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Before Palm Pilots and iPods, PCs and laptops, the term \"computer\" referred to the people who did scientific calculations by hand. These workers were neither calculating geniuses nor idiot savants but knowledgeable people who, in other circumstances, might have become scientists in their own right. When Computers Were Human represents the first in-depth account of this little-known, 200-year epoch in the history of science and technology. Beginning with the story of his own grandmother, who was trained as a human computer, David Alan Grier provides a poignant introduction to the wider world of women and men who did the hard computational labor of science. His grandmother's casual remark, \"I wish I'd used my calculus,\" hinted at a career deferred and an education forgotten, a secret life unappreciated; like many highly educated women of her generation, she studied to become a human computer because nothing else would offer her a place in the scientific world. The book begins with the return of Halley's comet in 1758 and the effort of three French astronomers to compute its orbit. It ends four cycles later, with a UNIVAC electronic computer projecting the 1986 orbit. In between, Grier tells us about the surveyors of the French Revolution, describes the calculating machines of Charles Babbage, and guides the reader through the Great Depression to marvel at the giant computing room of the Works Progress Administration. When Computers Were Human is the sad but lyrical story of workers who gladly did the hard labor of research calculation in the hope that they might be part of the scientific community. In the end, they were rewarded by a new electronic machine that took the place and the name of those who were, once, the computers.

Many competing criteria are under consideration for prioritizing COVID-19 vaccination. Two criteria based on age are demographic: lives saved and years of future life saved. Vaccinating the very old against COVID-19 saves the most lives, but, since older age is accompanied by falling life expectancy, it is widely supposed that these two goals are in conflict. We show this to be mistaken. The age patterns of COVID-19 mortality are such that vaccinating the oldest first saves the most lives and, surprisingly, also maximizes years of remaining life expectancy. We demonstrate this relationship empirically in the United States, Germany, and South Korea and with mathematical analysis of life tables. Our age-risk results, under usual conditions, also apply to health risks.

The author investigates the influence of the dominant culture characterizing mathematics education—which she terms the culture of exclusion—on efforts to teach for equity. Analyzing a year of observations in an urban high school mathematics department, she found that this culture structured everyday instruction even for teachers who expressed a strong commitment to equity and who participated in ongoing equity-oriented professional development.

Theoretical and numerical studies of fractional conformable stochastic integrodifferential equations are introduced in this study. Herein, to emphasize the solution’s existence, we provide proof based on Picard iterations and Arzela−Ascoli’s theorem, whilst the proof of the uniqueness mainly depends on the famous Gronwall’s inequality. Also, we introduce the basic concepts related to shifted Legendre orthogonal polynomials which are utilized to be the basic functions of the spectral collocation algorithm to obtain approximate solutions for the mentioned equations that are not easy to be solved analytically. The substantial idea of the proposed algorithm is to transform such equations into a system containing a finite number of algebraic equations that can be treated using familiar numerical methods. For computational aims, we make a suitable discretization to evaluate the values of the Brownian motion, the noise term considered in our problem, at specific points. In addition, the feasibility and efficiency of the proposed algorithm are proved through convergence analysis and mathematical examples. To exhibit the mathematical simulation, graphs and tables are lucidly shown. Obviously, the physical interpretation of the displayed graphics accurately describes the behavior of the solutions. Despite the simplicity of the presented technique, it produces accurate and reasonable results as notarized in the conclusion section.

Air–water interfacial adsorption represents a major source of retention for many per‐ and poly‐fluoroalkyl substances (PFAS). Therefore, transient hydrological fluxes that dynamically change the amount of air–water interfaces are expected to strongly influence PFAS retention in their source zones in the vadose zone. We employ mathematical modeling to study how seasonal groundwater table (GWT) fluctuations affect PFAS source‐zone leaching. The results suggest that, by periodically collapsing air–water interfaces, seasonal GWT fluctuations can lead to strong temporal variations in groundwater concentration and significantly enhance PFAS leaching in the vadose zone. The enhanced leaching is more pronounced for longer‐chain PFAS, coarser‐textured porous media, drier climates, and greater amplitudes of fluctuations. GWT fluctuations and lateral migration above the GWT introduce a downgradient persistent secondary source zone for longer‐chain PFAS. However, the enhanced leaching and the secondary source zone are greatly reduced when subsurface heterogeneity is present. In highly heterogeneous source zones, GWT fluctuations may even lead to overall slower leaching due to lateral flow (in the GWT fluctuation zone and above the GWT) moving PFAS into local regions with greater retention capacities. Model simplification analyses suggest that the enhanced source‐zone leaching due to GWT fluctuations may be approximated using a static but shallower GWT. Additionally, while vertical 1D models underestimate source‐zone leaching due to not representing lateral migration, they can be revised to account for lateral migration and provide lower‐ and upper‐bound estimates of PFAS source‐zone leaching under GWT fluctuations. Overall, our study suggests that representing GWT fluctuations is critical for quantifying source‐zone leaching of PFAS, especially the more interfacially active longer‐chain compounds. Plain Language Summary Per‐ and poly‐fluoroalkyl substances (PFAS) are contaminants that are now widespread in the environment. Many PFAS are interfacially active and tend to accumulate at solid surfaces and air–water interfaces. A growing body of field data at PFAS‐contaminated sites has shown that significant amounts of PFAS have accumulated in soils, posing great risks to the groundwater underneath. Because the accumulation at air–water interfaces is a primary mechanism that retains PFAS in soils, any transient water fluxes that dynamically collapse air–water interfaces may accelerate the downward movement of PFAS. One important type of temporal change to air–water interfaces can be caused by the fluctuation of groundwater, such as seasonal groundwater table fluctuations (GWT). We use mathematical models to study the impact of GWT on enhancing the downward movement of PFAS from soils to groundwater. Our analyses suggest that seasonal GWT fluctuations can significantly enhance PFAS downward movement by periodically collapsing air–water interfaces in soils. They also lead to seasonal variations in groundwater PFAS concentrations that may have important implications for groundwater sampling and risk assessment. Overall, representing groundwater table fluctuations is critical for quantifying groundwater contamination risks of PFAS, especially the more interfacially active compounds with longer carbon chains. Key Points Groundwater table (GWT) fluctuations enhance source‐zone poly‐fluoroalkyl substances (PFAS) leaching, but the enhanced leaching is reduced in heterogeneous source zones GWT fluctuations and lateral migration above the GWT lead to a downgradient persistent secondary source zone for longer‐chain PFAS Develop simplified modeling strategies to estimate the lower‐ and upper‐bounds of PFAS source‐zone leaching under GWT fluctuations

