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Stephan’s Quintet, HCG 92

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Editorial

by Fr Dr Abraham Mulamoottil

airis4D, Vol.1, No.7, 2023

www.airis4d.com

The relationship between AI and consciousness is a topic that airis4D Journal can delve into. While AI

systems can display intelligent behaviour, the question of whether they should possess higher consciousness like

humans remains a philosophical and ethical dilemma. In the competitive race for market dominance, ethical

AI and responsible humanity take centre stage. Ethical AI focuses on developing and utilizing AI systems that

adhere to ethical principles and prioritize human well-being. It involves integrating moral considerations into

AI design, decision-making, and impact assessment, going beyond technical capabilities to address societal

implications and ethical challenges. Similarly, responsible humanity underscores the collective responsibility

of individuals, organizations, policymakers, and society in ensuring the responsible development and use of

AI. It acknowledges the obligation to consider the societal impact of AI, prioritize ethics, and proactively tackle

ethical challenges associated with AI technologies. This Edition of airis4D Journal starts with the second part

of the article titled ”Diﬀerence Boosted Neural Network (DBNN)”. Blesson George discusses the training

process of the DBNN network, which combines deep learning techniques with Bayesian inference to optimize

performance. The network bins attribute values into intervals and compute histograms to estimate probabilities

for each bin and class. The DBNN identiﬁes overlapping regions in the feature space by measuring the distance

between probabilities. The article introduces boosting, an iterative procedure that focuses on diﬃcult-to-

classify instances by assigning weights to training examples based on performance. The article also explains

updating prior probabilities in Naive Bayes classiﬁers and mentions AdaBoost as a meta-algorithm that improves

performance. The Diﬀerence Boosting (DB) algorithm is introduced, which adjusts weights associated with

attribute probabilities for misclassiﬁed examples. The article ”Mastering Categorical Variable Encoding for

Improved Machine Learning” by Jinsu Ann Mathew explores challenges and encoding methods for categorical

variables in machine learning. It discusses one-hot encoding, one-hot encoding with multiple categories, mean

encoding, and target-guided ordinal encoding. The importance of understanding the strengths and appropriate

use cases of each method is emphasized. Selecting the right encoding technique enables informed decisions

in working with categorical data. This edition is also blessed with the article of Professor Ajit Kembhavi who

pioneered astronomy outreach activities from the late 80s to promote astronomy research in Indian universities.

His article ”Detection of Lone Black Holes” explores the challenges of detecting lone black holes and proposes

gravitational lensing as a potential detection method. Lone black holes, which do not emit light or radiation, are

diﬃcult to observe directly. Gravitational lensing, based on Einstein’s theory of general relativity, can be used

to indirectly detect them. The article highlights the signiﬁcance of gravitational lensing and its potential for

identifying these elusive objects. Robin Jacob Roy’s article ”Unveiling the Birth of Stars: A Cosmic Symphony

of Creation” explores the process of star formation and its signiﬁcance in the universe. Stars are born from

molecular clouds and contribute to galaxy evolution and the creation of essential elements. The process involves

gravitational collapse, protostellar evolution, and the formation of stellar clusters. Giant molecular clouds act as

primary star formation sites, studied using longer wavelength radiation. The balance between gas pressure and

gravity determines cloud collapse, leading to the formation of multiple stars. Fragments within the collapsing

cloud condense into rotating gas spheres, forming protostars surrounded by accretion disks. When conditions

are met, nuclear fusion begins, giving birth to a star. Star formation in clusters impacts the surrounding

cloud through stellar winds and radiation pressure. Understanding this process enhances our knowledge of

the universe’s complexity. The article ”Galaxy Morphologies” by Sheelu Abraham, provides a comprehensive

overview of galaxy classiﬁcations and morphologies. It discusses the historical context, including Edwin

Hubble’s contributions and the Great Debate in Astronomy. The Hubble Classiﬁcation Scheme is explained,

categorizing galaxies into elliptical, spiral, and lenticular types. It brieﬂy touches upon galaxy evolution and

highlights the importance of studying it for a deeper understanding of the universe. The article ”Rotating

Variable Stars” by Sindhu G provides an overview of rotating variable stars and their characteristics. Examples

include FK Comae Berenices (FK Com) stars, Alpha-2 Canum Venaticorum (Alpha-2 CVn) variables, SX

Arietis variables, ellipsoidal variables, optically variable pulsars, and BY Draconis-type variables. These stars

exhibit varying brightness due to rotation and oﬀer insights into stellar magnetic ﬁelds, evolution, and binary

systems. The article ”Agile Manufacturing Processes” by Arun Aniyan discusses traditional manufacturing

limitations and introduces 3D printing as a revolutionary technology. It eliminates costly and time-consuming

steps, reduces material waste, and allows for easy design modiﬁcations. 3D printing enables experimentation,

cost reduction, and increased creativity in design. It is changing the manufacturing landscape, making it more

accessible and sustainable.

iii

Contents

Editorial ii

I Artiﬁcial Intelligence and Machine Learning 1

1 Diﬀerence Boosted Neural Network(DBNN) - Part 2 2

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Probabilities in Bayes Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Diﬀerence Boosting algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Mastering Categorical Variable Encoding for Improved Machine Learning 5

2.1 Types of categorical variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 One hot Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 One Hot Encoding (multiple categories) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Mean Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 Target guided Ordinal Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.6 Label Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

II Astronomy and Astrophysics 11

1 Black Hole Stories-2

Gravitational Lensing for the Detection of Lone Black Holes 12

1.1 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.2 Gravitational Lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3 Gravitational Microlensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Unveiling the Birth of Stars: A Cosmic Symphony of Creation 17

2.1 Cosmic Nurseries: Molecular Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Cloud Collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Protostellar Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Stellar Clusters and Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Galaxy Morphologies 21

3.1 Galaxies in Our Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Observing the individual Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Galaxy Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.4 Galaxy Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Rotating Variable Stars 27

4.1 What Are Rotating Variable Stars? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

CONTENTS

4.2 Some Examples Of Rotating Variable Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

III Biosciences 31

1 Molecular Cloning 32

1.1 Gene Cloning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.2 Reproductive cloning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.3 Therapeutic cloning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.4 Other Cloning Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.5 Research and Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

IV General 38

1 Agile Manufacturing Processes 39

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

1.2 Traditional Manufacturing Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

1.3 3D printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

V Computer Programming 43

1 Fractal Geometry 44

1.1 Mandelbrot set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1.2 Cantor set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

1.3 Sierpinski Gasket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

1.4 Koch snowﬂake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

1.5 Koch curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Part I

Artiﬁcial Intelligence and Machine Learning

Diﬀerence Boosted Neural Network(DBNN) -

Part 2

by Blesson George

airis4D, Vol.1, No.7, 2023

www.airis4d.com

1.1 Introduction

Welcome to the second part of our discussion on Diﬀerence Boosting Neural Network (DBNN). In the

previous section, we explored how conditional independence is enforced within our network and provided a

brief explanation of the assumed Bayes components. Now, let’s delve into the training process of the DBNN

network.

In this article, we will focus on elucidating how the training occurs within the DBNN network. Training

a DBNN involves iteratively updating the network’s parameters to optimize its performance on a speciﬁc task.

This training procedure combines the power of deep learning techniques with the probabilistic nature of Bayesian

inference.

1.2 Probabilities in Bayes Theorem

Consider a Naive Bayes classiﬁer, in which the given dataset with k attributes (A

to A

) is having discrete

values and the objective is to predict the discrete class C based on these attribute values. For a given example

with attribute values a

to a

, the optimal prediction of class C = c is determined by maximizing the probability

P (C = c|A

= a

∩ A

= a

∩ ... ∩ A

= a

)

According to Bayes theorem, this probability is equal to

P (A

= a

∩ A

= a

∩ ... ∩ A

= a

|C = c) × P r(C = c)

P (A

= a

∩ A

= a

∩ ... ∩ A

= a

)

In the case of the DBNN (Diﬀerence Boosted Neural Network) network, a mechanism is implemented to ensure

conditional independence among the attributes. Instead of directly using the attribute values for probability

calculation, the values are binned into diﬀerent intervals, and the histogram of each bin is computed. This

approach allows us to estimate the probabilities based on the counts of attributes falling into each bin, speciﬁcally

for a given class.

Here’s a restatement of the process:

The attribute values are divided into intervals or bins, discretizing the continuous values.

1.3 Boosting

For each attribute and class combination, the number of occurrences of the attribute falling into each bin

is counted.

This count represents the frequency of the attribute having a speciﬁc value within the given class.

By dividing the count by the total number of instances in that class, the probability P (U

) is calculated.

P (U

) denotes the probability of attribute m taking the value U

within class C

The fundamental diﬀerence of this new formalism from popular gradient descent backpropagation algo-

rithms and similar neural networks lies in the choice of the distance function (Bin size). Instead of considering

the distance based on feature magnitudes, this new formalism measures the distance between probabilities. As

a result, it eﬀectively isolates overlapping regions in the feature space more eﬃciently compared to traditional

algorithms.

1.3 Boosting

Boosting is an iterative procedure that aims to modify the distribution of training examples to emphasize

diﬃcult-to-classify instances. It achieves this by assigning weights to each training example and updating them

at the end of each boosting round. The process involves sampling new training datasets based on the sampling

distribution derived from the current weights. A classiﬁer is then trained using the new dataset and used to

classify all examples in the original dataset. At the end of each round, the weights of the training examples are

adjusted based on their classiﬁcation performance. This iterative process continues until a predeﬁned number

of boosting rounds or until a speciﬁed performance criterion is met. By adaptively changing the weights and

focusing on challenging examples, boosting improves the overall performance of the classiﬁer ensemble.

1.3.1 Updating prior prababilities in Naive Bayes Classiﬁers

In Naive Bayes classiﬁers, the prior probabilities represent the initial beliefs or knowledge about the

distribution of classes before considering any evidence from the training data. Updating the prior probabilities

involves adjusting them based on the observed class distribution in the training data. This allows the Naive

Bayes model to adapt to the speciﬁc dataset and potentially improve its predictive performance.

To update the prior probabilities in Naive Bayes, we follow a general process. Initially, we collect a labeled

dataset that includes instances with their respective class labels. Next, we compute the class frequencies by

counting the number of instances belonging to each class in the training data. This step provides us with the

frequency of occurrence for each class. We then calculate the class proportions by dividing the class frequencies

by the total number of instances in the training data. This allows us to determine the relative frequencies or

probabilities of each class occurring in the dataset. Finally, we adjust the prior probabilities by replacing the

original values with the updated probabilities derived from the training data. These updated prior probabilities

now reﬂect the observed class distribution in the dataset. By incorporating the observed class frequencies,

Naive Bayes can make more informed predictions and eﬀectively capture the characteristics of the dataset.

