a smaller sample of the
students after the end of the unit, which included an unprompted topic recall
question. The semi-structured interviews also included a question on the
student’s view of the effectiveness of the format used to provide the content.

###  III-B RQ2: What relevance do students see in the addition of History to
ICT4S teaching?

Whilst the professional guidance literature is clear about the value and
relevance of History in ESD, we also wanted to understand students’
perceptions of the relevance. The pre- and post- surveys included questions on
perceived relevance of the History content to student’s degree and career, and
their level of interest in history. The semi-structured interviews included
questions about perceived relevance and about whether the content should be
continued for future students on the unit.

Surveys were administered online using Qualtrics and as paper copies in-class
for students who did not complete online. A Qualtrics distribution was used to
align pre- and post- responses so that respondent change in perception could
be measured. Semi-structured interviews were conducted online using MS Teams
with automatically generated transcripts. Errors in the automated transcripts
were corrected by the researchers. Transcripts were then analysed in the NVivo
qualitative research tool to identify themes arising.

##  IV Results and Discussion

###  IV-A Results

This section sets out the results of the questionnaire, semi-structured
interviews and content access statistics. The questionnaire was administered
in October 2023 at the start of the unit teaching and again in December 2023 –
January 2024 after the end of the teaching. Semi-structured interviews were
carried out in December 2023 – January 2024.

####  IV-A1 Questionnaire results

21 students were registered on the unit. 17 students responded to the
questionnaire at start of the unit and 11 respondents (65% of the initial
respondents) after the end of the teaching. Below are the results for each
question. Since the cohort is small we have chosen to report the results in a
qualitative fashion rather than evaluate statistical significance. We have not
differentiated the results between students who watched videos and those who
didn’t since most students saw the Historians in class twice and some of the
video views were anonymous and so the data sets do not match completely.

  * •

Q1 How relevant is a knowledge of history to your degree?

There was a 12 pp increase in the percentage of students rating history as
very relevant to their degree as shown in Figure 1. However, there was no
overall change in the percentage for very or somewhat relevant to their
degree. There was a small shift from somewhat / very irrelevant before to
neutral after (6 pp). At an individual level the results were mixed with three
students expressing an increased relevance, two finding it less relevant and
the majority (6) having an unchanged opinion as shown in Figure 2.

Figure 1: Relevance to Degree - All Figure 2: Relevance to Degree - Individual

  * •

Q2 How relevant is a knowledge of history to your career?

There was a very small increase in the percentage of students rating history
as very or somewhat relevant to their career (2 pp) as shown in Figure 3. In
this case there was also a small shift from somewhat / very irrelevant before
to neutral after (6 pp). At an individual level, two students came to see it
as more relevant and three as less relevant as shown in Figure 4.

Figure 3: Relevance to Career - All Figure 4: Relevance to Career - Individual

  * •

Q3 How interested are you in history?

There was a noticeable increase in the percentage of students stating they are
very or somewhat interested in history from 65% before to 73% afterwards as
shown in Figure 5. There was a stronger trend away from somewhat / very
uninterested from 12% before to none afterwards. At an individual level, most
had an unchanged view (8) with 2 more interested and 1 with less interested
than before as shown in Figure 6.

Figure 5: Interest in History - All Figure 6: Interest in History - Individual

  * •

Q4. What historical events are you aware of which are relevant to computing
and sustainability?

In the pre-questionnaire, 5 out of the 7 who answered mentioned events
relating to the history of computing and the internet. In the post-
questionnaire the pattern of responses changed with 6 out of 7 also referring
to broader historical events and the UN SDGs in addition to computing events.

####  IV-A2 Interview results

Semi-structured interviews were carried out with 4 respondents to explore
further the opinions of students. The four students volunteered in response to
an appeal for interviewees, so the sample is self-selecting, may not be
representative and includes students who generally had more engagement with
the history project. The transcripts were analysed using NVivo and the themes
are described below.

  * •

Topics From the eight topics covered in the videos, these are the unprompted
recollections of the participants: What makes a business dirty, the rise of
Environmentalism (Participant 1). Match Girls strike, Slavery abolition, East
India Company, London used to be a very dirty place, Silent Spring
(Participant 2). Dirty Business, East India Company, Match Girls, Medical
Technology (Participant 3). Medical History (Participant 4). Students were
also asked about what other history they would have wanted to hear about.
“What I’d have loved to hear, maybe a bit of history of computing as well.”
(Participant 2). “a lot of World War Two stuff is interesting” (Participant
4).

