Most Popular Posts of 2015

WordPress provides detailed statistics on views of posts. These are the five most-viewed posts published on thus blog in 2015.

  1. The Rise of Mixed Precision Arithmetic (October).
  2. Programming Languages: An Applied Mathematics View (September).
  3. The Princeton Companion to Applied Mathematics (July).
  4. Top Tips for New LaTeX Users (September).
  5. Numerical Methods That (Usually) Work (May).

WordPress has also prepared a 2015 annual report for this blog, which can be found here.

Publication Peculiarities: Author Lists

Continuing my series of posts on publication peculiarities, I turn to author lists with interesting features.

Repeated Surnames

We are looking for authors who share the same surnames and preferably are not related. It would be hard to beat

Allen Goodman, Joshua Goodman, Lucas Goodman and Sarena Goodman, A Few Goodmen: Surname-Sharing Economist Coauthors, Economic Inquiry, 2014.

These four economists got together to write their paper about surname-sharing economist co-authors with the ulterior motive of beating the previous record of three.

A weaker requirement is surnames beginning with the same letter, for which we offer

Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations, SIAM J. Matrix Anal. Appl. 28 (4), 1029-1051, 2006

Repeated Forenames

Since Nick Trefethen does not go by his first name, I claim that the following example is valid for three Nicks:

Nicholas Hale, Nicholas John Higham and Lloyd Nicholas Trefethen, Computing A^\alpha, \log(A), and Related Matrix Functions by Contour Integrals, SIAM J. Numer. Anal. 46, 2505-2523, 2008.

Reversed Names

Ideally I would like a pair of authors for which the first name of each is the last name of the other. The closest I’ve found is:

Philippe Chartier and Bernard Philippe, A Parallel Shooting Technique for Solving Dissipative ODE’s, Computing 51, 209-236, 1993.

Names Beginning with Consecutive Letters

Here is a run of four surnames beginning with consecutive letters:

D. Bremner, T. M. Chan, E. D. Demaine, J. Erickson, F. Hurtado, J. Iacono, S. Langerman, and P. Taslakian. Necklaces, convolutions, and X + Y. In Y. Azar and T. Erlebach, editors, Algorithms–ESA 2006, volume 4168 of Lecture Notes in Computer Science, pages 160–171. Springer-Verlag, Berlin, 2006.

The next paper goes even better by starting at “A”:

J. I. Aliaga, J. M. Badía, M. Castillo, D. Davidovic, Rafael Mayo and Enrique S. Quintana-Ortí, Out-Of-Core Macromolecular Simulations on Multithreaded Architectures, Concurrency and Computation: Practice and Experience, 2014.

A famous example, for the Greek alphabet, is

R. A. Alpher, H. Bethe and G. Gamow, The Origin of Chemical Elements, Physical Review 73, 803-804, 1948

According to Freeman Dyson, “Bethe had nothing to do with the writing of the paper but allowed his name to be put on it to fill the gap between Alpher and Gamow.”

Names Far Apart

In contrast to the previous section, here we are looking for names that are spaced as far apart in the alphabet as possible. For two authors this is the most extreme case:

H. Ashley and G. Zartarian, Piston Theory—A New Aerodynamic Tool for the Aeroelastician, Journal of the Aeronautical Sciences 23, 1109-1118, 1956.

Cyclic Repetition

Can we find an author list in which the surnames repeat cyclically? I offer

A. S. Lin, C. H. Chen, H. G. Hwu, H. N. Lin and J. A. Chen, Psychopathological Dimensions in Schizophrenia: a Correlational Approach To Items of the SANS and SAPS. Psychiatry Research 77, 121-130, 1998.

Titles that Look Like the Authors

If you’re going to write about the programming language R, it helps if your first name begins with “R”:

R. Ihaka and R. Gentleman, R: A Language for Data Analysis and Graphics, Journal of Computational and Graphical Statistics 5, 299-314, 1996

However, it would be hard to beat the next paper, whose author (Walter Russell Brain) not only got his name into the title, but also published the paper in a journal of the same name: a triple whammy!

