Measuring the irreversibility of numerical schemes for reversible stochastic differential equations

Abstract. For a Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s) time discretization numerical schemes usually destroy the property of time-reversibility. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of reversibility of the discrete-time approximation process. In this paper we provide such quantitative estimates by using the concept of entropy production rate, inspired by ideas from non-equilibrium statistical mechanics. The entropy production rate for a stochastic process is defined as the relative entropy (per unit time) of the path measure of the process with respect to the path measure of the time-reversed process. By construction the entropy production rate is nonnegative and it vanishes if and only if the process is reversible. Crucially, from a numerical point of view, the entropy production rate is an a posteriori quantity, hence it can be computed in the course of a simulation as the ergodic average of a certain functional of the process (the so-called Gallavotti-Cohen (GC) action functional). We compute the entropy production for various numerical schemes such as explicit Euler-Maruyama and explicit Milstein’s for reversible SDEs with additive or multiplicative noise. Additionally, we analyze the entropy production for th

Studying Ransomware Attacks Using Web Search Logs

Cyber attacks are increasingly becoming prevalent and causing significant damage to individuals, businesses and even countries. In particular, ransomware attacks have grown significantly over the last decade. We do the first study on mining insights about ransomware attacks by analyzing query logs from Bing web search engine. We first extract ransomware related queries and then build a machine learning model to identify queries where users are seeking support for ransomware attacks. We show that user search behavior and characteristics are correlated with ransomware attacks. We also analyse trends in the temporal and geographical space and validate our findings against publicly available information. Lastly, we do a case study on 'Nemty', a popular ransomware, to show that it is possible to derive accurate insights about cyber attacks by query log analysis.Comment: To appear in the proceedings of SIGIR 202

Second harmonic generating (SHG) nanoprobes: a new tool for biomedical imaging

Fluorescence microscopy has profoundly changed how cell and molecular biology is studied in almost every aspect. However, the need of characterizing biological targets is largely unmet due to deficiencies associated with the use of fluorescent agents. Dye bleaching, dye signal saturation, blinking, and tissue autofluorescence can severely limit the signal-to-noise ratio (SNR). Given the photophysical properties are fundamentally different to the fluorescent agents currently used in biomedical research, second harmonic generating (SHG) nanoprobes can be suitable for biomedical imaging and can eliminate most of the drawbacks encountered in classical fluorescence systems