Cover page
Will AI solve more problems than it generate? This scuplture at airis4D depicts the confusion of the modern
man. Some concerns include:
1. Bias: AI systems can learn and perpetuate biases present in the data they are trained on, leading to
discriminatory outcomes and unfair decisions.
2. Job displacement: Automation through AI can lead to job loss in certain industries, potentially creating
economic and social challenges.
3. Privacy and security: AI systems may collect and analyze massive amounts of personal data, raising
concerns about privacy and data security.
4. Safety and ethical concerns: Autonomous AI systems may raise questions about accountability and
decision-making in critical situations.
5. Disinformation and manipulation: AI can be used to create sophisticated fake content, leading to misin-
formation and manipulation of public opinion.
Managing Editor Chief Editor Editorial Board Correspondence
Ninan Sajeeth Philip Abraham Mulamootil K Babu Joseph The Chief Editor
Ajit K Kembhavi airis4D
Geetha Paul Thelliyoor - 689544
Arun Kumar Aniyan India
Jorunal Publisher Details
Publisher : airis4D, Thelliyoor 689544, India
Website : www.airis4d.com
Email : nsp@airis4d.com
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i
Editorial
by Fr Dr Abraham Mulamoottil
airis4D, Vol.1, No.8, 2023
www.airis4d.com
Recently, I was invited to give a talk on the ethical perspectives of AI at the Zacharias Memorial Lectures
at the Pontifical Institute of Theology and Philosophy, Alwaye, Kerala, India. My talk was titled “Ethical
AI and Responsible Humanity”. Artificial Intelligence (AI) has emerged as one of the most transformative
technologies o f the 21st century, with the potential to revolutionize our lives. However, as AI continues to
advance, it becomes crucial to address its ethical implications and ensure the responsible development and use
of AI systems. The talk explored the concept of ethical AI and the role of responsible humanity in shaping
the future of technology. The talk delved into the importance of understanding AI’s impact, the need for
ethical frameworks, and the global conversation surrounding AI regulation. The talk emphasized the ethical
responsibility towards the ”Other,” highlighting the need for compassionate and empathetic treatment of every
individual, including AI entities (The summary of the talk is included in this edition).
This 8th Edition of airis4D Journal starts with the article ”Difference Boosted Neural Network (DBNN)
- Part 3” by Blesson George discussing the applications and performance of the Difference Boosted Neural
Network (DBNN) in various problem domains. DBNN is a network based on Bayes’ theorem and was developed
in the 2000s to overcome the limitations of the Naive Bayes classifier by imposing conditional independence
and introducing the difference-boosting method. The article concludes that DBNN is a robust and flexible tool,
particularly well-suited for handling structured information and multiple features in complex datasets. The
exceptional performance of DBNN in various domains, including astronomy, makes it a preferred option for
data analysis and classification tasks.
The article ”From Information Overload to Clarity: The Power of Text Summarization” by Jinsu Ann
Mathew discusses the importance and applications of text summarization in today’s information-heavy digital
age. The article explores different types of text summarization methods based on the input type, including
single-document summarization and multi-document summarization. The article highlights the advantages of
text summarization in saving time and effort for readers and researchers by providing concise and relevant
information. It finds applications in various fields, including news aggregation, research papers, and customer
support chatbots. In the upcoming article, the author will delve into the techniques of extractive and abstractive
summarization and explore more insights and strategies to master the art of text summarization.
The article ”Black Hole Stories-3” by Ajit Kembhavi, an emeritus Professor at the Inter-University Centre
for Astronomy and Astrophysics (IUCAA) and the Principal Investigator of the Pune Knowledge Cluster,
discusses the detection of a lone black hole through gravitational microlensing. It explains how the phenomenon
of gravitational bending of light, as predicted by Albert Einstein’s theory of gravity, can be used to identify distant
black holes. The author concludes by highlighting the significance of ongoing observations with telescopes like
the Nancy Grace Roman Space Telescope and the Rubin Observatory LSST, which are expected to discover
many more lone black holes through gravitational microlensing events.
The article ”Unveiling the Cosmic Drama: The Fascinating Journey of Stellar Evolution” by Robin Jacob
Roy, explores the remarkable life cycle of stars, from their birth to their eventual fate. Stellar evolution,
influenced by gravity, nuclear reactions, and other fundamental forces, spans millions to billions of years. Stars
begin their journey as immense giant molecular clouds collapse under gravity, forming protostars. Throughout
the stellar life cycle, remnants of previous stars and interstellar gas and dust become stellar nurseries for new star
formation, perpetuating the cosmic dance of creation and destruction. Understanding stellar evolution not only
deepens our appreciation of the universe but also provides insights into our own existence as stardust beings in
this vast cosmos.
Sindhu G’s article ”Light Curves of Variable Stars” explores the significance and application of light
curves in the field of variable star astronomy. Light curves are graphs that depict the changes in brightness or
luminosity of astronomical objects over a specific period of time. They play a crucial role in understanding
the nature and behavior of variable stars, which are celestial objects whose brightness changes over time
in periodic, semi-regular, or irregular patterns. Understanding light curves and studying variable stars have
significant implications for astronomers in gaining insights into stellar properties, such as size, mass, and age,
and contributing to the broader understanding of stellar evolution and the universe.
The article ”The Tree of Life: Unraveling the Earth’s Evolutionary Tapestry through Phylogenetic Trees”
by Geetha Paul, explores the significance of phylogenetic trees in understanding the evolutionary relationships
between different organisms. Phylogenetic trees, also known as evolutionary trees or cladograms, visually repre-
sent the interconnectedness and diversification of living organisms on Earth. These trees are constructed based
on the principles of common ancestry, where closely related species are grouped, showing their evolutionary
lineage back to a common ancestor.
Finally, Ninan Sajeeth Philip’s article ”Fractals - Nature’s Building Block” discusses the significance of
fractal geometry in understanding natural phenomena and explores how fractals can be used as building blocks
for creating natural structures. Fractals are self-similar patterns that are recursive in nature and are commonly
observed in various aspects of nature. Overall, the article emphasizes the importance of fractal geometry in
understanding natural structures and phenomena. The provided Python codes offer a practical approach to
creating and exploring fractal patterns using the Turtle library and transformation equations.
iii
Contents
Editorial ii
I Artificial Intelligence and Machine Learning 1
1 Difference Boosted Neural Network(DBNN) - Part 3 2
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Performance of DBNN in tabular data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 DBNN in astronomy studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Transient classification in LIGO data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 From Information Overload to Clarity: The Power of Text Summarization 6
2.1 Single Document Summarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Multi-Document Summarization: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Domain-Specific Summarization: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Query-Based Summarization: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Generic Summarization: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Understanding the Support Vector Machine Algorithm 12
3.1 Linear Separability of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Margin and Support Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Quadratic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4 Soft Margin Classifier for Non Linearly Separable Problems . . . . . . . . . . . . . . . . . . 15
3.5 Kernel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
II Astronomy and Astrophysics 17
1 Black Hole Stories-3 18
1.1 The Detection of a Lone Black Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2 Gravitational Microlensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3 A Black Hole Lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4 Nature of the Lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5 A Different Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Unveiling the Cosmic Drama: The Fascinating Journey of Stellar Evolution 25
2.1 Birth of a Star . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 Main Sequence Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Evolution into Red Giant/Supergiant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 The Fate of Low-Mass Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 The Fate of High-Mass Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Stellar Nurseries and Star Formation Repeating the Cycle . . . . . . . . . . . . . . . . . . . . 30
CONTENTS
3 Light Curves Of Variable Stars 31
3.1 What Are Light Curves? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Light Curves Of Classical Cepheids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Light Curves of RR Lyrae stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
III Biosciences 39
1 The Tree of Life: Unravelling the Earth’s Evolutionary Tapestry through Phylogenetic
Trees 40
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.2 Types of Phylogenetic Tree based on topology . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.3 Methods to construct Phylogenetic trees can be classified into two major types. . . . . . . . . 45
1.4 Character-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.5 Limitations of the phylogenetic tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
IV General 49
1 Ethical AI and Responsible Humanity Building the Power of Technology for a Respon-
sible Future 50
V Computer Programming 52
1 Fractals - Nature’s building block 53
v
Part I
Artificial Intelligence and Machine Learning
Difference Boosted Neural Network(DBNN) -
Part 3
by Blesson George
airis4D, Vol.1, No.8, 2023
www.airis4d.com
1.1 Introduction
In the preceding articles, we explored Difference Boosting Neural Network (DBNN) and its key attributes.
The network relies on Bayes’ theorem, which finds wide application in numerous real-world scenarios. In this
current article, we will provide a brief overview of specific problem domains where the DBNN network has
demonstrated exceptional performance.
Artificial Intelligence (AI) experienced significant progress in the 1950s, but its growth was hampered
during the 1970s due to funding constraints and regulatory limitations, leading to what is known as the ”AI
winter.” Despite research resuming in the 1980s, another AI winter occurred in the 1990s. The limitations faced
by highly anticipated expert systems and symbolic AI approaches resulted in reduced investments and interest
in the field, causing many researchers to abandon AI during this period of stagnation. But in 2000s, the AI
research started to boom again and many new methods and networks were developed. There was a sudden surge
in the development of various new algorithms, with CNN (Convolutional Neural Network) algorithms gaining
tremendous popularity and attention. Despite the dominance of deep learning and CNN algorithms, tree-based
algorithms have continued to outperform deep learning methods, particularly in handling tabular data [1]. This
highlights the enduring effectiveness of tree-based approaches in certain contexts, where they surpass more
complex deep learning methods.
In 2000, Dr. Ninan Sajeeth Philip and Prof. Babu Joseph [2] developed the DBNN (Difference Boosting
Neural Network), which effectively addressed the limitations of the Naive Bayes classifier by adopting a
unique approach. While many other methods attempted to relax the conditional independence assumption,
which is fundamental to the Naive Bayes approach, DBNN tackled this challenge by imposing conditional
independence. Additionally, DBNN introduced the difference boosting method, an advancement over existing
boosting algorithms like Adaboost. Consequently, DBNN emerged as an improved version of the NB classifier,
leveraging Bayes’ theorem and delivering promising and favorable results.
1.2 Performance of DBNN in tabular data
The Difference Boosted Neural Network (DBNN) proved to be highly effective in classifying tabular data,
exhibiting comparable classification accuracy to the popular methods available at that time. NS Philip [3]
1.3 DBNN in astronomy studies
conducted a comprehensive investigation, analyzing various datasets to validate the efficacy of DBNN. Notably,
the study also delved into the unique task of English alphabet identification [4].
Furthermore, the inclusion of additional features in DBNN, such as active learning and the ability to predict
the probability of a second result, contributed significantly to the method’s overall success.
1.3 DBNN in astronomy studies
Machine learning (ML) has emerged as a transformative tool in astronomy, revolutionizing the way we
analyze and interpret vast amounts of astronomical data. With the advent of large-scale surveys and advanced
telescopes, astronomers are now generating massive datasets that traditional analysis methods struggle to handle
efficiently. ML techniques have proven invaluable in tasks like object classification, redshift estimation, and
transient detection.
The classification of astronomical objects based on their features saw remarkable success with the im-
plementation of DBNN. DBNN exhibited the ability to distinguish objects even when they shared numerous
overlapping features and differed only in a few aspects.
1.3.1 Star-Galaxy classification
In a study conducted by Philip et al. [5], the DBNN network was applied to perform star-galaxy
classification in the NOAO Deep Wide Field Survey (NDWFS) data. The study compared the results with those
obtained from the widely used tool at that time, called SExtractor. In star-galaxy classification, SExtractor
is employed to differentiate between point sources (stars) and extended sources (galaxies) based on various
morphological and photometric features. It analyzes the object’s shape, size, and brightness distribution to
make this distinction. The outcomes from DBNN were on par with those produced by SExtractor for most
objects. However, DBNN demonstrated superior performance in the case of marginal objects, and it also
provided more accurate prediction probabilities.
1.3.2 Determination of Quasar candidates
Quasars are highly luminous and distant celestial objects, powered by supermassive black holes at their
centers. Detecting and identifying quasar candidates is crucial because quasars provide valuable insights into
the early universe, galaxy formation, and the co-evolution of galaxies and black holes. They also serve as cosmic
beacons, allowing astronomers to study the intervening gas and dust in the universe.
The study done by Abraham et al. [7] and Sinha et al. [8] utilized DBNN for the photometric determination
of Quasar candidates in SDSS7 data. DBNN leveraged 10 independent color information obtained from 5
different filters during the training process. The resulting model exhibited the ability to detect quasars with over
97 % confidence in their true classification. Furthermore, the model proved successful in learning from failed
cases and effectively handling outliers within the dataset.