Lord Brain, Some Reflections on Brain and Mind, Brain 86, 381-402, 1963


Finally, we have a long author list with the first and last surnames the same:

Ling Zhang, Zhongshan Li, Ting-Zhu Huang, Qing-Fang Zhu, Jian Hua and Lihua Zhang, Periodic, Reducible, Powerful Ray Pattern Matrices, Linear Algebra Appl. 444, 81-88, 2014.

Punctuating Lists

Image courtesy of Stuart Miles at

Lists are common in all forms of writing. The list items can be included within the text or put on separate lines. Separate lines are used in order to draw attention to the items, to ease reading when the items are long or numerous, or to facilitate cross-reference to specific items.

The two main types of lists are enumerated lists, in which the items are numbered or labelled alphabetically, and itemized lists, in which each entry is preceded by a marker such as a bullet symbol. In \LaTeX these are produced by the enumerate and itemize environments, respectively. (The basic enumerate environment allows only numbers as labels, but the enumerate package extends the environment to allow letters, too.)

I have long felt unsure about how to punctuate lists, and especially the sentence that introduces the list. Advice is hard to find in books on English usage and there seems to be no agreed way to do it. Some recent reading, namely of the TUGboat article Makings Lists: A Journey Into Unknown Grammar by James. R. Hunt and the book Making a Point: The Pernickity Story of English Punctuation by David Crystal, has clarified my thinking. I will now explain how I intend to format lists in future.

My approach is based on a key principle, which stems from the fact that in English all sentences must be complete, and not mere fragments. (There is no universally agreed definition of what distinguishes a sentence from a fragment, but a sentence is usually required to contain a verb.) The principle is that

if the labels in a list are removed then what remains should make one or more complete and correctly punctuated sentences.

Here are three examples that are correctly formatted according to this principle.

Example 1. Programming languages from three decades will be compared:

  • C++ (1985),
  • Python (1991), and
  • Julia (2012).

This type of list could readily be collapsed inline into a regular sentence: “Programming languages from three decades will be compared: C++ (1985), Python (1991), and Julia (2012).” The author must judge whether the list form, with its clearer separation of the items, is preferable. Note the “and” after the second item. This is needed, though I think many people would find the example acceptable without it.

Example 2. We used three different algorithms in the experiments. The table reports the performance of

  • Algorithm 3.1 (based on a Taylor series),
  • Algorithm 3.2 (with parameter k = 1), and
  • Algorithm 3.3 (with tolerance 10^{-8}).

The sentence that precedes the list does not end with a colon. If it did, then the principle would be violated.

Example 3. Before printing the paper carry out the following steps.

  1. Run the paper through \LaTeX.
  2. Run the paper through BibTeX.
  3. Repeat steps 1 and 2 until no warnings occur about unresolved references.

In this example each list element is a complete sentence. The numbering of the elements is appropriate because they have a definite order. In some other list in which the ordering is arbitrary one might nevertheless decide to number the elements in order to be able to refer to the elements later on.

The next example does not conform to the principle.

Example 4. We will use three test matrices.

  • rosser: a classic symmetric matrix with close and repeated eigenvalues,
  • hilb: the Hilbert matrix, and
  • pascal: a matrix with elements taken from Pascal’s triangle.

If we remove the list markers then the list items turn into a sentence fragment containing no verb. I suspect few people would object to the formatting of this example. But we can easily modify it to conform.

Example 4 (modified). We will use three test matrices:

  • rosser, a classic symmetric matrix with close and repeated eigenvalues;
  • hilb, the Hilbert matrix; and
  • pascal, a matrix with elements taken from Pascal’s triangle.

Note the use of the semicolons to separate the items, which now contain commas. I much prefer the modified example, although in the past I might have been happy with the original.

Of course, style guidelines for individual publications may override what I have said above. However, my experience is that academic publishers tend not to change authors’ lists unless they are clearly grammatically incorrect. For example the SIAM Style Manual advises copy editors “Retain the author’s list style as long as it’s consistent”.

