Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies

Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX. If the $d$ tests are dependent, $d_{MAX} < d$. The second parameter is the fractional degrees of freedom $k$ of the chi-square distribution $\chi^2_k$ that fits the MAX null distribution. These two parameters, $d_{MAX}$ and $k$, can be independently defined, and $k$ can be non-integer even if $d_{MAX}$ is an integer. We illustrate these two parameters using the example of MAX2 and MAX3 statistics in genetic case-control studies. We speculate that $k$ is related to the amount of ambiguity of the model inferred by the test. In the case-control genetic association, tests with low $k$ (e.g. $k=1$) are able to provide definitive information about the disease model, as versus tests with high $k$ (e.g. $k=2$) that are completely uncertain about the disease model. Similar to Heisenberg's uncertain principle, the ability to infer disease model and the ability to detect significant association may not be simultaneously optimized, and $k$ seems to measure the level of their balance

Adversarial Data Augmentation for HMM-based Anomaly Detection

In this work, we concentrate on the detection of anomalous behaviors in systems operating in the physical world and for which it is usually not possible to have a complete set of all possible anomalies in advance. We present a data augmentation and retraining approach based on adversarial learning for improving anomaly detection. In particular, we first define a method for gener- ating adversarial examples for anomaly detectors based on Hidden Markov Models (HMMs). Then, we present a data augmentation and retraining technique that uses these adversarial examples to improve anomaly detection performance. Finally, we evaluate our adversarial data augmentation and retraining approach on four datasets showing that it achieves a statistically significant perfor- mance improvement and enhances the robustness to adversarial attacks. Key differences from the state-of-the-art on adversarial data augmentation are the focus on multivariate time series (as opposed to images), the context of one-class classification (in contrast to standard multi-class classification), and the use of HMMs (in contrast to neural networks)

HMMs for Anomaly Detection in Autonomous Robots

Detection of anomalies and faults is a key element for long-term robot autonomy, because, together with subsequent diagnosis and recovery, allows to reach the required levels of robustness and persistency. In this paper, we propose an approach for detecting anomalous behaviors in autonomous robots starting from data collected during their routine operations. The main idea is to model the nominal (expected) behavior of a robot system using Hidden Markov Models (HMMs) and to evaluate how far the observed behavior is from the nominal one using variants of the Hellinger distance adopted for our purposes. We present a method for online anomaly detection that computes the Hellinger distance between the probability distribution of observations made in a sliding window and the corresponding nominal emission probability distribution. We also present a method for o!ine anomaly detection that computes a variant of the Hellinger distance between two HMMs representing nominal and observed behaviors. The use of the Hellinger distance positively impacts on both detection performance and interpretability of detected anomalies, as shown by results of experiments performed in two real-world application domains, namely, water monitoring with aquatic drones and socially assistive robots for elders living at home. In particular, our approach improves by 6% the area under the ROC curve of standard online anomaly detection methods. The capabilities of our o!ine method to discriminate anomalous behaviors in real-world applications are statistically proved

Automated Lineament Extraction applied to high-resolution imagery Worldview-3 and LiDAR data for pegmatite mineral exploration

Lineament extraction is a commonly used technique in mineral exploration to identify geological structures such as fault scarps, joints, and folds. However, the accuracy of this technique can be limited by factors such as the low spatial resolution of the data. This study aims to address these limitations by exploring the potential of high spatial resolution data for extracting linear structures in Tysfjord, northern Norway. Two types of high-resolution data were utilized for lineament extraction: (i) WorldView-3 (WV3) satellite orbital imagery with a ground sample distance (GSD) of 2 meters, and (ii) Light Detection And Ranging (LiDAR) point cloud data, with a GSD of 1 meter. The LiDAR point cloud was utilized to generate a Digital Terrain Model (DTM), and automated lineament extraction was performed on both WV3 and LiDAR data using the lineament algorithm (LINE) available in PCI Geomatics software. A comparison was conducted using Sentinel 2 images to analyze the impact of utilizing high-resolution images on the final results. The outcomes illustrate that high-resolution images hold substantial potential for extracting lineaments and can aid in identifying mineral deposits and neotectonic activity. In the future, these findings could be integrated with other remote sensing methods to enhance the capabilities of remote sensing for mineral exploration. (c) 2023 SPIE. All rights reserved

