History of Our Collaboration

We met for the first time when Paul, a neuroscientist and biomedical engineer, was a new assistant professor seeking his first NIH R01 grant and trying to get his first sole-author manuscript published. First submissions of both failed, and the critiques focused on unclear writing. Paul contacted a local university, looking for help with scientific writing, and he was directed to Sandra, a discourse linguist with expertise in technical writing and scientific English. After a 2-month, intensive one-on-one training program, he resubmitted both documents. The grant was funded and the manuscript was accepted. Since then, Paul and Sandra have maintained a close relationship, both professionally and as friends. They began a study of narratives to grant proposals that continues to this day.

Fifteen years later, when Paul became the head of his research institute, he hired Sandra as a full-time scientific writer and editor. In 3 years, 21 of the 22 faculty members had at least one NIH R01, and the institute became the second best-funded department in the university.

Sandra and Paul decided to put what they had learned from studying narratives and helping investigators write and revise narratives into book form in order to share this experience with other researchers. This book is the result of that effort.

A scientific grant proposal is a request for funds to conduct original research in a discipline or a subject area typically associated with science, technology, or medicine. A principal investigator (PI) is the researcher who is responsible for the content of a scientific grant proposal and for submitting it to a funding agency on time, and who will be responsible for directing, developing, and executing the research on time. The PI is usually the person writing most of the narrative, if not the entire scientific grant proposal. The narrative comprises the major prose sections of the scientific grant proposal, including the abstract.

There may also be co-investigators (Co-Is) who help the PI design and develop the proposed research and write the narrative, and who will help the PI execute the research. Sometimes there are collaborators who will perform a significant part of the research and are, to a certain degree, responsible for designing their limited portion of the proposed research, subject to the PI’s approval. Finally, there may be contractors hired to perform a relatively small portion of the research, but who have not helped in designing or developing the research project.

There are many very good resources on the market dealing with strategies and other information to select funding mechanisms from public and private agencies that support scientific, technical, and medical research. However, there are far fewer resources dealing with how to write the narrative of the scientific grant proposal that describes and argues for the proposed research.

The Aims Section is the first major prose section in the narrative of a scientific grant proposal. Some funding agencies call this first section the Introduction. The Aims Section provides the conceptual framework for the proposed research in the sense that it introduces the proposed research topic or research area, the significance and novelty of the proposed research, the purpose of the proposed research, the proposed methodological approach, and the proposed aims. What is called the aims in this book is variously called objectives or specific aims by different funding agencies.

Figure 2-1 shows the basic layout of the Aims Section. Figure 2-2 shows the relationship among the long-term goal, the research objective, and the aims in the Aims Section. Cases 2-1 and 2-2 show Aims Sections from the narratives of scientific grant proposals addressing basic research; Case 2.3, applied research; and Case 2.4, clinical research.

Overview of length, content, organization, and layout

The Aims Section ranges from one-half page to 2 or 3 pages, depending on submission requirements and on the overall length of the narrative. Different funding agencies have different requirements for the Aims Section. In most cases, NIH requires that its first section of the narrative, which it terms the Specific Aims Section, not be longer than one page.

Chapter 6 continues the description of the Methods Section begun in Chapter 5 and focuses on:

1. Data-collection procedures

2. Data-analysis procedures

3. Data interpretation and expected outcomes

4. Potential problems and proposed solutions

5. Shared methods

6. Ending

In Chapter 5, Figure 5-1 gives the generic content and organization of a Methods Section. For convenience, this figure is reproduced and renumbered in Chapter 6 as Figure 6-1. Also for convenience, Case 5-9, showing a heading outline of a Methods Section, is also reproduced in this chapter as Case 6-1. Chapter 6 gives generic heading outlines in Tables 6-1 and 6-2. The term subsection will continue to be used in Chapter 6 to refer to a Methods subsection or sub-subsection, unless phrased otherwise for clarity.