1.3.3 Photometric catalogue of point sources in Sloan Digitial Sky Survey
A photometric catalog is a comprehensive compilation of photometric measurements, capturing the bright-
ness and colors of celestial objects across different wavelengths. This catalog serves as a valuable resource for
researchers to study and characterize various astronomical objects, including stars, galaxies, quasars, and more.
By providing a standardized and organized collection of data, photometric catalogs facilitate multi-wavelength
studies and time-domain analyses, enabling astronomers to explore transient and variable objects.
3
1.4 Transient classification in LIGO data
Another significant accomplishment of the DBNN network is in the creation of a Photometric catalog of
point sources in the Sloan Digital Sky Survey. In this study [6], color information from confirmed sources was
utilized as features for training the network. DBNN was used as the classifier and predicted the objects to make
the catalogue. The resulting catalog comprised nearly 6 million unresolved detections from the survey. The
algorithm demonstrated impressive performance, recovering 99.96 % of spectroscopically confirmed quasars
and 99.51 % of stars up to i - 21.3 within the studied color window. This study marked a significant advancement
in the understanding and investigation of astronomical objects.
1.4 Transient classification in LIGO data
LIGO holds immense significance in the field of astrophysics and has revolutionized our understanding
of the universe. LIGO’s primary purpose is to detect gravitational waves, ripples in spacetime caused by
the most violent and energetic cosmic events, such as the collision of black holes or neutron stars. This
achievement marked the first direct detection of gravitational waves, confirming a major prediction of Albert
Einstein’s General Theory of Relativity. In the context of LIGO (Laser Interferometer Gravitational-Wave
Observatory), transients refer to short-lived, intense signals that appear in the gravitational wave data. These
signals are typically caused by cataclysmic events in the universe, such as the merger of black holes or neutron
stars, or other violent astrophysical phenomena. Detecting transients in LIGO data is a complex task due to
the presence of various types of noise and instrumental artifacts. Scientists use sophisticated data analysis
techniques, including matched filtering, time-frequency analysis, and machine learning algorithms, to identify
and distinguish genuine transient signals from noise.
Mukund et al. [9] introduced a novel approach for classifying short-duration transients observed in
gravitational waves. Their method employs a hybrid classifier, combining DBNN as a supervised classifier.
The results from the trained classifier demonstrate high prediction accuracy across nine simulated classes of
gravitational wave transients, affirming the success of their proposed method for this task
1.5 Summary
The Difference Boosted Neural Network (DBNN) stands as a robust and flexible tool, finding widespread
applications across diverse domains, including astronomy. Its exceptional performance is evident in data analysis
and classification tasks, especially when dealing with tabular data. DBNN’s proficiency in handling structured
information and accommodating multiple features makes it a preferred option for tackling intricate datasets and
complex tasks.
Bibliography
[1] Grinsztajn, L
´
eo and Oyallon, Edouard and Varoquaux, Ga
¨
el (2022),Why do tree-based models still outper-
form deep learning on typical tabular data?
[2] Philip, Ninan Sajeeth and Joseph, K Babu (2000), Boosting the Differences: A Fast Bayesian classifier
neural network
[3] Ninan Sajeeth Philip, Studies in Artificial Neural Network Modeling
[4] Ninan Sajeeth Philip and K. Babu Joseph (2000), Distorted English Alphabet Identification : An application
of Difference Boosting Algorithm, APS
4
BIBLIOGRAPHY
[5] Ninan Sajeeth Philip, Yogesh Wadadekar, Ajit Kembhavi, K. Babu Joseph(2002),A difference boosting
neural network for automated star-galaxy classification
[6] Abraham, Sheelu and Philip, Ninan Sajeeth and Kembhavi, Ajit and Wadadekar, Yogesh G. and Sinha, Rita
(2011),A photometric catalogue of quasars and other point sources in the Sloan Digital Sky Survey
[7] Abraham, Sheelu and Philip, Ninan Sajeeth (2010), Photometric Determination of Quasar Candidates
[8] Sinha, Rameshwar P and Philip, Ninan S and Kembahvi, Ajit K and Mahabal, Ashish A (2006),Photometric
identification of quasars from the Sloan Survey,Cambridge University Press
[9] Mukund, Nikhil and Abraham, Sheelu and Kandhasamy, Shivaraj and Mitra, Sanjit and Philip, Ninan
Sajeeth(2017) Transient classification in LIGO data using difference boosting neural network, Physical
Review D
About the Author
Blesson George is currently working as Assistant Professor of Physics at CMS College Kottayam,
Kerala. His research interests include developing machine learning algorithms and application of machine
learning techniques in protein studies.
5
From Information Overload to Clarity: The
Power of Text Summarization
by Jinsu Ann Mathew
airis4D, Vol.1, No.8, 2023
www.airis4d.com
In today’s fast-paced digital age, information bombards us from all directions. Whether it’s news articles,
research papers, or business reports, the sheer volume of textual content can be overwhelming. As we strive
to stay informed and make efficient use of our time, the need for effective text summarization has become
paramount.
Imagine being able to distill the essence of a lengthy document into a concise summary, capturing the key
points and omitting the unnecessary details(Figure 1). Text summarization offers us precisely that power—a
way to extract the most important information and present it in a condensed form.
At its core, text summarization is the art of distilling the essence of a text while preserving its meaning . It
involves techniques and algorithms that automatically identify the most relevant sentences, phrases, or concepts
and weave them together into a coherent summary.
The goal of text summarization is twofold: to save time for readers and to enable them to grasp the core
ideas without having to delve into the entire document. Whether you’re a busy professional skimming through
emails or a researcher looking for key insights in a scientific paper, text summarization can be an invaluable
tool. This article aims to provide a comprehensive exploration of text summarization, delving into its various
types and approaches employed in the field.
(image courtesy: https://www.analyticsvidhya.com/blog/2018/11/introduction-text-summarization-textrank-python/)
Figure 1: Text Summarization
2.1 Single Document Summarization
(image courtesy:https://sakshi-nkulkarni.medium.com/text-summarization-models-874808a3e8c6)
Figure 2: Different Types of text summarization
Types of text summarization
Text summarization methods can be classified based on several factors(Figure 2). Below, we will explore
different classifications of text summarization methods. These categories shed light on the various factors that
help us understand and categorize the diverse approaches used in the field of text summarization
Based on Input Type:
2.1 Single Document Summarization
Single document summarization refers to the process of condensing the content of a single document into
a shorter version while retaining its key points and main ideas. It aims to capture the essential information
present in the document and present it in a concise and coherent manner.
In single document summarization, the focus is on extracting or generating a summary that accurately
represents the original document’s content. The length of the summary can vary, ranging from a few sentences
to a paragraph or two, depending on the desired level of detail. Extractive summarization is a commonly used
technique in single document summarization. It involves identifying important sentences or phrases from the
source document based on their relevance, importance, or other scoring criteria. These selected sentences are
then stitched together to form a summary.
On the other hand, abstractive summarization can also be employed in single document summarization.
Abstractive summarization involves generating new sentences that capture the essential meaning of the source
document. This approach goes beyond simple sentence extraction and involves natural language processing and
machine learning techniques to understand the content and create a summary that may not be present verbatim
in the original document. Single document summarization finds applications in various domains such as news
articles, research papers, legal documents, and more. It enables users to quickly grasp the main points and key
information from lengthy documents, saving time and providing an overview of the document’s content.
The quality of single document summarization is evaluated based on metrics such as coherence, informa-
tiveness, and coverage of important information. Researchers and developers continue to explore and improve
techniques to enhance the accuracy and effectiveness of single document summarization systems.
2.2 Multi-Document Summarization:
Multi-document summarization is the process of generating a concise summary that captures the main
points and key information from a collection of related documents. Instead of focusing on a single document,
7
2.2 Multi-Document Summarization:
(image courtesy:http://mogren.one/lic/)
Figure 3: Multi document summarization
(image courtesy:https://aylien.com/blog/multi-document-summarisation-and-the-wcep-dataset )
Figure 4: various news articles reporting the same event
this type of summarization involves aggregating information from multiple sources to provide a comprehensive
overview of a given topic or event(Figure 3)
The primary goal of multi-document summarization is to condense the essential content from the collection
of documents into a coherent and concise summary. This can be particularly valuable when dealing with vast
amounts of information on a specific subject, such as news events (Figure 4), research topics, or opinion pieces,
where multiple documents provide different perspectives or pieces of information.
Multi-document summarization has a wide range of applications, including news aggregation, literature
reviews, and research summaries. It provides a valuable tool for quickly gaining insights into complex topics
by efficiently extracting key information from a large corpus of related documents.
Evaluating the quality of multi-document summarization can be challenging due to the subjective nature of
summarization and the diversity of document collections. Researchers use various metrics, including ROUGE
(Recall-Oriented Understudy for Gisting Evaluation), to assess the summary’s effectiveness and its overlap with
reference summaries or human-created abstracts.
As with single document summarization, ongoing research and advancements in natural language process-
ing and machine learning continue to improve the accuracy and efficiency of multi-document summarization
systems.
8
2.3 Domain-Specific Summarization:
Figure 5: Query based summarization
Based on Purpose:
2.3 Domain-Specific Summarization:
Domain-specific text summarization is a type of text summarization that focuses on generating summaries
tailored to a particular domain or subject area. Instead of providing general overviews, this approach aims to
extract or generate key information specifically relevant to a defined domain, such as scientific research, medical
reports, legal documents, financial news, or sports updates.
The main idea behind domain-specific summarization is to consider the unique language conventions,
terminology, and context associated with a specific field. By doing so, the summarization system can create
more accurate and contextually appropriate summaries for users within that domain.
For instance, in the field of scientific research, domain-specific summarization systems can summarize
complex academic papers by extracting the most relevant hypotheses, methodologies, and findings. In the
medical domain, these systems can condense patient reports into concise summaries that highlight crucial
diagnosis and treatment information.
The advantages of domain-specific summarization lie in its ability to cater to the specific needs of profes-
sionals and researchers who require focused and specialized information within their area of expertise. It saves
time and effort by providing relevant insights while filtering out unnecessary details from a broader range of
documents.
Developing domain-specific summarization models often involves training the system on a large dataset
of documents specific to the target domain. This enables the system to learn domain-specific language patterns
and context, resulting in more accurate and relevant summaries.
Overall, domain-specific text summarization enhances the efficiency and effectiveness of information
retrieval and comprehension within specialized fields, making it a valuable tool for professionals seeking
concise and pertinent information within their domain of interest.
2.4 Query-Based Summarization:
Query-based summarization is a specific type of text summarization that aims to generate a summary in
response to a user’s query or question. Instead of providing a general overview of a document or collection
of documents, this approach focuses on addressing the specific information needs of the user. In query-based
summarization, the user inputs a query or a question, and the summarization system uses this query as a guide
to generate a summary that directly addresses the query (Figure 5). The summary is designed to provide the
most relevant information related to the question, extracting or generating sentences that answer the query in a
concise and coherent manner.
The process of query-based summarization involves analyzing the query and understanding its intent, then
9
2.5 Generic Summarization:
matching it to relevant information in the source documents. This often involves natural language processing
and information retrieval techniques to identify the most relevant sentences or passages.
Query-based summarization finds applications in search engines, where users enter a search query and
expect concise and informative summaries in the search results. It is also valuable in information retrieval
systems, customer support chatbots, and virtual assistants, where the system needs to provide relevant answers
to user questions in a summarized form.
The advantage of query-based summarization is that it directly addresses the specific information needs of
the user, saving time and effort in sifting through irrelevant content. It enables users to quickly access pertinent
information without having to read entire documents or search through lengthy texts, making it an efficient way
to obtain targeted insights.
2.5 Generic Summarization:
Unlike domain-specific or query-based methods, generic summarization is not limited to a specific content
domain and aims to generate summaries for various types of inputs. It focuses on creating summaries that
offer a broad overview of the main points and essential information found in a document or a collection
of documents. Unlike domain-specific summarization, which tailors summaries to a particular subject area,
generic summarization aims to capture the fundamental meaning of the text without being tied to any specific
domain or context. In generic summarization, the system analyzes the source text and extracts or generates
sentences that represent the most important information and main ideas. The resulting summary is designed
to be informative and coherent while being applicable to a broader audience without prior knowledge of the
subject matter.
The purpose of generic summarization is to provide a condensed version of the original text, making
it easier for readers to quickly grasp the main content and key takeaways without having to read the entire
document. It is commonly used in news aggregation, content curation, and automatic summarization for various
types of documents like articles, reports, and essays.
Generic summarization is valuable in scenarios where users seek a quick overview of the content or need
to manage large volumes of information efficiently. It saves time and effort by presenting the most relevant
information in a concise format, allowing users to prioritize and access essential details quickly.
Overall, generic summarization serves as a valuable tool in information management, helping users navigate
through vast amounts of textual data and gain insights without being overwhelmed by lengthy texts. It enhances
efficiency in understanding and processing information across different domains and subject areas.