  * •

History taught on Degree programme Students reported no formal history content
in the first two years of the course. They did mention one lecturer who had
discussed a little history of computing in one unit, though it was not
formally on the curriculum, and they recalled “the history of computers and
how like what the first computer was made and how it was created” (Participant
1). “bits on the history of the web” (Participant 2). “very, very little,
little to none” (Participant 4)

  * •

Format and accessibility When asked about the format there was a range of
opinions. On the length of the videos: “if the videos were longer, it would be
cool” (Participant 1), “I personally don’t mind, but I’ve heard some students
say I would have loved if all of them were shorter.” (Participant 2), “a
longer video would definitely lose my attention” (Participant 4). On videos
versus face-to-face: “I think it’s always better to do stuff in person”
(Participant 1), “, I prefer the face to face” (Participant 4), “a combination
of both would be good” (Participant 2), “I would prefer videos … so we can
watch it back whenever we need to” (Participant 3). One participant complained
that the videos were difficult to access though the University’s systems,
especially if using a phone “It is kind of hard to access, the materials cause
you have to go through like logging in and then clicking blackboard and then
you have to click another link and link and link.” (Participant 1).

  * •

Relevance to degree In discussing the relevance of the History content to
their degree programme, students noted: “the green IT one I think it was like
the rise of environmentalism that obviously again that links like I guess you
could say perfectly with the module that it was associated with you know
sustainable business computing that I would say is like I mean to be fair I
would say all of them were all the byte sized like history videos all had like
pretty relevant information that can be linked to that module specifically.”
(Participant 1), “of course it’s primarily relevant to this module we are
doing ’cause that touches on employees’ welfare which is part of the SDGs.
It’s also part touches on environment.” (Participant 2).

  * •

Relevance to career Students expressed views that the content had particular
relevance to their future career choices: “But another thing which I thought
about it’s because we are obviously working for companies whether we like it
or not. So it’s kind of know a history of corporations as a whole. I think
it’s very relevant to my career, at least.” (Participant 2). “I think I’m
gonna link back to the East Indian company. I feel like it got me
contemplating the motivations behind corporate actions, and it also helped me
to brainstorm the kind of companies or the kind of corporations that I would
wanna work for and the exemplary practices that they need to uphold.”
(Participant 3). Participant 4 mentioned that the industry they want to join
has particular ethical risks around technology.

  * •

Should this be continued for future students? “yeah, I think it should be 100%
like implemented not just this module, but like I feel like every module
really should have some elements of linking back to history” (Participant 1).
“I personally think so. But again. I think it’s more relevant for Year 3
’cause we kind of are more equipped to value this” (Participant 2). “Yes,
definitely.” (Participant 3).

  * •

Should it be mandatory? “maybe mandating it could really help some students“
(Participant 2), “if it’s relevant for the assignments, then yeah, but other
than that, I don’t think it should be mandatory” (Participant 4)

It is hard to provide a more concise summary than this comment from
Participant 3: “I believe incorporating the history content into the ICT
education helps us students to gain a comprehensive understanding of the past
and the skills to navigate the future and creating links between ICT and
history helps form a sort of an interdisciplinary approach, which is to
understand the impact of technology on historical events and societal changes
vice versa.”

####  IV-A3 Access to videos and resources

The access statistics for the videos showed low levels of access varying
between 1 and 5 unique student views. The access figures for each video are
shown in Table 1. It is possible for there to be under-counting if students
watched videos together on one device.

###  IV-B Discussion

The following section discusses the results and findings.

####  IV-B1 Relevance of History

The pre- and post- questionnaires showed a small (12 pp) increase in the
percentage of students finding history very relevant to their degree and small
(6 pp) shift from irrelevance towards neutrality. The majority of students did
not change their views which is unsurprising as most students did not watch
the videos. Of those who changed their view, slightly more came to view it as
more relevant to their degree. As one student observed in the semi-structured
interview, the History content was chosen to be relevant to the specific unit.
With respect to relevance to career, there was a small (6 pp) move from
perceived as irrelevant towards neutral and relevant. Again, the majority of
students did not change their view. The interviewees had much more to say in
favour of relevance to career, particularly about how they would consider the
companies they might want to be employed by. This was catalysed by their
learning about the activities of the East India Company. There was a small (12
pp) increase in the level of reported interest in history before and after the
unit.

