An Optimal Control Approach to National Settlement System Planning

In this paper, an optimal control approach to a problem in national settlement system planning is presented. The problem description is the same as considered by MacKinnon [6] and by Evtushenko and MacKinnon [4]. It is shown how the special structure of the model and the singular nature of the control can be used to reduce the solution of a nonlinear programming problem to the solution of sets of linear equations. A branch and bound integer programming algorithm is used to handle inequality constraints on the control variables. The organization of the paper is as follows. Section I considers problem formulation and an optimal control solution is discussed in Section II. A branch and bound technique for determining active constraints is presented in Section III. A more general problem is considered in Section IV and conclusions are stated in Section V

Credibility Theory and Kalman Filtering with Extensions

In this paper it is shown that the estimate and prediction problems considered in credibility theory are similar to those considered in Kalman filtering theory. The state vector of the risk model consists of the average risk variables such as the number of claims, cost of claims, etc. for a particular risk from the collective of risks. The observed data consists of the risk variables for the collective and for the individual risks. It is required to predict the values of risk variables in the next time period based on this data and to adjust the individual premiums based on claims experience in such a way as to converge to their true values

Chemical Kinetics and Catastrophe Theory

In this paper a continuous stirred tank reactor (CSTR) model of a first-order, exothermic reaction is examined and the existence of a cusp catastrophe is shown. Analytical solutions are developed for the ignition and quenching boundaries. The significance of the results and further extensions are discussed

On the Dynamics of the Ignition of Paper and Catastrophe Theory

The purpose of this note is to study the phenomenon of ignition of paper considered by Shivadev and Emmons from the viewpoint of stability theory and catastrophe theory. It is shown that ignition results from a sudden or catastrophic change of the kinetics governing temperature from a locally stable to a locally unstable equation. Using the model of Shivadev and Emmons and the above criterion, equations for the ignition temperature and the corresponding heat flux are derived. These equations are shown to provide a good match to the experimental data of Reference. Further extensions of this work to combustion and the appearance of cusp catastrophes are also discussed

Optimization of Measurement Schedules and Sensor Designs for Linear Dynamic Systems

This paper presents new results on the problem of measurement scheduling, sensor location and design for linear dynamic systems. Both time-invariant and time-varying systems are considered and different norms of the Observability and Information matrices are maximized with respect to the structural parameters of the system. A close connection is established between these problems and the Kiefer-Wolfowitz Theory of Experimental Design for Regression problems. Both randomized and nonrandomized designs are considered. It is shown that the optimal designs obey certain minmax properties that lead to rapidly convergent algorithms. The results are illustrated by an analytical and a numerical example

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. Methods: The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model—a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates—with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality—which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. Findings: The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2–100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1–290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1–211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4–48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3–37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7–9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. Interpretation: Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. Funding: Bill & Melinda Gates Foundation