1.3.2 AdaBoost

AdaBoost, also known as Adaptive Boosting, is a machine learning algorithm introduced by Yoav Freund

and Robert Schapire. It is a meta-algorithm that can be applied in conjunction with various learning algorithms

to enhance their performance. AdaBoost is considered adaptive because it adjusts its focus on instances that

were misclassiﬁed by previous classiﬁers. However, it is important to note that AdaBoost is sensitive to noisy

data and outliers. The boosting process in AdaBoost begins by assigning equal weights to all instances in

1.4 Diﬀerence Boosting algorithm

the training data. It then applies the learning algorithm to create a classiﬁer and adjusts the weights of each

instance based on the classiﬁer’s output. The weights of correctly classiﬁed instances are reduced, while those

of misclassiﬁed instances are increased. This iterative process continues, with subsequent classiﬁers adapting

to the reweighted instances, ultimately improving the overall performance of the ensemble model.

1.4 Diﬀerence Boosting algorithm

Diﬀerence Boosting (DB) algorithm closely resembles AdaBoost in that it also modiﬁes a weight function.

However, there are some key diﬀerences. Instead of computing the classiﬁcation error based on the overall

performance on the training set, diﬀerence network focuses on each individual misclassiﬁed example. DB

algorithm apply a correction to the weight of each misclassiﬁed example based on its own error. Additionally,

instead of increasing the weight of an example, the network increases the weight associated with the probability

P (U

) of each attribute in the example. This means that the modiﬁed weight will aﬀect all examples that

share the same attribute value, even if their other attributes are diﬀerent. Throughout the training process, there

is a competitive update of attribute weights to minimize the error produced by each example. It is expected

that by the end of the training epoch, the weights associated with the probability function of each attribute will

stabilize to some optimal values. This approach allows DB algorithm to eﬀectively adapt to the characteristics

of the data and improve its predictive performance.

Consider a misclassiﬁed example, where P

represents the computed probability for the actual class k, and

∗

represents the probability for the wrongly represented class. Our goal is to increase the computed probability

to a value greater than P

∗

. In our network, we achieve this by modifying the weight associated with each

P (U

) of the misclassiﬁed item using the negative gradient of the error. Speciﬁcally, we update the weight

∆W

= α(1 − P

∗

)

, where α is a constant that determines the rate of weight change and it is equivalent to the learning parameter

in neurel networks This process is repeated until all items are correctly classiﬁed or until a predeﬁned number

of rounds is completed. By adjusting the weights based on the gradient of the error, we aim to improve the

classiﬁcation accuracy and converge towards a more accurate model.

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.

References

1. Boosting the Diﬀerenes : A Fast Bayesian Classifer Neural Network

2. BOOSTING AND NAIVE BAYESIAN LEARNING

3. A Hybrid Classiﬁer using Boosting, Clustering, and Na

ıve Bayesian Classiﬁer

4. Implementation of Naive Bayesian Classiﬁer and Ada-Boost Algorithm Using Maize Expert System

5. A Learning Algorithm based on Primary School Teaching Wisdom

Mastering Categorical Variable Encoding for

Improved Machine Learning

by Jinsu Ann Mathew

airis4D, Vol.1, No.7, 2023

www.airis4d.com

In the ﬁeld of machine learning and data analysis, variables come in various forms, encompassing both

continuous numerical values and categorical attributes. Numerical variables represent quantities that can take

on a range of values and possess mathematical properties such as order and magnitude. The treatment of

numerical variables in machine learning is relatively straightforward, as algorithms can readily process and

analyze their numerical representations.

On the other hand, categorical variables introduce a distinct challenge. Categorical attributes are character-

ized by discrete values and lack inherent order or magnitude. Unlike numerical variables, categorical variables

capture qualitative characteristics or group memberships. Examples of categorical variables include gender

(male, female), colors (red, blue, green), or geographic regions (North America, Europe, Asia).

However, these seemingly discrete and non-numeric variables often carry valuable information that can

signiﬁcantly inﬂuence the performance and accuracy of machine learning models. Eﬀectively handling categor-

ical variables is crucial for extracting meaningful insights and building reliable models. The process involves

transforming categorical data into a numerical form that can be processed by machine learning algorithms,

allowing them to capture the underlying patterns and relationships within these variables. A variety of en-

coding methods have been developed to address the categorical variable conundrum, each with its strengths,

weaknesses, and suitable use cases.

This article explores and examines several popular encoding methods for categorical variables, shedding

light on their underlying principles and practical applications. By understanding the advantages and limitations

of these techniques, data scientists, machine learning practitioners, and researchers can make informed decisions

when handling categorical data in their projects.

2.1 Types of categorical variables

Categorical variables can be classiﬁed into two main types: nominal variables and ordinal variables.

2.1.1 Nominal Variables

Nominal variables are categorical variables that represent categories without any intrinsic order or ranking.

The categories are typically distinct and independent from each other. Examples of nominal variables include

2.2 One hot Encoding

Figure 1: Nominal variables

Figure 2: Ordinal variables

colors (red, blue, green),Marital Status(single, married, divorced, or widowed) etc(Figure 1). Nominal variables

simply indicate membership in a particular group or category. It is important to note that there is no inherent

hierarchy or order among the categories of nominal variables.

2.1.2 Ordinal Variables:

Ordinal variables, on the other hand, are categorical variables that possess a meaningful order or ranking

among their categories. The categories have a relative position or level that conveys a sense of hierarchy or

magnitude. Examples of ordinal variables include educational attainment (elementary, high school, bachelor’s

degree, master’s degree) or customer satisfaction ratings (poor, fair, good, excellent)(Figure 2). Unlike nominal

variables, the categories of ordinal variables have an inherent order or ranking based on some criteria or scale.

The distinction between nominal and ordinal variables is important as it aﬀects how we analyze and

interpret the data. Nominal variables are typically analyzed using frequency counts or proportions, while

ordinal variables allow for comparisons of the relative positions or levels of the categories. The appropriate

statistical methods and encoding techniques for handling these two types of categorical variables may also diﬀer,

considering the nature of the data and the research question at hand. Some commonly used encoding techniques

for categorical variables are discussed below(Figure 3).

2.2 One hot Encoding

One-Hot Encoding is a technique used to represent categorical variables as binary vectors. It is commonly

employed in machine learning tasks where categorical data needs to be transformed into a numerical format

that algorithms can process.

The process of One-Hot Encoding involves creating binary variables, also known as dummy variables, for

each category of the categorical variable. Each category is assigned a unique binary vector, where a value of 1

represents the presence of that category and a value of 0 represents the absence. For example, Consider a dataset

2.3 One Hot Encoding (multiple categories)

(image courtesy:https://ai-ml-analytics.com/encoding/)

Figure 3: Encoding Techniques

(imagecourtesy:https://pub.towardsai.net/5-useful-encoding-techniques-in-machine-learning-f735567399f4)

Figure 4: one hot encoding

containing a categorical variable ”Animal” with various animals such as cat, dog, lion, cow, sheep, and horse.

Let’s apply One-Hot Encoding to this dataset to represent the categorical variable as binary vectors(Figure 4).

After applying One-Hot Encoding, the encoded dataset will have separate binary variables for each animal

category: ”Cat,” ”Dog,” ”Lion,” ”Cow,” ”Sheep,” and ”Horse.” Each observation in the dataset will have a value

of 1 for the corresponding animal category and a value of 0 for the remaining animal categories. By applying

One-Hot Encoding, we transform the categorical variable ”Animal” into a set of binary variables, allowing

machine learning algorithms to eﬀectively interpret and process the categorical data. It enables the algorithms

to capture the presence or absence of each animal category for every observation, facilitating accurate analysis

and modeling tasks. One of the disadvantages of One-Hot Encoding is the curse of dimensionality, which arises

when dealing with categorical variables that have a large number of distinct categories. This encoding technique

creates a separate binary variable for each category, leading to a signiﬁcant increase in the dimensionality of the

dataset. As the number of dimensions grows, it becomes more challenging for machine learning algorithms to

eﬀectively process and analyze the data, requiring more computational resources and potentially larger amounts

of training data. Moreover, handling new or unseen categories in the test data poses a challenge, as One-Hot

Encoding assumes that all categories encountered during training will be present during testing, requiring

additional steps to accommodate such cases.

2.3 One Hot Encoding (multiple categories)

In this method, instead of encoding all categories of a categorical variable, only the top-k most frequent

or repeating categories are considered for One-Hot Encoding. By focusing on the categories with the highest

number of repetitions, this technique aims to capture the most signiﬁcant information while reducing the

dimensionality of the encoded representation.

To implement Top-k Encoding, we start by identifying the frequencies of each category in the dataset.

Then, we select the k categories with the highest frequencies, typically based on a predetermined threshold or

2.4 Mean Encoding

(image courtesy:https://www.shiksha.com/online-courses/articles/one-hot-encoding- for-multi-categorical-variables/)

Figure 5: one hot encoding multiple categories

a speciﬁc value of k. These top-k categories are then encoded using One-Hot Encoding, where each category

is represented as a binary vector with a value of 1 in the corresponding category’s position and 0 in all other

positions. For example, Suppose 200 categories are present in a feature then only those 10 categories which are

the top 10 repeating categories will be chosen and one-hot encoding is applied to only those categories(Figure

By employing Top-k Encoding, we strike a balance between capturing the most signiﬁcant categories and

reducing the dimensionality compared to encoding all categories. This approach can be particularly useful

when dealing with large categorical variables with numerous categories, where encoding all categories might

lead to excessive dimensionality or computational challenges.

It’s important to note that the value of k can be adjusted based on the speciﬁc data set, problem requirements,

or domain knowledge. Selecting an appropriate value of k is crucial to ensure that the encoded representation

retains the most informative categories while eﬀectively managing dimensionality.

2.4 Mean Encoding

Mean encoding is a technique used to encode categorical variables by replacing each category with the

mean of the target variable for that category. Unlike One-Hot Encoding, which creates binary variables for each

category, Mean Encoding transforms categorical variables into continuous representations.

The Mean Encoding process involves the following steps:

Calculate the target variable’s mean for each category in the categorical variable.

Replace the original category labels with their corresponding mean values.

Consider an example where we have a column named ”Pincode” that contains multiple occurrences of

diﬀerent pin codes within a city. To encode this column using Mean Encoding, we can utilize this technique to

transform the pin codes into their corresponding mean values based on an output column(Figure 6).

By applying Mean Encoding, the pin codes in the ”Pincode” column have been replaced with their

corresponding mean values based on the ”O/P” column.

This approach allows us to represent the categorical ”Pincode” column with continuous values that reﬂect

the average output for each pin code.

2.5 Target guided Ordinal Encoding

Target Guided Ordinal Encoding is a technique used to encode categorical variables by assigning ordinal

labels based on the relationship between the categories and the target variable. It incorporates the target

variable’s information into the encoding process, making it particularly useful for classiﬁcation tasks.

2.6 Label Encoding

(image courtesy:https://ai-ml-analytics.com/encoding/)

Figure 6: Mean Encoding

(image courtesy:https://ai-ml-analytics.com/encoding/)

Figure 7: Target encoding

The Target Guided Ordinal Encoding process involves the following steps:

Calculate the mean of the target variable for each category in the categorical variable.

Order the categories based on their mean values in ascending or descending order.

