A Memory-Efficient Sketch Method for Estimating High Similarities in Streaming Sets

Estimating set similarity and detecting highly similar sets are fundamental problems in areas such as databases, machine learning, and information retrieval. MinHash is a well-known technique for approximating Jaccard similarity of sets and has been successfully used for many applications such as similarity search and large scale learning. Its two compressed versions, b-bit MinHash and Odd Sketch, can significantly reduce the memory usage of the original MinHash method, especially for estimating high similarities (i.e., similarities around 1). Although MinHash can be applied to static sets as well as streaming sets, of which elements are given in a streaming fashion and cardinality is unknown or even infinite, unfortunately, b-bit MinHash and Odd Sketch fail to deal with streaming data. To solve this problem, we design a memory efficient sketch method, MaxLogHash, to accurately estimate Jaccard similarities in streaming sets. Compared to MinHash, our method uses smaller sized registers (each register consists of less than 7 bits) to build a compact sketch for each set. We also provide a simple yet accurate estimator for inferring Jaccard similarity from MaxLogHash sketches. In addition, we derive formulas for bounding the estimation error and determine the smallest necessary memory usage (i.e., the number of registers used for a MaxLogHash sketch) for the desired accuracy. We conduct experiments on a variety of datasets, and experimental results show that our method MaxLogHash is about 5 times more memory efficient than MinHash with the same accuracy and computational cost for estimating high similarities

Dissipation and detonation of shock waves in lipid monolayers

Lipid interfaces not only compartmentalize but also connect different reaction centers within a cell architecture. These interfaces have well defined specific heats and compressibilities, hence energy can propagate along them analogous to sound waves. Lipid monolayers prepared at the air-water interface of a Langmuir trough present an excellent model system to study such propagations. Here we propose that recent observations of two-dimensional shock waves observed in lipid monolayers also provide the evidence for the detonation of shock waves at such interfaces, i.e. chemical energy stored in the interface can be absorbed by a propagating shock front reinforcing it in the process. To this end, we apply the classical theory in shock waves and detonation in the context of a lipid interface and its thermodynamic state. Based on these insights it is claimed that the observed self-sustaining waves in lipid monolayers represent a detonation like phenomena that utilizes the latent heat of phase transition of the lipids. However, the general nature of these equations allows that other possible sources of chemical energy can contribute to the propagating shock wave in a similar manner. Consequently, the understanding is applied to the nerve pulse propagation that is believed to represent a similar phenomenon, to obtain a qualitative understanding of the pressure and temperature dependence of amplitude and threshold for action potentials. While we mainly discuss the case of a stable detonation, the problem of initiation of detonation at interfaces and corresponding heat exchange is briefly discussed, which also suggests a role for thunder like phenomena in pulse initiation.Comment: 6 Figure