Conclusion
In this article, we have delved into the world of text summarization, focusing on two crucial aspects:
summarization based on input type and summarization based on purpose. We explored how single-document
and multi-document summarization efficiently condense information from individual texts or collections of
related documents.
Additionally, summarization based on purpose encompasses three key types: generic summarization,
which provides an overview of main points without assumptions about the content’s domain; query-based
summarization, a specialized approach that caters to users’ specific information needs by generating summaries
directly addressing their queries or questions; and domain-specific summarization, which tailors summaries to
specific subject areas. As we proceed, the upcoming article will reveal the last piece of the summarization puzzle
10
2.5 Generic Summarization:
– text summarization based on output type. We will unravel the techniques of extractive summarization and
abstractive summarization, discovering how these methods create summaries by selecting essential information
or generating new sentences, respectively. Join us in the next article as we continue our exploration of this
fascinating field, revealing more insights and strategies to master the art of text summarization.
References
Text Summarization in Natural Language Processing,Sakshi Kulkarni, medium, May,2022
An Introduction to Text Summarization using the TextRank Algorithm,Prateek Joshi , analytics vidhya,
May,2023
Text summarization with Amazon SageMaker and Hugging Face, Text summarization with Amazon
SageMaker and Hugging Face, Dataintegration, June, 2022
Multi-Document Summarization and Semantic Relatedness, Olof Mogren
Adventures in Multi-Document Summarization: The Wikipedia Current Events Portal Dataset, Demian
Gholipou, April, 2021
Query-Based Summarization in Action, Fenil Dedhia, medium, January, 2021
About the Author
Jinsu Ann Mathew is a research scholar in Natural Language Processing and Chemical Informatics.
Her interests include applying basic scientific research on computational linguistics, practical applications of
human language technology, and interdisciplinary work in computational physics.
11
Understanding the Support Vector Machine
Algorithm
by Linn Abraham
airis4D, Vol.1, No.8, 2023
www.airis4d.com
The Support Vector Machine (SVM) is one of the most popular algorithms in modern machine learning.
Introduced by Vladimir Vapnik in 1992, the algorithm still finds use in several areas of research including
astronomy [2]. The major disadvantage that the SVM suffers from is that it does not scale well to extremely
large datasets because of the computational expense. This article is an effort to understand why the SVM
algorithm works and the reason for its efficiency. The article can be broken down into several sections. In the
first section, we explain the concept of a linearly separable problem. We see how non linearly separable problem
can sometimes be made linearly separable by adding extra dimensions. We then see the basic motivation behind
the SVM algorithm which is includes the definition of the margin and support vectors. In the third section we
briefly mention how the problem can be posed as a constrained optimisation problem which can be solved using
existing mathematical techniques. In the fourth section we motivate the need for a soft-margin classifier. In
the final section we introduce the kernel trick that the SVM makes use of which allows the algorithm to remain
computationally feasible inspite of adding extra dimensionality to the problem.
3.1 Linear Separability of Data
Let us start with a simple example to understand the concept of linear separability of data. Consider the
truth table of the OR logic gate. The data can be visualized as shown in Figure 1. We can see that the OR
gate is a function with two inputs and one output. In the visualization we have given different symbols to
the two possible outputs 0 and 1. The task to correctly predict the outputs from the inputs can be seen either
as a regression or classification problem. This is because a classification problem can be easily made into a
regression problem if we agree to use a threshold to map the predicted outputs to the allowed output values.
From the visualization it can be seen that there exists a straight line in the input space that can separate the
two different classes. This decision boundary is what machine learning algorithms are trying to learn. Now,
how would such an algorithm perform if there didn’t exist such a line. The XOR gate shown in Figure 2 is in
fact is such a function. In general if we don’t account for such factors in the design of the algorithm the results
will indeed be poor.
But there is a way to solve the XOR problem using a linear classifier. The trick is to use a suitable
transformation of the data. This is shown in Figure 3. Here a third input dimension has been added to the data
without changing any of the other input dimensions or the outputs. The input space is now three-dimensional
3.2 Margin and Support Vectors
Figure 1: The truth table and plot of the OR gate
Figure 2: The truth table and plot of the XOR gate
and there exists a plane that can separate the two classes. The class of machine learning algorithms that work
on this principle is called kernel classifiers.
3.2 Margin and Support Vectors
An important idea that SVMs make use of is to identify a way to tell apart a good classifier from a bad one.
The way the SVM does that is using the idea of a margin. Consider the following figure 4 that tries to compare
different linear classifiers. If you had to pick one classifier from the three which one would you pick? Even
though most people might choose the middle one, it is difficult to justify that choice.
The concept of a margin naturally arises while trying to find a criteria for the best classifier. Imagine that
we put a ‘no-man’s land’ around the line, so that any point that lies within that region is declared to be too close
to the line to be accurately classified, see Figure 5. How large can we make the boundary of this region until we
hit actual data points? That particular (half) width is called the margin M. The best classifier in Figure 4 can now
be identified as the maximum margin classifier. The data points in each class that lie closest to the classification
line are called support vectors. Two important statements that can be made on the above discussion are: first
that the margin should be as large as possible, and second that the support vectors are the most important data
points as they are the ones that we might more easily misclassify.
3.3 Quadratic Programming
How do we define a machine learning algorithm that can compute the best classification line based on the
concept of the margin and support vectors? Similar to the concept of a weight matrix in a neural network we
can consider a weight vector w and a bias b that the SVM algorithm tries to learn. Then the actual separating
hyperplane is specified by w
T
x+b = 0. It can be seen that the margin is given by 1/||w||. Therefore maximising
the margin implies minimizing the weight vector. But if this was the only constraint we could just put w = 0
13
3.3 Quadratic Programming
Figure 3: A decision boundary (the shaded plane) solving the XOR problem in 3D with the crosses below the
surface and the circles above it.
Figure 4: Comparing different linear classifiers. Is there any reason to prefer one over the other?
Figure 5: The margin is the largest region that separates the two classes without having any data points in it
14
3.4 Soft Margin Classifier for Non Linearly Separable Problems
and get it done. But we also need to make sure that the classifier classifies all the training examples correctly.
Therefore we need to simultaneously satisfy two problems, minimize w · w subject to some constraints that
ensure that the training examples are correctly classified.
The problem described is quadratic and hence convex with linear constraints. Convex functions have a
unique minimum, which is fairly easy to see in one dimension, and remains true in any number of dimensions.
Such problems can be solved directly and efficiently (in polynomial time). There exists quadratic programming
solvers that can solve these equations.
3.4 Soft Margin Classifier for Non Linearly Separable Problems
A non linearly separable dataset introduces an immediate problem. Now the constraints cannot be satisfied
for all of the data points. However this doesn’t mean that the algorithm is unusable. Consider a classifier that
misclassifies a point by putting it on the wrong side of the line but very close to it. This is obviously better than
another one that puts the same points a long way away from the line. This information can be incorporated into
the minimisation criterion. We can add a term such that we are now trying to minimize.
w
T
w + C × (distance of misclassified points from the boundary line)
Here, C is a trade-off parameter that acts as a weight to decide which of the two criteria to favour more. A
small C means we prize a large margin over a few errors, while large C means the opposite. This transforms the
problem into a soft-margin classifier, since we are allowing for a few mistakes.
3.5 Kernel Functions
In the case of a non linearly separable dataset, even though we can modify the minimisation criteria to
account for some misclassification, it wont do much good on it’s own. The real reason behind the efficiency of
the SVM is what is known as the kernel trick. As mentioned earlier, we can transform the data into a space such
that the data becomes linearly separable. We saw earlier that in the case of the XOR gate problem we could make
the problem linearly separable by adding a new dimension to the data. But since we cannot invent new data to
create extra dimensions, what can be done is create new functions from our existing input features. Is there any
disadvantages to adding more dimensions to the data in this way? Remember that we need to compute the dot
products of our inputs. By increasing the dimensionality of our data we will be increasing the computational
expense of our algorithm. But in reality, by selecting suitable basis functions for transforming the data we can
get away without computing the dot products in this computationaly expensive space and instead just compute
a kernel matrix K consisting of the dot products in the low-dimensional space. Any symmetric function that
is positive definite (meaning that it enforces positivity on the integral of arbitrary functions) can be used as a
kernel. This is a result of Mercer’s theorem. Some of the commonly used kernels correspond to basis functions
like polynomials of degree n, sigmoid functions, radial basis functions etc. In practice people experiment with
the different available functions using a validation set in order to select one that works best.
Bibliography
[1] Boser, Bernhard E and Guyon, Isabelle M and Vapnik, Vladimir N (1992) A training algorithm for optimal
margin classifiers
15
BIBLIOGRAPHY
[2] Bobra, M. G. and Couvidat, S. (2015) SOLAR FLARE PREDICTION USING SDO /HMI VECTOR
MAGNETIC FIELD DATA WITH A MACHINE-LEARNING ALGORITHM
[3] Marsland, Stephen (2014) Machine Learning: An Algorithmic Perspective
About the Author
Linn Abraham is a researcher in Physics, specializing in A.I. applications to astronomy. He is
currently involved in the development of CNN based Computer Vision tools for classifications of astronomical
sources from PanSTARRS optical images. He has used data from a several large astronomical surveys including
SDSS, CRTS, ZTF and PanSTARRS for his research.
16
Part II
Astronomy and Astrophysics
Black Hole Stories-3
by Ajit Kembhavi
airis4D, Vol.1, No.8, 2023
www.airis4d.com
1.1 The Detection of a Lone Black Hole
In Black Hole Stories-2 (https://airis4d.com/Journal/airis4DJournal 1.7.html#pf12), we considered gravi-
tational microlensing, which is the lensing of a distant star by another stellar-mass object. The lensing changes
the apparent position and the apparent brightness of the distant star. We will describe below how the precise
measurements of these changes, observed in a specific case of gravitational lensing, have led to the first confident
identification of a lone black hole.
1.2 Gravitational Microlensing
In Albert Einstein’s theory of gravity, the gravitational effect of a massive body manifests itself as the
curvature of four-dimensional space-time caused by the presence of matter and energy. The curvature implies
that the shortest distance between two points is no longer a straight line but a curved trajectory known as a
geodesic. Material particles and light rays travel along geodesics whose form can be calculated using Einstein’s
equations, given a distribution of matter and energy. As a consequence, a ray of light passing close to a body
with a large mass, like the Sun, deviates from a straight path. This is known as the gravitational bending of light
and is shown in Figure 2 of BHS2. Because of the gravitational bending, light rays from a distant object can
reach an observer in more than one direction. The addition of the energy brought by the different rays causes
the distant object to appear brighter than it really is, and the phenomenon is known as gravitational lensing.
When the lensed body is a star, and the lensing object also has a mass comparable to the mass of star,
then we have microlensing. In such cases the lensing object could be another star, or a neutron star, or a black
hole. Here the bending angle is typically very small, in the range of milliarcseconds (a milliarcsecond (mas) is
one-thousandth of an arcsecond, which is 1/3600 of a degree). At the same time, the brightness can increase
by hundreds of times. When the lensed object, the lensing object and the observer are in a straight line, then,
because of the symmetry, the lensed image is a circle as shown in Figure 3 of BHS2. Such an image is called as
an Einstein ring; its radius is known as the Einstein radius R
E
, and the angle subtended by the Einstein radius
at the observer is known as the Einstein angle θ
E.
In terms of the parameters defining the lensing, the Einstein
radius and angle are given by
where M is the mass of the lensing object, D
L
, D
S
, and D
LS
are the distance from the observer to the
1.3 A Black Hole Lens
lensing object, distance to the star and the distance from the lensing object to the star, respectively, G is Newton’s
constant of gravitation and c is the speed of light.
Stars in our galaxy are in incessant motion. Each star is in orbit around the centre of the galaxy and can
also have random motion, the net velocity being typically in the range of 100 km/s to a few hundred km/s, but
there are also stars which move with much higher velocities. A moving star can drift across the line of sight
from us to a much more distant star, which itself would be moving. As the moving star approaches the line of
sight, it can act as a gravitational lens, increasing the apparent brightness of the distant star and also changing
its position. These changes are time-dependent since the change depends on the separation of the lensing object
from the line of sight to the lensed star. This is illustrated in Figure 1. A useful parameter is the Einstein
timescale t
E
, which is the time taken by the lensing object to move across a distance equal to the Einstein radius.
In terms of the Einstein angle θ
E
and the angular velocity µ with which the lens moves in the sky relative to the
lensed star, the Einstein timescale is given by
An important point to note is that the greater the mass of the lensing object, the greater is its gravitational
influence, and so the greater is the time over which the brightness and position are affected. Since black holes
have a mass of several times the mass of the Sun or more, the events in which the lens is a black hole would
be of long duration. Also, in such events, the lens would not make any contribution to the observed light since
black holes do not emit any light.
