7.1 INTRODUCTION [LO1]

The problems of stresses and deformations in disks rotating at high speeds are important in the design of both gas and steam turbines, generators and many such rotating machinery in industry. As discussed in earlier chapters, this is another example of axisymmetric problems in polar coordinates. Although the theoretical treatment of a flat disk is simpler, in many industrial applications, disks are tapered. They are usually thicker near the hub, and their theoretical analysis is slightly more involved. We shall first take up the analysis for flat disks.

In the case of rotating disks with centrifugal force as body force, the equation of equilibrium reduces to as in equation (6.1.3).

Combining this with displacement equations, we have, as in equation (6.1.5), a general equation for determining the stress distribution in axisymmetric problems. This is given as

This is a nonhomogeneous differential equation. The associated homogeneous equation (complementary equation) is

The solution of this equation is Lame's equation as discussed in Chapter 6, equation (6.2.3), and taking into consideration the particular solution, the solution to equation (7.1.2) turns out to be

We may also determine the radial displacement from equation (6.2.11), and this is given as

We may therefore write the stresses and displacement for the rotating disk under one bracket as

With these introductory basic equations, we shall now set out to discuss the stress distribution and displacement in rotating disks.

Soon after the project was announced in 2007, the Bengaluru Metro Rail Corporation Limited (BMRCL) began putting together plans to acquire land. Unsurprisingly, a number of middle-class and wealthy neighbourhoods refused to move in order to make way for the construction. Two working-class neighbourhoods, densely populated and centrally located, entered the arduous process of negotiating with the BMRCL. As they were in close proximity to the Central Majestic bus station and railway station, the two neighbourhoods – Basaveshwara Nagara and Jai Bhim Nagara – were also well connected to the other parts of the city.5 Unlike illegal settlements that are often evicted brutally, the two neighbourhoods were offered the chance of consultation and options once they had vacated their homes.

14.1 Introduction to Association Rule Mining

Association rule mining is a rule-based technique to discover the relation between the attributes of a dataset. It is used to find the relation between the sales of item X and item Y. It is often called a “market basket” analysis, as shown in Figure 14.1. Here, the market analyst examines the items that consumers often purchase together to find the relation between the sale of item X and item Y.

In other words, when customers visit a store, they may buy a certain type of items together during a shopping trip. For example, as shown in Figure 14.1, a database of customer’s transactions (e.g., shopping baskets) is shown where each transaction consists of a set of items (e.g., products) purchased during a visit, machine learning (ML) engineers can use association mining for finding out a group of items which are frequently purchased together (customers purchasing behavior). This is also referred to as an analysis of customer purchasing behavior. For example, “IF one buys bread, THEN there is a high probability of buying butter with it”, as it is common that people who buy bread often buy butter with it. The store manager can use this information and arrange the items accordingly to increase sales and the overall efficiency of the store.

Let us consider a situation where the store manager feels that there is a lot of rush and customers always complain about the slow working of his store. He is exploring different ways to improve the efficiency of his store. He performed an association analysis and prepared a list of associated items like bread and butter. He may decide to put all these associated items together on the same shelf or near each other so that customers can find them quickly, reducing their shopping time. It will also improve the overall efficiency of the store and the sale of the products. To further improve the shopping experience of his customers, he can create different combos and put sales over these combos.

22.1 Intuition of Genetic Algorithm

Genetic algorithm (GA) is inspired by nature, and it plays a vital role in the field of machine learning (ML). It selects the best-optimized solution from all available possible solutions or candidates. As nature selects the best possible candidates using the theory of evolution, in the same way, the GA selects the best possible solution from the available solutions.

One of the applications of GAs in ML is to select the global minima from all possible (local) minima by using natural selection. In earlier chapters, we learned that during the training of an artificial neural network, the main goal is to obtain the weights with a minimum cost function value. The gradient descent algorithm is commonly used to find the local minima of the cost function. But, we must find the global minima to reach the optimal weights. A GA can be used to find the global minima out of all available local minima or possible solutions. In this case, the set of possible local minima becomes the population containing possible candidates.

In this chapter, we will discuss inspiration from nature which is the main driving concept in working of GAs and their implementation. To get a good idea about the GA, we will discuss the basics of natural selection by revisiting the theory of evolution in the next section.

22.2 The Inspiration behind Genetic Algorithm

The concepts discussed in this chapter are also available in the form of the free online Udemy Course, Genetic Algorithm for Machine Learning by Parteek Bhatia,

https://www.udemy.com/course/genetic-algorithm-for-machine-learning/

The GA is one of the first and most well-regarded evolutionary algorithms in computer science literature. John Holland, a researcher at the University of Michigan, gave this algorithm in the 1970s, but it became popular in the ‘90s.

