Combinatorial Formulas for the $r$th Standard Moment of the Sample Sum, of the Sample Mean, and of the Normal Curve

Abstract There are powerful fairness and efficiency arguments for making charitable donations to soup kitchens 100% deductible. These arguments have no purchase for donations to fund opulent church organs, yet these too are 100% deductible under the current tax code. This stark dichotomy is only the tip of the iceberg. Looking at a wider sampling of charitable gifts reveals a charitable continuum. Based on sliding scales for efficiency, multiple theories of fairness, pluralism, institutional competence and social welfare dictate that charitable deductions should in most cases be fractions between zero and one. Moreover, the Central Limit Theorem strongly suggests that combining this welter of largely independent criteria with the wide variety of charitable gifts results in a classic bell-shaped normal curve of optimal deductions, with a peak at some central value and quickly decaying to zero at the extremes of 0% and 100%. Given that those are the only two options under the current tax code, the current charitable deduction regime inevitably makes large errors in most cases. Actually calculating a precise optimal percentage for each type of charitable donation is of course impractical. This Article suggests, however, that we can do much better than the systematically erroneous current charitable deduction. Granting a 100% deduction only for donations to the desperately poor, along with 50%, 25%, and 0% for gifts yielding progressively fewer efficiency, fairness, pluralism, and institutional competence benefits, promises to deliver a socially more desirable charitable deduction.

Download Full-text

Periodontitis Is Related to Exercise Capacity: Two Cross-sectional Studies

Journal of Dental Research ◽

10.1177/0022034521995428 ◽

2021 ◽

pp. 002203452199542

Author(s):

B. Holtfreter ◽

B. Stubbe ◽

S. Gläser ◽

J. Trabandt ◽

H. Völzke ◽

...

Keyword(s):

Oxygen Uptake ◽

Disease Severity ◽

Cardiorespiratory Fitness ◽

Large Scale ◽

Cardiopulmonary Exercise Testing ◽

Exercise Duration ◽

Cross Sectional ◽

Sample Mean ◽

Cardiometabolic Diseases ◽

Number Of Teeth

Although a potential link between periodontitis and cardiorespiratory fitness might provide a reasonable explanation for effects of tooth-related alterations seen on cardiometabolic diseases, evidence is currently limited. Thus, we investigated the association between clinically assessed periodontitis and cardiopulmonary exercise testing (CPET). Data from 2 independent cross-sectional population-based studies (5-y follow-up of the Study of Health in Pomerania [SHIP-1; N = 1,639] and SHIP-Trend-0 [ N = 2,439]) were analyzed. Participants received a half-mouth periodontal examination, and teeth were counted. CPET was based on symptom limited-exercise tests on a bicycle ergometer. Associations of periodontitis parameters with CPET parameters were analyzed by confounder-adjusted multivariable linear regression. In the total sample, mean pocket probing depth (PPD), mean clinical attachment levels, and number of teeth were consistently associated with peak oxygen uptake (peakVO2) and exercise duration in both studies, even after restriction to cardiorespiratory healthy participants. Statistically significant associations with oxygen uptake at anaerobic threshold (VO2@AT), slope of the efficiency of ventilation in removing carbon dioxide, and peak oxygen pulse (VÉ/VCO2 slope) occurred. Further, interactions with age were identified, such that mainly older individuals with higher levels of periodontal disease severity were associated with lower peakVO2. Restricted to never smokers, associations with mean clinical attachment levels and the number of teeth mostly diminished, while associations of mean PPD with peakVO2, VO2@AT, VÉ/VCO2 slope, and exercise duration in SHIP-1 and SHIP-Trend-0 were confirmed. In SHIP-1, mean peakVO2 was 1,895 mL/min in participants with a mean PPD of 1.6 mm and 1,809 mL/min in participants with a mean PPD of 3.7 mm. To conclude, only mean PPD reflecting current disease severity was consistently linked to cardiorespiratory fitness in 2 cross-sectional samples of the general population. If confirmed in well-designed large-scale longitudinal studies, the association between periodontitis and cardiorespiratory fitness might provide a biologically plausible mechanism linking periodontitis with cardiometabolic diseases.

