On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n

In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers. As an application, we use the method for finding the number of solutions of a Diophantine inequality

Fumigant Toxicity and Oviposition Deterrency of the Essential Oil from Cardamom, Elettaria cardamomum, Against Three Stored—product Insects

Use of insecticides can have disruptive effects on the environment. Replacing the chemical compounds in these insecticides with plant materials, however, can be a safe method with low environmental risk. In the current study, chemical composition and insecticidal activities of the essential oil from cardamom, Elettaria cardamomum L. (Maton) (Zingiberales: Zingiberaceae) on the adults of three stored product pests was investigated. Results indicated that essential oil of E. cardamomum toxic to the bruchid beetle, Callosobruchus maculatus Fabricius (Coleoptera: Bruchidae), the red flour beetle, Tribolium castaneum Herbst (Coleoptera: Tenebrionidae), and the flour moth, Ephestia kuehniella Zeller (Lepidoptera: Pyralidae). Adults of E. kuehniella were more sensitive than the Coleoptera. Also, the highest mortality of these insects was seen after 12 hours. Results of the LT50 tests showed that the lethal time of mortality occurred between 10–20 hours in various test concentrations. Essential oil of E. cardamomum had a good efficacy on oviposition deterrence of C. maculatus females, too. The chemical constituents of the essential oils were analyzed by gas chromatography—mass spectrometry. The major constituents of cardamom were identified as 1,8-cineol, α-terpinyl acetate, terpinene and fenchyl alcohol. These results suggest that essential oil of E. cardamomum is a good choice for control of stored product pests

The design of an optimal Bonus-Malus System based on the Sichel distribution

This chapter presents the design of an optimal Bonus-Malus System (BMS) using the Sichel distribution to model the claim frequency distribution. This system is proposed as an alternative to the optimal BMS obtained by the traditional Negative Binomial model [19]. The Sichel distribution has a thicker tail than the Negative Binomial distribution and it is considered as a plausible model for highly dispersed count data. We also consider the optimal BMS provided by the Poisson-Inverse Gaussian distribution (PIG), which is a special case of the Sichel distribution. Furthermore, we develop a generalised BMS that takes into account both the a priori and a posteriori characteristics of each policyholder. For this purpose we consider the generalised additive models for location, scale and shape (GAMLSS) in order to use all available information in the estimation of the claim frequency distribution. Within the framework of the GAMLSS we propose the Sichel GAMLSS for assessing claim frequency as an alternative to the Negative Binomial Type I (NBI) regression model used by Dionne and Vanasse [9, 10]. We also consider the NBI and PIG GAMLSS for assessing claim frequency

Burden of disease scenarios for 204 countries and territories, 2022–2050: a forecasting analysis for the Global Burden of Disease Study 2021