####  IV-B2 Topics

Interviewees varied in their unprompted recall about the topics taught but
between them they remembered all but two of the topics – Slumming it, The
Nuclear Age. No single topic stood out as having higher recall than others. So
the variety of topics and periods was effective for the diverse interests of
the students. The finding that these students had very little teaching on the
history of computing suggests that this unit ought to include a topic on this
in future runs. The literature reviewed underlines the power of local history
but the selected topics were not particularly local to the university city.
This is an area of potential improvement for future runs of the unit. The
technical hurdles were clearly one reason for the low level of access to the
videos and resources but a larger reason seems to be that the content was
optional and students focus on what is mandatory. There is a bind - low uptake
if voluntary but risks being seen as a “chore” (Participant 1) if mandatory.
The team will reconsider the optional / mandatory choice after running a
similar exercise with a larger student cohort on a different teaching unit.

####  IV-B3 Format

There was not a consistent pattern of responses in the interviews – some
preferring video, some in-class face to face. There was a frustration from one
interviewee about the difficulty of accessing the videos and another only
became aware of the videos towards the end of the unit. Access to the videos
is clearly an issue which we need to improve. We may be able to do this by
including a direct link to the video in the teaching slides which students do
typically access. A student suggested that the videos should be uploaded to
YouTube with unlisted URL but the team are concerned that this would add
burdens of content production and clearance.

####  IV-B4 Reflections by academics

The team members provided reflection on their learning from the collaboration.

The ICT4S academic reported learning about various approaches to
historiography and a sense of the power of primary sources. He was also
trained out of a tendency to ask “what would you have done in that
situation?”. The experience provided a fund of examples of how the world can
be different and how it can be changed. He was surprised that, in a class
discussion, none of the students were aware of the term ‘Luddite’ and their
history, which seems particularly relevant for students on a technology
course. He reflected that thinking about the history of slums and of public
health made him aware that his teaching was often about sustainability impacts
of businesses and that there is gap between that and sustainability of
societies. The collaboration expanded his understanding of the mechanisms and
pace of change e.g. comparing the timescale it took for transatlantic trade in
enslaved peoples to go from acceptable, legal and profitable to unacceptable,
illegal and interdicted, with the timescale it will take for the fossil fuel
industry to go through a similar trajectory [44]. Whilst there is a growing
literature on sustainability in computing education [45, 46] this does not yet
appear to have integrated the power of history into such curricula.

The History academics, reflecting on the experience, reported that the
collaboration has helped them to think more explicitly about how their work
addresses the SDGs – and how History and ESD can mutually enrich one another.
They have thought a lot about how the goals of ESD can be supported by
incorporating History into the curriculum – one key next step might be to
explore the reverse. As a collaborative project this has supported them in
advancing their pedagogical approaches – not only as an additional experience
of communicating history to a broader audience, but in bringing together
different approaches, viewpoints and experiences. They also commented on
encountering an industry with different expectations e.g. finding that the ICT
sector has very low levels of unionisation and that unions are not perceived
as necessary. The Historians also perceived that the anticipated career paths
for computing students were more focused than those of history students. There
was more content in the unit which specifically career-focused. This changed
the nature of discussions about careers and employment expectations.

###  IV-C Answering the Research Questions

In summary, with respect to RQ1: What historical parallels can be used to
enhance the teaching of ICT4S? We used a range of historical parallels which
illuminated topics of direct environmental and social impacts as well as the
actions of individuals, companies and governments. The topics with the highest
unprompted recall were Dirty Business / East India Company, Match Girls
Strike, Medical Technology and the Rise of Environmentalism. Nevertheless, six
out of the 8 topics had unprompted recall. The topics are all from the modern
period when the rapid expansion of technology and limited companies provide
clear parallels with which students can relate. We could have included
parallels from the History of Computing. Reflecting on the literature, we
should have made more use of the local historical context. Concerning RQ2:
What relevance do students see in the addition of History to ICT4S teaching?
The pre- and post- questionnaires showed some perception of relevance to their
degree and career. In the interviews, those students who engaged with the
content expressed positive views about the relevance and discussed how it had
led them to ask more questions about the companies they might work for. They
recommended that the content should be included in future runs of the unit.

The small cohort and low levels of access to the videos and resources mean
that we cannot make strong claims for the findings in this study. However,
those students who engaged with the content found it worthwhile and saw
relevance to their degree and career. The effort to produce the videos was
relatively low, as the Historians were drawing on their existing expertise,
and these resources can be used in future runs of the unit. All members of the
teaching team have found the collaboration has enhanced their teaching in
ICT4S, ESD and History. On this basis we conclude that the project was a
useful contribution to our knowledge and to the students who chose to engage.
It has been a useful pilot with small class size, the research team have
approval to extend the project to another unit - Information, Networks and
Society - with 110 students, which should provide results with more
statistical significance.

###  IV-D Guidance for Implementation

Although this was a pilot exercise with a small cohort, we can formulate some
guidance for ourselves and others considering a similar use of history to
enhance their ICT4S teaching.

