Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

We prove two conjectures from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the expected number of critical points of random holomorphic sections of a positive line bundle. We show that, on average, the critical points of minimal Morse index are the most plentiful for holomorphic sections of {\mathcal O}(N) \to \CP^m and, in an asymptotic sense, for those of line bundles over general K\"ahler manifolds. We calculate the expected number of these critical points for the respective cases and use these to obtain growth rates and asymptotic bounds for the total expected number of critical points in these cases. This line of research was motivated by landscape problems in string theory and spin glasses.Comment: 14 pages, corrected typo

Correction for Johansson et al., An open challenge to advance probabilistic forecasting for dengue epidemics.

Correction for “An open challenge to advance probabilistic forecasting for dengue epidemics,” by Michael A. Johansson, Karyn M. Apfeldorf, Scott Dobson, Jason Devita, Anna L. Buczak, Benjamin Baugher, Linda J. Moniz, Thomas Bagley, Steven M. Babin, Erhan Guven, Teresa K. Yamana, Jeffrey Shaman, Terry Moschou, Nick Lothian, Aaron Lane, Grant Osborne, Gao Jiang, Logan C. Brooks, David C. Farrow, Sangwon Hyun, Ryan J. Tibshirani, Roni Rosenfeld, Justin Lessler, Nicholas G. Reich, Derek A. T. Cummings, Stephen A. Lauer, Sean M. Moore, Hannah E. Clapham, Rachel Lowe, Trevor C. Bailey, Markel García-Díez, Marilia Sá Carvalho, Xavier Rodó, Tridip Sardar, Richard Paul, Evan L. Ray, Krzysztof Sakrejda, Alexandria C. Brown, Xi Meng, Osonde Osoba, Raffaele Vardavas, David Manheim, Melinda Moore, Dhananjai M. Rao, Travis C. Porco, Sarah Ackley, Fengchen Liu, Lee Worden, Matteo Convertino, Yang Liu, Abraham Reddy, Eloy Ortiz, Jorge Rivero, Humberto Brito, Alicia Juarrero, Leah R. Johnson, Robert B. Gramacy, Jeremy M. Cohen, Erin A. Mordecai, Courtney C. Murdock, Jason R. Rohr, Sadie J. Ryan, Anna M. Stewart-Ibarra, Daniel P. Weikel, Antarpreet Jutla, Rakibul Khan, Marissa Poultney, Rita R. Colwell, Brenda Rivera-García, Christopher M. Barker, Jesse E. Bell, Matthew Biggerstaff, David Swerdlow, Luis Mier-y-Teran-Romero, Brett M. Forshey, Juli Trtanj, Jason Asher, Matt Clay, Harold S. Margolis, Andrew M. Hebbeler, Dylan George, and Jean-Paul Chretien, which was first published November 11, 2019; 10.1073/pnas.1909865116. The authors note that the affiliation for Xavier Rodó should instead appear as Catalan Institution for Research and Advanced Studies (ICREA) and Climate and Health Program, Barcelona Institute for Global Health (ISGlobal). The corrected author and affiliation lines appear below. The online version has been corrected

An open challenge to advance probabilistic forecasting for dengue epidemics.

A wide range of research has promised new tools for forecasting infectious disease dynamics, but little of that research is currently being applied in practice, because tools do not address key public health needs, do not produce probabilistic forecasts, have not been evaluated on external data, or do not provide sufficient forecast skill to be useful. We developed an open collaborative forecasting challenge to assess probabilistic forecasts for seasonal epidemics of dengue, a major global public health problem. Sixteen teams used a variety of methods and data to generate forecasts for 3 epidemiological targets (peak incidence, the week of the peak, and total incidence) over 8 dengue seasons in Iquitos, Peru and San Juan, Puerto Rico. Forecast skill was highly variable across teams and targets. While numerous forecasts showed high skill for midseason situational awareness, early season skill was low, and skill was generally lowest for high incidence seasons, those for which forecasts would be most valuable. A comparison of modeling approaches revealed that average forecast skill was lower for models including biologically meaningful data and mechanisms and that both multimodel and multiteam ensemble forecasts consistently outperformed individual model forecasts. Leveraging these insights, data, and the forecasting framework will be critical to improve forecast skill and the application of forecasts in real time for epidemic preparedness and response. Moreover, key components of this project-integration with public health needs, a common forecasting framework, shared and standardized data, and open participation-can help advance infectious disease forecasting beyond dengue

Prediction of Peaks of Seasonal Influenza in Military Health-Care Data

Influenza is a highly contagious disease that causes seasonal epidemics with significant morbidity and mortality. The ability to predict influenza peak several weeks in advance would allow for timely preventive public health planning and interventions to be used to mitigate these outbreaks. Because influenza may also impact the operational readiness of active duty personnel, the US military places a high priority on surveillance and preparedness for seasonal outbreaks. A method for creating models for predicting peak influenza visits per total health-care visits (ie, activity) weeks in advance has been developed using advanced data mining techniques on disparate epidemiological and environmental data. The model results are presented and compared with those of other popular data mining classifiers. By rigorously testing the model on data not used in its development, it is shown that this technique can predict the week of highest influenza activity for a specific region with overall better accuracy than other methods examined in this article