Background: Future trends in disease burden and drivers of health are of great interest to policy makers and the public at large. This information can be used for policy and long-term health investment, planning, and prioritisation. We have expanded and improved upon previous forecasts produced as part of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) and provide a reference forecast (the most likely future), and alternative scenarios assessing disease burden trajectories if selected sets of risk factors were eliminated from current levels by 2050. Methods: Using forecasts of major drivers of health such as the Socio-demographic Index (SDI; a composite measure of lag-distributed income per capita, mean years of education, and total fertility under 25 years of age) and the full set of risk factor exposures captured by GBD, we provide cause-specific forecasts of mortality, years of life lost (YLLs), years lived with disability (YLDs), and disability-adjusted life-years (DALYs) by age and sex from 2022 to 2050 for 204 countries and territories, 21 GBD regions, seven super-regions, and the world. All analyses were done at the cause-specific level so that only risk factors deemed causal by the GBD comparative risk assessment influenced future trajectories of mortality for each disease. Cause-specific mortality was modelled using mixed-effects models with SDI and time as the main covariates, and the combined impact of causal risk factors as an offset in the model. At the all-cause mortality level, we captured unexplained variation by modelling residuals with an autoregressive integrated moving average model with drift attenuation. These all-cause forecasts constrained the cause-specific forecasts at successively deeper levels of the GBD cause hierarchy using cascading mortality models, thus ensuring a robust estimate of cause-specific mortality. For non-fatal measures (eg, low back pain), incidence and prevalence were forecasted from mixed-effects models with SDI as the main covariate, and YLDs were computed from the resulting prevalence forecasts and average disability weights from GBD. Alternative future scenarios were constructed by replacing appropriate reference trajectories for risk factors with hypothetical trajectories of gradual elimination of risk factor exposure from current levels to 2050. The scenarios were constructed from various sets of risk factors: environmental risks (Safer Environment scenario), risks associated with communicable, maternal, neonatal, and nutritional diseases (CMNNs; Improved Childhood Nutrition and Vaccination scenario), risks associated with major non-communicable diseases (NCDs; Improved Behavioural and Metabolic Risks scenario), and the combined effects of these three scenarios. Using the Shared Socioeconomic Pathways climate scenarios SSP2-4.5 as reference and SSP1-1.9 as an optimistic alternative in the Safer Environment scenario, we accounted for climate change impact on health by using the most recent Intergovernmental Panel on Climate Change temperature forecasts and published trajectories of ambient air pollution for the same two scenarios. Life expectancy and healthy life expectancy were computed using standard methods. The forecasting framework includes computing the age-sex-specific future population for each location and separately for each scenario. 95% uncertainty intervals (UIs) for each individual future estimate were derived from the 2·5th and 97·5th percentiles of distributions generated from propagating 500 draws through the multistage computational pipeline. Findings: In the reference scenario forecast, global and super-regional life expectancy increased from 2022 to 2050, but improvement was at a slower pace than in the three decades preceding the COVID-19 pandemic (beginning in 2020). Gains in future life expectancy were forecasted to be greatest in super-regions with comparatively low life expectancies (such as sub-Saharan Africa) compared with super-regions with higher life expectancies (such as the high-income super-region), leading to a trend towards convergence in life expectancy across locations between now and 2050. At the super-region level, forecasted healthy life expectancy patterns were similar to those of life expectancies. Forecasts for the reference scenario found that health will improve in the coming decades, with all-cause age-standardised DALY rates decreasing in every GBD super-region. The total DALY burden measured in counts, however, will increase in every super-region, largely a function of population ageing and growth. We also forecasted that both DALY counts and age-standardised DALY rates will continue to shift from CMNNs to NCDs, with the most pronounced shifts occurring in sub-Saharan Africa (60·1% [95% UI 56·8–63·1] of DALYs were from CMNNs in 2022 compared with 35·8% [31·0–45·0] in 2050) and south Asia (31·7% [29·2–34·1] to 15·5% [13·7–17·5]). This shift is reflected in the leading global causes of DALYs, with the top four causes in 2050 being ischaemic heart disease, stroke, diabetes, and chronic obstructive pulmonary disease, compared with 2022, with ischaemic heart disease, neonatal disorders, stroke, and lower respiratory infections at the top. The global proportion of DALYs due to YLDs likewise increased from 33·8% (27·4–40·3) to 41·1% (33·9–48·1) from 2022 to 2050, demonstrating an important shift in overall disease burden towards morbidity and away from premature death. The largest shift of this kind was forecasted for sub-Saharan Africa, from 20·1% (15·6–25·3) of DALYs due to YLDs in 2022 to 35·6% (26·5–43·0) in 2050. In the assessment of alternative future scenarios, the combined effects of the scenarios (Safer Environment, Improved Childhood Nutrition and Vaccination, and Improved Behavioural and Metabolic Risks scenarios) demonstrated an important decrease in the global burden of DALYs in 2050 of 15·4% (13·5–17·5) compared with the reference scenario, with decreases across super-regions ranging from 10·4% (9·7–11·3) in the high-income super-region to 23·9% (20·7–27·3) in north Africa and the Middle East. The Safer Environment scenario had its largest decrease in sub-Saharan Africa (5·2% [3·5–6·8]), the Improved Behavioural and Metabolic Risks scenario in north Africa and the Middle East (23·2% [20·2–26·5]), and the Improved Nutrition and Vaccination scenario in sub-Saharan Africa (2·0% [–0·6 to 3·6]). Interpretation: Globally, life expectancy and age-standardised disease burden were forecasted to improve between 2022 and 2050, with the majority of the burden continuing to shift from CMNNs to NCDs. That said, continued progress on reducing the CMNN disease burden will be dependent on maintaining investment in and policy emphasis on CMNN disease prevention and treatment. Mostly due to growth and ageing of populations, the number of deaths and DALYs due to all causes combined will generally increase. By constructing alternative future scenarios wherein certain risk exposures are eliminated by 2050, we have shown that opportunities exist to substantially improve health outcomes in the future through concerted efforts to prevent exposure to well established risk factors and to expand access to key health interventions

A Preliminary Investigation into the Effect of Outlier(s) on Singular Spectrum Analysis

The aim of this paper is to study the effect of outliers on different parts of singular spectrum analysis (SSA) from both theoretical and practical points of view. The rank of the trajectory matrix, the magnitude of eigenvalues, reconstruction, and forecasting results are evaluated using simulated and real data sets. The performance of both recurrent and vector forecasting procedures are assessed in the presence of outliers. We find that the existence of outliers affect the rank of the matrix and increases the linear recurrent dimensions whilst also having a significant impact on SSA reconstruction and forecasting processes. There is also evidence to suggest that in the presence of outliers, the vector SSA forecasts are more robust in comparison to the recurrent SSA forecasts. These results indicate that the identification and removal of the outliers are mandatory to achieve optimal SSA decomposition and forecasting results