10.1 Support Vector Machines

Support vector machines (SVMs) are supervised machine learning (ML) models used to solve regression and classification problems. However, it is widely used for solving classification problems. The main goal of SVM is to segregate the n-dimensional space into labels or classes by defining a decision boundary or hyperplanes. In this chapter, we shall explore SVM for solving classification problems.

10.1.1 SVM Working Principle

SVM Working Principle | Parteek Bhatia, https://youtu.be/UhzBKrIKPyE

To understand the working principle of the SVM classifier, we will take a standard ML problem where we want a machine to distinguish between a peach and an apple based on their size and color.

Let us suppose the size of the fruit is represented on the X-axis and the color of the fruit is on the Y-axis. The distribution of the dataset of apple and peach is shown in Figure 10.1.

To classify it, we must provide the machine with some sample stock of fruits and label each of the fruits in the stock as an “apple” or “peach”. For example, we have a labeled dataset of some 100 fruits with corresponding labels, i.e., “apple” or “peach”. When this data is fed into a machine, it will analyze these fruits and train itself. Once the training is completed, if some new fruit comes into the stock, the machine will classify whether it is an “apple” or a “peach”.

Most of the traditional ML algorithms would learn by observing the perfect apples and perfect peaches in the stock, i.e., they will train themselves by observing the ideal apples of stock (apples which are very much like apples in terms of their size and color) and the perfect peaches of stock (peaches which are very much like peaches in terms of their size and color). These standard samples are likely to be found in the heart of stock. The heart of the stock is shown in Figure 10.2.

9.1 INTRODUCTION [LO1]

Stresses given by relatively simple equations in the strength of materials for structures or machine members are based on the assumed continuity of the elastic medium. However, the presence of discontinuity destroys the assumed regularity of stress distribution in a member and a sudden increase in stresses occurs in the neighborhood of the discontinuity. In developing machines, it is impossible to avoid abrupt changes in cross-sections, holes, notches, shoulders, etc. Abrupt changes in cross-section also occur at the roots of gear teeth and threads of bolts. Some examples are shown in Figure 9.1.

Any such discontinuity acts as a stress raiser. Ideally, discontinuity in materials such as non-metallic inclusions in metals, casting defects, residual stresses from welding may also act as stress raisers. In this chapter, however, we shall consider only the geometric discontinuity that arises from design considerations of structures or machine parts.

Many theoretical methods and experimental techniques have been developed to determine stress concentrations in different structural and mechanical systems. In order to understand the concept, we shall begin with a plate with a centrally located hole. The plate is subjected to uniformly distributed tensile loading at the ends, as shown in Figure 9.2.

Introduction

All metals and alloys exhibit a reduction in electrical resistance as they cool. As the temperature drops, atoms’ thermal vibrations become less intense, and conduction electrons scatter less frequently. The resistivity should decrease toward zero as the temperature approaches zero Kelvin for a perfect pure metal, where the only thing standing in the way of an electron's travel is the thermal vibrations of the lattice. This zero resistance, which a hypothetical perfect specimen would acquire if it could be cooled to absolute zero, is the phenomenon of superconductivity. Any real specimen of metal cannot be perfectly pure and will contain some impurities. As a result, in addition to being scattered by the thermal vibrations of the lattice atoms, the electrons are also dispersed by impurities, and this impurity scattering is largely temperature independent. As a result, at the lowest temperature, there will be some residual resistance. The residual resistivity of a metal increases with the degree of impurity.

The phenomenon of superconductivity was first discovered by Dutch physicist H. Kamerling Onnes of Leiden University in 1911 during the investigation of the variation of electrical resistance of mercury in the newly available range of low temperatures, in the neighborhood of temperature of liquid helium (or 4.2 K). He observed that the resistance of mercury suddenly falls from 0.08 ohm at about 4 K to less than 3 × 10−6 ohm over a very small temperature of 0.01 K.

Introduction

The nonconducting materials such as paper, wood, glass, ceramics, polymers and so on do not have free charge carriers, that is, electrons or holes. Therefore, they prevent the flow of electrical current and heat through them.

When the main function of nonconducting materials is to provide electrical isolation then they are called insulators.

When the main function of nonconducting materials is for charge storage then it is called dielectric.

The dielectrics are polarized under the influence of an external electric field.

Dielectric Constant

Let us consider two parallel plates separated by a distance “d” connected with a dc supply of voltage V, as shown in Figure 6.1(a). Now the circuit is disconnected, and the dielectric is inserted between the plates, as shown in Figure 6.1(b).

Then, the voltage across the capacitor is reduced from V to V′. The change in voltage across the plates can be related by a factor as

Since V < V , the relative permittivity or dielectric constant ɛr 1 >.

