Peer-review in a world with rational scientists: Toward selection of the average

One of the virtues of peer review is that it provides a self-regulating selection mechanism for scientific work, papers and projects. Peer review as a selection mechanism is hard to evaluate in terms of its efficiency. Serious efforts to understand its strengths and weaknesses have not yet lead to clear answers. In theory peer review works if the involved parties (editors and referees) conform to a set of requirements, such as love for high quality science, objectiveness, and absence of biases, nepotism, friend and clique networks, selfishness, etc. If these requirements are violated, what is the effect on the selection of high quality work? We study this question with a simple agent based model. In particular we are interested in the effects of rational referees, who might not have any incentive to see high quality work other than their own published or promoted. We find that a small fraction of incorrect (selfish or rational) referees can drastically reduce the quality of the published (accepted) scientific standard. We quantify the fraction for which peer review will no longer select better than pure chance. Decline of quality of accepted scientific work is shown as a function of the fraction of rational and unqualified referees. We show how a simple quality-increasing policy of e.g. a journal can lead to a loss in overall scientific quality, and how mutual support-networks of authors and referees deteriorate the system.Comment: 5 pages 4 figure

Quantum Phase and Quantum Phase Operators: Some Physics and Some History

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: Are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.Comment: 19 pages, 2 Figs. taken from published articles, LaTeX, to be published in Physica Scripta, Los Alamos preprint LA-UR-92-352

A flat plane that is not the limit of periodic flat planes

We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-6.abs.htm

Period-color and amplitude-color relations in classical Cepheid variables III: The Large Magellanic Cloud Cepheid models

Period-colour (PC) and amplitude-colour (AC) relations are studied for the Large Magellanic Cloud (LMC) Cepheids under the theoretical framework of the hydrogen ionization front (HIF) - photosphere interaction. LMC models are constructed with pulsation codes that include turbulent convection, and the properties of these models are studied at maximum, mean and minimum light. As with Galactic models, at maximum light the photosphere is located next to the HIF for the LMC models. However very different behavior is found at minimum light. The long period (P>10days) LMC models imply that the photosphere is disengaged from the HIF at minimum light, similar to the Galactic models, but there are some indications that the photosphere is located near the HIF for the short period (P<10 days) LMC models. We also use the updated LMC data to derive empirical PC and AC relations at these phases. Our numerical models are broadly consistent with our theory and the observed data, though we discuss some caveats in the paper. We apply the idea of the HIF-photosphere interaction to explain recent suggestions that the LMC period-luminosity (PL) and PC relations are non-linear with a break at a period close to 10 days. Our empirical PC and PL relations are also found to be non-linear with the F-test. Our explanation relies on the properties of the Saha ionization equation, the HIF-photosphere interaction and the way this interaction changes with the phase of pulsation and metallicity to produce the observed changes in the Cepheid PC and PL relations.Comment: 19 pages, 6 tables and 18 figures, MNRAS accepte

Odd values of the Klein j-function and the cubic partition function

In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function. Namely, we show that the number of integers $n\le x$ such that the Klein $j$-function --- or equivalently, the cubic partition function --- is odd is at least of the order of $$\frac{\sqrt{x} \log \log x}{\log x},$$ for $x$ large. This improves recent results of Berndt-Yee-Zaharescu and Chen-Lin, and approaches significantly the best lower bound currently known for the ordinary partition function, obtained using the theory of modular forms. Unlike many works in this area, our techniques to show the above result, that have in part been inspired by some recent ideas of P. Monsky on quadratic representations, do not involve the use of modular forms. Then, in the second part of the article, we show how to employ modular forms in order to slightly refine our bound. In fact, our brief argument, which combines a recent result of J.-L. Nicolas and J.-P. Serre with a classical theorem of J.-P. Serre on the asymptotics of the Fourier coefficients of certain level 1 modular forms, will more generally apply to provide a lower bound for the number of odd values of any positive power of the generating function of the partition function.Comment: A few minor revisions in response to the referees' comments. To appear in the J. of Number Theor

On integers which are representable as sums of large squares

We prove that the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set $\{n^2,(n+1)^2,\ldots \}$ is asymptotically $O(n^2)$, verifying thus a conjecture of Dutch and Rickett. Furthermore we ask a question on the representation of integers as sum of four large squares.Comment: 6 pages. To appear in International Journal of Number Theor