We model a stylized banking system where banks are characterized by the amount of capital, cash reserves and their exposure to the interbank loan market as borrowers as well as lenders. A network of interbank lending is established that is used as a transmission mechanism for the failure of banks through the system. We trigger a potential banking crisis by exogenously failing a bank and investigate the spread of this failure within the banking system. We find the obvious result that the size of the bank initially failing is the dominant factor whether contagion occurs, but for the extent of its spread the characteristics of the network of interbank loans are most important. These results have implications for the regulation of banking systems that are briefly discussed, most notably that a reliance on balance sheet regulations is not sufficient but must be supplemented by considerations for the structure of financial linkages between banks.

Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also known as accelerated greedy), both in theory and practice? In this paper, we develop the first linear-time algorithm for maximizing a general monotone submodular function subject to a cardinality constraint. We show that our randomized algorithm, STOCHASTIC-GREEDY, can achieve a (1 − 1/e − ε) approximation guarantee, in expectation, to the optimum solution in time linear in the size of the data and independent of the cardinality constraint. We empirically demonstrate the effectiveness of our algorithm on submodular functions arising in data summarization, including training large-scale kernel methods, exemplar-based clustering, and sensor placement. We observe that STOCHASTIC-GREEDY practically achieves the same utility value as lazy greedy but runs much faster. More surprisingly, we observe that in many practical scenarios STOCHASTIC-GREEDY does not evaluate the whole fraction of data points even once and still achieves indistinguishable results compared to lazy greedy.

The benefits of value at risk (VaR) are its simplicity and broad applicability. However, the limitations of VaR are only just being openly discussed by researchers and practitioners. This article provides a brief review of problems faced when applying VaR as a risk management tool. The author shows that VaR is not always a good risk measure and is often prone to substantial measurement error. The author concludes that VaR remains a useful risk management tool when appropriately applied with an understanding of its limitations.

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Understanding and predicting molecular responses in single cells upon chemical, genetic, or mechanical perturbations is a core question in biology. Obtaining single-cell measurements typically requires the cells to be destroyed. This makes learning heterogeneous perturbation responses challenging as we only observe unpaired distributions of perturbed or nonperturbed cells. Here we leverage the theory of optimal transport and the recent advent of convex neural architectures to present CellOT, a framework for learning the response of individual cells to a given perturbation by coupling these unpaired distributions. We achieve this alignment with a learned transport map that allows us to infer the treatment responses of unseen untreated cells. CellOT outperforms current methods at predicting single-cell drug responses, as profiled by scRNA-seq and a multiplexed protein imaging technology. Further, we illustrate that CellOT generalizes well in unseen settings by (a) predicting the scRNA-seq responses of heldout lupus patients exposed to IFN-β and (b) modeling the hematopoietic developmental trajectories of different subpopulations. We expect CellOT to lay the grounds for delineating the causes of heterogeneous single-cell responses to perturbations and predicting patient-specific drug response landscapes instead of population averages.