The capacitance without dielectric is given as

The capacitance with dielectric is given as

Now, put the value of C and C¢ in equation (6.1), the relative permittivity or dielectric constant is

If “A” is the area of the plates, then

where ɛ is the permittivity of the material.

The years leading up to Periyar's break from the Indian National Congress and the founding of the Self-Respect Movement (SRM) were marked by two significant events. The first was the controversy over discrimination in the Cheranmadevi Gurukulam, a nationalist school, of which the centenary history of The Hindu says: ‘The controversy was one of the contributing factors for E. V. Ramaswami Naicker drifting away from Congress and later forming an organisation of his own whose avowed objective was to eliminate Brahmins and Brahmin influence in Tamil Nad which it wanted to secede from India’ (Parthasarathy, 1978, p. 337).

The bitterness caused by the Cheranmadevi Gurukulam controversy was accentuated by the Vaikom Satyagraha, which Periyar for the most part led during 1924–1925. If the nationalist gurukulam in Cheranmadevi provided separate seating for Brahmins and non-Brahmins in the dining hall, in the temple town of Vaikom in Kerala, Ezhavas and other Depressed Classes were not even permitted entry into the streets surrounding the Mahadeva (Siva) Temple, not to speak of entry into the temple precincts. The Vaikom experience gave Periyar a fuller understanding of nationalist politics and left an indelible imprint on his future career. Periyar returned to these experiences in his speeches and writings all through his life.

These two struggles and the campaign for communal representation (equitable share of seats for non-Brahmins in representative political bodies and in employment and education) were what led Periyar to leave the Congress, of which he had been a part from around the time of the First World War.

1.1 Introduction

In today’s data-driven world, information flows through the digital landscape like an untapped river of potential. Within this vast data stream lies the key to unlocking a new era of discovery and innovation. Machine learning (ML), a revolutionary field, acts as the gateway to this wealth of opportunities. With its ability to uncover patterns, make predictive insights, and adapt to evolving information, ML has transformed industries, redefined technology, and opened the door to limitless possibilities. This book is your gateway to the fascinating realm of ML—a journey that empowers you to harness the power of data, enabling you to build intelligent systems, make informed decisions, and explore the boundless possibilities of the digital age.

ML has emerged as the dominant approach for solving problems in the modern world, and its wide-ranging applications have made it an integral part of our lives. Right from search engines to social networking sites, everything is powered by ML algorithms. Your favorite search engine uses ML algorithms to get you the appropriate search results. Smart home assistants like Alexa and Siri use ML to serve us better. The influence of ML in our day-to-day activities is so much that we cannot even realize it. Online shopping sites like Amazon, Flipkart, and Myntra use ML to recommend products. Facebook is using ML to display our feed. Netflix and YouTube are using ML to recommend videos based on our interests.

Data is growing exponentially with the Internet and smartphones, and ML has just made this data more usable and meaningful. Social media, entertainment, travel, mining, medicine, bioinformatics, or any field you could name uses ML in some form.

To understand the role of ML in the modern world, let us first discuss the applications of ML.

1.1 INTRODUCTION [LO1]

Mechanics is one of the oldest physical sciences, dating back to the times of Aristotle and Archimedes. The subject deals with force, displacement, and motion. The concepts of mechanics have been used to solve many mechanical and structural engineering problems through the ages. Because of its intriguing nature, many great scientists including Sir Isaac Newton and Albert Einstein delved into it for solving intricate problems in their own fields.

Engineering mechanics and mechanics of materials developed over centuries with a few experiment-based postulates and assumptions, particularly to solve engineering problems in designing machines and structural parts. Problems are many and varied. However, in most cases, the requirement is to ensure sufficient strength, stiffness, and stability of the components, and eventually those of the whole machine or structure. In order to do this, we first analyze the forces and stresses at different points in a member, and then select materials of known strength and deformation behavior, to withstand the stress distribution with tolerable deformation and stability limits. The methodology has now developed to the extent of coding that takes into account the whole field stress, strain, deformation behaviors, and material characteristics to predict the probability of failure of a component at the weakest point. Inputs from the theory of elasticity and plasticity, mathematical and computational techniques, material science, and many other branches of science are needed to develop such sophisticated coding.

The theory of elasticity too developed but as an applied mathematics topic, and engineers took very little notice of it until recently, when critical analyses of components in high-speed machinery, vehicles, aerospace technology, and many other applications became necessary. The types of problems considered in both the elementary strength of material and the theory of elasticity are similar, but the approaches are different. The strength of the materials approach is generally simple. Here the emphasis is on finding practical solutions to a problem with simplifying assumptions.

Wave optics is the branch of modern physics in which the nature of light and its propagation are studied.

Interference

When two waves of the same frequency, having a constant phase difference between them, and traveling in the same medium are allowed to superimpose each other, there is a modification in the intensity pattern. This phenomenon is known as interference of light.