3.1 Need for Data Pre-processing

We live in an age where data is considered oil because we need data to train machine learning (ML) algorithms. The most important job for a data analyst is to collect, clean, and analyze the data and build ML models on the cleaned dataset. But often, the raw data that we obtain is noisy. It consists of many discrepancies, inconsistencies, and often missing values. To understand this situation, let us consider an example.

Suppose we have to predict the house price, and for this, we have collected data from a few previous transactions, as shown in Figure 3.1.

In a perfect situation, the captured data should be of this format, as shown in Figure 3.1. Here, we have the size of the house and the number of bedrooms as input features, while the price is the output attribute. We can predict the price of an unknown instance through regression.

But practically, in most situations, the captured data is not of good quality, and usually, we have a dataset, as shown in Figure 3.2.

You can see that this data is messy. There are a lot of unknown or missing values, and if we trained the model on this data, its prediction would be very poor. Also, you can identify the noise and incorrect labels like the second record price is incorrect and will result in poor model training.

We can also consider some more examples like if someone entered –1 in the “salary credited” column in the case of employee dataset. It does not make any sense and will be considered noise. Sometimes, we may have an unrealistic and impossible combination of data; for example, let us consider a record where we have Gender–Male and Pregnant–Yes.

Within cities across the world, communal violence has often led to the formation of neighbourhoods segregated on religious lines. Colonies identified by the religion of its residents are now found in Indian metropolises such as Ahmedabad, Mumbai and New Delhi, occupied mainly by the Muslims who were pushed involuntarily to these spaces after decades of sociopolitical marginalisation and targeted communal violence. Due to their identification with the religious identity of its residents, these colonies faced systematic state neglect and lack of infrastructural development pushing them further towards spatial stigmatisation and social segregation (Gayer and Jaffrelot 2012; Mahadevia 2002). Given their specific context, these spaces are identified in both academic literature and policy papers as ‘ghettos’, pointing in turn to the many stigmas attached to them. These neighbourhoods are part of a city but ‘insulated’ and ‘do not benefit from the same kind of attention from the state as other parts of the city’ (Jaffrelot and Thomas 2012: 70). Tellingly, they lack state-run schools, colleges, technical institutions, healthcare amenities and other basic facilities like sanitation and water (Jaffrelot and Thomas 2012: 70).

This chapter examines the many exclusions and marginalities faced by residents of one such neighbourhood in New Delhi called Tilak Vihar. The context of this West Delhi space is distinct from other neighbourhoods that are formed as a result of communal violence. Tilak Vihar is a Sikh neighbourhood of nearly 1,000 families headed by the widows of those men who were killed in the 1984 anti-Sikh violence in Delhi. It is important to emphasise here that Tilak Vihar is not a self-segregated space. Tilak Vihar was demarcated by the state in order to rehabilitate women who lost their husbands in the 1984 violence and were hence displaced.

6.1 INTRODUCTION [LO1]

In earlier chapters, we have discussed axisymmetric problems in two-dimensional (2D) polar coordinate systems. Thick cylinders fall into this class of problems. Cylindrical pressure vessels, hydraulic cylinders, gun-barrels, and pipes carrying fluids at high pressure develop radial and tangential stresses (circumferential). Longitudinal stresses can also be developed if the ends are closed. Therefore, ideally, this is a triaxial stress system as shown in Figure 6.1.

• (a) Circumferential or hoop stress (σθ)

• (b) Longitudinal stress (σz)

• (c) Radial stress (σr)

If the wall thickness of a hollow cylinder is less than about 10% of its radius, it may be treated as a thin cylinder. Cylinders with higher wall thickness are considered to be thick cylinders. Before analyzing the stress in a thick cylinder, we should briefly consider the stress state in thin cylinders, where radial stress is small compared to the other stresses, and this can be neglected. Stress variation across the thin wall is also negligible. Analysis of thin-walled pressure vessels may therefore be carried out on the basis of biaxial stress system. Since the presence of shear stress at the cut section would lead to incompatible distortion, the longitudinal and circumferential stresses in this case are both principal stresses. We now take another section of the cut section as shown in Figure 6.2 (a) to consider the equilibrium of the section, and this is shown in Figure 6.2 (b).

The section is acted upon by internal pressure p and the circumferential stress developed at the cut section is σθ. Force on an infinitesimal small area subtended by angle dθ at θ inclination from the horizontal axis is pridθ.