Finally, I note that the The Princeton Companion to Applied Mathematics follows the principle recommended here, though that is purely a coincidence. I did not think about list punctuation at all while working on the book, leaving it in the hands of copy editor Sam Clark (T&T Productions, London).

Three BibTeX Tips

BibTeX is an important part of my workflow in writing papers and books. Here are three tips for getting the most out of it.

1. DOI and URL Links from Bibliography Entries

A digital object identifier (DOI) provides a persistent link to an object on the web, via the server at Most scholarly journals now assign DOIs to papers, and many papers from the past have been retrofitted with them. Books can also have DOIs, as in SpringerLink or the SIAM ebook program.

It is very convenient for a reader of a PDF document to be able to access items from the bibliography by clicking on part of the item. The links can be constructed from a DOI, and if one does not exist a URL can be used instead. How can we produce such links automatically with BibTeX? Simply add fields doi or url and use an appropriate BibTeX style (BST) file. I’m not aware of any standard BST file that handles these fields, so I modified my own BST file using these tips. The result, myplain2-doi.bst, is available in this GitHub repository. Example bib entries that work with it are as follows.

  author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D. Relton",
  title = "Computing the {Fr{\'e}chet} Derivative of the Matrix Logarithm
           and Estimating the Condition Number",
  journal = "SIAM J. Sci. Comput.",
  volume = 35,
  number = 4,
  pages = "C394-C410",
  year = 2013,
  doi = "10.1137/120885991",
  created = "2012.07.05",
  updated = "2013.08.06"

  author = "Horn, Roger A. and Piazza, Giuseppe and Politi, Tiziano",
  title = "Explicit Polar Decompositions of Complex Matrices",
  journal = "Electron. J. Linear Algebra",
  volume = "18",
  pages = "693-699",
  year = "2009",
  url = "",
  created = "2013.01.02",
  updated = "2015.07.15"

The journal in which the second example appears is one that does not itself provide DOIs or URLs for papers. However, the European Digital Mathematics Library provides URLs for this journal, so I have used the appropriate one from there.

My BST file hyperlinks the title of each item to the corresponding DOI or URL. For an example of the style in use, see the typeset version of njhigham.bib, for which here is a direct link. An alternative style is simply to print the DOI or URL with a hyperlink.

2. Web page from Bib File via BibBase

Once you have made a bib file of a group of publications a natural question is how you can automatically generate a web page that displays the publications in an easily browsable format. A great way to do this is with BibBase. You simply point BibBase at your online bib file and it generates some JavaScript, PHP, or iFrame code. When you include that code in your a web page it displays the Bib entries sorted by year, with each DOI or URL field made clickable and each BibTeX entry revealable. A menu allows sorting by author, type, or year and the list can be folded. My bib file njhigham.bib formatted by BibBase is available here.

BibBase is free to use. It was first released a few years ago and is still being developed, with improved support for LaTeX and for special characters added recently. Keep up to date with developments by following the BibBase Twitter feed.

Here are two screenshots. The first shows part of the default layout, with outputs from 2015 folded and one bib entry revealed. bibbase1.jpg

The second screenshot shows part of the list ordered by author. bibbase2.jpg

3. Bib Entry from DOI

If you happen to know the DOI of a paper and want to obtain a bib entry, go to the doi2bib service and type in your DOI. For further information see this blog post and follow the doi2bib Twitter feed.

Mathematics at the Victoria University of Manchester


The Victoria University of Manchester (VUM) merged with the University of Manchester Institute of Science and Technology (UMIST) in 2004 to form The University of Manchester. The two former Departments of Mathematics joined together to form the School of Mathematics. In 2007 the School moved into a new building at the heart of the campus: the Alan Turing Building. The School is one of the largest integrated schools of mathematics in the UK, with around 75 permanent lecturing staff and over 1000 undergraduates.

As the School moves ahead it is important to keep an eye on the past, and to maintain valuable historical information about the predecessor departments. I know from emails I receive and contact with alumni (most recently at a reception in London last summer) that former students and staff like to look at photos and documents relating to their time here.

