[I] Q. Mucius augur multa narrare de C. Laelio socero suo memoriter et iucunde solebat, nec dubitare illum in omni sermone appellare sapientem. ego autem a patre ita eram deductus ad Scaeuolam sumpta uirili toga ut quoad possem et liceret a senis latere numquam discederem. itaque multa ab eo prudenter disputata, multa etiam breuiter et commode dicta memoriae mandabam fierique studebam eius prudentia doctior.

Whatever their private religious convictions, nearly all contemporary psychologists of religion – when they act in professional roles – agree to operate in accordance with scientific rules. Recognition of the imperfections of individual methodologies has led to an emphasis on testing theories and verifying “facts” in multiple studies. Most of this chapter explores the pros and cons associated with various research methods, including experimentation, observation, and survey research. Although the logic of experimentation is undeniable and psychologists in various subfields frequently deem it the method of choice, many questions that we most want to answer in the psychology of religion cannot be addressed through experiments that are feasible, ethical, and convincing. Thus, the psychology of religion has always relied heavily on quantitative and qualitative survey research studies. Good surveys must strive to avoid biases rooted in question wording, question order, mode of data collection, social desirability, attitude-behavior discrepancies, and the tendency to overreport religious behavior. Fortunately, many existing measures of religious attitudes and behaviors have good psychometric qualities.

This chapter argues that many psychologists of religion have sought insights from the neighboring discipline of sociology. Generally speaking, sociologists focus more on social groups, social patterns, social institutions, sociohistorical context, and social structures. Sociologists also have emphasized various social justice perspectives, including those based on race, gender, age, and LGBT issues. The chapter tells in some detail how several of the founders of sociology – Auguste Comte, Karl Marx, Emile Durkheim, and Max Weber – thought about religion. Next, we delve into the influential theory of religion developed by sociologist Peter Berger who sees the main project of a society as the creation of a stable, predictable order that people believe in as objective reality. This, for Berger, matters greatly because we need a shield against the terror of anomie. After discussing Berger, we move on to the market theory of religion. We see how various thinkers – starting with the great economist Adam Smith – have applied fundamental principles of economics to the analysis of religious organizations.

The governing equations for the atmosphere belong to partial differential equations (PDEs). For PDEs, the behavior of the solution, proper initial and/or boundary conditions, and the numerical methods to find the equation solutions depend essentially on the type of PDEs. We focus on three prototypes of PDEs that are representative of describing atmospheric motion: studying the numerical discretization that allows the numerical integrations of these equations on a computer. We then cover some topics unique for numerical weather prediction (NWP), including setting the proper lateral boundary conditions for regional models, non-hydrostatic models, and the need to replace the spectral global models. Many promising NWP model emulators based on machine learning and artificial intelligence have popped up in recent years. We suggest some approaches to validate those NWP model emulators.

Some psychologists have argued that religion can be a prominent source of emotional disturbance and mental illness, while others – especially in recent years – have promoted faith and/or spirituality as a source of physical and mental strength. To make sense of an ocean of scientific research, researchers have frequently used meta-analysis, a technique that has both strengths and weaknesses. This chapter carefully summarizes research on the relationship between religion and specific aspects of physical and mental health. Much debate surrounds the interpretation of a largely correlational research literature, especially with regard to mental health. Although many reviewers have suggested that religiosity, spirituality, and involvement in religious organizations confer clear health benefits, numerous methodological concerns remain unresolved. One key matter is that research needs to pay more attention to potentially vital differences based on denomination and cultural context. Still, psychologists of religion have clarified the specific social and psychological pathways through which religion can lead to better physical and mental health, and some of this work has implications for both religious and non-religious orientations.

In practice, sometimes an estimate of the carrier phase for coherent signal reception is not possible with sufficient accuracy or carrier phase synchronization is not possible at all, in particular, in situations of very fast varying channel conditions (e.g., Doppler effect due to fast-moving transmitters or receivers). For such scenarios, digital transmission schemes have to be applied which are robust to non-perfect carrier frequency and carrier phase estimation. To that end we consider differential PSK which can tolerate phase errors and, to some amount, frequency errors. Then, schemes, which does not require phase (and frequency) synchronization at all, so-called non-coherent demodulation schemes, are developed and analyzed in detail.

A general view on digital modulation schemes beyond the concept of PAM is developed. This is required as many important modulation formats (e.g., digital frequency modulation) do not fall under the umbrella of PAM. To that end, the separation between the operations of coding and modulation is unambiguously defined. The key tool for the analysis and synthesis of transmission schemes is the representation of signals in a signal space. The concept is introduced and discussed in detail. Based on this view, methods for optimum coherent and non-coherent signal reception for any kind of general digital modulation scheme are derived. The principles of maximum-likelihood detection and maximum-likelihood sequence detection are discussed.

The preface falls into two parts. In the first (1–3), C. establishes his source for the dialogue he is about to recount: he claims to have heard it in 88 bce from his mentor Q. Mucius Scaevola Augur, who recounted to a group of friends a conversation on the topic of friendship that he and C. Fannius had with their father-in-law C. Laelius Sapiens in 129. Just as Scaevola had allegedly retained Laelius’ words, so too C. claims to report Scaevola’s account from memory. In the second part (4–5), the author turns to the work’s dedicatee, his friend Atticus, and explains his rationale in setting up the dialogue the way he has, with a venerable speaker from an earlier generation discoursing on a topic with expertise and authority. Thus, just as in C.’s earlier De senectute the old man Cato discusses old age, in Amic. Laelius – renowned for his friendship with the younger Scipio – talks about friendship. And just as C. had dedicated De senectute to Atticus as an old man to an old man, he now writes for the same dedicatee as one friend to another, encouraging him to immerse himself fully in the fiction of the dialogue and hear “Laelius” speak.

Lorenz discovered that the atmosphere, like any dynamical system with instabilities, has a finite limit of predictability. In this chapter, we briefly review the fundamental concepts of chaotic systems, from which we introduce the concepts of global and local Lyapunov vectors. We then discuss singular and bred vectors, two concepts closely related to Lyapunov vectors. To represent the uncertainties associated with each deterministic forecasting, ensemble forecasting methods are developed. We review early studies of ensemble forecasting and operational ensemble forecasting methods. The growth rate of errors and predictability of the atmosphere in different regions are discussed. We then discuss the role of different earth components in predictability for different time-scale phenomena, highlighting the dominant role of humans in the coupled Earth-Human system. We also give an outlook on the potential application of data assimilation to the coupled Earth-Human systems. While the chaotic nature of the atmosphere reveals the intrinsic difficulty of making accurate long-range predictions, it also indicates the possibility of deploying an initial small control that can grow large enough to alternate the future flow trajectory. Under this context, we introduce the Control Simulation Experiment (CSE), where we insert small perturbations into a chaotic system to let it evolve as we expect, essentially "controlling" the weather.