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The human immune system is determined by the functionality of the human lymph node. With the use of high-throughput techniques in clinical diagnostics, a large number of data is currently collected. The new data on the spatiotemporal organization of cells offers new possibilities to build a mathematical model of the human lymph node - a virtual lymph node. The virtual lymph node can be applied to simulate drug responses and may be used in clinical diagnosis. Here, we review mathematical models of the human lymph node from the viewpoint of cellular processes. Starting with classical methods, such as systems of differential equations, we discuss the values of different levels of abstraction and methods in the range from artificial intelligence techniques formalism.
Volatility clustering and fat tails are prominently observed in financial markets. Here, we analyze the underlying mechanisms of three agent-based models explaining these stylized facts in terms of market instabilities and compare them on empirical grounds. To this end, we first develop a general framework for detecting tail events in stock markets. In particular, we introduce Hawkes processes to automatically identify and date onsets of market turmoils which result in increased volatility. Second, we introduce three different indicators to predict those onsets. Each of the three indicators is derived from and tailored to one of the models, namely quantifying information content, critical slowing down or market risk perception. Finally, we apply our indicators to simulated and real market data. We find that all indicators reliably predict market events on simulated data and clearly distinguish the different models. In contrast, a systematic comparison on the stocks of the Forbes 500 companies shows a markedly lower performance. Overall, predicting the onset of market turmoils appears difficult, yet, over very short time horizons high or rising volatility exhibits some predictive power.