####  IV-D1 Seek Historians

Historians bring their training in their discipline and experience in their
period / topic. An interdisciplinary discussion around the unit content should
readily generate relevant historical parallels which address unit learning
objectives.

####  IV-D2 Focus on reuse

Stick to topics where colleagues already have expertise and resources, unless
there is development investment available for new research.

####  IV-D3 Short video, follow-up resources and in-class

A 10-15 minute video can give an overview of the historic topic. Ensure that
students can access the videos as easily as possible. Make readings and
resources available if a student wants to explore further. Adding some in-
class sessions enables interaction and response to students questions and
observations.

####  IV-D4 Local history

Where possible, add local history content to help students identify with the
potential for place-based change.

####  IV-D5 History of Computing

If the student cohort have not already been taught about the history of
computing then consider adding specific computing-related history.

####  IV-D6 Embrace uncertainty and complexity

Computing education often emphasises regularisation, simplification and
deterministic solutions. In contrast, the historical content may show
uncertainty, complexity and multi-factorial change. Embracing these
differences can be of great value for ESD in Computing disciplines.

###  IV-E Threats to Validity

This research was with a small class size (21) so is not generalisable. The
low level of access to the videos and materials means that many students did
not study the History content and only encountered it in the two in-class
sessions. The very small number of interviewees (4) were self-selecting and
cannot be claimed to be representative.

##  V Conclusion and Next Steps

We report on an interdisciplinary research pilot bringing history content into
teaching on ICT4S, specifically an undergraduate unit “Sustainable Business
and Computing”. We believe this is the first empirical, survey-based study of
the use of history to enhance ICT4S education.

Whilst UK subject benchmark statements emphasise the value of History as a
subject in Education for Sustainable Development, a literature review shows no
published papers on using history in ICT4S teaching and very few on History IN
ESD. What little has been published can be summarised along the following
themes: fewer papers about History IN ESD (16) than History OF ESD (40);
environmental legacies of history; History as a discipline which lends itself
to ESD teaching; a quarter of papers were about Teaching Teachers; local
history as a significant lever; learning from past failures; some description
of models used but no clear winner. These topics will inform the next stage of
this research, paying particular attention to the inclusion of local, place-
based history.

A pre and post survey of students on the unit showed that a majority of
students saw relevance of History to their degree and career. There was an
increase in the proportion of students with interest in History. This was a
small cohort and the findings are not statistically significant and are not
generalisable. Semi-structured interviews revealed that some of the
participants found great value from the added historical content and advised
that it should be continued for future runs of the unit. We also found that
there were perceived hurdles to accessing the content which we need to
address. The teaching / research team benefitted from the collaboration and
sharing insights from history, sustainability and computing. The project has
created a set of videos and resources which will be of value to future runs of
the Sustainable Business and Computing unit.

Based on the student feedback and our lessons learned, we believe this pilot
was worthwhile considering the level of effort required to develop the
content. The team will extend the research to a larger unit - Information,
Networks and Society - in order to increase the sample size and range of
Computer Science degrees represented. Based on the findings of the literature
review we encourage ICT4S educators to explore local historical parallels in
their locations. The literature review should be extended to include the
keyword ‘heritage’ as relevant studies do not all use the keyword ‘history’.
We encourage History organisations to address their own contribution to
sustainability.

Sustainability is a field where interdisciplinary working is essential and it
has been a valuable experience for the team to work together, learning from
each other’s discipline, expertise and methods. It has been a privilege to see
History speak to present Business Computing students whose careers will shape
future systems.

##  VI Acknowledgments

We thank the students on the Sustainable Business and Computing unit for their
participation in this research.