1.3 A Black Hole Lens
The first discovery of a lone black hole using microlensing was reported by Kailash Sahu of the Space
Telescope Science Institute and his team and collaborators in 2022 (Sahu, Kailash et al. 2022, Astrophysical
Journal Volume 933, page 22; arXiv:2201.13296; hereafter KS1). They had a programme to study microlensing
events which were of long duration, and in which there was no contribution to the observed brightness from the
lens. Such events can be due to a gravitational lens which is a black hole, as explained in Section 1. But they
could also be due to a slow-moving low-mass star, as such a lens would take a relatively long time to drift across
the line of sight and would contribute very little to the brightness. To distinguish between these possibilities,
it is necessary to study the pattern of the change in brightness as well as the position of the distant star. The
change in brightness can be studied from Earth-based observatories. But because the change in position is in the
milliarcsecond range, measuring it necessarily involves observations with the Hubble Space Telescope (HST).
The pattern of changes expected from a black hole are shown in Figure 2.
For convenience, the time on the x-axis of both panels is given as the dimensionless quantity t-t
0
t
E
, where
t
0
is the time at which the black hole is closest to the line of sight, and t
E
is the Einstein timescale defined
above. The closest distance to the line of sight reached is 5 per cent of the Einstein radius of the system. It is
seen from the lower panel that the maximum brightness indeed occurs at time t=t
0
. The minimum in the change
in position occurs at the same time, as seen from the upper panel. The maximum change in position is only
about 1.4 mas, which occurs at a time before t
0
and the same time after t
0
. The change in position persists for a
longer time than the change in brightness. This is useful in making accurate measurements. The figure is from
reference KS1.
Sahu et al. have a programme for observing with the HST long-duration microlensing events, discovered
in various surveys for gravitational lensing carried from ground-based optical telescopes. One of these was
a source with the rather long name MOA-2011-BLG-191/OLG-2011-BLG-0462 (which we will refer to as
19
1.3 A Black Hole Lens
( Image Credit: NASA, ESA and A. Field (STScI). )
Figure 1: A gravitational lens consisting of a black hole is shown drifting across the line of sight from a
ground-based observatory to a distant star is shown. When the lens is away from the line of sight, the brightness
of the star is unaffected, but as it approaches the line of sight, the apparent brightness increases. The brightness
is maximum when the lens is closest to the line of sight, and decreases as the lens moves away. There is also a
small change in the apparent position of the star which is not shown in the figure. If the lens were a star instead
of a black hole, then similar changes in the brightness would be seen, but the light emitted by the lensing star
would also add to the changing brightness.
20
1.3 A Black Hole Lens
Figure 2: The figure shows the calculated gravitational lensing of a star by a black hole lens (this is not an
actual observation). In the calculation, the black hole is of 5 Solar masses and is taken to be at a distance of 2
kpc (kpc = kiloparsec = one thousand parsec; 1 parsec is about 3.26 light-years) from the Earth, while the star
is taken to be at a distance of 8 kpc.
source S1) which was discovered independently by the microlensing surveys OGLE and MOA and announced
on 2
nd
June 2011. The event had a peak brightness increase of about 20 on July 11, 2011, and had a timescale
t
E
longer than 200 days. The change in the apparent brightness of the lensed star during the microlensing
event, as measured by various ground-based observatories, is shown in Figure 3. It was soon realised from the
ground-based observations that the lensed star was likely to be blending with other stars in the field, and so the
brightness increase could be as high as about 400. Accounting for the blending also increases the timescale of
the event.
As explained above, finding the mass of the lensing object requires measuring the change in the apparent
position of the lensed star, for which observations from space are necessary. Sahu et al., therefore, undertook
observations of the event with the HST and obtained eight observations in all, spread over a period of six years,
with the first observation made just 19 days after the peak was reached as per the ground observations. It was
found that there was a bright star located at 0.4 arcseconds from the lensed star and other faint stars in the field,
as had been expected from the ground-based observations. The effect of the stars, particularly the bright star,
has to be taken into account in the analysis. The eight observations made by the HST were through two different
filters, which provided the brightness of the lensed star at different wavelengths. Using the ground- based data,
it was possible to develop a model of the variation in brightness over the duration of the event, which is shown
in Figure 4. As determined from the model, the peak amplification in the brightness is by a factor 369 and the
time scale of the event is t
E
= 270.7 days. The lensing object makes no contribution to the observed brightness,
which is consistent with it being a black hole.
Because of the high resolution in the HST images, it is possible to measure the position of the lensed
star accurately. But determining how much the position has changed due the gravitational lensing is a difficult
measurement as various factors have to be considered. If the lensed star and the lensing object were both
21
1.3 A Black Hole Lens
Figure 3: The ground-based observations of the gravitational microlensing event discovered in the OGLE
and MOA surveys. The event is spread over 300 days. A sharp peak is seen during the passage at minimum
separation from the line of sight to the lensed star. The figure is taken from reference KS1.
Figure 4: The change in brightness, or the light curve, over the duration of the event. The red curve corresponds
to the model for the filter (I), and the blue curve to the model in the filter (J). The eight observed points are
shown on each curve. In the small lower panel, the difference in the brightness observed in the two filters is
shown. It is seen that the change in brightness is the same in the two filters for the entire event. This is an
important observation since in general relativity, gravitational lensing is independent of the wavelength of the
radiation.
22
1.4 Nature of the Lens
stationary in the sky, then there would be a fixed bending angle, as explained in BHS2. However, in the present
case, both the star and the lens are moving in the sky. Moreover, over the period of the observations lasting six
years, the Earth keeps moving around the Sun, thus affecting the position from which the event is viewed. This
leads to changes in the measured positions in the sky, known as stellar parallax. The parallax also has to be
considered in the determination of the light curve of the event.
Using the light curve and position data, and spectroscopic observations with the HST, which were also
available, and applying various complex corrections, Sahu et al. were able to determine several important
parameters: the mass of the lensing object 7.1 ± 1.3 Solar masses, the distance to the lens 1.58 ± 0.18 kpc,
Einstein radius 5.18 ± 0.51 mas, and a space velocity of the lens of about 45 km/sec relative to the Sun. From
the spectroscopic data, it was determined that the distance to the lensed star was 5.9 ± 1.3 kpc.
1.4 Nature of the Lens
Sahu et al. provide several arguments to show that the lensing object is a black hole. Given the mass of 7.1
Solar masses for the lensing object, it cannot be either a white dwarf or a neutron star since these objects have
a maximum mass of 1.4 and about 3 Solar masses, respectively. The lens cannot even be a binary system made
up of these objects. So, it could only be a massive star, a black hole, or a binary made up of these objects. It
can be estimated that a star with a mass of about 7 Solar masses, would at the lens distance of 1.58 kpc have the
brightness to be detected in the observations. Observed limits on the brightness are about 100 times less than
the expected brightness for such a star, so the lens could not be a massive star. It can further be argued that to
be consistent with the brightness constraint, the mass of the star cannot be more than 0.2 Solar masses. That
only leaves a black hole as a possibility.
But then, is the lensing object a single massive back hole, or a binary of two black holes, or a combination
of a sufficiently massive black hole and another lower mass object with a combined mass of the lensing object?
It can be argued that in such a binary system, the two components have either to be very close together or quite
far apart. For a close binary of the kind needed, the emission of gravitational radiation would be so high that the
two components would merge in less than 10
7
years. The lens system would therefore have to be rather young,
so there should be ongoing star formation in the surrounding region, for which there is no evidence. On the
other hand, if the binary were to be very wide, then the lensing would be due to just the more massive object,
which would need to be a massive black hole with the measured mass of 7.1 Solar masses. So one cannot really
say that a wide binary could be present in preference to a single 7.1 Solar mass black hole. The black hole has
high space velocity compared to nearby stars, which shows that it probably received a kick when it was formed,
possibly in the supernova explosion of a massive star.
The work of Sahu et al. seems to have led to the detection of the first lone black hole. In the future
observations with the Nancy Grace Roman Space Telescope and the Rubin Observatory LSST are expected to
provide accurate data on thousands of microlensing events, leading to the discovery of many lone black holes.
1.5 A Different Result
Casey Lam, Jessica Lu and their collaborators have used HST and ground-based data to analyse the same
gravitational wave event MOA-2011-BLG-191/OLG-2011-BLG-0462 (Lam, Casey et al. 2022, Astrophysical
Journal Volume 933, page L28; arXiv:2202.01903). They follow techniques similar to those used by Sahu et
al. but arrive at a different result. They find that the mass of the lensing object is in the range of 1.6-4.4 Solar
masses, and that it is at a distance of 0.72-1.92 kpc. The lower mass obtained allows the lensing object to be a
23
1.5 A Different Result
neutron star or a low-mass black hole. This is in contrast to the higher value of 7.1 Solar masses obtained for
the lens by Sahu et al., which ruled out its being a neutron star. The reasons for the different results obtained by
the two groups are not clear at the present.
About the Author
Professor Ajit Kembhavi is an emeritus Professor at Inter University Centre for Astronomy and
Astrophysics and is also the Principal Investigator of the Pune Knowledge Cluster. He was the former director
of Inter University Centre for Astronomy and Astrophysics (IUCAA), Pune, and the International Astronomical
Union vice president. In collaboration with IUCAA, he pioneered astronomy outreach activities from the late
80s to promote astronomy research in Indian universities. The Speak with an Astronomer monthly interactive
program to answer questions based on his article will allow young enthusiasts to gain profound knowledge about
the topic.
24
Unveiling the Cosmic Drama: The
Fascinating Journey of Stellar Evolution
by Robin Jacob Roy
airis4D, Vol.1, No.8, 2023
www.airis4d.com
Stars are celestial giants that fill the vast expanse of our universe, radiating light and energy. Stellar
evolution encompasses the life cycle of a star, from its formation to its ultimate fate, unfolding through various
stages of development. This remarkable process spans millions to billions of years and is orchestrated by the
interplay of gravity, nuclear reactions, and other fundamental forces.
Like people, stars are not immortal beings. They experience a journey involving birth, transformation over
time, and eventual death. Just as each individual’s life is unique, the path of every star is influenced significantly
by its mass, specifically its Main Sequence mass. This critical parameter dictates when a star initiates hydrogen
fusion in its core, establishing a delicate equilibrium with gravity that prevents it from collapsing inward.
As a star consumes its hydrogen fuel, the core undergoes changes, leading to its eventual demise. The
transformations in this phase vary depending on the star’s mass. The entire process is incredibly lengthy, far
exceeding the lifespan of any living being, and its duration is determined by the star’s mass. Figure 1 illustrates
the life cycle of a star. Now, let us delve into the captivating journey of a star, from its inception to its eventual
end.
Figure 1: Life Cycle of a Star. Source: NASA
2.1 Birth of a Star
Figure 2: Interstellar clouds composed of gas and dust undergo a process of contraction, flattening, and spinning
as they condense. Eventually, a star is born at the center of this swirling mass, while any remaining material in
the form of a disc may coalesce to form planets. Source: Bill Saxton/NRAO/AUI/NSF
2.1 Birth of a Star
Stellar evolution commences with the gravitational collapse of immense giant molecular clouds. These
colossal clouds span about 100 light-years across and can contain an astounding 6,000,000 solar masses of
material. As these clouds collapse, they fragment into smaller pieces. Within these fragments, the gas
undergoes collapse, releasing gravitational potential energy as heat. This process leads to the formation of
rotating balls of superhot gas known as protostars.
Filamentary structures are prevalent throughout the molecular cloud, with dense molecular filaments
breaking into gravitationally bound cores, the precursors of stars. The manner of fragmentation in these
filaments is influenced by continuous gas accretion, geometrical bending, and magnetic fields. In certain
cases, observations have revealed quasi-periodic chains of dense cores in supercritical filaments, with spacing
comparable to the filament’s inner width, sometimes hosting two protostars with gas outflows.
As the protostar grows, it continues to accrete gas and dust from the surrounding molecular cloud,
gradually becoming a pre-main-sequence star until it reaches its final mass. The subsequent development and
characteristics of the star are primarily determined by its mass, typically compared to the mass of our Sun,
where 1 solar mass is equal to 1.0 M
⊙
(2.0×1030 kg).
Infrared observations, particularly from the Wide-field Infrared Survey Explorer (WISE), have played
a vital role in discovering numerous galactic protostars and their parent star clusters, as protostars are often
shrouded in dust and more easily observable at infrared wavelengths. These observations have provided valuable
insights into the early stages of stellar evolution and the formation of stars in our universe. Figure 2 depicts the
summary of the formation process of a star and its planetary system.
