How to write a paper - Blogs

How to write a (hopefully good) paper
by Martin Vetterli
1. Introduction
2. To write well.....
3. The structure of the paper
4. Figures and experimental results
5. The talk and the paper
6. Open access, open data, reproducibility
7. Conclusions and outlook
Those from whom I learned....
• teachers
• co-authors
• J. Kovacevic
• V. Goyal
• former students
• students
A. Ortega, USC
“Writing a technical paper: A few random thoughts on making life
easier for the reader (and your advisor!)”
M. Püschel, J. Kovacevic,
“How to write a paper”
M. Püschel,
“Small guide to giving presentations”
To get started...
Do you want to know what knowledge is?
• When you know something, recognize that you
know it,
• and when you don’t know something,
recognize that you don’t know it.
That is knowledge.
The Analects of Confucius, Book 2 Chapter 17
writing is about transmission of knowledge
there is a ‘’channel’’ between you and the reader
Try to maximize capacity!
it is a multiuser channel (you compete for reading time...)
the reader, by definition, is never wrong! (same goes for reviewers
and editors...)
• there is a very slow/long feedback loop (e.g. your career…)
Writing is also about understanding!
Many questions appear once you write your results
• What you thought was clear isn’t once you try to explain it on
• New interesting questions emerge
• Leads to more research
• Maybe initial result was not so interesting after all…
• Keep notes
• Write about your progress
• This is not a paper yet, but it shapes and sharpens your thinking
Halmos’ view
The basic problem in writing mathematics is
the same as writing in biology, writing a
novel, or writing directions for assembling a
harpsichord: the problem is to
communicate an idea.
do so, and to do it clearly, you must
have something to say,
have someone to say it to,
organize what you want to say,
arrange it in order you want to say it
write it, rewrite it, re-rewrite it, and rerewrite several times,
6. be willing to think hard about and
7. work hard on mechanical details such as
diction, notation, and punctuation.
That’s all there is to it.
P. Halmos, “How to write mathematics”
Bertsekas’ view
Mathematical writing is the type of writing where mathematics is used as a primary
means for expression, deduction, or problem solving.
It is fundamentally different from creative and expository writing for two main reasons:
1. It involves the interplay of two languages (natural and math),
2. It requires much slower reading (it expresses complex ideas that must often be read
and several times)
As a result, many of the rules and suggestions found in writing style manuals are
inadequate and/or dot not apply.
We propose an approach to mathematical writing based
on a set of simple composition rules.
1. Organize in segments,
2. Write segments linearly
3. Consider a hierarchical development
4. Use consistent notation and nomenclature
5. State results consistently
6. Don’t under explain, don’t over explain
7. Tell them what you will tell them,
8. Use suggestive references
9. Consider examples and counterexamples
10. Use visualization when possible
The basic assumptions...
What are we trying to accomplish?
• you have some worthwhile research results
• they are solving a real problem (open problem, new problem)
• you are ahead of the crowd
You have complete results (...)
• no holes as far as you can see
• a complete picture
• a coherent picture
You are willing to communicate your results
• no killer patent killed
• you feel ready to confront the world (that is, 2.35 reviewers of some
Full disclosure always pays....
• nothing under the carpet, please
• only latex spoken here
To write well..... read, read and read!
The classics:
• any good book is a good start (my favorite is J.L.Borges. e.g. Fictiones)
The scientific classics
• C.E.Shannon, A Mathematical Theory of Communication, Bell Syst. Tech.
Journal, 1948 (do reread this on a regular basis)
• I. Daubechies (yes, yes, the 100p. paper)
The great authors (around our topics)
• R.Gallager
• G. Strang
• S.Mallat
Note to all....
• there has to be a reading culture
• I know this is ‘’Playstation generation’’ but for this job, people have to
devour the Transactions and arXiv
• there has to be a library culture (go find that obscure paper/book)
• there has to be a book culture (what book have you bought/read lately?)
• (do not read too much on a particular topic before starting research, it can
be demotivating.... optimal # of papers to read!)
My approach on reading versus research
To write well.....write, write and write!
Writing is a painful process:
• I still write on paper, do many iterations, cut-and-paste, drafts, etc.
• so do many people...
• it takes a lot of time
Writing is an iterative process
• the spiral method of Halmos (1, 1&2, 1&2&3, ...)
• write, rewrite, re-rewrite (and not cut-and-paste!)