Assign ordinal labels to the categories based on their order.

Table below illustrate this(Figure 7)

2.6 Label Encoding

Label encoding, also known as integer encoding, is a simple technique used to transform categorical

variables into numerical representations. In label encoding, each unique category is assigned a unique integer

label. This encoding is based on the assumption that the numerical order of the labels carries some ordinal

meaning or relationship.

Here’s how label encoding works:

Identify the distinct categories in the categorical variable. Assign a unique integer value to each category,

starting from 0 or 1. Replace the original categorical values with their corresponding integer labels.

For example, consider a categorical variable ”Color” with three categories: ”Red,” ”Green,” and ”Blue.”

Applying label encoding would assign the labels as follows:

”Red” becomes 0 ”Green” becomes 1 ”Blue” becomes 2 After label encoding, the transformed variable

2.6 Label Encoding

(https://medium.com/@chexki /using- label-encoder-on-unbalanced-categorical- data-in-machine-learning-using-python)

Figure 8: working of label encoders

would consist of the numerical labels: [0, 1, 2](Figure 8).

Label encoding is straightforward to implement and does not introduce additional dimensions to the dataset.

It can be useful when there is an inherent order or ranking among the categories, allowing the encoded labels

to capture this ordinal relationship. However, it is important to note that label encoding may not be suitable for

categorical variables without any ordinal signiﬁcance, as it can unintentionally introduce a false sense of order.

Summary

In conclusion, encoding methods for categorical variables play a vital role in eﬀectively handling and

utilizing these discrete and non-numeric variables in machine learning and data analysis. Categorical variables

pose unique challenges due to their lack of inherent order or magnitude, yet they often contain valuable

information that can signiﬁcantly impact the performance and accuracy of machine learning models.

Throughout this article, we have explored several popular encoding methods for categorical variables,

including one-hot encoding, mean encoding, target-guided ordinal encoding, and label encoding. Each method

has its own strengths, weaknesses, and suitable use cases, allowing data scientists, machine learning practitioners,

and researchers to make informed decisions when working with categorical data.

References

Diﬀerent types of Encoding

Ways of encoding categorical variables

5 Useful Encoding Techniques in Machine Learning

Understanding Categorical Encoding Techniques: Ordinal, One-Hot, and Label Encoding

One hot encoding for multi categorical variables

Using Label Encoder on Unbalanced Categorical Data in Machine Learning Using Python

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.

Part II

Astronomy and Astrophysics

Black Hole Stories-2

Gravitational Lensing for the Detection of

Lone Black Holes

by Ajit Kembhavi

airis4D, Vol.1, No.7, 2023

www.airis4d.com

1.1 Black Holes

In an earlier article on the mass of black holes in [1] we have considered some properties of black holes,

and how black holes in binary star systems and at the centres of galaxies can be detected. It is much more

diﬃcult to detect lone black holes which are produced as the end state of massive stars. As we have seen in the

earlier article, when a star with mass greater than about 25 Solar masses reaches the end point of its evolution,

the star explodes as a supernova, leaving a black hole as a remnant. If the exploding star is not a part of a

binary system, or if the binary is disrupted in the explosion, then the black hole moves as an isolated object in

the galaxy, a lone black hole. It can be estimated that there are about a hundred million such black holes in

our galaxy. But since no light or any other radiation can escape for the black holes, they cannot be observed

directly. And since such black holes would be quite distant from other objects, the eﬀect of their gravitational

ﬁelds on other stars are not discernable either.

Detecting such black holes would be very useful of course, as their numbers and masses would help

astronomers trace the history of the formation of stars in our galaxy. In this article, and in the next one, we will

see how gravitational lensing makes the detection possible.

1.1.1 Gravitational Bending of Light

There are many observed phenomena, like shadows, which demonstrate that rays of light travel in a straight

line. This consistent with a straight line being the shortest distance between any two points in space of our

ordinary experience. As explained in [1], the situation is diﬀerent in Albert Einstein’s theory of gravity, the

general theory of relativity. Here gravity 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 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 . The shapes so calculated correspond to

deviations from a straight line due to the force of gravity, in the simpler Newtonian theory of gravitation.

The masses of objects on the Earth are too small to cause observable bending of rays light. But the Sun

1.1 Black Holes

has a large mass and a light ray from a source behind it, passing close to the Sun would bend by an angle which

can be measured on the Earth. This is shown in Figure.1. It is seen that a star behind the Sun would appear to

be displaced because of bending of the rays coming from the star to the Earth. The displacement shown in the

Figure is greatly exaggerated, the bending angle is actually very small. Einstein calculated from his theory that

for a ray of light just grazing the Sun, and reaching us at the Earth, the bending angle ϕ is

ϕ =

4GM

(1.1)

where M and R are the mass and radius of the Sun, G is Newton’s constant of gravitation and c is the speed

of light. Inserting numerical values, the bending angle is 1.75 arcsec, where 1 arcsec is about 0.00028 degrees.

Image credit: Kaushal Sharma

Figure 1: The bending of star light due to the gravity of the Sun. The observer sees the position of the star

shifted relative to its true position.

The light we receive during the day time from the Sun is very bright. It is therefore not possible to see the

light from any stars close to the Sun, or the bent light from a star just behind it, against the bright light of the

sky. But such stars can be seen during a total Solar eclipse during which the light from the Sun is completely

blocked by the Moon, and the sky gets dark as at night. At such a time we can see stars in the sky. During a

total Solar eclipse, if there is a star close to the Sun’s disc, and rays of light from it are bent from their path due

to the gravity of the Sun, then the star should appear to be displaced from its actual position to a new apparent

position. We can determine the apparent direction of such a star during a total Solar eclipse, and determine its

real direction at other times, say six months later when the Sun is not close to it and when we can see the star at

night. The diﬀerence between the directions gives the amount of bending produced, and this can be compared

with the prediction of general relativity, which is 1.75 arcsecond.

1.1.2 First observation of light bending

It was realised by the great British astronomer Sir Arthur Eddington that an opportunity for measuring the

bending of light was available on the 29th of May, 1919, when a total Solar eclipse was to take place. This would

be almost exactly four years after the birth of the theory. Eddington and Sir Frank Dyson, who was then the

Astronomer Royal, organised expeditions to Sorbal in Brazil, and the island of Sao Tome in the Atlantic Ocean

oﬀ the coast of Gabon in West Africa. Eddington led a team to Sao Tome , while another team went to Sobral.

From analysis of data obtained during the eclipse, the positions of some stars in accordance with predictions of

the general theory. Einstein soon became a household name because of the wide publicity obtained all over the

1.2 Gravitational Lensing

world by Eddington’s demonstration of the bending of light.

1.2 Gravitational Lensing

The gravitational bending of light can lead to many interesting eﬀects, which are broadly known as

gravitational lensing. Einstein considered a situation when a star which is far away, which we will call A, lies

exactly behind a nearer star or galaxy, which we will call B. In such a case, most of the light rays emitted by

A, if they travelled in straight lines, would have passed us by; those which were travelling along the line AB,

would have hit B and either would have been absorbed there or would have been scattered and we would not

have been able to see A. However, as per Einstein’s theory, the divergent rays from A, which pass close to B

will be bent from their straight paths due to the Sun’s gravity and will be able to reach us from slightly diﬀerent

directions. This is shown in Figure 2. Thus, one can see light from A coming to us from all directions along

the cone centred at the Earth as shown in the ﬁgure. We will therefore see a ring instead of a point source

like a star, which is called an Einstein ring. Einstein published this work in the journal Science in 1936. Such

gravitational lensing had in fact been originally considered by Einstein even before he published his theory of

gravitation in 1915, and by several others subsequently. Soon after Einstein’s publication, the astronomer Fritz

Zwick considered the possibility of gravitational lensing by galaxies, whose existence as extragalactic objects

had by then been established by Edwin Hubble. In Figure 2, the gravitational lens is depicted as a galaxy in a

cluster of galaxies, instead of a single star as considered by Einstein.

Image credit: Kaushal Sharma

Figure 2: A sketch of the ring visible to an observer on the Earth who is exactly in line with two astronomical

sources. The ring is the image of the background source A made because of bending of rays by the gravity of

the foreground source B.

As the stars and galaxies are very thinly distributed in space, the probability of two sources being exactly

aligned is extremely small. Also, the radius of the ring would be so small that even if it were to be observed, it

would have appeared as a point source, rather than as a ring with the then available telescopes and instruments.

Because of these reasons, Einstein dismissed the idea that such an occurrence could ever be seen. If the

alignment of A and B is slightly oﬀ from being exact, i.e., A, B and the Earth do not lie on a straight line, the

symmetry is broken. So, if B is slightly away from the line joining us and A, in place of a ring, we would see

multiple images of A. As glass lenses are used to bend light and form images in laboratories, the phenomenon

is called gravitational lensing. As in the case of more familiar optical convex lenses, gravitational lenses too

1.3 Gravitational Microlensing

converge light rays and so they make an image brighter than it would have been in absence of lensing. This can

help us to observe distant objects, which would otherwise be too faint to observe because of their great distance.

In 1979, three astronomers, Dennis Walsh, Robert Carswell and Ray Weyman actually observed a twin

image of a very distant source, called a quasar. The astronomers observed two quasars, which had identical

properties and which appeared to be very closely spaced in the sky. It was conformed through a detailed study

that these two quasars were not diﬀerent but were two images of the same quasar, with a distant intervening

galaxy acting as a gravitational lens. Einstein rings have also been observed and an example of such a ring

observed at radio wavelengths is shown in Figure. 3.

Image Credit: ALMA (NRAO/ESO/NAOJ); B. Saxton NRAO/AUI/NSF

Figure 3: An Einstein ring observed with the Atacama Large Millimeter/submillimeter Array (ALMA) radio

telescope. A distant galaxy SDP.81 and a foreground galaxy line up so perfectly as seen from an observer on

the Earth that the light from the distant galaxy forms a nearly perfect circle due to gravitational lensing. The

foreground galaxy which acts as a gravitational lens is too faint to be observed..

1.3 Gravitational Microlensing

Gravitational lensing is now a very important tool for astronomers to study various aspects of the Universe.

We are here concerned with gravitational microlensing, which is the lensing of a distant background star (A),

by an object (B) with mass comparable to the mass of the Sun. If B passes between an observer on the Earth and

star A, lensing takes place when drifting object is close to the line of sight. The deﬂection in the position of the

distant star due to lensing is very small, of the order of a milliarcsecond, and is diﬃcult to measure. But there is

also change in the observed brightness of A due to the lensing. As B approaches the line of sight the intensity

of the A increases due to the lensing, reaches a maximum and then decreases as B moves away. The greater the

mass of the lensing object, the longer is the duration of the event, because of the stronger gravitational ﬁeld of

the lens. The lensing object can be a star, an exoplanet, neutron stars, black holes, or other objects which may

constitute the dark matter in our galaxy. Several surveys have been carried out to detect microlensing events

and more than 30,000 microlensing events have been found and observed over a period of time. An even from

the MACHO survey is shown in Figure 4. Microlensing has been used in the discovery of exoplanets.