26
2.2 Main Sequence Phase
Figure 3: The Hertzsprung-Russell diagram is a graphical representation that plots the temperatures of stars
against their luminosities. The position of a star in the diagram provides information about its present stage and
its mass. Source: ESO
2.2 Main Sequence Phase
For protostars with masses greater than roughly 0.08 M
⊙
, their core temperatures eventually soar to around
10 million kelvin, initiating the proton-proton chain reaction. This nuclear fusion process allows hydrogen to
fuse, first into deuterium and then into helium. In stars slightly exceeding 1 solar mass (2.0×1030 kg), the
carbon-nitrogen-oxygen fusion reaction (CNO cycle) plays a significant role in energy generation. As nuclear
fusion sets in, it swiftly establishes a hydrostatic equilibrium, where the energy released by the core maintains a
high gas pressure, balancing the gravitational forces and preventing further collapse. This marks the beginning
of the main-sequence phase of the star’s evolution.
A new star finds its place on a specific point of the main sequence in the Hertzsprung-Russell diagram,
with the spectral type on the main sequence determined by its mass. Small, cool, low-mass red dwarfs undergo
slow hydrogen fusion and can remain on the main sequence for hundreds of billions of years or even longer. On
the other hand, massive, hot O-type stars leave the main sequence after just a few million years. For instance, a
mid-sized yellow dwarf star like our Sun will remain on the main sequence for approximately 10 billion years.
Currently, the Sun is estimated to be in the middle of its main sequence lifespan. The Hertzsprung diagram is
shown in Figure where the evolution of sun-like stars is traced.
27
2.3 Evolution into Red Giant/Supergiant
2.3 Evolution into Red Giant/Supergiant
Main sequence stars, like our Sun, are in a stable phase of their life cycle where they steadily fuse hydrogen
into helium in their cores. However, as these stars exhaust their hydrogen fuel, they eventually undergo a
transformative process leading to the formation of red giants or supergiants.
The first step in this evolution occurs when the hydrogen fuel in the core becomes depleted. As a result,
the core contracts under gravity’s pull, while the outer layers of the star expand. This expansion causes the star
to swell in size, and it enters the red giant phase.
Red giants are characterized by their enlarged size and cooler surface temperatures. Despite their cooler
surface, they radiate more energy due to their large surface area, making them appear brighter than they were
during their main sequence phase.
In some cases, particularly for more massive stars, the evolution doesn’t stop at red giants. The most
massive stars, those with several times the mass of our Sun, continue evolving into supergiants. Supergiants are
even larger and more luminous than red giants, making them some of the most massive and brilliant stars in the
universe.
As the star transitions into a red giant or supergiant, its outer layers may undergo pulsations, causing it
to vary in brightness. These pulsations are influenced by complex interactions between pressure, gravity, and
nuclear reactions within the star.
The evolution into a red giant or supergiant marks a critical stage in the life of a star, eventually leading to
further transformations that depend on its mass. For some stars, this journey may eventually end in a dramatic
supernova explosion, while others may evolve into white dwarfs or even collapse into black holes.
2.4 The Fate of Low-Mass Stars
Low-mass stars, those with masses similar to or less than that of our Sun, follow a different path of evolution
compared to their more massive counterparts. Despite their relatively less spectacular destinies, their life cycle
holds significant implications for the cosmic ecosystem.
As low-mass stars exhaust the hydrogen fuel in their cores during their main sequence phase, they undergo
changes that eventually lead to their transformation into different stellar remnants.
1. Red Giant Phase: As the core’s hydrogen depletes, the core contracts while the outer layers of the star
expand, turning the star into a red giant. During this phase, the outer layers cool down, giving the star
a reddish appearance. Red giants are larger than their main sequence counterparts and often have a size
that reaches the orbits of inner planets.
2. Helium Flash and Horizontal Branch: In the core of a red giant, helium starts to fuse into carbon and
oxygen in a rapid burst known as the helium flash. This event stabilizes the core, and the star enters the
horizontal branch phase. In this stage, the star’s energy output remains relatively stable for a significant
period.
3. Planetary Nebula and White Dwarf: Eventually, the outer layers of the red giant are expelled into space,
forming a beautiful shell of ionized gas called a planetary nebula. The remaining core contracts further to
become a small and extremely dense object known as a white dwarf. White dwarfs are composed mainly
of carbon and oxygen and are about the size of Earth but with a mass comparable to the Sun.
4. Cooling and Fading: Over a very long period, white dwarfs gradually cool and fade away, eventually be-
coming ”black dwarfs.” These celestial remnants no longer emit significant light or energy and essentially
become cold and dark objects.
28
2.5 The Fate of High-Mass Stars
Figure 4: The Crab Nebula, a famous supernova remnant. Source: NASA, ESA, J. Hester and A. Loll (Arizona
State University)
The fate of low-mass stars is relatively peaceful compared to more massive stars, which may end their lives
in spectacular supernova explosions or collapse into black holes. Nevertheless, the contributions of low-mass
stars to the cosmos are profound. They play a vital role in recycling elements back into space through planetary
nebulae, enriching the interstellar medium with essential building blocks for the formation of new stars, planets,
and potentially even life. The study of low-mass stars provides valuable insights into the long-term evolution of
stars and the overall evolution of galaxies and the universe as a whole.
2.5 The Fate of High-Mass Stars
High-mass stars, those with masses much larger than that of our Sun, have a far more dramatic and intense
journey throughout their life cycle. Their massive cores and the tremendous energy they generate lead to
extraordinary events that significantly impact the cosmos.
1. Red Supergiant Phase: High-mass stars follow a similar path to low-mass stars during their main sequence
phase. However, due to their larger size and higher core temperatures, they consume their hydrogen fuel
at a much faster rate. As a result, they quickly evolve into red supergiants. These colossal stars are among
the largest and most luminous objects in the universe, with sizes that can exceed hundreds to thousands
of times that of our Sun.
2. Fusion of Heavier Elements: High-mass stars have enough gravitational pressure and core temperature
to continue nuclear fusion beyond helium. They can fuse helium into heavier elements such as carbon,
oxygen, neon, and others. This process releases an immense amount of energy and leads to the formation
of an ”onion-like” structure within the star, with successive shells of elements undergoing fusion.
3. Supernova Explosion: As high-mass stars reach the end of their fusion cycles and form iron in their cores,
a critical turning point occurs. Iron cannot undergo further fusion to release energy, and instead, it absorbs
energy from the star’s core. This disrupts the balance between gravity and the outward pressure from
nuclear reactions. The core then collapses rapidly, leading to a colossal explosion known as a supernova.
29
2.6 Stellar Nurseries and Star Formation Repeating the Cycle
Supernovae are some of the most energetic events in the universe, temporarily outshining an entire galaxy
and dispersing heavy elements into space. Figure 4 shows The Crab Nebula, the shattered remnants of a
star which exploded as a supernova visible in 1054 AD.
4. Neutron Stars or Black Holes: The core remnants of a high-mass star after a supernova explosion depend
on the star’s mass. If the core’s mass is between about 1.4 and 3 solar masses, it collapses into a neutron
star, an incredibly dense and compact object composed mainly of neutrons. Neutron stars can have a
diameter of only about 10 kilometers (6 miles) but contain the mass of several Suns.
However, if the core’s mass is greater than around 3 solar masses, even neutron degeneracy pressure cannot
prevent further collapse, leading to the formation of a black hole. Black holes are regions of space where gravity
is so intense that nothing, not even light, can escape from them.
The fate of high-mass stars plays a crucial role in the cosmic cycle of matter and energy. Their supernova
explosions enrich the interstellar medium with heavy elements, which are essential for the formation of new
stars, planets, and even life. The study of high-mass stars and their dramatic end states provides profound
insights into the evolution of galaxies and the universe’s grand design.
2.6 Stellar Nurseries and Star Formation Repeating the Cycle
Throughout the life cycle of stars, the remnants of previous stars, along with interstellar gas and dust,
become stellar nurseries for new star formation. These regions are often found in spiral arms of galaxies, where
the density of gas and dust is higher. The process starts anew as the gravitational forces pull matter together,
leading to the birth of new stars and the continuation of the fascinating life cycle.
The life cycle of a star is a mesmerizing journey, spanning billions of years and shaping the universe as we
know it. From their birth in vast nebulae to their dramatic demise as supernovae or the peaceful fading of white
dwarfs, stars play a crucial role in the cosmic dance of creation and destruction. Understanding the intricacies
of stellar evolution not only deepens our appreciation of the universe but also sheds light on our own existence
as stardust beings in this vast cosmos.
References:
Subsequent development on the main sequence
Star birth and death
Lives and Deaths of Stars
Evolution of high mass stars
The process of star formation
About the Author
Robin is a researcher in Physics specializing in the applications of Machine Learning for Astronomy
and Remote Sensing. He is particularly interested in using Computer Vision to address challenges in the fields of
Biodiversity, Protein studies, and Astronomy. He is presently engaged in utilizing machine learning techniques
for the identification of star-forming knots.
30
Light Curves Of Variable Stars
by Sindhu G
airis4D, Vol.1, No.8, 2023
www.airis4d.com
This article provides an explanation of light curves and delves into phase-folded light curves. Light curves
play a vital role in the field of variable star astronomy as essential and foundational tools. We will be examining
light curves from Classical Cepheids, RRab, RRc and RRd variables. Variable stars are astronomical objects
whose brightness changes over time. These changes can be periodic, semi-regular, or irregular in nature.
Variable stars are classified based on the patterns of their brightness variations, and they provide valuable
information to astronomers about stellar properties, such as size, mass, and age. Studying variable stars has
contributed significantly to our understanding of stellar evolution and the broader universe.
3.1 What Are Light Curves?
A light curve is a graph that displays the changes in brightness or luminosity of an astronomical object over
a specific period of time. The horizontal axis of the light curve represents time, while the vertical axis shows the
object’s brightness or magnitude. Brightness increases as you go up the graph and time advances as you move
to the right. The light curve proves to be an essential and uncomplicated tool for scientists examining objects
that experience fluctuations in brightness over time. By analyzing the patterns and trends in the light curve,
scientists can gain valuable insights into the nature, behavior, and characteristics of the observed astronomical
object.
The information captured in a light curve regarding the fluctuations in brightness assists astronomers in
comprehending the internal processes of the studied object and in classifying specific categories of stellar events.
With a general understanding of the typical appearance of light curves for different objects, astronomers can
compare a newly generated light curve to these standard patterns. This comparative analysis serves as a valuable
tool in potentially identifying the type of astronomical object being observed.
Fig: 1 shows the light curve of epsilon Aurigae. The star’s light curve indicates that in 1982, it initially
shone with a magnitude of 3. As the year progressed, it underwent a rapid dimming, reaching a magnitude of
3.8 by the year’s end. It maintained this brightness until the start of 1984 when it gradually started recovering
to its usual luminosity. By the middle of 1984, it had nearly returned to its normal brightness. It’s important to
note that the presented light curve is an idealized version, as it was carefully processed to include only the most
accurate observations, ensuring clarity.
Here, you can find a more complicated, real-world light curve (Fig: 2). This is the light curve of the
bright star Betelgeuse. The values along the X-axis represent Julian Dates. The Julian date is a standardized
format commonly employed by astronomers, especially those studying variable stars, to document dates.
3.2 Phase Diagrams
Figure 3: Phase folded light curves Source: feets
Since astronomers often gather data spanning several months or even years, and occasionally analyze ancient
observations dating back thousands of years, an efficient method of recording time becomes crucial. To simplify
timekeeping, astronomers adopt a straightforward approach of counting days. Starting from Julian Day 0, which
commenced at noon on January 1, 4713 B.C., all days are consecutively numbered. For instance, January 1st,
1993, corresponds to JD 2448989, and January 1st, 2000, corresponds to JD 2451545. Notably, Julian Day
begins at noon, Greenwich Mean Time.
3.2 Phase Diagrams
When a pattern repeats consistently and predictably, much like the precision of clockwork, we classify this
as periodic behavior. In such cases, it becomes inconsequential which specific cycle we observe, as every cycle
mirrors the others identically. What becomes significant is the particular phase of the cycle being observed at
any given moment. Hence, if a star (or any other phenomenon) exhibits perfect periodicity, its fluctuations are
solely determined by its position within the cycle, which is known as the phase.
Phase plots (Fig: 3) exhibit folded data that is compressed to fit within a mathematically determined period.
They are commonly known as folded light curves. When an incorrect period is chosen, the resulting phase plot
may appear disorderly or messy. To rectify this, an alternative period is selected, and the data is refolded. This
iterative process continues until a clean and coherent phase plot is achieved. Unlike a light curve, the x-axis
of the phase plot does not represent time. Instead, it denotes the phase from 0 to 1 (although the values may
slightly exceed or fall short of this range). In some cases, the plot might even display two full cycles to showcase
all the object’s significant features effectively.