Download Full-text

10.5. The Sample Mean of a Vector Process

Time Series Analysis ◽

10.1515/9780691218632-087 ◽

1994 ◽

pp. 279-285

Keyword(s):

Sample Mean ◽

Vector Process

Download Full-text

Biochemical Validation of a Self-Administered Food Frequency Questionnaire to Assess Diet Using Carotenoids and Vitamins E and D in Male Adolescents in Spain

Antioxidants ◽

10.3390/antiox10050750 ◽

2021 ◽

Vol 10 (5) ◽

pp. 750

Author(s):

Leyre Notario-Barandiaran ◽

Eva-María Navarrete-Muñoz ◽

Desirée Valera-Gran ◽

Elena Hernández-Álvarez ◽

Encarnación Donoso-Navarro ◽

...

Keyword(s):

Vitamin E ◽

Food Frequency Questionnaire ◽

Vegetable Intake ◽

Correlation Coefficients ◽

Fruit And Vegetable Intake ◽

Fruit And Vegetable ◽

Sample Mean ◽

Food Frequency ◽

Male Adolescents ◽

Β Carotene

Reliable tools to evaluate diet are needed, particularly in life periods such as adolescence in which a rapid rate of growth and development occurs. We assessed the biochemical validity of a self-administered food frequency questionnaire (FFQ) in a sample of Spanish male adolescents using carotenoids and vitamin E and D data. We analyzed data from 122 male adolescents aged 15–17 years of the INMA-Granada birth cohort study. Adolescents answered a 104-item FFQ and provided a non-fasting blood sample. Mean daily nutrient intakes and serum concentration were estimated for main carotenoids (lutein-zeaxanthin, β-cryptoxanthin, lycopene, α-carotene and β-carotene), vitamins E and D and also for fruit and vegetable intake. Pearson correlation coefficients (r) and the percentage of agreement (same or adjacent quintiles) between serum vitamin concentrations and energy-adjusted intakes were estimated. Statistically significant correlation coefficients were observed for the total carotenoids (r = 0.40) and specific carotenoids, with the highest correlation observed for lutein–zeaxanthin (r = 0.42) and the lowest for β-carotene (0.23). The correlation coefficient between fruit and vegetable intake and serum carotenoids was 0.29 (higher for vegetable intake, r = 0.33 than for fruit intake, r = 0.19). Low correlations were observed for vitamin E and D. The average percentage of agreement for carotenoids was 55.8%, and lower for vitamin E and D (50% and 41%, respectively). The FFQ may be an acceptable tool for dietary assessment among male adolescents in Spain.

Download Full-text

Re-identification Attack to Privacy-Preserving Data Analysis with Noisy Sample-Mean

Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining ◽

10.1145/3394486.3403148 ◽

2020 ◽

Author(s):

Du Su ◽

Hieu Tri Huynh ◽

Ziao Chen ◽

Yi Lu ◽

Wenmiao Lu

Keyword(s):

Data Analysis ◽

Privacy Preserving ◽

Sample Mean

Download Full-text

Identifying individuals with high risk of Alzheimer’s disease using polygenic risk scores

Nature Communications ◽

10.1038/s41467-021-24082-z ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Ganna Leonenko ◽

Emily Baker ◽

Joshua Stevenson-Hoare ◽

Annerieke Sierksma ◽

Mark Fiers ◽

...

Keyword(s):

High Risk ◽

Risk Score ◽

Genetic Risk ◽

Prediction Accuracy ◽

Genetic Risk Score ◽

Low Risk ◽

Risk Scores ◽

Sample Mean ◽

Polygenic Risk ◽

Reliable Identification

AbstractPolygenic Risk Scores (PRS) for AD offer unique possibilities for reliable identification of individuals at high and low risk of AD. However, there is little agreement in the field as to what approach should be used for genetic risk score calculations, how to model the effect of APOE, what the optimal p-value threshold (pT) for SNP selection is and how to compare scores between studies and methods. We show that the best prediction accuracy is achieved with a model with two predictors (APOE and PRS excluding APOE region) with pT<0.1 for SNP selection. Prediction accuracy in a sample across different PRS approaches is similar, but individuals’ scores and their associated ranking differ. We show that standardising PRS against the population mean, as opposed to the sample mean, makes the individuals’ scores comparable between studies. Our work highlights the best strategies for polygenic profiling when assessing individuals for AD risk.

Download Full-text