[CR has previously published a review of this book (see Review CR139890). The author of the book has written a rebuttal to the review. A re-rebuttal by the reviewer follows the rebuttal.]

There are major errors of fact in the review.

The reviewer states, “There is not a single pseudocode fragment in the book.” This is false. See (for example) pages 101, 177, and 317.

The reviewer states, “There is also no attempt to prove the correctness, or analyze the performance, of any of the algorithms presented.” This statement is false. See chapter 12, page 92 (a section entitled “Complexity Analysis”); pages 151-152; page 386; or most of chapters 36, 37, and 38. There is an entry in the index entitled “Complexity analysis.” Chapter 5 is a detailed proof of correctness. Chapter 50 contains rigorous and formal proofs of complexity. Or, see pages 3, 24, and 44. These are just some examples.

The reviewer says there are no proofs of correctness in my book. This is false. There are mathematical theorems about correctness: for example, Proposition 18.2 (page 164), Proposition 18.3 (page 171), Laman’s theorem (page 201), and the graph cut theorems (pages 317 and 320). Most of chapter 50 is a detailed proof of correctness. Sometimes, a theorem is stated or summarized and, instead of detailed proofs, a reference is given providing the proof. In other cases, I give detailed proofs.

There are other books on computational structural biology, but only mine foregrounds provable algorithms that have proofs of complexity and correctness. No one wanting theorems can be disappointed by chapters 15-18, 36, 37, 38, and 50, which contain many rigorous lemmata. Dozens more proofs are provided in the bibliography to these chapters, and those theorems are discussed when they are cited.

These false claims could mislead readers.

Let us turn from fact to style and opinion. While my book foregrounds provable algorithms that can be characterized in terms of completeness, correctness, and computational complexity, some heuristic algorithms are also discussed. Since these heuristic algorithms often are based on stochastic Monte Carlo or simulated annealing schemes, they do not have a well-defined complexity, nor proofs of correctness. However, this issue is discussed extensively in the book. For example, see pages 372, 111, and 241. Indeed, a tension in the field is that, historically, most protocols relied on unprovable stochastic methods, manual modeling, and graphical user interface (GUI)-based interactive iterative fitting. But now rigorous and provable techniques are emerging, and they are highlighted in my book. These issues are extensively discussed in the pages given as examples above.

In criticizing (erroneously) the lack of pseudocode, Rao states, “The algorithms are suggested in plain English and mathematical expressions only.” I claim: sometimes English is more compact than pseudocode. For example, consider the following steps of the Z-module matrix diagonalization algorithm (page 406, explaining Theorem 50.7):

1. Add an integer multiple of row i to row j.

2. Interchange rows i and j.

3. Multiply row i by a unit (in our case, +/- 1).

Surely this is just as rigorous as any pseudocode.

Finally, Rao claims the book “presumes knowledge of certain mathematical areas such as tensor calculus, which many computer scientists may not have studied.” The truth is more nuanced. Tensors are used in the book. But, in the book, they can be understood simply as matrices that can be post-multiplied or pre-multiplied by other mathematical objects such as vectors. Since some readers may be unfamiliar with tensors, the necessary basics are taught in the first few chapters. In particular, I point out that the famous singular value decomposition (SVD) algorithm captures most of what the reader needs to know about tensors. I chose to embrace, not avoid, the word “tensor” because it is used in biophysics, and computer scientists need to know what these matrices are called by physical chemists.