Hobbes argues that in a “condition of meer nature,” lacking a common power, reason requires that we appoint one, lest our lives be “solitary, poore, nasty, brutish, and short.” No covenant of peace can be effective without a Sovereign arbiter to enforce it. Therefore, reason requires each of us to surrender the natural right to judge for ourselves, and to appoint a Sovereign. An effective Sovereign must have authority to determine religious practice and to raise an army – precisely the powers the “Roundhead” rebels had denied Charles I.

In 1974, I travelled as a young graduate student volunteer to join Kishore Bharati (KB), an organisation working for rural education and development in Palia Pipariya village on the eastern tip of Hoshangabad district in Madhya Pradesh. The train made a short halt at Pipariya station, leaving me with only faint memories of yet another nondescript small town. Over the next 20 years, however, Pipariya was to be my nearest market town, and eventually my home. It also became a major centre of KB's educational and social mobilisation activities.

After moving to Delhi in 1992, I continued to visit the town and kept in touch with its people. Over the years, the educational landscape of the town and the aspirations of its young population underwent a striking change. Young students started to enrol in private engineering and management colleges across the country. Graduates from the town gained employment in national and international companies in Mumbai, Bengaluru, Pune, the United States (US), Europe and Canada. I was curious to know what developments had made these changes possible and who had been left behind.

On one such visit to Pipariya in 2018, I met two old friends: a couple who work as schoolteachers and who graduated from the Pipariya Government College (PGC). Hailing from the Other Backward Class (OBC) social category, they were among the last few young science and mathematics graduates recruited as permanent government schoolteachers in the mid-1980s. At their home, the couple introduced me to their two children who had completed secondary education in Pipariya.

Today, Python is known to be one of the most in-demand programming languages. As per the stats of GitHub (a provider of Internet hosting for software development), Python is the second most popular programming language, following JavaScript, as shown in Figure 2.1, and soon it may be on the top of the chart. Python surpassed Java, PHP, and other prominent languages in 2019.

Python is easy and versatile. So it is acclaimed as the major programming language to work on many new-age technologies like machine learning (ML), artificial intelligence, data science, and natural language processing. The creator of Python, Guido van Rossum, in 1991, stated that Python is a high-level programming language, and its core design philosophy is about code readability and syntax, which allows programmers to express concepts in a few lines of code. Interestingly, the name Python is inspired by Guido's favorite television show Monty Python's Flying Circus.

In this chapter, we will discuss various programming constructs of Python so that you can easily implement ML algorithms by using it. Before writing the actual code in Python, let us focus on the features of Python that make it so popular and unique.

2.1 Features of Python

Features offered by Python can be visualized in Figure 2.2. Talking about them profoundly, the main features of Python are as follows:

• • Beginner's Language: Python is not only just easy to code and learn, but also fast to grasp, and hence it is a suitable choice for any novice user who wants to learn to program. This is why nowadays this language is introduced to students in schools.

• • Interpreted: Unlike other programming languages such as C or C++, Python does not require you to compile programs before executing them. It is an interpreted language, i.e., the code written in Python gets processed in real-time line by line.

• • Interactive: The interactive feature of Python enables real-time feedback, allowing programmers to experiment, debug, and make adjustments on the go.

5.1 Introduction to Simple Linear Regression

As discussed in earlier chapters, regression predicts a continuous value or real-valued output. This chapter will discuss how regression works (from a mathematical aspect) to predict the continuous value for the given dataset. Our first learning algorithm is simple linear regression. In this section, we will discuss the fundamental concepts and mathematical modeling of simple linear regression.

We usually have a dependent variable having a continuous value whose value we wish to predict based on one or more independent variables. If we have only one independent or input variable, this situation is known as simple linear regression (also called univariate regression). If we have multiple independent or input variables, it is known as multiple linear regression or multivariate regression.

Linear regression could be used for studying patterns in different real-life scenarios. Consider a research lab where a researcher wants to understand how the stipend is effected by the years of experience, or, in simple words, we wish to predict the stipend based on the years of experience of the researcher. Machine learning (ML) is about learning from past experiences or data. Thus, to predict the researcher's stipend, we have to collect some data about past researchers, specifically their stipend and experience.

In the supervised learning models, we need a dataset called a training set. We will use the dataset as given in Table 5.1 for training the model, and our job will be to build the ML model that learns from this data and hence predicts the stipend of a researcher based on his experience. Here, the stipend will be considered the dependent or output variable because it depends on the researcher's years of experience. Thus, years of experience will be considered an independent or input variable. So, we will use simple linear regression to build the ML model. For proceeding with this problem, we will use a dataset of researchers’ stipends with their corresponding years of experience, as shown in Table 5.1.

