Archive for Lognormal

Three New Publications at the Open Journal of Astrophysics

Posted in OJAp Papers, Open Access, The Universe and Stuff with tags , , , , , , , , , , , , , , , , , on June 8, 2024 by telescoper

Time for another roundup of business at the  Open Journal of Astrophysics. This time I have three papers to announce, which brings the total we have published so far this year (Vol. 7) to 45 and the total published by OJAp to 160. We’re still on track to publish around 100 papers this year or more, compared to last year’s 50.

First one up, published on 3rd June 2024, is “Log-Normal Waiting Time Widths Characterize Dynamics” by Jonathan Katz of Washington University (St Louis, Missouri, USA). This paper presents a discussion of the connection between waiting time distributions and dynamics for aperiodic astrophysical systems, with emphasis on log-normal distributions.  This paper is in the folder marked High-Energy Astrophysical Phenomena.

Here is a screen grab of the overlay, which includes the abstract:

 

You can read the paper directly on arXiv here.

The second paper to present is “An Empirical Model For Intrinsic Alignments: Insights From Cosmological Simulations” by Nicholas Van Alfen (Northeastern University, Boston, USA), Duncan Campbell (Carnegie Mellon University, Pittsburgh, USA), Jonathan Blazek (Northeastern University), C. Danielle Leonard (Newcastle University, UK), Francois Lanusse (Université Paris-Saclay, France), Andrew Hearin (Argonne National Laboratory, USA), Rachel Mandelbaum (Carnegie Mellon University) and The LSST Dark Energy Science Collaboration.  This paper presents an extension of the halo model (specifically the Halo Occupation Distribution, HOD) to include intrinsic alignment effects for the study of weak gravitational lensing. This paper is in the folder marked Cosmology and Nongalactic Astrophysics. It was published on Tuesday June 4th 2024.

The overlay looks like this:

 

 

You can read this paper directly on the arXiv here.

Last, but by no means least, comes  “Towards Cosmography of the Local Universe”  which proposes the multipoles of the distance-redshift relation as new cosmological observables that have a direct physical interpretation in terms of kinematical quantities of the underlying matter flow. This was also published on 4th June. The authors are Julian Adamek (IfA Zurich, Switzerland), Chris Clarkson (Queen Mary, London, UK), Ruth Durrer (Geneva, Switzerland), Asta Heinesen (U. Lyon, France & NBI Copenhagen, Denmark), Martin Kunz (Geneva), and Hayley J. Macpherson (Chicago, USA).

Here is a screengrab of the overlay:

 

 

To read the accepted version of this on the arXiv please go here. This paper is also in the folder marked Cosmology and Nongalactic Astrophysics.
That’s it for this week. I aim to post another update next weekend.

 

 

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Lognormality Revisited (Again)

Posted in Biographical, Science Politics, The Universe and Stuff with tags , , , , , , , on May 10, 2016 by telescoper

Today provided me with a (sadly rare) opportunity to join in our weekly Cosmology Journal Club at the University of Sussex. I don’t often get to go because of meetings and other commitments. Anyway, one of the papers we looked at (by Clerkin et al.) was entitled Testing the Lognormality of the Galaxy Distribution and weak lensing convergence distributions from Dark Energy Survey maps. This provides yet more examples of the unreasonable effectiveness of the lognormal distribution in cosmology. Here’s one of the diagrams, just to illustrate the point:

Log_galaxy_countsThe points here are from MICE simulations. Not simulations of mice, of course, but simulations of MICE (Marenostrum Institut de Ciencies de l’Espai). Note how well the curves from a simple lognormal model fit the calculations that need a supercomputer to perform them!

The lognormal model used in the paper is basically the same as the one I developed in 1990 with  Bernard Jones in what has turned out to be  my most-cited paper. In fact the whole project was conceived, work done, written up and submitted in the space of a couple of months during a lovely visit to the fine city of Copenhagen. I’ve never been very good at grabbing citations – I’m more likely to fall off bandwagons rather than jump onto them – but this little paper seems to keep getting citations. It hasn’t got that many by the standards of some papers, but it’s carried on being referred to for almost twenty years, which I’m quite proud of; you can see the citations-per-year statistics even seen to be have increased recently. The model we proposed turned out to be extremely useful in a range of situations, which I suppose accounts for the citation longevity:

nph-ref_historyCitations die away for most papers, but this one is actually attracting more interest as time goes on! I don’t think this is my best paper, but it’s definitely the one I had most fun working on. I remember we had the idea of doing something with lognormal distributions over coffee one day,  and just a few weeks later the paper was finished. In some ways it’s the most simple-minded paper I’ve ever written – and that’s up against some pretty stiff competition – but there you go.