TABLE I: Teaching and History topics by week Week |  Sustainable Business and Computing Unit topic |  Historical topic and Reason To add |  Unique Student views of video
---|---|---|---
1 (3 Oct 2023) |  What’s the problem? Introduction to sustainability concepts, definitions and problems. Climate and Ecological Emergency. Reasons for hope. UN Sustainable Development Goals (SDGs). |  Introduction: History & Sustainability |  Live, in-class introduction
2 |  What makes a good business? The pressures on businesses to be dirty - Sordid Sectors, Impatient Investors, Distracting Duties, Vicious Value Chains, Externalised Expenses, Careless Consumers, Dirty Darkness. Pulling the Levers of Change. Sustainability reporting. Global Reporting Initiative (GRI). Greenwash. Critical reading of sustainability reports. |  Dirty Business: Limited Companies and Corporations. Most students in this class (and most people) will work for corporations in their post-graduate careers. Therefore, this session drew students’ attention to the longer history of corporations, including the form’s entanglement with the history of colonialism in South Asia. This is not meant to simplistically disparage corporations in students’ minds, but to encourage them to think carefully about how their potential employers engage with the wider world and how the products students may create may be used and circulated in the global economy. |  3
3 |  Environmental impacts - Climate Emergency. IPCC AR6. Ending burning of fossil fuels. Net Zero, Carbon Management. Scope 1,2 and 3 reporting. GRI305. Comparing carbon footprints. Climate Adaptation. |  The Atlantic Economy and Abolition. This session drew explicit parallels between past moral campaigns centered on international economic activity (against slavery) and current political activism around economic activities central to world trade (e.g., against inequality, for decarbonisation). By looking at concrete datasets such as the Trans-Atlantic Slave Trade database and the Legacies of British Slavery project, students saw the scale of the trans-Atlantic slave trade’s impact on the British economy, and how activist-generated solutions sought to create political and moral change in the face of that economic power. |  3
4 |  Environmental impacts – Ecosystems. Earth system concepts. Safe Operating Space for humanity. Circular Economy. GRI 300 series. |  Dirty Cities: Pollution and the Urban Environment. The aim of this class was to draw a historical parallel by focusing on the impact of industry on Victorian cities (eg. The Great Stink) – but also looking at ideas of pollution in a broader sense, as a moral issue. Students were also introduced to the digitised Charles Booth poverty maps. |  2
5 |  Social impacts. Health, Education, Discrimination. Sustainability motivations and values. Doughnut Economy. GRI 400 series. |  Slumming It: ‘Improving’ the Urban Environment. This topic was another relatively straightforward historical parallel – and discussed the language of ‘slums’ and the process of slum clearance from the 19th century to the present day – highlighting issues of forced evictions and demolitions that have often been carried out in the name of “progress”. Also offered some thoughts about how we might approach the past – looking at the actions of those who enacted slum clearance vs the experience of those who lived and worked in “the slums”. |  5
6 |  Economic impacts. Impacts of inequality. Fair wages / Modern Slavery, Taxation, Corruption. Progress towards SDGs. B Corps. GRI 200 series. |  Women, children and sweated labour. The London Match Girls’ Strike of 1888 was chosen as a direct parallel to modern sweated labour, reminding students that this is not a new mode of production. It was also selected to consider the agency and activism of workers, and particularly those from often marginalised groups – in this instance young women. This was useful as many of the students were unfamiliar with trades unions and considering work in industries where unionisation is low. The case study also raised questions about the cyclical intersection of poverty, consumption, and production. |  1
7 |  Green IT – Hilty & Aebischer LES model. 1st order Climate Impacts of IT. Clean / Dirty Cloud. Energy efficient computing. Sustainable IT market. Tech company Net Zero progress. Adaptation - Climate impacts on IT. |  Silent Spring: The Rise of Environmentalism. The historical content explored the beginnings of the environmental movement – with a focus on Carson’s Silent Spring and the development of Earth Day. |  4\. Additional in-class Q&A session.
8 |  Green IT – Other 1st order / Lifecyle Impacts. Complex supply chains. Mineral sources. WEEE. Circular economy for Electronics. Worker exploitation. |  Make do and Mend. This topic was intended to explore the ‘make do and mend’ campaign during the Second World War. |  No video due to illness
9 |  ICT4S, #Tech4Good, GeSI (Global Enabling Sustainability Initiative). 2nd & 3rd order impacts. IT and decarbonisation. IT for UN SDGs. #Tech4Good market. |  The Medical Revolution. This topic was intended to explore the development of medical knowledge and the practice of medicine in the eighteenth and nineteenth centuries. Different ways of thinking about the history of medicine and asking questions about a linear history of medicine as the development of #Tech4Good were raised. |  2
10 |  #Tech4Bad. Dieselgate, Autonomous Weapons, Gig economy models, Social Media. The Tech that enables dirty businesses e.g. Fossil Fuels. AI X-risk versus current AI harms. Technology Assessment. Responsible Innovation. SusAF. Regulation and remedies. |  The Nuclear Age. This topic was intended to invite thinking about the ‘nuclear age’ inaugurated by the bombing of Hiroshima and Nagasaki. Questions were raised about policy, culture and campaigning, including recent debates about nuclear power as a green non-carbon solution. In this case the #Tech4Good / #Tech4Bad issue is not clear-cut. |  2
11 |  Revision and career opportunities. Working in the sector - employers and jobs. LinkedIn networks. |  No video |