Data-collection and data-analysis subsections and procedures

Proposed procedures are the actions and tasks that you intend to execute in order to acquire data that you will then analyze, interpret, and ultimately disseminate in professional journals and at professional meetings.

In the narrative, the specific actions that you and members of your research team intend to perform in order to achieve your proposed research objective and aims are variously termed procedures, protocols, tasks, methods, experiments, and methodological activities. These terms are not synonymous even though they are often used synonymously.

This chapter addresses technical issues with sentences that PIs typically encounter when drafting the narrative of a grant proposal. These issues involve citations, definitions, active grammar and passive grammar, and guidelines for shortening the text while keeping content changes to a minimum.

Citations

A citation is a reference that identifies the source of information, whether that source is from a journal, a book, the internet, a committee, or a person. Citations are important in academic documents in general, and they are particularly important in narratives to scientific grant proposals. Citations can enhance your credibility by demonstrating to reviewers the quality, breadth, and depth of your understanding of published research that relates to your research topic.

Some writers include citations while drafting the narrative, others begin including citations when they are close to the final draft, and others are somewhere in between: early in the drafting process, they fill in citations that they readily know and leave the others to later stages of drafting. If you do not include citations in early drafts of your grant proposal, you should at least include placeholders for them. Citation placeholders are symbols, such as XX, that do not ordinarily show up in a search of text and that you insert into the text while drafting to remind you where you need citations.

Abstracts

An abstract is a section separate from the narrative of a grant proposal. The abstract summarizes the most important information from each major section of the narrative. The abstract typically precedes the narrative and is often made available to the public separately from the narrative. Reviewers will likely read the abstract before the narrative, so it plays an important role in helping them form favorable impressions about you and your credibility, and in attracting their interest about your research topic and its significance and novelty.

Different funding agencies name the abstract differently. For example, NIH refers to its abstract as the Project Summary. The Michael J. Fox Foundation refers to the abstract as the Grant Abstract, and the Society of Family Planning calls it a Project Abstract. NSF refers to a similar section as the Project Summary but cautions that the NSF Project Summary “should not be an abstract.” However, as discussed in Chapter 7.1.2, for all practical purposes the NSF Project Summary is an abstract. The Robert Wood Johnson Foundation also calls its abstract a Project Summary. Regardless what a funding agency calls its summary to the narrative, in this book it is called an abstract.

Most grant applications fail because of problems in the Methods Section. You need to provide enough detailed, accurate, and clear methods information for reviewers:

• To understand your proposed research design and methods.

• To understand why you decided on particular features of your proposed research design and methods.

• To conclude that your proposed research design and methods will result in valid findings.

• To conclude that your proposed research design and methods are appropriate for you to achieve your proposed research objective and aims.

• To conclude that your proposed research design represents sound scientific methodology.

• To conclude that you, personally or through members of your research team, can successfully execute all of your proposed methods.

• To visualize your executing the proposed methods in a logical order.

• To view your credibility favorably.

In addition, you need to provide enough detailed, clear, and accurate information so that researchers – with your same or closely similar training and background – can (at least in theory) replicate your methods and come up with essentially the same data, results, and statistical analyses that you are proposing to achieve.

Chapter 5 covers basic organizational alternatives for the Methods Section and information to include when you are: (a) presenting your proposed research design and methods, (b) describing your SOS (subjects, objects of study, and specimens), and (c) describing your MET (materials, equipment, and tools). Chapter 6 focuses on how to draft procedures for collecting data and analyzing the data; and how to explain your potential methodological problems and proposed solutions. Chapter 6 includes guidelines on how to organize the Methods Section when some of the methodological features are the same or similar across aims or experiments – that is, when some of the methodological features are shared across the proposed aims or experiments. Chapter 6 also discusses the ending to the narrative.

As mentioned in Chapter 3.5, background research presents 4 types of information: (1) common knowledge; (2) other investigators’ previous research that is relevant to your proposed research and proposed methods; (3) your previous research that is relevant to your proposed research and to the research skills needed in the execution of your proposed methods. Chapter 3 described the Background Section as it relates to the first 2 types of information. This chapter focuses on the third type, your previous research and your research skills, that is presented in a Preliminary Studies/Progress Report Section or as part of a Background Section.

