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A flag is a nested sequence of vector spaces. The type of the flag encodes the sequence of dimensions of the vector spaces making up the flag. A flag manifold is a manifold whose points parameterize all flags of a fixed type in a fixed vector space. This paper provides the mathematical framework necessary for implementing self-organizing mappings on flag manifolds. Flags arise implicitly in many data analysis contexts including wavelet, Fourier, and singular value decompositions. The proposed geometric framework in this paper enables the computation of distances between flags, the computation of geodesics between flags, and the ability to move one flag a prescribed distance in the direction of another flag. Using these operations as building blocks, we implement the SOM algorithm on a flag manifold. The basic algorithm is applied to the problem of parameterizing a set of flags of a fixed type. 

Finding prototypes (e.g., mean and median) for a dataset is central to a number of common machine learning algorithms. Subspaces have been shown to provide useful, robust representations for datasets of images, videos and more. Since subspaces correspond to points on a Grassmann manifold, one is led to consider the idea of a subspace prototype for a Grassmann-valued dataset. While a number of different subspace prototypes have been described, the calculation of some of these prototypes has proven to be computationally expensive while other prototypes are affected by outliers and produce highly imperfect clustering on noisy data. This work proposes a new subspace prototype, the flag median, and introduces the FlagIRLS algorithm for its calculation. We provide evidence that the flag median is robust to outliers and can be used effectively in algorithms like Linde-Buzo-Grey (LBG) to produce improved clusterings on Grassmannians. Numerical experiments include a synthetic dataset, the MNIST handwritten digits dataset, the Mind's Eye video dataset and the UCF YouTube action dataset. The flag median is compared the other leading algorithms for computing prototypes on the Grassmannian, namely, the l_2-median and to the flag mean. We find that using FlagIRLS to compute the flag median converges in 4 iterations on a synthetic dataset. We also see that Grassmannian LBG with a codebook size of 20 and using the flag median produces at least a 10% improvement in cluster purity over Grassmannian LBG using the flag mean or l_2-median on the Mind's Eye dataset. 

A fully-integrated mixed reality game system called multiphysics enriched mixed reality for integrated geotechnical education (MERGE) is developed to improve student education in the context of geotechnical engineering. This work allows students to learn the design of geothermal pile in a more inclusive way while playing a game and gain an "integrated geotechnical learning experience". Several mini games are designed for students to enhance the geotechnical knowledge. Players can earn points and update their appearance by playing these mini games, which stimulates their interests in geotechnical engineering. By providing students with visualization, collaboration, and simulation tools, we hope to promote the understanding of geotechnical experiments. Based on the laboratory results, numerical experiments are conducted to help students understand the geotechnical application. The leveraging mixed reality technology offers an opportunity for students to access advanced equipment in geotechnical experiments. The main contribution of this work is a discussion of the educational technology and processes behind implementing a mixed reality educational game. We provide developmental insights and educational background to inform researchers who seek to develop similar games. 

As systems that utilize computer vision move into the public domain, methods of calibration need to become easier to use. Though multi-plane LiDAR systems have proven to be useful for vehicles and large robotic platforms, many smaller platforms and low cost solutions still require 2D LiDAR combined with RGB cameras. Current methods of calibrating these sensors make assumptions about camera and laser placement and/or require complex calibration routines. In this paper we propose a new method of feature correspondence in the two sensors and an optimization method capable of calibration target with unknown lengths in its geometry. Our system is designed with an inexperienced layperson as the intended user, which has lead us to remove as many assumptions about both the target and laser as possible. We show that our system is capable of calibrating the 2-sensor system from a single sample in configurations other methods are unable to handle. 

Busjahn et al. [4] on the factors influencing dwell time during source code reading, where source code element type and frequency of gaze visits are studied as factors. Unlike the previous study, this study focuses on analyzing eye movement data in large open source Java projects. Five experts and thirteen novices participated in the study where the main task is to summarize methods. The results examine semantic line-level information that developers view during summarization. We find no correlation between the line length and the total duration of time spent looking on the line even though it exists between a token’s length and the total fixation time on the token reported in prior work. The first fixations inside a method are more likely to be on a method’s signature, a variable declaration, or an assignment compared to the other fixations inside a method. In addition, it is found that smaller methods tend to have shorter overall fixation duration for the entire method, but have significantly longer duration per line in the method. The analysis provides insights into how source code’s unique characteristics can help in building more robust methods for analyzing eye movements in source code and overall in building theories to support program comprehension on realistic tasks. 

ABSTRACT We present K2-2016-BLG-0005Lb, a densely sampled, planetary binary caustic-crossing microlensing event found from a blind search of data gathered from Campaign 9 of the Kepler K2 mission (K2C9). K2-2016-BLG-0005Lb is the first bound microlensing exoplanet discovered from space-based data. The event has caustic entry and exit points that are resolved in the K2C9 data, enabling the lens-source relative proper motion to be measured. We have fitted a binary microlens model to the Kepler data and to simultaneous observations from multiple ground-based surveys. Whilst the ground-based data only sparsely sample the binary caustic, they provide a clear detection of parallax that allows us to break completely the microlensing mass-position-velocity degeneracy and measure the planet’s mass directly. We find a host mass of 0.58 ± 0.04 M⊙ and a planetary mass of 1.1 ± 0.1 MJ. The system lies at a distance of 5.2 ± 0.2 kpc from Earth towards the Galactic bulge, more than twice the distance of the previous most distant planet found by Kepler. The sky-projected separation of the planet from its host is found to be 4.2 ± 0.3 au which, for circular orbits, deprojects to a host separation $a = 4.4^{+1.9}_{-0.4}$ au and orbital period $P = 13^{+9}_{-2}$ yr. This makes K2-2016-BLG-0005Lb a close Jupiter analogue orbiting a low-mass host star. According to current planet formation models, this system is very close to the host mass threshold below which Jupiters are not expected to form. Upcoming space-based exoplanet microlensing surveys by NASA’s Nancy Grace Roman Space Telescope and, possibly, ESA’s Euclid mission, will provide demanding tests of current planet formation models. 

The evolution and effort in designing and implementing iTrace, an infrastructure for integrating eye tracking into developer environments, is presented. The goal is to make eye tracking practical for various stakeholders in software engineering namely researchers, practitioners, and educators. An overview of iTrace and the general process involved in conducting an eye tracking study with human subjects using iTrace is presented in this tool demo paper. Upcoming features and ongoing plans for community involvement are also presented.