Preventing climate change and ensuring sustainable development is one of the most talked about concepts in recent years. The issue of climate change and global warming is closely related to carbon dioxide (CO2) emissions. The rising level of CO2 in the environment is a major concern because of the resulting global warming and its associated adverse effects. In 2015 the United Nations executed the Paris Agreement. The agreement aims to limit the global temperature rise to 2°C, and to make best efforts to keep it to 1.5°C.

This objective has an important connection with energy and, particularly, electrical energy. The most common conventional method for producing electricity is by burning coal, which leads to CO2 emissions. Electricity produced from solar energy and wind energy is considered green electricity because it does not contribute to CO2 emissions. An important component of the CO2 emission reduction initiative of the UN, therefore, is the installation of green energy sources on a large scale throughout the world.

In line with this vision, the most important part of a carbon emission reduction plan worldwide is installation of these sources on a large scale. India, for example, has committed to having 50% of the total installed capacity by 2030 from green sources of electricity generation. This push towards a shift to solar, wind, and hydro-based energy sources is happening at a very fast rate. Under this changed scenario, these technologies are set to become the main technologies in the electric power network. In the Indian grid, for example, the share of solar energy has grown from about 2.6 GW in 2014 to more than 100 GW in 2025. This shift is set to change the fundamental way in which electricity has been generated, transmitted, and utilized.

In this chapter, I offer an account of the kind of freedom that alreadypertains to natural life. It begins by laying out how Hegel’s account of the freedom of life is related back to his critiques of Kant’s practical philosophy: his objections against the empty formalism of the moral law, the bad infinity of the ought, and the paradox of self-legislation. It reveals that all of these critiques are based on Hegel’s fundamental insight that self-determination has to be construed as a mode of living self-constitution. Hegel first develops this notion of self-constitution in his account of animal life, revealing both the freedom of natural life and why it still falls short of true spiritual freedom. Drawing on his Philosophy of Nature, the chapter reconstructs the ways in which animal life constitutes itself through the process of shape, the process of assimilation, and the genus-process. This reconstruction gives us a concrete understanding of self-constitution and reveals how self-determination can be a natural reality. At the same time, Hegel’s analysis of the inherent limitations of animal nature reveals the ways in which the freedom of spiritual self-constitution goes beyond animal self-constitution. The chapter argues that Hegel does not hold an additive view according to which our spiritual self-constitution is just tacked onto our animal self-constitution, but endorses a transformative view. It develops the way in which Hegel’s dialectical version of the transformative view is superior to contemporary Neo-Aristotelian varieties of the transformative view.

2.1 Groundwork and Motivation for the Definition

• To begin with, consider the following questions.

  (1) Are the intervals [0, 1] and [0, 5] the same?

  (2) Are the intervals [0, 1] and (0, 1) the same?

  (3) In the plane R2, is a circle the same as a square? Or is a circle of radius 1 the same as the circle of radius 2?

  (4) In R2, is the unit circle the same as the unit disk?

  (5) Is R the same as R2?

  (6) Is the interval (0, 1) the same as R?

  (7) Is the interval (0, 1) the same as the union of intervals (0,#½) ∪ ( #½ , 1)?

  (8) Is the interval [0, 1) the same as the unit circle in R2? Or is (0, 1) or [0, 1] the same as the unit circle in R2?

Of course, to answer this, we must first specify what we mean by the word “same”. Geometrically speaking, clearly, none of the pairs in each of the above questions are the same. For instance, in (1), geometrically the intervals [0, 1] and [0, 5] are of different lengths and as sets [0, 1] ⊆ [0, 5]. However, if we think of the interval [0, 1] as a rubber band of length 1, then we can stretch it from one end to transform it into the interval [0, 5]. Mathematically, we can do this by defining a function f : [0, 1] → [0, 5] by f(x) = 5x. Then we may identify the intervals [0, 1] and [0, 5]. Similarly, in (3), it may not be easy to come up with a function, but if we think of the circle made of a rubber or elastic rope, then we can reshape it into a square to call the circle and a square as “same”. Similarly, we can stretch the circle of radius 1 to form a circle of radius 2. On the other hand, in (7), the interval (0, 1) is a one-piece connected set, but the union (0, ,# ½) ∪ ( #½ , 1) is disconnected as it is missing the point 1 2 . So they do not seem to be the “same” from what we discussed above. In (8), it is difficult to say anything as the interval [0, 1) is a subset of R while the unit circle is in R2.