I have previously made available various documents and photos concerning the VUM Mathematics Tower on Oxford Road.

Now I have scanned five documents that provided information for prospective and current VUM mathematics undergraduates.


Applied Mathematics Workflow

Image courtesy of Stuart Miles at

This blog, which is almost three years old, is titled “Applied mathematics, software and workflow”. Workflow refers to everything involved in a research activity except the actual research. It’s about how to do many different things: edit and typeset a document, store and access your bibliographic references, carry out reproducible numerical experiments, produce figures, back up your files, collaborate with others, and so on. These tasks all need to be done multiple times, so small gains in efficiency can have a big payoff in the long run.

My article Workflow in the The Princeton Companion to Applied Mathematics gives a brief overview of the subject and can be downloaded in pre-publication form as an EPrint.

Workflow is not just about efficiency, though, or about producing the best possible end result. It’s also about enjoying carrying out the various tasks. Don Knuth put it perfectly when he said, in The Art of Computer Programming (Volume 2, Seminumerical Algorithms),

The enjoyment of one’s tools is an essential ingredient of successful work.

A search of this blog shows that I have barely used the term “workflow” so far. But a number of posts relate to this topic, namely

In the future I will write further posts about workflow as I continue to refine my own.

Publication Peculiarities: Acknowledgements

It is always interesting to look at the acknowledgements section of a paper, if one is present, in the hope of finding something (often unintentionally) humorous or unexpected. Here are some that I’ve collected, all from published mathematics papers.

Faulty English

The first group comprises examples where the acknowledgement doesn’t say what it was meant to say. The explanatory comments are aimed at those whose first language is not English or who are new to the publishing game.

“I would like to thank the unknown referees for their valuable comments.”

This is quite a common usage. Unknown should be replaced by anonymous in order to avoid the interpretation that the referee is someone who is not known in the community.

“I thank the anonymous referees, particularly Dr. J. R. Ockendon, for numerous suggestions and for the source of references.”

A referee is not anonymous if his name is known.

“I am grateful to the referee whose suggestions greatly improved this paper.”

Ambiguous. Were there other referees whose suggestions did not improve the paper? A comma after “referee” would avoid the ambiguity.

“I am also glad about some suggestions of the referee.”

Non-idiomatic and implies that the author did not like some other suggestions of the referee.

“The authors wish to thank the valuable suggestions of the referee.”

It’s the referee who should be thanked, not the referee’s suggestions.

Unexpected Thanks

Here are some more unusual acknowledgements. The first, from

Gregory Ammar and Volker Mehrmann, On Hamiltonian and Symplectic Hessenberg Forms, Linear Algebra Appl., 55-72, 1991

reports a speeding ticket:

“We thank Dr. A. Bunse-Gerstner for many helpful discussions (and the German police for a speeding ticket during one discussion). We also thank the referee for several insightful comments.”

What a shame that the discussion did not take place on an unrestricted autobahn.

Sometimes an acknowledgement is about help that has “oiled the wheels”. The authors of

Alan Feldstein and Peter Turner, Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction, IMA J. Numer. Anal., 6, 241-251, 1986


The authors wish to thank Mr. and Mrs. Peter Taplin of the Stone House Hotel, near Hawes, North Yorkshire whose helpful service and friendly hospitality eased the preparation of this paper considerably.

It seems that, thirty years later, the Stone House Hotel is still up and running with the same hosts. Let this serve as an unsponsored recommendation.

Marriage Proposal

The paper

Caleb M. Brown and Donald M. Henderson (2015). A New Horned Dinosaur Reveals Convergent Evolution in Cranial Ornamentation in Ceratopsidae. Current Biology, 25(12), 1641–1648.

contains a marriage proposal in the acknowledgements, which end

“C.M.B. would specifically like to highlight the ongoing and unwavering support of Lorna O’Brien. Lorna, will you marry me?”

Earlier posts in this series can be found at publication peculiarities.