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 New Estimating Equation Based Approach for Secondary Trait Analyses in Genetic Case-control Studies

Background/Aims: Case-control designs are commonly employed in genetic association studies. In addition to the primary trait of interest, data on additional secondary traits, related to the primary trait, are often collected. Traditional association analyses between genetic variants and secondary traits can be biased in such cases, and several methods have been proposed to address this issue, including the inverse-probability-of-sampling-weighted (IPW) approach and semi-parametric maximum likelihood (SPML) approach. Methods: Here, we propose a set of new estimating equation based approach that combines observed and counter-factual outcomes to provide unbiased estimation of genetic associations with secondary traits. We extend the estimating equation framework to both generalized linear models (GLM) and non-parametric regressions, and compare it with the existing approaches. Results: We demonstrate analytically and numerically that our proposed approach provides robust and fairly efficient unbiased estimation in all simulations we consider. Unlike existing methods, it is less sensitive to the sampling scheme and underlying disease model specification. In addition, we illustrate our new approach using two real data examples. The first one is to analyze the binary secondary trait diabetes under GLM framework using a stroke case-control study. The second one is to analyze the continuous secondary trait serum IgE levels under linear and quantile regression models using an asthma case-control study. Conclusion: The proposed new estimating equation approach is able to accommodate a wide range of regressions, and it outperforms the existing approaches in some scenarios we consider

IMPROVED SENSITIVITY OF RESONANT MASS SENSOR BASED ON MICRO TILTING PLATE AND MICRO CANTILEVER

Vapor sensors have been used for many years. Their applications range from detection of toxic gases and dangerous chemicals in industrial environments, the monitoring of landmines and other explosives, to the monitoring of atmospheric conditions. Microelectrical mechanical systems (MEMS) fabrication technologies provide a way to fabricate sensitive devices. One type of MEMS vapor sensors is based on mass changing detection and the sensors have a functional chemical coating for absorbing the chemical vapor of interest. The principle of the resonant mass sensor is that the resonant frequency will experience a large change due to a small mass of gas vapor change. This thesis is trying to build analytical micro-cantilever and micro-tilting plate models, which can make optimization more efficient. Several objectives need to be accomplished: (1) Build an analytical model of MEMS resonant mass sensor based on micro-tilting plate with the effects of air damping. (2) Perform design optimization of micro-tilting plate with a hole in the center. (3) Build an analytical model of MEMS resonant mass sensor based on micro-cantilever with the effects of air damping. (4) Perform design optimization of micro-cantilever by COMSOL. Analytical models of micro-tilting plate with a hole in the center are compared with a COMSOL simulation model and show good agreement. The analytical models have been used to do design optimization that maximizes sensitivity. The micro-cantilever analytical model does not show good agreement with a COMSOL simulation model. To further investigate, the air damping pressures at several points on the micro-cantilever have been compared between analytical model and COMSOL model. The analytical model is inadequate for two reasons. First, the model’s boundary condition assumption is not realistic. Second, the deflection shape of the cantilever changes with the hole size, and the model does not account for this. Design optimization of micro-cantilever is done by COMSOL