When the resultant amplitude at certain points is the sum of the amplitudes of the two waves, this interference is known as constructive interference.

When the resultant amplitude at certain points is the difference of the amplitudes of the two waves, this interference is known as destructive interference, as shown in Figure 11.1.

COHERENT SOURCES

Two sources are said to be coherent if the waves emitted from them have a constant phase difference with time.

THEORY OF INTERFERENCE

Let us consider two coherent sources S1 and S2 that are equidistant from source S. Let a1 and a2 be the amplitudes of the waves originated from source S1 and S2, respectively, as shown in Figure 11.2. Then the displacement y1 from the source S is given by

where δ is the phase difference between the two waves.

Now, according to the law of superposition, the resultant wave is given by

Band Theory ofSolids

The band theory of solids is different from the others because the atoms are arranged very close to each other such that the energy levels of the outermost orbital electrons are affected. But the energy level of the innermost electrons is not affected by the neighboring atoms.

In general, if there is n number of atoms, then there will be n discrete energy levels in each energy band. In such a system of n number of atoms, the molecular orbitals are called energy bands shown in Figure 7.1.

CLASSIFICATION OF SOLIDS ON THE BASIS OF BAND THEORY

The solids can be classified on the basis of band theory. The parameter that differentiates the solids among insulator, conductor, and semiconductor is known as energy band gap and represented by (Eg), as shown in Figure 7.2. When the energy band gap (Eg) between conduction band and valence band is greater than 5 eV (electron-volt) then the solid is classified as insulator. When the energy band gap (E g)between conduction band and valence band is 0 eV (electron-volt), that is, overlapping of bands occurs then the solid is classified as conductor. When the energy band gap (Eg) between conduction band and valence band is approximately equals to 1 eV (electron-volt) then the solid is classified as semiconductors.

4.1 CONSTITUTIVE EQUATIONS [LO1]

So far, we have discussed the strain and stress analysis in detail. In this chapter, we shall link the stress and strain by considering the material properties in order to completely describe the elastic, plastic, elasto-plastic, visco-elastic, or other such deformation characteristics of solids. These are known as constitutive equations, or in simpler terms the stress–strain relations. There are endless varieties of materials and loading conditions, and therefore development of a general form of constitutive equation may be challenging. Here we mainly consider linear elastic solids along with their mechanical properties and deformation behavior.

Fundamental relation between stress and strain was first given by Robert Hooke in 1676 in the most simplified manner as, “Force varies as the stretch”. This implies a load–deflection relation that was later interpreted as a stress–strain relation. Following this, we can write P = kδ, where P is the force, δ is the stretch or elongation, and k is the spring constant. This can also be written for linear elastic materials as σ = E∈, where σ is the stress, ∈ is the strain, and E is the modulus of elasticity. For nonlinear elasticity, we may write in a simplistic manner σ = E∈n, where n ≠ 1.

Hooke's Law based on this fundamental relation is given as the stress–strain relation, and in its most general form, stresses are functions of all the strain components as shown in equation (4.1.1).

Periyar's writings on women were at the heart of his commitment to a radical concept of freedom. Periyar is known most not only for his atheism and radical critique of religion (Manoharan, 2022a) but also for his commitment and contribution to anti-caste thought and politics (Manoharan, 2020; 2022b). However, crucial, perhaps even central, to Periyar's politics of Self-Respect was his approach to the women's question. In this chapter, we discuss how Periyar's approach to the women's question was grounded not only in a rights-based discourse, but also in a freedom-based discourse; not just freedom from patriarchy, but also sexual freedom in a radically libertarian sense. More importantly, Periyar argued that freedom for women took priority over freedom from colonialism, and challenged patriarchal tendencies within Indian nationalism.

Scholars engaged with feminist politics have looked at the critical importance given to the women's question and gender in the Self-Respect Movement (SRM). In their readings on gender politics in India, Anandhi and Velayuthan (2010) highlight the ‘limitations in theory itself in dealing with diversities and subalternity’ and argue that in a scenario where gender intersects with caste and class, the theory and methods used ‘should generate knowledge from the margins’. While feminist scholars such as Uma Chakravarti (2018) and Sharmila Rege (2013) have discussed the intersections of caste and patriarchy, others who have studied the Periyarist politics of gender—Anandhi (1991), Geetha (1998), and Hodges (2005)—have meticulously captured what we very broadly call Self-Respect perspectives and made important contributions to the study of women’s politics of and from the margins of Tamil Nadu.

16.1 Introduction to Artificial Neural Network

Neural networks and deep learning are the buzzwords in modern-day computer science. And, if you think that these are the latest entrants in this field, you probably have a misconception. Neural networks have been around for quite some time, and they have only started picking up now, putting up a huge positive impact on computer science.

