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The separation of measured arterial pressure into a reservoir pressure and an excess pressure was introduced nearly 20 years ago as an heuristic hypothesis. We demonstrate that a two-time asymptotic analysis of the 1-D conservation equations in each artery coupled with the separation of the smaller arteries into inviscid and resistance arteries, based on their resistance coefficients, results, for the first time, in a formal derivation of the reservoir pressure. The key to the two-time analysis is the existence of a fast time associated with the propagation of waves through the arteries and a slow time associated with the convective velocity of the blood. The ratio between these two time scales is given by the Mach number; the ratio of a characteristic convective velocity to a characteristic wave speed. If the Mach number is small, a formal asymptotic analysis can be carried out which is accurate to the order of the square of the Mach number. The slow-time conservation equations involve a resistance coefficient that models the effect of viscosity on the convective velocity. On the basis of this resistance coefficient, we separate the arteries into the larger inviscid arteries where the coefficient is negligible and the smaller resistance arteries where it it is not negligible. The slow time pressure in the inviscid arteries is shown to be spatially uniform but varying in time. We define this pressure as the reservoir pressure. Dynamic analysis using mass conservation in the inviscid arteries shows that the reservoir pressure accounts for the storage of potential energy by the distension of the elastic inviscid arteries during early systole and its release during late systole and diastole. This analysis thus provides a formal derivation of the reservoir pressure and its physical meaning.

The 1-D theory of flow in the arteries yields an equation for the wave speed in terms of the density of blood and the distensibility of the vessel. By means of this equation there is a duality between the equation for the wave speed and the tube law describing the area of the vessel as a function of pressure. We explore this duality for the equations for wave speed and tube laws that are most commonly used in theoretical arterial hemodynamics. We see that there are qualitative differences between these laws and the experimental data on wave speed in canine arteries measured by Anliker and his colleagues 50 years ago. We suggest an empirical equation for wave speed (and its dual tube law) that fits the experimental data as well as the common expectation that arteries become stiffer as the pressure increases. We conclude with a cautionary historical tale about the differences between the theoretical predictions and the experimental measurements of the speed of sound in air that persisted for more than 200 years., Comment: 14 pages, 4 figures

A new Pew Research Center analysis of Census Bureau data finds that the "post-Millennial" generation is already the most racially and ethnically diverse generation, as a bare majority of 6- to 21-year-olds (52%) are non-Hispanic whites. And while most are still pursuing their K-12 education, the oldest post-Millennials are enrolling in college at a significantly higher rate than Millennials were at a comparable age. The parents of post-Millennials are more well educated than the parents of Millennials and those of previous generations, and this pattern most likely contributes to the relative affluence of the households in which post-Millennials live. The changing patterns in educational attainment are driven in part by the shifting origins of young Hispanics. Post-Millennial Hispanics are less likely than Millennial Hispanics to be immigrants -- 12% of post-Millennial Hispanics were born outside the U.S., compared with 24% of Millennial Hispanics in 2002. Previous research has shown that second-generation Hispanic youth tend to go further in school than foreign-born Hispanic youth. That is borne out in this analysis, as 61% of second-generation Hispanics ages 18 to 20 who were no longer in high school were enrolled in college in 2017, compared with 40% of their foreign-born counterparts. The oldest post-Millennials are less likely than their predecessors to be in the labor force. Only 58% of today's 18- to 21-year-olds worked in the prior calendar year; this compares with 72% of Millennial 18- to 21-year-olds in 2002. And employment among post-Millennials is less likely to be full-time compared with earlier generations. The living arrangements of post-Millennial children are similar to those of Millennials when they were growing up. About two-thirds (65%) of today's 6- to 17-year-olds live with two married parents, slightly lower than the share (68%) of Millennials in that age range who lived in this type of household in 2002. The median household income of post-Millennials exceeds that of earlier generations when they were young. The typical post-Millennial in 2018 lives in a household with an annual income of roughly $63,700 after adjusting for household size. That is slightly higher than the income for the typical household in which Millennials grew up. The generation labeled "post-Millennials" in this report -- referred to elsewhere as Generation Z, the iGen, or Homelanders -- includes those born after 1996. Pew Research Center uses the label "post-Millennials" as a placeholder until more consensus emerges as to their name. For purposes of this analysis, the post-Millennial generation spans 16 years, the same number of years as the Millennial generation (now ages 22 to 37). This report compares the post-Millennials in 2018 with earlier generations when they were ages 6 to 21, examining their demographic characteristics as well as those of their parents and households.

This report is based on findings from a pair of Pew Research Center surveys conducted in spring 2011. One is a telephone survey of a nationally representative sample of 2,142 adults ages 18 and older. The other is an online survey, done in association with the Chronicle of Higher Education, among the presidents of 1,055 two-year and four-year private, public, and for-profit colleges and universities. Here is a summary of key findings: (1) The Value of Online Learning. The public and college presidents differ over the educational value of online courses. Only 29% of the public says online courses offer an equal value compared with courses taken in a classroom. Half (51%) of the college presidents surveyed say online courses provide the same value; (2) The Prevalence of Online Courses. More than three-quarters of college presidents (77%) report that their institutions now offer online courses. These courses are more prevalent in some sectors of higher education than in others. While 89% of four-year public colleges and universities offer online classes, just 60% of four-year private schools offer them; (3) Online Students. Roughly one-in-four college graduates (23%) report that they have taken a class online. However, the share doubles to 46% among those who have graduated in the past ten years. Among all adults who have taken a class online, 39% say the format's educational value is equal to that of a course taken in a classroom; (4) The Future of Online Learning. College presidents predict substantial growth in online learning: 15% say most of their current undergraduate students have taken a class online, and 50% predict that 10 years from now most of their students will take classes online; (5) Digital Textbooks. Nearly two-thirds of college presidents (62%) anticipate that 10 years from now, more than half of the textbooks used by their undergraduate students will be entirely digital; (6) The Internet and Plagiarism. Most college presidents (55%) say that plagiarism in students' papers has increased over the past 10 years. Among those who have seen an increase in plagiarism, 89% say computers and the internet have played a major role; (7) Do Laptops and Smartphones Belong in the Classroom? More than half of recent college graduates (57%) say when they were in college they used a laptop, smartphone or tablet computer in class at least sometime. Most colleges and universities do not have institutional guidelines in place for the use of these devices in class. Some 41% of college presidents say students are allowed to use laptops or other portable devices during class; at 56% of colleges and universities it is up to the individual instructors. Only 2% of presidents say the use of these devices is prohibited; (8) College Presidents and Technology. The leaders of the nation's colleges and universities are a tech-savvy group. Nearly nine-in-ten (87%) use a smartphone daily, 83% use a desktop computer and 65% use a laptop. And they are ahead of the curve on some of the newer digital technologies: Fully half (49%) use a tablet computer such as an iPad at least occasionally, and 42% use an e-reader such as a Kindle or Nook; and (9) College Presidents and Social Networking. Roughly one-third of college presidents (32%) report that they use Facebook weekly or more often; 18% say they use Twitter at least occasionally. Appended are: (1) Survey Methodology; and (2) Topline Survey Results. (Contains 9 footnotes.)

We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this low-dimensional, nonlinear model exhibits bistability between a low and a high cholesterol state. A sensitivity analysis indicates that the intracellular concentration of cholesterol is robust to parametric variations while the plasma cholesterol can vary widely. We show how the dynamical response to time-dependent inputs can be used to diagnose the state of the system. We also establish the connection between parameters in the system and medical and genetic conditions., Comment: To appear in Bulletin of Mathematical Biology