Decision Trees with Soft Numbers

In this paper we develop the foundation of a new theory for decision trees based on new modeling of phenomena with soft numbers. Soft numbers represent the theory of soft logic that addresses the need to combine real processes and cognitive ones in the same framework. At the same time soft logic develops a new concept of modeling and dealing with uncertainty: the uncertainty of time and space. It is a language that can talk in two reference frames, and also suggest a way to combine them. In the classical probability, in continuous random variables there is no distinguishing between the probability involving strict inequality and non-strict inequality. Moreover, a probability involves equality collapse to zero, without distinguishing among the values that we would like that the random variable will have for comparison. This work presents Soft Probability, by incorporating of Soft Numbers into probability theory. Soft Numbers are set of new numbers that are linear combinations of multiples of ”ones” and multiples of ”zeros”. In this work, we develop a probability involving equality as a ”soft zero” multiple of a probability density function (PDF). We also extend this notion of soft probabilities to the classical definitions of Complements, Unions, Intersections and Conditional probabilities, and also to the expectation, variance and entropy of a continuous random variable, condition being in a union of disjoint intervals and a discrete set of numbers. This extension provides information regarding to a continuous random variable being within discrete set of numbers, such that its probability does not collapse completely to zero. When we developed the notion of soft entropy, we found potentially another soft axis, multiples of 0log(0), that motivates to explore the properties of those new numbers and applications. We extend the notion of soft entropy into the definition of Cross Entropy and Kullback–Leibler-Divergence (KLD), and we found that a soft KLD is a soft number, that does not have a multiple of 0log(0). Based on a soft KLD, we defined a soft mutual information, that can be used as a splitting criteria in decision trees with data set of continuous random variables, consist of single samples and intervals.

GPS-Spoofing Attack Detection Technology for UAVs Based on Kullback–Leibler Divergence

Here, we developed a method for detecting cyber security attacks aimed at spoofing the Global Positioning System (GPS) signal of an Unmanned Aerial Vehicle (UAV). Most methods for detecting UAV anomalies indicative of an attack use machine learning or other such methods that compare normal behavior with abnormal behavior. Such approaches require large amounts of data and significant “training” time to prepare and implement the system. Instead, we consider a new approach based on other mathematical methods for detecting UAV anomalies without the need to first collect a large amount of data and describe normal behavior patterns. Doing so can simplify the process of creating an anomaly detection system, which can further facilitate easier implementation of intrusion detection systems in UAVs. This article presents issues related to ensuring the information security of UAVs. Development of the GPS spoofing detection method for UAVs is then described, based on a preliminary study that made it possible to form a mathematical apparatus for solving the problem. We then explain the necessary analysis of parameters and methods of data normalization, and the analysis of the Kullback—Leibler divergence measure needed to detect anomalies in UAV systems.

Multitarget Detection of Transmission Lines Based on DANet and YOLOv4

In order to accurately identify targets such as insulators, shock hammers, bird nests, and spacers on high-voltage transmission lines, this paper proposes a multitarget detection model for transmission lines based on DANet and YOLOv4. First, the DANet and YOLOv4 are fused to solve the difficulty in understanding the scene and the discrimination of pixels caused by the complex and diverse scenes of UAV’ (unmanned aerial vehicle) aerial images (lighting, viewing angle, scale, occlusion, and so on) so as to improve the significance of the detection target. Gaussian function and KL (Kullback–Leibler) divergence are used to improve the nonmaximum suppression in YOLOv4 so as to improve the recognition rate of occluded targets; the focal loss function and the balanced cross entropy function are used to improve the loss function of YOLOv4 in order to reduce the impact of not only the imbalance between the background and the detection target but also the imbalance among the samples, which is aimed at improving the accuracy of the detection. Then, a data set is made for the experiment by using the UAV inspection image provided by a power grid company in Eastern Inner Mongolia. Finally, the algorithm proposed in this paper is compared with other target detection algorithms. Experimental results show that the average detection accuracy of the proposed algorithm can reach 94.7%, and the detection time of each image is 0.05 seconds. The method has good accuracy, real-time, and robustness.