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# Identifying Clusters on a Discrete Periodic Lattice via Machine Learning

Everest Law  Department of Physics & Astronomy and Molecular Computational
Biology Program, Department of Biological Sciences, University of Southern
California, Los Angeles, California 90089, USA

###### Abstract

Given the ubiquity of lattice models in physics, it is imperative for
researchers to possess robust methods for quantifying clusters on the lattice
— whether they be Ising spins or clumps of molecules. Inspired by biophysical
studies, we present Python code for handling clusters on a 2D periodic
lattice. Properties of individual clusters, such as their area, can be
obtained with a few function calls. Our code invokes an unsupervised machine
learning method called hierarchical clustering, which is simultaneously
effective for the present problem and simple enough for non-experts to grasp
qualitatively. Moreover, our code transparently merges clusters neighboring
each other across periodic boundaries using breadth-first search (BFS), an
algorithm well-documented in computer science pedagogy. The fact that our code
is written in Python — instead of proprietary languages — further enhances its
value for reproducible science.

###### keywords:

hierarchical clustering , lattice simulations , breadth-first search ,
periodic boundary conditions

††journal: Computer Physics Communications

PROGRAM SUMMARY

Program Title: Cluster Collector
Licensing provisions: Creative Common by 4.0
Programming language: Python
Nature of problem: Lattice simulations of, say, membrane proteins model the
spatiotemporal organization of a system. In order to extract insights from
such simulations, we need robust methods for identifying clusters of simulated
objects on the lattice.
Solution method: Hierarchical clustering first identifies all potential
clusters. Then, breadth-first search connects together clusters that neighbor
each other across periodic boundaries.

##  1 Introduction

There has long been an interplay between physics and subsets of “machine
learning”, before the latter became widely known outside technical fields. For
instance, clustering methods has been utilized to speed up force calculations
in N-body cosmological simulations [1]. In turn, physics has inspired new
algorithms, such as Super Paramagnetic Clustering (SPC), which was applied to
image classification problems [2]. In general, clustering methods expose
natural classes within data while making as few assumptions as possible. These
methods are well-documented by pedagogical publications [3, 4] and can be
readily adopted by physicists.

This paper will apply hierarchical clustering to discrete lattice systems in
biophysics. These lattices arise when we model the spatiotemporal organization
of cell membrane proteins, the study of which would shed light on synaptic
transmission [5, 6], viral infections [7], and inter-cellular communication
[8] among other areas. In these lattice models, the membrane is discretized
into patches according to specific biophysical considerations [9, 10], with
each patch described by, for instance, a $k-$dimensional vector recording the
amounts of the $k$ chemical species present. Making certain assumptions such
as fast diffusion within each lattice site [9, 10], we can simulate the
system’s (stochastic) time evolution using Gillespie’s algorithm; see [11] for
a recent review.

Given the importance of membrane protein organization, it is vital to develop
techniques for identifying and describing molecular clusters on a simulation
lattice. Hierarchical clustering is one possible choice. To our knowledge,
this technique has first been utilized in membrane biophysics by Shomar _et
al_ [6], who in turn were inspired by a nanoscopy experiment [12]. The MATLAB
clustering code in [6] was published as part of its Supplementary Materials.
Unfortunately, that code does not model diffusion, and therefore does not
correspond to any particular boundary conditions.

Here we present an improved implementation which may be useful to
biophysicists and practitioners of other fields alike. First and foremost,
assuming a diffusive system, our code readily connects together lattice sites
that touch across periodic boundaries. Given the prevalence of periodic
boundary conditions, we believe this is an important feature. Second, our code
is written in Python, which unlike MATLAB is non-proprietary and free-to-use.
As Python becomes one of the most popular programming languages globally
111See for example the 2018 survey on Stack Overflow, a leading forum for
exchanging ideas on software development.
https://insights.stackoverflow.com/survey/2018/, we believe that research code
written in Python is easier to maintain and adopt for other purposes, thus
leading to more reproducible scientific results.

This paper is structured as follows. Section 2 gives an overview of the
hierarchical clustering method. Section 3 describes the 2D lattices to which
our code is applied, and how periodic boundaries are handled. A summary and
conclusion follow in Section 4. All code can be found online at
https://github.com/openerror/PhysicsLatticeClustering.

##  2 Hierarchical Clustering — Theory and Example

###  2.1 Overview of Algorithm

There are many implementations of hierarchical clustering [13, 14], some of
which are parallelized [15, 16, 17]. In this paper we will work with the
_agglomerative_ variant, which forms clusters from the bottom-up — i.e.
starting from single observations [4]. Below we will give a qualitative
overview of the procedure, assuming serial computations, followed by a toy
example.

