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The unprecedented impact and modeling efforts associated with the 2014–2015 Ebola epidemic in West Africa provides a unique opportunity to document the performances and caveats of forecasting approaches used in near-real time for generating evidence and to guide policy. A number of international academic groups have developed and parameterized mathematical models of disease spread to forecast the trajectory of the outbreak. These modeling efforts often relied on limited epidemiological data to derive key transmission and severity parameters, which are needed to calibrate mechanistic models. Here, we provide a perspective on some of the challenges and lessons drawn from these efforts, focusing on (1) data availability and accuracy of early forecasts; (2) the ability of different models to capture the profile of early growth dynamics in local outbreaks and the importance of reactive behavior changes and case clustering; (3) challenges in forecasting the long-term epidemic impact very early in the outbreak; and (4) ways to move forward. We conclude that rapid availability of aggregated population-level data and detailed information on a subset of transmission chains is crucial to characterize transmission patterns, while ensemble-forecasting approaches could limit the uncertainty of any individual model. We believe that coordinated forecasting efforts, combined with rapid dissemination of disease predictions and underlying epidemiological data in shared online platforms, will be critical in optimizing the response to current and future infectious disease emergencies.

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions. Significance Growth and division of individual cells are the fundamental events underlying many biological processes, including the development of organisms, the growth of tumors, and pathogen–host interactions. Quantitative studies of bacteria can provide insights into single-cell growth and division but are challenging owing to the intrinsic noise in these processes. Now, by using a unique combination of measurement and analysis technologies, together with mathematical modeling, we discover quantitative features that are conserved across physiological conditions. These universal behaviors reflect the physical principle that a single timescale governs noisy bacterial growth and division despite the complexity of underlying molecular mechanisms.

A new sigmoid growth equation is presented for curve-fitting, analysis and simulation of growth curves. Like the logistic growth equation, it increases monotonically, with both upper and lower asymptotes. Like the Richards growth equation, it can have its maximum slope at any value between its minimum and maximum. The new sigmoid equation is unique because it always tends towards exponential growth at small sizes or low densities, unlike the Richards equation, which only has this characteristic in part of its range. The new sigmoid equation is therefore uniquely suitable for circumstances in which growth at small sizes or low densities is expected to be approximately exponential, and the maximum slope of the growth curve can be at any value. Eleven widely different sigmoid curves were constructed with an exponential form at low values, using an independent algorithm. Sets of 100 variations of sequences of 20 points along each curve were created by adding random errors. In general, the new sigmoid equation fitted the sequences of points as closely as the original curves that they were generated from. The new sigmoid equation always gave closer fits and more accurate estimates of the characteristics of the 11 original sigmoid curves than the Richards equation. The Richards equation could not estimate the maximum intrinsic rate of increase (relative growth rate) of several of the curves. Both equations tended to estimate that points of inflexion were closer to half the maximum size than was actually the case; the Richards equation underestimated asymmetry by more than the new sigmoid equation. When the two equations were compared by fitting to the example dataset that was used in the original presentation of the Richards growth equation, both equations gave good fits. The Richards equation is sometimes suitable for growth processes that may or may not be close to exponential during initial growth. The new sigmoid is more suitable when initial growth is believed to be generally close to exponential, when estimates of maximum relative growth rate are required, or for generic growth simulations.

The most effective way to stem the spread of a pandemic such as coronavirus disease 2019 (COVID-19) is social distancing, but the introduction of such measures is hampered by the fact that a sizeable part of the population fails to see their need. Three studies conducted during the mass spreading of the virus in the United States toward the end of March 2020 show that this results partially from people’s misperception of the virus’s exponential growth in linear terms and that overcoming this bias increases support for social distancing. Study 1 shows that American participants mistakenly perceive the virus’s exponential growth in linear terms (conservatives more so than liberals). Studies 2 and 3 show that instructing people to avoid the exponential growth bias significantly increases perceptions of the virus’s growth and thereby increases support for social distancing. Together, these results show the importance of statistical literacy to recruit support for fighting pandemics such as the coronavirus.