In the Preliminary Studies/Progress Report Section, your credibility comes sharply into focus. Reviewers look to this section to evaluate your preparedness (e.g., your training, competence, and experience) to perform your proposed methods; to assess the likelihood of your successfully achieving your proposed research objective and within the funding period; and to assess the relationship between your preliminary research and your proposed aims.

The Preliminary Studies Section is sometimes termed the Progress Report Section when describing your previous research that was funded by a funding agency, the same funding agency from which you are seeking additional funds in order to continue the line of research.

This chapter deals with approximation methods, mainly through the use of series. After a short discussion of approximation of known functions, we focus on approximately solving equations for unknown functions. One might wonder why anyone should bother with an approximate solution in favor of an exact solution. There are many justifications. Often physical systems are described by complicated equations with detailed exact solutions; the details of the solution may in fact obscure easy interpretation of results, rendering the solution to be of small aid in discerning trends or identifying the most important causal agents. A carefully crafted approximate solution will often yield a result that exposes the important driving physics and filters away extraneous features of the solution. Colloquially, one hopes for an approximate solution that segregates the so-called signal from the noise. This can aid the engineer greatly in building or reinforcing intuition and sometimes lead to a more efficient design and control strategy. In other cases, including those with practical importance, exact solutions are not available. In such cases, engineers often resort to numerically based approximation methods. Indeed, these methods have been established as an essential design tool; however, short of exhaustive parametric studies, it can be difficult to induce significant general insight from numerics alone. Numerical approximation is a broad topic and is not is studied here in any real detail; instead, we focus on analysis-based approximation methods. They do not work for all problems, but in those cases where they do, they are potent aids to the engineer as a predictive tool for design.

Often, though not always, approximation methods rely on some form of linearization to capture the behavior of some local nonlinearity. Such methods are useful in solving algebraic, differential, and integral equations. We begin with a consideration of Taylor series and the closely related Padé approximant. The class of methods we next consider, power series, employed already in Section 4.4 for solutions of ordinary differential equations, is formally exact in that an infinite number of terms can be obtained. Moreover, many such series can be shown to have absolute and uniform convergence properties as well as analytical estimates of errors incurred by truncation at a finite number of terms.

Linear algebra is part of the foundation of mathematics and has widespread usage in engineering. In this chapter, we specialize the linear analysis of Chapter 6 to finite-dimensional vector spaces in which the linear operator is a constant matrix. Many of the topics will be familiar, and some will likely be new. Considerable effort is spent defining terms and finding the best solution to systems of linear algebraic equations. As nearly all computational methods for solution of equations modeling physical systems rely on linear algebra, our expansive treatment is justified. Throughout the chapter, geometric interpretations are applied when appropriate. Some topics introduced in previous chapters are more fully explored, including matrices that effect rotation and reflection, projection matrices, eigenvalues and eigenvectors, and quadratic forms. New topics include a variety of matrix decompositions that are widely used in computational linear algebra. Of these the most important is the so-called singular value decomposition (SVD). We also give a matrix interpretation of two methods in wide use in engineering: (1) the least squares method and (2) the discrete Fourier transform. We close with a general strategy to find the best solution to linear algebra systems based on the SVD. In contrast to Chapter 6, we return in this chapter to Gibbs notation for vectors and matrices. Thus, matrices will be represented by uppercase bold-faced letters, such as A, and vectors by lowercase bold-faced letters, such as x.

Paradigm Problem

One of the most important problems in linear algebra lies in addressing the equation

A · x = b, (7.1)

where A is a known constant matrix, b is a known column vector, and x is an unknown column vector. We note the analog to linear differential equations with the general form of Eq. (4.1), Ly = f(x). Here the matrix A plays the role of the differential operator L, the vector x plays the rule of the function y, and the vector b plays the role of the forcing function f(x).