3.3 Light Curves Of Classical Cepheids
3.3.1 Fundamental-mode pulsators
Fundamental-mode Cepheids display periods that span from approximately 1 to over 200 days, with typical
periods being a few days. Their light curves typically exhibit asymmetry, characterized by a rapid rise to
maximum brightness followed by a slower decline. Cepheids with periods falling within the 6-20 day range
exhibit a secondary bump in both their light and velocity curves. For Cepheids with approximately 6-day
periods(Fig: 4), this bump emerges on the descending branch of their light curves. As the periods increase,
the bump gradually shifts backward in phase. Around periods of 10 days(Fig: 5), the bump reaches its peak
33
3.3 Light Curves Of Classical Cepheids
Figure 4: Light curves of fundamental-mode Classical Cepheids with period 6 days Source: OGLE
Figure 5: Light curves of fundamental-mode Classical Cepheids with period 10 days Source: OGLE
brightness, then moves down during the ascending branch, eventually disappearing for periods longer than 20
days(Fig: 6). In contrast, Cepheids with the longest periods, exceeding 100 days(Fig: 7), generally display light
curves that are nearly sinusoidal with small amplitudes. Below, we have 4 light curves that illustrate typical
fundamental-mode classical Cepheids observed in the Large Magellanic Cloud.
3.3.2 First-overtone pulsators
Certain fundamental-mode Cepheids, typically with periods ranging from 6 to 12 days, exhibit light curves
that deviate from the standard pattern. These Cepheids display significantly smaller amplitudes compared to
typical ones within this period range, and the secondary bumps are either invisible or barely noticeable. First-
overtone Cepheids, in general, display smaller light amplitudes and more symmetric light curves compared to
fundamental-mode pulsators. Below, we present some example light curves of first-overtone Cepheids(Fig: 8)
observed in the Galactic bulge and Large Magellanic Cloud.
3.3.3 Second-overtone pulsators
Second-overtone oscillations result in nearly sinusoidal light curves characterized by small amplitudes,
typically below 0.1 magnitudes. Light curves of Second-overtone pulsators(Fig: 9) are given below.
34
3.3 Light Curves Of Classical Cepheids
Figure 6: Light curves of fundamental-mode Classical Cepheids with period greater than 30 days Source:
OGLE
Figure 7: Light curves of fundamental-mode Classical Cepheids with period greater than 100 days Source:
OGLE
Figure 8: Light curves of the first-overtone Cepheids Source: OGLE
35
3.4 Light Curves of RR Lyrae stars
Figure 9: Light curves of the second-overtone Classical Cepheids Source: OGLE
Figure 10: Light curves of the Multi-mode pulsators Source: OGLE
3.3.4 Multi-mode pulsators
Certain classical Cepheids exhibit simultaneous pulsation in two or even three modes. Light curves of
Multi-mode pulsators are given in Fig: 10, Fig: 11. When their light curves are collected over an extended
timespan and phased with one of the pulsation periods, they appear scattered due to the superimposition of
secondary periodicity upon the primary one. By utilizing Fourier techniques, it becomes feasible to separate
both light curves.
3.4 Light Curves of RR Lyrae stars
Considering their pulsation modes, RR Lyrae stars can be categorized into three groups: fundamental-
mode pulsators, often referred to as RRab stars or RR0 stars, first-overtone pulsators known as RRc or RR1
stars, and double-mode pulsators denoted as RRd or RR01 stars.
3.4.1 RRab stars
RRa and RRb stars both pulsate in the fundamental mode, and as a result, they were combined into
a single type known as RRab(Fig: 12). The pulsation periods of fundamental-mode RR Lyrae stars range
Figure 11: Light curves of the Multi-mode pulsators Source: OGLE
36
3.4 Light Curves of RR Lyrae stars
Figure 12: Light curves of RRab stars Source: OGLE
Figure 13: Light curves of RRc stars Source: OGLE
from approximately 0.3 to 1.0 days, with the majority having periods longer than 0.45 days. These stars
exhibit asymmetric light curves with a sharp rising branch and a gradual brightness decrease after reaching the
maximum. The amplitude of photometric variations is strongly correlated with the periods. The RRab variables
with the shortest periods tend to have the largest amplitudes, reaching up to 1.5 magnitudes in the V band and
up to 1 magnitude in the I band. As we progress to RRab stars with longer periods, the amplitudes typically
decrease.
3.4.2 RRc stars
RR Lyrae variables pulsating in the first-overtone mode(Fig: 13) exhibit periods ranging from approx-
imately 0.2 days to just over 0.5 days. These stars display much more symmetric light curves and smaller
amplitudes compared to RRab pulsators. Typically, RRc stars show a small secondary bump positioned on the
ascending branch of their light curves.
37
3.4 Light Curves of RR Lyrae stars
Figure 14: Light curves of RRd stars Source: OGLE
3.4.3 RRd stars
Certain RR Lyrae stars may exhibit the simultaneous excitation of two pulsation modes: the fundamental
and the first overtone. These stars are commonly referred to as RRd stars(Fig: 14). In most RRd stars, the
ratios of the two pulsation periods fall within a very narrow range, typically ranging from 0.74 to 0.75. The
majority of RRd stars display first-overtone components with larger amplitudes than the fundamental mode.
Once the modes are separated, the first-overtone light curve often resembles the shape and amplitude observed
in single-mode RRc stars. On the other hand, the fundamental-mode component clearly differs from RRab light
curves, exhibiting a small amplitude and nearly sinusoidal shape.
References:
Understanding Variable Stars, John R Percy, Cambridge University Press.
Variable Stars
About Light Curves
About Julian Dates
Chapter 12: Variable Stars and Phase Diagrams
LIGHT CURVES - Phase Diagram
Variable star
Variable Star Classification and Light Curves
Classical Cepheids
RR Lyrae stars
About the Author
Sindhu G is a research scholar in Physics doing research in Astronomy & Astrophysics. Her research
mainly focuses on classification of variable stars using different machine learning algorithms. She is also doing
the period prediction of different types of variable stars, especially eclipsing binaries and on the study of optical
counterparts of x-ray binaries.
38
Part III
Biosciences
The Tree of Life: Unravelling the Earth’s
Evolutionary Tapestry through Phylogenetic
Trees
by Geetha Paul
airis4D, Vol.1, No.8, 2023
www.airis4d.com
1.1 Introduction
A phylogenetic tree is a branching diagram or tree-like structure visually representing the evolutionary
relationships between different organisms. The Tree of Life is fundamental to understanding the interconnect-
edness and diversification of living organisms on Earth. Phylogenetic trees are also known as evolutionary
trees or cladograms. Phylogenetic trees are constructed based on the principles of common ancestry, where
closely related species are grouped, forming branches that trace their evolutionary lineage back to a common
ancestor. These trees depict the speciation, divergence, and adaptation patterns that have occurred over billions
of years. The construction of phylogenetic trees relies on various data sources, including genetic sequences,
anatomical features, and fossil records. Scientists can infer the relationships between different organisms and
classify them into related groups by examining these shared characteristics. Advances in DNA sequencing
technologies have revolutionised the field. Computational algorithms and statistical methods aid in analysing
vast amounts of data, enabling the construction of highly resolved and robust phylogenetic trees. In evolutionary
biology, they shed light on the origins and relationships of species, revealing common ancestors and helping to
decipher evolutionary patterns. Additionally, phylogenetic trees are valuable tools for understanding the spread
of infectious diseases, designing conservation strategies, and exploring the diversity of life on Earth.
1.1.1 Scientific Classification
Classification allows scientists to organise and better understand organisms’ basic similarities and differ-
ences. This knowledge is necessary to understand the present diversity and the evolutionary history of life on
Earth.
Why do biologists classify organisms? The primary reason is to make sense of the incredible diversity of
life on Earth. Scientists have identified millions of different species of organisms. Among animals, the most
diverse group of organisms is the insects. More than one million other species of insects have already been
described. An estimated nine million insect species have yet to be identified. A tiny fraction of insect species
is shown in the beetle collection in Figure 1.
1.1 Introduction
Figure 1: Only a few known insect species are represented in this beetle collection. Beetles constitute a
significant subgroup of insects. They make up about 40 per cent of all insect species and about 25 per cent of
all known species of organisms.
As diverse as insects are, there may be even more species of bacteria, another major group of organisms.
There is a need to organise the tremendous diversity of life.
1.2 Steps in building a phylogenetic tree
Data: (Relevant genetic sequences (DNA/proteins) from the organisms of interest)
Sequence Alignment: (Aligning sequences accurately for comparison)
Evolutionary Models: (Choosing appropriate models reflecting data characteristics) Computational
Resources: (Sufficient computing power and resources for analysis) Phylogenetic Software: (Reliable tools
for alignment, model selection, and tree construction)
Statistical Analysis: (Applying statistical methods for accurate interpretation)
Expertise: (Understanding evolutionary biology, bioinformatics, and statistical methods)
Quality Control: ( Rigorous checks to ensure data integrity and reliable results)
Data Representation: (Clear and informative visualisation of the tree)
Iteration and Validation: (Iterative process and validation for accuracy)
1.3 Parts of Phylogenetic tree
Branches: The branches of a phylogenetic tree represent evolutionary lineages or the descent line. They
connect the nodes or divergence sites.
Nodes: Nodes represent a common ancestor of the species or groups that diverged from it. Nodes can be
called internal nodes or internal branches when they represent non-observable common ancestors.
Tips or Leaves: The tips or leaves of a phylogenetic tree represent extant or alive species or groups.
Terminal taxa are taxa that are located at the extremities of branches.
Root: The root of the phylogenetic tree represents the most recent common ancestor of all the included
species or groups. Typically, it is depicted at the base of the tree.
Branch Length: In a phylogenetic tree, the length represents the quantity of evolutionary change along a
particular branch. The duration can be quantified in terms of time (e.g., millions of years) or genetic variation
(e.g., DNA substitutions).
41
1.2 Types of Phylogenetic Tree based on topology
Image courtesy: https://microbiologynote.com/how- to-construct-a- phylogenetic-tree/#steps-in- phylogenetic-analysisconstruct-a-phylogenetic-tree
Figure 2: The figure represents the primary components of a phylogenetic tree.
Phylogenetic Distance: The phylogenetic distance between two species or groups quantifies their rela-
tionship. Typically, it is estimated using genetic or morphological differences.
Taxa: Taxa are the categories of organisms or species that comprise the phylogenetic tree. Individual
species to higher taxonomic levels, such as genera, families, orders, and even larger groups.
Clades: Clans are monophyletic entities in a phylogenetic tree, composed of an ancestor and its descendants.
They share unique characteristics that are derived from a common ancestor.
It is essential to observe that phylogenetic trees can be represented in various ways, including cladograms,
phylograms, and chronograms, each emphasising a different aspect of evolutionary relationships or time.
1.1.2 Types of phylogenetic trees based on preference or absence of common root
Rooted trees have a specified root node, representing the common ancestor of all the organisms in the
tree.
Unrooted trees do not have a specified root node and show only the branching pattern of the evolutionary
relationships among taxa or OTUs, without any information about their common ancestor.
Both rooted and unrooted phylogenetic trees offer unique benefits and applications. When the relative
timing of divergence events and the direction of evolution is essential, rooted trees are frequently employed.
They are treasured for studying the history of evolution and deducing ancestral states. In contrast, unrooted
trees are commonly used for exploratory analysis, clustering analysis, and initial visualisation of taxonomic
relationships. When the concentration is on the relative relationships between taxa as opposed to their absolute
evolutionary history, they are particularly useful.
Rooted and unrooted tree | Both of these phylogenetic trees show the relationship of the three domains
of life—Bacteria, Archaea, and Eukarya—but the (a) rooted tree attempts to identify when various species
diverged from a common ancestor while the (b) unrooted tree does not.
42
1.2 Types of Phylogenetic Tree based on topology
Image courtesy: modification of work by Eric Gaba. https://microbiologynote.com/phylogenetic-tree-definition- types-steps-methods-uses
Figure 3
1.2 Types of Phylogenetic Tree based on topology
Based on their topology, phylogenetic trees can be divided into the following categories:
1.2.1 Cladogram
A cladogram is a phylogenetic tree that illustrates the branching pattern of evolutionary relationships
between taxa. It indicates the order of divergence but not the quantity of time or evolutionary change that has
taken place. Cladograms consist of branches that divide at nodes, representing common ancestors, and their
lengths are typically equal.
1.2.2 Phylogram
A phylogram is a phylogenetic tree that uses branch lengths to represent the degree of evolutionary change.
Indicating the relative amount of time or evolutionary distance between nodes, branch lengths can be proportional
to genetic or morphological differences. Phylograms add to our understanding of the magnitude of evolutionary
change.