Mapping NYF pegmatite outcrops through high-resolution Worldview-3 imagery

Several studies on remote sensing and mineral exploration have been developed or improved in the last decade. However, the low spatial resolution of satellites is a recurring problem in many cases where the mineral or rock is much smaller than the pixel size of the satellite images. This phenomenon, called sub-pixel occurrence, generates an extremely mixed pixel that difficult the performance of conventional classification algorithms. Satellites with high spatial resolution, such as the Worldview-3 (2 m Ground Sample Distance), have become an essential tool for mineral exploration studies. In addition to its high spatial resolution, the Worldview-3 has 16 bands, 8 in the Visible and Near-infrared (VNIR) and 8 in the Short-Wave Infrared (SWIR) region, which further increases its potential for mineral exploration. This study applies a spectral unmixing-based method, using the Spectral Hourglass Wizard Workflow (SHW), to extract and select pegmatites endmembers from the WorldView-3 images. Further, these endmembers were used for a subpixel classification, performed through Mixture Tuned Matched Filtering (MTMF), to map possible pegmatite outcrops in the Tysfjord pegmatite field, Norway. After classification a high Digital Terrain Model (DTM) hillshade acquired from LiDAR technology and geological data were used to eliminate false positives. The subpixel classification results were compared with geological data and 17 points of interest for pegmatite exploration were selected for further field validation. This work shows the potential of the Worldview-3 high-resolution images processed with a spectral unmixing-based method for mineral exploration in an area of subpixel occurrence. The results are encouraging and show great value for the scientific field of pegmatite exploration. (c) 2023 SPIE. All rights reserved

The contributing external load factors to internal load during small-sided games in professional rugby union players

Introduction: This study aimed to investigate which external load variables were associated with internal load during three small-sided games (SSG) in professional rugby union players. Methods: Forty professional rugby union players (22 forwards, 18 backs) competing in the English Gallagher Premiership were recruited. Three different SSGs were designed: one for backs, one for forwards, and one for both backs and forwards. General linear mixed-effects models were implemented with internal load as dependent variable quantified using Stagno's training impulse, and external load as independent variables quantified using total distance, high-speed (&gt;61% top speed) running distance, average acceleration-deceleration, PlayerLoad™, PlayerLoad™ slow (&lt;2 m·s −1), number of get-ups, number of first-man-to-ruck. Results: Internal load was associated with different external load variables dependent on SSG design. When backs and forwards were included in the same SSG, internal load differed between positional groups (MLE = −121.94, SE = 29.03, t = −4.20). Discussion: Based on the SSGs investigated, practitioners should manipulate different constraints to elicit a certain internal load in their players based on the specific SSG design. Furthermore, the potential effect of playing position on internal load should be taken into account in the process of SSG design when both backs and forwards are included.</p

SPECTRAL UNMIXING AND THE POTENTIAL OF WORLDVIEW-3 SATELLITE DATA FOR PEGMATITE EXPLORATION

Remote Sensing has been successfully applied in the identification of pegmatitic targets. However, the spatial resolution of open data satellites, which is often much larger than the outcrop size of the target mineral or rock, has been a recurrent challenge in this scientific field. This restricts remote sensing methods that are dependent on large outcrop sizes for successful identification. This work applied spectral unmixing approach on WorldView-3 satellite imagery, to evaluate the potential for high spatial resolution imagery on the Tysfjord Niobium-Yttrium-Fluorine (NYF) pegmatite field (Norway). The preliminary results of this research are encouraging and make a strong contribution to the scientific field of mineral exploration

The Bivariate Normal Copula

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page