Lognormal_abstract

The lognormal seemed an interesting idea to explore because it applies to non-linear processes in much the same way as the normal distribution does to linear ones. What I mean is that if you have a quantity Y which is the sum of n independent effects, Y=X1+X2+…+Xn, then the distribution of Y tends to be normal by virtue of the Central Limit Theorem regardless of what the distribution of the Xi is  If, however, the process is multiplicative so  Y=X1×X2×…×Xn then since log Y = log X1 + log X2 + …+log Xn then the Central Limit Theorem tends to make log Y normal, which is what the lognormal distribution means.

The lognormal is a good distribution for things produced by multiplicative processes, such as hierarchical fragmentation or coagulation processes: the distribution of sizes of the pebbles on Brighton beach  is quite a good example. It also crops up quite often in the theory of turbulence.

I’ll mention one other thing  about this distribution, just because it’s fun. The lognormal distribution is an example of a distribution that’s not completely determined by knowledge of its moments. Most people assume that if you know all the moments of a distribution then that has to specify the distribution uniquely, but it ain’t necessarily so.

If you’re wondering why I mentioned citations, it’s because they’re playing an increasing role in attempts to measure the quality of research done in UK universities. Citations definitely contain some information, but interpreting them isn’t at all straightforward. Different disciplines have hugely different citation rates, for one thing. Should one count self-citations?. Also how do you apportion citations to multi-author papers? Suppose a paper with a thousand citations has 25 authors. Does each of them get the thousand citations, or should each get 1000/25? Or, put it another way, how does a single-author paper with 100 citations compare to a 50 author paper with 101?

Or perhaps a better metric would be the logarithm of the number of citations?

6 Comments »

Lognormality Revisited

Posted in Biographical, Science Politics, The Universe and Stuff with tags , , , , , on January 14, 2015 by telescoper

I was looking up the reference for an old paper of mine on ADS yesterday and was surprised to find that it is continuing to attract citations. Thinking about the paper reminds me off the fun time I had in Copenhagen while it was written.   I was invited there in 1990 by Bernard Jones, who used to work at the Niels Bohr Institute.  I stayed there several weeks over the May/June period which is the best time of year  for Denmark; it’s sufficiently far North (about the same latitude as Aberdeen) that the summer days are very long, and when it’s light until almost midnight it’s very tempting to spend a lot of time out late at night..

As well as being great fun, that little visit also produced what has turned out to be  my most-cited paper. In fact the whole project was conceived, work done, written up and submitted in the space of a couple of months. I’ve never been very good at grabbing citations – I’m more likely to fall off bandwagons rather than jump onto them – but this little paper seems to keep getting citations. It hasn’t got that many by the standards of some papers, but it’s carried on being referred to for almost twenty years, which I’m quite proud of; you can see the citations-per-year statistics even seen to be have increased recently. The model we proposed turned out to be extremely useful in a range of situations, which I suppose accounts for the citation longevity:

lognormal

I don’t think this is my best paper, but it’s definitely the one I had most fun working on. I remember we had the idea of doing something with lognormal distributions over coffee one day,  and just a few weeks later the paper was  finished. In some ways it’s the most simple-minded paper I’ve ever written – and that’s up against some pretty stiff competition – but there you go.

Picture1

The lognormal seemed an interesting idea to explore because it applies to non-linear processes in much the same way as the normal distribution does to linear ones. What I mean is that if you have a quantity Y which is the sum of n independent effects, Y=X1+X2+…+Xn, then the distribution of Y tends to be normal by virtue of the Central Limit Theorem regardless of what the distribution of the Xi is  If, however, the process is multiplicative so  Y=X1×X2×…×Xn then since log Y = log X1 + log X2 + …+log Xn then the Central Limit Theorem tends to make log Y normal, which is what the lognormal distribution means.