In this chapter, the contrast between two models of expatriate masculinity developed earlier is brought to a head, with a fresh twist on the history of masculine identity. In retirement William Cooper indulged his passion for global wanderlust at the expense of his family, whereas Edgar Wilson happily abandoned his expatriate frustrations for a conventional model of settled suburban domesticity with his wife in England, spurning the mobile attractions of the cosmopolitanism they had long nurtured, but with Winifred continuing to exercise her public activism and independence. Ironically, the domestic model, rather than William’s continuing mobility, was most closely associated with the lower middle class, recalling Edgar’s origins and early white-collar labours. The disparity is underlined by a tragic account of William’s last years, interned by the Nazis in wartime Paris after an ill-advised excursion across France. Wartime domesticity for Edgar and Winifred was a struggle, only relieved by a comfortable inheritance from William. Winifred’s Will reflected her long commitment to chosen causes like the Mothers’ Union, a statement of her lifetime priorities.

5.1 INTRODUCTION [LO1]

In any three-dimensional (3D) elasticity problem, there are 15 unknown parameters: 6 stress components, 6 strain components, and 3 displacements. There are 15 related equations: 3 equations of equilibrium, 6 compatibility equations, and 6 constitutive equations. Solutions to a particular elasticity problem require evaluation of these 15 unknown parameters using 15 equations, satisfying all the boundary conditions. As discussed in the earlier chapters, there may be displacement or stress, or mixed boundary conditions. In many cases, solutions to 3D problems are not easy analytically. Even numerical solutions may be difficult.

There are mainly three methods of simplification of solution techniques:

• (a) If the boundary conditions are in terms of stresses, stress function approach may be made as discussed in the earlier chapter. This makes the solution simpler.

• (b) Assumptions of plane stress and plane strain reduce 3D problems to two-dimensional (2D) ones and this also makes the solution simpler.

• (c) Use of St. Venant's principle and superposition principle also makes the solution of elasticity problems simpler.

An introduction to stress function approach has been discussed in Chapter 4. We therefore start our discussion on plane stress and plane strain approaches.

5.2 PLANE STRESS AND PLANE STRAIN PROBLEMS [LO2]

The idealizations of both plane stress and plane strain states are suitable for certain classes of problems that are made to reduce the complexity of solutions. We shall consider the plane stress state first.

During the century-and-a-half slumber of social contract theory the idea of universal adult suffrage became commonplace. It had long been assumed that formal political equality would more than suffice to defend the less advantaged against class legislation (although the worry shared by Ireton and Mill, that majority rule would enable class legislation favoring the less advantaged, has never disappeared). Rawls argued that a well-ordered constitutional democracy must guarantee the fair value of the equal political liberties (and those liberties alone: The others come within the difference principle in its special form). Rawls complained that this position seemed “never to have been taken seriously.” Rawls suggested a number of devices to secure fair value: promotion devices, such as subsidies of political parties and public debate; insulation devices, such as limits upon campaign contributions and expenditures; and anti-accumulation devices, such as inheritance taxes and public ownership of the means of production. Why, though, would parties in the original position insist on the fair-value guarantee? One argument extends the argument for the priority of the whole family of basic liberties, with special emphasis on stability “for the right reasons” and the shared sense of justice essential to it.

In the prevalent modes of reckoning of the Indian middle classes, education has long remained a crucial factor in achieving social mobility and improving social status. During the period of colonial modernity, the appeal of ‘modern’ education had been one of the major factors that pushed many to migrate to the upcoming urban centres in hopes of securing education and accessing the new occupational opportunities presented by an expanding colonial regime. In many cases, such efforts had also helped individuals to shed the dictates of tradition and escape the deep-seated hierarchies of the Indian village. The liberating potential of modern education has since been evident in the ways it has helped individuals and communities to overcome the compulsions of class, caste, language and religion to join the modern workforce and secure employment premised on the tenets of equality and dignity. While the relationship between education and urbanity has remained deeply and historically intertwined, perceptions around what qualifies as ‘desirable’ education have evolved over the years in keeping with the shifts in the broader sociopolitical trends in the country.

Particularly, in the last three decades or so, neoliberal social and economic policy has made deep inroads into Indian society, once again leaving its mark on its burgeoning urban fabric. Apart from introducing ‘global urban imaginaries’ (Anjaria and McFarlane 2011) around consumption and lifestyle choices, it has also produced new bases of inequality based on digital literacy and global access that have further fragmented an already divided urban landscape. The deep inequalities thus created between the dominant and the marginal social groups are evident in the layered access they have to the city and its amenities. Education, apart from housing and healthcare, figures prominently in this discourse.