This chapter focuses in on how individuals invest in or harm their health. This is done using the concept of the health production function. Various inputs to the function such as medical care, illness and injury, lifestyle choices, age, genetics, and environmental factors are discussed along with their interactions with each other. Key health economics concepts such as the flat of the curve, the tradeoff between health and utility, and the role of technological innovation in medical care effectiveness are discussed, as well as the key economic concept of the margin. The end of chapter supplement introduces the concept of standardized units for measuring effectiveness of care.

In this chapter we cover clustering and regression, looking at two traditional machine learning methods: k-means and linear regression. We briefly discuss how to implement these methods in a non-distributed manner first, to then carefully analyze the bottlenecks of these methods when manipulating big data. This enables us to design global-based solutions based on the DataFrame API of Spark. The key focus is on the principles for designing solutions effectively. Nevertheless, some of the challenges in this chapter are to investigate tools from Spark to speed up the processing even further. k-means is an example of an iterative algorithm, and how to exploit caching in Spark, and we analyze its implementation with both RDD and DataFrame APIs. For linear regression, we first implement the closed form, which involves numerous matrix multiplications and outer products, to simplify the processing in big data. Then, we look at gradient descent. These examples give us the opportunity to expand on the principles of designing a global solution, and also allow us to show how knowing the underlying platform, Spark in this case, well is essential to really maximize the performance.

Spark SQL is a module in Spark for structured data processing, which improves upon RDDs. The chapter explains how imposing structure on the data helps Spark perform further optimizations. We talk about the transition from RDDs to DataFrames and Datasets, including a brief description of the Catalyst and Tungsten projects. In Python, we don’t have Datasets, and we focus on DataFrames. With a learn-by-example approach, we see how to create DataFrames, inferring the schema automatically or manually, and operate with them. We show how these operations usually feel more natural for SQL developers, but we can interact with this API following an object-oriented programming style or SQL. Like we did with RDDs, we showcase various examples to demonstrate the functioning of different operations with DataFrames. Starting from standard transformations such as select or filter, we move to more peculiar operations like Column transformations and how to perform efficient aggregations using Spark functions. As advanced content, we include implementing user-defined functions for DataFrames, as well as an introduction to pandas-on-Spark, a powerful API for those programmers more used to pandas.

This chapter introduces the concept of insurance as a product and explores why people want to purchase insurance in general (and health insurance in particular). The main discussion centers around explaining that health insurance (and all insurance) is primarily financial protection: health insurance does not protect your health but instead protects your wealth from health-related risk. The chapter then moves on to discuss the operations of an insurance company: how premiums are set, the difference between correlated and uncorrelated risk, group insurance, and experience rating. The chapter ends by discussion moral hazard in the context of an individual with insurance coverage. The end of chapter supplement provides a mathematical example of why someone who is risk averse would want to purchase insurance.

This chapter takes the basics of demand developed in Chapter 3 and applies them to understanding how features of a health insurance plan influence individual decision-making in the market for medical care. The chapter unpacks how plan cost sharing characteristics (copayments, coinsurance, and indemnity), as well as pricing change and triggers (deductibles and payment limits) influence demand and individual consumption decisions.

This chapter discusses the healthcare workforce. The chapter begins by discussing how we think about how much labor is available at any given time. It then moves on to discuss inflows and outflows from the overall labor force with deeper discussions of education and training as well as of locational choice of workers. Next, the role of licensure is explored. Finally, the chapter covers labor markets, how they adjust to changes in demand, and the role of market concentration of employers. The end of chapter supplement shows how to calculate the Herfindahl–Hirschman Index, a commonly used measure of market concentration.

Quantum mechanics originally developed for describing non-relativistic systems. It was a natural question to ask how the formalism can be extended to relativistic systems. Besides, it turned out that some of the properties of nonrelativistic systems can be understood naturally in the light of the relativistic theory. One example is the spin of the electron, which has to be introduced in an ad-hoc manner in non-relativistic theory, but appears naturally in the relativistic theory, as we will explain in this chapter. The aim of this chapter is to indicate, rather than elaborate, the kind of questions that can be asked and answered using hints of relativity. A full-edged relativistic theory takes us beyond quantum mechanics, as we argue in §15.1. We also clarify that when we talk of relativity, we only mean the special theory. The general theory of relativity is not discussed at all.