The lognormal is a good distribution for things produced by multiplicative processes, such as hierarchical fragmentation or coagulation processes: the distribution of sizes of the pebbles on Brighton beach  is quite a good example. It also crops up quite often in the theory of turbulence.

I’ll mention one other thing  about this distribution, just because it’s fun. The lognormal distribution is an example of a distribution that’s not completely determined by knowledge of its moments. Most people assume that if you know all the moments of a distribution then that has to specify the distribution uniquely, but it ain’t necessarily so.

If you’re wondering why I mentioned citations, it’s because it looks like they’re going to play a big part in the Research Excellence Framework, yet another new bureaucratical exercise to attempt to measure the quality of research done in UK universities. Unfortunately, using citations isn’t straightforward. Different disciplines have hugely different citation rates, for one thing. Should one count self-citations?. Also how do you aportion citations to multi-author papers? Suppose a paper with a thousand citations has 25 authors. Does each of them get the thousand citations, or should each get 1000/25? Or, put it another way, how does a single-author paper with 100 citations compare to a 50 author paper with 101?

Or perhaps the REF panels should use the logarithm of the number of citations instead?

5 Comments »

Returning to Lognormality

Posted in Biographical, Science Politics, The Universe and Stuff with tags , , , on June 7, 2009 by telescoper

I’m off later today for a short trip to Copenhagen, a place I always enjoy visiting. I particularly remember a very nice time I had there back in 1990 when I was invited by Bernard Jones, who used to work at the Niels Bohr Institute.  I stayed there several weeks over the May/June period which is the best time of year  for Denmark; it’s sufficiently far North that the summer days are very long, and when it’s light until almost midnight it’s very tempting to spend a lot of time out late at night.

As well as being great fun, that little visit also produced my most-cited paper. I’ve never been very good at grabbing citations – I’m more likely to fall off bandwagons rather than jump onto them – but this little paper seems to keep getting citations. It hasn’t got that many by the standards of some papers, but it’s carried on being referred to for almost twenty years, which I’m quite proud of; you can see the citations per year statistics are fairly flat. The model we proposed turned out to be extremely useful in a range of situations, hence the long half-life.

nph-ref_history

I don’t think this is my best paper, but it’s definitely the one I had most fun working on. I remember we had the idea of doing something with lognormal distributions over coffee one day,  and just a few weeks later the paper was  finished. In some ways it’s the most simple-minded paper I’ve ever written – and that’s up against some pretty stiff competition – but there you go.

Picture1

The lognormal seemed an interesting idea to explore because it applies to non-linear processes in much the same way as the normal distribution does to linear ones. What I mean is that if you have a quantity Y which is the sum of n independent effects, Y=X1+X2+…+Xn, then the distribution of Y tends to be normal by virtue of the Central Limit Theorem regardless of what the distribution of the Xi is  If, however, the process is multiplicative so  Y=X1×X2×…×Xn then since log Y = log X1 + log X2 + …+log Xn then the Central Limit Theorem tends to make log Y normal, which is what the lognormal distribution means.

The lognormal is a good distribution for things produced by multiplicative processes, such as hierarchical fragmentation or coagulation processes: the distribution of sizes of the pebbles on Brighton beach  is quite a good example. It also crops up quite often in the theory of turbulence.

I;ll mention one other thing  about this distribution, just because it’s fun. The lognormal distribution is an example of a distribution that’s not completely determined by knowledge of its moments. Most people assume that if you know all the moments of a distribution then that has to specify the distribution uniquely, but it ain’t necessarily so.

If you’re wondering why I mentioned citations, it’s because it looks like they’re going to play a big part in the Research Excellence Framework, yet another new bureaucratical exercise to attempt to measure the quality of research done in UK universities. Unfortunately, using citations isn’t straightforward. Different disciplines have hugely different citation rates, for one thing. Should one count self-citations?. Also how do you aportion citations to multi-author papers? Suppose a paper with a thousand citations has 25 authors. Does each of them get the thousand citations, or should each get 1000/25? Or, put it another way, how does a single-author paper with 100 citations compare to a 50 author paper with 101?

Or perhaps the REF should use the logarithm of the number of citations instead?

6 Comments »