1.2.3 Chronogram
A chronogram, also known as a time tree, is a scaled phylogenetic tree that depicts the estimated time of
divergence between species or groups. In a chronogram, the branch lengths are proportional to the estimated
43
1.3 Methods to construct Phylogenetic trees can be classified into two major types.
Image courtesy: https://microbiologynote.com/phylogenetic-tree- definition-types-steps-methods- uses/
Figure 6: Chronogram and phylogram
Image courtesy: https://microbiologynote.com/phylogenetic-tree- definition-types-steps-methods- uses/
Figure 7: Network tree
time since divergence, typically derived from fossil records or molecular clock analyses. Chronograms provide
a temporal perspective, enabling the visualisation of evolutionary event timing.
1.2.4 Network Tree
A network or reticulated tree is a phylogenetic representation consisting of reticulations or interconnected
branches. This method is employed when complex evolutionary processes, such as hybridisation, horizontal
gene transfer, or recombination, cannot adequately represent by a simple bifurcating tree structure. The exchange
of genetic material between distinct lineages can be visualised via network structures.
1.2.5 Fan Tree
A fan tree is a phylogenetic tree that illustrates the relationships between taxa by utilising multiple branches
emanating from a single node. It is frequently used to represent rapid radiations or evolutionary events in which
multiple lineages emerge from a common ancestor within a brief period. Fan trees illustrate the divergence of
lineages without specifying their sequence.
1.3 Methods to construct Phylogenetic trees can be classified into two major
types.
1.3.1 Distance-based methods
Distance-based tree construction methods involve calculating evolutionary distances between sequences
using substitution models, which are then used to construct a distance matrix. Using the distance matrix, a
phylogenetic tree is constructed. The two popular distance-based methods are UPGMA and NJ.
45
1.4 Character-Based Methods
Image courtesy: https://microbiologynote.com/phylogenetic-tree- definition-types-steps-methods- uses/
Figure 8: Fan tree
(a) Unweighted Pair Group Method with Arithmetic Mean (UPGMA)
UPGMA is the simplest distance-based method that uses sequential clustering to construct a rooted
phylogenetic tree. First, all sequences are compared using pairwise alignment to calculate the distance matrix.
Using this matrix, the two sequences with the smallest pairwise distance are clustered as a single pair. A node is
placed at the midpoint between them. Next, the distance between this pair and all other sequences is recalculated
to form a new matrix. This new matrix is used to identify and cluster the sequence that is closest to the first
pair. This process is repeated until all sequences have been placed on the tree. UPGMA method assumes that
the evolutionary rate of all taxa is constant, and they are equidistant from the root, indicating the presence of a
molecular clock mechanism.
(b). Neighbour-Joining (NJ)
The neighbour-joining method is the most widely used distance-based method. It is similar to the UPGMA
method in building the tree using a distance matrix. However, it does not assume the molecular clock and
produces an unrooted tree. The neighbour-joining algorithm starts with an utterly unresolved star tree, where all
sequences are connected to a single node. It then iteratively adds branches between the two closest neighbours
and the remaining sequences in the tree. The algorithm calculates the pairwise distances between all sequences
and uses these distances to determine the closest neighbours. Once the nearest neighbours are identified, the
algorithm consolidates them into a new node, effectively reforming the star tree. This process is repeated until
all sequences are connected in a fully resolved tree.
1.4 Character-Based Methods
Character-based methods involve analysing sequence data by directly examining the sequence characters
rather than relying on pairwise distance comparisons. These methods evaluate all sequences by analysing one
character or site at a time. Character-based methods are generally more accurate than distance-based methods.
However, character-based methods are more computationally intensive and require more sophisticated statistical
models. The two most commonly used character-based tree construction methods are the maximum parsimony
(MP) and maximum likelihood (ML) methods.
46
1.5 Limitations of the phylogenetic tree
(a). Maximum parsimony (MP)
The maximum parsimony method is a character-based method that selects the tree with the least number of
evolutionary changes or the shortest total branch length. Multiple sequence alignment is initially performed to
identify potential positions in the sequences that correspond to each other. Each aligned position is analysed to
determine the trees that require the smallest number of evolutionary changes to produce the observed sequence
changes. This process is repeated for all positions in the sequence alignment, and the trees that produce the
lowest overall number of changes for all positions are selected. This method works best for relatively similar
sequences and small numbers of sequences.
(b). Maximum likelihood (ML)
Maximum likelihood is a statistical method that uses probabilistic models to identify the most appropriate
tree with the maximum probability of generating the observed data. Similar to the maximum parsimony method,
this approach evaluates each column of a multiple sequence alignment during the analysis. However, unlike
maximum parsimony, ML considers all possible trees to explain the observed data. The likelihood of each
possible tree is calculated, and the tree with the highest probability is selected as the most likely evolutionary
history of the sequences.
1.5 Limitations of the phylogenetic tree
Phylogenetic trees are valuable tools for understanding evolutionary relationships among organisms. How-
ever, they are subject to various challenges and limitations, which can lead to incomplete or inaccurate repre-
sentations of evolutionary history. Some of these challenges include:
Incomplete Data: Phylogenetic trees heavily depend on available genetic or morphological data. The
absence of data or insufficient sampling can result in biased or incomplete trees, leading to potential errors in
determining genuine relationships among taxa.
Long-Branch Attraction: Long branches in a phylogenetic tree can lead to a phenomenon called long-
branch attraction. This occurs when distantly related taxa appear closely related due to shared evolutionary
changes along their lengthy branches, misleadingly suggesting a closer relationship than exists.
Convergence and Parallelism: Convergent evolution occurs when unrelated organisms independently de-
velop similar traits due to similar environmental pressures. This can create the appearance of close evolutionary
relationships when, in fact, the organisms are not closely related. Similarly, parallel evolution among closely
related organisms can lead to misleading relationship interpretations.
Horizontal Gene Transfer: Phylogenetic trees are typically based on the assumption of vertical gene transfer,
where genetic information is passed from parent to offspring. However, horizontal gene transfer, the transfer of
genetic material between unrelated organisms, can complicate the interpretation of evolutionary relationships
and lead to inaccuracies in tree construction.
Rate Variation: The rate of evolution can vary among different lineages or genes. Some branches may
evolve more quickly or slowly than others, leading to discrepancies in the inferred relationships and the estimation
of branch lengths in the phylogenetic tree.
Researchers must carefully consider these challenges and apply appropriate methods to mitigate their
impact on the accuracy and reliability of phylogenetic trees. Techniques like data pruning, model selection,
and using more sophisticated models that account for rate heterogeneity help address some of these issues.
Additionally, incorporating multiple lines of evidence, such as genomic data and fossil evidence, can provide a
more comprehensive understanding of evolutionary history and help refine phylogenetic relationships.
47
1.5 Limitations of the phylogenetic tree
References
1. https://thebiologynotes.com/phylogenetic-tree/
2. https://microbiologynote.com/phylogenetic-tree-definition-types-steps-methods-uses/
3. Bawono, P., & Heringa, J. (2014). Phylogenetic Analysis. Comprehensive Biomedical Physics, 93–110.
doi:10.1016/b978-0-444-53632-7.01108-4
4. Molecular Biology and Evolution, Volume 30, Issue 5, May 2013, Pages 1229–1235, https://doi.org/10.
1093/molbev/mst012
5. Choudhuri, S. (2014). Phylogenetic Analysis. Bioinformatics for Beginners, 209–218. doi:10.1016/b978-
0-12-410471-6.00009-8
6. Scott, A. D., & Baum, D. A. (2016). Phylogenetic Tree. Encyclopaedia of Evolutionary Biology,
270–276. doi:10.1016/b978-0-12-800049-6.00203-1
About the Author
Geetha Paul is one of the directors of airis4D. She leads the Biosciences Division. Her research
interests extends from Cell & Molecular Biology to Environmental Sciences, Odonatology, and Aquatic Biology.
48
Part IV
General
Ethical AI and Responsible Humanity
Building the Power of Technology for a
Responsible Future
by Dr. Fr. Abraham Mulamoottil
airis4D, Vol.1, No.8, 2023
www.airis4d.com
(Zacharias Memorial Lectures at the Pontifical Institute of
Theology and Philosophy, Alwaye, Kerala, India. 22 July 2023)
The talk highlighted the importance of addressing the ethical implications of artificial intelligence (AI) and
ensuring responsible development and use of AI systems. The speaker emphasized the need for understanding
AI’s impact, the development of ethical frameworks, and the global conversation surrounding AI regulation.
The concept of ethical AI is explored, which refers to the development and deployment of AI systems that
align with ethical principles and promote human well-being. This involves creating AI algorithms, models,
and systems that prioritize fairness, transparency, accountability, and inclusivity. By incorporating ethical
considerations into AI development, potential biases, discrimination, and unintended consequences can be
mitigated.
The talk introduced the concept of responsible humanity, which emphasizes human involvement and
decision-making in the development and use of AI technologies. It advocates for AI to be a tool for human
empowerment rather than a replacement for human judgment and values. Responsible humanity entails active
engagement in shaping AI systems, setting ethical guidelines, and taking responsibility for the societal impact
of AI.
The talk outlined key principles of ethical AI, including autonomy, agency, assurance, interfaces, indicators,
and intentionality. These principles focus on understanding the limits of AI’s autonomy, implementing controls
and limits on AI systems, ensuring safety and transparency, developing user-friendly interfaces, assessing
AI-driven systems, and aligning AI with human values and aspirations.
Three major ethical concerns with AI were highlighted: potential misuse for malicious purposes, ensuring
accessibility and inclusivity to prevent exacerbating disparities, and the differences in values between AI systems
and humans, raising ethical questions about decision-making processes and potential conflicts.
The talk also discussed challenges associated with AI, such as addressing power imbalances, minimizing
bias, ensuring explainability, maintaining security and privacy, and balancing automation and employment. It
emphasizes the need to consider the broader ethical and social implications of AI technologies.
The ethical implications of the global AI race were also explored, emphasizing the importance of collabo-
ration, responsible and ethical AI development, transforming society, governmental challenges, and the impact
of AI on humanity’s future. Proactive regulation of AI is advocated to protect public conversations, ensure AI
serves humanity’s best interests, and promote informed discussions and democratic decision-making.
To promote ethical AI adoption, the talk suggested embedding ethical principles into the design and
implementation of AI technologies, promoting education and awareness, and addressing global challenges
collaboratively. It acknowledges the global conversation on AI regulation and the need for collaboration,
multidisciplinary approaches, responsible AI development, and regulatory frameworks.
In short, the talk emphasized the intertwining of ethical AI and responsible humanity in shaping the future
of technology. By embracing ethical principles, prioritizing human values, fostering collaboration, promoting
public awareness, and establishing comprehensive regulatory frameworks, AI can be harnessed to drive positive
change and build a more inclusive, fair, and sustainable society. It underscores the collective responsibility to
ensure AI serves humanity’s best interests while upholding ethical standards and ensuring accountability.
References:
1 World Economic Forum: ”Ethical AI Guidelines: The Complete Guide” (https://www.weforum.org/
whitepapers/ethical-ai-guidelines-the-complete-guide)
2 MIT Technology Review: ”The Ethics of Artificial Intelligence” (https://www.technologyreview.com/
2019/01/02/137754/the-ethics-of-artificial-intelligence/)
3 European Commission: ”Ethics Guidelines for Trustworthy AI” (https://ec.europa.eu/digital-single-market/
en/news/ethics-guidelines-trustworthy-ai)
4 Forbes: ”Why Ethical AI Matters and How to Get There” (https://www.forbes.com/sites/cognitiveworld/
2020/01/30/why-ethical-ai-matters-and-how-to-get-there/?sh=39676c1715a3)
About the Author
Dr. Fr. Abraham Mulamoottil (https://en.wikipedia.org/wiki/Abraham Mulamoottill) has marked
his distinctive footprint in diverse fields, from business to education, public service to social initiatives. He
founded MACFAST College and RadioMACFAST 90.4 FM and has been the Chairman & Chief Executive
of Pushpagiri Group of Medical Institutions. He started the ”Keeping Religion Private Movement,”(http:
//kripamovement.in/). He is a Catholic Priest of the Archdiocese of Tiruvalla, Kerala, India.
51
Part V
Computer Programming
Fractals - Nature’s building block
by Ninan Sajeeth Philip
airis4D, Vol.1, No.8, 2023
www.airis4d.com
In our previous article, we wrote code for creating a few fractal structures and found it easy to create
fractals using a few lines of code. But besides being elegant and straightforward, fractals also play a significant
role as building blocks for the natural beauty we see around us. In this issue, we shall code a few commonly
observed phenomena as a derivative of fractal geometry. One key feature that makes fractal geometry so elegant
is self-similarity. You start with a function and recursively call itself. Eventually, you will end up with a fractal
structure.