Conict between relativity and quantum mechanics

The special theory of relativity can be interpreted as a theory of the geometry of the 4D space-time, composed of the three spatial dimensions and time. Thus, time and space are treated on equal footing in special relativity.

This is what causes a conict with quantum mechanics. We have used time as a parameter with respect to which we study the evolution of systems. On the other hand, the spatial coordinates indicating the position are treated as operators, acting on the vector space of state vectors. There is no way that one can make a truly relativistic quantum theory if one maintains this status for time and space.

There are two ways out of the impasse. First, we might contemplate making time an operator as well, just as the position coordinates are. In §3.8, we have argued that this cannot be done. The second alternative is to make the spatial coordinates parameters, just like time is. In this case, one needs to study the evolution of objects in space and time, and the objects to be studied should therefore be some kind of functions of position and time. In physics, a function of space and time is called a field. Examples are electromagnetic and gravitation fields, which can depend on both position and time. In order to do relativistic quantum mechanics, i.e., do quantum mechanics in a way that is compatible with the special theory of relativity, one must therefore do some kind of field theory.

Classical mechanics is governed by Newton's laws of motion. It has been very successful, for over three centuries, in explaining motions of objects that we see around us. However, around the beginning of the twentieth century, when it came to understanding the properties of small systems like an atom, classical mechanics seemed inadequate. In this chapter, we will review the basic formulas of classical mechanics and indicate why it could not describe small systems.

Classical mechanics

Classical mechanics seeks a description of the motion of a particle, by specifying the path of motion of the particle, i.e., the position and velocity of the particle at any given instant. In the Newtonian formulation, this is done by invoking the idea of forces, and using Newton's second law of motion, which says that the rate of change of momentum of a particle is equal to the force that acts on the particle:

If we know the forces as a function of time, we can in principle solve this equation. It is a second-order differential equation in time, so we will need two initial conditions to solve the position vector r as a function of time. In particular, if we know the position r and velocity c = dr/dt at an initial instant, we can solve for the position and velocity of the particle at any instant, given the knowledge of the force F.

There are alternative ways of formulating classical mechanics. One of these is the Lagrangian formulation. In this formulation, one defines a function L of coordinates and velocities of all particles in the system, called the Lagrangian. The equation of motion is then given by

where the xa's denote different independent coordinates and ẋa's their time derivatives, i.e., the corresponding velocities.

Delta function

In earlier chapters, we have analyzed the quantum behavior of particles in many different kinds of Hamiltonian. Some of these Hamiltonians are quite contrived and used for exemplary purposes only. Some are realistic cases, like the case of the hydrogen atom in Chapter 9. In this chapter, we continue discussing realistic interactions, viz., interactions of particles with magnetic fields.

The Hamiltonian

Classical electrodynamics is described by Maxwell equations, which connect the derivatives of the electric field E and magnetic field B to the sources of the electromagnetic field, the charge density ρ and the current density J. All the quantities mentioned are in general functions of position and time. The behavior of a particle of charge q in such a field is described by the Lorentz force law. In the SI units, this force is given by

If we want to solve the classical problem of the path of a particle in an electromagnetic field, we can just set up Newton's equation of motion with the force shown above.

Clearly, this method does not help us solve the corresponding quantum mechanical problem, because the concept of force is not used in the formulation of quantum mechanics. We need to set up the Hamiltonian of the particle in an electromagnetic field. This cannot be done by using the field strength vectors E and B. Instead, we need to use the potentials A and ϕ, which are related to the fields by the relations

With these potentials, there is a very simple prescription for finding the Hamiltonian of a charged particle in an electromagnetic field.

As we have seen throughout this book, material deposition and material removal are critical steps in integrated circuit (IC) fabrication. A wide variety of materials, insulators, semiconductors and conductors must be deposited at various stages in chip manufacturing. Usually, these materials are deposited in blanket form covering the entire wafer surface, although there are some deposition methods which are selective and deposit materials only in specific locations on the wafer surface. We will discuss deposition methods in detail in Chapter 10. Selective removal of material is usually accomplished using a lithography-defined mask followed by etching. We will discuss a variety of etching methods in this chapter.

Material removal can also be accomplished using chemical–mechanical polishing (CMP). This process is usually not selective but uses a combination of chemical etching and mechanical polishing to remove materials. The original motivation for developing CMP was to planarize wafer surfaces in back-end structures, since the polishing produces a flat surface.