Georg M. Goerg

Optimizing Treatment Regimes to Hinder Antiviral Resistance in Influenza across Time Scales

The large-scale use of antivirals during influenza pandemics poses a significant selection pressure for drug-resistant pathogens to emerge and spread in a population. This requires treatment strategies to minimize total infections as well as the emergence of resistance. Here we propose a mathematical model in which individuals infected with wild-type influenza, if treated, can develop de novo resistance and further spread the resistant pathogen. Our main purpose is to explore the impact of two important factors influencing treatment effectiveness: i) the relative transmissibility of the drug-resistant strain to wild-type, and ii) the frequency of de novo resistance. For the endemic scenario, we find a condition between these two parameters that indicates whether treatment regimes will be most beneficial at intermediate or more extreme values (e.g., the fraction of infected that are treated). Moreover, we present analytical expressions for effective treatment regimes and provide evidence of its applicability across a range of modeling scenarios: endemic behavior with deterministic homogeneous mixing, and single-epidemic behavior with deterministic homogeneous mixing and stochastic heterogeneous mixing. Therefore, our results provide insights for the control of drug-resistance in influenza across time scales.

Testing for white noise against locally stationary alternatives

Many real-world systems have dynamics that evolve over time, yet stationary models still remain a popular choice in empirical time series studies. In this work, I show that one reason for seemingly correct stationary fits is a very low power of classic white noise tests against locally varying dynamics. In particular, if autocorrelations change over time but on average equal zero, standard white noise tests cannot detect this deviation from the null hypothesis due to their fundamental design. Here I introduce a moving-window version of the Ljung–Box statistic with an asymptotic \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}

A nonparametric frequency domain EM algorithm for time series classification with applications to spike sorting and macro-economics

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Lambert W random variables—a new family of generalized skewed distributions with applications to risk estimation

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LICORS: Light Cone Reconstruction of States for Non-parametric Forecasting of Spatio-Temporal Systems

I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pmf) on the unit circle: signals with similar dynamics have similar pdfs; distinct patterns have distinct pdfs. An advantage of this approach is that it does not rely on any parametric form of the dynamic structure, but can be used for non-parametric, robust and model-free classification. This new method works for non-stationary signals of similar shape as well as stationary signals with similar auto-correlation structure. Applications to neural spike sorting (non-stationary) and pattern-recognition in socio-economic time series (stationary) demonstrate the usefulness and wide applicability of the proposed method.