The prevalence of many urban phenomena changes systematically with population size 1 . We propose a theory that unifies models of economic complexity 2, 3 and cultural evolution 10 to derive urban scaling. The theory accounts for the difference in scaling exponents and average prevalence across phenomena, as well as the difference in the variance within phenomena across cities of similar size. The central ideas are that a number of necessary complementary factors must be simultaneously present for a phenomenon to occur, and that the diversity of factors is logarithmically related to population size. The model reveals that phenomena that require more factors will be less prevalent, scale more superlinearly and show larger variance across cities of similar size. The theory applies to data on education, employment, innovation, disease and crime, and it entails the ability to predict the prevalence of a phenomenon across cities, given information about the prevalence in a single city.Scaling is ubiquitous across many phenomena 5 , including physical 6 and biological 7 systems, plus a wide range of human 8,9 and urban activities 1,10 . Figure 1 shows, for US Metropolitan Statistical Areas, ten different phenomena classified in five broad types: employment, innovation, crime, educational attainment, and infectious disease. We observe scaling in the sense that the counts of people in each phenomenon scale as a power of population size. This relation takes the form E{Y |N } = Y 0 N β , where E{·|N } is the expectation operator conditional on population size N , Y is the random variable representing the output of a phenomenon in a city, Y 0 is a measure of general prevalence of the activity in the country, and β is the scaling exponent, i.e., the relative rate of change of Y with respect to N . From Fig. 1 we can also observe notable differences in the average prevalence, the slopes of the regression lines and the variance across all ten phenomena. Hence, we seek to explain four empirical facts: Prevalence follows a power-law scaling with population size, different phenomena have different general prevalence, different scaling exponents, and variance for cities of similar size. Remarkably, these observations appear to be pervasive across phenomena as we find them to be present in more than forty different urban activities. In this paper we propose a mechanism to explain them simultaneously.Scaling laws are important in science because they constrain the development of new theories: any theory that attempts to explain a phenomenon should be compatible with the empirical 3 scaling relationships that the data exhibit. A number of mechanisms have been proposed to explain the origins of scaling. Most theories are based on a network description of the underlying phenomena and derive the scaling properties from the way the number of links grow with the number of nodes in the network, under some energy or budget constraints [11][12][13][15][16][17] . Other scaling relationships are the result of how lines relate to surfaces, and...

Background The rapidly evolving 2014 Ebola virus disease (EVD) outbreak in West Africa is the largest documented in history, both in terms of the number of people infected and in the geographic spread. The high morbidity and mortality have inspired response strategies to the outbreak at the individual, regional, and national levels. Methods to provide real-time assessment of changing transmission dynamics are critical to the understanding of how these adaptive intervention measures have affected the spread of the outbreak. Methods In this analysis, we use the time series of EVD cases in Guinea, Sierra Leone, and Liberia up to September 8, 2014, and employ novel methodology to estimate how the rate of exponential rise of new cases has changed over the outbreak using piecewise fits of exponential curves to the outbreak data. Results We find that for Liberia and Guinea, the effective reproduction number rose, rather than fell, around the time that the outbreak spread to densely populated cities, and enforced quarantine was imposed on several regions in the countries; this may indicate that enforced quarantine may not be an effective control measure. Conclusions If effective control measures are not put in place, and the current rate of exponential rise of new cases continues, we predict 4400 new Ebola cases in West Africa during the last half of the month of September, with an upper 95% confidence level of 6800 new cases.

Introductionnab-Paclitaxel plus gemcitabine (nab-P + G) and FOLFIRINOX (FFX) are among the most common first-line (1L) therapies for metastatic adenocarcinoma of the pancreas (MPAC), but real-world data on their comparative effectiveness are limited.MethodsThis retrospective cohort study compared the efficacy and safety of 1L nab-P + G versus FFX, overall and under specific treatment sequences. Medical records were reviewed by 215 US physicians who provided information on MPAC patients who initiated 1L therapy with nab-P + G or FFX between April 1, 2015 and December 31, 2015. Study outcomes were overall survival (OS) and tolerability. OS was compared using Kaplan–Meier curves and adjusted Cox proportional hazards models.ResultsIn total, 654 medical records were reviewed, including those of 337 and 317 patients initiated on nab-P + G and FFX as 1L MPAC therapy, respectively. nab-P + G-initiated patients were older, less likely to have ECOG ≤ 1, and had more comorbidities than FFX-initiated patients. Median OS (mOS) was 12.1 and 13.8 months for nab-P + G- and FFX-initiated patients, respectively (HR = 0.99, P = 0.96). Among patients with ECOG ≤ 1, mOS was 14.1 and 13.7 months, respectively (HR = 1.00, P = 0.99). Among patients with 1L nab-P + G and FFX, 36.1% and 41.3% received 2L therapy and experienced mOS of 16.3 and 16.6 months, respectively (HR = 1.04, P = 0.76). The rates of diarrhea, fatigue, mucositis, and nausea and vomiting were significantly higher in the FFX than nab-P + G cohort.ConclusionThe real-world survival was similar between patients receiving 1L nab-P + G or FFX both overall and among patients who received active 2L treatments. In addition, nab-P + G was associated with significantly lower rates of common AEs compared with FFX.FundingCelgene.Electronic supplementary materialThe online version of this article (10.1007/s12325-018-0784-z) contains supplementary material, which is available to authorized users.

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