Breast cancer is one of the leading causes for cancer related deaths in women, and early detection is extremely important to improve survival rates. Currently, x-ray mammogram is the only modality for mass screening of asymptomatic women. However, it has decreased sensitivity in radiographically dense breasts, which is also associated with a higher risk for breast cancer. Photoacoustic (PA) imaging is an emerging modality that enables deep tissue imaging of optical contrast at ultrasonically defined spatial resolution, which is much higher than that can be achieved in purely optical imaging modalities. Because of high optical absorption from hemoglobin molecules, PA imaging can map out hemo distribution and dynamics in breast tissue and identify malignant lesions based on tumor associated angiogenesis and hypoxia. We review various PA breast imaging systems proposed over the past few years and summarize the PA features of breast cancer identified in these systems.

In this work, we consider a coupled nonlinear viscoelastic Kirchhoff equations with degenerate damping, dispersion and source terms. Under suitable hypothesis, we will prove that when the initial data are large enough (in the energy point of view), the energy grows exponentially and thus so the$ L^{2(p+2)} $ -norm.

Abstract In this paper, we study the existence of normalized ground state solutions to the following biharmonic equation: Δ 2 u = λ u + μ | u | q − 2 u + f ( u ) in  R 4 , ∫ R 4 | u | 2 d x = a 2 ,$$ \\left \\{ \\textstyle\\begin{array}{l} \\Delta ^{2} u = \\lambda u+ \\mu |u|^{q-2}u +f(u) \\quad \\text{in } \\mathbb{R}^{4}, \\\ \\displaystyle ınt _{\\mathbb{R}^{4}} |u|^{2} \\: dx = a^{2}, \\end{array}\\displaystyle \\right . $$where a , μ > 0$a,\\mu > 0 $, q > 4$q>4$, λ ∈ R$\\lambda \\in \\mathbb{R}$is an unknown parameter that appears as a Lagrange multiplier, and f is a nonlinear function that possesses critical exponential growth motivated by the Adams inequality. To prove the existence of solutions, we construct an augmented functional that possesses a mountain-pass-type geometry.

The growth rate of scientific publication has been studied from 1907 to 2007 using available data from a number of literature databases, including Science Citation Index (SCI) and Social Sciences Citation Index (SSCI). Traditional scientific publishing, that is publication in peer-reviewed journals, is still increasing although there are big differences between fields. There are no indications that the growth rate has decreased in the last 50 years. At the same time publication using new channels, for example conference proceedings, open archives and home pages, is growing fast. The growth rate for SCI up to 2007 is smaller than for comparable databases. This means that SCI was covering a decreasing part of the traditional scientific literature. There are also clear indications that the coverage by SCI is especially low in some of the scientific areas with the highest growth rate, including computer science and engineering sciences. The role of conference proceedings, open access archives and publications published on the net is increasing, especially in scientific fields with high growth rates, but this has only partially been reflected in the databases. The new publication channels challenge the use of the big databases in measurements of scientific productivity or output and of the growth rate of science. Because of the declining coverage and this challenge it is problematic that SCI has been used and is used as the dominant source for science indicators based on publication and citation numbers. The limited data available for social sciences show that the growth rate in SSCI was remarkably low and indicate that the coverage by SSCI was declining over time. National Science Indicators from Thomson Reuters is based solely on SCI, SSCI and Arts and Humanities Citation Index (AHCI). Therefore the declining coverage of the citation databases problematizes the use of this source.

In the present paper, we study the existence of solutions for the following classes of elliptic problems where Ω ⊂ R 2 is a smooth bounded domain and where V ∈ C 0 ( R 2 ) is periodic in Z 2 with 0 ∉ σ ( - Δ + V ) . In the both problems above, f is a continuous function of the form f ( t ) = h ( t ) e α 0 | t | τ , t ∈ R for some α 0 > 0 and τ ≥ 2 and h satisfying some technical conditions. By using variational methods, we show that problems ( P ) and ( P V ) have a nontrivial solution for different types of α 0 > 0 and τ ≥ 2 .

Autocatalytic chemical reaction networks can collectively replicate or maintain their constituents despite degradation reactions only above a certain threshold, which we refer to as the decay threshold. When the chemical network has a Jacobian matrix with the Metzler property, we leverage analytical methods developed for Markov processes to show that the decay threshold can be calculated by solving a linear problem, instead of the standard eigenvalue problem. We explore how this decay threshold depends on the network parameters, such as its size, the directionality of the reactions (reversible or irreversible), and its connectivity, then we deduce design principles from this that might be relevant to research on the Origin of Life.