• let it sit for a while
• have other people read it (inc. boy/girlfriend!)
• read aloud
• make short sentences (many times I have seen “this phrase no verb”...)
• do get started (e.g. Camus, “The Pest”)
You should be the most critical reader
• otherwise, somebody else will....
Is the hardest paper the best paper?
• who are you trying to impress ;)
• people often spend most space on what took most time...
Real estate is at premium
Space in paper
Research effort
The tools of the trade
The books:
• E.B. White, Elements of Style
• N.J. Higham, Handbook of writing for the mathematical sciences
• P. Halmos, How to write mathematics.
• Edward R. Tufte , The Visual Display of Quantitative Information
The journals:
• IEEE Tr on SP, IP, SAP
• IEEE Tr on IT, ToN, Comm, JSAC
• the IEEE magazines (SP mag etc)
• SIAM Review
• Nature, Science, PNAS
Some of the data bases:
• The (in) famous web of science
• all of IEEE on line
Size matters
The IEEE societies (IEEE 300K)
• IEEE Computer
IEEE Communications
IEEE Circuit and Systems
IEEE Signal Processing
IEEE Information Theory
The journals (circulation, impact factor)
• Signal Processing Magazine
• IEEE Tr. on SP
• IEEE Tr. On IP
• IEEE Tr. on IT
• IEEE Tr. A&S
• IEEE SP Letters
• IEEE Tr. On Multimedia
16K, 4.9
5K, 3.2
3K, 3.1
4K, 2.6
2K, 2.6
1.5K, 1.6
1K, 1.7
Of course, the question is who reads them…
• Impact factors of high visibility journals in an order of magnitude bigger
Impact factor
An example (just for fun)
• Laemmli UK, Cleavage of structural proteins during assembly of head
of bacteriophage T4, Nature 227 (5259): 680: 1970.
Times Cited : 214’799 !
• Now the man says (Interview, NZZ Folio, Nov. 2005)
Q: Would you recommend to a young researcher to develop a
method so as to get cited of the?
A: No, I would say: Be creative and take risk. Try something new.
What is important in science is to ask the right question. And if to
answer the right question, you need a method, then develop it.
Another example… Grigori Perelman
The tyranny of the impact factor...
• Web of science: a database of papers and citations from other papers,
mostly journal papers.
• Impact Factor: average number of citations a paper gets in the first 2
years after publication in a given journal
• Note: Nature ~ 32, IEEE Tr. on IT ~ 2,5)
• H-index: max. number N of papers cited more than N times (example :
E. Witten-120! See Hirsch’s paper for details)
• Etc. etc.
Then the game can start......
• Bottom line: better work in life sciences ;-)
• “Not everything that can be counted counts
and not everything that counts can be counted” (A.Einstein)
IF: “Houston, we have a problem”
Statistics on what parts of a paper are read...
title & abstract
section 1
other sections
So do proper waterpouring !
The various reading levels of a paper
The title should be catchy, or self-explanatory
• Costa: Writing on dirty paper,
• Shannon, A Mathematical Theory of Communication
• Gallager, Variations on a theme by Huffman
• Dubois-Ferrière, Age matters: Efficient route discovery …
• M.Kac, Can one hear the shape of a drum
Or: no second chance to make a first impression!
The abstract is the sales pitch for the paper
• why would anybody want to read this paper
• it has to pose the problem explicitly, and indicate clearly what is accomplished
• Beware of acronyms
The Table of Content (ToC) should a l low to survey the pa per
• sections have to make sense, with headings that do too
• flow, sizes
The figures should be self-contained
• browsing the p a per through figures only
• caption self-contained (be able to read the figure without the text)
• text and caption complementary
The classic structure of the paper (1)
Title and abstract
be careful with affiliations (e.g. EPFL and not Swiss Federal Lausanne Institute)
be careful with acks, e.g. to funding agencies (ERC, NCCR, SNF)
the author order headache... In doubt, αβtical
Different fields have different cultures
1. Introduction and outline
• why shall I (the reader ) spend N hours on this
• motivation for the problem (why is this important...sorry, it might not be)
• it is either the proof of Fermat’s last theorem (no further motivation needed)
or you need to properly pose the problem
2. Related work
• give credit where credit is due
• “good manners” in referencing (you know when you see it)
• make sure you set the stage for indicating why what you present is new,
better, cheaper, glitzier, cuter...
3. Contributions
• You probably know what you have contributed, but no one else does….
