One of the most significant developments in computational atomic and molecular physics in recent years has been the introduction of B-spline basis sets in calculations of atomic and molecular structure and dynamics. B-splines were introduced in applied mathematics more than 50 years ago, but it has been in the 1990s, with the advent of powerful computers, that the number of applications has grown exponentially. In this review we present the main properties of B-splines and discuss why they are useful to solve different problems in atomic and molecular physics. We provide an extensive reference list of theoretical works that have made use of B-spline basis sets up to 2000. Among these, we have focused on those applications that have led to the discovery of new interesting phenomena and pointed out the reasons behind the success of the approach.

https://iopscience.iop.org/article/10.1088/0034-4885/64/12/205/pdf

Applications of B-splines in atomic and molecular physics

This paper proposes and estimates a static transferable utility model of the marriage market. The model generates a nonparametric marriage matching function with spillover effects. It rationalizes the standard interpretation of marriage rate regressions and points out its limitations. The model was used to estimate U.S. marital behavior in 1971/72 and 1981/82. The marriage matching function estimates show that the gains to marriage for young adults fell substantially over the decade. Unlike contradictory marriage rate regression results, the marriage matching function estimates showed that the legalization of abortion had a significant quantitative impact on the fall in the gains to marriage for young men and women.

/pdf/who-marries-whom-and-why-314govzrub.pdf

Who marries whom and why

Continuing increases in life expectancy beyond previously-held limits have brought to the fore the critical importance of mortality forecasting. Significant developments in mortality forecasting since 1980 are reviewed under three broad approaches: expectation, extrapolation and explanation. Expectation is not generally a good basis for mortality forecasting, as it is subjective; expert expectations are invariably conservative. Explanation is restricted to certain causes of death with known determinants. Decomposition by cause of death poses problems associated with the lack of independence among causes and data difficulties. Most developments have been in extrapolative forecasting, and make use of statistical methods rather than models developed primarily for age-specific graduation. Methods using two-factor models (age-period or age-cohort) have been most successful. The two-factor Lee–Carter method, and, in particular, its variants, have been successful in terms of accuracy, while recent advances have improved the estimation of forecast uncertainty. Regression-based (GLM) methods have been less successful, due to nonlinearities in time. Three-factor methods are more recent; the Lee–Carter age-period-cohort model appears promising. Specialised software has been developed and made available. Research needs include further comparative evaluations of methods in terms of the accuracy of the point forecast and its uncertainty, encompassing a wide range of mortality situations.

/pdf/mortality-modelling-and-forecasting-a-review-of-methods-57ywz2mf1x.pdf

Mortality modelling and forecasting: a review of methods

Demographic forecasting: 1980 to 2005 in review

Continuing increases in life expectancy beyond previously-held limits have brought to the fore the critical importance of mortality forecasting. Significant developments in mortality forecasting since 1980 are reviewed under three broad approaches: expectation, extrapolation and explanation. Expectation is not generally a good basis for mortality forecasting, as it is subjective; expert expectations are invariably conservative. Explanation is restricted to certain causes of death with known determinants. Decomposition by cause of death poses problems associated with the lack of independence among causes and data difficulties. Most developments have been in extrapolative forecasting, and make use of statistical methods rather than models developed primarily for age-specific graduation. Methods using two-factor models (age-period or age-cohort) have been most successful. The two-factor Lee^Carter method, and, in particular, its variants, have been successful in terms of accuracy, while recent advances have improved the estimation of forecast uncertainty. Regression-based (GLM) methods have been less successful, due to nonlinearities in time. Three-factor methods are more recent; the Lee^Carter age-periodcohort model appears promising. Specialised software has been developed and made available. Research needs include further comparative evaluations of methods in terms of the accuracy of the point forecast and its uncertainty, encompassing a wide range of mortality situations.