Identifying protein sites contributing to vaccine escape via statistical comparisons of short-term molecular dynamics simulations

The identification of viral mutations that confer escape from antibodies is crucial for understanding the interplay between immunity and viral evolution. We describe a molecular dynamic (MD) based approach that scales well to a desktop computer with a high-end modern graphics processor and enables the user to identify protein sites that are prone to vaccine escape in a viral antigen. We first implemented our MD pipeline to employ site-wise calculation of Kullback-Leibler divergence in atom fluctuation over replicate sets of short-term MD production runs to compare influenza hemagglutinin’s rapid motions in the presence and absence of three well-known neutralizing antibodies. Using this simple comparative method applied to motions of viral proteins, we successfully identified in silico all previously empirically confirmed sites of escape in hemagglutinin, predetermined via selection experiments and neutralization assays. After this validation of our computational approach, we identified potential hot spot residues in the receptor binding domain (RBD) of the SARS-CoV-2 virus in the presence of COVOX-222 and S2H97 antibodies. We identified sites in the antigen-antibody interface with strong dampening of fluctuation that may indicate potential antibody escape due to single mutations. Many of these sites were found to match known sites of mutations in SARS-CoV-2 variants of concern. The determination of single sites with large effect on antigen-antibody binding interfaces is crucial to discriminating neutral variants from potential escape variants. In summary, we provide a cheap, fast, and accurate in silico method to identify and quantify potential hot spots of functional evolution in antibody binding footprints.

Urban noise distributions and the influence of geometric spreading on skewness

Statistical distributions of urban noise levels are influenced by many complex phenomena, including spatial and temporal variations in the source level, multisource mixtures, propagation losses, and random fading from multipath reflections. This article provides a broad perspective on the varying impacts of these phenomena. Distributions incorporating random fading and averaging (e.g., gamma and noncentral Erlang) tend to be negatively skewed on logarithmic (decibel) axes but can be positively skewed if the fading process is strongly modulated by source power variations (e.g., compound gamma). In contrast, distributions incorporating randomly positioned sources and explicit geometric spreading [e.g., exponentially modified Gaussian (EMG)] tend to be positively skewed with exponential tails on logarithmic axes. To evaluate the suitability of the various distributions, one-third octave band sound-level data were measured at 37 locations in the North End of Boston, MA. Based on the Kullback-Leibler divergence as calculated across all of the locations and frequencies, the EMG provides the most consistently good agreement with the data, which were generally positively skewed. The compound gamma also fits the data well and even outperforms the EMG for the small minority of cases exhibiting negative skew. The lognormal provides a suitable fit in cases in which particular non-traffic noise sources dominate.

Domain decomposition for entropy regularized optimal transport

We study Benamou’s domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove linear convergence of the algorithm with respect to the Kullback–Leibler divergence and illustrate the (potentially very slow) rates with numerical examples. On problems with sufficient geometric structure (such as Wasserstein distances between images) we expect much faster convergence. We then discuss important aspects of a computationally efficient implementation, such as adaptive sparsity, a coarse-to-fine scheme and parallelization, paving the way to numerically solving large-scale optimal transport problems. We demonstrate efficient numerical performance for computing the Wasserstein-2 distance between 2D images and observe that, even without parallelization, domain decomposition compares favorably to applying a single efficient implementation of the Sinkhorn algorithm in terms of runtime, memory and solution quality.

Development of an expected possession value model to analyse team attacking performances in rugby league

This study aimed to evaluate team attacking performances in rugby league via expected possession value (EPV) models. Location data from 59,233 plays in 180 Super League matches across the 2019 Super League season were used. Six EPV models were generated using arbitrary zone sizes (EPV-308 and EPV-77) or aggregated according to the total zone value generated during a match (EPV-37, EPV-19, EPV-13 and EPV-9). Attacking sets were considered as Markov Chains, allowing the value of each zone visited to be estimated based on the outcome of the possession. The Kullback-Leibler Divergence was used to evaluate the reproducibility of the value generated from each zone (the reward distribution) by teams between matches. Decreasing the number of zones improved the reproducibility of reward distributions between matches but reduced the variation in zone values. After six previous matches, the subsequent match’s zones had been visited on 95% or more occasions for EPV-19 (95±4%), EPV-13 (100±0%) and EPV-9 (100±0%). The KL Divergence values were infinity (EPV-308), 0.52±0.05 (EPV-77), 0.37±0.03 (EPV-37), 0.20±0.02 (EPV-19), 0.13±0.02 (EPV-13) and 0.10±0.02 (EPV-9). This study supports the use of EPV-19 and EPV-13, but not EPV-9 (too little variation in zone values), to evaluate team attacking performance in rugby league.

A New Linear Regression Kalman Filter with Symmetric Samples

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.