BIBLIOGRAPHY

Image Credit: ALMA (NRAO/ESO/NAOJ); B. Saxton NRAO/AUI/NSF

Figure 4: The light curve of a microlensing event from the MACHO survey for microlenses. The event lasted

for about six months. There is increase in the observed intensity of the star as the lens approaches the line of

sight to star, the intensity peaks when the lens is at the closest point to the line of sight and then decreases as the

lens moves away. Detailed studies show that the lensing object could be a brown dwarf star in the bulge of our

galaxy, or an M-dwarf star at a distance of 2 to 6 thousand parsec (one parsec is 3.26 light years), or a star with

greater mass closer to the Sun. (Fig. from K. Griest et. al. (the Macho Collaboration), arXiv:astro-ph/9506016.

In the next part of this series on Black Hole Stories, we will see how microlensing is used in the detection

of lone black holes.

Bibliography

[1] https://airis4d.com/Journal/airis4DJournal 1.4.html

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.

Unveiling the Birth of Stars: A Cosmic

Symphony of Creation

by Robin Jacob Roy

airis4D, Vol.1, No.7, 2023

www.airis4d.com

The universe is a vast and captivating tapestry of celestial wonders. Among its most mesmerizing phe-

nomena is the process of star formation. Stars, the celestial beacons that illuminate the night sky, emerge from

colossal clouds of gas and dust known as molecular clouds. Stars hold a prominent position as universally

recognized celestial entities, serving as the fundamental constituents of galaxies. Within a galaxy, the age,

distribution, and composition of stars provide valuable insights into the galaxy’s history, dynamics, and evo-

lutionary processes. Additionally, stars play a crucial role in the creation and dispersal of vital elements like

carbon, nitrogen, and oxygen, which greatly inﬂuence the characteristics of planetary systems that may form

around them. Hence, the investigation of star formation, lifespan, and demise occupies a central role within the

realm of astronomy. This article delves into the captivating journey of star formation, exploring the intricate

interplay of gravitational collapse, protostellar evolution, and the birth of stellar nurseries.

Figure 1: In the Orion constellation, situated about 800 light-years away, an expansive and enigmatic cloud

known as the ”Witch Head” nebula is currently nurturing newborn stars. These young stellar entities appear as

delicate pink dots in an awe-inspiring image captured by NASA’s Spitzer Space Telescope. Amidst the cloud,

wisps of verdant hues manifest as carbon-rich molecules called polycyclic aromatic hydrocarbons, commonly

found on Earth in sources like barbecue grills and vehicle exhaust. This captivating infrared image is a composite

representation combining three colors, with light of 4.5-micron wavelength depicted as blue, 8.0-micron light

represented as green, and 24-micron light appearing as radiant red. Source: NASA/JPL-Caltech/L.Rebull

(SSC/Caltech)

2.1 Cosmic Nurseries: Molecular Clouds

The coldest and densest regions of the interstellar medium are primarily composed of dust and gas, with

hydrogen molecules being the dominant component. These regions, known as molecular clouds, exhibit low

temperatures of approximately 10 Kelvin and high densities surpassing 102 particles/cm

. They range in mass

from a few solar masses to over a million solar masses and have diameters spanning from 20 to 200 parsecs.

Molecular clouds, particularly the Giant Molecular Clouds, serve as the exclusive sites for star formation.

Observations have revealed their prevalence in the spiral disk of galaxies and the active regions of irregular

galaxies.

Due to their cold and opaque nature, molecular clouds cannot be directly observed in visible light.

Although some closer clouds may appear as dark silhouettes against bright nebulae or background stars, the

majority of clouds remain undetectable due to the dimming eﬀect caused by interstellar extinction. However,

these clouds emit longer wavelength radiation in the millimeter range, which can traverse the interstellar medium

without signiﬁcant disruption. Similar to how electrons in atoms transition between speciﬁc energy levels by

absorbing or releasing energy, molecules exhibit speciﬁc rotational and vibrational states. As molecules change

their rotational state, they absorb or emit energy at small energy diﬀerences, corresponding to millimeter

wavelengths. Figure 1 showcases the captivating Witch Head Nebula located in the Orion constellation. This

nebula serves as a prime illustration of a star-forming molecular cloud.

2.2 Cloud Collapse

The equilibrium of an interstellar gas cloud relies on a balance between the kinetic energy from gas pressure

and the potential energy from gravitational forces. This equilibrium is described by the virial theorem, which

states that for stability, the gravitational potential energy must be twice the internal thermal energy. If the gas

pressure cannot support the cloud due to its mass, the cloud will undergo gravitational collapse. The critical

mass at which collapse occurs is known as the Jeans mass, typically ranging from thousands to tens of thousands

of solar masses. During this collapse, numerous stars form simultaneously, giving rise to embedded clusters.

The result of core collapse is an open cluster of stars.

Triggered star formation can occur through various mechanisms. Collisions between molecular clouds

or the impact of a nearby supernova explosion can compress a cloud and initiate collapse. Galactic collisions

can also induce massive starbursts as tidal forces agitate and compress gas clouds within each galaxy. Such

interactions may contribute to the formation of globular clusters.

In the nucleus of a galaxy, the presence of a supermassive black hole can regulate the rate of star formation.

An active black hole accreting matter can emit a powerful wind or relativistic jet, limiting further star formation.

Ejections from massive black holes traveling close to the speed of light can also inhibit star formation in aging

galaxies. However, these jets’ radio emissions may trigger star formation, and weaker jets colliding with clouds

can have a similar eﬀect.

As a molecular cloud collapses, it fragments hierarchically into smaller pieces until reaching stellar mass.

During this process, the collapsing gas releases gravitational potential energy through radiation. However,

as density increases, the fragments become less eﬃcient at radiating away energy, leading to a temperature

increase that inhibits further fragmentation. The fragments condense into rotating gas spheres, serving as stellar

embryos.

Turbulence, macroscopic ﬂows, rotation, magnetic ﬁelds, and cloud geometry complicate the collapsing

cloud scenario. Rotation and magnetic ﬁelds can impede collapse, while turbulence promotes cloud fragmen-

2.3 Protostellar Evolution

tation and collapse on smaller scales. These factors inﬂuence the intricate dynamics of star formation within

molecular clouds.

Figure 2: This image is an enlargement of a three-colour composite of the young object Herbig-Haro 34

(HH-34) situated in the Orion constellation, in the protostar stage of evolution. Source: European Southern

Observatory(ESO)

2.3 Protostellar Evolution

As the collapse progresses, a protostar emerges at the center of the collapsing core. The protostar is

shrouded in an envelope of gas and dust, making it invisible to optical telescopes. However, infrared and radio

observations allow astronomers to study the protostellar evolution. The protostar accretes material from the

surrounding envelope, gradually increasing in mass and temperature. Figure 2 portrays Protostar HH 34 in

Orion constellation.

Accretion Disks and Outﬂows

During the accretion process, a rotating disk of gas and dust forms around the protostar known as an

accretion disk. Material from the disk spirals onto the protostar, fueling its growth. Simultaneously, powerful

outﬂows, called bipolar jets, emanate from the protostar, blasting through the surrounding material. These jets

carry away excess angular momentum and regulate the protostellar accretion.

Birth of a Star

As the protostar continues to accrete matter and release energy, it undergoes further gravitational contraction

and heats up. Eventually, the core reaches a critical temperature and pressure where nuclear fusion ignites,

marking the birth of a star. The star enters the main sequence, a phase where it achieves a stable equilibrium

between the inward pull of gravity and the outward pressure generated by nuclear fusion.

2.4 Stellar Clusters and Feedback

In giant molecular clouds, star formation often occurs in clusters, with multiple stars forming simultaneously

from nearby collapsing regions. The collective energy and radiation from these young stars can have a profound

impact on the surrounding molecular cloud. Stellar winds, radiation pressure, and supernova explosions create

feedback eﬀects, inﬂuencing the dynamics and evolution of the cloud and potentially triggering further star

formation.

Stellar birth in giant molecular clouds is an intricate dance of gravitational collapse, accretion, and the

interplay of physical forces. Through extensive observations and simulations, astronomers strive to unravel

the mysteries surrounding this cosmic phenomenon. The ongoing study of stellar birth not only deepens our

understanding of the universe but also highlights the awe-inspiring beauty and complexity of the processes that

shape the cosmos. The journey of star formation is a captivating spectacle that showcases the cosmic symphony

of creation. From the colossal molecular clouds to the birth of protostars and their eventual emergence as

radiant celestial entities, the process exempliﬁes the intricate interplay of gravity, turbulence, and the laws of

physics. Through diligent observations and advanced astrophysical models, scientists continue to deepen their

understanding of the complex mechanisms driving star formation. With each new revelation, the beauty and

marvel of the cosmos unfold, reminding us of the immense power and creativity embedded in the vast expanse

of the universe.

References:

How do stars form and evolve

Star birth and death

Star forming regions

Stellar Evolution

The process of star formation

About the Author

Robin is a researcher in Physics specializing in the applications of Machine Learning for Remote

Sensing. He is particularly interested in using Computer Vision to address challenges in the ﬁelds of Biodiversity,

Protein studies, and Astronomy. He is currently working on classifying satellite images with Landsat and Sentinel

data.

Galaxy Morphologies

by Sheelu Abraham

airis4D, Vol.1, No.7, 2023

www.airis4d.com

3.1 Galaxies in Our Universe

A clear night sky is a real visual feast for our eyes, with countless stars appearing as points of light dots.

As we observe continuously over a month or so, we can see the hazy patches of light spanning a larger area

forming an arc-like structure, representing our own Milky Way, the home to all the stars we see with our naked

eye.

The Great Debate in Astronomy about the scale of the Universe took place in 1920 by the astronomers

Harlow Shapley and Heber Curtis. Before this, it was commonly believed that the Milky Way constituted the

entire Universe. It was Edwin Powell Hubble who changed our understanding of the Universe by studying the

Universe with the help of Mount Wilson Observatory in California. In 1923, he spotted a Cepheid variable

star from a nebula later known as the Andromeda Galaxy. Subsequently, he photographed multiple Cepheids

from other spiral nebulae, which opened the doors to the ﬁeld of extragalactic astronomy. The observations of

Hubble changed our understanding of galaxies which are distinct entities with collections of stars, gas, and dust.

3.2 Observing the individual Galaxies

Hubble pointed his 100-inch Hooker telescope at Mount Wilson Observatory to the diﬀerent hazy structures

in the sky. He started studying the physical properties of galaxies. By the end of 1925, he could observe enough

galaxies to compare the visual appearance of these objects. In 1926, he developed a system for classifying

galaxies based on their visual appearance, currently known as the Hubble Classiﬁcation Scheme. In this scheme,

the galaxies are categorised into two main classes based on their shapes: elliptical and spiral, which are again

subdivided into diﬀerent sub-classes based on the speciﬁc characteristics of the galaxy. A third group of

galaxies, called lenticular galaxies, is a transition between the spiral and elliptical galaxies. This system for

classifying galaxies, called Hubble tuning fork diagram, laid the foundation for understanding galaxy evolution

and formation. The spiral galaxies are subdivided into two groups - normal spirals and barred spirals.