/pdf/mortality-modelling-and-forecasting-a-review-of-methods-by-h-59z7kwtdti.pdf

MORTALITY MODELLING AND FORECASTING: A REVIEW OF METHODS By H. Booth and L. Tickle

In this paper we study the underlying Gompertz distribution and develop formulae for the moments and other characteristics of this useful but apparently unknown distribution. We find that the skewness and kurtosis of the distribution are fixed constants independent of the two distribution parameters and this would appear to be the reason for the mixed success writers have experienced fitting the curve to fertility data. We also show the distribution of the minimum of n independent Gompertz variables all having the same c-parameter is itself a Gompertz variable with the same c-parameter. (SUMMARY IN FRE AND ITA) (EXCERPT)

The Gompertz distribution and its applications.

Modelling the interaction between the sexes

In recent times there has been considerable discussion of the wide disparity between the numbers of unmarried males and unmarried females in the younger and mid adult ages in Germany....To study this phenomenon and understand it a two-sex population model is essential....In this paper we develop a two-sex model using behavioural arguments and show that the model obeys criteria which have been prescribed by earlier writers....The model is relatively easy to use produces consistent results and projects marriage numbers which accord with intuitive expectation. It also leads us to the conclusion that the excess of unmarried males at the younger marriageable ages observed in Germany is a phenomenon to be expected in all western-type populations in which more males than females are born and there is a strong preference for a partner about the same age with the bride a little younger than the groom on average. (SUMMARY IN FRE AND GER) (EXCERPT)

The interaction between the sexes.

Mortality data are often gathered using 5‐year age groups rather than individual years of life. Furthermore, it is common practice to use a large open‐ended interval (such as 85 and over) for mortality data at the older ages. These limitations of the data pose problems for the actuary or demographer who wishes to compile a full and accurate life table using individual years of life. In this paper, we devise formulae which handle these problems. We also devise methods for handling mortality during the first year of life and for dealing with other technical problems which arise in the compilation of the full life table from grouped data.

On the derivation of a full life table from mortality data recorded in five-year age groups.

Over the course of the twentieth century, mortality rates in Australia have shown substantial improvements at all ages. The improvements which have taken place at different ages, however, have not occurred at a uniform pace, and as a result, the shapes of the national mortality curves have varied over time. The most noticeable change for males has been the development of an ‘accident hump’ in the late teens and early twenties mid-century, the growth of this ‘hump’ in the 1960s and 1970s, and its sudden disappearance, or transformation into a ‘bulge’, in the late 1980s. This paper examines the reasons for the disappearance of the male ‘accident hump’, and the changes in mortality by cause which have occurred over the decade to 1992 and influenced the level and shape of the whole mortality curve both for males and for females. Extrapolating the trends observed for the various cause-specific mortality rates obtains projected life tables for Australian males and females in the year 2002. The Australian population has enjoyed remarkable improvements in mortality over the twentieth century. Expectation of life at birth for females rose from 59 years in the early years of the century to more than 80 years in 1992, and these improvements in longevity show no signs of abating. For males, the corresponding increase has been from 55 to 74. The improvements in mortality which have taken place have not occurred at a uniform pace in all age groups, and as a result, the mortality curve (q x plotted against age x) has undergone several important changes in shape. The increasing prominence of the so-called ‘accident hump’ at the younger adult ages for males (Figure 1), has been remarkable. A similar but less spectacular pattern for females emerged rather later (Figure 2). But even more remarkable, perhaps, than the development of the male accident hump has been its sudden disappearance in the late 1980s (Figure 3), and its transformation to an ‘accident bulge’ not unlike that observed for the females a few years earlier. Random breath testing of drivers for alcohol was introduced in 1983, and there would appear to be a change in attitude among young adults concerning drink-driving. At the same time, compulsory use of seat-belts has been legislated, and there has been greater use and awareness of radar

/pdf/on-the-changing-shape-of-the-australian-mortality-curve-aaiji2bf0x.pdf

John H. Pollard

Papers

The Gompertz distribution and its applications.

Modelling the interaction between the sexes

The interaction between the sexes.

On the derivation of a full life table from mortality data recorded in five-year age groups.

On the changing shape of the Australian mortality curve