The classic structure of the paper (1)
Title and abstract: An example
Scrutiny of the abstract
By Kenneth K. Landes
• The behavior of editors is discussed. What should be covered by an abstract is
considered. The importance of the abstract is described. Dictionary definitions
of “abstract” are quoted. At the conclusion a revised abstract is presented.
Abstract (bis)
• The abstract is of utmost importance for it is read by 10 to 500 times more
people than hear or read the entire article. It should not be a mere recital of the
subjects covered, replete with such expressions as “is discussed” and “is
described”. It should be a condensation and concentration of the essential
qualities of the paper.
The classic structure of the paper (2)
Introduction: An example
Scrutiny of the introduction
Jon Claerbout
• The introduction to a technical paper should be an invitation to readers
to invest their time reading it.
• Typically this invitation has three parts
1. The review
2. The claim, and
3. The agenda.
• In the claim the author should say why the paper’s agenda is a
worthwhile extension of its historical review.
• Personal pronouns should be used in the claim and anywhere else the
author expresses judgment, opinion, or choice.
The classic structure of the paper (3)
4. The meat
structure the development carefully
make adequate sectioning/subsectioning
decide on Lemmas, Propositions, and Theorem(s) (the “1 Thm/paper algorithm”)
put details in appendices (for ex., for each Thm, decide if proof is in appendix)
theory is never made too easy
think of examples, inc. toy examples, figures, diagrams, illustrations, tables
5. The experimental section
describe the experimental set up precisely
the results should be reproducible
the data should be available
the presentation of the results is key (see later)
6. Conclusion(s), outlook, further work
don’t take the reader for a ride (e.g. Fermat again)
7. Appendices: can be most helpful!
8. Literature: careful please
The classic structure of the paper (4)
So write an outline first!
• structure of thoughts
• what are the main ideas you want to get across
• make it detailed enough
• is the flow adequate (not a random juxtaposition...)
• these are not lab notes, chronological, etc.
The outline will change
• a manuscript is a living animal
• it will bite back
• it will give you nightmares
The skeleton of the paper is
• the motivation, problem setting
• the “main” theorem(s)
• the lemmas and propositions that allow it
• the examples that highlight how it all works
• the experiments that justify it all
Presenting an idea
The logic should be clear to anybody (not just you)
• logical progression
• idea 1 -> idea 2, etc .
Be clear:
• there are 2 reasons why XYZ is not used in practice.
(i) it is not robust in case of. .. (ii) it is absurdly complex for ...
Do not let the reader guess what you solved, and what not
• this is clear in the math mode, but the same is true in the experimental
mode as well
• the ‘iff ”. The converses. Strengthening the results.
Repeat NO, develop YES
• multiresolution approach can be best
• like in a good plot of a novel, hints can lead the reader
• wet the appetite, give a main course, highlight with dessert
How to get ideas and results across (1)
Be explicit
• put examples (toy examples, real examples)
• put tables with usable results
(the famous “Daubechies’ filter tables)
• spell algorithms out
• put matlab/python code in paper or on line
Make life easy for the reader
• the reader is just as lazy as the writer
• it can be shown... show it
But don’t be boring!
• too explicit can be boring
Always ask the dual question also
• there might be new research right there!
• Or the next paper ;)
How to get ideas and results across (2)
Make it easy for the user… he/she will use your results!
On the most misused word(s) in the literature
• if all the claimed “optimality” were true... we could all retire!
Complexity (computational)
• what is complex, what measure, O(.), constants, etc.
It is easy to see/verify
• probably it is not, otherwise it would be written
• it can be shown... show it (Fermat again)
• it is left as an exercise... probably you can come up with new results
As can be clearly seen in the figure...
• by the time it is printed, most ‘’obvious’’ differences are washed out
• blow up the point
On theorems...
Halmos’ view
• present statement first
• statement should be short
• assumptions thus provided
• no “associated results” in statement
• proof follows
In engineering
• often along the way: “blabla. .. Thus we have proved: Thm 1”
• not so nice...
I am not ideological about it....
• what flows best is best
Presenting graphical information (1)
The classic books by E.R.Tufte
• The Visual Display of Quantitative Information is about pictures of numbers, how to
depict data and enforce statistical honesty
• Envisioning Information is about pictures of nouns (maps , aerial photos are about
nouns in space, for ex). It is also about visual strategies and colors
• Visual Explanations is about pictures of verbs, the representation of
mechanism, processes, dynamics, causes and effects (inc. magic tricks!)