3.3 Galaxy Morphology

Hubble published his classiﬁcation of galaxy types in 1936 in ”The Realm of the Nebulae”. Since then,

several people have suggested modiﬁcations to his original scheme, but the basic idea of his ”tuning fork

3.3 Galaxy Morphology

Figure 1: Edwin Hubble used the Hooker Telescope at Mount Wilson Observatory to discover Cepheids in

multiple nebulae. In a 1924 paper called “Cepheids in Spiral Nebula,” he proved that galaxies existed outside

our own.

3.3 Galaxy Morphology

Figure 2: Edwin Hubble’s Classiﬁcation Scheme, also known as the tuning fork diagram, is shown. The

galaxies are divided into elliptical and spiral galaxies. The letters indicate the level of compactness of their

spiral arms. The spiral class with “a” being the most tightly wound and “c” being the least. Normal and

barred spirals also subdivide galaxies. While this diagram oﬀers a strong foundation for galaxy classiﬁcation,

it does not ﬁt all types, including irregular, dwarf, and massive elliptical galaxies. credit: NASA/ESA, PD,

en.wikipedia.org/wiki/File:HubbleTuningFork.jpg

diagram” has continued to be beneﬁcial for astronomers. Below is a diagrammatic representation of one

commonly used simple modiﬁcation of his diagram.

3.3.1 Ellipticals

Based on the elliptical galaxy’s ellipticity, Hubble gave them numbers as E0, representing the spherical

symmetry and E7 as very elliptical. Ellipticals have almost no noticeable structure but, just as a gathering

of stars, appear as no more than a round, fuzzy patch of light against the dark background of the night sky.

Elliptical galaxies are composed of old stars with little ongoing star formation activity. They typically contain a

high proportion of red or yellow stars, which give them a reddish color. Due to a little interstellar dust and gas

presence, they have shallow levels of ongoing star-forming regions.

3.3.2 Lenticulars

Lenticular galaxies, represented as S0 galaxies, are in the transition zones between ellipticals and spirals

and bridge these two types. The lens-like or disk-like shape they are named lenticular. Lenticular galaxies

exhibit a prominent central bulge, like elliptical galaxies, but lack the distinct spiral arms seen in spiral galaxies.

Lenticular galaxies contain older and younger stars but have less interstellar gas and dust than spiral galaxies.

Some lenticular galaxies have a bar, similar to spiral galaxies, so known as barred lenticular galaxies.

3.3.3 Spirals

Spiral galaxies are another type of galaxy commonly observed in the universe. They are characterised

by the presence of spiral arm-like structures that extend outward from the central bulge. The bulge contains a

dense concentration of stars, while the arms consist of curved lanes of stars, gas, and dust. The arms of spiral

galaxies are the regions of active star formation, while the nucleus of a spiral galaxy contains many old stars.

Stars in spiral galaxies tend to rotate around the galactic centre. Depending on the compactness of their spiral

3.3 Galaxy Morphology

Figure 3: The image shows NGC 1132, a giant elliptical galaxy 300 million light-years away from Earth. With

a roughly 240,000 light-year diameter, it’s over twice the size of our Milky Way.

Figure 4: Showing the ellipticity variation of galaxies in the Hubble Classiﬁcation scheme. Elliptical galaxies

are allocated a number from 0 to 7, indicating their ellipticity.

3.4 Galaxy Evolution

Figure 5: NGC 5866, commonly known as Spindle Galaxy, is an example of a lenticular galaxy. Credit: NASA,

ESA and The Hubble Heritage Team (STScI/AURA)

arms, the spirals were subdivided into Sa, Sb, and Sc. The tightly wound types are Sa, whereas Sc spirals are

more loosely wound.

3.3.4 Barred Spirals

These have a well-deﬁned BAR structure at the centre of the bulge. They behave as normal spirals except

for the presence of the bar. Hubble classiﬁed these galaxies as SB galaxies with subclasses a, b, and c, just like

the normal spirals. In barred spirals, the spiral arms start at the end of the bar instead of from the bulge as they

do in normal spirals. Our Milky Way is believed to be a barred spiral and probably belongs to either the SBb or

SBc class.

Figure 7: The image of UGC 6093 galaxy captured by the Hubble Space Telescope. It is an active galaxy with

swirling arms and a supermassive black hole at its center emitting intense radiation. Credit: ESA/Hubble &

NASA

3.4 Galaxy Evolution

Figure 6: M101 is a spiral galaxy like our Milky Way, but about 70 percent bigger. It is located about 21

million light years from Earth. Image credit: X-ray: NASA/CXC/SAO; Optical: Detlef Hartmann; Infrared:

NASA/JPL-Caltech

3.4 Galaxy Evolution

The galaxies we observe in the Universe show various morphologies besides the one we discussed above.

The various characteristics of galaxies, like morphologies, colors, luminosity and dynamics, indicate the speciﬁc

evolutionary phase of the galaxy. The discussion will not end here, and we can meet with more details in the

next edition.

3.5 References

1. Sidney Van den Bergh, Galaxy Morphology and Classiﬁcation, 1998.

2. Ronald J. Buta, Harold G. Corwin, and Stephen C. Odewahn, Atlas of Galaxies, 2007.

About the Author

Dr Sheelu Abraham is an Assistant Professor at Department of Physics, Mar Thoma College,

Chungathara and a Visiting Associate at Inter University Center for Astronomy & Astrophysics, Pune. Her area

of specialisation is ML applications for Astronomy.

Rotating Variable Stars

by Sindhu G

airis4D, Vol.1, No.7, 2023

www.airis4d.com

4.1 What Are Rotating Variable Stars?

Rotating variable stars are a type of extrinsic variable star that exhibit changes in brightness as a result of

their rotation. Stars with extreme ”sunspots” (Fig: 1) or stars that have fast rotation speeds causing them to

become ellipsoidal in shape are both examples of rotating variable stars. Their variability is directly related to

the phenomena associated with their rotation. Some stars, like our Sun, can exhibit regions of intense magnetic

activity that result in dark spots on their surfaces. These spots are cooler and less luminous than the surrounding

areas. As the star rotates, these spots come into and go out of view, causing variations in the apparent brightness

of the star. These brightness changes can be periodic or irregular, depending on the rotation and evolution of the

star. Stars with fast rotation speeds can become ellipsoidal in shape as a result of the gravitational interaction

between the stars in a binary system. This non-spherical shape causes the stars to present varying amounts

of surface area to the observer as they orbit each other. Consequently, the apparent brightness of the system

changes periodically as the stars rotate. By studying such rotating variable stars, astronomers can gain insights

into the properties of stellar magnetic ﬁelds, stellar evolution, and binary star systems. The examples shown in

below demonstrate how rotation can induce variability in the brightness of stars.

4.2 Some Examples Of Rotating Variable Stars

4.2.1 FK Comae Berenices Variables

FK Comae Berenices (FK Com) stars exhibit characteristics similar to our Sun but display unusually short

periods and/or exceptionally high levels of activity. Due to their extremely rapid rotation, FK Comae Berenices

stars attain speeds of approximately 100 km/s at the equator, resulting in their ellipsoidal shape. FK Comae

Berenices-type variables, or FK Com stars, are rapidly rotating giants with nonuniform surface brightness.

They typically have G-K spectral types and exhibit broad H and K Ca II emission lines, and sometimes H-

alpha emission as well. These stars may also exhibit characteristics of spectroscopic binary systems. The light

variation in FK Com stars is directly related to their rotational periods, with periods of light variation typically

ranging from a few days to several days. The amplitude of these variations can be several tenths of a magnitude.

One possible explanation for the rapid rotation observed in FK Comae stars is that they may have formed through

the merger of a binary system, speciﬁcally a contact binary.

4.2 Some Examples Of Rotating Variable Stars

Figure 1: Sunspots Source: NASA.

4.2.2 Alpha-2 Canum Venaticorum

Alpha-2 CVn variables (Fig.2) are main-sequence stars with spectral classes ranging from B8p to A7p.

The ”p” in the spectral type denotes peculiar features in their spectra, which include abnormally strong lines

of elements such as silicon (Si), strontium (Sr), chromium (Cr), and rare earths. These stars exhibit brightness

ﬂuctuations in the range of 0.01 to 0.1 magnitudes, which corresponds to a variation of 1% to 10% in their

apparent brightness. These stars possess strong magnetic ﬁelds that contribute to the peculiar spectral lines

observed in their spectra. Alpha-2 CVn variables display variations in both their magnetic ﬁeld strength and

brightness. The variability periods range from 0.5 to 160 days or even longer.

Figure 2: Alpha Canum Venaticorum Source: Wikisky.

4.2 Some Examples Of Rotating Variable Stars

Figure 3: Pulsar Source: MARK GARLICK/SCIENCE PHOTO LIBRARY via Getty Images.

4.2.3 SX Arietis Variables

SX Arietis variables are a speciﬁc class of variable stars. These stars are typically B-type main sequence

stars with spectral types ranging from B0p to B9p. They are considered as high-temperature analogues of

Alpha2 Canum Venaticorum (ACV) variables. They are known for their variability in the intensity of helium

(He I) and silicon (Si III) spectral lines, as well as the presence of magnetic ﬁelds. SX Arietis-type variables are

sometimes referred to as helium variables due to the prominence of helium lines in their spectra. The variability

of SX Arietis variables is characterized by ﬂuctuations in brightness of approximately 0.1 magnitudes. These

variations occur with periods of about one day, which corresponds to the rotational period of the star.

4.2.4 Rotating Ellipsoidal Variables

Ellipsoidal variables are close binary star systems where the components are non-spherical due to tidal

interactions, and their varying surface areas presented towards the observer result in changes in brightness as

seen from Earth. These systems do not show eclipses, unlike other types of binary systems. The amplitude of the

brightness variations in ellipsoidal variables is typically modest, with light amplitudes generally not exceeding

0.1 magnitudes in the visible band (V).

4.2.5 Optically Variable Pulsars

Pulsars(Fig: 3) are highly magnetized, rapidly rotating neutron stars that emit beams of electromagnetic

radiation. There are optically variable pulsars, such as CM Tau, which are rapidly rotating neutron stars with

strong magnetic ﬁelds. These pulsars emit radiation across multiple regions of the electromagnetic spectrum,

including radio waves, optical light, and X-rays. Periods of the light changes of pulsars coincide with their

rotational periods, which typically range from 0.004 to 4 seconds. The amplitudes of the light pulses from

optically variable pulsars can reach up to 0.8 magnitudes.

4.2.6 BY Draconis Variable Stars

BY Draconis-type variables are a class of emission-line dwarfs with spectral types ranging from dKe to

dMe. These stars exhibit quasi periodic changes in their light, with periods ranging from fractions of a day to

120 days. The amplitudes of their light variations can vary from several hundredths to 0.5 magnitudes in the

V-band. The light variability is caused by axial rotation of a star with a variable degree of nonuniformity of the

4.2 Some Examples Of Rotating Variable Stars

surface brightness (spots) and chromospheric activity. The light curve of BY Draconis exhibits irregularities

throughout its period, and the shape of the light curve undergoes slight changes from one period to the next.