Artificial neural network (ANN) was invented in the 1960s and 1970s. It became a part of common tech talks, and people started thinking that this machine learning (ML) technique would solve all the complex problems that were challenging the researchers during that time. But sooner, the hopes and expectations died off over the next decade.

The decline could not be attributed to some loopholes in neural networks, but the major reason for the decline was the “technology” itself. The technology back then was not up to the right standard to facilitate neural networks as they needed a lot of data for training and huge computation resources for building the model. During that time, both data and computing power were scarce. Hence, the resulting neural network remained only on paper rather than taking centerstage of the machine to solve some real-world problems.

Later on, at the beginning of the 21st century, we saw a lot of improvements in storage techniques resulting in reduced cost per gigabyte of storage. Humanity witnessed a huge rise in big data due to the Internet boom and smartphones.

‘Periyar had hatred towards the Brahmins and preached violence against them.’ ‘Periyar favoured the powerful among the non-Brahmin castes.’ ‘Periyar sidelined the Dalits.’ These are the three main accusations against Periyar by his critics on the issue of caste. In an earlier paper (Manoharan, 2020), I have questioned the last two criticisms. In this chapter, I will address the first. Periyar was opposed to casteism in all its forms. In India, he identified the dominant form of casteism to be Brahminism, a ritual birth-based social hierarchy that derived legitimacy from scriptures, practices, traditions, and values associated with Hinduism and had material consequences. This led Periyar to be vehement in his criticism of the castes that were scripturally considered the highest, the Brahmins, and most sympathetic to the castes that were considered to be the lowest, the ‘untouchables’. He understood that caste had a secular–material dimension as well, which was interconnected to the ideological–ritual dimension.

Working in the historical context that he did in Tamil Nadu, Periyar's approach to caste identified three broad social categories—the Brahmins, the Dalits,1 and the ‘Shudras’. His primary target of criticism was the first, the Brahmins. This led to counter-accusations that he was unfairly targeting only one community for casteism. But as I have discussed earlier (Manoharan, 2022), he often challenged the non-Brahmins for internalizing casteism, for subscribing to notions of hierarchy over others, and for the lack of an egalitarian spirit.

learning Outcomes

After reading this chapter, the reader will be able to

• Understand the meaning of three processes of heat flow: conduction, convection, and radiation

• Know about thermal conductivity, diffusivity, and steady-state condition of a thermal conductor

• Derive Fourier's one-dimensional heat flow equation and solve it in the steady state

• Derive the mathematical expression for the temperature distribution in a lagged bar

• Derive the amount of heat flow in a cylindrical and a spherical thermal conductor

• Solve numerical problems and multiple choice questions on the process of conduction of heat

6.1 Introduction

Heat is the thermal energy transferred between different substances that are maintained at different temperatures. This energy is always transferred from the hotter object (which is maintained at a higher temperature) to the colder one (which is maintained at a lower temperature). Heat is the energy arising due to the movement of atoms and molecules that are continuously moving around, hitting each other and other objects. This motion is faster for the molecules with a largeramount of energy than the molecules with a smaller amount of energy that causes the former to have more heat. Transfer of heat continues until both objects attain the same temperature or the same speed. This transfer of heat depends upon the nature of the material property determined by a parameter known as thermal conductivity or coefficient of thermal conduction. This parameter helps us to understand the concept of transfer of thermal energy from a hotter to a colder body, to differentiate various objects in terms of the thermal property, and to determine the amount of heat conducted from the hotter to the colder region of an object. The transfer of thermal energy occurs in several situations:

• When there exists a difference in temperature between an object and its surroundings,

• When there exists a difference in temperature between two objects in contact with each other, and

• When there exists a temperature gradient within the same object.

Introduction

Statistical mechanics bridges the gaps between the laws of thermodynamics and the internal structure of the matter. Some examples are as follows:

• 1. Assembly of atoms in gaseous or liquid helium.

• 2. Assembly of water molecules in solid, liquid, or vapor state.

• 3. Assembly of free electrons in metal.

The behavior of all these abovementioned assemblies is totally different in different phases. Therefore, it is most significant to relate the macroscopic behavior of the system to its microscopic structure.

In this mechanics, most probable behavior of assembly are studied instead of individual particle interactions or behavior.

The behavior of assembly that is repeated a maximum time is known as most probable behavior.

hase Space

Six coordinates can fully characterize the state of any system:

• 1. Three for describing the position x, y, z and three for momentum Px, Py, Pz.

• 2. The combined position and momentum space (x, y, z, Px, Py, Pz) is called phase space.

• 3. The momentum space represents the energy of state,

For a system of N particles, there exists 3N position coordinates and 3N momentum coordinates. A single particle in phase space is known as a phase point, and the space occupied by it is known as µ-space.

olume Element ofµ-Space

4. Consider a particle having the position and momentum coordinates in the range.