Abstract   Calculating and comparing survival rate indicators across different population groups is essential for identifying disparities in treatment outcomes and understanding their underlying causes. Continuous monitoring in this regard is also crucial. In Japan, comparisons of net survival rates are often conducted at the prefectural level. The calculation of net survival rates requires life tables for the general population that share similar characteristics with the cancer patient cohort. However, in current practice, a common national life table is used across all prefectures in Japan, which may introduce bias in estimating true prefecture-specific net survival rates. To address this issue, the present study developed prefecture-specific life tables using a mathematical modeling approach that assumes a Poisson regression model for mortality counts. This method was designed to overcome the instability of estimates caused by limited data in certain regions. Our evaluation showed that the life tables constructed using this model not only accurately reflected average life expectancy across prefectures, but also reduced variability compared to conventional methods. These findings suggest that the proposed approach can be effectively applied to calculate net survival rates for smaller geographic units or populations stratified by socioeconomic status. It thus holds promise for enabling more flexible and context-sensitive cancer control strategies. Key messages • Using a Poisson model, we developed stable, prefecture-specific life tables that improve the accuracy of net survival estimates over a single national life table. • This method supports region-specific and fair cancer control by enabling survival analysis that reflects local and socioeconomic differences.

When students are faced with complicated w, primary school students need to use methods they can follow. The purpose of this research is to use table guides method and check the video-aided learning to solve the mathematical word problem. The method used in this study is a quasi-experimental method with the subject of research on third-grade students in elementary school. The research instruments used are tables guides and checks and flow tables. Based on the results of the research indicates that this method allows students to be able to solve mathematical word problem more easily. The method of tables and checks with the help of video learning can be used like a math game so that students are actively involved in learning mathematics.

In this paper, an algebraic construction of regular QC‐LDPC codes by using the modular multiplication table mod P and Golomb rulers are proposed. It is proved that the proposed QC‐LDPC codes based on a Golomb ruler of length L have girth at least 8 if P>2L $P>2L$ . The error performance of the proposed QC‐LDPC codes are simulated with various Golomb rulers. The proposed codes of length around 300 from the optimal 6‐mark Golomb ruler have an additional coding gain of at least 0.1 dB over 5G NR LDPC codes, 0.5 dB over those given earlier by others, both at FER 10−3. Some non‐trivial techniques to increase the length of a given Golomb ruler with and without an additional mark for improving the performance of the codes from Golomb rulers up to 0.7 dB are also found.

In the remarkable paper Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, Mats Boij and Jonas Söderberg conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring is a positive linear combination of Betti tables of modules with pure resolutions. We prove a strengthened form of their conjectures. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fan naturally associated to the Young lattice. With the same tools we show that the cohomology table of any vector bundle on projective space is a positive rational linear combination of the cohomology tables of what we call supernatural vector bundles. Using this result we give new bounds on the slope of a vector bundle in terms of its cohomology.

It has been difficult to open up the black box of knowledge production. We use unique international data on the publications, citations, and affiliations of mathematicians to examine the impact of a large, post-1992 influx of Soviet mathematicians on the productivity of their U.S. counterparts. We find a negative productivity effect on those mathematicians whose research overlapped with that of the Soviets. We also document an increased mobility rate (to lower quality institutions and out of active publishing) and a reduced likelihood of producing \"home run\" papers. Although the total product of the preexisting American mathematicians shrank, the Soviet contribution to American mathematics filled in the gap. However, there is no evidence that the Soviets greatly increased the size of the \"mathematics pie.\" Finally, we find that there are significant international differences in the productivity effects of the collapse of the Soviet Union, and these international differences can be explained by both differences in the size of the émigré flow into the various countries and in how connected each country is to the global market for mathematical publications.