However, in the case of the star BY Draconis, the shape of its light curve remained relatively consistent over a

month-long period. The spectra of BY Draconis variables, speciﬁcally in their H and K lines, bear resemblance

to that of RS CVn stars, which belong to another class of variable stars known for their active chromospheres.

Some of these stars exhibit ﬂares similar to those observed in UV Ceti stars. In such cases, these stars are

classiﬁed as belonging to the UV Ceti type and are also considered eruptive variables.

References:

Understanding Variable Stars, John R Percy, Cambridge University Press.

Variable Stars

GCVS variability types, Samus N.N., Kazarovets E.V., Durlevich O.V., Kireeva N.N., Pastukhova

E.N.,General Catalogue of Variable Stars: Version GCVS 5.1,Astronomy Reports, 2017, vol. 61, No. 1,

pp. 80-88 2017ARep...61...80S

Variable star

BY Draconis variables

Variable Star Classiﬁcation and Light Curves

Types of Variable Stars: Cepheid, Pulsating and Cataclysmic

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.

Part III

Biosciences

Molecular Cloning

by Geetha Paul

airis4D, Vol.1, No.7, 2023

www.airis4d.com

Molecular Cloning refers to the process of creating an exact genetic copy of an organism, cell, or DNA

fragment. It involves replicating the genetic material to produce an identical or nearly identical copy of the

original organism. Cloning encompasses various techniques, including gene cloning, reproductive cloning, and

therapeutic cloning. Gene cloning, also known as DNA cloning, is a fundamental tool in genetic engineering,

enabling the creation of precise genetic replicas of organisms, cells, or DNA sequences. It has revolutionized

biological research by facilitating gene expression analysis, PCR, and DNA sequencing, allows scientists to

study gene structure, function, and interactions. Gene cloning ﬁnds applications in medicine, agriculture, and

industrial biotechnology. Reproductive cloning aims to produce genetically identical copies of entire organisms

called the clones. By transferring the nucleus of a somatic cell into an enucleated egg cell, an embryo is created

and can be implanted into a surrogate mother for gestation. This type of cloning has raised ethical concerns and

is generally prohibited due to considerations of individuality, identity, and potential harm. Therapeutic cloning,

involving somatic cell nuclear transfer, focuses on generating embryonic stem cells for medical research and

potential therapeutic use. By transferring the nucleus of a somatic cell into an enucleated egg cell, an embryo is

formed, but it is not implanted for reproduction. Instead, embryonic stem cells are derived for studying diseases,

developing drugs, and potentially regenerating damaged tissues or organs. While reproductive and therapeutic

cloning has ethical implications and faces signiﬁcant restrictions, gene cloning remains a valuable tool for

advancing scientiﬁc knowledge and applications. These cloning techniques have signiﬁcantly contributed to

understanding genetics, developing novel treatments, and addressing challenges in various ﬁelds, including

medicine, agriculture, and biotechnology.

1.1 Gene Cloning

Gene cloning or DNA cloning, is a technique widely employed in genetic engineering to create precise

genetic replicas of living organisms, cells, or DNA sequences. This process has revolutionized biological

research, enabling advancements in gene expression techniques like polymerase chain reaction (PCR) and DNA

sequencing. By generating multiple copies of a targeted gene or DNA segment, scientists can investigate its

structure, function, and interactions with other genes. Recent years have witnessed remarkable progress in

gene cloning, leading to its extensive applications in medicine, agriculture, and industrial biotechnology. This

abstract explores the concept of gene cloning, highlights notable advancements, and elucidates its practical

implications. Gene cloning involves a series of key steps: DNA extraction, gene ampliﬁcation, insertion into

a vector (e.g., plasmid), and transformation into host cells. Through the precise utilisation of enzymes like

1.2 Reproductive cloning

image courtesy:urlhttps://images.app.goo.gl/19ocxsNsK3Hbr5hx9

Figure 1: Molecular Cloning - construction of a recombinant DNA

restriction enzymes and DNA ligase, scientists can manipulate DNA fragments and create recombinant DNA

molecules. These molecules are then introduced into host cells, such as bacteria or yeast, where they undergo

replication, resulting in large quantities of the desired gene or DNA segment. Distinct from cellular or organism

cloning in reproductive genetics, molecular cloning allows for the ampliﬁcation of DNA in the laboratory. This

technique ﬁnds utility in the study of molecules, as well as in genetic testing using small samples of blood,

saliva, or tissues from patients. Overall gene cloning has emerged as a powerful tool in genetic engineering,

with profound implications for diverse ﬁelds. Its ability to produce identical genetic copies facilitates research,

the development of advanced techniques, and practical applications across various sectors.

1.2 Reproductive cloning

Reproductive cloning involves creating a genetically identical copy, or clone, of a whole organism. This

process can be achieved through various methods, such as splitting an early embryo (similar to the natural

occurrence of identical twins) or somatic cell nuclear transfer (SCNT). Somatic cell nuclear transfer (SCNT)

is commonly used to clone adult animals. The process begins with the removal of an egg cell from an animal,

followed by the extraction of its nucleus, resulting in an enucleated egg. Next, a somatic cell (any non-sex

cell) is taken from the animal intended for cloning. The nucleus of the somatic cell is then transferred into the

enucleated egg, either through direct injection or fusion using an electrical current.

By transferring the somatic cell nucleus into the enucleated egg, the resulting reconstructed egg contains

the complete genetic information of the animal to be cloned. This reconstructed egg is stimulated to divide and

develop into an embryo, which can be implanted into a surrogate mother for gestation and birth. The clone

born from this process will possess the same genetic makeup as the original animal from which the somatic cell

was taken. Reproductive cloning, although it has been used to successfully clone various animal species such

as sheep, cows, mules, rabbits, and dogs, presents challenges and limitations. The success rate of the cloning

process is generally low, with only a small percentage of embryos surviving to birth. Moreover, cloned animals

often exhibit premature ageing and have a shorter lifespan due to the telomere shortening in their DNA, which

occurs during the normal ageing process in adult cells.

Cloned animals may have diﬀerent mitochondrial DNA compared to the nucleus donor because the mito-

chondria come from the egg cell’s cytoplasm, which is typically sourced from a diﬀerent animal. Additionally,

phenotypic diﬀerences between the clone and the original animal can arise due to environmental factors and

1.2 Reproductive cloning

Image courtesy: https://www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/molecular- cloning

Figure 2: The steps in DNA cloning. The plasmid vector and desired DNA fragment are digested with the

same restriction enzyme. The desired DNA is ligated into the plasmid by DNA ligase to form recombinant

DNA.mBacterial cells are transformed by recombinant DNA. Several copies of the recombinant are produced

during the growth and multiplication of bacterial cells.

1.3 Therapeutic cloning

epigenetic inﬂuences. For example, the coat pattern of the ﬁrst cloned cat, Cc, diﬀered signiﬁcantly from the

original cat due to random X-chromosome inactivation in diﬀerent cells.

Despite these challenges, reproductive cloning holds potential for various applications. It can be used

to produce genetically identical research animals, livestock with desirable traits, and oﬀspring of endangered

species. Additionally, there are potential applications in human infertility and disease, although human cloning

has not been carried out and would raise signiﬁcant ethical concerns.

Somatic cell Nuclear Transfer Technique (SCNT), which is used to create one of the world’s most famous

cloned Sheep, Dolly Ian Wilmut, Keith Campbell and their colleagues). Dolly was born on 5 July 1996 and

died on 14 February 2003. Dolly was the ﬁrst mammal which was produced by SCNT.

Image courtesy: https://www.imedpub.com/animal-sciences-and-livestock-production/

Figure 3: Cloning procedure of Dolly, the ﬁrst mammal clone.

The methods involved in reproductive cloning, speciﬁcally somatic cell nuclear transfer (SCNT), includes

the following steps:

Egg Cell Collection: Egg cells, also known as oocytes, are collected from a female animal of the same

species.

Enucleation: The nucleus of the collected egg cell is removed, creating an enucleated egg.

Somatic Cell Collection: A somatic cell, typically taken from the animal to be cloned, is obtained.

Somatic cells are any cells that are not reproductive cells.

Nuclear Transfer: The nucleus of the somatic cell is transferred into the enucleated egg, either by direct

injection or fusion using electrical current.

Embryo Stimulation: The reconstructed egg with the transferred nucleus is stimulated to initiate cell

division and development, resembling an embryo.

Embryo Implantation: The developed embryo is then implanted into the uterus of a surrogate mother or

foster mother, who will carry the pregnancy to term.

Gestation and Birth: The surrogate mother carries the cloned embryo throughout the gestation period,

resulting in the birth of a genetically identical clone of the original animal.

Reproductive cloning through SCNT has been used to successfully clone various animal species, although

it has low success rates and often results in premature ageing and health issues in cloned animals.

1.3 Therapeutic cloning

Therapeutic cloning does not involve the implantation of the embryo into a surrogate mother to produce

a cloned individual. The primary aim is to derive embryonic stem cells for therapeutic purposes rather than

creating a fully developed organism. Gene cloning has paved the way for signiﬁcant advancements in the ﬁeld of

medicine. One of the most notable applications is the production of therapeutic proteins, such as insulin, human

growth hormone, and clotting factors. By cloning the genes responsible for these proteins and introducing

them into host cells, scientists can generate large-scale production of these vital molecules. This technique

has revolutionized the treatment of various diseases, including diabetes, growth disorders, and haemophilia,

ensuring a steady and reliable supply of therapeutic proteins.

Image courtesy: https://www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/molecular- cloning

Figure 4: Therapeutic cloning showing the process

1.4 Other Cloning Areas

1.4.1 Gene Therapy

Molecular cloning has also played a pivotal role in the development of gene therapy, a promising ﬁeld

aimed at treating genetic disorders by introducing functional genes into a patient’s cells. Through gene cloning,

scientists can isolate and modify speciﬁc genes associated with genetic diseases, such as cystic ﬁbrosis or

muscular dystrophy. These modiﬁed genes can then be delivered to the patient’s cells, potentially correcting the

underlying genetic defects and providing a potential cure or treatment for these disorders.

1.4.2 Agricultural Advancements

Molecular cloning has revolutionized agriculture by enabling the development of genetically modiﬁed

organisms (GMOs) with desirable traits. Through gene cloning techniques, scientists can introduce genes from

one organism into another, resulting in crops that exhibit enhanced resistance to pests, diseases, or environmental

stress. This has led to the development of genetically engineered crops that oﬀer increased yields, improved

nutritional content, and reduced dependence on chemical pesticides.