Assume that we have $N$ observations in a $D$ dimensional space. To begin, we
need a “dissimilarity measure” for quantifying the difference between
observations; Euclidean distance is a common choice, and a natural one when
considering physical separations. With a dissimilarity measure defined, the
algorithm iteratively merges the two observations or _clusters_ that are the
most similar. After $N-1$ steps we obtain a single “megacluster” containing
all the original $N$ observations, and the algorithm terminates.

To make concrete the dissimilarity $d$ between clusters of observations,
various schemes or _linkages_ have been developed. For this work we have
adopted “single” linkage [4]:

$\displaystyle d(u,v)=\textnormal{min}(dist(u[i],v[j])$ (1)

for all points $i$ in cluster $u$ and $j$ in cluster $v$. In other words, we
compute all pairwise dissimilarities between points from $u$ and $v$, take the
minimum, and let that be the dissimilarity between the two clusters.

The next and final step is to extract clusters at a desired scale from the
“megacluster” produced. It involves retaining all clusters that are merged at
a dissimilarity lower than some chosen threshold. To make this more concrete,
we present a toy example below.

###  2.2 An Example

Say we have a 5-by-5 lattice with 6 occupied sites:
$(x,y)=(0,4),(1,1),(2,3),\\\ (2,1),(3,1),(4,4)$. (See Figure 1.) Assume that
sites neighboring each other belong to the same cluster, and that only non-
diagonal neighbors are considered. With the stated criteria, we expect to
obtain 4 clusters.

We can visualize the merger of observations and clusters through a tree-like
“dendrogram”. The leaves nodes at the bottom of the dendrogram represent the
original $N$ observations. As we move up the graph, we see the leaves merging
into new nodes, which may undergo further mergers. The height in the
dendrogram, at which a pair of nodes combine, indicate the dissimilarity
between the nodes.

The dendrogram in Figure 1B is consistent with the hierarchical clustering
described. Going from the bottom to the top, we see that the sites 0, 1, 2,
which are neighboring each other, are first merged together. The 3-member
cluster produced is then merged with the sites at the top left and right
corners successively.

Figure 1: Sample data showcasing hierarchical clustering with single linkage.
A) The 5x5 lattice on which we ran the clustering algorithm; yellow squares
indicate “occupied” sites, and touching sites are considered part the same
cluster. B) Dendrogram tree demonstrating mergers of observations and clusters
throughout the procedure. Leaf nodes indicate single observations, which are
merged at nodes higher in the graph; the vertical height at which nodes are
located represent the dissimilarity between the pair of merged
clusters/observations. C) The six observations, labeled with the same numbers
as the dendrogram leaves.

In order to obtain clusters at the desired scale, we cut the dendrogram
horizontally. Any mergers performed above the cut are ignored, while those
that occur at one level below are retained. For our particular example, any
cut between unity and $\sqrt{2}$ would work, and allow us to identify sites
that touch each other through their “top”, “bottom”, “left” and “right”. In
the end, we obtain four clusters — as expected from the definition of clusters
laid out in the beginning of Section 2.

###  2.3 Sample Code and Required Libraries

For the code that produced Figure 1, please see the Jupyter notebook submitted
with this publication. All functionality presented so far is implemented in
the function detectClusters, located within the file clustering.py. Please see
the docstring under the function declaration for details.

All required Python libraries are listed in requirements.txt; the hierarchical
clustering routines in particular are shipped with the SciPy. Given an
existing Python installation, these libraries can be installed quickly using
the console command.

pip install -r requirements.txt

or through whichever package manager preferred.

##  3 Handling Periodic Boundaries of the 2D Lattice

When simulating large systems, periodic boundaries are commonly adopted to
make computations more tractable. How then can we take into account periodic
boundaries in hierarchical clustering? While it would be costly to modify an
existing implementation directly, we can achieve our goal by processing the
simulation lattice and the clustering output together. The logic is as
follows:

  1. 1.

Identify clusters that are touching the boundary, and determine the
coordinates where the touching occurs.

  2. 2.

For the clusters identified, check if they neighbor each other across the
periodic boundaries.

  3. 3.

If they do, consider the touching clusters as one.

The above logic is implemented in the functions extractClusterCoordinates()
and grouping(), located within clustering.py and grouping.py respectively. The
former function takes the output of detectClusters(), and determines which
clusters touch the boundaries. The data thus processed is then sent into
grouping() to generate the final output. The function grouping() returns a
Python list containing integer tuples, each of which describes a cluster —
merged across periodic boundaries or otherwise.