Medical imaging mostly deals with the visualization ofinternal organs, tissues, etc., using noninvasive orsemi-invasive methods. The primary motive is tounderstand any anomalies in the anatomies and theirfunctions. The signals are acquired inone-dimensional (1-D), two-dimensional (2-D),three-dimensional (3-D), or as videos, depending onthe purpose and mode of imaging. There are variousmodalities in medical imaging. The major modalitiesare as follows.

• • Projection X-ray (radiography)

• • X-ray computed tomography (CT scan)

• • Nuclear medicine images (emissiontomographies like, single photon emission computedtomography (SPECT) and positron emissiontomography (PET))

• • Magnetic resonance imaging (MRI)

• • Ultrasound

There are also several other modalities of medicalimaging. In this chapter, only the above mentionedtechniques are discussed.

14.1 | Projection X-ray imaging

The X-ray imaging technique was discovered by WilhelmConrad Rontgen (inaugural Nobel Prize, 1901) in 1895in Wurzburg, Germany. In its basic form, themechanism for generation of X-ray consists of avacuum tube with a cathode and an anodeappropriately placed as illustrated in Fig. 14.1(a). A beam of electron that emanates from thecathode hits the anode at a very high speed.Depending upon the material of the surface in theanode, there are sub-atomic interactions due to thestriking of sub-atomic particles, which releaseenergy in the form of electromagnetic waves of acertain wavelength band, called X-rays.

QUEUES FEATURE IN our daily lives like never before. From the checkout counter in the community grocery store to customer support over the phone, queues are theatres of great social and engineering drama. Entire business operations of many leading companies are geared towards providing hassle-free customer support and experience – timely and effective resolution of client queries about services on a regular basis. Alternatively, it could be effective traffic management and resource optimization for a multiplex cinema operator involved in ticket sales. Sometimes it may not involve humans at all, like in the case of a database query to a computer server for specific information that may be routed through a job queue. How a queue moves in time and how services are offered over epochs determine how businesses will be able to make profit or how efficiently computer servers will execute tasks. All these have a huge technological and economical impact. No wonder we have seen huge investments by concerned stakeholders to upgrade and upscale hardware and software infrastructure to re-engineer queues towards greater system efficiency and profitability. The mathematical technology of queues is crafted out of models that investigate and replicate stochastic behavior of engineering systems. This is the subject of our study in this chapter.

Definition 1.1 (Binary Operation) Let 𝐺 be a non-empty set. A binary operation on 𝐺 is a function that assigns each ordered pair of elements of 𝐺 an element of 𝐺.

Definition 1.2 (Group) Let 𝐺 be a set together with a binary operation (usually called multiplication) that assigns to each ordered pair (𝑎, 𝑏) of elements of 𝐺 an element in 𝐺 denoted by 𝑎𝑏. We say 𝐺 is a group under this operation if the following three properties are satisfied.

DIFFRACTION

Diffraction is a phenomenon in which a light beam bends around the corner of an obstacle and spreads into the geometric shadow of that obstacle.

FRESNEL AND FRAUNHOFER DIFFRACTION

Diffraction can be classified into two categories:

• 1. Fresnel diffraction

• 2. Fraunhofer diffraction

The distinction between these two categories is as follows:

• a. In Fresnel diffraction, the screen and source are at a finite distance from an obstacle. The distances are important in this class. In Fraunhofer diffraction, the source and screen are at an infinite distance from an obstacle. Therefore, inclination is important.

• b. The incident wavefront in Fresnel diffraction is either spherical or cylindrical, whereas the incident wavefront in Fraunhofer diffraction is planar.

• c. In Fresnel diffraction, the central point of the screen is either bright or dark depending on the number of zones, whereas in Fraunhofer diffraction, the central point of the screen is always bright.