1.4.3 Industrial Biotechnology

Molecular cloning has found numerous applications in industrial biotechnology. By cloning genes respon-

sible for the production of enzymes or other bioactive molecules, scientists can create microorganisms that serve

1.5 Research and Discovery

as eﬃcient factories for the production of valuable products. For example, gene cloning has been instrumental

in the production of enzymes used in laundry detergents, the synthesis of biofuels, and the development of

bio-based materials.

1.5 Research and Discovery

Molecular cloning continues to be a vital tool in scientiﬁc research, enabling scientists to explore the

structure and function of genes in detail. By creating cloned copies of genes, researchers can investigate

their role in various biological processes, study their interactions with other genes, and gain insights into

the mechanisms underlying diseases. Gene cloning has also facilitated the development of gene expression

techniques, such as polymerase chain reaction (PCR) and DNA sequencing, which have become fundamental

tools in modern biological research.

References

https://www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/molecular-cloning

https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/cloning-animals

https://www.primescholars.com/articles/role-of-reproductive-cloning-in-livestock-and-their-applications-a-review.

pdf

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.

Part IV

General

Agile Manufacturing Processes

by Arun Aniyan

airis4D, Vol.1, No.7, 2023

www.airis4d.com

1.1 Introduction

Physical objects used as tools and for convenience are essential to human life. It is impossible for a modern

human being to live in an empty space without an object which has been manufactured. Apart from the food

and naturally available resources, at every point in time, we interact with an object which was manufactured.

Starting from the stone age when man started to make tools with stones and sticks, we have been making objects

for utility purposes and even art. Today we manufacture tools that are used to manufacture other objects.

The manufacturing industry is a key component for any other industry that needs to survive. Say for

example IT industry, the computing systems themselves have to be manufactured. The individual components

need to be separately manufactured. The housing case has to be manufactured by a diﬀerent manufacturer. In

essence, even for a single product, there are several manufacturing processes and manufacturers involved.

1.2 Traditional Manufacturing Methodology

The manufacturing process since the days of industrialization has not changed much. The process starts

with designing the product out of the requirements using speciﬁc design tools such as CAD tools. One would

think, the next immediate step is to manufacture the designed product. But that is not the case. Let’s see we

designed a completely new product. In that case, the instruments and molds for that new product have to be

designed in order to start manufacturing it. Think of Airbus or Boeing starting to manufacture a completely new

plane that is bigger than their existing one. Once they have the new plane designed, they must start building a

new facility itself to manufacture the plane. The facility then needs to have maybe new types of equipment or

automation tools to start building them. Once all the facilities and tools are ready, they need to be tested and

calibrated to start the manufacturing process. So if one of the equipment is not producing the expected result,

then the equipment may have to be reﬁt or re-calibrated.

Then after the manufacturing facility is set up, the actual product manufacturing can begin. Still, the process

does not guarantee the ﬁnal product. Let’s say the ﬁrst product had a ﬂaw after being built that was caused

because of a design ﬂaw, in that case, the design has to be changed, and also maybe one of the manufacturing

tools. This again is expensive in terms of time as well as money. Therefore it takes time to roll out a new product

with the existing approach.

Another important aspect of the traditional manufacturing process is the wastage of material. In most of

the products that are produced for our daily use, there is a substantial amount of material waste. The traditional

1.3 3D printing

Figure 1: Representation of the SLA mechanism. The material is at the bottom which is a light-sensitive

material. A laser shines light on the material which solidiﬁes the material which is repeated in a layered

approach. [Image Credit: Review of 3D printing]

process of using molds and casting will have excess material on the product itself which is usually cut out before

going to ﬁnal delivery. This excess material is then of no use and generally cannot be recycled. The excess

materials then simply increase the amount of waste produced by the manufacturing facility. This will cause

further environmental issues and pollution.

The aforementioned points tell us about the general failures of the traditional manufacturing process.

1.3 3D printing

3D printing is a fairly new technology that has been revolutionizing things manufactured these days. Even

though it seems to be a recent technology. Its initial designs go back to the 1980s with a technology called

Stereolithography(SLA)refer. This method basically adds thin layers of an object using a medium curable by

ultraviolet light to fully manufacture the object. SLA was patented by European inventor Charles Hull in 1986

and Figure 1 shows its representation.

Fused Deposition Modelling

A few years later in 1992, Scott Crump, a co-founder of Stratasys Inc. which was involved in Stereolithog-

raphy, ﬁled the patent for a technology called Fused Deposition Modelling (FDM) which is the hallmark of 3D

printing technology.

The principle of FDM is basically melting a plastic ﬁlament through a nozzle onto a surface in a structured

and layered approach to ﬁnally complete the object. The material is melted and extruded through a nozzle to

create the 3D cross-section of the object, one layer at a time. The extruding nozzle or printing head has the

ability to move in the x, y, and z-axis. The printing head melts the material at speciﬁc positions and hardens to

complete the object. Since the process is in a layered approach, the object is built from down to top by either

moving the printing head in the z direction or moving the printing base in the downward direction. Figure 2

shows how FDM printing works in a nutshell.

In the FDM method, the quality of the object is determined by two factors. First is the size of the extruder

needle. The ﬁner the extrusion hole on the needle, the more you can add ﬁner details. The second quality factor

is the height of the layer which is also determined by the nozzle head size. Ideally one would like to have the

1.3 3D printing

Figure 2: FDM manufacturing method is shown. The layered printing approach allows the production of any

shape.

Figure 3: The amount of detail that resin-based 3D printing can produce is very high shown by these examples.

smallest nozzle size and layer height to get high-quality objects.

FDM technology is not simply limited to plastic material, but also a variety of materials such as metal and

organic materials. This choice of materials has led to the application hnology to build rocket engines, synthetic

body parts, and even food. People have even started to manufacture houses based on FDM methods.

Resin 3D printing

Resin 3D printing is another variation of 3D printing that makes use of the principle of Stereolithography.

In essence, it is the same as SLA but more advanced. The resin-based method is used when one needs to go

for more ﬁne details of the object. For FDM where the ﬁneness is decided by the size of the extrusion needle,

the resin-based method gives extreme resolution because it makes use of laser light to harden a layer from a

photo-reactive resin bed. This method also prints a bottom-top approach. Figure 3 shows some examples of

objects created with resin printing.

In contrast to FDM, resin printing is a lot faster and also has less material waste. One of the major

limitations of resin printing is the size of the object that it can produce and the complexity of the equipment

itself.

1.4 Conclusion

Agility of 3D printing

3D printing provides a lot of ﬂexibility in terms of manufacturing and is a lot faster in comparison to the

traditional manufacturing approach. But the most important advantage is the agile process of manufacturing. We

discussed the diﬃculties with traditional manufacturing where, one has to ﬁrst create, calibrate and manufacture

the equipment for manufacturing the object. Once the equipment is manufactured, then the same may not be

useful to other objects. The options for experimenting are limited as well as costly.

When it comes to 3D printing methods, there is no need to build a separate infrastructure. All one need

is a printer. The design can be done with CAD software and experimented with many times at a very less cost

as compared to the traditional approach. Let’s say an initial design failed, there is no need to change the 3D

printer. Only the design needs to be updated and the object can be printed again and tested. This agile approach

of testing and experimenting is very much limited to the traditional approach.

With 3D printing, it is also easy to switch the material simply by changing the printer head and also

extrusion component. So in theory one piece of equipment can be used to manufacture multiple material

objects. Most importantly this can be done at scale with multiple printers printing the same objects, also with

diﬀerent materials.

1.4 Conclusion

3D printing is revolutionizing the manufacturing industry with cost-eﬀectiveness and also democratizing

the process. 3D printers can be purchased at a lower cost as compared to other equipment and it does not limit

a manufacturer’s ability to few products. 3D printed materials are also cost-eﬀective and cause less pollution.

This technology has also enabled people to be more innovative and creative when it comes to designing. One

of the creative solutions recently proposed was to 3D print other 3D printers for space exploration. So a single

3D printer can be sent to Mars to produce other 3D printers which can manufacture essential products to live

on Mars. In essence, 3D printing or agile printing is changing the landscape of the manufacturing industry.

Reference

Introduction to FDM

History of 3D printing

About the Author

Dr.Arun Aniyan is leading the R&D for Artiﬁcial intelligence at DeepAlert Ltd,UK. He comes from

an academic background and has experience in designing machine learning products for diﬀerent domains. His

major interest is knowledge representation and computer vision.

Part V

Computer Programming

Fractal Geometry

by Ninan Sajeeth Philip

airis4D, Vol.1, No.7, 2023

www.airis4d.com

Fractal geometry is a captivating ﬁeld of mathematics that explores the intricate patterns and structures

found in nature, art, and various mathematical phenomena. Unlike traditional Euclidean geometry, which

focuses on regular shapes and smooth curves, fractal geometry delves into the realm of complexity and self-

similarity. We know of zero dimension, one dimension, two and three and higher integer dimensions. But

fractals have fractional dimensions! It provides a robust framework for understanding and describing the

irregular and fragmented shapes that abound in the natural world. In this article, we will learn how to code in

Python to generate these fractals and explore their wonderful properties.

1.1 Mandelbrot set

The term “fractal” was coined by the mathematician Benoit Mandelbrot in 1975, derived from the Latin

word “fractus”, meaning “broken” or “irregular”. Mandelbrot’s pioneering work in the ﬁeld revolutionised our

perception of geometry and inspired a new way of thinking about the intricate structures present in the universe.

Mandelbrot’s most notable contribution is the discovery and popularisation of the Mandelbrot set, a mesmerising

fractal that showcases the beauty and intricacy of self-similarity. The Mandelbrot set is generated by a simple

iterative process involving complex numbers. It reveals an astonishingly intricate structure, characterised by

inﬁnitely repeating patterns at diﬀerent scales. This iconic fractal not only captivated mathematicians but also

captured the imagination of the general public, becoming a symbol of the beauty and complexity inherent in the

natural world. You can run the following code to generate the Mandelbrot set yourself and explore by zooming

in and out diﬀerent portions of it with the zoom tool-in menu.

import matplotlib.pyplot as plt

import numpy as np

class FractalDrawer:

def __init__(self, width, height, x_min, x_max, y_min, y_max, max_iterations):

self.width = width

self.height = height

self.x_min = x_min

self.x_max = x_max

self.y_min = y_min

1.1 Mandelbrot set

self.y_max = y_max

self.max_iterations = max_iterations

def draw_fractal(self):

# Create a 2D grid of complex numbers

real_vals = np.linspace(self.x_min, self.x_max, self.width)

imag_vals = np.linspace(self.y_min, self.y_max, self.height)

real, imag = np.meshgrid(real_vals, imag_vals)

complex_nums = real + 1j * imag

# Initialize the fractal image with zeros

fractal_image = np.zeros(complex_nums.shape, dtype=int)

# Iterate and compute the fractal escape time

z = np.zeros_like(complex_nums)

for i in range(self.max_iterations):

mask = np.less(np.abs(z), 2.0)

fractal_image += mask.astype(int)

z = z * z + complex_nums

# Plot the fractal

plt.imshow(fractal_image, cmap=’hot’, extent=(self.x_min, self.x_max, self.y_min, self.y_max))

plt.title(’Mandelbrot Set’)

plt.xlabel(’Re’)

plt.ylabel(’Im’)

plt.colorbar()

plt.show()

# Set the desired properties for the Mandelbrot Set visualization

width = 800

height = 600

x_min = -2.5

x_max = 1.5

y_min = -1.5

y_max = 1.5

max_iterations = 100

# Create an instance of FractalDrawer with the specified properties

fractal_drawer = FractalDrawer(width, height, x_min, x_max, y_min, y_max, max_iterations)

# Call the draw_fractal method to generate and display the Mandelbrot Set

fractal_drawer.draw_fractal()

1.2 Cantor set

Figure 1: This is the Mandelbrot set that will be output by the code. You can click the lens icon on top to select

rectangular regions in the image and zoom in to see the fractal structure.

