Anomaly Detection in Paleoclimate Records using Permutation Entropy

Permutation entropy techniques can be useful in identifying anomalies in paleoclimate data records, including noise, outliers, and post-processing issues. We demonstrate this using weighted and unweighted permutation entropy of water-isotope records in a deep polar ice core. In one region of these isotope records, our previous calculations revealed an abrupt change in the complexity of the traces: specifically, in the amount of new information that appeared at every time step. We conjectured that this effect was due to noise introduced by an older laboratory instrument. In this paper, we validate that conjecture by re-analyzing a section of the ice core using a more-advanced version of the laboratory instrument. The anomalous noise levels are absent from the permutation entropy traces of the new data. In other sections of the core, we show that permutation entropy techniques can be used to identify anomalies in the raw data that are not associated with climatic or glaciological processes, but rather effects occurring during field work, laboratory analysis, or data post-processing. These examples make it clear that permutation entropy is a useful forensic tool for identifying sections of data that require targeted re-analysis---and can even be useful in guiding that analysis.Comment: 15 pages, 7 figure

WPU-Net: Boundary Learning by Using Weighted Propagation in Convolution Network

Deep learning has driven a great progress in natural and biological image processing. However, in material science and engineering, there are often some flaws and indistinctions in material microscopic images induced from complex sample preparation, even due to the material itself, hindering the detection of target objects. In this work, we propose WPU-net that redesigns the architecture and weighted loss of U-Net, which forces the network to integrate information from adjacent slices and pays more attention to the topology in boundary detection task. Then, the WPU-net is applied into a typical material example, i.e., the grain boundary detection of polycrystalline material. Experiments demonstrate that the proposed method achieves promising performance and outperforms state-of-the-art methods. Besides, we propose a new method for object tracking between adjacent slices, which can effectively reconstruct 3D structure of the whole material. Finally, we present a material microscopic image dataset with the goal of advancing the state-of-the-art in image processing for material science.Comment: technical repor

Minimum and maximum entropy distributions for binary systems with known means and pairwise correlations

Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with these constraints has not been explored. We provide upper and lower bounds on the entropy for the {\em minimum} entropy distribution over arbitrarily large collections of binary units with any fixed set of mean values and pairwise correlations. We also construct specific low-entropy distributions for several relevant cases. Surprisingly, the minimum entropy solution has entropy scaling logarithmically with system size for any set of first- and second-order statistics consistent with arbitrarily large systems. We further demonstrate that some sets of these low-order statistics can only be realized by small systems. Our results show how only small amounts of randomness are needed to mimic low-order statistical properties of highly entropic distributions, and we discuss some applications for engineered and biological information transmission systems.Comment: 34 pages, 7 figure