How to properly label graphs that can be dimensionless?

One of reviewers of my document strongly emphasised on labelling plots with which I generally strongly agree. On this occasion, however, I was explaining a general mathematical model on generated time series and by time series I mean an observation (value of a variable) that changes. Non of the variables I’m plotting has any units and the only reason why I added label Time [s] on x axis so that reader doesn’t have to think too much what is there. Reviewer suggested adding units to all other labels, such as dimensionless amplitude, amplitude square and inverse of amplitude square. It seems that adding Density [1/|1|^2] or making up a unit might be considered a bit offensive.

Here are examples, where I am supposed to label axes. None of used variables requires a unit.

Density of dimensionless variable.

Time series

I’ve been on a couple of research projects with a few professors and have had some success recently and plan to do more collaborative work through the end of this calendar year. One student is constantly leeching off of me and imposing himself, such as wanting specifics about my work, specifics about private meetings between me and my research advisors, wanting to come to lab while I am there to do some work. (he is not part of the lab.) How do I tell this person to back off and do his own work, establish his own connections and stop creeping on me and stalking my every move in hopes of leapfrogging me, just because I’ve had some recent success? Do I have to continually say, “this is private and ongoing research that isn’t published yet”?

I’m not sure if this is the place to ask, but I need a formula that will generate a list of numbers based on input.


  • Number of teams in league
  • The team’s draft selection position
  • Number of draft picks


  • Lets say there are 12 teams in the league
  • This team has the 12th overall pick
  • Each team gets 18 draft pick selections
  • A snake draft looks like this:

Example of Snake Draft:

Round 1 = 1,2,3,4,5,6,7,8,9,10,11,12 (1,2,3,4,5,6,7,8,9,10,11,12)

Round 2 = 12,11,10,9,8,7,6,5,4,3,2,1 (13,14,15,16,17,18,19,20,21,22,23,24)

Round 3 = 1,2,3,4,5,6,7,8,9,10,11,12 (25,26,27,28,29,30,31,32,33,34,35,36)

etc….. through 18 rounds.

I would like a spreadsheet formula and an algebraic formula if at all possible.

To start with, let me confess a sin that I have committed a few years ago. A friend of mine asked me to proofread several of his papers before sending them for publication. After helping him several times without expecting anything in return, he offers to included me as one of the authors of another paper after I proofread it. Being immature and greedy, I have accepted the offer, which is a great mistake. Later the paper was published and I was listed as one of the authors of the paper, and I understand nothing about the paper itself. Now I am facing the mistake that I have made and have decided to do something about it.

  1. Should I always exclude the paper from my resume? Although I was officially listed as one of the authors, I do not feel that I contributed to any part of the paper except proofreading.
  2. Is there anything else that I should do about this situation?

In the United States, are the startup packages offered for tenure-track positions at research universities typically significantly different for the assistant and associate professor levels?

Background: I am a researcher in computer science considering moving from an industrial position to a university tenure track position. I have recently received an offer for a tenure-track position at the associate professor level (expected, given my career position).

The startup package being offered seems rather weak to me, however, particularly comparing it against a startup package that I know was offered to another person who recently entered this department in a similar position but at the assistant professor level.

Is it typical for a new associate professor to be offered a much smaller startup package than a new assistant professor (perhaps on the theory that they are already established in their career), or is the university giving me a weak offer?

I would like to have suggestions of good software for drawing illustrations in research papers. I already know about Xfig, but this works only on Linux and is at times, clunky when it comes to text. Moreover the resolution is not always perfect making it difficult to manoeuvre the objects. Besides it is tough to learn and master, with all its weird click procedures.

I would love to know about better alternatives. Not talking about graphs here, just block diagrams and explanatory illustrations.

I am from one of the top UK institutions studying mathematics. I am under the impression that UK universities tend to have a larger cohort (~150 per year) than US but perhaps I am wrong.

I would like to know is there any difference ranking 1st, ranking in top 5 or ranking in top 10 when it comes to PhD applications especially in the US, or is the personal ranking only serves the purpose as a benchmark (say top 5% is enough).

I have heard different theories about this as some would say it’s extremely important to get top first or second to get into top graduate programs, and some say that having one or two marks higher than your course mates makes no difference and tells nothing more about your ability.

Thanks for advance.