Broad distribution effects in sums of lognormal random variables

The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g., for the current flowing through small tunnel junctions, are pointed out.Comment: 14 pages, 9 figures. Minor changes + Gini coefficient and 4 refs. adde

A rule of thumb for riffle shuffling

We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, e.g. suits disregarded or only the colors of interest. For these features, the number of shuffles drops from 3/2 log_2(n) to log_2(n). We derive closed formulae and an asymptotic `rule of thumb' formula which is remarkably accurate.Comment: 27 pages, 5 table

Fair Shares for All? The development of needs based governmental funding in education, health and housing

Furthering equity as an achievable public policy objective is based on the ability to assess needs accurately, and distribute resources accordingly. This paper plots the development of the formulae governing resouce allocation in education, health and social housing, and charts their course as a tool with which governments attempted to achieve various objectives. The paper begins by suggesting that allocation systems can be explained through a form of public choice theory. It then charts the development of needs-based resource allocation from its origin in the nineteenth century, through the pre- and post Second World War period, and into the major flowering of needs-based formulae since 1970 - when resources were constrained and attempts were made to push allocation even further down and apply the formulae to smaller units. The conclusion looks at equity, public choice and technical ability as over-riding features governing the development of resource allocation within the English state sector.Resource allocation, funding formulae, geographical equity

On the extension of the Bethe-Weizsacker mass formula to light nuclei

Some general features of the Bethe-Weizsacker mass formula recently extended to light nuclei have been explored. Though this formula improves fits to the properties of light nuclei and it does seem to work well in delineating the positions of all old and new magic numbers found in that region, yet it is not well tuned for predicting finer details. The mass predictions have also been found to be less accurate compared to those by the macroscopic-microscopic calculations. It is concluded that such semi-empirical mass formulae can not be a substitute for more fundamental mass formulae having its origin based upon the basic nucleon-nucleon effective interaction.Comment: 3 page