Nature has explored fractal geometry as one of its most potent building units. For example, look at a tree.
It starts as a sprout with a long stem and two leaves. As it grows, the same pattern is repeated to form branches,
sub-branches and so forth until the big tree is formed! Our nerve system uses the same branching method to
supply equal amounts of vital ingredients to every cell in our body. Let’s explore how this can be illustrated
using simple Python programs.
Those of you who have studied LOGO language in schools must have encountered a Turtle that you direct
to draw images on the canvas. You tell the turtle to move forward, turn left or right at some angle and complete
the drawing. There is a Python library called Turtle that does the same! Because of its simplicity, it is used as
the most popular platform for drawing fractals.
So, without much explanation, let us start doing it. First step ofcource is to import the turtle library. The
next step is to define our drawing turtle by initialising an instant of it. Let us call it t.
That is
import turtle
t= turtle.Turtle()
Now by saying t.right(angle), we can turn the turtle right by angle, t.forward(length) to move forward by
length etc. So simple.
To build the tree, we will start with the simple assumption that the tree branches into two at every node.
Let us also assume for simplicity that this is uniformly in both left and right directions. Once you understand
the steps, you can explore all other possibilities by modifying the code.
The turtle function also has a few more important functions that help the drawing process. To draw, you
first need a canvas. This is created by the function:
screen = turtle.Screen()
You can then set up the size of the screen by setting its width and height. screen.setup(width, height) and
the canvas’s colour by calling screen.bgcolour(colour). The canvas is now ready.
The screen coordinates have their origin at the centre. We need to place our turtle where we want to start
drawing. This is done by the function setpos(x,y). In our example, let us set it to the centre of the page but from
the bottom. So if the height of the canvas is 800, y has to be -400, and x should be zero. Then there is also an
up() and down() function that may be used to lift up the pen from drawing and put it down on paper to draw.
You can also decide the colour of the drawing ink to make your drawings look nice.
So, the first step is to define our branching function, which in our example tells the turtle to draw a straight
line of a given length and then draw another with a reduced size towards the right at a given angle, move in the
opposite direction by twice the angle and draw another line symmetrically on the left side and finally return to
the mean position.
In our example, the branching function produces a symmetric Y structure with the following function
definition:
def draw_fractal_tree(branch_length, t, level):
colors = [ "black","brown", "brown", "gray", "green"]
if branch_length > mblength/2:
color_index = min(level, len(colors) - 1) # Choose a color based on branch level
t.color(colors[color_index])
t.pensize(branch_length / 10) # Adjust the branch thickness based on length
t.forward(branch_length)
# Right sub-branch
t.right(20) # turn by 20 degree to right from mean position
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
# Left sub-branch
t.left(2*20) # turn by twice that to left to make second branch on left
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
t.right(20) # return to mean position
t.backward(branch_length)
As you can see, as long as the branch length is greater than half some number defined by mblength which
also is the length of the initial branch, the function calls itself iteratively after reducing the branch size to
branch length-branch length/5. This makes sure that the tree size converges and stops at some value (in this
case, hlaf of the length of the longest branch). The rest of the code is straightforward.
Here is the complete code:
import turtle
mblength=150
def draw_fractal_tree(branch_length, t, level):
colors = [ "black","brown", "brown", "gray", "green"]
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if branch_length > mblength/2:
color_index = min(level, len(colors) - 1) # Choose a color based on branch level
t.color(colors[color_index])
t.pensize(branch_length / 10) # Adjust the branch thickness based on the length
t.forward(branch_length)
# Right sub-branch
t.right(20) # Turn by 20 degrees to the right from the mean position
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
# Left sub-branch
t.left(2*20) # turn by twice that to left to make the second branch on the left
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
t.right(20) # return to mean position
t.backward(branch_length)
def main():
screen = turtle.Screen()
screen.setup(width=800, height=800)
screen.bgcolor("white")
t = turtle.Turtle()
t.speed(0)
t.up()
t.setpos(0, -400)
t.down()
t.left(90)
branch_length = mblength
draw_fractal_tree(branch_length, t, 1) # Start at level 1
t.hideturtle()
screen.mainloop()
if __name__ == "__main__":
main()
The code should produce a simple tree shown in Figure 1
The first modification you may want to try is the change the number of iterations. Let us change if
55
Figure 1: The simple fractal tree.
branch length > mblength/2 to if branch length > mblength/6. The resulting tree is shown in Figure 2.
A close observation of Figure 2 reveals that by repeatedly doing the same function, one can end up in a
space-filling path that reaches every pixel in that region with the same strength starting from a single point.
Those who have studied anatomy might immediately recollect the similarity of the structure of our nerve cells
that carry vital elements to each cell in our body. Many of our discoveries were known to nature before life and
intelligence were born!
Modifying the basic bifurcation function to make three or four branches at the same node is possible.
All one need to do is add appropriate turtle turns and line drawings. Make the following modification to the
branching function to get four branches per node. The logic is the same as before, but look at how each of those
edges has completely filled the boundary without touching each other. Figure 3, which depicts the resulting
image, looks very much like the nerve system, broccoli buds, or mosses that create space-filling leaf edges to
capture maximum available light in their growing environments without shading one another. Also, note that
though we have not explicitly mentioned what the surface should look like in the code, instead of our familiar
flat surface, the resulting image has a curved surface required to populate the entire edges nonoverlapping. The
distance of all the end nodes to the central main branch is the same and is uniform. What a clever arrangement
to uniformly feed the cells or gather light in each application!
# Right sub-branch
t.right(20) # Turn by 20 degrees to right from mean position
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
# Left sub-branch
t.left(40) # Turn by twice that to left to make second branch on left
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
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Figure 2: Increasing the number of iterations produces a fractal structure that tends to fill the space.
t.right(25) # turn 5 degree extra to make a third branch on right
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
# Left sub-branch
t.left(10) # turn 5 degree extra to make a forth branch on left
draw_fractal_tree(branch_length-branch_length/5, t, level + 1)
t.right(5)# return to mean position
t.backward(branch_length)
We will conclude our coding exercise with an alternate and faster method for fractal image creation using
transformation equations.
The Fern has a fractal structure. Copy the code below and run it. After plotting the image, zoom in to look
at the different regions and explore the self-similarity of the structure. This self-similarity is one of the most
striking features of fractal structures.
import matplotlib.pyplot as plt
import numpy as np
def draw_fern(n_points):
# Initialize the starting point
x, y = 0.0, 0.0
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Figure 3: A relatively simple modification to the code to create four branches at each node has resulted in a
space-filling nonoverlapping pattern very much similar to many natural structures we observe in nature.
# Initialize the arrays to store the points
x_points = np.zeros(n_points)
y_points = np.zeros(n_points)
# Define the transformation functions for the fern
def transformation_1(x, y):
x_new = 0.85 * x + 0.04 * y
y_new = -0.04 * x + 0.85 * y + 1.6
return x_new, y_new
def transformation_2(x, y):
x_new = 0.2 * x - 0.26 * y
y_new = 0.23 * x + 0.22 * y + 1.6
return x_new, y_new
def transformation_3(x, y):
x_new = -0.15 * x + 0.28 * y
y_new = 0.26 * x + 0.24 * y + 0.44
return x_new, y_new
58
def transformation_4(x, y):
x_new = 0.0
y_new = 0.16 * y
return x_new, y_new
# Perform the chaos game iterations
for i in range(n_points):
# Choose a random transformation
rand = np.random.random()
if rand <= 0.85:
x, y = transformation_1(x, y)
elif rand <= 0.92:
x, y = transformation_2(x, y)
elif rand <= 0.99:
x, y = transformation_3(x, y)
else:
x, y = transformation_4(x, y)
# Store the point
x_points[i] = x
y_points[i] = y
# Plot the points
plt.scatter(x_points, y_points, s=0.2, c=’green’)
# Set plot limits and show the image
plt.xlim(-3, 3)
plt.ylim(0, 10)
plt.axis(’off’) # Hide axis
plt.show()
# Call the function to draw the fern
draw_fern(1000000)
Working with transformation equations is an easy way to create a large collection of fractal images. Below
is a modified version of the same transformation equations with their coefficients arranged in a matrix format.
The given setting creates a bouquet, as shown in Figure 5.
import matplotlib.pyplot as plt
import numpy as np
def draw_fractal(transformations, n_points):
# Starting point
59
Figure 4: The self-similarity of the fractal structure is evident in the fern image. Every part of it is a scaled
replication of the same pattern defined by the transformation equation, and the code allows zoom in and zoom
out facility to explore it.
60
x = 0
y = 0
# Lists to store the coordinates
x_coords = [x]
y_coords = [y]
# Iterate and generate the fractal points
for _ in range(n_points):
# Choose a random transformation index
transformation_index = np.random.choice(len(transformations))
# Select the transformation
transformation = transformations[transformation_index]
# Apply the chosen transformation
x_new = transformation[0] * x + transformation[1] * y + transformation[4]
y_new = transformation[2] * x + transformation[3] * y + transformation[5]
# Update the coordinates
x = x_new
y = y_new
# Store the new coordinates
x_coords.append(x)
y_coords.append(y)
# Plot the fractal flower
plt.scatter(x_coords, y_coords, c=’red’, s=0.2)
plt.title(’Fractal Flower’)
plt.axis(’off’)
plt.show()
def draw_fractal_flower(n_points):
# Define the transformation matrices for the flower
transformations = [
[0.5, -0.5, 0.5, 0.5, 0.0, 0.0],
[0.5, 0.5, -0.5, 0.5, 0, 0],
[-0.5, 0.0, -0.41, 0.5, -0.38, 0.26],
[0.5, 0, 0, 0.5, 0, 0]
]
# Call the draw_fractal function to generate and display the fractal flower
draw_fractal(transformations, n_points)
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Figure 5: The bouquet created using fractal geometry is just a demonstration of its similarity to natural patterns.
The coefficients in the transformation matrix used in the code can be modified to create a large variety of fractal
images.
To conclude, fractal geometry is a fascinating field with many similarities to naturally occurring patterns
and phenomena. The above codes may be mastered and modified to explore more possibilities.
About the Author
Professor Ninan Sajeeth Philip is a Visiting Professor at the Inter-University Centre for Astronomy
and Astrophysics (IUCAA), Pune. He is also an Adjunct Professor of AI in Applied Medical Sciences [BCMCH,
Thiruvalla] and a Senior Advisor for the Pune Knowledge Cluster (PKC). He is the Dean and Director of airis4D
and has a teaching experience of 33+ years in Physics. His area of specialisation is AI and ML.
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About airis4D
Artificial Intelligence Research and Intelligent Systems (airis4D) is an AI and Bio-sciences Research Centre.
The Centre aims to create new knowledge in the field of Space Science, Astronomy, Robotics, Agri Science,
Industry, and Biodiversity to bring Progress and Plenitude to the People and the Planet.
Vision
Humanity is in the 4th Industrial Revolution era, which operates on a cyber-physical production system. Cutting-
edge research and development in science and technology to create new knowledge and skills become the key to
the new world economy. Most of the resources for this goal can be harnessed by integrating biological systems
with intelligent computing systems offered by AI. The future survival of humans, animals, and the ecosystem
depends on how efficiently the realities and resources are responsibly used for abundance and wellness. Artificial
intelligence Research and Intelligent Systems pursue this vision and look for the best actions that ensure an
abundant environment and ecosystem for the planet and the people.
Mission Statement
The 4D in airis4D represents the mission to Dream, Design, Develop, and Deploy Knowledge with the fire of
commitment and dedication towards humanity and the ecosystem.
Dream
To promote the unlimited human potential to dream the impossible.
Design
To nurture the human capacity to articulate a dream and logically realise it.
Develop
To assist the talents to materialise a design into a product, a service, a knowledge that benefits the community
and the planet.
Deploy
To realise and educate humanity that a knowledge that is not deployed makes no difference by its absence.
Campus
Situated in a lush green village campus in Thelliyoor, Kerala, India, airis4D was established under the auspicious
of SEED Foundation (Susthiratha, Environment, Education Development Foundation) a not-for-profit company
for promoting Education, Research. Engineering, Biology, Development, etc.
The whole campus is powered by Solar power and has a rain harvesting facility to provide sufficient water supply
for up to three months of drought. The computing facility in the campus is accessible from anywhere through a
dedicated optical fibre internet connectivity 24×7.
There is a freshwater stream that originates from the nearby hills and flows through the middle of the campus.
The campus is a noted habitat for the biodiversity of tropical Fauna and Flora. airis4D carry out periodic and
systematic water quality and species diversity surveys in the region to ensure its richness. It is our pride that
the site has consistently been environment-friendly and rich in biodiversity. airis4D is also growing fruit plants
that can feed birds and provide water bodies to survive the drought.
