Automated Generation of Geometric Theorems from Images of Diagrams

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial Intelligence (special issue on Geometric Reasoning

A Neural Network Gravitational Arc Finder based on the Mediatrix filamentation Method

Automated arc detection methods are needed to scan the ongoing and next-generation wide-field imaging surveys, which are expected to contain thousands of strong lensing systems. Arc finders are also required for a quantitative comparison between predictions and observations of arc abundance. Several algorithms have been proposed to this end, but machine learning methods have remained as a relatively unexplored step in the arc finding process. In this work we introduce a new arc finder based on pattern recognition, which uses a set of morphological measurements derived from the Mediatrix Filamentation Method as entries to an Artificial Neural Network (ANN). We show a full example of the application of the arc finder, first training and validating the ANN on simulated arcs and then applying the code on four Hubble Space Telescope (HST) images of strong lensing systems. The simulated arcs use simple prescriptions for the lens and the source, while mimicking HST observational conditions. We also consider a sample of objects from HST images with no arcs in the training of the ANN classification. We use the training and validation process to determine a suitable set of ANN configurations, including the combination of inputs from the Mediatrix method, so as to maximize the completeness while keeping the false positives low. In the simulations the method was able to achieve a completeness of about 90% with respect to the arcs that are input to the ANN after a preselection. However, this completeness drops to $\sim$ 70% on the HST images. The false detections are of the order of 3% of the objects detected in these images. The combination of Mediatrix measurements with an ANN is a promising tool for the pattern recognition phase of arc finding. More realistic simulations and a larger set of real systems are needed for a better training and assessment of the efficiency of the method.Comment: Updated to match published versio

Methodology and Algorithms for Pedestrian Network Construction

With the advanced capabilities of mobile devices and the success of car navigation systems, interest in pedestrian navigation systems is on the rise. A critical component of any navigation system is a map database which represents a network (e.g., road networks in car navigation systems) and supports key functionality such as map display, geocoding, and routing. Road networks, mainly due to the popularity of car navigation systems, are well defined and publicly available. However, in pedestrian navigation systems, as well as other applications including urban planning and physical activities studies, road networks do not adequately represent the paths that pedestrians usually travel. Currently, there are no techniques to automatically construct pedestrian networks, impeding research and development of applications requiring pedestrian data. This coupled with the increased demand for pedestrian networks is the prime motivation for this dissertation which is focused on development of a methodology and algorithms that can construct pedestrian networks automatically. A methodology, which involves three independent approaches, network buffering (using existing road networks), collaborative mapping (using GPS traces collected by volunteers), and image processing (using high-resolution satellite and laser imageries) was developed. Experiments were conducted to evaluate the pedestrian networks constructed by these approaches with a pedestrian network baseline as a ground truth. The results of the experiments indicate that these three approaches, while differing in complexity and outcome, are viable for automatically constructing pedestrian networks

The Agile Alert System For Gamma-Ray Transients

In recent years, a new generation of space missions offered great opportunities of discovery in high-energy astrophysics. In this article we focus on the scientific operations of the Gamma-Ray Imaging Detector (GRID) onboard the AGILE space mission. The AGILE-GRID, sensitive in the energy range of 30 MeV-30 GeV, has detected many gamma-ray transients of galactic and extragalactic origins. This work presents the AGILE innovative approach to fast gamma-ray transient detection, which is a challenging task and a crucial part of the AGILE scientific program. The goals are to describe: (1) the AGILE Gamma-Ray Alert System, (2) a new algorithm for blind search identification of transients within a short processing time, (3) the AGILE procedure for gamma-ray transient alert management, and (4) the likelihood of ratio tests that are necessary to evaluate the post-trial statistical significance of the results. Special algorithms and an optimized sequence of tasks are necessary to reach our goal. Data are automatically analyzed at every orbital downlink by an alert pipeline operating on different timescales. As proper flux thresholds are exceeded, alerts are automatically generated and sent as SMS messages to cellular telephones, e-mails, and push notifications of an application for smartphones and tablets. These alerts are crosschecked with the results of two pipelines, and a manual analysis is performed. Being a small scientific-class mission, AGILE is characterized by optimization of both scientific analysis and ground-segment resources. The system is capable of generating alerts within two to three hours of a data downlink, an unprecedented reaction time in gamma-ray astrophysics.Comment: 34 pages, 9 figures, 5 table