The integers themselves correspond to each individual cluster identified and
returned by detectClusters(). For identical input data, SciPy’s hierarchical
clustering implementation would give identical cluster IDs. For instance, the
system depicted in Figure 1 corresponds to the output [(0), (1), (2,3)]; 0
corresponds to the 3-member cluster, and (2,3) are the two observations on the
top left and right corners, which would be merged across periodic boundaries.

###  3.1 The Use of Breadth-First Search To Merge Clusters

One non-trivial task that our code has to accomplish is to identify clusters
that are touching “transitively”. For instance, clusters A and C may be
neighbors of cluster B, but they do not touch directly. How then can we
robustly identify all three of them as one single cluster?

To accomplish the task above we have utilized Breadth-First Search (BFS), a
standard technique in computer science. Given a graph comprised of _nodes_ and
(undirected) _edges_ , starting from a given node BFS would find all other
nodes reachable by traversing an edge222For an illustration, see the first
1:40 of https://www.youtube.com/watch?v=0u78hx-66Xk.

Figure 2: Using BFS to identify cluster neighbors from across periodic
boundaries. A) The lattice on which we ran the clustering routines. Clusters 2
and 3 are not neighbors themselves, but they both touch cluster 0 across
periodic boundaries. Therefore all three together are considered as one
cluster. B) Graph representing the connectivities of the clusters in A.
Applying BFS onto this graph, represented as a matrix $C$ in computations,
gives us the connected pieces: (0, 2, 3), (1), (4), (5).

The problem of merging transitively-neighboring clusters can be translated
into a graph-search problem: clusters become “nodes” that connect to their
direct neighbors through “edges”. Given the direct connectivities between each
pair of clusters, we can form a square _connectivity matrix_ $C$, whose height
is the same as the number of clusters. Each entry $C_{ij}=1$ indicates an
“edge” between clusters $i$ and $j$; $C_{ij}=0$ otherwise. For the lattice
presented in Figure 2, the corresponding matrix $C$ is

$\displaystyle\begin{bmatrix}0&0&1&1&0&0\\\ 0&0&0&0&0&0\\\ 1&0&0&0&0&0\\\
1&0&0&0&0&0\\\ 0&0&0&0&0&0\\\ 0&0&0&0&0&0\\\ \end{bmatrix}.$

Since clusters touching do not involve directions, the BFS algorithm is
working with an undirected graph, which leads to a symmetric matrix $C$.
Starting from any given cluster or “node”, BFS would find all other “nodes”
connected to it; repeat for all nodes and obtain the desired output.

Implementation-wise, the function connectedComponents() in BFS.py takes as
input a matrix $C$; it starts at each (unvisited) cluster, and finds all
others connected to it. Finally it returns the groups of connected clusters as
a Python list. This is in fact what grouping() does, _after_ processing its
own input to form the matrix $C$.

For clarity, we present below pseudocode describing the entire procedure
depicted in Sections 2 and 3.

array $\leftarrow$ 2D simulation lattice

if array not binarized then

binarize(array) $\triangleright$ i.e. turns into 1s and 0s, with a
thresholding scheme

end if

HCStats $\leftarrow$ detectCluster(array) $\triangleright$ Performs
hierarchical clustering

$\triangleright$ Determine which clusters touch the boundaries

lattice$\\_$params $\leftarrow$ { ‘sizeY’: lattice height, ‘sizeX’: lattice
width}

cluster_coordinates $\leftarrow$ extractClusterCoordinates(HCStats,

lattice$\\_$params)

$\triangleright$ Obtain tuples of integer clusters IDs

cluster_groups $\leftarrow$ grouping(HCStats)

##  4 Conclusions

To sum up, this paper has solved a common problem in lattice simulations,
using only a combination of standard techniques from machine learning and
computer science. All algorithms used — namely, hierarchical clustering and
breadth-first search — are well-documented, and optimized implementations of
clustering are easily available as pre-built libraries. We hope that our work
would inspire further imports of information-technological techniques into
physics.

Although this paper has only worked on 2D lattices, with a few modifications
the same code can be applied to a rectangular 3D lattice. However, for more
complicated geometries substantial edits would be necessary. In particular, we
may need a new measure for the dissimilarity between observations, in addition
to alternative methods for handling boundary points or even non-periodic
boundary conditions. Non-trivial geometries arise in attempts to accurately
describe molecular diffusion on cellular membranes [18, 19], and present
additional needs for appropriate analytical techniques.

##  5 Acknowledgements

This work was supported by NSF award number DMR-1554716 and the USC Center for
High-Performance Computing. Declarations of interests: none.

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