So, making figures is an art!
• takes a lot of effort (that is why most people skip it!)
• gets you a lot of mileage (that is what most people forget...)
Note: caption format is
• Figure X: Block diagram of MP3. (a) Encoder. (b) Decoder.
• That is: a main caption and subcaptions
Presenting graphical information (2)
from a start-up I know…
Presenting graphical information (3)
Ten Simple Rules for Better Figures (PLOS, 11.9.14)
1. Know your audience
2. Identify your message
3. Adapt the figure to the support medium
4. Captions are not optional
5. Do not trust defaults
6. Use color effectively
7. Do not mislead the reader
8. Avoid chart junk
9. Message trumps beauty
10. Get the right tool
Presenting experimental results (1)
Explicit experimental conditions
• one realization (the Lena syndrome)
• what method on what data set
• was there training, was the data outside the training set (no joke!)
• apples and oranges?
Often, lousy statistics...
• confidence intervals
• statistical tests
• comparisons to bounds (Remember Cramer-Rao)
data better than less...
at least if presented well
data must be analyzed and interpreted
avoid the boring tables ….
If you gained insights, so should the reader
• the experiments should make a point
• make sure the point is not lost (e.g. prove/disprove a model)
Presenting experimental results (2)
Typical scenarios
The (nasty) details (1)
• it is like style
• it can be a headache
• usually, conform to the norm
• think about the alphabet, but think
about it first
• starting with a bad notation will bog
you down, sooner or later
• simplify, simplify, but not too much
• Nk Θk
• avoid pedantry, unnecessary generality,
etc .
• be rigorous
The (nasty) details (2)
• probably the easiest to fix (take courses)
• but be careful, it is the most obviously annoying thing
• “on the other hand”: a poor orphan?
• we have found -> we found
• in this paper we have found -> we found that
• etc.
• Cutting, cutting, cutting….
• Make a simple as possible, but not more
• punctuation: spaces, no spaces, lower cases, vs; vs etc....
• L.Truss ‘’Eat, shoots, leaves’’:
• the title of the book is an amphibology
The (nasty) details (3)
• Yes, it is EPFL (not Université Polytechnique Fédérale de Lausanne) from a
famous CV
• Who paid for gets an ack (e.g.: ERC Advanced Investigators Grant: Sparse
Sampling: Theory, Algorithms and Applications – SPARSAM – no 247006)
The size problem
• our overlength page charges seems to overtake the travel budget!
• 8 page limit for Tr SP, IP, etc.
• hard to predict, but please be careful
• (I don’t like the Part I and II slicing either...) even though it works well for
some colleague (double citation count...)
The (nasty) details (4)
Make short sentences, because, unless you are Proust....
« Mais au lieu de la simplicité, c'est le faste que je mettais au plus haut rang, si, après que j'avais forcé
Françoise, qui n'en pouvait plus et disait que les jambes " lui rentraient ", à faire les cent pas pendant une
heure, je voyais enfin, débouchant de l'allée qui vient de la Porte Dauphine - image pour moi d'un
prestige royal, d'une arrivée souveraine telle qu'aucune reine véritable n'a pu m'en donner l'impression
dans la suite, parce que j'avais de leur pouvoir une notion moins vague et plus expérimentale, - emportée
par le vol de deux chevaux ardents, minces et contournés comme on en voit dans les dessins de
Constantin Guys, portant établi sur son siège un énorme cocher fourré comme un cosaque, à côté d'un
petit groom rappelant le « tigre « de » feu Baudenord », je voyais - ou plutôt je sentais imprimer sa forme
dans mon coeur par une nette et épuisante blessure - une incomparable victoria, à dessein un peu haute
et laissant passer à travers son luxe " dernier cri « des allusions aux formes anciennes, au fond de laquelle
reposait avec abandon Mme Swann, ses cheveux maintenant blonds avec une seule mèche grise ceints
d'un mince bandeau de fleurs, le plus souvent des violettes, d'où descendaient de longs voiles, à la main
une ombrelle mauve, aux lèvres un sourire ambigu où je ne voyais que la bienveillance d'une Majesté et
où il y avait surtout la provocation de la cocotte, et qu'elle inclinait avec douceur sur les personnes qui la
saluaient. »
243 words!
Conclusions and further work
Conclusion (if at all ;)
• DO NOT TAKE THE ABSTRACT and put it in the past tense.