FRAUNHOFER DIFFRACTION DUE TO SINGLE SLIT

Let us consider a monochromatic light source of wavelength ƛ placed at the focus of convex lens L1. The collimated rays of plane wavefront are incident on a single-slit AB of width “e.” The un-deviated rays from the slit reaches at point O, and the rays diffracted by an angle θ reach at P on the screen, as shown in Figure 12.1.

In graph theory, planar graphs introduce a fascinating area of study that intersects geometry, topology and network analysis. A graph is called planar if it can be drawn on a plane without any edges crossing each other. This property of planarity has significant implications in fields like circuit design, geographic mapping and urban planning where minimizing crossings leads to more efficient and visually accessible structures. In this chapter we will be covering important topics like the Euler’s formula which provides a basis for understanding the structural constraints of a planar graph. We will also be discussing Kuratowski’s and Wagner’s theorems that provide a criteria for non-planarity. As we will see later in Chapter 9, one of the intriguing mathematical characteristics of planar graphs is that their vertices can be colored by at most four colors.

What lurks behind appeals to “community” and a “democracy of the common” as models for the organization of political life is the desire for an existential authenticity that has overcome the contradictions and antagonisms that are part of normal political life under the conditions of democratic pluralism. Placing our hopes in community and the common as alternative, and somehow more authentic, models for the organization of political life always comes at the cost of preparing the ground for abandoning democracy altogether. Real democracy, counterintuitively, does not require community, but it involves distance among those who are represented, those who represent, and those who govern. We might experience this distance as alienating, or as inauthentic, but it allows for what we might call the self-control of self-government. In contrast to appeals to “community” and “the common,” the task of democracy is to negotiate the irreducible pluralism of political life through a normative organization that can be justified to, and is also justifiable by, all those who are subject to such norms.

The subject, Computer Vision, deals with the science ofimparting to a machine or a computer the capabilityof seeing and understanding the environment as wehumans are able to do, and seeks to apply itstheories and models in various applications of ourlife and society. From the late sixties of the lastcentury, there have been efforts in analyzingdigital images captured by a scanner or a camera.Initially, it was the 2-D digital geometry in adiscrete grid of integral coordinate space whichdrew primary attention of the researchers. Inparticular, Prof. Azriel Rosenfeld (1931–2004) ofthe University of Maryland, USA, took a leading andpioneering role in developing theories of digitalpicture processing. Subsequently, the area wasstrengthened by the development and application oftheories of mathematical morphology, textureprocessing, pattern recognition techniques, etc.However, the major development in the theory ofcomputer vision, following the psycho-physiologicalmodels of human vision, happened in the seventies ofthe last century, when Prof. David Marr (1945–1980)of the Massachusetts Institute of Technology (MIT),Cambridge, USA, hypothesized three stages ofprocessing and representation of images by primalsketches consisting of edges, regions, 2.5-Dsketches of the scene, and finally 3-D models.

Over the years, theories of computer vision have beendeveloped from different areas of mathematical andphysical sciences, such as digital geometry,projective geometry, differential geometry, linearand nonlinear systems, human cognition andpsycho-visual perception, color representation andprocessing, computational learning, patternrecognition, etc. As we see, the theoreticalfoundation of the subject has been built fromdifferent domains, and it requires to learn thefundamentals across these disciplines in asystematic and organized manner in the context ofcore agenda of computer vision, which is to solveproblems related to the understanding of a 3-Dscene, static or dynamic, given visual inputs fromimaging systems.

The ways in which human interaction was restructured during complexification in fifty-seven natural experiments from around the world, is characterized in twenty-one variables in the domains of interaction, demography, and political economy. Examination of the data in this way reveals an enormous range of variation among early complex societies on all counts.

In graph theory, independent sets represent collections of vertices that are pairwise nonadjacent, meaning no two vertices within an independent set share an edge. The study of independent sets is often linked to cliques (sets of mutually adjacent vertices) and covering numbers (the smallest set of vertices and edges that cover the entire graph) as they provide contrasting perspectives on how elements within a graph relate to each other.