Key Validity Using the Multiple-Parameter Fractional Fourier Transform for Image Encryption

As a symmetric encryption algorithm, multiple-parameter fractional Fourier transform (MPFRFT) is proposed and applied to image encryption. The MPFRFT with two vector parameters has better security, which becomes the main technical means to protect information security. However, our study found that many keys of the MPFRFT are invalid, which greatly reduces its security. In this paper, we propose a new reformulation of MPFRFT and analyze it using eigen-decomposition-type fractional Fourier transform (FRFT) and weighted-type FRFT as basis functions, respectively. The results show that the effective keys are extremely limited. Furthermore, we analyze the extended encryption methods based on MPFRFT, which also have the security risk of key invalidation. Theoretical analysis and numerical simulation verify our point of view. Our discovery has important reference value for a class of generalized FRFT image encryption methods.

Magnitude Estimation for Earthquake Early Warning with Multiple Parameter Inputs and a Support Vector Machine

Accurately estimating the magnitude within the initial seconds after the P-wave arrival is of great significance in earthquake early warning (EEW). Over the past few decades, single-parameter approaches such as the τc and Pd methods have been applied to EEW magnitude estimation studies considering the first 3 s after the P-wave onset. However, these methods present considerable scatter and are affected by the signal-to-noise ratio (SNR) and epicentral distance. In this study, using Japanese K-NET strong-motion data, we propose a machine-learning method comprising multiple parameter inputs, namely, the support vector machine magnitude estimation (SVM-M) model, to determine earthquake magnitudes and resolve the aforementioned problems. Our results using a single seismological station record show that the standard deviation of the magnitude prediction errors of the SVM-M model is 0.297, which is less than those of the τc (1.637) and Pd (0.425) methods. The magnitudes estimated by the SVM-M model within 3 s after the P-wave arrival are not obviously affected by the SNR or epicentral distance, and not overestimated for MJMA≤5. In addition, in an offline EEW application, the magnitude estimation error of the SVM-M model gradually decreases with increasing time after the first station is triggered, and the underestimation of event magnitudes for 6.5≤MJMA gradually improves. These results demonstrate that the proposed SVM-M model can robustly estimate earthquake magnitudes and has potential for EEW.

Geospatial Suitability Indices Toolbox (GSI Toolbox)

Habitat suitability models are widely adopted in ecosystem management and restoration, where these index models are used to assess environmental impacts and benefits based on the quantity and quality of a given habitat. Many spatially distributed ecological processes require application of suitability models within a geographic information system (GIS). Here, we present a geospatial toolbox for assessing habitat suitability. The Geospatial Suitability Indices (GSI) toolbox was developed in ArcGIS Pro 2.7 using the Python® 3.7 programming language and is available for use on the local desktop in the Windows 10 environment. Two main tools comprise the GSI toolbox. First, the Suitability Index Calculator tool uses thematic or continuous geospatial raster layers to calculate parameter suitability indices based on user-specified habitat relationships. Second, the Overall Suitability Index Calculator combines multiple parameter suitability indices into one overarching index using one or more options, including: arithmetic mean, weighted arithmetic mean, geometric mean, and minimum limiting factor. The resultant output is a raster layer representing habitat suitability values from 0.0 to 1.0, where zero is unsuitable habitat and one is ideal suitability. This report documents the model purpose and development as well as provides a user’s guide for the GSI toolbox.

Weighted Fractional-Order Transform Based on Periodic Matrix

Tao et al. proposed the definition of the linear summation of fractional-order matrices based on the theory of Yeh and Pei. This definition was further extended and applied to image encryption. In this paper, we propose a reformulation of the definitions of Yeh et al. and Tao et al. and analyze them theoretically. The results show that many weighted terms are invalid. Therefore, we use the proposed reformulation to prove that the effective weighted terms depend on the period of the matrix. This also shows that the image encryption methods based on the weighted fractional-order transform will lead to the security risk of key invalidation. Finally, our hypothesis is verified by the unified theoretical framework of multiple-parameter discrete fractional-order transforms.

Fitting Compound Archimedean Copulas to Data for Modeling Electricity Demand

Modeling dependence between random variables is accomplished effectively by using copula functions. Practitioners often rely on the single parameter Archimedean family which contains a large number of functions, exhibiting a variety of dependence structures. In this work we propose the use of the multiple-parameter compound Archimedean family, which extends the original family and allows more elaborate dependence structures. In particular, we use a copula of this type to model the dependence structure between the minimum daily electricity demand and the maximum daily temperature. It is shown that the compound Archimedean copula enhances the flexibility of the dependence structure and provides a better fit to the data.