• Laziness always shows
• Make a wrap up, people will look for your assessment of the work
• Contributions can be emphasized and placed in context
Future work
• Put ideas you think are worthwhile to pursue
• Not necessarily ideas you are pursuing already…
• Invite others to pursue your path (and get these citations ;)
• Do not mislead (Fermat ;)
• Put the earliest references, even if they are from 1927
• Put all necessary references
• It is nice to get cited, so please be nice in citing ;)
Checklist (A.O.)
Can a reader with the right background:
get the basic ideas
understand the paper
remember what is new in this work
follow the proofs
replicate the experiments
find all assumptions in the text
be convinced that this is useful
not fall asleep ;)
On reproducible research
Clairbout’s initiative at Stanford
• geophysics
• lots of data , code, etc.
Donoho’s wavelab, etc.
• lot of mileage
• SPIHT, wavelab, safecast, sensorscope
We should, collectively, make much more!
A paper should be
• a manuscript (eventually a publication)
• a set of documented code (matlab, C, libraries, etc.)
• all data that was used
• a web document
Lab initiative: blue print for what we want to accomplish
(A.H.Salavati’s talk) and quality control
The art of the quote
Finding good quotes is a challenge, here a few
On why we do research
• I don't want to achieve immortality through my work... I want to
achieve it through not dying (Woody Allen)
On writing
• Most rock journalism is people who can’t write, interviewing
people who can’t talk, for people who can’t read (Frank Zappa)
How to write?
Different people have different habits
Victor Hugo
• Standing
• Eating oranges without peeling them
Walking around
• It seems it makes us creative
Writing well is a hard task
• we are all students of the art
• no easy short-cuts (it will show...)
• no pain, no gain...
But it is a central task!
• you can prove the hardest results, if nobody
reads it, it was futile a endeavor
• like teaching, one learns by writing
• writing things down leads to new in sights , better ways to
understand the problem, new research, etc.
Your papers are your thesis!
• take these 3 or 4 journal papers, and staple them ;)
• for good measure, add a good introduction and conclusion
• you are done (3 months rather than 6 or 9!)
I am looking forward to reading your next paper!
How not to do it...
Cogno-Intellectualism, Rhetorical logic, and the Crase-Trump Theorem
Michael H. F. Wilkinson
Institute for Mathematics and Computing Science
University of Groningen
Abstract- This paper presents a breakthrough in rhetorical logic, a promising
field of science, of great value to those writing research proposals. It
provides new, and utterly convincing tools for closing embarrassing gaps in
your reasoning, without resorting to brute-force methods, such as actually
thinking about the problem in the first place. The Craske-Trump Theorem,
along with the Trump-Craske Conjecture will allow researchers in any field
to use the technique of “Proof by Intimidation” fully.
From the Annals of Improbable Research.
In preparation:
How to do (hopefully) interesting research
The most exciting phrase to hear in science,
the one that heralds new discoveries,
is not 'Eureka!' but 'That's funny...’
Isaac Asimov
Coming attraction: The art of talk....
Power point is evil, Power Corrupts. PowerPoint Corrupts Absolutely.
by Edward Tufte, Wired Magazine, 2003
I am looking forward to the discussion!
Coming attraction: The art of talk....
From: Power point is evil, Power Corrupts. PowerPoint Corrupts Absolutely.
How to Write Mathematics, P.R. Halmos, L'Enseignement Mathematique, t. XVI, fasc. 2,
Ten Simple Rules For Mathematical Writing, Dimitri Bertsekas, M.I.T. , APRIL 2002,
Can We Make Mathematics Intelligible? R. P. Boas, American Mathematical Monthly,
Vol. 88, No. 10 (Dec., 1981), pp. 727–731.
The Science of Scientific Writing, George D. Gopen and Judith A. Swan, American
Scientist, Volume 78.
Scrutiny of the abstract, Landes, Kenneth K., 1966
Scrutiny of the introduction, Jon Claerbout, 1995.,
F.Jabr, Why walking helps us think, The New Yorker, Sept 3
Sylvia Nasar, David Grube, Manifold Destiny, A legendary problem and the battle over who
solved it. New Yorker, August 28, 2006.
Rougier NP, Droettboom M, Bourne PE (2014) Ten Simple Rules for Better Figures. PLoS
Comput Biol 10(9): e1003833. doi:10.1371/journal.pcbi.1003833

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