How to write a (hopefully good) paperby Martin Vetterli Introduction To write well..... The structure of the paper Figures and experimental results The talk and the paper Open access, open data, reproducibility Conclusions and outlook
Acknowledgements • 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 So: • 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 paper • New interesting questions emerge • Leads to more research • Maybe initial result was not so interesting after all… So: • Keep notes • Write about your progress • This is not a paper yet, but it shapes and sharpens your thinking
P.Halmos 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. To 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 re-rewrite several times, be willing to think hard about and 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 Bertsekas 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: It involves the interplay of two languages (natural and math), 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 D.Bertzekas, TEN SIMPLE RULES FOR MATHEMATICAL WRITING
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 Transaction) • Full disclosure always pays.... • nothing under the carpet, please • Note: • 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 Reading 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 natural adapted 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 writemathematics. • 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 magetc) • SIAM Review • Nature, Science, PNAS • Some of the data bases: • http://apps.webofknowledge.com: The (in) famous web of science • http://ieeexplore.org/lpdocs/epic03: all of IEEE on line • http://scholar.google.ch/ • http://www.researchgate.net/
Size matters • The IEEE societies (IEEE 300K) • IEEE Computer 120K • IEEE Communications 75K • IEEE Circuit and Systems 25K • IEEE Signal Processing 20K • IEEE Information Theory 6K • The journals (circulation, impact factor) • Signal Processing Magazine 16K, 4.9 • IEEE Tr. on SP 5K, 3.2 • IEEE Tr. On IP3K, 3.1 • IEEE Tr. on IT 4K, 2.6 • IEEE Tr. A&S 2K, 2.6 • IEEE SP Letters 1.5K, 1.6 • IEEE Tr. On Multimedia 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... • Definitions: • 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...... • http://apps.webofknowledge.com • http://www.cs.ucla.edu/~palsberg/h-number.htmlhttp://scholar.google.com • Bottom line: better work in life sciences ;-) • “Not everything that can be counted counts and not everything that counts can be counted” (A.Einstein)
Statistics on what parts of a paper are read... title& abstract introduction bio.!!! section1 lit. conc. 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: nosecond 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 • 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 • 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... • 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 • Abstract • 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 • Abstract: • The introduction to a technical paper should be an invitation to readers to invest their time reading it. • Typically this invitation has three parts • The review • The claim, and • 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. • 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 • Optimal • 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 C.J.Minard
Presenting graphical information (2) from a start-up I know…
Presenting graphical information (3) Ten Simple Rules for Better Figures (PLOS, 11.9.14) Know your audience Identify your message Adapt the figure to the support medium Captions are not optional Do not trust defaults Use color effectively Do not mislead the reader Avoid chart junk Message trumps beauty 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) • More 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) • Notations • 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 • NkΘk • avoid pedantry, unnecessary generality, etc . • be rigorous
The (nasty) details (2) • English • 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) • Affiliations • Yes, it is EPFL (not UniversitéPolytechniqueFédérale de Lausanne) from a famous CV • Acknowledgments • 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 TrSP, 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 ;) • Literature • 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’swavelab, etc. • lot of mileage • Examples • SPIHT, wavelab, safecast, sensorscope • We should, collectively, make muchmore! • 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'twant to achieveimmortalitythroughmywork... I want to achieveitthrough 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
Conclusions • 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.
References 1. How to Write Mathematics, P.R. Halmos, L'EnseignementMathematique, t. XVI, fasc. 2, http://www.math.uga.edu/~azoff/courses/halmos.pdf Ten Simple Rules For Mathematical Writing, Dimitri Bertsekas, M.I.T. , APRIL 2002, http://www.mit.edu/~dimitrib/Ten_Rules.pdf 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., 1966http://sepwww.stanford.edu/sep/prof/abscrut.html Scrutiny of the introduction, Jon Claerbout, 1995.,http://sepwww.stanford.edu/sep/prof/Intro.html F.Jabr, Why walking helps us think, The New Yorker, Sept 3 2014http://www.newyorker.com/tech/elements/walking-helps-us-think?src=mp Sylvia Nasar, David Grube, Manifold Destiny, A legendary problem and the battle over who solved it. New Yorker, August 28, 2006. http://www.newyorker.com/magazine/2006/08/28/manifold-destiny 9. RougierNP, Droettboom M, Bourne PE (2014) Ten Simple Rules for Better Figures. PLoSComputBiol 10(9): e1003833. doi:10.1371/journal.pcbi.1003833