25 research outputs found
Data Driven Computing by the Morphing Fast Fourier Transform Ensemble Kalman Filter in Epidemic Spread Simulations
The FFT EnKF data assimilation method is proposed and applied to a stochastic
cell simulation of an epidemic, based on the S-I-R spread model. The FFT EnKF
combines spatial statistics and ensemble filtering methodologies into a
localized and computationally inexpensive version of EnKF with a very small
ensemble, and it is further combined with the morphing EnKF to assimilate
changes in the position of the epidemic.Comment: 11 pages, 3 figures. Submitted to ICCS 201
Spectral diagonal ensemble Kalman filters
A new type of ensemble Kalman filter is developed, which is based on
replacing the sample covariance in the analysis step by its diagonal in a
spectral basis. It is proved that this technique improves the aproximation of
the covariance when the covariance itself is diagonal in the spectral basis, as
is the case, e.g., for a second-order stationary random field and the Fourier
basis. The method is extended by wavelets to the case when the state variables
are random fields, which are not spatially homogeneous. Efficient
implementations by the fast Fourier transform (FFT) and discrete wavelet
transform (DWT) are presented for several types of observations, including
high-dimensional data given on a part of the domain, such as radar and
satellite images. Computational experiments confirm that the method performs
well on the Lorenz 96 problem and the shallow water equations with very small
ensembles and over multiple analysis cycles.Comment: 15 pages, 4 figure
Forecasting the 2013--2014 Influenza Season using Wikipedia
Infectious diseases are one of the leading causes of morbidity and mortality
around the world; thus, forecasting their impact is crucial for planning an
effective response strategy. According to the Centers for Disease Control and
Prevention (CDC), seasonal influenza affects between 5% to 20% of the U.S.
population and causes major economic impacts resulting from hospitalization and
absenteeism. Understanding influenza dynamics and forecasting its impact is
fundamental for developing prevention and mitigation strategies.
We combine modern data assimilation methods with Wikipedia access logs and
CDC influenza like illness (ILI) reports to create a weekly forecast for
seasonal influenza. The methods are applied to the 2013--2014 influenza season
but are sufficiently general to forecast any disease outbreak, given incidence
or case count data. We adjust the initialization and parametrization of a
disease model and show that this allows us to determine systematic model bias.
In addition, we provide a way to determine where the model diverges from
observation and evaluate forecast accuracy.
Wikipedia article access logs are shown to be highly correlated with
historical ILI records and allow for accurate prediction of ILI data several
weeks before it becomes available. The results show that prior to the peak of
the flu season, our forecasting method projected the actual outcome with a high
probability. However, since our model does not account for re-infection or
multiple strains of influenza, the tail of the epidemic is not predicted well
after the peak of flu season has past.Comment: Second version. In previous version 2 figure references were
compiling wrong due to error in latex sourc
The 1st International Electronic Conference on Algorithms
This book presents 22 of the accepted presentations at the 1st International Electronic Conference on Algorithms which was held completely online from September 27 to October 10, 2021. It contains 16 proceeding papers as well as 6 extended abstracts. The works presented in the book cover a wide range of fields dealing with the development of algorithms. Many of contributions are related to machine learning, in particular deep learning. Another main focus among the contributions is on problems dealing with graphs and networks, e.g., in connection with evacuation planning problems
Handbook of Mathematical Geosciences
This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described