Fractals possess a remarkable characteristic called self-similarity, which means that their intricate patterns

repeat at diﬀerent scales. No matter how much you zoom in or out, you will encounter similar patterns and

details. (In the code, we have limited the iterations to 100 to reduce computation time. If you add more zeros

to it, that will increase the depth and the levels to which you can zoom in.) This property allows fractals to

capture the complexity and irregularity seen in natural phenomena such as coastlines, clouds, trees, and even

the structure of our lungs and circulatory systems.

1.2 Cantor set

The simplest fractal structure you can think of is the Cantor set. The Cantor set, named after the German

mathematician George Cantor is a remarkable fractal that embodies the concept of self-similarity and inﬁnite

divisibility. Constructed by removing the middle third of a line segment, and recursively repeating this process

with the remaining line segments, the Cantor set emerges as a fascinating mathematical object. It exhibits

several intriguing properties, such as being disconnected, having zero length while still being uncountably

inﬁnite, and possessing a fractal dimension of

log(2)

log(3)

. The Cantor set has become a classic example in the study

of fractal geometry, oﬀering insights into the nature of inﬁnity, mathematical paradoxes, and the concept of

dimensionality. The simplicity and yet profound characteristics of the Cantor set have made it an object of

fascination for mathematicians, serving as a foundation for the exploration of more intricate fractal structures.

In our next example, we will write the code for generating a Cantor set. We restrict the depth to 10 to reduce

computational time. You can increase it to see the pattern repeat as you zoom in even small portions of the

segment until you are left with single points.

import matplotlib.pyplot as plt

def generate_cantor_set(x, y, length, depth):

1.3 Sierpinski Gasket

Figure 2: This is the Cantor set that will be output by the code.You can click the lens icon on top to select

rectangular regions in the image and zoom in to see the fractal structure.

if depth == 0:

return [(x, y), (x + length, y)]

new_length = length / 3

left_points = generate_cantor_set(x, y + 20, new_length, depth - 1)

right_points = generate_cantor_set(x + 2 * new_length, y + 20, new_length, depth - 1)

return left_points + right_points

# Set the initial parameters for the Cantor set

x_start = 0

y_start = 0

length = 600

depth = 10

# Generate the Cantor set

cantor_points = generate_cantor_set(x_start, y_start, length, depth)

# Create lists of x and y coordinates for plotting

x_coords = [x for x, _ in cantor_points]

y_coords = [y for _, y in cantor_points]

# Plot the Cantor set

plt.figure(figsize=(8, 2))

plt.scatter(x_coords, y_coords, color=’black’, s=1)

plt.title(’Cantor Set’)

plt.axis(’off’)

plt.show()

Fractal geometry provides a rich language to describe and quantify these intricate patterns, oﬀering insights

into the underlying order and complexity of natural forms. It has applications in various scientiﬁc disciplines,

including physics, biology, computer science, and economics.

1.3 Sierpinski Gasket

The Sierpinski Gasket, named after the Polish mathematician Waclaw Sierpinski, is a captivating fractal that

showcases the beauty of self-similarity and recursive construction. It is formed by starting with an equilateral

triangle and recursively dividing it into smaller equilateral triangles. At each iteration, the middle triangle of

the previous iteration is removed, leaving behind three smaller triangles. This process is repeated inﬁnitely,

resulting in a fractal pattern with an intricate structure that resembles a gasket or a mesh-like arrangement.

The Sierpinski Gasket is a classic example of a fractal that exhibits a fascinating property called fractional

dimensionality. Although it is made up of only 2-dimensional triangles, its fractal dimension is log(3)/log(2),

which is approximately 1.585. The Sierpinski Gasket has captivated mathematicians, artists, and enthusiasts

alike, serving as a source of inspiration for exploring the concepts of self-similarity, recursive algorithms, and

the delicate balance between simplicity and complexity in the realm of fractal geometry. So our next code

example shall plot the Sierpinski Gasket.

import matplotlib.pyplot as plt

def generate_sierpinski_triangle(x, y, size, depth):

if depth == 0:

# Base case: draw a single triangle

triangle_points = [(x, y), (x + size, y), (x + size/2, y + size)]

plt.fill([point[0] for point in triangle_points],

[point[1] for point in triangle_points],

’black’)

else:

# Recursive case: divide the triangle and call the function on each smaller triangle

generate_sierpinski_triangle(x, y, size/2, depth - 1)

generate_sierpinski_triangle(x + size/2, y, size/2, depth - 1)

generate_sierpinski_triangle(x + size/4, y + size/2, size/2, depth - 1)

# Set the initial parameters for the Sierpinski Triangle

x_start = 0

y_start = 0

size = 60

depth = 7

# Generate the Sierpinski Triangle

generate_sierpinski_triangle(x_start, y_start, size, depth)

# Set plot limits and show the Sierpinski Triangle

plt.xlim(x_start, x_start + size)

plt.ylim(y_start, y_start + size)

plt.title(’Sierpinski Triangle’)

plt.axis(’off’)

plt.show()

1.4 Koch snowﬂake

Figure 3: This is the Sierpinski Triangle that will be output by the code. You can click the lens icon on top to

select rectangular regions in the image and zoom in to see the fractal structure.

1.4 Koch snowﬂake

Another interesting example is the Koch snowﬂake. It is an enchanting fractal that embodies the beauty of

intricate self-replication and inﬁnite complexity. It is formed by iteratively adding smaller equilateral triangles

to the edges of an initial equilateral triangle. At each iteration, the middle third of each line segment is replaced

with two equal segments, forming a zigzag pattern. As this process is repeated inﬁnitely, the Koch snowﬂake

reveals an astonishingly detailed and inﬁnitely self-similar structure. Despite being constructed from a simple

geometric shape, the Koch snowﬂake exhibits a fractal dimension of approximately 1.2619, which signiﬁes its

intricate and space-ﬁlling nature. Here is the code to create it yourself!

import matplotlib.pyplot as plt

import numpy as np

def generate_koch_snowflake(x, y, length, depth):

if depth == 0:

# Base case: draw a straight line

points = [(x, y), (x + length, y)]

plt.plot([point[0] for point in points],

[point[1] for point in points],

color=’black’)

else:

# Recursive case: divide the line into four segments and call the function on each segment

segment_length = length / 3

angle = np.pi / 3 # 60 degrees in radians

# Calculate the coordinates of the new points

1.5 Koch curve

Figure 4: This is the Koch Snowﬂake that will be output by the code. You can click the lens icon on top to

select rectangular regions in the image and zoom in to see the fractal structure.

x1 = x + segment_length * np.cos(angle)

y1 = y + segment_length * np.sin(angle)

x2 = x + 2 * segment_length * np.cos(angle)

y2 = y + 2 * segment_length * np.sin(angle)

# Recursively call the function on each segment

generate_koch_snowflake(x, y, segment_length, depth - 1)

generate_koch_snowflake(x1, y1, segment_length, depth - 1)

generate_koch_snowflake(x2, y2, segment_length, depth - 1)

generate_koch_snowflake(x + length, y, segment_length, depth - 1)

# Set the initial parameters for the Koch snowflake

x_start = 0

y_start = 0

length = 600

depth = 4

# Generate the Koch snowflake

generate_koch_snowflake(x_start, y_start, length, depth)

# Set plot limits and show the Koch snowflake

plt.xlim(x_start, x_start + length)

plt.ylim(y_start, y_start + length)

plt.title(’Koch Snowflake’)

plt.axis(’off’)

plt.show()

1.5 Koch curve

The Koch curve, named after the Swedish mathematician Helge von Koch, is a fractal that showcases the

power of recursive construction and inﬁnite detail. It exhibits fascinating properties, such as being continuous

but nowhere diﬀerentiable, meaning it lacks a well-deﬁned tangent at any point. It is created by starting with

a straight line segment and iteratively replacing each line segment with four smaller segments. The added

segments form equilateral triangles on the outer side of the original line segment, resulting in a zigzag pattern.

This process is repeated inﬁnitely, leading to the creation of a stunningly intricate and self-similar curve. The

fractal dimension of the Koch curve is approximately 1.2619, indicating its complex and space-ﬁlling nature.

Here is the code to create it.

import numpy as np

import matplotlib.pyplot as plt

class KochCurveFractal:

def __init__(self, num_iterations=4):

self.num_iterations = num_iterations

self.points = []

def generate_fractal(self):

# Starting points of the curve

p1 = np.array([0.0, 0.0])

p2 = np.array([1.0, 0.0])

self.points = [p1]

# Recursive generation of Koch Curve

self._generate_curve(p1, p2, self.num_iterations)

def _generate_curve(self, p1, p2, iteration):

if iteration == 0:

self.points.append(p2)

else:

# Calculate the four intermediate points

p1_new = p1 + (p2 - p1) / 3

p3 = p1 + (p2 - p1) / 2

p4 = p1 + 2 * (p2 - p1) / 3

angle = np.pi / 3

p2_new = p4 + (p2 - p4) * np.cos(angle) + np.cross((p2 - p4), np.array([0, 1])) * np.sin(angle)

# Recursively generate the remaining segments

self._generate_curve(p1, p1_new, iteration - 1)

self._generate_curve(p1_new, p3, iteration - 1)

self._generate_curve(p3, p4, iteration - 1)

self._generate_curve(p4, p2_new, iteration - 1)

1.5 Koch curve

Figure 5: This is the KochCurve that will be output by the code.You can click the lens icon on top to select

rectangular regions in the image and zoom in to see the fractal structure.

def plot_fractal(self):

points = np.array(self.points)

plt.figure(figsize=(6, 3))

plt.plot(points[:, 0], points[:, 1], color=’blue’, linewidth=0.8)

plt.axis(’off’)

plt.show()

# Example usage:

fractal = KochCurveFractal(num_iterations=7)

fractal.generate_fractal()

fractal.plot_fractal()

Fractal geometry represents a fusion of mathematics and aesthetics, blending the rigour of mathematical

inquiry with the beauty and complexity of the natural world. It challenges our conventional notions of geometry

and invites us to explore the boundless intricacies that lie beyond the familiar world of regular shapes and

smooth curves. Embark on this fascinating journey into fractal geometry and unlock the secrets of the irregular,

the fragmented, and the endlessly captivating.

WILL CONTINUE..

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.

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.